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itinerant ferromagnetism ( fm ) is not only a representative strong - correlation problem , but also a highly non - perturbative one @xcite . it is widely known as a long - standing problem of condensed matter physics , and also a current research focus in ultra - cold atom physics @xcite . the stoner mechanism states that polarized electron systems can save the exchange interaction energy . nevertheless , because of the associated cost of kinetic energy , fm is not guaranteed even in the presence of very strong repulsions . for example , in rigorously one - dimensional ( 1d ) systems , no matter how strong the repulsive interactions are , the ground state is always a spin singlet , which is known as the famous lieb - mattis theorem @xcite . in other words , electrons can remain unpolarized but avoid each other to reduce interaction , nevertheless , their wave functions are strongly - correlated . certainly the lieb - mattis theorem in 1d only applies for spin - independent systems . ferromagnetism in 1d is still possible if the interaction is spin - dependent . because of the strong correlation nature of itinerant fm , exact theorems are important to provide reference points . nagaoka s theorem is an early example , which applies to the infinite @xmath5 hubbard model with a single hole in the half - filled background @xcite . the fully polarized fm state facilitates the hole s coherent motion , which minimizes the kinetic energy of the hole and is therefore selected as the ground state . another class of fm theorems is based on the flat band structure on line graphs @xcite . because of the divergence of density of states in the flat band , the kinetic energy cost because of spin polarization is suppressed . metallic fm states with a dispersive band structure have also been proved @xcite . recently , a ground state fm theorem has been proved in both two - dimensional ( 2d ) square and three - dimensional ( 3d ) cubic lattices systems with multiorbital structures @xcite . the band structure behaves like decoupled orthogonal 1d chains ; while , different chains are coupled at their crossing site through multiorbital hubbard interactions . in particular , spins of each chain are not conserved but coupled by hund s interaction . hence , the ground state fm ordering is genuinely 2d or 3d . different from nagaoka s theorem , the result of multiorbital fm allows a stable fm phase over a large region of filling factors in both 2d and 3d . an important consequence of this theorem is that the sign structure of the many - body hamiltonian matrix leads to the absence of the quantum monte - carlo ( qmc ) sign problem @xcite . consequently , qmc simulations on finite temperature thermodynamic properties of itinerant fm have been performed @xcite , which yield asymptotically exact results and shed light on the mechanism of magnetic phase transitions in the strong - coupling limit . in this article , we generalize nagaoka s theorem of itinerant fm from the single orbital system to multiorbital systems . we consider the 3d cubic lattice and each site consists of three @xmath0 orbitals : @xmath1 , @xmath2 , and @xmath3 . each orbital has a planar orientation , and the associated band structure is quasi-2d like . electrons of different orbitals interact through the on - site multiorbital interactions including hund s coupling . in the limit of intra orbital interaction @xmath6 , states with doubly occupied orbitals are projected out . when each plane of the cubic lattice has one and only one hole in the in - plane orbital band , this system can be be viewed as crossing layers of nagaoka fm states . we prove that , in this limit , the ground state of this system is the fully spin - polarized itinerant ferromagnetic state , and it is non - degenerate apart from the trivial spin degeneracy . furthermore , when this system is reduced to a single 2d layer system of @xmath0 orbitals , the @xmath3 and @xmath2 orbital bands become quasi-1d and coupled to the quasi-2d band of @xmath1 through hund s coupling . the ground state fm is still valid , where the quasi-1d @xmath3 and @xmath2 bands are allowed to take general values of filling , while , the @xmath1 band can possess a single hole or be fully filled . although the above exact results require an idealized strong - coupling limit , the strong correlation physics that they imply sheds important light on the mechanism of itinerant fm in transition metal oxides . the rest of this paper is organized as follows : in sec . [ sect : model ] , the multiorbital hubbard model for the @xmath0 orbital in the 3d cubic lattice is defined . in sec . [ sect:3d ] , theorem 1 of the ground state itinerant fm in the 3d @xmath0 orbital system is proved . in sec . [ sect : layer ] , theorem 2 of the ground state itinerant fm for the reduced 2d layered system is proved . discussion on connections to experiment systems is provided in sec . [ sect : exp ] . conclusions are presented in sec . [ sect : cons ] . in this section , we define a 3d multiorbital hubbard model in the 3d cubic lattice , which will be shown to possess itinerant fm ground states under conditions ( i ) and ( ii ) in sec . [ sect:3d ] . we consider a @xmath0 orbital system filled with spin -@xmath7 electrons ; _ i.e. _ , each site possesses @xmath1 , @xmath2 and @xmath3 orbitals . the wannier wavefunction of the @xmath0 orbitals is planar - like as shown in fig . [ fig : orbital ] . the kinetic energy of each orbital band exhibits a 2d structure : say , for electrons in the @xmath1 orbital , they can only move in the @xmath8-plane with a hopping amplitude @xmath9 . however , their hopping amplitude @xmath10 along the transverse direction of the @xmath11 axis is very small . the in - plane hopping @xmath9 is assisted by the @xmath12 orbitals of oxygen anions lying at the middle point of the bond , which leads to large hopping amplitudes ; while , the transverse hopping @xmath10 can only be attributed to the direct overlap between two @xmath1 orbitals offset along the @xmath11 axis . since @xmath13 orbital wannier functions are nearly localized and the @xmath11 axis is perpendicular to the orbital plane , @xmath9 is negligible in realistic transition metal oxides . similarly , electrons in the @xmath2 and @xmath3 orbitals only hop along the @xmath14 and @xmath15-planes , respectively . because of the different parity eigenvalues of these three @xmath0 orbitals with respect to the @xmath8 , @xmath14 , and @xmath15-planes , they do not hybridize by the nearest neighbor hopping . if we neglect the longer range hopping terms , the kinetic energy part can simply be written as h^k = h^k_xy + h^k_yz + h^k_zx , where @xmath16 , @xmath17 , and @xmath18 are the kinetic energies of electrons in the @xmath8 , @xmath14 , and @xmath15 orbital bands , respectively . the kinetic energy for the @xmath8 orbital band is expressed as h^k_xy&= & _ t_(d^_xy , ( ) d_xy,(+a_0x ) + & + & d^_xy , ( ) d_xy,(+a_0 y)+h.c . ) , [ eq : kin ] where @xmath19 is the lattice constant ; @xmath20 is the annihilation operator in the @xmath1 orbital on site @xmath21 with the spin - index @xmath22 or @xmath23 . for convenience later , we choose @xmath9 positive . for the bipartite lattice such as the cubic one , the sign of @xmath9 can be flipped by a gauge transformation , which does not affect any physical observable . the transverse hopping @xmath10 term is neglected in eq . ( [ eq : kin ] ) . similarly , @xmath24 can also be defined by permuting the indices of orbitals and hopping directions in @xmath16 , whose expressions are not repeated here . the interaction term is the standard multiorbital hubbard interaction @xcite defined on - site as h^i&=&u _ , a n_a , ( ) n_a , ( ) + & - & j _ , ab(s_a ( ) s_b ( ) - n_a ( ) n_b ( ) ) + & + & v _ , ab n_a ( ) n_b ( ) + & + & _ , a b ( d^_a , ( ) d^_a , ( ) d_b , ( ) d_b , ( ) + h.c . ) , [ eq : hint ] where @xmath25 is the orbital index ; @xmath26 is the number of electrons occupying the @xmath27 orbital at site @xmath21 with spin - index @xmath28 ; @xmath29 ; @xmath30 is the spin operator of the @xmath27-th orbital at site @xmath21 . equation ( [ eq : hint ] ) contains all the possible terms satisfying the spin su(2 ) symmetry and the lattice cubic symmetry . the @xmath5 term is the usual intra orbital hubbard interaction ; the @xmath31 term is the inter orbital hubbard interaction ; the @xmath32 term is hund s coupling with @xmath33 ; and the @xmath34 term describes the singlet pairing hopping process among different orbitals . the expressions of @xmath5 , @xmath31 , @xmath32 , and @xmath34 are presented in appendix [ appdx : parameter ] following the standard physical meaning of two - body coulomb interactions . in this section , we consider the 3d @xmath0 orbital systems in the cubic lattice of size @xmath35 . we also assume the following two conditions , + ( i ) _ @xmath36 , @xmath34 is finite _ ; + ( ii ) _ for each orbital band , there is one and only one hole in every layer parallel to the orbital plane . e.g. , there is one and only one hole in every @xmath8-plane in the @xmath1 orbital band , and similarly for the @xmath2 and @xmath3 orbital bands_. + condition ii can be well - defined because of the following lemma whose proof is obvious . the hamiltonian of eqs . ( [ eq : kin ] ) and ( [ eq : hint ] ) conserves particle number in each orbital band in each plane parallel to the orbital orientation . + accordingly , the hilbert space of the system can be factorized as the tensor product of the hilbert space of each orbital band in each layer as = _ l_z=1^l_zh_l_z^xy _ l_x=1^l_xh_l_x^yz _ l_y=1^l_yh_l_y^zx , where @xmath37 are the indices of the @xmath8 , @xmath14 , and @xmath15-planes , respectively . under condition i , states with doubly occupied orbitals are projected out , and each orbital can only be occupied at most by one particle . further , condition ii restricts one and only one hole for each orbital band in a layer . in each given hilbert space @xmath38 , each state is determined by the location of the hole and the spin configuration at other sites . for example , in the hilbert space of the @xmath1 orbital of the @xmath39-th layer , we can label all the @xmath1 orbitals of this layer in an arbitrary order by the index @xmath40 . then , the states in this layer can be represented as |h^xy_l_z;\{}_l_z= ( -)^h^xy_l_z _ i_l_z^d^_xy , ( i_l_z)|0 , [ eq : sign ] where @xmath41 labels the location of the hole ; @xmath42 represents the spin configuration ; @xmath43 means the ordered product of the creation operators except the one at the location of the hole , @xmath44 with the hat " means the operator below it does not appear . then , we can define the bases of the product hilbert space for our entire system as & & _ l_y=1^l_y |h^zx_l_y;\{}_l_y , [ eq : bases ] where , @xmath45 represents the locations of all the holes in a given state and @xmath46 represents the spin configuration of this state with the labels of orbitals and layers omitted , . because of the spin conservation , we can decompose the hilbert space into different sectors @xmath47 by the value of the @xmath11 component of total spin @xmath48 , denoted as @xmath49 . nevertheless , @xmath47 can not be further factorized as the product space of different orbital bands and layers . next , let us prove two lemmas as the preparation of the fm theorem 1 . under the bases @xmath50 defined above for the hilbert space @xmath51 with total spin @xmath48 , the off - diagonal matrix elements of the many - body hamiltonian @xmath52 ( see eqs . ( [ eq : kin ] ) and ( [ eq : hint ] ) ) are non - positive . : the off - diagonal matrix elements are contributed by the hopping part and hund s interaction part . the pairing hopping term does not exist in the limit of @xmath36 since states with doubly occupied orbitals have been projected out . for the hopping term , because of the sign convention of the many - body bases defined in eq . ( [ eq : bases ] ) inherited from eq . ( [ eq : sign ] ) , it is easy to check that = -t 0 . this step is the same as that in the proof of the usual nagaoka theorem for a 2d single orbital hubbard model @xcite : although here are ( @xmath53 ) holes in our system , the fermion ordering does not change under hopping because of lemma 1 . for the @xmath8 component of hund s interaction @xmath54 with @xmath55 , it does not change the fermion ordering either , and thus , its matrix elements read = -j/2 0 , , which are also non - positive . the @xmath31 term and the @xmath11 component of hund s interaction only contribute to the diagonal part of the many - body matrix . _ _ let us consider a general hole and spin configuration satisfying conditions ( i ) and ( ii ) . we pick up a bond @xmath56 and consider the @xmath57 orbital of site @xmath58 and the @xmath59 orbital of site @xmath60 . if they are occupied by spin @xmath28 and @xmath61 , respectively , let us denote this bond configuration as @xmath62 $ ] . we have the following lemma : the spin configuration in @xmath62 $ ] can be flipped to @xmath63 $ ] by applying a series of hopping and hund s interaction processes without finally affecting spin and hole configurations in the rest of the system . without loss of generality , we assume the bond @xmath56 is along the @xmath11 axis , and only discuss how to flip @xmath64 $ ] to @xmath65 $ ] . since @xmath27 and @xmath66 can take any of the @xmath8 , @xmath14 , and @xmath15 , there are 9 possible orbital configurations for a bond . nevertheless , they can be classified into 4 non - equivalent classes because of the lattice geometry as shown in figs . [ fig : t2g_tran ] @xmath67 to @xmath68 . for later convenience , the single hole assisted spin - flipping in the 2d single orbital infinite @xmath5 hubbard model is reviewed in appendix [ appdx : nagaoka ] , which played an important role in the proof of the nagaoka fm ground state and will be employed repeatedly below . class @xmath67 : let us consider @xmath69 . the same reasoning can also apply to the case of @xmath70 . since two orbitals and the bond are coplanar and there is one hole in this plane , we can directly use the result in appendix [ appdx : nagaoka ] to exchange their spins @xmath71\rightarrow [ d_{zx,\downarrow}(i);d_{zx,\uparrow}(j)]$ ] . class @xmath72 : let us consider @xmath73 and @xmath74 , _ i.e. _ , the configuration @xmath75 $ ] . the reasoning below also applies to the case of @xmath76 and @xmath77 . let us use another orbital , @xmath2 at site @xmath58 . first , we assume that it is occupied since we can always move an electron from other neighboring sites and return it back afterwards . if it is occupied by spin-@xmath78 , a familiar bond configuration @xmath79 $ ] appears . as already shown in class @xmath67 , their spins can be exchanged to give an intermediate configuration @xmath80 $ ] for class ( b ) . then , on site @xmath58 , we have both @xmath81 and @xmath82 , whose spins can be further exchanged by the @xmath83 term to become @xmath84 and @xmath85 . combining these two steps of spin exchange , the initial configuration @xmath75 $ ] is flipped to @xmath86 $ ] and the third @xmath87 orbital remains spin-@xmath78 finally . if the @xmath87 orbital is occupied by spin-@xmath23 , we can first apply hund s interaction to exchange spins between the @xmath88 and @xmath87 orbitals , and then apply the process in class @xmath67 to further exchange the spins between two @xmath2 orbitals on sites @xmath58 and @xmath60 . class @xmath89 contains four equivalent configurations @xmath90 , @xmath91 ; @xmath92 , @xmath91 ; @xmath93 , @xmath94 ; @xmath93 , @xmath95 . class @xmath68 only contains one configuration @xmath96 . the proof for these two classes are similar to that of class @xmath72 by combining hund s interaction and hole s hopping . the detailed proofs are given in appendix [ appdx : flip ] . _ q.e.d . _ based on lemma 3 , we can have an important property of transitivity for the many - body matrix in any sub - hilbert space @xmath47 . * ( transitivity ) * consider the hamiltonian matrix in the subspace @xmath47 . for any two basis vectors , @xmath50 and @xmath97 , there always exists a series of basis vectors @xmath98 , @xmath99 , .... , @xmath100 connected with nonzero matrix elements of @xmath101 , such that & & + & & ... 0 . firstly , we can always apply the hopping term to @xmath102 to rearrange the locations of holes of each orbital band in each layer . then we reach an intermediate state @xmath103 in which the locations of holes are the same as that in @xmath104 . since the two states @xmath104 and @xmath103 have the same z component of the total spin @xmath48 , they only differ by their spin configurations with a permutation of spins . since any permutation can be generated by exchanges , it suffices to show as below that in @xmath103 two opposite spins in any two orbitals can be exchanged by consecutively applying hoppings and hund s interactions without finally affecting the configuration of the rest of the system . if the two orbitals are on the same site , it is easy to exchange their spins by applying hund s interaction with @xmath83 once . if they are located at different sites , we can always find a path of successive bonds connecting these two site , and passing through nonempty sites ( here are at most a number of @xmath105 sites with all three orbitals empty ) . then , we can have a sequence of occupied orbitals in which every two adjacent orbitals are located on two nearest neighbor sites . we can exchange the two spins at two ends of this path as follows : following lemma 3 , we can flip different spins at occupied orbitals on two neighboring sites . then , by successively applying this operation , we are able to exchange the spins of two ends without affecting other parts of the system . _ _ now we are ready to prove the following theorem . * ( 3d fm ground state ) * consider the hamiltonian @xmath106 satisfying conditions @xmath107 and @xmath108 . the physical hilbert space is @xmath47 . for any values of @xmath31 and @xmath33 , the ground states are fully spin - polarized and are unique apart from the trivial spin degeneracy . they can be expressed as | _ g^s_z = ^c_\{h},\ { } | \{h},\ { } [ eq : groundstate ] where all the coefficients are strictly positive and @xmath109 means the summation over states in @xmath47 . because of lemma 2 of non - positivity and lemma 4 of transitivity , the hamiltonian matrix within @xmath47 satisfies the prerequisites of the perron - frobenius theorem theorem . the importance of the transitivity to the non - degenerate ground state is also explained in sec . iii of the supplementary material of ref . [ ] . then it is straightforward to conclude that eq . ( [ eq : groundstate ] ) is true which is non - degenerate within each @xmath47 . to show that @xmath110 in eq . ( [ eq : groundstate ] ) is a fully spin - polarized state , we introduce a reference state in @xmath47 by summing over all its bases with equal weights , | _ ref^s_z = ^| \{h},\ { } . since @xmath111 is symmetric under exchanging spins of any two orbitals , it is a fully spin - polarized state with the total spin @xmath112 and its @xmath11 component @xmath48 . apparently , @xmath113 . since @xmath110 is the unique ground state in @xmath47 , these two non - orthogonal states must share the same good quantum numbers of @xmath114 and @xmath48 . _ q.e.d . _ because of the spin @xmath115 symmetry , all ground states @xmath110 in different @xmath47 with @xmath116 are degenerate , and form a set of spin multiplets with the maximal total spin @xmath112 . theorem 1 is true for both the periodic and open boundary conditions . based on theorem 1 , we have the following two corollaries with their proofs presented in appendix [ appdx : corollary ] . under condition i and a modified condition ii : there is one and only one doubly occupied orbital for each orbital band in each layer ; we have that the hamiltonian of eqs . ( [ eq : kin ] ) and ( [ eq : hint ] ) also possesses the fully spin - polarized fm ground state which is unique up to the trivial spin degeneracy . if there is one and only one particle in each orbital band in each layer , we also have that the ground state is fully spin - polarized and unique up to the trivial spin degeneracy for any values of @xmath33 and @xmath31 . in this section , we will consider the same multiorbital hubbard hamiltonian of eqs . ( [ eq : kin ] ) and ( [ eq : hint ] ) but in a single layer along the @xmath8-plane . the @xmath1 orbital band remains 2d ; while , the @xmath3- and @xmath2 orbitals form crossed 1d bands with dispersion perpendicular to each other . the fm ground state of this system will be discussed when both 1d and 2d bands present . when only the two quasi-1d bands are considered , the fm ground state has been proved in ref . [ ] under condition ( i ) and the following two conditions : + ( iii ) : _ open boundary condition or periodic ( anti - periodic ) boundary condition with odd ( even ) number of particles in each row or column ; _ + ( iv ) : _ arbitrary filling with at least one hole and one particle in each row and each column . _ to describe the part of @xmath3 and @xmath2 bands with general fillings , let us first recapture the many - body bases constructed for the quasi-1d system in ref . [ ] and rewrite them in terms of @xmath3 and @xmath2 bands . by lemma 1 , for any generic filling , we can always specify a partition of particle numbers into rows @xmath117 and columns @xmath118 as , @xmath119 , where @xmath120 and @xmath121 are the particle numbers of @xmath3- and @xmath2 orbitals conserved in the @xmath122-th row and the @xmath123-th column , respectively . we can order electrons in each row from the left most particle to the right most one , followed by the ordering in each column from the top to bottom . the corresponding many - body basis can be set up as & & | , _ _ , _ = _ j=1^l_x d_yz , c_j^ _ j=1^l_y d_zx , r_j^ | 0 + & = & d_yz , c_l_x^ d_yz , c_2^ d_yz , c_1^ d_zx , r_l_y^ d_zx , r_2^ d_zx , r_1^ | 0 , + [ eq:1d_basis ] where @xmath60 denotes the index of columns and rows ; @xmath124 all @xmath58 s and @xmath60s@xmath125 represents the coordinates of occupied sites ; @xmath126 all @xmath58 s and @xmath60s@xmath125 represents their the spin configurations . the operator @xmath127 ( @xmath128 ) creates a whole line of @xmath129(@xmath130 ) @xmath3(@xmath2 ) electrons in the row @xmath131 ( column @xmath132 ) ordered from left to right ( from top to bottom ) , @xmath133 , and @xmath128 can be similarly defined . now , let us consider the additional quasi-2d @xmath1 band with one and only one hole . the basis for this layer of @xmath1 orbital @xmath134 is defined following eq . ( [ eq : sign ] ) but without the layer index . then , the basis for the hilbert space of this 2d system @xmath135 can be constructed by the direct product of the basis for the 1d bands and that for the 2d band , | , _ _ , _ @xmath11 component of the total spin , this hilbert space can be decomposed as @xmath136 . following the same steps in ref . [ ] and in sec . [ sect:3d ] , it is straightforward to show that for the basis defined in eq . ( [ eq : basis_rs ] ) , and under condition ( iii ) for 1d bands , the off - diagonal matrix elements of the many - body hamiltonian are non - positive . below , we further show the transitivity of the hamiltonian matrix in the sub - hilbert space @xmath137 under condition ( iv ) for @xmath3- and @xmath2 bands . since the locations of electrons can be easily adjusted by applying hopping terms , it suffices to show the transitivity between two bases only differ by spin configurations , @xmath138 and @xmath139 . again , we only need to show that for the state of @xmath140 , we can exchange any two different spins by applying hopping and hund s interaction terms . if these two electrons are both in quasi-1d bands @xmath3 and @xmath2 , this situation has been proved in ref . [ ] . if these two electrons are both in the @xmath1 band , it is reduced to the usual case of the nagaoka system . now let us consider the case of one electron in the quasi-1d bands , without loss of generality , in the @xmath3 orbital band with spin-@xmath78 ; and another electron in the @xmath1 band with spin-@xmath23 . we denote their locations as @xmath141 and @xmath142 , respectively . let us identify the site @xmath143 which is in the same row of the @xmath3 electron and in the same column of the @xmath1 electron , and consider the @xmath2 orbital at this site . we assume that there is an electron of the @xmath2 orbital at @xmath143 . if not , because of condition ( iv ) , we can always move a @xmath2 electron of that column to @xmath143 by hopping . and the configuration in this column can be restored by reversing the hopping afterward . if the electron of the @xmath2 orbital at @xmath143 has spin-@xmath78 , it can first be moved to @xmath142 by hoppings . then , it can exchange the spins with the @xmath1 electron at @xmath142 by hund s interaction . after reversing the hopping , this @xmath2 electron can be moved back to @xmath143 but with spin-@xmath23 . further , it can be moved to @xmath141 to exchange the spins with the @xmath3 electron and be moved back to @xmath143 again with its original spin-@xmath78 recovered . the net effect is the exchange of spin configurations between the @xmath1 and @xmath3 electrons without affecting other configurations . the case of the @xmath2 electron at @xmath143 with spin-@xmath23 can be similarly proved . so far , we have shown both the non - positivity of off - diagonal matrix elements and the transitivity of the hamiltonian matrix in the sub - hilbert space @xmath137 . then , following the same reasoning in the proof of theorem 1 , it is straightforward to have the following theorem * ( 2d fm ground state ) * consider the case in which there is one and only one hole in the @xmath1 band . under conditions @xmath107 , @xmath144 , and @xmath145 , for any values of @xmath31 and @xmath33 , the ground states are fully spin - polarized which is unique apart from the trivial spin degeneracy . next , we consider the situation in which the @xmath1 band is half - filled , _ i.e. _ , there is no hole . in this case , the @xmath1 band by itself is not ferromagnetic . because of the coupling to the quasi-1d band , we have the following theorem if the @xmath1 band is half - filled , under the same conditions in theorem 2 , for any values of @xmath31 and @xmath33 , the ground states are fully spin - polarized which is unique apart from the trivial spin degeneracy . we first define the basis for the local moments for the half - filled @xmath1 band , which can be ordered in an arbitrary way as arbitrary spin distribution . then for the combined system , the basis is defined as | , _ _ , _ |\{}. again because of spin conservation , the hilbert space in this case @xmath146 can be further decomposed into the direct sum of different sectors of @xmath48 s as @xmath147 . similarly to theorem 2 , the off - diagonal elements of the hamiltonian matrix is non - positive . we next show the transitivity of the hamiltonian matrix in each physical sub - hilbert space @xmath148 . again , we only need to show that for any state in @xmath148 , opposite spins of any two electrons can be exchanged by applying hopping and hund s interaction without affecting other parts of the system . the proof is very similar to that of theorem 2 , nevertheless , a new situation needs to be addressed : both electrons are in the @xmath1 band with spin-@xmath78 and -@xmath23 , respectively . their locations are denoted as @xmath21 and @xmath149 , respectively . then we can choose an electron in the @xmath3 band , and , without loss of generality , assume its spin-@xmath78 . then according to the proof of theorem 2 , we can first flip the pair of electrons @xmath150 and @xmath151 , then their spins become @xmath152 and @xmath153 . next , we consider the pair of @xmath152 and @xmath154 and exchange their spins . the net result is the exchange of the spins of two @xmath1 electrons . with both results of non - positivity and transitivity , it is also straightforward to arrive at corollary 3 by similar proof of theorem 1 . _ although theorems 1 and 2 are under ideal conditions and limits , they do have close connections to realistic systems of transition - metal oxides . for the multiorbital hubbard hamiltonian of eqs . ( [ eq : kin ] ) and ( [ eq : hint ] ) , they are actually a good approximation of the @xmath0 orbital systems of transition metal oxides in 3d . for example , the itinerant fm srruo@xmath4 belongs to this class of materials @xcite , which is a @xmath0-active material of 4@xmath13 electrons in a cubic lattice . even though , typical interaction strength in the 4@xmath13 electron systems are intermediately strong , it already exhibits the fm phase with @xmath155 . furthermore , the magnetic moment of this system is observed as 1.6@xmath156 per site with the electron filling in srruo@xmath4 as four electrons per site . therefore , the fm ground state stated in theorem 1 would possibly persist to the intermediate interaction regime and with finite electron or hole density away from half - filling . nevertheless , the magnetization would be no longer fully polarized but partially polarized to save the kinetic energy cost . another important system is the laalo@xmath4/srtio@xmath4 interface between two component insulators . this interface is experimentally found metallic and ferromagnetic with large magnetization @xcite . this is a @xmath0 orbital active material with 3@xmath13 electrons in 2d layered systems , whose @xmath3 and @xmath2 are quasi-1d orbital bands while its @xmath1 orbital forms the quasi-2d band . for 3@xmath13 electrons , the interaction strength is stronger than that of 4@xmath13 materials . the rkky , itinerant , and double - exchange mechanisms were proposed to explain the fm in this system @xcite.here , we have shown that the ground state itinerant fm is fully spin polarized and robust for general densities in the @xmath3 and @xmath2 bands under strong intra orbital interactions . in summary , we have investigated the nagaoka type itinerant fm in @xmath0 orbital systems in a 3d cubic lattice . the hole motion in each orbital band is constrained in the plane parallel to the orbital orientation . effectively , this system behaves as crossing planes of 2d nagaoka fm coupled by on - site inter orbital hund s coupling . consequently , 3d itinerant fm ground states are developed , which are proved fully polarized and unique apart from the trivial spin multiplet degeneracy . also , we have considered the 2d layer of @xmath0 orbital systems : the quasi-1d bands are itinerant with arbitrary generic fillings and the quasi-2d band can have a single hole or be half - filled . its ground state is shown remaining the fully spin - polarized itinerant fm . the theorems established in this article can be helpful for further understanding the mechanism of fm in srruo@xmath4 and the transition - metal oxides interface . y.l . is grateful to elliott h. lieb and congjun wu for their helpful discussion and encouragement . thanks the princeton center for theoretical science for support . the expressions of @xmath5 , @xmath31 , @xmath32 and @xmath34 in eq . ( [ eq : hint ] ) are standard two - body coulomb integrals under the @xmath0 orbital basis . we assume the bare coulomb interaction as @xmath157 , and express the wannier @xmath0 orbital wavefunctions @xmath158 with @xmath159 and @xmath15 , respectively . then @xmath5 , @xmath31 , @xmath32 and @xmath34 can be represented @xcite as u&= & _ 1 _ 2 _ a^ * ( _ 1 ) _ a^ * ( _ 2 ) v(_1-_2 ) _ a ( _ 2 ) _ a ( _ 1 ) , + v&= & _ 1 _ 2 _ a^ * ( _ 1 ) _ b^ * ( _ 2 ) v(_1-_2 ) + & & \ { _ b ( _ 2 ) _ a ( _ 1 ) - _ a ( _ 2 ) _ b ( _ 1 ) } , + j&=&2 _ 1 _ 2 _ a^ * ( _ 1 ) _ b^ * ( _ 2 ) v(_1-_2 ) _ a ( _ 2 ) _ b ( _ 1 ) , + & = & _ 1 _ 2 _ a^ * ( _ 1 ) _ a^ * ( _ 2 ) v(_1-_2 ) _ b ( _ 2 ) _ b ( _ 1 ) . + [ eq : multiband ] where @xmath160 and no summation over repeated indices is assumed . let us explain the physical meanings of @xmath5 , @xmath31 , @xmath32 and @xmath34 by considering a single - site problem filled with only two fermions . in total there are 15 states , which can be classified as 3 sets of spin triplets and 6 spin singlets . the three sets of spin triplet states can be expressed as & & d^_a , d^_b , |0 , d^_a , d^_b , |0 + & & \{d^_a , d^_b , + d^_a , d^_b , } |0[eq : inter_trp ] with @xmath160 , and their energy is @xmath31 . the 6 spin singlets can be further classified as the orbital angular momentum ( oam ) singlet , doublet and triplet as follows . the splitting between the oam doublet and triplet states is because of the cubic symmetry , which is a two - particle analogy to the single - particle version of the @xmath0 and @xmath161 level splitting . the orbital angular momentum singlet state is expressed as \{d^_xy , d^_xy , + d^_yz , d^_yz , + d^_zx , d^_zx , } |0 , whose energy is @xmath162 . the orbital angular momentum doublet states have the energy @xmath163 , and they are expressed as & & \{d^_yz , d^_yz , + d^_zx , d^_zx , -2 d^_xy , d^_xy , } |0 , + & & \ { d^_yz , d^_yz , -d^_zx , d^_zx , } |0 . the orbital angular momentum triplet states have energy @xmath164 , whose wavefunctions are expressed as & & \ { d^_yz , d^_zx , -d^_yz , d^_zx , } |0 , + & & \ { d^_zx , d^_xy , -d^_zx , d^_xy , } |0 , + & & \ { d^_xy , d^_yz , -d^_xy , d^_yz , } |0 . [ eq : inter_sng ] clearly , the energy difference between the inter orbital singlet and triplet states is @xmath32 as comes from hund s coupling . to keep this paper self - contained , we review an important step showing the transitivity in the single orbital nagaoka system @xcite . we only consider the case of the 2d hubbard model in the square lattice with @xmath165 with a single hole [ ] . the hamiltonian can be written as h = t _ p \ { c^_i c_j + h.c.}p , [ eq : kin_2 ] where @xmath166 is the projection operator projecting out the doubly occupied state . consider a bond @xmath56 with its two sites @xmath58 and @xmath60 occupied by spins @xmath28 and @xmath61 in orbitals @xmath57 and @xmath59 , respectively . this configuration is denoted as @xmath167 $ ] . as shown below , the spins in this configuration can be exchanged to be @xmath168 $ ] by applying a series of hoppings in eq . ( [ eq : kin_2 ] ) without affecting hole and spin configurations of other sites . obviously , we only need to consider the case of @xmath169 . spin flipping can be realized by the following motion of the single hole . we can choose a plaquette unit containing the bond @xmath56 . if here is a hole in this plaquette , without loss of generality , we can assume that here are two spin-@xmath78 s and one spin-@xmath23 in the rest 3 sites of this plaquette . they can form in total @xmath170 possible combinatorial configurations . as shown in fig . [ fig : nagaoka ] , they can be connected to each other by simply applying hole hoppings clockwise in the plaquette for at most three rounds . therefore , it is possible to exchange the spins on the bond @xmath56 without affecting other sites . if this plaquette does not contain a hole , we can first apply the hopping process to move the hole to this plaquette . during this process , we require that the hole should not pass sites @xmath58 and @xmath60 , which is possible because even when we remove all the bonds connecting @xmath58 and @xmath60 , the remaining part of the lattice is still connected . following the conclusion above , we can flip the spin configuration on the bond @xmath56 without affecting other sites . afterwards , we can restore the rest of the spin configuration by reversing the hole s motion along the same path on which it was brought to the plaquette before . finally , the spin configuration on @xmath56 becomes flipped , _ i.e. _ , @xmath167 \rightarrow [ d_{a,\sigma ' } ( i ) , d_{b,\sigma}(j)]$ ] . meanwhile , the hole returns to its original location and spin configurations on other sites are restored . in this section , we complete the proof of lemma 3 for the orbital configurations of classes @xmath89 and @xmath68 below . class @xmath89 : we consider the case of @xmath73 and @xmath171 , _ i.e. _ , the configuration @xmath172 $ ] . the reasoning below also applies to the other 3 situations of @xmath76 , @xmath171 ; @xmath173 , @xmath77 ; and @xmath173 , @xmath74 . here , the spin exchange between @xmath81 and @xmath174 can be aided by the @xmath175 orbital . following the reasoning in the main text , @xmath175 can always be assumed occupied . if it has spin-@xmath78 , on site @xmath60 , we have @xmath176 and @xmath174 , whose spins can be exchanged by hund s interaction to be @xmath177 and @xmath178 . then bond @xmath56 has a new spin configuration @xmath71 $ ] , which can be flipped as shown in class @xmath67 . as a result , the initial configuration of @xmath172 $ ] is flipped to @xmath179 $ ] without affecting @xmath176 . similarly , if the @xmath175 orbital is occupied by spin-@xmath23 , we can first apply the process in class @xmath67 to flip the spin configuration of @xmath3 orbitals on sites @xmath58 and @xmath60 , and then apply hund s interaction to flip spins on @xmath175 and @xmath180 orbitals . class @xmath68 : we consider the case in which both orbitals on @xmath56 are transverse , _ i.e. _ , the configuration @xmath181 $ ] . this time we check the @xmath88 orbital , and first assume it is occupied . if its configuration is @xmath81 , then along the bond @xmath56 we have @xmath172 $ ] , which can be flipped to @xmath179 $ ] following the steps in class ( c ) . then on site @xmath58 , the spin configuration is changed to @xmath182 $ ] , which can be flipped to @xmath183 $ ] by hund s interaction . as a result , the initial configuration of @xmath181 $ ] is flipped to @xmath184 $ ] and @xmath81 is maintained . if @xmath88 is occupied by spin-@xmath23 , we can first apply hund s interaction on site @xmath58 and then apply the steps presented in class @xmath89 . finally , if the @xmath88 orbital is empty , we can move this hole to a neighboring site , and perform the above process , and then move the hole back . in this part , we prove the two corollaries in sec . [ sect:3d ] . ( corollary 1 ) we perform a particle - hole transformation , _ i.e. _ , @xmath185 . under this transformation , the hopping hamiltonian eq . ( [ eq : kin ] ) remains the same except for the reversed sign of @xmath9 . nevertheless , for the bipartite lattice , the sign of @xmath9 can be reversed by a gauge transformation , which will not change the physics . the physical quantities transform as follows : n_a,1-n_a , , s_a -s_a . it is easy to check that for the interaction part @xmath186 , @xmath5 , @xmath31 , @xmath32 , and @xmath34 remain the same apart from a constant and a term proportional to electron density . in the case of fixing particle numbers , the difference is just a constant which does not affect real physics . under this transformation , the doubly occupied orbitals are mapped to holes . according to theorem 1 , the ground states are fm states with the total spin @xmath187 and are unique up to spin degeneracy . ( corollary 2 ) we order the @xmath1 electrons layer by layer and define |\{r_xy},\{}_xy=_l_z=1^l_z d^_xy,(^xy_l_z , l_z)| 0 , where @xmath142 is the in plane location of the electron in the @xmath39-th layer . similar bases can also be defined for @xmath2 and @xmath3 electrons as @xmath188 and @xmath189 , respectively . the many - body bases for the entire system can be defined as |\{r } , \{}&= & we also need to perform a gauge transformation to flip the sign of @xmath9 to be negative . then in this case , the off - diagonal matrix elements of hopping are negative because hopping does not change the ordering of electrons in the definition of eq . ( [ eq : basis_2 ] ) . because each orbital bands of each layer only contains one electron , only @xmath32 and @xmath31 terms contribute . again the off - diagonal matrix elements arise from @xmath32 , which are also negative . next , we show the transitivity . since we can also move the positions of electrons freely , we only need to consider two bases with the same electron locations but different spin configurations , denoted as @xmath191 and @xmath192 . then , it suffices to show that for any two electrons in @xmath191 , we can flip their spin configuration . if these two electrons live in different orbitals , say , @xmath1 and @xmath2 , then the planes of their motions cross and share a common line parallel to the @xmath193 axis . we can move these two electrons to any site of this line , and then apply hund s interaction to flip their spins , and then move back to their original locations . if these two electrons live in the same orbital with opposite spins , say , two @xmath1 electrons but in two parallel layers . then we can find another electron in @xmath3 orbitals . we first choose the @xmath1 electron with the spin opposite to that of @xmath3 , and switch their spins . then combine the new configuration of the @xmath3 and the other @xmath1 electron , and switch their spins . the net effect is that two @xmath1 electron spins are flipped , and the @xmath3 electron spin is restored . 46ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/physrev.125.164 [ * * , ( ) ] @noop _ _ ( , , ) link:\doibase 10.1103/physrev.147.392 [ * * , ( ) ] link:\doibase 10.1103/physrev.149.306 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevb.14.1165 [ * * , ( ) ] http://link.springer.com/book/10.1007/978-3-642-82499-9/page/1[__ ] , edited by , , vol . 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we study itinerant ferromagnetism in a @xmath0 multiorbital hubbard system in the cubic lattice , which consists of three planar oriented orbital bands of @xmath1 , @xmath2 , and @xmath3 . electrons in each orbital band can only move within a two - dimensional plane in the three - dimensional lattice parallel to the corresponding orbital orientation . electrons of different orbitals interact through the on - site multiorbital interactions including hund s coupling . the strong coupling limit is considered in which there are no doubly occupied orbitals but multiple on - site occupations are allowed . we show that in the case in which there is one and only one hole for each orbital band in each layer parallel to the orbital orientation , the ground state is a fully spin - polarized itinerant ferromagnetic state , which is unique apart from the trivial spin degeneracy . when the lattice is reduced into a single two - dimensional layer , the @xmath3 and @xmath2 bands become quasi - one - dimensional while the @xmath1 band remains two - dimensional . the ground state ferromagnetism also appears in the strong coupling limit as a generalization of the double exchange mechanism . possible applications to the systems of srruo@xmath4 and laalo@xmath4/srtio@xmath4 interface are discussed .

the ising model is widely used for illustrating concepts in statistical mechanics and field theory . in 2-dimensions it is exactly solvable and provides the classic example of a theory which exhibits non - mean - field critical exponents . there are three representations of the model : that as a magnetic spin system , as a theory of random paths @xcite-@xcite and as a fermionic lattice field theory with gaussian action ( grassmann representation ) @xcite . the connections between these are interesting , since they illustrate a deep relationship between dynamics and geometry . the random paths can be thought of as euclidean world lines of the fermions and in turn as domain boundaries in the spin system . even more fascinating are the corresponding relationships in the 3-@xmath0 ising model . the 3-@xmath0 model is not exactly solvable . however , it does share some of the geometrical features of the 2-@xmath0 model . its partition function can be represented as a spin model , as a model of decorated random surfaces @xcite-@xcite and as a fermionic lattice model which is no longer gaussian @xcite . there is an intriguing suggestion @xcite that the continuum limit of the 3-@xmath0 ising model could be some sort of non - critical string theory . the precise form of such a string theory is yet unknown . even the representation in terms of lattice surfaces ( or loops ) remains to be completely understood . in particular the calculus of surfaces ( loops ) is rather cumbersome to work with . handling the symmetry and geometry factors in the loop and surface representations is a non - trivial problem . it would be desirable to have an exact algebraic representation of the geometrical objects . in this article we shall show that such an algebraic representation can be obtained from the hopping expansion ( see e.g. @xcite ) of the grassmann representation of the model . we obtain several new results which serve to demonstrate the power of this calculus . the language of the hopping expansion allows for a simple algebraic formulation of the combinatorics of surfaces and loops . in particular all geometric factors are obtained as traces of ordered products of the hopping generators (= generators of shifts on the lattice ) . also , counting problems which correspond to some symmetries of the geometric objects , such as iteration of loops ( i.e. the loop runs through its links several times ) can be tackled in a simple manner . as an application of the latter we shall give the corrected version of the loop expansion of the free energy in the 2-@xmath0 case . it differs from previous results by extra factors for iterated loops . also the computation of the radius of convergence of loop- or surface expansion is a rather intractable problem if one has to work with the geometrical objects . for the 2-@xmath0 case we show that our calculus reduces this problem to the computation of the norm of the hopping matrix . for the 3-@xmath0 case we derive a representation of the 3-@xmath0 ising model as a product of 2-@xmath0 ising models coupled to an auxiliary field . based on this representation we give an elegant derivation of the geometric factor which eliminates overcounting of surfaces . our approach also allows for a simple classification of surfaces to be summed over in the surface representation . we show that this classification can be reduced to a 2-dimensional problem : the surfaces can be characterized by the loops that emerge as intersections of the surfaces with the coordinate planes of the lattice . there is some freedom in the choice of admissible loops in these planes . different choices lead to different classes of surfaces . for both 2- and 3-@xmath0 we derive an elegant formula for 2@xmath1-point functions in terms of loops and surfaces , respectively . the paper is organized as follows : in section 1.2 we review the representations of the ising model in terms of loops ( 2-@xmath0 ) and surfaces ( 3-@xmath0 ) and introduce our conventions . section 2 is dedicated to the 2-@xmath0 case . in 2.1 we set up the grassmann representation and perform the hopping expansion . this is followed by sub - section 2.2 where we show how to obtain the representation in terms of loops from the hopping expansion and show that the latter is an exact , algebraic representation of the loop calculus . the radius of convergence of the loop expansion of the free energy is shown to be determined by the critical temperature in 2.3 . section 3 gives our results for the 3-@xmath0 case . in 3.1 we first decompose the quartic term in the grassmann representation by introducing an auxiliary field and set up the hopping expansion . in 3.2 we extract the surface picture from the hopping expansion , derive the geometric factors and discuss the above mentioned classification of surfaces . in sub - section 3.3 we derive the formula for the 2@xmath1-point functions in terms of surfaces ( loops ) . the article closes with a discussion in section 4 . since we will make extensive use of the representation of the partition function in terms of loops and surfaces we will review these representations here and introduce our conventions . the ising model in terms of spin variables has the partition function @xmath2 where @xmath3 runs over all sites of the @xmath0-dimensional lattice @xmath4zz@xmath5 ( @xmath6 and @xmath7 denotes nearest neighbors . the 2-@xmath0 partition function has a representation in terms of closed loops @xcite-@xcite,@xcite on the dual lattice @xmath8 ( for the square lattice @xmath9 ) . this representation is obtained by drawing closed loops @xmath10 on the dual lattice around patches of negative spins on the original lattice . each link in @xmath10 crosses a link of the original lattice which has anti - aligned spins at its endpoints . by drawing loops around all such patches every anti - aligned link is taken into account . each of these links has a boltzmann weight exp@xmath11 , and since the total length @xmath12 of all loops is equal the number of anti - aligned neighbors , this gives rise to the weight exp@xmath13 . if @xmath14 denotes the number of all sites , there remain @xmath15 links with aligned spins at the endpoints . they have boltzmann weight exp@xmath16 and one finds @xmath17 here we introduced @xmath18 exp@xmath11 . the factor 2 emerges , since every loop configuration corresponds to 2 spin configurations related by the zz@xmath19 symmetry of the model . @xmath20 is defined to be the set of closed loops ( not necessarily connected ) which can be obtained by drawing lines on the dual lattice around patches of negative spins , so that a curve @xmath10 in @xmath20 is given by a collection of links that have no boundary . this defines loops by their so - called _ extrinsic geometry_. the series ( [ z2ext ] ) will converge for small @xmath21 , hence is a low temperature expansion ( the convergence properties will be discussed in section 2.3 ) . it is known that the partition function can also be written in terms of loops which have intrinsic geometry : @xmath22 here we introduced the number of self - intersections @xmath23 of a loop @xmath10 . we define @xmath24 to be the set of all closed , not necessarily connected , loops @xmath10 on the dual lattice with a fixed chosen orientation and with the restriction that each of the links of @xmath10 is occupied only once . the loops may however intersect themselves or each other . thus a loop @xmath10 in @xmath24 consists of a base point ( or several base points when there are disconnected pieces ) and a set of directions with the above restrictions . this is what we refer to as loops with _ intrinsic geometry_. a representation of the partition function in terms of loops with intrinsic geometry is a powerful tool , since it allows to exponentiate the sum over loops in ( [ z2int ] ) . this gives an expression of the free energy in terms of loops . we will discuss the precise form of this representation later in detail . the density of the free energy is a well defined physical quantity also in the infinite volume limit , and its representation in terms of loops is a beautiful illustration of the interplay between dynamics and geometry . there is a canonical mapping from @xmath24 onto @xmath20 , with the image of a loop @xmath25 under this mapping given by the collection of links traced out by that loop @xmath25 . obviously there exist many loops in @xmath24 with distinct intrinsic geometries which get mapped to a single loop in @xmath20 . however , the self - intersection factor @xmath26 leads to a cancellation of this over - counting in the sum ( [ z2int ] ) . this is illustrated in fig . [ selfinter ] . every pinch structure of a loop in @xmath20 ( as depicted in fig . [ selfinter ] , left - hand side ) is the image of each of the three pieces of loops in @xmath24 shown on the right - hand side of the figure . = 0.8 in note that larger classes of loops than @xmath24 can be used to represent the ising model . for example , the restriction that links are occupied only once in a loop can be relaxed to the restriction that the loops are non - back - tracking , i.e. they must not turn around at a site and run back on their last link . again , the same self - intersection factor @xmath26 gives rise to the necessary cancellations . however , for our presentation the above definition of @xmath24 is most convenient . + it is straightforward to generalize ( [ z2int ] ) to the case of the variable bond ising model , where the coupling @xmath27 is allowed to vary over links @xmath7 . the generalization of ( [ z2int ] ) to the case of the variable bond model is given by @xmath28 here we have generalized @xmath21 to @xmath29 exp@xmath30 and @xmath31 denotes the collection of links on the original lattice dual to the loop @xmath10 . all of these representations can be generalized to the 3-@xmath0 case . the representation analogous to ( [ z2ext ] ) is given by a sum over random surfaces with extrinsic geometry , @xmath32 here @xmath33 denotes all closed , but not necessarily connected surfaces @xmath34 made from plaquettes on the dual lattice which can be obtained by enclosing lumps of negative spins in the surface @xmath34 . analogous to the 2-@xmath0 case the surface @xmath34 in @xmath33 is a collection of plaquettes with zero boundary . we introduced the notation @xmath35 for the area of the surface @xmath34 . also for the 3-@xmath0 case one is interested in a representation in terms of surfaces that allow for intrinsic geometry @xcite,@xcite,@xcite-@xcite . it is given by @xmath36 here @xmath37 denotes the number of links where the surface self - intersects . again different choices for the set @xmath38 of surfaces with intrinsic geometry are possible . we will be more explicit on the possible choices of @xmath38 in section 3 , where we also give an elegant proof of formula ( [ z3int ] ) . in this section we discuss the 2-dimensional case . this serves to outline the general strategy for the hopping expansion , to introduce some notation and we also obtain results that will be needed for the 3-@xmath0 case . finally we give the correct result for the loop expansion of the free energy ( exponentiation formula ) which contains an additional factor for iterated loops which has previously been overlooked in the literature . the partition function in the form ( [ z2ext ] ) can be written as an integral over grassmann variables @xcite , which in two dimensions is given by @xmath39 } \ ; , \label{zferm2d}\ ] ] where the line- , corner- and monomer - terms of the action are given by @xmath40 \ ; , \nonumber \\ s_{c } ( \eta ) \!\!\ ! & \!=\ ! & \!\!\!\!\sum_{x \in \lambda^*}\!\left [ \eta_{+1}(x ) \eta_{-2}(x)\!+\!\eta_{+2}(x ) \eta_{-1}(x)\!+\ ! \eta_{+2}(x ) \eta_{+1}(x)\!+\!\eta_{-2}(x ) \eta_{-1}(x ) \right ] , \nonumber \\ s_{m } ( \eta)\!\!\ ! & \!=\ ! & \!\!\!\!\sum_{x \in \lambda^*}\!\left [ \eta_{-1}(x ) \eta_{+1}(x ) + \eta_{-2}(x ) \eta_{+2}(x ) \right ] \ ; . \label{action2d}\end{aligned}\ ] ] when the exponent in ( [ zferm2d ] ) is expanded , the non - vanishing contributions to the grassmann integral exactly reproduce ( without the overall factor @xmath41 ) the representation ( [ z2ext ] ) of the partition function as a sum of loops with extrinsic geometry . the subscripts @xmath42 and @xmath43 refer to the elements : lines , corners and monomers of the loops as they are produced by the corresponding terms in the action . these building blocks give the extrinsic geometry loops in the following way : a line coming into a site has to have a partner going out . this property of having a partner is enforced by the integration rules for grassmann variables . the outgoing line can continue in the direction of the incoming line , in this case the grassmann integral is saturated by the monomer term . the outgoing line can also turn by @xmath44 in which case the grassmann integral is made non - vanishing by the corner terms . the line can however not turn back since the square of a grassmann variable vanishes . finally there is the possibility that 4 lines are attached to a site and so saturate the grassmann integral . this gives rise to the pinch structure already discussed above . thus the loops produced by the expansion of ( [ zferm2d ] ) are closed ( every incoming line has an outgoing partner ) and non - back - tracking ( square of the grassmann variable vanishes ) . they are loops in extrinsic geometry since they simply occur as a set of links . thus the expansion of ( [ zferm2d ] ) reproduces ( [ z2ext ] ) . for details concerning the ordering of the grassmann variables see @xcite . for the following we need to write the action in a more compact and also anti - symmetrized form . we introduce the vector @xmath45 and the @xmath46 matrices @xmath47 ( the same matrices will be used in the 3-@xmath0 case where it is more convenient to denote them as @xmath48 and @xmath49 @xmath50 they obey @xmath51 . we also define @xmath52 we remark that @xmath53 and @xmath54 . with these definitions the action can be written as ( the overall factor 1/2 comes from the anti - symmetrization ) @xmath55 where the kernel @xmath56 is given by @xmath57 it is easy to see that @xmath56 is anti - symmetric . we remark that the representation ( [ quadra ] ) , ( [ kmatrix ] ) is a natural way of writing the action for the grassmann variables . it was already introduced in @xcite . the partition function is given by a pfaffian which , since @xmath56 is anti - symmetric , reduces to the root of a determinant is always even - dimensional . ] @xmath58 } = \sqrt{\det [ 1 + m^{-1 } r ] } . \label{zferm}\ ] ] expanding the determinant one obtains @xmath59 \right ) , \label{hopexp}\ ] ] where the hopping matrix @xmath60 is defined as @xmath61 . in the last step we used the well known formula for the expansion of determinants of the form @xmath62 $ ] . this series converges for @xmath63 , and in section 2.3 we will show that @xmath64 saturates this bound . the hopping matrix @xmath60 has the form @xmath65 the trace of powers of @xmath60 is given by @xmath66\!\!\ ! & = & \!\!\sum_{x_1 , x_2 \dots x_n } \sum_{\mu_1 , \mu_2 \dots \mu_n}\!\ ! \delta(x_1 + \hat{\mu}_1 , x_2 ) \dots \delta(x_n + \hat{\mu}_n , x_1 ) \ ; \mbox{tr } [ h_{\mu_1 } \dots h_{\mu_n } ] \nonumber \\ & = & \sum_{x_1 } \sum_{\mu_1 , \mu_2 \dots \mu_n } \delta(x_1 + \hat{\mu}_1 + \hat{\mu}_2 + \dots \hat{\mu}_n , x_1 ) \ ; \mbox{tr } \ ; [ h_{\mu_1 } h_{\mu_2 } \dots h_{\mu_n } ] \ ; . \nonumber \\ \label{htrace}\end{aligned}\ ] ] structures of this type are well known from the hopping expansion ( see e.g. @xcite ) of the fermion determinant in lattice gauge theories with fermions . due to the kronecker delta the terms in the sum have support on closed loops . in the next section we will show that these loops have simple properties due to the algebra of the @xmath67 s and this will also lead to a straightforward computation of the trace @xmath68 $ ] for arbitrary closed loops @xmath10 . from the remarks in the end of the last section it is clear that the loops supporting the contributions to ( [ htrace ] ) are closed loops with a base point @xmath69 and described by the _ ordered _ set of directions @xmath70 , where each @xmath71 can have the values @xmath72 . these loops are more general than the ones we included in @xmath24 . they are connected and are allowed to self - intersect , however in addition , they can occupy links several times or even iterate their whole path many times . since closed loops have even length : tr@xmath73 = 0 $ ] , and only even terms contribute in ( [ hopexp ] ) . some examples of loops occuring in the hopping expansion are depicted in fig . [ loopsfig ] . = 1.0 in in order to compute the weights for the loops in ( [ htrace ] ) the properties of the matrices @xmath74 have to be studied . the @xmath67-matrices will be encountered again in the 3-@xmath0 case where it will be convenient to denote them as @xmath75 and @xmath76 . they are explicitly given by ( compare @xcite ) @xmath77 we will now show that the algebra of these matrices restricts the set of loops occuring in the hopping expansion . the first observation is that @xmath78 , this property excludes back - tracking loops in ( [ htrace ] ) . furthermore one can show that the trace of a product of @xmath67 s is invariant under reversing the orientation of the loop . this can be seen by using the definition @xmath74 and the transposition properties @xmath79 and @xmath80 , @xmath81 & = & \mbox{tr } \ ; [ m^{-1 } p_{\mu_{2n}}^t \dots m^{-1 } p_{\mu_1}^t ] \ ; = \nonumber \\ \mbox{tr } \ ; [ p_{\mu_1 } m^{-1 } \dots p_{\mu_{2n } } m^{-1 } ] ^t & = & \mbox{tr } \ ; [ h_{\mu_1 } h_{\mu_2 } \dots h_{\mu_{2n } } ] \ ; . \nonumber\end{aligned}\ ] ] one can then fix an orientation for each loop in ( [ htrace ] ) and write a factor 2 in front of the sum . this factor cancels the overall factor of 1/2 from the square root in ( [ zferm ] ) . thus far we have shown that the paths which contribute in ( [ htrace ] ) are closed , connected , non back - tracking loops , @xmath10 , with a chosen orientation . we finally prove that the trace over the product of @xmath67 s along a loop @xmath10 yields the self - intersection factor @xmath82 as before @xmath83 denotes the number of self - intersections of the loop @xmath10 . the proof is decomposed into several steps . using the explicit form ( [ hmatrices ] ) of the @xmath67 s it is straightforward to show the following rules : + + _ basic loop _ : @xmath84 \ ; = \ ; -1 \ ; . \label{basic}\ ] ] _ telescope rule _ : @xmath85 _ kink rule _ : @xmath86 _ intersection rule _ : @xmath87 the four rules have the obvious graphical interpretation depicted in fig . [ rules ] . = 1.7 in the result ( [ basic ] ) is just formula ( [ traceformula ] ) for the simplest loop , i.e. the one running around a single plaquette . formula ( [ telescope ] ) allows one to stretch or shrink a loop without altering the trace ( [ traceformula ] ) . the kink rule ( [ kink ] ) allows one to remove kinks in the path , and finally the intersection rule ( [ intersection ] ) allows one to remove sub - loops , giving rise to a factor of @xmath88 for each self - intersection . formula ( [ intersection ] ) gives the result ( for both possible orientations ) for the sub - loop depicted in fig . [ rules ] ( d ) . the other 6 possibilities for ( [ intersection ] ) follow immediately from invariance of the formalism under rotations by @xmath44 . the above rules allow for a constructive reduction of the trace tr@xmath89 for an arbitrary closed , connected , non - back - tracking loop @xmath10 as follows : + + ( 1 ) start with a sub - loop which has only one self - intersection point ( an example for such a sub - loop is e.g. given in fig . [ redex ] , second line ) . if the loop we started with has no self - intersection at all , proceed to ( 2 ) , otherwise there exist at least two such sub - loops . + + ( 2 ) use telescope and kink rules to bring the sub - loop to the standard form as depicted in the left picture of fig . [ rules ] ( d ) . under these transformations the trace ( [ traceformula ] ) remains invariant . in case the loop had no self - intersection to begin with , bring it to the standard form for loops without self - intersection as depicted in fig . [ rules ] ( a ) , and ( [ basic ] ) is the final result . + + ( 3 ) use the intersection rule to remove the sub - loop and collect an overall factor of @xmath88 . repeat the steps ( 1 ) - ( 3 ) until finished . + + we remark that if nested sub - loops coincide on some links , it is always possible to disentangle them using the telescope rule . let s elaborate a little bit more on the actual implementation of step ( 2 ) : the idea is to replace products of @xmath67 s , corresponding to some sub - chain of links , by another product of @xmath67 s ( obtained from the first one using kink and telescope rules ) , such that the new chain corresponds to a new piece of loop which is smoother , but still leaves the whole loop closed . the necessary condition for the new sub - chain to match the starting- and end - point of the old sub - chain is that the number of @xmath90-moves minus the number of @xmath88-moves as well as the number of @xmath91-moves minus the number of @xmath92-moves remains invariant ( compare the example in fig . [ redex ] ( a ) . in order to illustrate the steps involved we discuss two examples ( see fig . [ redex ] ) . = 2.0 in the first two pictures in fig . [ redex ] demonstrate how the telescope and kink rules are used to smoothen a contour ( step ( a ) in the figure ) . the dotted part of the contour in the left figure is represented by the left - hand side of the following equation @xmath93 here we used the kink rule ( [ kink ] ) to replace @xmath94 by @xmath95 and then expanded , using the telescope rule ( [ telescope ] ) , to obtain the form on the right - hand side . this is once again a contour which matches starting- and end - points and corresponds to the second dotted contour in fig . [ redex ] ( a ) . thus step ( a ) in fig . [ redex ] is simply the replacement of the left - hand side of ( [ subchain ] ) inside some trace over @xmath67 s by its right - hand side . with combinations of telescope and kink rules all ( sub- ) loops can be transformed into squares , which can then be shrunk to loops around single plaquettes using the telescope rule . under such a set of operations the trace ( [ traceformula ] ) remains invariant . an example of such a transformation is depicted in step ( b ) of fig . [ redex ] . finally in step ( c ) of fig . [ redex ] the sub - loop is removed using the intersection rule ( [ intersection ] ) and an overall factor of @xmath88 emerges . these steps can be applied iteratively to prove ( [ traceformula ] ) for an arbitrary closed , connected , non - back - tracking loop @xmath10 . on inserting ( [ traceformula ] ) in ( [ htrace ] ) and the result in ( [ hopexp ] ) one finds @xmath96 here @xmath97 denotes the set of closed , connected , non - back - tracking loops of length @xmath98 based at @xmath3 with a chosen orientation . recall that ( [ htrace ] ) is non - vanishing only for even @xmath1 and thus the alternating sign of ( [ hopexp ] ) disappears . the overall factor of 1/2 in ( [ hopexp ] ) is gone since we chose only one of the two possible orientations of a loop , and the overall minus sign in ( [ hopexp ] ) is cancelled by the overall sign in ( [ traceformula ] ) . it is possible to simplify the exponential in ( [ expsum1 ] ) even further : to do that we discuss ( in order of increasing complexity ) loops with singly occupied links , iterated loops where the whole set of links is run through several times and finally loops where only some links are occupied several times . to start take some loop @xmath10 in @xmath97 where each link in the loop is occupied only once for the contour corresponding to this loop @xmath10 there are all together @xmath98 inequivalent choices of a base point . each of these points can serve as the base point for a different loop giving rise to the same contribution to ( [ expsum1 ] ) as @xmath10 . as such , one can choose a single representative of this class of loops and remove the factor of @xmath99 in ( [ expsum1 ] ) . now consider a loop which runs through its contour twice , i.e. each link occurs exactly twice ( an example of such a loop is given in fig . [ loopsfig ] ( c ) ) . for such an iterated loop we have only @xmath100 possible choices of inequivalent base points . in general for a loop @xmath10 that is iterated @xmath101-times there are @xmath102 inequivalent choices for the base point . as for the non - iterated loops , one can choose a single representative and remove the factor of @xmath99 in ( [ expsum1 ] ) , however , the factor of @xmath103 remains . finally we remark that for loops where only a sub - loop is iterated no such factor can occur , since the set of directions @xmath104 is different ( cyclicly permuted ) for some starting point @xmath3 , and the same point visited by the loop after running through a sub - loop . the partition function thus reads : @xmath105 where @xmath106 denotes the set of all closed , connected , non - back - tracking loops ( without base point ) and @xmath101 is the number of iterations of the loop @xmath10 . we stress that this result differs from previous formulas for the exponentiation of ( [ z2int ] ) by the factor @xmath103 for iterated loops . this factor is , however , essential for the correct cancellation of loops that have no counterpart in @xmath20 . this can be seen by the following simple example : consider the basic loop of length 4 which runs around a plaquette . when the exponent in ( [ expsum2 ] ) is expanded , this loop will , in the quadratic term of the expansion , give rise to the plaquette which is occupied by two such loops running around this single plaquette ( see the left - hand side of fig . [ example ] ) . it has the factor @xmath107 , where the factor 1/2 comes from the expansion of the exponential function . this loop has no counterpart in @xmath20 and thus has to be cancelled by some other loop . it is clear that the only loop which can cancel this loop is the one depicted on the right - hand side of fig . [ example ] . it appears in the linear term of the expansion of the exponential function and comes with the factor @xmath108 and thus exactly cancels the first loop . the overall minus sign is due to the self - intersection and the factor 1/2 comes from the term @xmath109 . hence this factor is essential for the cancellation of unphysical loops . = 0.6 in with the derivation of ( [ expsum2 ] ) we have established that the hopping expansion ( [ hopexp ] ) of the grassmann formulation gives an exact algebraic representation of the loop expansion . it is straightforward to generalize ( [ expsum2 ] ) to the case of the variable bond ising model by running through the derivation once more but allowing for varying boltzmann factors @xmath29 exp@xmath30 . the result is ( neglecting the overall factor @xmath110 ) : @xmath111 we remark that when a loop @xmath10 occupies some links several times , its dual @xmath31 has multiply occupied links . thus in the last equation the product includes a link - factor whenever the link is intersected by the loop . in particular for iterated loops each link factor @xmath112 occurs @xmath101-times . the formula ( [ expsum2 ] ) is a physically interesting result , since the exponent is proportional to the loop expansion of the free energy density @xmath113 @xmath114 the sum ( [ freee ] ) will converge for sufficiently small @xmath21 , and the radius of convergence corresponds to the critical temperature . however , computing the radius of convergence of the loop expansion in the form ( [ freee ] ) is a rather intractable problem . it is very convenient to make use of the form ( [ hopexp ] ) of the expansion , where it is clear that the expansion converges for @xmath115 the norm @xmath116 is defined as sup@xmath117 where @xmath21 is some test - function and @xmath118 , and the inner product is defined to be the @xmath119 product obtained by summing over all lattice and spinor indices . it is straightforward to compute @xmath120 the lattice indices of this matrix can be diagonalized using fourier transformation , giving @xmath121 where the transformation matrix @xmath122 is given by @xmath123 . the eigenvalues @xmath124 for the remaining @xmath46 problem can be easily computed giving ( each @xmath124 is two - fold degenerate ) @xmath125 the norm @xmath126 is then given by the square root of the larger eigenvalue . from ( [ converge ] ) and ( [ eigenvalues ] ) we obtain for the critical @xmath127 : @xmath128 this is the well known result for the critical inverse temperature . we thus have achieved an elegant proof that the radius of convergence of the loop expansion ( [ freee ] ) for the free energy is determined by the critical temperature . computing the radius of convergence of ( [ freee ] ) without the grassmann representation is a rather intractable problem . we now discuss the 3-@xmath0 case . we will see that the 3-@xmath0 model factorizes into products of 2-@xmath0 models coupled to an auxiliary field and many of the concepts developed in the previous section will become very useful . also for the 3-@xmath0 case there exists a grassmann integral for the representation of the partition function in terms of surfaces with extrinsic geometry @xcite . here we use a notation different from the original work , which is however more convenient for our expansion . each link of the dual lattice carries 4 grassmann variables denoted by @xmath129 as depicted in fig . [ 3dgrass ] . here @xmath3 and @xmath130 denote the link the variable lives on , and @xmath131 distinguishes the 4 different variables on each link . = 2.5 in the action for the grassmann variables is again a sum of three terms @xmath132 producing the elements of the surfaces : plaquettes , edges and monomers . the terms are given by @xmath133 & = & t^2 \sum_x \sum_{\stackrel{\scriptstyle \mu , \nu = 1}{\mu < \nu}}^3 \eta_{+\mu}(x,\nu ) \eta_{-\mu}(x+\hat{\mu},\nu ) \ ; \eta_{+\nu}(x,\mu ) \eta_{-\nu}(x+\hat{\nu},\mu ) \ ; , \nonumber \\ s_e[\eta ] & = & \sum_x \sum_{\mu = 1}^3 \sum_{\stackrel{\scriptstyle \nu , \rho \neq \mu}{\nu < \rho } } \big [ \eta_{+\nu}(x,\mu ) \eta_{-\rho}(x,\mu ) + \eta_{+\rho}(x,\mu ) \eta_{+\nu}(x,\mu ) \nonumber \\ & + & \eta_{+\rho}(x,\mu ) \eta_{-\nu}(x,\mu ) + \eta_{-\rho}(x,\mu ) \eta_{-\nu}(x,\mu ) \big ] \ ; , \nonumber \\ s_m[\eta ] & = & \sum_x \sum_{\mu = 1}^3 \sum_{\stackrel{\scriptstyle \nu , \rho \neq \mu}{\nu < \rho } } \big [ \eta_{-\nu}(x,\mu ) \eta_{+\nu}(x,\mu ) + \eta_{-\rho}(x,\mu ) \eta_{+\rho}(x,\mu ) \big ] \ ; . \label{3daction}\end{aligned}\ ] ] the grassmann representation of the 3-@xmath0 ising model @xcite is a straightforward generalization of the 2-@xmath0 case . again the exponential of ( [ 3daction ] ) has to be expanded , and the grassmann integral reproduces the terms corresponding to the representation of the partition function in terms of surfaces with extrinsic geometry . similar to the 2-@xmath0 case plaquettes , produced by @xmath134 , that are incoming to a link must have an outgoing partner to saturate the grassmann integral . possible choices for the direction of the outgoing plaquette are either the same direction as the incoming plaquette ( monomer terms ) or rotated by @xmath44 ( edge terms ) . the outgoing plaquette can however not fold back on the incoming one due to the fact that the square of a grassmann variable vanishes . also 4 plaquettes attached to a link can saturate the grassmann integral , producing the pinch structure of the surfaces . the resulting terms of the grassmann integral thus correspond to the closed surfaces in @xmath33 . for details concerning the ordering of the grassmann variables see @xcite . the quartic interaction , from @xmath135 $ ] , can be decomposed into a yukawa - like term with a tensor field by using the following identity for grassmann variables @xmath136 @xmath137 \big ) \ ; .\ ] ] thus , @xmath135 $ ] can be replaced by @xmath138 = t \sum_x \sum_{\stackrel{\scriptstyle \mu , \nu = 1}{\mu < \nu}}^3 a_{\mu \nu}(x ) \big [ \eta_{+\mu}(x,\nu ) \eta_{-\mu}(x+\hat{\mu},\nu ) + \eta_{+\nu}(x,\mu ) \eta_{-\nu}(x+\hat{\nu},\mu ) \big],\ ] ] and the partition function now contains a sum over auxiliary fields @xmath139 associated with the plaquettes @xmath140 of the dual lattice , @xmath141 + s_e[\eta ] + s_m[\eta ] } \ ; .\ ] ] the introduction of the auxiliary fields transformed the action for the grassmann variables to a quadratic form , and the hopping expansion methods can be applied . as in the 2-@xmath0 case , the next step is to introduce the vectors @xmath142 containing all 12 variables living on the 3 links associated with the site @xmath3 of the dual lattice @xmath143 with this ordering of the variables , the edge and monomer terms of the action can be written as a quadratic form @xmath144 , which is a simple generalization of the expression already used in the 2-@xmath0 case . the kernel @xmath145 for the corresponding terms is block - diagonal , with the blocks given by the matrix @xmath43 from the 2-@xmath0 formulation ( [ mmatrix ] ) , @xmath146 @xmath145 inherits the following properties from @xmath43 : det @xmath147 and @xmath148 diag@xmath149 with @xmath150 given in ( [ mmatrix ] ) . also , the terms containing the auxiliary fields have a simple form if one makes use of the matrices @xmath151 already defined in ( [ pmatrix ] ) , @xmath152 where the fields @xmath153 are composed from the auxiliary fields @xmath154 as follows : @xmath155 using these definitions , the action takes the simple form , @xmath156 where , @xmath157 the kernel @xmath56 is obviously anti - symmetric . with this form for the action , the partition function can be partially evaluated , @xmath158 } \label{3z}\end{aligned}\ ] ] as in the 2-@xmath0 case the determinant can be expanded ( use det@xmath159 ) to give the expansion for the partition function , @xmath160 \right ) \ ; , \label{3exp}\ ] ] where the hopping matrix @xmath60 takes the form @xmath161 the fields @xmath162 are obtained from @xmath163 by multiplication with @xmath164 from the left . making use of the block - diagonal form of @xmath145 we find their explicit expression @xmath165 the hopping generators @xmath166 were already used in the 2-@xmath0 case ( [ hmatrices ] ) . to compute the partition function we once again must study the traces of powers of the hopping matrix , @xmath167\!\ ! & = & \!\!\sum_{x } \sum_{\mu_1 , \dots \mu_n } \delta(x + \hat{\mu}_1 + \dots + \hat{\mu}_n , x ) \nonumber \\ & & \!\!\mbox{tr } [ c_{\mu_1}(x ) c_{\mu_2}(x + \hat{\mu}_1 ) \dots c_{\mu_n } ( x + \hat{\mu}_1 + \dots + \hat{\mu}_{n-1 } ) ] . \label{3htrace}\end{aligned}\ ] ] the result is similar to the 2-@xmath0 case but the remaining traces now also depend on @xmath3 . again it can be seen immediately from the kronecker delta , that the terms in the sum have support on connected , closed loops with base point @xmath3 . the fact that closed loops have even length forces tr@xmath168 $ ] to vanish for odd @xmath1 . we remark that since the partition function ( [ 3exp ] ) is now a sum over auxiliary fields a simple computation of the radius of convergence of the expansion is not available . this also prevents a simple exponentiation of the terms in the statistical sum to obtain the free energy . for an alternative approach , using different geometric factors see @xcite . in this section we will show that the expansion ( [ 3z ] ) , ( [ 3exp ] ) , ( [ 3htrace ] ) gives rise to an interpretation in terms of surfaces with intrinsic geometry ( see also @xcite , @xcite , @xcite-@xcite ) . there is however an intermediate step , which we discuss first , where the terms in ( [ 3htrace ] ) are interpreted as loops corresponding to ribbons of plaquettes . it was already mentioned that the loops supporting the contributions to ( [ 3htrace ] ) have to be closed and connected . using essentially the same arguments as in the 2-@xmath0 case one can show that the trace over the fields @xmath162 remains invariant under reversing the orientation of the loop . thus , as in the 2-@xmath0 case , one can fix an orientation for each loop and write a factor 2 in front of the sum in ( [ 3htrace ] ) , which will later cancel the factor of 1/2 from the square root in ( [ 3exp ] ) . it is crucial to observe , that the special form ( [ cfields ] ) of the matrix valued fields @xmath162 reduces the contributions to ( [ 3htrace ] ) to effectively 2-dimensional objects . in particular the matrices diag@xmath169 , diag@xmath170 , diag@xmath171 in ( [ cfields ] ) form a complete set of projectors , corresponding to the three coordinate planes of the dual lattice . this has two important implications : firstly we note , that the loops in ( [ 3htrace ] ) are non - back - tracking . this is a consequence of @xmath172 ( compare the discussion for the 2-@xmath0 case ) and the fact that the mentioned projectors do not allow for cross - terms in @xmath173 ( each @xmath162 is a sum of two terms ) . secondly , the projectors imply that the choice of just two of the matrices @xmath162 in the trace tr@xmath174 $ ] already fixes a coordinate plane for all the terms in this trace . assume , for example , that the first factor in the trace is one of @xmath175 and any other factor is one of @xmath176 , then from the explicit representation ( [ cfields ] ) it is clear that only the terms containing the projector diag@xmath171 can contribute . one is confined to the 1 - 2 plane , since only the @xmath177 and @xmath176 contain this projector . the formula for all terms in this plane ( i.e. all terms associated with the projector diag@xmath171 ) can be read of from ( [ 3htrace ] ) and ( [ cfields ] ) and is given by @xmath178 \ ; \prod_{(y,\nu ) \in \gamma } a_{\nu 3 } ( y ) \ ; . \label{plane12}\ ] ] to abbreviate the notation we defined @xmath179 for @xmath180 . the set @xmath181 is defined to be the set of all closed , non - back - tracking loops with a chosen orientation and length @xmath98 in the 1 - 2 plane , with base point @xmath3 . in the product under the trace the indices @xmath130 of @xmath67 can have the values @xmath182 ( corresponding to @xmath183 and @xmath184 directions on the dual lattice ) . the trace was already computed in the 2-@xmath0 case and the result is @xmath185 . the product over the auxiliary field picks up all the terms @xmath186 along the loop @xmath10 . actually the geometrical objects that appear in the above sum should be thought of as ribbons of plaquettes . these ribbons are defined to be the set of plaquettes spanned by the links of @xmath10 together with the unit vector in @xmath187-direction . in the above expression ( [ plane12 ] ) one can interpret the ribbons as being dressed with the auxiliary fields @xmath188 defined on the plaquettes of the ribbon . for the other coordinate planes the ribbons are constructed likewise . the concept of ribbons is illustrated in fig . [ ribbon ] . = 1.1 in the contributions to ( [ 3htrace ] ) in the other two coordinate planes have the same structure as ( [ plane12 ] ) , giving the final result @xmath189 & = & \!\!- 2 \sum_x \big ( \sum_{\gamma \in l^{(2n)}_{x,12 } } ( -1)^{n(\gamma ) } \prod_{(y,\nu ) \in \gamma } a_{\nu 3 } ( y ) \nonumber \\ & + & \!\!\!\ ! \sum_{\gamma \in l^{(2n)}_{x,13 } } ( -1)^{n(\gamma ) } \prod_{(y,\nu ) \in \gamma } a_{\nu 2 } ( y ) + \sum_{\gamma \in l^{(2n)}_{x,23 } } ( -1)^{n(\gamma ) } \prod_{(y,\nu ) \in \gamma } a_{\nu 1 } ( y ) \big ) . \nonumber\end{aligned}\ ] ] to shorten our notation we identified @xmath190 and introduced @xmath191 ( both definitions for @xmath192 ) . inserting the result for the trace tr@xmath193 $ ] into the expansion ( [ 3exp ] ) and this into the expression ( [ 3z ] ) for the partition function one ends up with @xmath194 this formula is a representation of the 3-@xmath0 ising model as a product of 2-@xmath0 ising models in their loop representation coupled to an external field . we introduced @xmath195 to be the set of loops @xmath196 already discussed in the 2-@xmath0 case , but living in particular in the 1 - 2 plane of the 3-@xmath0 lattice with 3-coordinate @xmath197 . the sets @xmath198 and @xmath199 are defined likewise . by comparing ( [ 3za ] ) with the 2-@xmath0 expression ( [ expsumlocal ] ) one finds that the 3-@xmath0 partition function is a product of 2-@xmath0 partition functions with locally varying boltzmann factors @xmath200 . making use of the fact that the representations ( [ expsumlocal ] ) and ( [ z2local ] ) are equal ( drop the overall factor in ( [ z2local ] ) ) we obtain @xmath201 @xmath202 is the set of loops @xmath24 defined in the 2-@xmath0 case , but living in the 1 - 2 coordinate plane with 3-coordinate @xmath197 . @xmath203 and @xmath204 are defined likewise . the representation ( [ surf1 ] ) has an interesting interpretation in terms of surfaces . the last term in ( [ surf1 ] ) , i.e. the sum over products of @xmath139 , is non - vanishing only if each @xmath139 occurs an even number of times otherwise the sum will cancel terms which differ only by a minus sign . all non - vanishing contributions to the sum can be given a geometrical interpretation . this is achieved by associating a ribbon to every loop ( as described earlier ) , and then dressing the ribbons with the auxiliary fields @xmath205 defined on the plaquettes of that ribbon . the evenness condition on the auxiliary fields forces non - vanishing contributions to come from networks of ribbons that cover each plaquette an even number of times ( or not at all ) . the set of loops in the sum , @xmath24 , was restricted to loops without iterated links , hence , the double covering of a plaquette has to come from ribbons corresponding to different coordinate planes . the surfaces are thus built by ribbons wrapping around the surface , such that each plaquette is covered by 2 ribbons corresponding to different coordinate planes . this ensures that the sum over the @xmath139 is nonvanishing , in particular it produces a factor of @xmath206 which cancels the overall factor in ( [ surf1 ] ) . as an example , we show in fig . [ cube ] how the surface of a simple cube is generated from three ribbons in the three coordinate planes . in fig . [ selfintsurf ] we give an example for a surface which self - intersects on one link and show how it is composed from the ribbons . = 0.5 in = 1.3 in when one sums over all loops in all coordinate planes , all possible surfaces @xmath34 on the dual lattice are summed over . since each plaquette is covered twice by the ribbons , the factor @xmath21 is counted twice , giving the overall factor @xmath207 , where @xmath35 denotes the area of the surface . the factor @xmath208 turns into @xmath209 , where @xmath210 is the number of links where the surface self - intersects . the final result for the 3-@xmath0 partition function is @xmath211 the set @xmath38 are the surfaces which can be obtained by wrapping ribbons corresponding to the subset of loops in @xmath24 onto each other . more explicitly the surfaces in @xmath38 are closed , not necessarily connected surfaces , which are allowed to self - intersect , but plaquettes may not touch each other . we remark , that when the set of loops in @xmath24 is extended , so is the class of allowed surfaces in @xmath38 . for example if loops , where links can be occupied several times , are taken into account , one can generate surfaces where plaquettes of the surface touch each other . however , they are no longer necessarily closed surfaces . consider e.g. the loop depicted in fig . [ loopsfig ] ( c ) . it gives rise to a ribbon where each of the plaquettes is covered twice , and the contribution thus survives summing over the auxiliary fields @xmath139 . the corresponding surface has however a boundary . thus as in the 2-@xmath0 case it is possible to allow for a larger class of surfaces than @xmath212 . many of these surfaces , such as our example of the doubly covered ribbon have no counterparts in the set @xmath33 of surfaces with extrinsic geometry and get cancelled . all these more general sets of surfaces can be generated by allowing for generalized sets of loops @xmath24 . in other words , the surfaces are classified by the behavior of the loops which are obtained as an intersection of the surfaces with all possible coordinate planes on the lattice . this makes ( [ surf1 ] ) and ( [ surf2 ] ) very powerful for a simple characterization of possible classes of surfaces with intrinsic geometry . for all these cases the geometry factor is @xmath209 and the partition function is given by ( [ surf2 ] ) . in this section we derive a simple formula for 2@xmath1-point functions in terms of surfaces . we will compute these correlation functions by making use of the variable bond ising model , @xmath213 this expression can serve as a generating functional for 2-point functions ( or more general 2n - point ) functions : let 0 and z be the two lattice sites where the spins in the 2-point function are located . connect them by an arbitrary set of links , @xmath214 , forming a path from @xmath215 to @xmath216 . it is convenient to encode the path @xmath214 by the set of directions @xmath217 which trace it out when starting at 0 ( here @xmath218 denotes the length of @xmath214 . ) then one can write , @xmath219 we remark that it is not necessary to set the coupling constants equal ( this was done only for notational convenience ) , and all results below can easily be generalized to the variable bond model . also , the generalization to 2@xmath1-point functions is straightforward : simply replace the single path @xmath214 by a network of paths , consisting of links on the lattice , which connect all sites occuring in the 2@xmath1-point function . we will show in the end , that the result is independent of the choice of the network . the essential step is to replace the partition function of the variable bond model by the corresponding expression in terms of surfaces . for notational convenience we will work with the representation in terms of surfaces with extrinsic geometry rather than the more cumbersome intrinsic geometry however , it is of course possible to express the final result in terms of surfaces with intrinsic geometry . for the variable bond model the surface representation is given by , @xmath220 here @xmath221 denotes the set of links dual to the plaquettes of @xmath34 . a straightforward but lengthy calculation gives @xmath222 we introduced an ( arbitrary ) ordering @xmath223 of the links in @xmath214 . in the last term we introduced @xmath224 to be the number of links in @xmath214 which are also in @xmath221 . the final step is to interpret all the contributions in terms of surfaces . let @xmath34 be a surface that intersects @xmath214 at @xmath225 links , then @xmath34 is counted in the first @xmath226 terms on the right hand side of ( [ longform ] ) . to begin with , @xmath34 is certainly counted in @xmath227 , which is the first term on the right hand side of ( [ longform ] ) , with a factor @xmath228 . of course , there is also the factor @xmath229)$ ] but this will appear in all terms in ( [ longform ] ) , so we will neglect it for the moment . in the second term in ( [ longform ] ) the surface @xmath34 gets firstly an overall factor of @xmath92 and then it is counted @xmath225-times , since the first sum in this term runs over all links . thus , in the second term of ( [ longform ] ) @xmath34 acquires the factor @xmath230 . in the third term the overall factor is @xmath231 and since the links in the sum are ordered the surface occurs @xmath232 times . thus the factor is @xmath233 . in general a surface which intersects @xmath214 at @xmath225 links obtains a factor of @xmath234 from the @xmath235-th term in ( [ longform ] ) . these factors can be summed up to give @xmath236 we thus end up with the surprisingly simple result ( the overall factor @xmath237 gets cancelled when dividing by @xmath227 ) @xmath238 where @xmath214 is an arbitrary network of paths connecting the sites @xmath239 and @xmath21 denotes @xmath240 . it is simple to see the independence of ( [ npoint ] ) from the choice of @xmath214 : the network @xmath214 can be deformed arbitrarily by adding single plaquettes to @xmath214 and since a plaquette always intersects an even number of times ( 0 , 2 or 4-times ) with a given surface , the intersection term @xmath241 remains invariant under such deformations . we finally remark , that the same formula holds if one works with the representation in terms of surfaces with intrinsic geometry ( certainly the self - intersection factor @xmath209 has to be re - inserted ) . the formula also holds in 2-@xmath0 , when the surfaces @xmath34 are replaced by the loops @xmath10 . in this paper we discussed the hopping expansion of the grassmann representation of the ising model in both 2 and 3 dimensions . for the 3-@xmath0 case an auxiliary field was introduced in order to write the action in quadratic form . in both dimensions the expansion was interpreted in terms of loops or surfaces . it was shown that the hopping expansion , with its calculus of hopping generators , provides an exact algebraic representation of the expansions in terms of loops and surfaces , respectively . this connection allows for a simple algebraic treatment of many of the problems which emerge in the loop or surface expansion and are rather intractable when working with the original geometrical objects . counting problems and symmetry factors can be analyzed in a rather simple fashion using the algebraic representation . as an application , in 2-@xmath0 , we gave the corrected result of the loop representation of the free energy and computed its radius of convergence showing that it is determined by the critical temperature . in 3-@xmath0 we derived a representation of the partition function as a product of 2-@xmath0 ising models in their loop representation coupled to an auxiliary field . we gave a simple proof that the self intersection factor leads to the cancellations necessary so that the sum over surfaces with intrinsic geometries reproduces the correct partition function . the possible classes of surfaces to be summed over were characterized by their intersections with all coordinate planes of the lattice . our formula for the @xmath98-point functions in terms of surfaces illustrates the tight relation between dynamics and geometry in 2- and 3-dimensional ising models . + the fermionic representation of the ising model is also known in dimensions higher than 3 . it involves however terms of order larger than the quartic contributions generating the plaquettes in 3-@xmath0 . by introducing several auxiliary fields one could write the action as a quadratic form and perform the hopping expansion along the lines of this paper . however , the geometrical interpretation of the emerging structures might turn out to be rather involved . the results obtained here might have a more or less straightforward generalization to other models where grassmann representations exist @xcite , such as vertex models and the ashkin - teller model . it would be interesting to work out representations of these models in terms of geometrical objects with intrinsic geometry . in particular representations of @xmath1-point functions in terms of these surfaces could be analyzed further . the outcome of such an enterprise might be a better understanding of the relation between dynamics and geometrical concepts . + + * acknowledgement : * this work is supported in part by nserc of canada , nato crg 970561 and the fonds zur frderung der wissenschaftlichen forschung in sterreich under project number j1577-phy .

starting from the known representation of the partition function of the 2- and 3-@xmath0 ising models as an integral over grassmann variables , we perform a hopping expansion of the corresponding pfaffian . we show that this expansion is an exact , algebraic representation of the loop- and surface expansions ( with intrinsic geometry ) of the 2- and 3-@xmath0 ising models . such an algebraic calculus is much simpler to deal with than working with the geometrical objects . for the 2-@xmath0 case we show that the algebra of hopping generators allows a simple algebraic treatment of the geometry factors and counting problems , and as a result we obtain the corrected loop expansion of the free energy . we compute the radius of convergence of this expansion and show that it is determined by the critical temperature . in 3-@xmath0 the hopping expansion leads to the surface representation of the ising model in terms of surfaces with intrinsic geometry . based on a representation of the 3-@xmath0 model as a product of 2-@xmath0 models coupled to an auxiliary field , we give a simple derivation of the geometry factor which prevents overcounting of surfaces and provide a classification of possible sets of surfaces to be summed over . for 2- and 3-@xmath0 we derive a compact formula for 2@xmath1-point functions in loop ( surface ) representation . hep - th/9801098 * c.r . gattringer , s. jaimungal and g.w . semenoff * department of physics and astronomy , university of british columbia , vancouver b.c . ,

this review presents a brief overview of the health effects and exposures of two criteria pollutants -- ozone and particulate matter -- and two toxic air pollutants -- benzene and formaldehyde . these pollutants were selected from the six criteria pollutants and from the 189 toxic air pollutants on the basis of their prevalence in the united states , their physicochemical behavior , and the magnitude of their potential health threat . the health effects data included in this review primarily include results from epidemiologic studies ; however , some findings from animal studies are also discussed when no other information is available . health effects findings for each pollutant are related in this review to corresponding information about outdoor , indoor , and personal exposures and pollutant sources.imagesfigure 3figure 8figure 9

The seed for this crawl was a list of every host in the Wayback Machine This crawl was run at a level 1 (URLs including their embeds, plus the URLs of all outbound links including their embeds) The WARC files associated with this crawl are not currently available to the general public. ||||| JUNEAU - UPDATE: The Department of Fish and Game has reconsidered its decision to kill the five bears that frequent Government Hill, officials wrote in a press release, Saturday evening. "After receiving waves of requests from the public to spare the sow and her four yearling cubs, Gov. Bill Walker and the department made a collective decision today to instead relocate the bears," officials wrote. According to the release, relocating bears has not always been a good option. A trash-eating bear that was killed last year on the University of Alaska Anchorage campus, had previously been relocated to a remote area near Eklutna, though she returned to Anchorage with her cubs, shortly after. ORIGINAL STORY: A family of trash-eating bears that made headlines as they traipsed around Government Hill is getting a stay of execution from Alaska’s governor. Department of Fish and Game officials said earlier this week there was no choice but to kill the five black bears that have been wandering around the Anchorage neighborhood due to the cost involved with relocation, potential diseases that may result, and the complexities of finding a welcoming home. However, Gov. Bill Walker said Saturday from the Capitol — amid the frenetic close to the 90-day lawmaking session — that he found a minute to contact Fish and Game Commissioner Sam Cotten to instruct them to take another approach. Walker said he was concerned when he saw news reports that the bears could be put down. “I've been following it, watching it,” he said. “I just think this is the season that we can give them another try elsewhere. I really didn’t think the bears had done anything wrong.” Grace Jang, the governor’s spokeswoman, said the department will make another attempt to relocate the animals but will keep public safety as the top priority. Fish and Game officials previously said the city needs to deal with its garbage problem to prevent future incidents where bears are put down due to public safety concerns. Residential areas known to be frequented by bears often have no bear-proof trash cans: “If we can deal with the bear garbage attraction situation properly, they’ll still be around but you won’t see them as much,” said Sean Farley, a research biologist. WATCH: Gov. Bill Walker talks about his decision outside of his Juneau office

– A female black bear and four yearling cubs who have been making a living Dumpster diving in Anchorage will get a new home—and not that great trout stream in the sky, thanks in part to the actions of Alaska Gov. Bill Walker. As the Alaska Dispatch News reports, Walker yesterday intervened to plead for the lives of the quintet, which were set to be euthanized, by asking the state Fish and Game commissioner if there was another solution. "I’m sure there will be plenty of criticism about the governor getting involved in this," Walker said. "But I’m a person too. I have a soft spot for individuals in circumstances not of their own making." The bears will now likely be trapped and transported about 60 miles away, so as to inhibit their return. "I'm here in Juneau being inundated with budget issues and having to say no to all these programs," Walker continues. "I felt these bears had done nothing wrong and just thought it was the right thing to do." Speaking of those budget issues, the Fish and Game chief says it won't be too pricey to move the bears—but don't expect relocation to replace euthanasia as the norm. "There are a lot of bears so it would be expensive if you had somebody doing it full time," he says. Both men underscore that it was a request from Walker that resulted in "a collective decision," per KTUU, not an order.

considerable progress has been made in recent years in understanding the fundamental processes involved in gas - surface interactions . this has been based on the parallel developments of large - scale electronic structure calculations based on density functional theory , combined with multi - dimensional quantum and classical analysis of the dynamics @xcite . despite these advances there remains one key area that is still largely unexplored and poorly understood ; the process of energy dissipation into substrate degrees of freedom . although this is known to be of central importance in many situations @xcite , there exist no ` real ' calculations to date for the energy loss to either phonons or electrons in the surface . in particular there have been a number of recent experiments that have shown convincing evidence that energy dissipation by the creation of electron - hole pairs is a significant effect in gas - surface dynamics . gostein et al @xcite carried out a detailed state - to - state analysis of h@xmath2 scattering from pd(111 ) and showed that , for example , in the vibrational relaxation of ( @xmath3 ) to ( @xmath4 ) an average of 120 mev is lost to the substrate during the scattering event , presumably to electron - hole pair formation . nienhaus and co - workers @xcite measured directly the hot electrons and holes created at ag and cu surfaces by the adsorption of thermal hydrogen and deuterium in the form of ` chemicurrents ' in a schottky diode . finally , huang et al @xcite have studied no scattering from au(111 ) and have concluded that the main sink of energy for the vibrational relaxation of @xmath5 molecules is the surface , with the strong dependence of the de - excitation probability on incident energy providing evidence that an electron - hole pair mechanism is the dominant factor . we carry out a calculation of the ground state properties of an interacting surface / molecule system using a plane - wave basis and a super - cell geometry , and use these results to evaluate the friction coefficient associated with the motion of a molecule at a chosen position and in a direction of choice . this is achieved using the well established ` golden rule ' expression @xcite that may be obtained by applying time dependent density functional theory ( tddft ) together with a quasi - static limit @xcite , or less stringently by applying the golden rule directly to the available kohn - sham states @xcite . essentially the theory is as described by hellsing and persson @xcite or liebsch @xcite . the super - cell method has the advantage that it retains the continuous spectrum of one - electron excitations , unlike cluster models @xcite , and this is important for the interactions considered here . in first principles calculations of molecule - surface systems a super - cell of sufficient size is usually chosen to prevent any significant interaction between the adsorbates in neighbouring super - cells . when considering electron - hole pair excitation a slightly more subtle effect must be taken into account , arising from the enforced periodicity of the perturbation that produces the electron - hole pairs . we are primarily interested in the energy loss by electron - hole pair excitation due to the motion of an isolated molecule interacting with the surface , whereas the super - cell geometry will naturally describe the damping of an ordered over - layer . for the periodic system , conservation of crystal momentum prevents transitions occurring that will occur for an isolated molecule interacting with the surface . results for an isolated molecule are derived from the available periodic perturbation , and a significant difference is found between the energy loss behaviour of the periodic and isolated systems . to test our method we investigate the friction coefficient of an h atom above the hcp hollow site of a cu(111 ) surface . spin is included explicitly in the kohn - sham theory using the gradient corrected local spin density approximation for exchange - correlation ( lsda - gc ) . in the next section the evaluation of the dynamic self - energy and friction coefficient from kohn - sham results using a plane - wave basis is described . in section [ sec : alg ] the implementation of this as a parallel algorithm is described , along with a brief description of the performance of the algorithm . results for h / cu(111 ) are discussed in section [ sec : results ] , and section [ sec : conc ] is the conclusion . the experimentally measurable energy loss spectrum for a particular mode is directly related to the dynamic self - energy , @xmath6 . since we are interested in the energy loss , the imaginary part of this self - energy is the required quantity and this can be expressed using @xcite @xmath7 where @xmath8 and @xmath9 are the kohn - sham wavefunctions and energies resulting from a density - functional description of the ground state , and @xmath10 is the fermi - dirac occupation function . spin degeneracy is assumed in eq . ( [ e2.1 ] ) , hence the factor of 2 ; the extension to spin polarised systems is straightforward . the effective field , @xmath11 , is the tddft effective field with contributions from the field of the displaced nuclei , the coulomb field of the induced charge density and a contribution from exchange - correlation . equation ( [ e2.1 ] ) can be derived by direct application of the golden - rule and a single electron approximation @xcite , or through tddft with the assumption of a slow time - dependent perturbation ( see @xcite and @xcite for more clarification of the role of tddft ) . equation ( [ e2.1 ] ) provides the rate of energy loss of a mode of frequency @xmath12 due to the excitation of electron - hole pairs as @xmath13 . taking the quasi - static limit @xmath14 results in the rate of energy loss for the motion of the atom , and this can be expressed as the friction coefficient @xmath15 defined via the standard langevin equation . for motion in the direction @xmath16 , @xmath15 is given by ( see hellsing and persson @xcite , or plihal and langreth @xcite ) @xmath17 where @xmath18 is the fermi energy , @xmath19 is the mass of the molecule , and @xmath20 is the static limit of @xmath21 given by the derivative of the kohn - sham self - consistent potential in the direction @xmath16 . equation ( [ e2.2 ] ) is evaluated using wavefunctions of the form @xmath22 where @xmath23 is the volume of the super - cell , and only the wavefunctions sampled at a finite number of @xmath0 points in the irreducible wedge of the brillouin zone are available . the change in the kohn - sham potential due to the motion of an isolated atom is not directly available from a super - cell calculation , but we can obtain the change due the motion of a periodic lattice of atoms , @xmath24 , as a finite difference . to calculate the dynamic interaction of an isolated molecule with a surface within a super - cell geometry care must be taken with the interpretation of eq . ( [ e2.1 ] ) . if @xmath20 is obtained directly as a periodic function , drastic consequences result - the integral becomes zero for @xmath25 . this is due to the super - cell geometry enforcing a conservation of crystal momentum that would be correct for describing the interaction of a real over - layer of molecules in coherent motion , but is not physically realistic for the aperiodic single molecule / surface system that concerns us here . in light of this we must obtain the change in the kohn - sham potential due to the motion of an isolated molecule , @xmath26 , from the change due to the coherent motion of an over - layer , @xmath24 . the relationship between the two can be found by applying linear response theory @xcite . although the theory is given here for a local pseudopotential , the generalisation to non - local pseudopotentials is straightforward . we begin by considering the change in the total pseudopotential , @xmath27 , due to an infinitesimal change in the position of the atom in each super - cell , @xmath28 . with the pseudopotential due to an atom at @xmath29 denoted @xmath30 this takes the form @xmath31 where @xmath32 is a lattice vector . the change in the kohn - sham potential can be obtained from @xmath33 via the static inverse dielectric function , @xmath34 that corresponds to the original kohn - sham calculation @xcite . this gives @xmath35 or @xmath36 where @xmath37 is the derivative of the kohn - sham potential with respect to the change in the position of an atom at @xmath38 . for an isolated atom we require @xmath39 , the change in the kohn - sham potential due to the change in the position of an atom at @xmath29 . the formally correct way to obtain this is to obtain @xmath40 from the original dft calculation ( for an example of this type of calculation see godby et al @xcite ) , obtain @xmath41 , and use this to evaluate @xmath42 however , provided @xmath41 is well localised around the site of the perturbed atom such that there is little overlap between the responses to the motion of atoms in adjacent unit cells we may take @xmath43 where @xmath44 within a wigner - seitz cell centred on the perturbed atom , and is zero elsewhere . from the super - cell calculation the kohn - sham potential for the atom at @xmath45 is evaluated to obtain @xmath20 as @xmath46_{{\bf x}+{\bf h}}- [ v^{\mathrm{ks}}_{\mathrm{lattice } } - \epsilon_{\mathrm{f}}]_{{\bf x}-{\bf h } } \right ) \label{e2.3}\end{aligned}\ ] ] where the variation of the zero of the kohn - sham potential has been corrected for using the fermi energy associated with the self - consistent results for each atomic position . equation ( [ e2.3 ] ) will be accurate providing the response is isolated within the wigner - seitz cell centred on the perturbed atom ( or , equivalently , @xmath47 is negligible at the border of this wigner - seitz cell ) , and @xmath48 is small enough . in practice ( [ e2.3 ] ) corresponds to reducing the volume of integration in eq . ( [ e2.1 ] ) from the entire lattice to one wigner - seitz cell . in section [ sec : results ] the consequences of considering the motion of an isolated atom , as described above , are investigated by comparing results with those obtained by treating the motion as that of an ordered over - layer of atoms . a plane - wave calculation results in a set of kohn - sham states on a finite grid ( in real space or reciprocal space ) sampled at a finite number of @xmath0 points and for a finite number of bands , hence we must obtain the discrete equivalent of eq . ( [ e2.2 ] ) to evaluate @xmath15 . it is also desirable to apply the space - group symmetry to reduce the number of @xmath0 points that must be considered . this is achieved as follows . ( [ e2.1 ] ) is discretised using a uniform grid of @xmath0 points throughout the @xmath49 brillouin zone , and a conventional smearing function @xmath50 where @xmath51 is the number of @xmath0 points , @xmath10 is the fermi - dirac occupation function , and @xmath52 is the derivative of the ` squashed fermi - dirac ' @xcite function used for occupation numbers in the original kohn - sham calculation . @xmath53 is given by @xmath54 where @xmath55 is an energy parameter describing the width of the function , and @xmath56 . to obtain @xmath15 we take @xmath57 , resulting in @xmath58 where @xmath59 is the @xmath60 derivative of the ` squashed fermi - dirac ' function , and we have taken the static limit of @xmath11 . equation ( [ e2.7b ] ) reduces to eq . ( [ e2.2 ] ) in the zero temperature and continuum limit . it is important to note that eq . ( [ e2.2 ] ) can not be directly discretised by replacing the @xmath61 functions with @xmath62 as this corresponds to taking the continuum and zero temperature limits before discretisation . this would result in the inclusion of a contribution to @xmath15 from transitions that should not be present ( such as from a state to itself ) . next we reduce the @xmath0 points that must be considered to those within the irreducible wedge of the brillouin zone using the space - group of the lattice . since the set of @xmath0 points possess point group symmetry eq . ( [ e2.7b ] ) immediately takes the form @xmath63 where @xmath64 denotes a sum over points in the irreducible wedge , and @xmath65,@xmath66 are space - group operators composed of a unitary transformation , @xmath67 , and a non - symmorphic translation , @xmath68 . the number of operators in the space - group is denoted by @xmath69 , and @xmath70 where @xmath71 is the number of distinct @xmath0 points in the entire brillouin zone created by applying the complete set of @xmath69 space group operators to the point @xmath0 in the irreducible wedge . there are no symmetry operators associated with the eigenvalues since @xmath72 . transforming the integrand in real space by @xmath73 and using the identity @xcite @xmath74 results in @xmath75 where repeated sums over the same operator are removed and @xmath20 is required to possess the space - group symmetry corresponding to the available @xmath0 points . this requirement means that the original kohn - sham calculations must be performed with symmetry low enough to allow the motion of the atom in the direction we are interested in , even if the instantaneous position of the atom corresponds to a higher symmetry . in practise we also only calculate the quantities within the sum where the @xmath76 factor is greater than some small value , preventing the cost of calculating matrix elements that make negligible contribution to @xmath15 and limiting the sum to a finite number of bands . for the the motion of an over - layer of atoms , where @xmath20 is periodic , a similar treatment results in @xmath77 where only @xmath78 transitions contribute . in order to obtain the matrix elements we require the kohn - sham states corresponding to the images of the available @xmath0 points under transformation by a point group operator , @xmath79 . transforming @xmath80 in reciprocal space gives us the coefficients of each @xmath79 , and this is achieved by applying eq . ( [ e2.9 ] ) to eq . ( [ e2.4 ] ) and projecting out the required coefficients to give @xmath81 the wavefunctions in real space are then obtained using a fft @xmath82\ ] ] and the required integrals are evaluated as sums over a unit cell ( this is analytically correct for a plane - wave basis ) . this cell must be chosen such that @xmath20 is negligible at its borders and such that the ` truncated ' potential possesses the correct space - group symmetry . as mentioned previously the ideal choice is a wigner - seitz cell centred at the interacting atom , as is shown schematically in fig . [ fig1 ] for a @xmath83 hexagonal unit cell with the atom of interest at @xmath84 . integration must be performed over the wigner - seitz unit cell centred at @xmath84 ( dashed line ) . for the parallelogram ( which represents the originally chosen unit cell ) the function @xmath20 is not localised within the unit cell , and does not possess space - group symmetry . ] to perform the sum it is necessary to divide the integration volume into different regions @xmath85 such that transforming region @xmath85 by a vector @xmath86 constructs the wigner - seitz cell from the original unit cell . the matrix element then takes the form @xmath87 where @xmath20 and the wavefunctions are available over a grid of @xmath88 real space points , @xmath89 . it should be noted that for an isolated atom the integral is carried out over one unit cell as a consequence of @xmath90 being localised in that cell , whereas for the coherent motion of an over - layer the integral is carried out over one unit cell as a consequence of the periodicity of the integrand . hence , to evaluate @xmath91 the rearrangement of eq . ( [ e2.13 ] ) is not necessary . we are interested in large scale systems , hence a parallel implementation of both the original kohn - sham calculation and the evaluation of @xmath15 is desirable . multiprocessor algorithms for plane - wave kohn - sham methods are available , so we describe the latter only . first we consider the distribution of data between the @xmath92 available processors . these are divided into @xmath93 groups of @xmath94 processors , and the @xmath0 points are distributed equally between these groups of processors . data specific to a @xmath0 point is stored on the associated group . the @xmath1 points are then distributed across the @xmath94 processors in each group , and data associated with each @xmath1 point held on the associated processor . data that is not dependent on @xmath0 is the same for each group but distributed across processors within the group , and data that is not dependent on @xmath1 is the same within each group but distributed across groups . this distribution is shown figuratively in fig . [ fig2 ] , where the @xmath0 points in the @xmath95 group are denoted @xmath96 , and the @xmath1 vectors on the @xmath95 processor in each group are denoted @xmath97 . points . ] wavefunctions in real space are obtained by a parallel fft , so real space points are distributed as for reciprocal space points , and this fft is performed in parallel across all processors in each group . as efficient parallel fft algorithms are available and a distributed sum is trivial these sections of the algorithm parallelise well . the integral must also be must be summed over _ pairs _ of @xmath0 points , with each point in a different group , and it is this part of the algorithm that requires a large amount of waiting and communication , and is not as efficient . the algorithm for evaluation of eq . ( [ e2.10 ] ) takes the following form , with the current processor in group @xmath98 . * for * = @xmath99 + * for * = @xmath100 + * for * = @xmath101 space - group + + @xmath102*transform*[@xmath103 + @xmath104 $ ] + + * for * = @xmath105 + * for * = @xmath106 + * for * = @xmath107 + + * if * @xmath108 * then * @xmath109 $ ] + * bcast * @xmath110 , @xmath111 , @xmath112 , @xmath113 from group @xmath114 to all groups + sum @xmath115 over group @xmath98 + evaluate @xmath116 + add contribution to @xmath15 using weights + @xmath117,@xmath112 , @xmath116 + + * end * + * end * + * end * + * end * + * end * + * end * + sum @xmath15 over all groups + the subprogram * transform : * obtains the image of the wavefunction in reciprocal space , as defined by eq . ( [ e2.12 ] ) . it takes the following form , where the current processor is in the group associated with @xmath0 , and holds vectors @xmath118 * transform : * + * for * = @xmath119 + * bcast * @xmath120,@xmath121 from @xmath122 to all processors in group + * for * = @xmath1 @xmath123 @xmath118 + * if * @xmath124 @xmath123 @xmath125 * then * @xmath126 + * end * + * end * + * return * @xmath127 + it is useful to know the scaling of this algorithm with respect to the distribution of data across the processors , @xmath128 , and the number of processors available @xmath129 . the time taken for a reasonably large system is dominated by the time spent carrying out the fft contained within the inner loop ( or waiting for another group to broadcast the result of this fft ) and is given by @xmath130 where @xmath131 is the time taken to carry out a parallel fft on m processors . the speedup of the parallel fft with increasing number of processors is complex and depends on the architecture of the parallel system @xcite , but some general conclusions about how this effects the performance of the entire algorithm can be made . if a linear speedup of the fft with respect to the available processors ( @xmath132 ) occured then the total run time would be independent of the distribution of the processors among @xmath0 and @xmath1 points . however , the actual speedup will be worse than linear due to the communication times , so for a given @xmath92 the best efficiency is achieved when the @xmath0 points are distributed amongst as many processors as possible , or @xmath133 is as small as possible . test calculations have been carried out for a h atom moving above the hcp hollow site of a cu(111 ) surface . this system has been chosen for its simplicity ( although we note that spin polarisation is needed to obtain the correct electronic structure at larger atom - surface separations ) and because of its relevance to the chemicurrent experiment of nienhaus et al @xcite . the surface is modelled by a five - layer slab , with a vacuum gap equivalent to another five layers . a @xmath134 in - plane super - cell is used - tests show that the deformation potential caused by the displacement of h atoms is well localised within this unit cell . a spin - polarised version of the pw91 functional is used for exchange - correlation effects ( @xcite , and references therein ) , a troullier - martins @xcite pseudopotential is used for cu , and h is represented by a coulomb potential . the plane - wave , pseudopotential code castep is used to obtain the self - consistent potentials and kohn - sham states that are required for the calculation of the matrix elements in eq . ( [ e2.10 ] ) . calculations are performed with a plane - wave cut - off of 830 ev , 54 k - points are included in the full surface brillouin zone , and a fermi surface broadening of 0.25 ev is used . in order to test the convergence of the method we present results for the h atom 2.5 above the surface , and with @xmath16 perpendicular to the surface . to obtain the perturbative field , @xmath20 , calculations are performed with h at @xmath135 . equation ( [ e2.3 ] ) is then applied to the resulting self - consistent potentials to obtain @xmath20 . the finite difference introduces two errors in the final result . first a quadratic error is introduced by the finite difference itself , and second any small errors in the kohn - sham potentials are magnified for small @xmath48 . it follows that @xmath48 must be carefully chosen to be small enough to minimise the first of these errors , but large enough to minimise the second . tests for a number of @xmath48 suggest that @xmath136 results in a quadratic error @xmath137 and an error due to noisy kohn - sham potentials of @xmath138 . quantifying the latter of these is not straightforward , hence a pessimistic estimate has been given . with these parameters eq . ( [ e2.10 ] ) was evaluated using the algorithm described in section [ sec : alg ] . if the factor @xmath76 in eq . ( [ e2.10 ] ) was less than @xmath139 the contribution to @xmath15 was not calculated , increasing the efficiency of the calculation . enough bands are included for the highest energy bands at each @xmath0 point to be discarded . two parameters remain , which describe the temperature of the system , and how the discretisation of @xmath0 space is dealt with through the smearing , @xmath55 . the temperature enters through the fermi - dirac occupation functions in eq . ( [ e2.10 ] ) , and may be chosen to take any value . for the metallic system considered here a weak temperature dependence is expected , so the zero - temperature limit is the quantity of interest . we chose to use a ` squashed fermi - dirac ' distribution , @xmath140 , related to the function defined in eq . ( [ e2.7 ] ) by @xmath141 if @xmath142 is the width associated with @xmath53 then the properties of the system are very close to those of a system described by a fermi - dirac distribution with a temperature given by @xmath143 , where @xmath144 is the boltzmann constant . [ defparagcl ] [ cols=">,<,^,^ " , ] table [ tab1 ] shows results for @xmath15 summed over both spins , calculated over a range of temperatures for @xmath145 ev ( this is discussed below ) and for both the isolated atom ( @xmath146 , see eq . ( [ e2.10 ] ) ) and the coherent over - layer ( @xmath147 , see eq . ( [ e2.10b ] ) ) . results for an isolated atom are weakly dependent on temperature , and we take @xmath148 ev to represent the low temperature limit . for the coherent over - layer the temperature dependence is stronger , which is understandable since a greater proportion of the available ( band to band ) transitions are expected to be of higher energy . the approximation that requires the most attention is the discretisation of @xmath0 space and the reintroduction of a continuum through smearing . as described in section [ sec : theory ] we derive a continuous self - energy function using the @xmath53 of eq . ( [ e2.7 ] ) with width @xmath55 , and extract the linear behaviour of this function close to zero energy . for a given set of @xmath0 points we must find a value of @xmath55 large enough for the approximate self - energy to have converged to a linear function near zero energy . this critical @xmath55 must be small enough ( and so the density of the @xmath0 point mesh must be high enough ) to avoid the higher energy structure of the self - energy influencing the structure close to zero energy . results were calculated as above , with @xmath148 ev and @xmath55 ranging from @xmath149 to @xmath150 ev . these are shown in fig . [ fig3 ] for both the isolated atom and coherent over - layer . . results are given for @xmath148 ev ( @xmath151 k ) . the solid line shows the friction coefficient for an isolated atom above the surface , @xmath152 , whereas the dashed line shows the friction coefficient for an over - layer of atoms in coherent motion , @xmath147 . ] for the isolated atom @xmath15 shows good convergence by @xmath153 ev , and this value is low enough to conserve the structure of the self - energy . convergence has not been achieved for the coherent over - layer , and the strong variation of the friction coefficient with @xmath55 in this range suggests that the @xmath154 k - points are insufficient to achieve convergence for this system . this difference in the convergence behaviour is due to far fewer transitions being available in the coherent over - layer system due to the @xmath155 condition , and so fewer transitions to approximate a continuous self - energy . an _ ab initio _ method has been presented that allows the evaluation of the friction due to electron - hole pair creation experienced by an isolated molecule in motion near a metal surface . the approach described combines kohn - sham super - cell methods employing a plane - wave basis with a description of the electron - hole pair creation process via tddft . results have been presented for a h atom above a cu(111 ) surface , and convergence of the calculations has been tested . we find a significant difference in the results for motion of an isolated atom and those for a coherent over - layer of atoms , both in the physical properties of the system and in their numerical calculation . since the calculation is relatively expensive to perform for systems of interest an efficient parallel implementation of method has been given . bird , p.a . gravil , _ surface science _ * 377 - 379 * , ( 1997 ) 555 . darling , s. holloway , _ rep . phys . _ * 58 * , ( 1995 ) 1595 . m. gostein , e. watts , g.o . sitz , _ phys . * 79 * , ( 1997 ) 2891 . h. nienhaus h , h.s . bergh , b. gergen , a. majumdar , w.h . weinberg , e.w . mcfarland , _ phys . lett . _ * 82 * , ( 1999 ) 446 . y. huang y , a.m. wodtke , h. hou , c.t . rettner , d.j . auerbach , _ phys . lett . _ * 84 * , ( 2000 ) 2985 . g. grimvall , _ the electron phonon interaction in metals_. north - holland , amsterdam , 1981 . b. hellsing , m. persson , _ physica scripta _ * 29 * ( 1984 ) 360 . a. liebsch , _ phys . * b55 * ( 1997 ) 13263 . m. head - gordon , j.c . tully , _ phys . _ * b46 * ( 1992 ) 1853 . amusia , v.r . shaginyan , _ phys . _ * a250 * , ( 1998 ) 157 . m. plihal , d.c . langreth , _ phys . * b58 * ( 1998 ) 2191 . gross , w. kohn , _ phys . lett . _ * 55 * , ( 1985 ) 2850 . inkson , _ many - body theory of solids _ ( plenum press , new york , 1986 ) . godby , m. schluter , l.j . sham , _ phys . rev . _ * b37 * , ( 1988 ) 10159 . white , d.m . bird , m.c . payne , _ phys . rev . _ * b53 * , ( 1996 ) 1667 . altmann , _ band theory of solids : an introduction from the point of view of symmetry _ ( oxford university press , oxford , 1991 ) . a. gupta , v. kumar . _ ieee t. parall . distr . _ * 4 * ( 1993 ) 922 . perdew , k. burke , m. ernzerhof , _ phys . lett . _ * 77 * , ( 1996 ) 3865 . n. troullier , j. martins , _ phys . rev . _ * b43*,(1991 ) 1993 .

a method for the calculation of the damping rate due to electron - hole pair excitation for atomic and molecular motion at metal surfaces is presented . the theoretical basis is provided by time dependent density functional theory ( tddft ) in the quasi - static limit and calculations are performed within a standard plane - wave , pseudopotential framework . the artificial periodicity introduced by using a super - cell geometry is removed to derive results for the motion of an isolated atom or molecule , rather than for the coherent motion of an ordered over - layer . the algorithm is implemented in parallel , distributed across both @xmath0 and @xmath1 space , and in a form compatible with the castep code . test results for the damping of the motion of hydrogen atoms above the cu(111 ) surface are presented .

These crawls are part of an effort to archive pages as they are created and archive the pages that they refer to. That way, as the pages that are referenced are changed or taken from the web, a link to the version that was live when the page was written will be preserved.Then the Internet Archive hopes that references to these archived pages will be put in place of a link that would be otherwise be broken, or a companion link to allow people to see what was originally intended by a page's authors.The goal is to fix all broken links on the web . Crawls of supported "No More 404" sites. ||||| Former House Speaker Newt Gingrich's announcement that he is taking his campaign to the Republican convention in Tampa is being dismissed as typical election season bluster. How else to describe a candidate without much money, dwindling momentum, and a truly narrowing path to the GOP nomination who is pledging to stick it out for the long haul? But what if Gingrich isn't bluffing? The Republican primary process is, at its heart, a race for delegates: the first candidate to net 1,144 wins. By the time Floridians finish voting on Tuesday, just five percent of the total delegate pool will have been awarded. The upcoming states include a number of caucuses and southern primaries, the former of which play to Rep. Ron Paul (R-Texas)'s strengths and the latter of which work to Gingrich's advantage. The more delegates a candidate accrues, the larger his influence becomes over the party platform. As one top Republican Party official said of Gingrich's proclamation: "Why would he quit?" "We are already active in Nevada," Gregg Phillips, a top official with the Gingrich-allied super PAC Winning our Future, told The Huffington Post, of a state that will caucus on Feb. 4. "Our team has been competing in Nevada for about a month." If, indeed, Gingrich refuses to dislodge himself from the process, the question then becomes just how many delegates he will be able to gain. The process of unraveling that mystery begins precisely where he and the rest of the GOP candidates currently reside: in the Sunshine State. Just how Florida will award its delegates is currently the subject of intense debate, with a section of the Republican Party adamant that the current structure -- which dictates that the winner of Tuesday's primary gets all the delegates -- is in violation of party rules. In a letter to Florida GOP State Chairman Lenny Curry on December 21, 2011, RNC Chairman Reince Priebus noted that under committee rules, states other than Iowa, New Hampshire, Nevada, and South Carolina could not be "winner-take-all" if they held their primaries or caucuses prior to April 1, 2012. Florida violated that bylaw by moving its primary up to January 31. Instead of forcing Florida to award its delegates proportionately, however, the RNC punished the state by cutting its number of delegates in half, from 99 to 50. This was, as Priebus noted, the punishment under the rules (emphasis ours): Rule No. 16 imposes penalties upon any state that chooses to elect, select, allocate or bind delegates to the 2012 Republican National Convention earlier than the first day of the month in which that state is authorized to do so under Rule No. 15(b). Those penalties include a fifty percent (50%) reduction in the number of delegates that such a state is authorized to send to the 2012 Republican National Convention, as well as a prohibition on the three Republican National Committee members from the state serving as delegates or alternate delegates. That seemed like it would put an end to the debate. But a number of GOP officials continued to argue that voters who don't back former Massachusetts Gov. Mitt Romney, the likely winner of the Florida primary, were being disenfranchised by the way delegates were being awarded. They also said that other states chose not to jump ahead like Florida did out of a belief that their primaries would no longer be winner-take-all if they did so. "I just want to know when the RNC members agree to a further rule change that would allow only Florida to jump the line and not have its delegates allocated proportionally," former RNC Chairman Michael Steele told The Huffington Post. "I'm almost certain California, Michigan and Ohio didn't agree to such a change cause I know if they could be in the mix right now they would be." For those, like Steele, who believe that Florida's 50 delegates shouldn't go squarely to Romney, planning has turned toward ways to remedy the wrong. All it would take to get a hearing on the matter is for one registered Florida Republican voter to file a protest with the RNC. The party's contest committee would have to issue a decision at the convention. It seems probable, at this juncture, that someone will file such a protest. Mark Cross, an Osceola County committeeman and executive board member of the state Republican Party, wrote Priebus a letter in November 2011, making the case that it would be simple for the committee to change Florida's delegation from a winner-take-all to proportional. RNC Rules supersede any state rules or state statutes and should be enforced as to the application of delegate allocation. The rules as to the allocation and recording of delegates at the convention are completely and solely within the authority of the RNC. The rules must be applied equally to each and every state or they become meaningless without any reasonable expectation of application to any other state. Certified results of elections are easily available from the Secretary of State for each state. The RNC can calculate, report and record the proportional vote and easily enforce this rule. The proper counting and allocation is simply a matter of mathematical enforcement of the rules and should not be confused with any penalty because a state and its voters will not be losing their voice in any way. Even Priebus seemed to acknowledge that a challenge to the contest committee was likely. "In addition," he wrote Curry, "it has come to my attention that one or more Florida voters may file a contest seeking proportional allocation of Florida's delegation based on the primary taking place prior to April 1." Asked for comment on the matter, Kirsten Kukowski, Press Secretary at the Republican National Committee, emailed over the following statement: "Florida lost half of its delegates and received additional discretionary penalties for breaking the party rules. The contest committee is designed to look at any delegate concerns that may arise." But while the RNC itself is publicly deferring ultimate say on the issue for the time being, others in the party aren't acting so ambivalent. "Michael Steele can say all he wants, but he's not the chairman anymore," Brian Hughes, a spokesman for the Florida GOP, told the Tampa Bay Times. "The RNC accepted our rule and that's it. We are winner-take-all." Even if a challenge is made to the contest committee, there is no telling whether it will be successful. Different states have different models for proportionality, meaning that despite what Cross wrote, breaking up Florida's delegates would be a controversial move. Meanwhile, the odds are still likely that by the time the convention rolls around, the party will have firmly united behind one nominee with little reason to, or appetite for, refiguring the delegate count of one state. "That's usually an indication that you think you're gonna lose," Romney said, when informed of Gingrich's proclamation that he would remain in the contest until the convention. "When you say 'I'm gonna go on no matter what happens,' that's usually not a good sign." Even if the convention isn't ultimately brokered, the number of delegates each candidate earns and the way in which they are allotted are still significant. With the right number, candidates can force votes on certain issues, and they can make a motion on the convention floor to amend the party agenda or change the rules. They could also make a play for a key speaking role. It's why Rep. Ron Paul (R-Texas) has pledged to keep campaigning until Tampa and why Gingrich is now offering the same posture. Asked on Monday whether there was a chance he would drop out if he loses the Florida primary, Gingrich declared, "None... We’ll be in every state." ||||| 4 years ago (CNN) - Days before the Republican National Convention kicks off in Tampa next week, former presidential candidate Newt Gingrich released his delegates in a symbolic gesture and urged them to vote for Mitt Romney. "I hereby release all delegates bound or pledged to me under any and all state laws or party rules," Gingrich wrote in a letter to delegates, which was posted on his website Tuesday night. "At the same time, I call upon them and all Americans committed to a safer and more prosperous American future to join Callista and me in strongly supporting the Romney-Ryan ticket." - Follow the Ticker on Twitter: @PoliticalTicker - Check out the CNN Electoral Map and Calculator and game out your own strategy for November. During his own White House bid earlier this year, Gingrich repeatedly vowed to continue his campaign all the way to the convention. Faced with mounting debt and Romney's all-but-certain lock-up of the Republican nomination, Gingrich ended his campaign in early May. He has since endorsed Romney, though he's been known to offer less-than-enthusiastic praise for the former Massachusetts governor. Instead, Gingrich largely focuses on a need to defeat President Barack Obama, a message he reiterated in his letter Tuesday. "With the Republican National Convention beginning in Tampa within the next few days, it is time now for all Republicans to come together in common purpose to defeat President Barack Obama and Vice President Joe Biden," Gingrich wrote. "Everyone must do their part and Callista and I are committed to doing everything that we can." Romney passed the 1,144 delegate threshold needed to clinch the nomination on May 30. According to CNN estimates, Gingrich had collected 142 delegates by the time he ended his presidential bid. READ MORE: Ron Paul delegates set to strike deal with RNC While the former House speaker won't be delivering an address at the GOP convention next week, he's slated to host "a series of public policy workshops for delegates." Earlier this month, Gingrich said on CNN's "The Situation Room" that his role at the convention will make him more than visible in Tampa. "Trust me, anybody who wants to see me will have more than enough opportunity during the convention. I'll probably have more total time than anybody thought possible," Gingrich said.

– Newt Gingrich exited the race for the GOP nomination on May 2, but it took him another three and a half months to let go of his 142 delegates. The former GOP candidate released his delegates last night via a letter posted to his website, reports the AP. And though CNN notes that he had, on more than one occasion, vowed to hang in there right up until the convention began, he is now urging those delegates to back the Romney-Ryan ticket. "It is time now for all Republicans to come together in common purpose to defeat President Barack Obama and Vice President Joe Biden," he wrote, going on to release all delegates "bound or pledged" to him. "At the same time, I call upon them and all Americans committed to a safer and more prosperous American future to join Callista and me in strongly supporting the Romney-Ryan ticket. Together, we can and will defeat Barack Obama in November."

graphene , a two - dimensional ( 2d ) crystal of carbon atoms tightly packed in a honeycomb lattice , is at the center of an ever growing research effort , due to its potential as a platform material for a variety of applications in fields ranging from electronics , to food packaging @xcite . in particular , in optoelectronics , photonics , and plasmonics graphene has decisive advantages , such as wavelength - independent absorption , tunability via electrostatic doping , large charge - carrier concentrations , low dissipation rates , high mobility , and the ability to confine electromagnetic energy to unprecedented small volumes @xcite . these unique properties make it an ideal material for a variety of photonic applications @xcite , including fast photodetectors @xcite , transparent electrodes in displays and photovoltaic modules @xcite , optical modulators @xcite , plasmonic devices @xcite , microcavities @xcite , ultrafast lasers @xcite , just to cite a few . therefore , understanding the microscopic interactions between light and matter is an essential requirement to progress these emerging research areas into technological applications . when light arrives on a graphene sample it creates a highly non - equilibrium `` hot '' electron distribution ( he d ) , which first relaxes on an ultrafast timescale to a thermalized ( but still hot ) fermi - dirac ( fd ) distribution and then slowly cools , _ via _ optical and acoustic phonon emission , eventually reaching thermal equilibrium with the lattice . pump - probe spectroscopy is a very effective tool to study the non - equilibrium dynamics of hot carriers and has been extensively applied to a variety of graphene samples and other carbon - based materials @xcite . there is consensus in the literature on the fact that the time scales of the thermalization process , primarily controlled by electron - electron ( e - e ) interactions , are extremely short , of the order of tens of femtoseconds . indeed , early theoretical calculations @xcite based on the _ equilibrium _ many - body diagrammatic perturbation theory for an interacting system of massless dirac fermions ( mdfs ) all pointed to ultrashort e - e inelastic carrier lifetimes , with a sensitive dependence on doping . of electron states . light - gray and dark - gray shaded areas denote occupied states . these plots correspond to a non - equilibrium hot - electron distribution . arrows mark electron transitions from initial to final states . the electron population in each band is conserved in ( a ) and ( b ) , but not in ( c ) and ( d ) . ( c ) and ( d ) represent `` auger processes , '' which can only take place when the wave vectors of the initial and final states are _ [ fig : scatteringprocesses ] ] the theory of the _ non - equilibrium _ dynamics of hot carriers in graphene has also been extensively investigated @xcite . previous works , however , heavily relied on numerical analysis and did not address the following issues . when electrons in graphene are described by the low - energy 2d mdf model @xcite , a special class of two - body scattering processes poses a serious conundrum . these are `` collinear '' events , in which incoming and outgoing momenta of the scattering particles lie on the same line @xcite ( see fig . [ fig : scatteringprocesses ] ) . on one hand , due to the geometrical nature of these events , one is very tempted to conclude that they are irrelevant , since they lie on a one dimensional ( 1d ) manifold embedded in a 2d space , i.e. a set of zero measure . as we will see in sec . [ ssec : coulombkernel ] , this intuitive statement can be formally proven by employing conservation of energy and momentum . thus , the phase space for collinear scattering events vanishes in the case of 2d mdf bare bands . on the other hand , when e - e interactions are taken into account going beyond the single - particle picture , several interesting things happen . i ) mdfs moving in a collinear way along the same directrix `` spend a lot of time together '' since they travel with the same speed @xcite , the fermi velocity @xmath1 . they thus interact very strongly through the non - relativistic coulomb interaction . a simple analysis based on the fermi golden rule shows that this yields @xcite logarithmically - divergent quasiparticle decay rates and transport coefficients , such as viscosities and conductivities . ii ) interactions ( even at the hartree - fock level @xcite ) are responsible for deviations of the energy - momentum dispersion relation from linearity . the renormalized quasiparticle spectrum , controlled by the real part of the quasiparticle self - energy , displays a concave curvature @xcite , an effect that suppresses collinear scattering . iii ) the broadening of the energy - momentum dispersion , which follows from the finiteness of the quasiparticle lifetime ( an effect beyond the hartree - fock theory ) , opens up the phase space for collinear scattering , as thoroughly discussed in sec . [ sect : auger ] . the broadening of the quasiparticle spectrum is controlled by the imaginary part of the quasiparticle self - energy , a quantity directly probed by angle - resolved photoemission spectroscopy @xcite . iv ) the situation is further complicated by the role of _ screening _ , a key phenomenon in systems with long - range coulomb interactions @xcite . as we will discuss in sec . [ sect : screening ] , static screening does not have a detrimental effect on collinear scattering . the opposite occurs when dynamical screening is considered at the level of the random phase approximation ( rpa ) . v ) non - linearities and anisotropies in the band structure beyond the mdf model ( such as `` trigonal warping '' @xcite ) may affect the efficiency of screening . these issues were recently addressed in ref . by means of the equilibrium many - body perturbation theory , as we will discuss in sec . [ ssec : screeningmodels ] . all these issues raise the following question : is collinear scattering relevant or irrelevant to understand quasiparticle dynamics and transport in graphene ? collinear ( or forward ) scattering plays a special role in the dynamics of quasiparticles @xcite and photo - excited carriers in graphene @xcite . the finiteness of the quasiparticle lifetime on the mass shell @xcite can be traced back to the divergence of the density of electron - hole pairs in the collinear direction . in this case , it is the only configuration in which `` impact ionization '' ( imi ) and `` auger recombination '' ( ar ) processes are possible @xcite ( see fig . [ fig : scatteringprocesses ] ) . imi and ar ( which we will refer to with the generic term `` auger processes '' ) have been studied since the later fifties @xcite . in recent years they attracted attention in the context of semiconductors @xcite and quantum dots @xcite . imi and ar are of fundamental interest because they strongly influence the relaxation dynamics of a he d . e.g. , ar in optically - pumped 2d electron systems in the quantum hall regime is responsible @xcite for emission from states with energy higher than those optically pumped , and thwarts the realization of a landau - level laser , i.e. a laser that would operate under the 2d landau quantization , with population inversion in the landau levels @xcite . most importantly , auger processes can be exploited to design solar cells @xcite or other photovoltaic devices that can overcome fundamental limitations @xcite to photocurrent production by relying on `` carrier multiplication '' ( cm ) . we reported evidence of auger processes in graphene @xcite , proving the existence of imi and cm in a short transient following ultrafast photo - excitation in the optical domain @xcite . the excess energy of photo - excited electrons can also be transferred to secondary electron - hole pairs by intra - band scattering , _ without _ cm from the valence to conduction band . this process , also recently experimentally demonstrated @xcite , proceeds by promotion of electrons from below to above the fermi energy and does not involve processes b)-d ) in fig . [ fig : scatteringprocesses ] . on the other hand , refs . , by probing the non - equilibrium dynamics of mdfs by time- and angle - resolved photo - emission spectroscopy , found no evidence for cm . we note , however , that refs . operated in a regime of pump fluences @xmath2 where cm is not expected on the basis of calculations relying on static screening @xcite . moreover , both experiments lacked sufficient time resolution to observe cm . indeed , the higher the pump fluence , the shorter is the time window in which cm exists @xcite . e.g. , for a pump fluence @xmath3 as in ref . , cm exists in a time window @xmath4 ( substantially larger than the time resolution in ref . ) . refs . used much higher pump fluences , i.e. @xmath5 and @xmath6 , respectively . ref . reported strong evidence of population inversion in graphene after intense photoexcitation , similar to what reported in ref . , where evidence of stimulated emission was seen for pump fluences @xmath7 . because of the large fluences in refs . , the existence of population inversion can not be ascribed to the absence of auger processes . in semiconductors , imi ( ar ) creates ( annihilates ) an electron - hole pair and takes place when the energy transfer to ( from ) one electron is sufficient to overcome the band gap . since graphene is a zero - gap semiconductor , the scattering rates of auger processes are generally larger than in most other common semiconductors , as discussed in ref . . however , ref . did not address the issue of the vanishing phase space for 2d mdf bare bands . moreover , the imi and ar rates calculated in ref . refer to fd distributions [ eq . ( 20 ) in ref . ] , thus do not apply to generic non - equilibrium situations . finally , ref . did not discuss the role of dynamical screening , now known to play a pivotal role in the electronic and optoelectronic properties of graphene @xcite . here we analyze in detail the interplay between collinear scattering and e - e interactions in the context of the non - equilibrium dynamics of photo - excited electrons . we first show that electron lifetime effects open up a finite phase space for collinear scattering processes , thereby regularizing the pathologies mentioned above . here we consider the broadening of the energy - momentum dispersion , but we neglect its deviations from linearity due to e - e interactions . although these two effects could be treated in principle on an equal footing ( since they are described by the imaginary and real part of the quasiparticle self - energy , respectively ) , changes in the dispersion due to the real part of the quasiparticle self - energy are relevant only for low carrier densities @xcite . while our theory is general , the numerical calculations we present in sec . [ sec : results ] are focused on a regime with large density of photo - excited carriers , @xmath8 . this is a value that is typically used in experimental time - resolved techniques for mapping the relaxation dynamics of electron distributions @xcite . we then discuss the contribution of collinear processes to the coulomb collision integral in the semiclassical boltzmann equation ( sbe ) , which determines , _ together _ with electron - optical phonon ( e - ph ) scattering , the early stages ( sub-@xmath0 ) of the time evolution . most importantly , we go beyond the fermi golden rule , by introducing screening at the rpa level . contrary to what happens in a conventional 2d parabolic - band electron gas @xcite , the introduction of _ dynamical _ screening brings in _ qualitative _ new features . on one hand , rpa dynamical screening represents the most natural and elementary way to regularize @xcite the logarithmic divergences of quasiparticle decay rates and transport coefficients @xcite . on the other hand , due to a @xmath9 divergence that arises in the polarization function @xcite @xmath10 of 2d mdfs when the collinear scattering condition @xmath11 is met , rpa dynamical screening completely suppresses auger processes . this article is organized as follows . [ sec : hamiltonian ] describes the model mdf hamiltonian and the sbe for the coupled dynamics of electrons and optical phonons . it also reviews the typical timescales , as set by e - e and e - ph interactions . [ sect : collinearscattering ] introduces the isotropic sbe and discusses in detail the treatment of collinear scattering in the coulomb collision integral . the role of screening is considered in sec . [ sect : screening ] . [ sec : results ] presents our main numerical results for the electron and phonon dynamics , as obtained from the solution of the isotropic sbe . finally , sec . [ sec : conclusions ] , summarizes our main conclusions . carriers in graphene are described in a wide range of energies ( @xmath12 ) by the mdf hamiltonian @xcite , @xmath13 where the field operator @xmath14 annihilates an electron with 2d momentum @xmath15 , valley @xmath16 , band index @xmath17 ( or @xmath18 , @xmath19 for conduction and valence band , respectively ) , and spin @xmath20 . the quantity @xmath21 represents the mdf band energy , with a slope @xmath22 . mdfs interact through the non - relativistic coulomb potential @xmath23 with the following 2d fourier transform @xmath24 where @xmath25 is an average dielectric constant @xcite calculated with the dielectric constants @xmath26 and @xmath27 of the media above and below the graphene flake . intra - valley e - e interactions are described by the following hamiltonian ( in the eigenstate representation ) : @xmath28 where @xmath29 is 2d electron system area and the delta distribution imposes momentum conservation . the matrix element of the coulomb potential reads @xmath30 where @xmath31 / 2 $ ] is the so - called `` chirality factor '' @xcite , which depends on the polar angle @xmath32 of the wave vector @xmath33 . the following dimensionless coupling constant @xcite controls the strength of e - e interactions ( relative to the typical kinetic energy ) : @xmath34 the distribution function @xmath35 represents the probability that a given single - particle state with quantum numbers @xmath36 is occupied . the equation of motion ( eom ) for this distribution function in the presence of e - e interactions is given by @xcite : @xmath37~.\end{aligned}\ ] ] the right - hand side of the previous equation is the collision integral and the dirac delta distributions enforce conservation of momentum and energy in each e - e scattering event . the quantity @xcite @xmath38 in the collision integral includes a direct ( hartree ) and an exchange ( fock ) term , non - vanishing if two colliding electrons have parallel spins ( @xmath39 ) . this expression for the kernel in the collision integral corresponds to the second - order hartree - fock approximation @xcite . if spin - flip processes are absent ( as in the case considered here ) , the distribution function does not depend on the spin label , which can be dropped . the summation over @xmath40 in eq . ( [ eq : eescattering ] ) can be performed explicitly , obtaining the spin - independent kernel @xmath41 in agreement with ref . . electrons scatter with lattice vibrations and lose ( gain ) energy by emitting ( absorbing ) phonons . only optical phonons in the neighborhood of the @xmath42 and @xmath43 points of the brillouin zone ( bz ) matter for electrons with energy of several hundred @xmath44 above the fermi energy . at each point , both the transverse ( t ) and the longitudinal ( l ) phonon modes are considered . the distribution function of the @xmath45-th phonon mode with @xmath46 and 2d momentum @xmath47 is denoted by the symbol @xmath48 . the electron - phonon ( e - ph ) contribution to the eom for the electron distribution is @xcite @xmath49\nonumber \\ & & + \frac{2 \pi}{\hbar } \frac{1}{a}~\sum_{\bm q}\sum_{s',\ell ' , \nu } { \cal a}_{0 } |g^{(\nu)}_{{\bm k } + { \bm q},\ell ' \to { \bm k},\ell}|^{2 } f_{{\bm k } + { \bm q},\ell ' , s ' } ( 1 - f_{{\bm k } , \ell , s } ) \nonumber \\ & & \times \left[\delta ( \varepsilon_{{\bm k } , s } - \varepsilon_{{\bm k } + { \bm q } , s ' } + \hbar\omega^{(\nu)}_{\bm q } ) ( n^{(\nu)}_{\bm q } + 1 ) + \delta ( \varepsilon_{{\bm k } , s } - \varepsilon_{{\bm k } + { \bm q } , s ' } - \hbar\omega^{(\nu)}_{\bm q } ) n^{(\nu)}_{\bm q } \right]~,\end{aligned}\ ] ] where @xmath50 is the area of the elementary cell of graphene s honeycomb lattice . the terms proportional to @xmath51 represent electronic transitions from the single - particle state with quantum numbers @xmath52 , @xmath53 , @xmath54 , to the state @xmath55 , @xmath56 , @xmath57 . the transition is suppressed if the value @xmath58 of the distribution function in the final state is close to unity ( pauli blocking ) . the terms proportional to @xmath59 correspond to absorption of phonons , while the terms proportional to @xmath60 correspond to emission of phonons . the latter coefficient is larger than the former ( bose enhancement ) because phonons , being bosonic excitations , experience bunching . the kernels @xmath61 can be written as : @xmath62 \nonumber \\ & = & \langle g_{\gamma}^{2 } \rangle [ 1 - \cos{(\theta_{{\bm k } , { \bm q } } + \theta_{{\bm k } + { \bm q } , { \bm q } } ) } ] \nonumber \\ & = & \langle g_{{\rm k},1}^{2 } \rangle \nonumber \\ & = & \langle g_{{\rm k},2}^{2 } \rangle [ 1 + \cos{(\theta_{{\bm k } , { \bm k } + { \bm q}})}]~,\end{aligned}\ ] ] where @xmath63 denotes the angle between the wave vectors @xmath52 and @xmath47 and @xmath64 are the electron - phonon couplings ( epcs ) @xcite . phonons at the @xmath42 ( @xmath43 ) point are responsible for intra - valley ( inter - valley ) scattering only . the complete eom for the electron distribution is the sum of eqs . ( [ eq : eescattering ] ) and ( [ eq : electronphononboltzmann ] ) , i.e. : @xmath65 finally , the sbe for the phonon distribution is : @xmath66 \nonumber \\ & & - \frac{\gamma_{\rm ph}}{\hbar } \left [ n^{(\nu)}_{\bm q } - \frac{1}{\exp{(\hbar\omega^{(\nu)}_{\bm q } / ( k_{\rm b } t_0 ) ) } - 1 } \right ] ~.\end{aligned}\ ] ] the right - hand side of the previous equation includes a phenomenological decay term which describes phonon - phonon interactions ( due to the anharmonicity of the lattice ) . indeed anharmonic couplings play an important role in the graphene lattice @xcite and , in principle , the decay coefficient @xmath67 could be calculated by means of atomistic monte carlo simulations based on a realistic description of interatomic interactions @xcite . the decay term induces relaxation of the phonon distribution towards the equilibrium value , given by a bose - einstein distribution at the temperature @xmath68 of the lattice . accurate calculations of relaxation timescales in e.g. semiconductors pose a challenging problem of great theoretical and practical relevance @xcite . in graphene , three stages of the time evolution have been identified @xcite , which follow the creation of a he d due to the action of a laser - light `` pump '' pulse promoting a certain density of electrons from valence to conduction band . in the first stage , @xmath69 , the initial he d thermalizes to a hot fd distribution and the two bands are characterized by different chemical potentials . recently , we were able to track this initial stage with sufficient time - resolution to directly measure the transition from a non - thermal to a hot fd distribution @xcite . cooling of the hot fd distribution and equilibration of the chemical potentials between the two bands take place in the second and third stage , where the dominant process is phonon emission . the second stage , @xmath70 , is dominated by the emission of _ optical _ phonons @xcite , which in graphene are associated with an unusually large energy scale ( @xmath71 ) @xcite and are moderately coupled to the electronic degrees of freedom . this cooling channel experiences a bottleneck when the phonon distribution heats up @xcite . the third stage , which occurs when the bulk of the electron distribution lies below the optical - phonon energy scale , is characterized by the emission of _ acoustic _ phonons @xcite . these processes take place for @xmath72 , but can experience a substantial speed - up ( @xmath73 ) in the case of disorder - assisted collisions @xcite . since here we focus on the electron relaxation dynamics in the sub-@xmath0 time scale , we neglect the contribution of acoustic phonons in our sbe formulation . throughout the relaxation dynamics , phonons dissipate energy into the lattice by means of phonon - phonon interactions . in this section we simplify eqs . ( [ eq : summingrates])-([eq : phonon ] ) by assuming that the electron and phonon distributions are _ isotropic_. while this assumption does not apply _ during _ the application of the pump pulse ( since this couples anisotropically @xcite ) , it has been shown that e - e interactions restore isotropy in the very short time scale of a few fs @xcite . hence , our assumption applies to the thermalization and cooling stages of the time evolution , i.e. what we aim to study here . the electron distribution @xmath74 is therefore assumed to depend on the wave vector @xmath52 only through the energy @xmath75 . similarly , the phonon distribution @xmath76 is assumed to depend only on the magnitude @xmath77 of the phonon wave vector @xmath47 . since the slope of the phonon dispersion @xmath78 is negligible with respect to @xmath79 , we drop the momentum dependence and use constant values @xmath80 and @xmath81 . equations for isotropic distributions can be obtained by performing the angular integrations in the collision integrals of eqs . ( [ eq : summingrates ] ) and ( [ eq : phonon ] ) . we now outline our approach in the case of a single summation over a wave vector @xmath52 , involving a generic function @xmath82 , which depends on the direction of @xmath52 and another wave vector @xmath47 , and a functional @xmath83 $ ] , which depends only on the isotropic quantities @xmath84 and @xmath85 . we have @xcite : @xmath86 \nonumber \\ & & = \int_{-\infty}^{\infty } d\varepsilon ' \ , \int_{-\infty}^{\infty}d\varepsilon '' \ , { \cal f}[\varepsilon',\varepsilon '' ] { \cal q}[\varepsilon',\varepsilon'']~,\end{aligned}\ ] ] where the kernel @xmath87 = \sum_{\bm k } \delta ( \varepsilon ' -\varepsilon_{{\bm k},s } ) \delta ( \varepsilon '' - \varepsilon_{{\bm k } + { \bm q},s ' } ) g({\bm k } , { \bm q})$ ] depends now only on isotropic quantities . the calculation of the isotropic kernels in eqs . ( [ eq : summingrates ] ) and ( [ eq : phonon ] ) is summarized in the following . this approach is convenient from a computational point of view since it reduces the number of variables in the integrations that have to be carried out numerically ( see app . [ ssec : numerical ] ) . most importantly , it also allows us to handle analytically the contribution of collinear scattering to the e - e interaction in the boltzmann collision integral . the final results for the e - ph contributions are : @xmath88 \int_{-\infty}^{\infty } d\varepsilon f_{\ell}(\varepsilon)[1-f_{\ell'}(\varepsilon^{(\nu,-)})]{\cal q}^{(\nu,-)}_{\ell,\ell'}(\varepsilon , q ) \nonumber \\ & - & n^{(\nu)}(q ) \int_{-\infty}^{\infty } d\varepsilon f_{\ell}(\varepsilon)[1-f_{\ell'}(\varepsilon^{(\nu,+ ) } ) ] { \cal q}^{(\nu,+)}_{\ell,\ell'}(\varepsilon , q ) \bigg\ } - \frac{\gamma_{\rm ph}}{\hbar } \left [ n^{(\nu)}(q ) - \frac{1}{\exp{(\hbar\omega^{(\nu ) } / ( k_{\rm b } t_{0 } ) ) } - 1 } \right ] \end{aligned}\ ] ] and @xmath89 \int_{0}^{\infty } dq ( \hbar v_{\rm f})[n^{(\nu)}(q ) + 1]~{\cal i}^{(\nu,-)}_{\ell,\ell'}(\varepsilon , q ) \nonumber\\ & - & f_{\ell}(\varepsilon)[1-f_{\ell'}(\varepsilon^{(\nu,+)})]\int_{0}^{\infty } dq ( \hbar v_{\rm f } ) n^{(\nu)}(q)~{\cal i}^{(\nu,+)}_{\ell,\ell'}(\varepsilon , q ) \nonumber \\ & + & f_{\ell'}(\varepsilon^{(\nu,+ ) } ) [ 1-f_{\ell}(\varepsilon)]\int_{0}^{\infty } dq ( \hbar v_{\rm f } ) [ n^{(\nu)}(q ) + 1]~{\cal i}^{(\nu,+)}_{\ell,\ell'}(\varepsilon , q ) \nonumber \\ & + & f_{\ell'}(\varepsilon^{(\nu,- ) } ) [ 1-f_{\ell}(\varepsilon ) ] \int_{0}^{\infty } dq ( \hbar v_{\rm f } ) n^{(\nu)}(q ) ~ { \cal i}^{(\nu,-)}_{\ell,\ell'}(\varepsilon , q)\bigg\}~,\end{aligned}\ ] ] with the shorthand @xmath90 . in eqs . ( [ eq : phononsisotropic])-([eq : electronsphononsisotropic ] ) , we introduced the following functions : @xmath91\ ] ] and @xmath92 with @xmath93 \equiv \theta(x_{0 } - |x_{1 } - 1| ) \theta(x_{1 } + 1 - x_{0 } ) \nonumber \\ & & \times \frac{2 x_{0}}{\sqrt{4x_{1}^{2}-(x_{0}^{2}-x_{1}^{2}-1)^{2 } } } \nonumber \\ & & \times { \cal f } \left ( x_{1},\arccos[(x_{0}^{2 } - x_{1}^{2 } - 1)/(2 x_{1 } ) ] \right ) ~.\end{aligned}\ ] ] here @xmath94 is the heaviside distribution and the quantities @xmath95 are dimensionless . for notational convenience , we write the wave vector dependence of the e - ph kernel @xmath96 in the form @xmath97 , where @xmath98 and @xmath99 . finally , the e - e contribution reads @xmath100 [ 1 - f_{\ell}(\varepsilon_{2})]f_{\ell}(\varepsilon_{3 } ) f_{\ell}(\varepsilon_{4 } ) \right . \nonumber \\ & & - \left . f_{\ell}(\varepsilon_{1 } ) f_{\ell}(\varepsilon_{2 } ) [ 1 - f_{\ell}(\varepsilon_{3})][1 - f_{\ell}(\varepsilon_{4 } ) ] \right \rbrace~.\end{aligned}\ ] ] where the coulomb kernel @xmath101 , with physical dimensions @xmath102 , represents a two - particle scattering rate . the energies of the incoming ( with indexes @xmath103 and @xmath104 ) and outgoing particles ( with indexes @xmath105 , @xmath106 ) are fixed . the total energy @xmath107 is conserved and , finally , @xmath108 . simplifying eq . ( [ eq : eescattering ] ) along the lines of eq . ( [ eq : haugtrick ] ) leads to the following expression for the coulomb kernel : @xmath109 here , the wave vector @xmath110 has modulus @xmath111 , while its direction can be fixed at will ( i.e. along the @xmath112 axis ) because the final result @xmath113 is scalar under rotations . the total wave vector @xmath114 is conserved in all scattering processes . in the summation over @xmath115 and @xmath116 , the dirac delta distributions ensure that only scattering configurations that are compatible with the choice of incoming @xmath117 and outgoing @xmath118 energies are considered . moreover , the three delta distributions restrict the 4d integral to a 1d integral ( at most ) , after the usual continuum limit @xmath119 is performed . we choose to reduce the summations to an integration over the modulus @xmath120 of the total momentum , in terms of which we are able to represent with clarity the phase space available for coulomb scattering ( see fig . [ fig : integrationdomain ] ) . we stress that in eq . ( [ eq : coulombkernel ] ) we introduced an _ infinitesimal _ quantity @xmath121 in the argument of one of the delta distributions . as we will see in the next section , if the limit @xmath122 is taken _ before _ calculating the 4d integral in eq . ( [ eq : coulombkernel ] ) , collinear scattering processes do not contribute to @xmath113 . we introduced @xmath121 to slightly relax the condition of energy conservation . the latter is recovered only in the limit @xmath122 . we can justify this by considering the following physical explanation . the delta distribution of conservation of energy in eq . ( [ eq : eescattering ] ) originates from the so - called `` quasiparticle approximation , '' applied to the kadanoff - baym equations ( kbes ) , from which the sbe is derived @xcite . more precisely , the kbes involve the true quasiparticle spectral function , which has a finite width . in the quasiparticle approximation , the spectral function is substituted with a delta distribution , which is a reasonable approximation when the width of the quasiparticle spectral function can be neglected . as we will see in this section , in the quasiparticle approximation applied to 2d mdfs an entire class of two - body collisions ( collinear processes ) yields vanishing scattering rates . our procedure takes effectively into account the fact that quasiparticles have a finite lifetime @xcite , thereby allowing for a finite collinear scattering contribution to the coulomb kernel . we first calculate the coulomb kernel with a finite @xmath121 and then apply the quasiparticle @xmath122 approximation at the end of the calculation . to make analytical progress , we now introduce elliptic coordinates for the evaluation of the coulomb kernel @xcite . this is most natural because , for every fixed value of @xmath115 , the equation @xmath123 for the total energy defines a conic section in momentum space . more precisely , if @xmath124 ( @xmath125 ) , the vector @xmath126 lies on an ellipse ( hyperbola ) with focuses located at @xmath127 and major axis of length @xmath128 . elliptic coordinates @xmath129 are related to the cartesian coordinates @xmath130 by the transformation @xmath131 , @xmath132 , with area element @xmath133 \ , du \ , dv$ ] . in these coordinates , @xmath134 $ ] and @xmath135 $ ] , so that non - linear combinations between integration variables in eq . ( [ eq : coulombkernel ] ) disappear . elliptic coordinates are also extremely useful to prove that imi and ar can only occur when @xmath136 are collinear ( see figs . 4a and b in ref . ) . carrying out algebraic manipulations , we rewrite eq . ( [ eq : coulombkernel ] ) in the following simplified manner : @xmath137[(\hbar v_{\rm f } q)^{2 } - e_{1,{\rm min}}^{2 } ] \right \rbrace ^{1/2 } } \frac { ( e_{3,{\rm max } } + \eta)^{2 } - ( e_{3,{\rm min } } - \eta)^{2 } } { \left \lbrace [ ( e_{3,{\rm max}}+\eta)^{2 } - ( \hbar v_{\rm f } q)^{2}][(\hbar v_{\rm f } q)^{2 } - ( e_{3,{\rm min } } - \eta)^{2 } ] \right \rbrace ^{1/2}}~. \nonumber \\ % \end{aligned}\ ] ] we stress that this is the most important analytical result of this article . note that the integrand in eq . ( [ eq : kernelintegralsimplified ] ) is given by the product of the kernel ( [ eq : matrixelementsummed ] ) and a complicated expression arising from the phase space of the e - e scattering processes , the term in the second line of eq . ( [ eq : kernelintegralsimplified ] ) . in eq . ( [ eq : kernelintegralsimplified ] ) , @xmath138 and the dependence of @xmath33 on @xmath117 , @xmath118 , @xmath139 , and @xmath120 is left implicit for the sake of simplicity . the primed sum symbol indicates summation over the available configurations of vectors @xmath140 , @xmath116 , and @xmath141 . to identify these configuration , one may proceed as follows . when @xmath117 , @xmath118 , @xmath139 , and @xmath120 are given , the lengths of all the sides of the two triangles @xmath142 and @xmath143 are uniquely fixed . these two triangles , which share the side of length @xmath120 , can be drawn on the same half - plane ( with respect to a line containing the vector @xmath115 ) or on opposite half - planes . thus , four geometric configurations for the wave vectors @xmath140 , @xmath116 , and @xmath141 are available in total . however , when all vectors @xmath33 are collinear , the triangles are degenerate and only one configuration is possible . finally , in eq . ( [ eq : kernelintegralsimplified ] ) we also introduced @xmath144 , @xmath145 , and @xmath146 let us first discuss the case in which @xmath121 is set to zero before carrying out the integral in eq . ( [ eq : kernelintegralsimplified ] ) . in this case , one can prove that @xmath147 by using the triangular and reverse triangular inequalities , @xmath148 . when the previous inequalities turn into equalities , the length of the vector @xmath115 is fixed at @xmath149 , @xmath150 , and the integration domain vanishes . ) for the variable @xmath120 in the integral ( eq.[eq : kernelintegralsimplified ] ) . the regions labeled by i , ii , and iii identify the values of the parameters @xmath151 and @xmath152 for which intra - band , inter - band , and auger processes take place , respectively . at @xmath149 collinear scattering takes place . this value is the maximum ( minimum ) of the integration domain in region i ( ii ) . the minimum ( maximum ) of the integration domain in region i ( ii ) is shown in the color scale , in units of @xmath128 . [ fig : integrationdomain ] ] fig . [ fig : integrationdomain ] plots the integration domain relative to the variable @xmath120 in eq . ( [ eq : integrationdomain ] ) , as a function of @xmath117 and @xmath118 , in the case @xmath153 . in region i , @xmath154 implies @xmath155 ( if the total energy is negative , all the inequalities are reversed ) . all the particles are either above ( @xmath156 ) or below ( @xmath157 ) the dirac point . region i , therefore , pertains to intra - band scattering events . similarly , one concludes that regions of type ii pertain to inter - band scattering ( two electrons are in opposite bands before and after the scattering ) . finally , regions of type iii pertain to imi and ar . in these regions the integration domain [ and , therefore , @xmath158 in eq . ( [ eq : kernelintegralsimplified ] ) vanishes . we note that classification of regions i , ii , and iii holds true for arbitrary values of @xmath121 . ( [ eq : kernelintegralsimplified ] ) is extremely helpful since it can be used to solve the sbe ( [ eq : summingrates ] ) with arbitrary non - equilibrium initial conditions , more so since analytical expressions for the coulomb kernel of 2d mdfs such as that in eq . ( [ eq : kernelintegralsimplified ] ) were not reported before , to the best of our knowledge . we now proceed to calculate @xmath159 in regions of type iii . in this case , a finite value of @xmath121 restores a non - vanishing integration domain for imi and ar and a finite contribution to @xmath159 due to these processes . note that the sign of @xmath121 should be chosen such that @xmath160 . let us consider , for the sake of definiteness , the region of type iii where @xmath161 . we have @xmath162 . the integrand in eq . ( [ eq : kernelintegralsimplified ] ) factors into two portions , one that depends smoothly on @xmath120 and can therefore be evaluated at @xmath163 and taken out of the integral , and another singular at the boundaries of the integration domain . the integral of the latter part must be carefully evaluated and is : @xmath164^{1/2 } } = \pi~.\ ] ] note that the result of the previous integral does _ not _ depend on @xmath121 , therefore remains finite in the limit @xmath122 . the final result for the auger contribution to the coulomb kernel , valid in _ all _ regions of type iii , can be written as : @xmath165 where the convention for @xmath166 and @xmath33 has been introduced after eq . ( [ eq : kernelintegralsimplified ] ) . the term on the second line of eq . ( [ eq : augerresult ] ) comes from the smooth portion of the integrand in eq . ( [ eq : kernelintegralsimplified ] ) . we stress that eq . ( [ eq : augerresult ] ) follows from the general expression ( [ eq : kernelintegralsimplified ] ) without _ a priori _ restrictions to collinear scattering configurations . although eq . ( [ eq : augerresult ] ) mathematically coincides with eq . ( 14 ) of ref . , ref . does not report any discussion on how to bypass the vanishing phase space problem for 2d mdfs . here , the finiteness of imi and ar contributions to the coulomb kernel , as for eq . ( [ eq : augerresult ] ) , originates from electron - lifetime effects . incidentally , since the value of the integral in eq . ( [ eq : abeautifulintegral ] ) does not depend on the value of @xmath121 , the precise mechanism ( e - e interactions , electron - impurity scattering , etc . ) responsible for the broadening of the delta distribution in eq . ( [ eq : eescattering ] ) into a finite - width quasiparticle spectral function is unimportant . finally , we emphasize that imi and ar scattering rates were calculated in ref . for fd distributions only , as seen in eq . ( 20 ) of ref . . on the contrary , eqs . ( [ eq : kernelintegralsimplified ] ) and ( [ eq : augerresult ] ) can be used to solve the sbe ( [ eq : summingrates ] ) with _ arbitrary _ non - equilibrium initial conditions . we finally consider @xmath159 in regions of type i and ii . the integrand in eq . ( [ eq : kernelintegralsimplified ] ) diverges as @xmath167 for @xmath168 , which coincides with the upper @xmath169 or lower @xmath170 boundaries of the integration domain for regions of type i and ii . when @xmath168 , intra - band or inter - band scattering occur in a collinear fashion . this strong divergence of the integrand physically arises from the expression for the phase space of e - e scattering , while @xmath171 is well behaved . therefore , @xmath159 diverges for both intra - band and inter - band scattering processes . a possible way to cure this divergence @xcite is to introduce an ultraviolet cut - off @xmath172 , which yields a coulomb kernel @xmath173 . logarithmic enhancements for 2d fermions with a linear dispersion were discussed in ref . , and allow one to find a sbe solution in the form of an effective equilibrium distribution , with parameters depending on the direction of motion @xcite . peculiar properties of mdfs , which are sensitive to collinear scattering , include a finite conductivity in the absence of impurities @xcite and an unusually low shear viscosity @xcite . a different way to treat this divergence is to invoke _ screening _ , which suppresses the kernel @xmath174 and regularizes the behavior of the integrand in a neighborhood of @xmath149 . this approach is discussed in the next section in great detail . the sbe is a second - order expression in the _ bare _ coulomb potential @xmath175 and describes e - e interactions at level of the fermi golden rule @xcite . this approximation neglects many - body effects , and most importantly electronic screening . formally , screening can be taken into account @xcite by substituting the bare coulomb potential @xmath176 with a _ screened _ potential @xmath177 . when the 2d mdf system is out of equilibrium , the screening properties change in time and the screened potential depends on time @xmath178 as well . it has been pointed out @xcite that screening may preempt the strong collinear scattering singularity mentioned above and suppress auger processes . indeed , the rpa dynamical dielectric function at equilibrium @xmath179 diverges for collinear scattering configurations for which @xmath11 ( see sec . [ ssec : dielectric ] ) . when substituted into eq . ( [ eq : kernelintegralsimplified ] ) , the screened potential @xmath177 vanishes like @xmath180 , thereby compensating the aforementioned divergence arising from the expression of the phase space . the integral in eq . ( [ eq : kernelintegralsimplified ] ) is then finite , while the contribution to the coulomb kernel due to auger processes vanishes . the matrix element of the screened potential is obtained by the replacement : @xmath181 where @xmath182 is defined in eq . ( [ eq : matrixinteraction ] ) and @xmath179 is the dynamical dielectric function @xcite . here , @xmath183 and @xmath184 are the momentum and energy transferred in the scattering process , respectively . we stress that the prescription ( [ eq : screenedpotential ] ) must be applied only to the first term on the right hand side of eq . ( [ eq : hf ] ) , i.e. to the _ direct _ term . in principle , one could apply eq . ( [ eq : screenedpotential ] ) to screen both direct and exchange contributions in eq . ( [ eq : hf ] ) . the latter procedure was previously used in refs . to compute scattering rates , but has a major drawback : it is easy to see that the corresponding sbe does _ not _ conserve the particle number . in other words , the approximation obtained by screening both direct and exchange terms in eq . ( [ eq : hf ] ) according to eq . ( [ eq : screenedpotential ] ) is not conserving in the sense of kadanoff and baym @xcite . on the contrary , retaining the direct term only corresponds to the well - known shielded potential approximation " @xcite , which is conserving in the sense of kadanoff and baym . this is the approach we follow below , setting @xmath185 in eq . ( [ eq : hf ] ) . in the rpa , the dielectric function is given by @xcite @xmath186 where @xmath175 is the bare coulomb potential , defined in eq . ( [ eq : coulomb ] ) , and @xmath10 is the non - interacting polarization function @xcite ( or lindhard function ) for 2d mdfs : @xmath187 where @xmath188/2 $ ] and the factor @xmath189 accounts for spin degeneracy . it is intended that @xmath179 and @xmath10 depend _ explicitly on time _ @xmath178 through the time - dependence of the distribution function @xmath74 . one route to include screening in the sbe calculations is to compute @xcite the polarization function @xmath10 at each time @xmath178 according to eq . ( [ eq : polarization ] ) and use it to evaluate the expressions ( [ eq : kernelintegralsimplified ] ) and ( [ eq : augerresult ] ) for the coulomb kernel . in this article , however , we prefer to use a more analytical approach , which turns out to reduce dramatically the computational costs associated with solving the sbe with screening . since thermalization occurs on a very fast time scale @xcite , we calculated the polarization function analytically by employing the following _ thermal _ ansatz for the distribution function @xmath74 in eq . ( [ eq : polarization ] ) : @xmath190 where @xmath191 } + 1}\ ] ] is the usual fd distribution . in eq . ( [ eq : distrotwomu ] ) , @xmath192 and @xmath193 are chemical potentials in conduction and valence band , respectively , and @xmath194 is the temperature . the values of the three parameters @xmath192 , @xmath193 , and @xmath194 can be obtained at each time @xmath178 by fitting eq . ( [ eq : distrotwomu ] ) to the he d derived by solving the sbe . in writing eq . ( [ eq : distrotwomu ] ) we assumed that conduction- and valence - band electrons thermalize at the same @xmath194 . this approximation is certainly valid for times longer than @xmath195 ( see sec . [ ssec : timescales ] ) , because energy equilibration between the two bands sets in on the time scale induced by e - e interactions . at earlier times , the estimate of @xmath194 and @xmath196 obtained by fitting the profile ( [ eq : distrotwomu ] ) to the he d is certainly not precise , but can be improved _ a posteriori _ by extrapolating to @xmath69 the results of the fits obtained at later times . although a common @xmath194 between the two bands is established in the very early stages of the dynamics , carrier equilibration between the two bands , on the contrary , is mainly due to phonon - assisted inter - band transitions , which act on a much longer time scale ( @xmath197 ) . assuming two different chemical potentials is thus essential to obtain a correct representation of screening in the non - equilibrium dynamics after photo - excitation . our analytical approach to the calculation of @xmath10 allows us to describe well the rapidly changing dielectric function and , at the same time , to determine analytically its behavior for collinear configurations , crucial to the issues discussed in sec . [ ssec : divergencies ] . in the rest of this section we outline the calculation of the polarization function of a photo - excited 2d mdf fluid . we start by noting that the polarization function @xmath10 as obtained from eq . ( [ eq : polarization ] ) with the thermal ansatz ( eq.[eq : distrotwomu ] ) physically represents the polarization function @xmath198 of a 2d mdf fluid with _ two _ chemical potentials @xmath192 and @xmath193 , at a finite @xmath194 . to the best of our knowledge , this function is unknown . we therefore proceed to calculate @xmath198 following a well - known procedure due to maldague @xcite . this route allows us to write this polarization function in terms of an integral involving the well - known lindhard function @xmath199 of a 2d mdf fluid at zero @xmath194 and at a fermi energy @xmath200 the final result is : @xmath201 \nonumber \\ & & - \left . \pi_0(q,\omega)\right|_{\varepsilon_{\rm f } \to 0 } \left [ f(0;\mu_{\rm c},t ) - f(0;\mu_{\rm v},t ) \right ] ~,\end{aligned}\ ] ] where @xmath202 note that @xmath199 is particle - hole symmetric ( therefore identical for positive and negative values of the fermi energy @xmath200 ) and that @xmath203 is the lindhard function of an undoped 2d mdf system @xcite . here we have @xmath204 . eq . ( [ eq : lindhardtwomu ] ) is the main result of this section and reveals that the thermal polarization function @xmath198 naturally decomposes into the sum of two contributions stemming from each band . however , the extra correction in the second line of eq . ( [ eq : lindhardtwomu ] ) needs to be taken into account at finite @xmath194 . the following three identities are necessary to derive eq . ( [ eq : lindhardtwomu ] ) : i ) @xmath205 , ii ) @xmath206 f(\varepsilon;0,0)$ ] , and iii ) @xmath207 illustrative plots of the real and imaginary parts of the polarization function ( [ eq : lindhardtwomu ] ) are reported in figs . [ fig : chi2d],[fig : chicuts ] . in these plots we rescaled @xmath208 with the conduction - band fermi energy @xmath209 , @xmath210 and the wave vector @xmath77 with the conduction - band fermi wave number @xmath211 . in eq . ( [ eq : fermienergyconduction ] ) , @xmath212 is the spence s function @xcite . we note that the reactive part of the polarization function manifests a singularity along the `` light cone '' @xmath213 , entirely inherited from @xmath199 . the dissipative part displays a striking difference with respect to @xmath214 $ ] : the usual triangular region above the light cone where both intra- and inter - band particle - hole pairs are suppressed @xcite is not present in fig . [ fig : chi2d](b ) . moreover , above the light cone and for @xmath215 , a region where the imaginary part of @xmath216 is _ positive _ appears . fig03(2,60)(a ) fig04(2,60)(b ) fig05(2,60)(a ) fig06(2,60)(b ) here we approximate the time - dependent polarization function @xmath10 in eq . ( [ eq : polarization ] ) as : @xmath217 in this article we focus on the following three screening models : \i ) _ dynamical screening_. in this case the polarization function @xmath216 in eq . ( [ eq : finalapproximation ] ) is evaluated on shell " , i.e. at @xmath218 , which is the energy transferred in the two - body scattering process . as mentioned above , in this case inter - band and intra - band scattering rates are finite while the auger contribution ( [ eq : augerresult ] ) to the coulomb kernel vanishes . static screening_. in this case the polarization function @xmath216 in eq . ( [ eq : finalapproximation ] ) is evaluated at @xmath219 . this approximation is justified when the energy @xmath218 transferred in the two - body scattering process is significantly smaller than the energy @xmath220 , necessary to excite a plasmon @xcite . in the static screening approximation , inter - band and intra - band scattering rates diverge and can be regularized by employing an infrared and an ultraviolet cutoff @xcite ( further details are reported in the appendix ) . we find , however , that the resulting non - equilibrium dynamics does not depend on the values of these two cutoffs . the reason is the following . intra- and inter - band scattering processes are responsible only for redistributing energy , rapidly driving the two bands towards thermal equilibrium . therefore , for @xmath151 and @xmath152 varying in regions of type i and ii ( see fig . [ fig : integrationdomain ] ) the quantity in curly brackets in eq . ( [ eq : finalboltzmann ] ) vanishes . in the static approximation the auger contribution ( [ eq : augerresult ] ) to the coulomb kernel is finite . \iii ) _ regularized screening_. finally , we introduce a `` regularized '' screening model @xcite in which the polarization function @xmath216 in eq . ( [ eq : finalapproximation ] ) is evaluated on shell , but its singularity around the light cone @xmath213 is _ smeared _ by means of a cutoff @xmath221 ( see app . [ ssec : numerical ] for more details ) . in the limit @xmath222 this model reduces to dynamical screening , as described at point i ) above . various physical mechanisms can smear the singularity of the polarization function on the light cone , including many - body effects beyond rpa ( as suggested in ref . ) or single - particle effects beyond the 2d mdf model , e.g. trigonal warping ( as suggested in ref . ) . in our regularized screening model the auger contribution ( [ eq : augerresult ] ) to the coulomb kernel is finite and , in particular , its magnitude is intermediate between that evaluated within the dynamical and static screening models . in this section we summarize our main numerical results , obtained from the solution of the isotropic sbe within the three screening models listed in sec . [ ssec : screeningmodels ] . we compared the outcome of a closely related approach with our experimental measurements in ref . . there we applied screening to both direct and exchange terms in eq . ( [ eq : hf ] ) . the data that we present in this section are in agreement with our previous results in ref . , therefore fully support the interpretation of the experimental data given there . more precisely , very good quantitative agreement is found for the static and dynamical screening models , which do not depend on free parameters . there are some differences , however , between the dynamical behavior illustrated in ref . and that discussed in this section , when the regularized screening model is used . although the mathematical definition of the cutoff @xmath221 here is analogous to the definition of @xmath172 in ref . , the equations of motion induced by the regularized screening models differ . as repeatedly stressed above , in the present paper we never screen dynamically the exchange contribution to eq . ( [ eq : hf ] ) . moreover , here we mostly focus on undoped samples , although some results for @xmath223-doping are presented in fig . [ fig : maximumtransmission ] . on the other hand , ref . reported experiments and calculations for a @xmath224-doped sample . even though ref . already allowed us to conclude that rpa dynamical screening is not capable of explaining the experimental results , in this article for sake of completeness we will present a comparative study of all screening models listed in sec . [ ssec : screeningmodels ] . as initial condition for the solution of the sbe we use a distribution function which is the sum of a fd distribution , with chemical potential @xmath225 and temperature @xmath68 , and two gaussian - shaped peaks ( one below and one above the dirac point ) : @xmath226}\nonumber\\ & - & g_{\rm max } \exp{\left[-\left(\frac{\varepsilon + \hbar \omega_{\rm p}/2}{\hbar \delta \omega_{\rm p}/2}\right)^2\right]}~.\end{aligned}\ ] ] the initial distribution function is identical in both @xmath16 valleys . the choice ( [ eq : initialstate ] ) is motivated by pump - probe spectroscopy experiments on graphene , where electrons are promoted from valence to conduction band by using a laser light pulse . before the pump pulse is applied , the electronic subsystem is at equilibrium with the lattice at a given @xmath194 , say @xmath227 ( room @xmath194 ) . the momentum transferred by the laser light to the electrons is negligible , hence the transitions are `` vertical '' in momentum space , from energy @xmath228 in valence band to energy @xmath229 in conduction band . the width @xmath230 of the light pulse determines the width of the resulting he d . consistent with our recent experiments @xcite , and for the sake of definiteness , we take @xmath231 , @xmath232 , and @xmath233 . we point out that these parameters correspond to a strongly non - equilibrium distribution , obtained by shining a light pulse with fluence @xmath234 . finally , we note that , although in general the light - matter coupling is anisotropic , the he d has been shown to relax to an isotropic profile in @xmath235 @xcite . as we mentioned above , the description of these very early stages of the non - equilibrium dynamics , which comprise the buildup of the he d , is beyond the scope of the present article . here , we study the time evolution of the isotropic initial state ( [ eq : initialstate ] ) , as dictated by the sbe . the energies of the phonon modes are @xcite @xmath236 and @xmath237 . the epc of the @xmath238 phonon at the brillouin - zone center ( @xmath42 point ) , associated to the @xmath239 peak of the raman spectrum , is taken from ref . : this value , which we use in our numerical calculations , is in good agreement with experimental results @xcite . on the other hand , the value of the epc relative to the transverse mode at the @xmath43 point has been debated @xcite . the value calculated by density - functional theory @xcite is @xmath241 , but e - e interactions renormalize this value by a factor @xmath242 @xcite . in our numerical calculations we take @xmath243 . the epc of the longitudinal phonon mode at @xmath43 point is taken to be @xmath244 , as in ref . . following ref . , we take @xmath245 for the phenomenological phonon decay rate in eq . ( [ eq : phonon ] ) . fig07a(2,60)(a ) fig07b(2,60)(b ) fig08(2,60)(c ) fig09(2,60)(a ) fig10(2,60)(b ) we start by discussing the role of different screening models , and choose a strength of e - e interactions @xmath246 , appropriate @xcite for graphene on a sio@xmath247 substrate , see eq . ( [ eq : fsc ] ) . the corresponding sbe solution for undoped graphene is shown in panels ( a)(c ) of fig . [ fig : evolutiondistro ] for static , regularized , and dynamical screening , respectively . in all cases we see that the peak ( dip ) of the he d above ( below ) the dirac point shifts rapidly towards the dirac point . there is however a striking difference between panels ( a),(b ) and panel ( c ) : in dynamical screening , panel ( c ) , a much larger electron ( hole ) population persists in conduction ( valence ) band even at times as long as @xmath248 . the reason is that dynamical screening suppresses ar events , thus delays equilibration of the electron populations across the two bands . indeed , in the initial stage of the time evolution , auger processes are the most important processes for the equilibration of the electron populations . on a longer time scale , relaxation by phonon emission allows the system to reach inter - band equilibrium . however , in this case , the existence of a substantial inverted carrier population around the dirac point at times as long as @xmath249 is due to the suppression of ar processes . we point out that thermal equilibrium between the two bands , on the contrary , mainly occurs _ via _ inter - band scattering , and is reached after a much shorter time @xmath195 . a more quantitative analysis of the inter - band equilibration dynamics is shown fig . [ fig : thermalization ] . here we also report numerical results based on the regularized screening model . a fd distribution with time - dependent temperature @xmath250 and chemical potential @xmath251 [ @xmath252 in conduction ( valence ) band can be fitted to the numerical results from the solution of the isotropic sbe for @xmath253 . @xmath250 remains well above room @xmath194 for @xmath254 . in the absence of ar processes , a much faster cooling of the initial he d occurs , at the price of a larger chemical potential @xmath251 in conduction band . the energy stored in the electronic degrees of freedom is then transferred to the phonon modes and dissipated into the lattice by means of phonon - phonon interactions , responsible for the phenomenological decay term proportional to @xmath67 in eq . ( [ eq : phonon ] ) . eventually , equilibration with the lattice at room @xmath250 is achieved ( data not shown ) . figs . [ fig : evolutiondistro ] , [ fig : thermalization ] indicate that different screening models strongly affect the he d time evolution . per unit cell area and energy obtained from the numerical solution of the isotropic sbe as a function of energy @xmath255 ( in units of @xmath256 ) . black curves refer to @xmath257 . gray curves to @xmath248 . different line styles refer to the three screening models : static ( dashed lines ) , regularized ( solid lines ) , and dynamical ( dotted lines ) . the initial state at @xmath258 ( dash - dotted line ) was divided by a factor @xmath105 to fit into the frame of the figure.[fig : evolutiondensity ] ] time evolution of the differential transmission @xmath259 as calculated from the numerical solution of the sbe . different line styles refer to the three screening models : static ( dashed line ) , regularized ( solid line ) , and dynamical ( dotted line ) . the data in this figure refer to a probe energy @xmath260 . each curve is normalized to have maximum @xmath261 . note that dynamical screening gives a much slower time evolution since it completely suppresses auger scattering . ] in fig . [ fig : evolutiondensity ] we illustrate the dependence of the electron density per unit cell area and energy , @xmath262 on the energy @xmath255 . note that @xmath263 has dimensions @xmath264 . in eq . ( [ densityversusenergy ] ) @xmath265 is the 2d mdf density of states as a function of energy . the quantity @xmath266 represents the valley degeneracy . the energy at which @xmath263 peaks strongly depends on the screening model . the optical properties of the mdf system are very sensitive to the time evolution of @xmath263 since light absorption is strongly inhibited ( pauli blocking ) when the corresponding electronic transitions are towards states with a larger occupation . by shining a probe laser pulse with frequency @xmath267 through the sample one can measure the time evolution of the electron distribution , a procedure enabled by pauli blocking . a viable experimental route to directly measure the impact of screening is thus available , provided that short enough probe pulses of appropriate frequency are used @xcite . the propagation of the probe pulse through the sample can be quantified by calculating the differential transmission @xcite ( dt ) @xmath268~ , \nonumber \\\end{aligned}\ ] ] where @xmath269 is the fine - structure constant and @xmath225 and @xmath68 are the chemical potential and temperature of the electron system before the pump pulse is applied . the time evolution of the normalized dt is shown in fig . [ fig : transmission ] for the three screening models , at a fixed value of the probe energy @xmath270 . the much slower dynamics in the absence of auger processes ( dynamical screening , dotted line ) is clearly seen . the time @xmath271 at which the dt peaks is a convenient measure of the speed of the electron dynamics . below we discuss the dependence of @xmath271 on various relevant parameters , see fig . [ fig : maximumtransmission ] . as a function of wave vector @xmath272 ( in @xmath273 ) and time @xmath178 ( in units of @xmath274 ) , showing the distribution function @xmath275 for the transverse phonon mode at @xmath43 ( @xmath276 ) . the inset shows the same quantity at @xmath248.[fig : evolutionphonon ] ] although the focus of the present article is on the time evolution of the electron distribution function , for the sake of completeness in fig . [ fig : evolutionphonon ] we illustrate the time evolution of the distribution function of the transverse optical phonon mode at @xmath43 , i.e. the mode most strongly coupled to the electronic subsystem @xcite . in a sub-@xmath0 time a large population accumulates in the mode ( with respect to the equilibrium population ) and remains steady up to the maximum time @xmath248 considered here . this hot phonon distribution @xcite cools on a longer time scale as outlined in sec . [ ssec : timescales ] by anharmonic phonon - phonon interactions , which dissipate the thermal energy into the lattice . thus , electronic screening is responsible for qualitative modifications of the dynamics in the sub-@xmath0 time scale , which were not unveiled previously to the best of our knowledge . this early stage of the dynamics is temporally decoupled from other relaxation channels ( phonon and radiative emission ) , thus the effects of electronic screening do not modify the hot - electron relaxation picture as outlined in sec . [ ssec : timescales ] . at later times , our numerical results broadly agree with previous theoretical works @xcite . fig14(2,60)(a ) fig15(2,60)(b ) fig16(2,60)(a ) fig17(2,60)(b ) we now show that the results presented in the previous section are robust with respect to changes in parameter space . we find that , to a large extent , the speed of the relaxation dynamics in the sub-@xmath0 time range is controlled by the particular screening model one chooses . [ fig : maximumtransmission](a ) plots @xmath271 as a function of @xmath277 for two choices of the largest epc , @xmath278 , gray - shading the region in - between . the largest epc ( then used in all other figures ) yields the smallest @xmath271 , i.e. a faster relaxation dynamics . this is due to the fact that a larger coupling of the electrons to the phonon bath allows a more efficient dissipation of the excess energy . the dt peaks later for smaller energy , reflecting the shifting of the peak of the electron density @xmath263 towards the dirac point ( see fig . [ fig : evolutiondensity ] ) . the three screening models give quantitatively different results , with static screening remaining in the sub-@xmath0 range , and dynamical screening showing a much more pronounced dependence on electron energy . most importantly , there is very limited overlap between gray - shaded regions , meaning that the three screening models yield distinctly different relaxation speeds , even if the epc is increased by a factor @xmath104 . these results are robust with respect to doping : fig . [ fig : maximumtransmission](b ) , e.g. , illustrates essentially unchanged results for an @xmath223-doped sample , with a finite positive chemical potential @xmath279 . fig . [ fig : effectsee ] compares the time evolution of the electron density @xmath263 as calculated for @xmath246 , with results obtained for @xmath280 ( describing graphene on hexagonal boron nitride @xcite ) and @xmath281 , the maximum value corresponding to a suspended graphene @xcite . as expected , the broadening of the initial photo - excited electron distribution is faster for larger @xmath282 ( due to enhanced coulomb repulsion ) but , in general , @xmath263 at a given @xmath178 depends weakly on the e - e interaction strength . using regularized dynamical screening instead of static further reduces the effects of increasing @xmath282 . this behavior can be understood by recalling that electron thermalization takes place in a sub-@xmath283 time interval , as pointed out earlier @xcite . this means that the electron distribution rapidly reaches the form of a quasi - equilibrium fd distribution which nullifies the intra- and inter - band contributions of the collisional integral ( eq.[eq : finalboltzmann ] ) , as remarked in sec . [ ssec : screeningmodels ] as well . variations in the the e - e coupling constant , which multiplies the collisional integral , contribute minor corrections to the dynamics in the collisional regime . and _ static screening_. black ( gray ) lines refer to @xmath284 ( @xmath285 ) . solid ( dashed ) lines refer to results without ( with ) the exchange contribution to the scattering amplitude , second term in eq . ( [ eq : hf ] ) . the initial state at @xmath258 ( dash - dotted line ) is divided by a factor @xmath105 to fit into the frame of the figure.[fig : effectsexchange ] ] finally , fig . [ fig : effectsexchange ] shows the role of the exchange term @xmath286 in eq . ( [ eq : hf ] ) , by treating screening statically to ensure a particle - number - conserving collision integral . in this case @xmath287 is calculated at @xmath288 for the direct term and at @xmath289 for the exchange term . as clearly seen in fig . [ fig : effectsexchange ] , the exchange term is responsible for small corrections to the electron density @xmath263 , although it is expected @xcite that larger corrections may arise in a fermi liquid when perturbations are applied close to the fermi surface . we studied the non - equilibrium dynamics of a high - density photo - excited electron distribution in graphene . we used the massless dirac fermion model and a semiclassical boltzmann equation approach , which includes electron and optical phonon degrees of freedom . our approach neglects light - matter interactions in the very early stages of the dynamics ( before the electron distribution becomes isotropic ) , quantum effects ( coherences ) , and non - markovian memory effects . a quantitative analysis of these effects is beyond the scope of this work . taking into consideration light - matter interactions allowed us to describe the buildup of an anisotropic he d . calculated that the electron distribution evolves to an isotropic profile on a 10-fs timescale . we therefore decided for computational convenience to consider an isotropic distribution as initial condition for the semiclassical boltzmann equation , without loss of generality . we also assumed the pump pulse , which creates the initial he d , to be sufficiently short to neglect phonon - scattering - induced dephasing . indeed , it was experimentally shown @xcite that the latter effect should be considered when applying pump pulses with duration comparable to the electron - phonon scattering time , which exceeds the @xmath0 time scale of our present work . the effect of phonon - scattering - induced dephasing is to broaden the initial he d . we checked that our results are very stable with respect to changes of this type . the coulomb - scattering - induced broadening of the he d in the initial @xmath290 is much larger than the broadening due to phonons . we took into account both electron - electron and electron - phonon scattering during the whole time evolution , and showed that electron - phonon scattering does indeed play a minor role also in the initial , coulomb - scattering - dominated , stage of the dynamics . intra- and inter - band coherences were previously considered @xcite in the framework of the density - matrix formalism ( semiconductor bloch equations " ) . in the range of parameters we used here , the solution of the semiclassical boltzmann equation agrees with these results . taking coherences into consideration gives minor oscillations of the electron density ( analogous to the rabi oscillations in a two - level system @xcite ) , which damp out quickly due to dephasing induced by electron and phonon scattering . genuine quantum kinetic effects @xcite affect the dynamics on time scales of a few fs . to the best of our knowledge , quantum kinetic theory was never applied to ultrafast electron dynamics in graphene . although quantum kinetic effects are fundamental to describe the _ coherent buildup _ of screening @xcite , here we targeted the role of screening in the time window @xmath291 . the effects of screening on this time scale are a dominant contribution to the dynamics , and it is unlikely that a more precise description of the buildup of screening can substantially alter this picture . indeed , it is known @xcite that quasi - classical theories can be used to fit coulomb quantum kinetics on a timescale longer than @xmath283 . we also point out that it is an extremely difficult task to estimate _ a priori _ the short initial transient in which the coherent buildup of screening takes place . in an equilibrium state , basic consideration of the screening dynamics @xcite suggests that the buildup of screening , on a given length scale , should take place on a time scale comparable with the period of the plasma oscillations at the corresponding wavelength . this implies that coherent screening buildup is faster in systems with a large carrier density ( several hundreds @xmath44 ) , which corresponds to the parameters that we use in this work . however , the initial state that we consider is strongly displaced from equilibrium and the relation between coherent buildup of screening and carrier density is less clear . it is arguable that electron - electron scattering is much more effective in a non - equilibrium state than in a thermal state , thus the electron - scattering - induced dephasing further reduces the time span where coherent buildup of screening plays a relevant role . a second outcome of quantum kinetic theory is the ability to describe memory ( or non - markovian ) effects , which could play in principle an important role on ultrafast time scales . as discussed in ref . , the general effect of using a quantum kinetic equation is to introduce oscillations in the response of the system on very short timescales , typically of the order of @xmath274 in solid state systems . we focused here on the time window @xmath292 , where memory effects which survive for a few @xmath274 only are likely to be irrelevant . moreover , memory effects seem to be very important in systems with long - range coulomb interactions @xcite . in our system , instead , electron - electron interactions are well screened since we are studying the dynamics of a high - density droplet of excited carriers . in the case of effectively short - range interactions , memory effects are much less pronounced @xcite and seem to be more important at low energies @xcite . in graphene the density - of - states vanishes at low energies , therefore further suppressing them . thus , although our theory does not apply down to the few-@xmath274 time scale , where the coherent buildup of screening and memory effects take place , these effects do not change the dynamics in the window of interest , @xmath291 . in this time window we demonstrated that it is of utmost importance to have an accurate description of screening , which dominates the relaxation dynamics . an analytical treatment of the coulomb collision integral distinguishes our work from previous ones @xcite . in this respect , our main result , eq . ( [ eq : kernelintegralsimplified ] ) , expresses the coulomb collision integral in terms of a compact and computationally - convenient 1d integral over the modulus @xmath120 of the total momentum of a two - particle scattering process . this approach allows us to carefully deal with _ all _ the singularities that arise in the limit of collinear electron - electron scattering . different screening models have been analyzed , and their impact on the collinear scattering singularities elucidated . we also proposed a computationally - efficient way to take into account screening in eqs . ( [ eq : lindhardtwomu ] ) , ( [ eq : finalapproximation ] ) , which is fully quantitative after thermalization occurs . solving numerically the semiclassical boltzmann equation , we concluded that the particular form of screening one uses largely controls the speed of the relaxation dynamics in the sub-@xmath0 time range . different screening models yield markedly different time evolutions in a large portion of parameter space . our semi - analytical approach can be easily generalized to other carbon - based materials , such as bilayer and trilayer graphene and carbon nanotubes . we thank denis basko , annalisa fasolino , misha katsnelson , frank koppens , leonid levitov , allan macdonald , jairo sinova , justin song , and giovanni vignale for very useful and stimulating discussions . this work was supported by the italian ministry of education , university , and research ( miur ) through the program `` firb - futuro in ricerca 2010 '' grant no . rbfr10m5bt ( `` plasmograph : plasmons and terahertz devices in graphene '' ) , erc grants nanopot and stratus ( erc-2011-adg no . 291198 ) , eu grants rodin and genius , a royal society wolfson research merit award , epsrc grants ep / k017144/1 , ep / k01711x/1 , ep / go30480/1 and ep / g042357/1 , and the cambridge nokia research centre . we have made use of free software ( www.gnu.org , www.python.org ) . the electron energy states are discretized on a uniform mesh @xmath293 , centered around the dirac point . we take up to @xmath294 , with step @xmath295 . the wave vectors of the phonon modes are discretized on a matching mesh @xmath296 with @xmath297 . the phonon energies are approximated to a multiple of the energy step . the total number of variables , including spin and valley degeneracy for the electrons and the four phononic modes , is then @xmath298 . the sbe are first - order differential equations which are solved using a standard fourth - order runge - kutta algorithm @xcite , with a time step @xmath299 as small as @xmath300 . the kernels ( [ eq : phononkernels ] ) of the e - ph interactions are computed at the beginning of the time evolution . the largest computational burden is the evaluation of the coulomb kernel ( [ eq : coulombkernel ] ) , which scales cubically with the number of states @xmath301 . the coulomb kernel is updated at a variable rate , depending on the stage of the time evolution . for @xmath302 , when the system has not reached a thermal state yet , we update the kernel each @xmath303 . we use @xmath304 in the early cooling stage @xmath305 and @xmath306 afterwards . we checked that the numerical results do not depend on the specific choice of these parameters . before updating the coulomb kernel at time @xmath178 , we estimate @xmath194 and @xmath196 of the electron population in the two bands . to this end , we define the two functionals @xmath307 \equiv \int_{0}^{\infty } d\varepsilon \varphi(\varepsilon)$ ] and @xmath308 \equiv \int_{0}^{\infty } d\varepsilon \varphi(\varepsilon)^{2}$ ] . the values of the two functionals applied to the fd distribution can be computed exactly : @xmath309 & = & - k_{\rm b } t \ln{f(\mu;0,t ) } \nonumber \\ \phi_{2}[f(\varepsilon ; \mu , t ) ] & = & k_{\rm b } t \left [ f(\mu;0,t ) - 1 \right ] + \mu \nonumber \\ & & - k_{\rm b } t \ln{f(-\mu;0,t)}~.\end{aligned}\ ] ] we tabulated these values on a mesh of @xmath225 and @xmath194 . then , during the time evolution , we evaluate @xmath310 $ ] and @xmath311 $ ] . we then find the values @xmath225 and @xmath194 on the mesh which minimize @xmath312 - \phi_{i}[f(\varepsilon ; \mu , t)]|$ ] . this procedure yields our estimate for @xmath194 and @xmath313 , @xmath314 , with the advantage that can be applied automatically during the time evolution and is more robust than a standard fitting procedure . the consistency of the estimate for @xmath315 and @xmath194 is checked at the end of the time evolution using a more precise fitting procedure for the electron distribution . the values of @xmath196 and @xmath194 are used to compute @xmath216 , according to eq . ( [ eq : lindhardtwomu ] ) . the polarization function is evaluated on a 2d mesh for the modulus of the transferred wave vector @xmath77 [ with step @xmath316 and maximum value @xmath317 and frequency @xmath318 ( symmetric about @xmath219 , with @xmath319 ) . the integration over @xmath320 in eq . ( [ eq : lindhardtwomu ] ) is performed over a rather rough mesh with @xmath321 points up to @xmath322 using rectangles rule . this is sufficient to capture the effects of @xmath194 to good accuracy , as we tested by reproducing with this method the lindhard function at equilibrium @xcite . the procedure of regularization of the polarization function introduced in sec . [ ssec : screeningmodels ] is implemented by replacing @xmath216 with @xmath323 when @xmath324 $ ] below the light cone ( and similarly above the light cone ) . special care has to be taken when @xmath325 in the proximity of the origin . in this article we used @xmath326 . finally , the coulomb kernel is computed according to eqs . ( [ eq : kernelintegralsimplified ] ) and ( [ eq : augerresult ] ) . for each choice of the energies of the incoming and outgoing particles , and the modulus @xmath120 of the total momentum ( only one value is possible for auger processes ) the closer values for the transferred wave vector and frequency are matched on the mesh for the polarization function . for intra - band and inter - band terms , the integral over the total momentum is performed using the standard simpson rule @xcite mesh with @xmath327 points . before performing the integration , a change of variables is performed to an effective angle variable @xmath328 given by @xmath329 \cos\phi$ ] , to improve the precision of the integral at the extremes . to numerically avoid the collinear divergence we restrict the integration variable in the interval @xmath330 $ ] , where we take @xmath331 ( different choices over a few orders of magnitude do not contribute substantial changes to the results ) . the speed in solving the sbe with this method can be increased substantially by reducing @xmath301 , and the final results are qualitatively correct even with @xmath332 and @xmath333 although , in this case , the different phonon energies are not resolved . d. brida , a. tomadin , c. manzoni , y.j . kim , a. lombardo , s. milana , r.r . nair , k.s . novoselov , a.c . ferrari , g. cerullo , and m. polini , nature commun . 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we present a combined analytical and numerical study of the early stages ( sub-@xmath0 ) of the non - equilibrium dynamics of photo - excited electrons in graphene . we employ the semiclassical boltzmann equation with a collision integral that includes contributions from electron - electron ( e - e ) and electron - optical phonon interactions . taking advantage of circular symmetry and employing the massless dirac fermion ( mdf ) hamiltonian , we are able to perform an essentially analytical study of the e - e contribution to the collision integral . this allows us to take particular care of subtle collinear scattering processes processes in which incoming and outgoing momenta of the scattering particles lie on the same line including carrier multiplication ( cm ) and auger recombination ( ar ) . these processes have a vanishing phase space for two dimensional mdf bare bands . however , we argue that electron - lifetime effects , seen in experiments based on angle - resolved photoemission spectroscopy , provide a natural pathway to regularize this pathology , yielding a finite contribution due to cm and ar to the coulomb collision integral . finally , we discuss in detail the role of physics beyond the fermi golden rule by including screening in the matrix element of the coulomb interaction at the level of the random phase approximation ( rpa ) , focusing in particular on the consequences of various approximations including static rpa screening , which maximizes the impact of cm and ar processes , and dynamical rpa screening , which completely suppresses them .

rare @xmath8 decays involving flavour - changing - neutral - current ( fcnc ) transitions , such as @xmath12 and @xmath13 , have received a lot of theoretical interest @xcite , especially after the first measurements reported by the cleo collaboration @xcite of the @xmath14 decay . the current world average based on the improved measurements by the cleo @xcite , aleph @xcite and belle @xcite collaborations , @xmath15 , is in good agreement with the estimates of the standard model ( sm ) @xcite , which we shall take as @xmath16 , reflecting the parametric uncertainties dominated by the scheme - dependence of the quark masses . the decay @xmath14 also provides useful constraints on the parameters of the supersymmetric theories , which in the context of the minimal supersymmetric standard model ( mssm ) have been recently updated in @xcite . exclusive decays involving the @xmath12 transition are best exemplified by the decay @xmath17 , which have been measured with a typical accuracy of @xmath18 , the current branching ratios being @xcite @xmath19 and @xmath20 . these decays have been analyzed recently @xcite , by taking into account @xmath2 corrections , henceforth referred to as the next - to - leading - order ( nlo ) estimates , in the large - energy - effective - theory ( leet ) limit @xcite . as this framework does not predict the decay form factors , which have to be supplied from outside , consistency of nlo - leet estimates with current data constrains the magnetic moment form factor in @xmath17 in the range @xmath21 . these values are somewhat lower than the corresponding estimates in the lattice - qcd framework , yielding @xcite @xmath22 , and in the light cone qcd sum rule approach , which give typically @xmath23 @xcite . ( earlier lattice - qcd results on @xmath17 form factors are reviewed in @xcite . ) it is imperative to check the consistency of the nlo - leet estimates , as this would provide a crucial test of the ideas on qcd - factorization , formulated in the context of non - leptonic exclusive @xmath8-decays @xcite , but which have also been invoked in the study of exclusive rare @xmath8-decays @xcite . the exclusive decays @xmath4 , @xmath24 have also been studied in the nlo - leet approach in @xcite . in this case , the leet symmetry brings an enormous simplicity , reducing the number of independent form factors from seven to only two , corresponding to the transverse and longitudinal polarization of the virtual photon in the underlying process @xmath25 , called hereafter @xmath26 and @xmath27 . the same symmetry reduces the number of independent form factors in the decays @xmath1 from four to two . moreover , in the @xmath28-range where the large energy limit holds , the two set of form factors are equal to each other , up to @xmath3-breaking corrections , which are already calculated in specific theoretical frameworks . thus , knowing @xmath29 precisely , one can make theoretically robust predictions for the rare @xmath8-decay @xmath4 from the measured @xmath30 decay in the sm . the leet symmetries are broken by qcd interactions and the leading @xmath2 corrections in perturbation theory are known @xcite . in this talk we present the results of @xcite , where a systematic analysis of the various independent helicity amplitudes in the decays @xmath4 and @xmath1 were performed in the nlo accuracy in the large energy limit . we recall that a decomposition of the final state @xmath31 in terms of the helicity amplitudes @xmath32 and @xmath33 , without the explicit @xmath2 corrections , was undertaken in a number of papers @xcite . combining the analysis of the decay modes @xmath4 and @xmath1 , we show that the ratios of differential decay rates involving definite helicity states , @xmath10 and @xmath34 , can be used for testing the sm precisely . at the quark level , the rare semileptonic decay @xmath35 can be described in terms of the effective hamiltonian @xmath36 where @xmath37 are the ckm matrix elements @xcite and @xmath38 is the fermi coupling constant . following the notation and the convention used in ref . @xcite , the above hamiltonian leads to the following free quark decay amplitude and the hat denotes normalization in terms of the @xmath8-meson mass , @xmath39 , e.g. @xmath40 , @xmath41 . ] : @xmath42 [ \bar{\ell } \gamma^{\mu } \l ] \label{eq : m}\\ & & \hspace{-1.5 cm } + c_{10 } [ \bar{s } \gamma_{\mu } l b ] [ \bar{\ell } \gamma^\mu \gamma_5 \l ] - 2 \hat{m_{b } } c_{7}^{\bf eff } [ \bar{s } i \sigma_{\mu \nu } { \hat{q^{\nu}}\over\hat{s } } r b ] [ \bar{\l } \gamma^{\mu } \l ] \big\ } .\nn\end{aligned}\ ] ] here , @xmath43 , @xmath44 , @xmath45 $ ] and @xmath46 , where @xmath47 are the four - momenta of the leptons . since we are including the next - to - leading corrections into our analysis , we will take the nlo @xmath48 definition of the @xmath49-quark mass @xmath50 and the wilson coefficients in next - to - leading - logarithmic order given in table 1 in @xcite . exclusive @xmath51 transitions stands for the corresponding vector meson . ] are described by the matrix elements of the quark operators in eq . ( [ eq : m ] ) over meson states , which can be parameterized in terms of the full qcd form factors ( called in the literature @xmath52 ) . however , the factorization ansatz enables one to relate in the restricted kinematic region decay , this region is identified as @xmath53 . ] , the form factors in full qcd and the two corresponding leet form factors , namely @xmath54 and @xmath55 @xcite ; @xmath56 where the quantities @xmath57 @xmath58 encode the perturbative improvements of the factorized part @xmath59 and @xmath60 is the hard spectator kernel ( regulated so as to be free of the end - point singularities ) , representing the non - factorizable perturbative corrections , with the direct product understood as a convolution of @xmath60 with the light - cone distribution amplitudes of the @xmath8 meson ( @xmath61 ) and the vector meson ( @xmath62 ) . with this ansatz , it is a straightforward exercise to implement the @xmath2-improvements in the various helicity amplitudes . for further details we refer to @xcite . lacking a complete solution of non - perturbative qcd , one has to rely on certain approximate methods to calculate the above form factors . we take the ones given in @xcite , obtained in the framework of light - cone qcd sum rules . the corresponding leet form factors @xmath63 and @xmath64 are illustrated in ref .@xcite . the range @xmath65 is determined by the @xmath66 decay rate , calculated in the leet approach in nlo order @xcite and current data . this gives somewhat smaller values for @xmath67 and @xmath68 than the ones estimated with the qcd sum rules . using the @xmath70 helicity amplitudes @xcite , namely @xmath71 , the dilepton invariant mass spectrum reads @xmath72 where @xmath73 $ ] . using the input parameters presented in @xcite , we have plotted in fig . ( [ figdbrk * ] ) , the dilepton invariant mass spectrum @xmath74 and the total dilepton invariant mass , showing in each case the leading order and the next - to - leading order results . -0.8 cm @xmath75 @xmath76 + -0.8 cm @xmath77 @xmath78 as can be seen from fig . ( [ figdbrk * ] ) the total decay rate is dominated by the contribution from the helicity @xmath79 component , whereas the contribution proportional to the helicity amplitude @xmath80 is negligible . the next - to - leading order correction to the lepton invariant mass spectrum in @xmath81 is significant in the low dilepton mass region ( @xmath82 gev@xmath83 ) , but small beyond that shown for the anticipated validity of the leet theory ( @xmath84 gev@xmath83 ) . theoretical uncertainty in our prediction is mainly due to the form factors , and to a lesser extent due to the parameters @xmath85 and the @xmath8-decay constant , @xmath86 . besides the differential branching ratio , @xmath4 decay offers other distributions ( with different combinations of wilson coefficients ) to be measured . an interesting quantity is the forward - backward ( fb ) asymmetry defined in @xcite @xmath87 where the kinematic variable @xmath88 . , @xmath89 , with @xmath90 and @xmath91 . ] our results for fba are shown in fig . [ figfba ] in the lo and nlo accuracy . at the lo the location of the fb - asymmetry zero is @xmath92 , which is substantially shifted at the nlo by @xmath93 leading to @xmath94 . we essentially confirm the results obtained in the nlo - leet context by _ beneke et al . the helicity amplitudes for @xmath96 , namely @xmath97 , can in turn be related to the two axial - vector form factors , @xmath98 and @xmath99 , and the vector form factor , @xmath100 , which appear in the hadronic current @xcite . the @xmath101 total branching decay rate ] can be expressed in terms of the corresponding helicity amplitudes as @xcite @xmath102 the contributions from the @xmath103 , @xmath104 , @xmath105 and the total are shown in fig . ( [ dbhrho ] ) . contrary to the @xmath106 decay rate , the @xmath107 decay is dominated by the helicity-0 component . the impact of the nlo correction on the various branching ratios in @xmath108 is less significant than in the @xmath109 decay , reflecting the absence of the penguin - based amplitudes in the former decay . to dilepton invariant mass distributions for @xmath95 at nlo order ( solid center line ) and lo ( dashed).the band reflects the theoretical uncertainties from input parameters.__,title="fig:",width=143,height=113 ] 0.8 cm @xmath110 to dilepton invariant mass distributions for @xmath95 at nlo order ( solid center line ) and lo ( dashed).the band reflects the theoretical uncertainties from input parameters.__,title="fig:",width=143,height=113 ] + -0.5 cm @xmath111 to dilepton invariant mass distributions for @xmath95 at nlo order ( solid center line ) and lo ( dashed).the band reflects the theoretical uncertainties from input parameters.__,title="fig:",width=143,height=113 ] 0.8 cm @xmath112 to dilepton invariant mass distributions for @xmath95 at nlo order ( solid center line ) and lo ( dashed).the band reflects the theoretical uncertainties from input parameters.__,title="fig:",width=143,height=113 ] concerning the @xmath107 form factors , one has to consider the su(3)-breaking effects in relating them to the corresponding form factors in @xmath4 . for the form factors in full qcd , they have been evaluated within the qcd sum - rules @xcite . these can be taken to hold also for the ratio of the leet form factors . thus , we take @xmath113 while admitting that this is a somewhat simplified picture , as the effect of @xmath3-breaking is also present in the @xmath114-dependent functions , but checking numerically the functions resulting from eq . ( [ eq : paraball ] ) with the ones worked out for the full qcd form factors in the qcd sum - rule approach in @xcite , we find that the two descriptions are rather close numerically in the region of interest of @xmath114 . the measurement of exclusive @xmath116 decays is one of the major goals of b physics . it provides a good tool for the extraction of @xmath117 , provided the form factors can be either measured precisely or calculated from first principles , such as the lattice - qcd framework . to reduce the non - perturbative uncertainty in the extraction of @xmath29 , we propose to study the ratios of the differential decay rates in @xmath1 and @xmath118 involving definite helicity states . these @xmath114-dependent ratios @xmath119 , @xmath120 are defined as follows : @xmath121 the ratio @xmath10 suggests itself as the most interesting one , as the form factor dependence essentially cancels . from this , one can measure the ratio @xmath122 . in fig . [ rvub ] , we plot @xmath10 and @xmath34 for three representative values of the ckm ratio @xmath123 , @xmath124 , and @xmath125 . ( left - hand plot ) and @xmath9 ( right - hand plot ) with three indicated values of the ckm ratio @xmath126 . the bands reflect the theoretical uncertainty from @xmath127 and @xmath128.__,title="fig:",width=143,height=113 ] ( left - hand plot ) and @xmath9 ( right - hand plot ) with three indicated values of the ckm ratio @xmath126 . the bands reflect the theoretical uncertainty from @xmath127 and @xmath128.__,title="fig:",width=143,height=113 ] however , as we remarked earlier , the ratio @xmath10 may be statistically limited due to the dominance of the decay @xmath1 by the helicity-@xmath129 component . hence , we also show the ratio @xmath34 , where the form factor dependence does not cancel . for the leet form factors used here , the compounded theoretical uncertainty is shown by the shaded regions . this figure suggests that high statistics experiments may be able to determine the ckm - ratio from measuring @xmath34 at a competitive level compared to the other methods _ en vogue _ in experimental studies . in order to look for new physics in @xmath131 , we propose to study the ratio @xmath132 , introduced in eq . ( [ ratio ] ) . to illustrate generic susy effects in @xmath133 , we note that the wilson coefficients @xmath134 , @xmath135 , @xmath136 and @xmath137 receive additional contributions from the supersymmetric particles . we incorporate these effects by assuming that the ratios of the wilson coefficients in these theories and the sm deviate from 1 . these ratios are defined as follows : @xmath138 they depend on the renormalization scale ( except for @xmath137 ) , for which we take @xmath139 . for the sake of illustration , we use representative values for the large(small)-@xmath140 sugra model , in which the ratios @xmath141 and @xmath142 actually change ( keep ) their signs . the supersymmetric effects on the other two wilson coefficients @xmath136 and @xmath137 are generally small in the sugra models , leaving @xmath143 and @xmath144 practically unchanged from their sm value . to be specific , we take @xmath145 ( @xmath146 ) . in the sm with @xmath147 , @xmath148 , @xmath149 and in sugra , with @xmath150 ( left - hand plots ) and @xmath151 ( right - hand plots ) . the sm and the sugra contributions are represented respectively by the shaded area and the solid curve . the shaded area depicts the theoretical uncertainty on @xmath152 and on @xmath128.__,title="fig:",width=143,height=113 ] in the sm with @xmath147 , @xmath148 , @xmath149 and in sugra , with @xmath150 ( left - hand plots ) and @xmath151 ( right - hand plots ) . the sm and the sugra contributions are represented respectively by the shaded area and the solid curve . the shaded area depicts the theoretical uncertainty on @xmath152 and on @xmath128.__,title="fig:",width=143,height=113 ] + in the sm with @xmath147 , @xmath148 , @xmath149 and in sugra , with @xmath150 ( left - hand plots ) and @xmath151 ( right - hand plots ) . the sm and the sugra contributions are represented respectively by the shaded area and the solid curve . the shaded area depicts the theoretical uncertainty on @xmath152 and on @xmath128.__,title="fig:",width=143,height=113 ] in the sm with @xmath147 , @xmath148 , @xmath149 and in sugra , with @xmath150 ( left - hand plots ) and @xmath151 ( right - hand plots ) . the sm and the sugra contributions are represented respectively by the shaded area and the solid curve . the shaded area depicts the theoretical uncertainty on @xmath152 and on @xmath128.__,title="fig:",width=143,height=113 ] in fig . [ rsmetsugra ] , we present a comparative study of the sm and sugra partial distribution for @xmath153 and @xmath154 . in doing this , we also show the attendant theoretical uncertainties for the sm , worked out in the leet approach . for these distributions , we have used the form factors from @xcite with the su(3)-symmetry breaking parameter taken in the range @xmath155 . from fig . [ rsmetsugra]-_left - hand plots _ , where @xmath156 , it is difficult to work out a signal of new physics from the sm picture . there is no surprise to be expected , due to the fact that in these scenario the corresponding ratio @xmath157 is approximatively one , which makes the sugra picture almost the same as in the sm one . however , fig . [ rsmetsugra]-_right - hand plots _ with @xmath158 illustrates clearly that despite non - perturbative uncertainties , it is possible , in principle , in the low @xmath114 region to distinguish between the sm and a sugra - type models , provided the ratios @xmath157 differ sufficiently from 1 . in this talk , we have reported an @xmath2-improved analysis of the various helicity components in the decays @xmath4 and @xmath1 , carried out in the context of the large - energy - effective - theory . the results presented here make use of the form factors calculated in the qcd sum rule approach . the leet form factor @xmath159 is constrained by current data on @xmath160 . as the theoretical analysis is restricted to the lower part of the dilepton invariant mass region in @xmath4 , typically @xmath84 gev@xmath83 , errors in this form factor are not expected to severely limit theoretical precision . this implies that distributions involving the @xmath161 helicity component can be calculated reliably . precise measurements of the two leet form factors @xmath162 and @xmath163 in the decays @xmath1 can be used to largely reduce the residual model dependence . with the assumed form factors , we have worked out a number of single ( and total ) distributions in @xmath164 , which need to be confronted with data . we also show the @xmath2 effects on the fb - asymmetry , confirming essentially the result found in @xcite . combining the analysis of the decay modes @xmath4 and @xmath1 , we show that the ratios of differential decay rates involving definite helicity states , @xmath10 and @xmath34 , can be used for testing the sm precisely . we work out the dependence of these ratios on the ckm matrix elements @xmath165 . we have also analyzed possible effects on these ratios from new physics contributions , exemplified by representative values for the effective wilson coefficients in sugra models . finally , we remark that the current experimental limits on @xmath166 decay ( and the observed @xmath167 and @xmath168 decays ) @xcite are already probing the sm - sensitivity . with the integrated luminosities over the next couple of years at the @xmath8 factories , the helicity analysis in @xmath1 and @xmath4 decays presented here can be carried out experimentally . it is a great pleasure to thank ahmed ali for the fruitful collaboration and useful remarks on the manuscript . for the work presented here , i also gratefully acknowledge desy for financial support . 99 a. ali and a. s. safir , [ hep - ph/0205254 ] . see , e.g. , c. greub , talk given at the 8th international symposium on heavy flavour physics , southampton , england , 25 - 29 jul 1999 . 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we calculate the independent helicity amplitudes in the decays @xmath0 and @xmath1 in the so - called large - energy - effective - theory ( leet ) . taking into account the dominant @xmath2 and @xmath3 symmetry - breaking effects , we calculate various single ( and total ) distributions in these decays making use of the presently available data and decay form factors calculated in the qcd sum rule approach . differential decay rates in the dilepton invariant mass and the forward - backward asymmetry in @xmath4 are worked out . measurements of the ratios @xmath5 , involving the helicity amplitudes @xmath6 , @xmath7 , as precision tests of the standard model in semileptonic rare @xmath8-decays are emphasized . we argue that @xmath9 and @xmath10 can be used to determine the ckm ratio @xmath11 and search for new physics , where the later is illustrated by supersymmetry .

By By Kim I. Hartman May 22, 2010 in Entertainment Tampa - Hulk Hogan is back in federal court in Florida, this time over a cartoon commercial. Hulk claims his reputation was harmed in a Cocoa Pebbles ad featuring Bamm-Bamm tossing " Hulk Boulder" into the air and winning the match. Hogan, whose real name is Terry Bollea, is suing the maker of In the "Cocoa Smashdown" commercial, a cartoon character resembling Hogan easily beats Fred and Barney inside the ring. But then Bamm-Bamm steps in and pounds the blond-haired, mustachioed wrestler to bits. Hulk, the federal lawsuit states, "is shown humiliated and cracked into pieces with broken teeth, with the closing banner, 'Little Pieces…BIG TASTE!'" The commercial character goes by the name "Hulk Boulder," which Hogan's lawsuit says is a name he used early in his career until wrestling promoter Vince McMahon decided he should have an Irish name. The lawsuit says Post Foods never sought or received Hogan's permission to use his likeness to promote the cereal. Hogan says he raised his objections with Post in August, but the ads continued. The wrestler contends he has been harmed by, among other things, "the unauthorized and degrading depictions in the Cocoa Smashdown advertisements." Hogan has recently been in the news when he Hogan blames Wells Fargo and claims he was inadequately insured when his teenage son, Nick Bollea, got into a Hulk Hogan is going to the mat against The Flintstones, reports Tampa Bay Online. Hogan, whose real name is Terry Bollea, is suing the maker of Cocoa Pebbles, Post Cereal , accusing the company of appropriating his image in commercials for the cereal.In the "Cocoa Smashdown" commercial, a cartoon character resembling Hogan easily beats Fred and Barney inside the ring. But then Bamm-Bamm steps in and pounds the blond-haired, mustachioed wrestler to bits.Hulk, the federal lawsuit states, "is shown humiliated and cracked into pieces with broken teeth, with the closing banner, 'Little Pieces…BIG TASTE!'"The commercial character goes by the name "Hulk Boulder," which Hogan's lawsuit says is a name he used early in his career until wrestling promoter Vince McMahon decided he should have an Irish name.The lawsuit says Post Foods never sought or received Hogan's permission to use his likeness to promote the cereal. Hogan says he raised his objections with Post in August, but the ads continued.The wrestler contends he has been harmed by, among other things, "the unauthorized and degrading depictions in the Cocoa Smashdown advertisements."Hogan has recently been in the news when he filed suit in state court , that was later moved to Federal Court against Wells Fargo Insurance for failing to upgrade his coverage when his exposure to risk grew.Hogan blames Wells Fargo and claims he was inadequately insured when his teenage son, Nick Bollea, got into a wreck that grievously injured passenger John Graziano . Hogan settled a lawsuit with the seriously injured victim Graziano in February. More about Hulk, Hogan, Bollea, Wwf, Wrestling More news from hulk hogan bollea wwf wrestling wrestler car accident divorce flintstones cocoa pebbles federal court florida legal terry terrybollea cocoasmashdown smashdown bammbamm bamm post cereal wells fargo insurance ||||| TBO > News > Breaking News Yabba-Dabba-Sue! Hulk Hogan files suit against Cocoa Pebbles maker Hulk Hogan says this character from a Cocoa Pebbles commercial was based on his likeness. TAMPA - Hulk Hogan is going to the mat against The Flintstones. Hogan, whose real name is Terry Bollea, is suing the maker of Cocoa Pebbles, accusing the company of appropriating his image in commercials for the cereal. In the "Cocoa Smashdown" commercial, a cartoon character resembling Hogan easily beats Fred and Barney inside the ring. But then Bamm-Bamm steps in and pounds the blond-haired, mustachioed wrestler to bits. Hulk, the federal lawsuit states, "is shown humiliated and cracked into pieces with broken teeth, with the closing banner, 'Little Pieces…BIG TASTE!'" The commercial character goes by the name "Hulk Boulder," which Hogan's lawsuit says is a name he used early in his career until wrestling promoter Vince McMahon decided he should have an Irish name. The lawsuit says Post Foods never sought or received Hogan's permission to use his likeness to promote the cereal. Hogan says he raised his objections with Post in August, but the ads continued. Hogan says he is marketing his own products, including the Hogan Energy drink and Hulkster Burgers, a line of microwaveable hamburgers and chicken sandwiches sold at Walmart. The wrestler contends he has been harmed by, among other things, "the unauthorized and degrading depictions in the Cocoa Smashdown advertisements." A Post spokesperson could not immediately be reached for comment. Reporter Elaine Silvestrini can be reached at (813) 259-7837. Share this:

– Hulk Hogan is back in federal court in Florida, this time over a cartoon commercial. Hulk claims his reputation was harmed in a "Cocoa Smashdown" featuring Hulk Boulder vs Fred and Barney when Bamm-Bamm steps in, tosses him into the air, and wins the match. Hulk is suing Post cereal over the use of the look-a-like character, reports the Tampa Tribune. More details at Digital Journal here.

stochastic resonance ( sr ) @xcite is the best - known example of the constructive role of noise . the sr is a phenomenon in which the response of a system is optimized by the presence of a specific level of noise . it has been detected in so many seemingly different systems that it has been claimed to be `` an inherent property of rate - modulated series of events '' @xcite . it has been recently suggested that the functioning of important natural devices , e.g. , communication and information processing in neural systems or subthreshold signal detection in biological receptors , rely on phase synchronization rather than stochastic resonance @xcite , but this does not exclude the possibility that some natural devices may rely on the sr or that effective artificial detectors that use this feature may be constructed and operated . it has been observed that the sr gets enhanced if an array of similar nonlinear elements collectively responds to the same signal . this phenomenon has been termed the array enhanced stochastic resonance ( aesr ) . it was first observed in chains of nonlinear oscillators @xcite and later , mostly without explicitly using the term aesr , in arrays of fritzhugh - nagumo model neurons @xcite , in ion channels @xcite , in ensembles of nondynamical elements with internal noise independent on the incoming signal or modulated by it @xcite , in multilevel threshold systems @xcite , in a globally coupled network of hodgkin - huxley model neurons @xcite , and , recently , in arrays of josephson junctions @xcite . the experimental work on detecting the sr in the mammalian brain tissue @xcite should also be mentioned as a whole _ array _ of neurons was stimulated . the accumulated knowledge of systems exhibiting the aesr is now considerable , but there are still important issues that need to be clarified . we want to address two such points in the present paper . first , in nearly all papers mentioned above , the specific dynamics the `` internal '' dynamics of systems such as nonlinear oscillators or model neurons , or dynamical coupling between various elements played an important role . it is thus not entirely clear what features of the aesr are generic , and what depends on the details of interactions . we will discuss the aesr in arrays of nondynamical threshold elements . such elements , first introduced in ref . @xcite and later discussed in refs . @xcite , are known to display the sr when subjected to a periodic subthreshold signal with an additive noise . the aesr , if indeed present in such an array , is not obscured by any effects resulting from a specific dynamical model , and only its generic features should show up . the interesting research presented in ref . @xcite already considered the aesr in ensembles of nondynamical elements , but we want to re - examine this problem because of the special treatment of noises in ref . @xcite see a discussion below . second , the role of spatial correlations between the noises has been almost neglected in the existing research on the aesr . the noises discussed were local and uncorrelated in refs . @xcite , global in ref . @xcite , and in the form of a mixture of uncorrelated local and global noises in refs . @xcite . as correlations between various noises can result in very interesting physical phenomena , ranging from drastic changes in activation rates @xcite , through current reversal in brownian ratchets @xcite , to an effective nullifying one of the noises @xcite , and many others , it is interesting to examine their impact on the aesr . the authors of ref . @xcite claimed that spatial correlations between the noises weakened the response of an array of neurons , but the spatial correlations discussed there were induced by the presence of a global noise . we will show that spatial correlations between _ local _ noises can have a constructive effect . this paper is organized as follows : in section ii we present numerical results for arrays of uncoupled threshold elements . in section iii we discuss the role of spatial correlations between the noises in a chain of nonlinear oscillators . concluding remarks are given in section iv . a single threshold device fires whenever the signal on its input exceeds the threshold . here we consider an array of @xmath0 such devices , acting in parallel in response to a common signal ; the average ( or integrated ) output of all individual devices is taken as the output of the whole array : [ aesr : array ] @xmath1 here @xmath2 is the frequency of the signal ( we take @xmath3 ) , @xmath4 is the initial phase , and @xmath5 is the amplitude ; we take @xmath6 to make the signal subthreshold . @xmath7 is the output of the array and @xmath8 are the noises . we take them to be zero - mean gaussian white noises ( gwns ) , possibly spatially correlated : @xmath9 the matrix @xmath10 $ ] represents spatial correlations of the noises . it must be symmetric and positively definite . @xmath11 is a parameter controlling the intensity of the noises . this system is similar to , but different from that discussed in the first part of ref . @xcite , where the local noise was added to the output of each element _ after _ the element had decided whether to fire in a response to the signal contaminated by a global noise . thus , the output of a single element was not binary . rather than that , it could assume , in principle , any value , positive or negative . moreover , as all elements received identical inputs , they all fired or not fired in unison . after an appropriate scaling , the collective output of the whole array was equivalent to a binary series contaminated by a gwn . the local noises in ref . @xcite were , by assumption , spatially uncorrelated . in our approach , the internal noise is added to the signal at each site _ before _ the threshold elements make their decisions whether to fire or not . the internal noise represents fluctuations in the connections or environmentally induced random perturbations , but the output of every threshold element remains binary . . ] we also start with uncorrelated , or local , noises , @xmath12 . we calculate the signal and the noises with a time step @xmath13 and calculate the output of the nondynamical system . we use marsaglia algorithm @xcite to generate the gwns ; we use the famous mersenne twister @xcite as the underlying uniform generator . for each array , we collect a time series of 4096 elements , calculate its power spectrum and calculate the signal - to - noise ratio ( snr ) : @xmath14 for each @xmath0 and @xmath15 we average the results over 512 realizations of the noises and initial phases of the signal . final results are presented in fig . [ aesr : fig - aesr ] and their interpretation is clear : the snr increases significantly for all noise strengths as the array size doubles . we can see that the aesr is not a result of any specific dynamics but is present also in arrays of uncoupled elements . this , together with previous results for coupled systems , shows that the aesr is a generic feature of arrays of elements that individually display the sr . note that we have observed the aesr for a _ local _ noise . if the noise were _ global _ , @xmath16 ( or @xmath17 ) , no array enhancement would be possible . indeed , for a global noise , each element of the array receives identical input , and the collective output of the whole array is identical with that of a single element . the array does not display the aesr , but only the conventional sr . this simple argument shows that it is the differences between the noises at different sites that cause the aesr . this observation leads to the question of the role of spatial correlation between the noises . qualitatively speaking , noises with large correlations are `` nearly identical '' and the enhancement of the sr should be small . the enhancement of the sr should increase as the correlations decrease . we will now see that this is indeed the case . let @xmath18 be the cholesky decomposition @xcite of the correlation matrix @xmath19 and let @xmath20 be a vector of spatially uncorrelated , zero mean gwns , @xmath21 . then @xmath22 has correlations of the form . in the following , we will consider only correlations between the nearest neighbors in the array of threshold elements . specifically , @xmath23 where @xmath24 in order to keep the matrix @xmath19 positively definite . for each specific value of @xmath15 , the cholesky decomposition needs to be performed only once ; later , during the simulation , vectors of independent gaussian variables are generated and multiplied by the cholesky factor @xmath25 . since for a tridiagonal correlation matrix @xmath19 , the cholesky factor has only two non - zero elements per row , generating gwns with nearest - neighbor correlations is only twice as computationally expensive as generating independent gwns , or even less than that given the fact that generating the independent gaussian variables is the most computationally intensive part of the procedure . we now simulate the system in the manner described above for various values of @xmath15 . results for an array of @xmath26 elements are plotted in fig . [ aesr : fig - near ] . we can see that noises with positive spatial correlations lead to a smaller enhancement of sr than the independent noises . on the other hand , the snr increases as @xmath15 becomes negative and approaches @xmath27 . the effect of negative correlations ( anticorrelations ) becomes larger as the noise strength increases . similar results have been observed for arrays of different lengths . , @xmath28 , @xmath29 , @xmath30 , and @xmath31 , respectively . the array consists of 128 threshold devices . ] and the strength @xmath11 of the additional noise applied to the array . the additional noise has spatial correlations in the form with @xmath32 , and the array size @xmath33 . ] clean signals are rare in nature . suppose that the incoming signal is contaminated by a noise that can not be controlled . to improve detection of this signal , we pass it through an array of threshold elements and we apply additional noise that we can control to each of the elements . the external noise acts here as a global noise ; the additional ( local ) noise is not correlated to the global noise . the above discussion suggests that the additional noise should have negative spatial correlations . if the global noise is weak ( below the peak of the ordinary sr ) , the additional anticorrelated noise can significantly enhance the snr , fig . [ aesr : fig - addnoise ] . however , if the global noise is large , the enhancement provided by the array is only marginal . this is similar to the result reported in ref . @xcite , where the presence of a strong global noise markedly deteriorated the performance of the system studied . it is important to understand the `` microscopic '' mechanism responsible for the aesr . in the conventional sr , the threshold element may occasionally misfire or miss some peaks of the signal , cf . [ aesr : fig - panels]a . also the shape of the incoming signal is not resolved by the outgoing binary signal . when an array of such elements acts in parallel , if one of the elements makes a mistake ( fires when the signal is low or fails to fire when the signal is strong ) , other elements that are not positively correlated with it are not likely to repeat the mistake ( figs . [ aesr : fig - panels]b and c ) . this effect is even stronger when the other elements are negatively correlated with the one that makes the mistake : negative correlations between noises at different sites tend to correct the mistakes , while positive correlations tend to repeat them . as a result , the shape of the incoming signal is resolved much better . this does not lead to a visible increase in the height of the signal peak in the power spectrum , but it does lead to a significant decrease of the noise background , fig . [ aesr : fig - panels ] , bottom row . thus , lowering of the flat noise background is primarily responsible for the increase in the snr . on a more formal level , let @xmath34 be the probability that a single element fires . this probability depends on the current phase of the incoming signal , on the signal s amplitude , and on the noise level . if exactly @xmath35 out of @xmath0 elements fire , the array s output equals @xmath36 . if the noises at different sites are mutually independent ( uncorrelated ) , the probability of such an event is given by the binomial distribution : [ aesr : binomial ] @xmath37 in an array twice as large with other parameters the same , exactly @xmath38 elements should fire to produce the same output . the probability of this event is @xmath39 the distributions have the same expectation values @xmath40 , but for all values of @xmath41 the distribution is narrower than the distribution . more importantly , the distribution , corresponding to the larger array , allows for a more dense output , with values @xmath42 being more probable than @xmath43 etc . consequently , in larger arrays , wildly `` wrong '' outputs are less probable . this leads to lowering of the noise background and to an increase of the snr . if the noises are spatially correlated , the probability that exactly @xmath35 elements fire is no longer given by the binomial distribution . we have not been able to derive an exact formula for this probability , but the general mechanism of the snr increase with the array size appears to be similar to that for the uncorrelated noises . note that for the case presented in fig . [ aesr : fig - panels ] , introducing the maximal negative correlations between the nearest neighbors lowers the background by a factor of the order of 2 , increasing the snr by @xmath44 db , or about 10% of the total . in order to verify whether similar effects are present in coupled systems , we consider the same system that was discussed in ref . @xcite where the aesr was first observed . namely , we consider a chain of overdamped , coupled , nonlinear ( double well ) oscillators @xmath45 where @xmath46 , @xmath47 , @xmath48 ( these are the values used in ref . @xcite ) , @xmath3 , @xmath4 is the initial phase of the signal , and @xmath49 are gwns , possibly spatially correlated according to . if the system responds to the external periodic stimulation , the central oscillator switches between the two wells in synchrony with the stimulation . we show results for the `` extreme '' cases of a global noise , a local ( uncorrelated ) noise , and noises maximally correlated and anticorrelated between the nearest neighbors . the noises are generated by the algorithm presented in the preceding section . we choose a chain of a modest length of @xmath50 , integrate the equations numerically using the heun scheme @xcite with a time step @xmath51 and analyze the behavior of the central oscillator . we filter the analog time series to generate the time series of @xmath52 , reflecting which well the oscillator is in . from the power spectrum of the binary time series we calculate the snr and average over 64 realizations of the noises and the initial phases of the signal . results are presented in fig . [ aesr : fig - coupled ] . as we can see , for low noises the snr curves display rather wild oscillations , but for larger noises the effect is much the same as for the nondynamical system discussed above : as the correlations decrease , the snr maximum shifts towards higher noise levels . the maximal value , as well as values for large noise levels , are the largest for the noise maximally anticorrelated between the nearest oscillators and the smallest for the global noise . this effect grows as the coupling strength increases . a more thorough analysis shows that for large noise intensities , and increase in the snr is again achieved mainly by lowering the noise background . note that in case of the global noise , the response practically does not change with the coupling strength . in this case , all the oscillators receive identical inputs and there is no aesr , but only the ordinary sr , exactly as in the nondynamical system . to understand the mechanism that is responsible for the aesr in this case , observe that the oscillators exchange energy via the elastic coupling . we calculate the change in the elastic energy between two neighboring oscillators that occurs during a time interval @xmath53 , @xmath54 , where @xmath55 . to the lowest order in @xmath56 , @xmath57 , where @xmath58 has contributions from the elastic interactions , the nonlinear part of the potential , the external signal , and the noise . if either the coupling constant @xmath59 is large , or the oscillator happens to be in the vicinity of the barrier between the wells , the nonlinear part may be neglected . straightforward calculations show that the noises contribute to the expectation value @xmath60 a term equal to @xmath61 . we can see that noises with negative correlations maximize this contribution : noises with negative correlations tend to pull the neighboring oscillators in the opposite directions , thus maximizing the energy transfer between the oscillators and providing one of the oscillators with the extra energy needed to cross the barrier . this simple argument explains why the aesr grows when the coupling strength increases , why the aesr is larger for anticorrelated noises , and why the system with a global noise , corresponding to @xmath62 , does not display the aesr . note that if the coupling were repulsive , the situation would be the opposite . the effects that the correlations have on the spatiotemporal synchronization of the system will be discussed separately . we have discussed the aesr in arrays of nondynamical threshold elements . we have not observed any saturation of the snr curves that was reported previously in ref . however , the input signal in that reference was aperiodic and the output snr is not a natural measure for such signals @xcite . this problem has been already discussed @xcite . we have shown in the present paper that for arrays of nondynamical elements , noises with negative spatial correlations lead to an enhancement of the aesr . in case of positive spatial correlations the aesr is weaker than for the independent noises , and arrays with a global noise do not display the aesr , but only the ordinary sr . this happens because detectors with negative correlations tend to correct each other s mistakes , while positively correlated detectors tend to repeat the mistakes . as a result , negatively correlated detectors better resolve the shape of the incoming signal . the mechanism of enhancing the snr relies on lowering the noise background , not on elevating the signal peak . note that we have analyzed these facts for spatial correlations between the nearest neighbors only . we expect that noises with long - ranging negative correlations would resolve the shape of the incoming signal even better ; this point will be discussed elsewhere . it should be noted , though , that long - ranging correlations are more costly to generate . these results are , superficially , in disagreement with those of ref . @xcite , where it has been claimed that spatial correlations between the noises diminished the positive effect of passing the signal through an array of model neurons . this discrepancy is easily solved : in ref . @xcite , each neuron was subjected to a superposition of a subthreshold periodic signal , a local gwn noise , and a global orstein - uhlenbeck noise . the local noises were mutually uncorrelated and the spatial correlations resulted solely from the presence of the global noise . it was the strong global noise that was responsible for the deterioration of the output signal . we have observed a similar effect see fig . [ aesr : fig - addnoise ] above and the subsequent discussion . the beneficial effects of negative spatial correlations reported here result from the correlations between the local noises . our results suggest that from a technological point of view , not only the additive noises should be incorporated into the design of multi - component signal - detection systems , as was already suggested in ref . @xcite , but also that these noises should have , if possible , negative spatial correlations to further improve the system s ability to detect weak signals , even with a weak global noise present . we have also shown that spatial correlations of the noise act similarly in the aesr in a coupled system . while we have discussed this for the specific system only , we have shown that the aesr is enhanced by noises with negative spatial correlations due to the nature of the attracting harmonic interactions between the individual oscillators , regardless of the properties of the nonlinear part , provided the nonlinear part admits the conventional sr . for such interactions , positive spatial correlations of the noise reduce the aesr and a global noise eliminates it altogether , leaving only the ordinary sr , just like in the case of the aesr in arrays of nondynamical elements . as harmonic interactions between different particles are ubiquitous in many physical models , we expect similar phenomena to happen in a variety of situations . this analysis has also some interesting consequences for the interpretation of experimental results with interacting agents ( particles , oscillators , detectors etc . ) and a global noise , like those reported in ref . @xcite : even though one can not examine a single agent and has to excite a group of interacting ones , with only a global noise added to the signal , the snr response of the whole array is the same as that of a single agent . previous research on systems that display the aesr and our present results let us conclude that the following features appear not to depend on the details of the dynamics : ( i ) for periodic subthreshold inputs , the snr is systematically enhanced as the size of the array grows ; ( ii ) negative spatial correlations between the local noises provide further enhancement of the snr ; ( iii ) the snr enhancement is mainly due to lowering the noise background , not due to increasing the signal peaks ; ( iv ) positive spatial correlations reduce the enhancement ; in particular , a purely global noise eliminates the array enhancement altogether . the detailed shape of the snr curves , their slope , locations of the maxima , depend on particulars of the system studied and on properties of the input signals . gun sang jeon , hyun jin kim , m. y. choi , beom jun kim , and p. minnhagen , phys . b * 65 * , 184510 , ( 2002 ) ; gun sang jeon , jong soo lim , hyun jin kim , and m. y. choi , phys . b * 66 * , 024511 ( 2002 ) ; gun sang jeon and m. y. choi , phys . b * 66 * , 064514 ( 2002 ) . k. wiesenfeld and f. moss , nature ( london ) * 373 * , 33 ( 1995 ) ; s. m. bezrukov and i. voydanoy , nature ( london ) * 385 * , 319 ( 1997 ) ; s. m. bezrukov and i. voydanoy , nature ( london ) * 386 * , 738 ( 1997 ) ; f. chapeau blondeau and x. godivier , phys e * 55 * , 1478 ( 1997 ) ; j. m. g. vilar , g. gomila , and j. m. rubi , phys . lett . * 81 * , 14 ( 1998 ) . g. marsaglia and t. a. bray , siam review * 6 * , 260 ( 1964 ) ; a. j. kinderman and j. g. ramage , j. amer . 71 * , 893 ( 1976 ) ; r. wieczorkowski and r. zieliski , _ komputerowe generatory liczb losowych _ ( wnt , warszawa , 1997 ) ( in polish ) .

we discuss the role of spatial correlations of the noise in the array enhanced stochastic resonance . we show numerically that the noises with negative correlations between different sites lead to significantly larger values of the signal - to - noise ratio than the uncorrelated noises or noises with positive correlations . if the noise is global , the system displays only the conventional stochastic resonance , without any array enhancement .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Space Leadership Preservation Act of 2012''. SEC. 2. ADMINISTRATOR AND DEPUTY ADMINISTRATOR. Section 20111 of title 51, United States Code, is amended-- (1) in subsection (a)-- (A) by striking ``Administrator.--There is established'' and inserting ``Administrator.-- ``(1) In general.--There is established''; (B) in paragraph (1), as so designated by subparagraph (A) of this paragraph-- (i) by inserting ``, pursuant to paragraph (2),'' after ``who shall be appointed''; and (ii) by inserting ``The Administrator shall serve for a term of 10 years.'' after ``and activities thereof.''; and (C) by adding at the end the following new paragraph: ``(2) Board of directors nominations.--The President shall appoint the Administrator under paragraph (1) from among the list of nominees provided by the Board of Directors pursuant to section 20118(l)(2)(A). The President shall appoint a new Administrator not later than 3 months after the first set of nominees is so provided by the Board of Directors. The sitting Administrator may serve in the position until a new Administrator appointed pursuant to this paragraph is confirmed by the Senate.''; and (2) in subsection (b)-- (A) by striking ``Administrator.--There shall be'' and inserting ``Administrator.-- ``(1) In general.--There shall be''; (B) in paragraph (1), as so designated by subparagraph (A) of this paragraph, by inserting ``, pursuant to paragraph (2),'' after ``who shall be appointed''; and (C) by adding at the end the following new paragraph: ``(2) Board of directors nominations.--The President shall appoint the Deputy Administrator under paragraph (1) from among the list of nominees provided by the Board of Directors pursuant to section 20118(j)(2)(B).''. SEC. 3. BOARD OF DIRECTORS. (a) Establishment.--Subchapter II of chapter 201 of title 51, United States Code, is amended by adding at the end the following new section: ``Sec. 20118. Board of Directors ``(a) Establishment.--There shall be established a Board of Directors for the National Aeronautics and Space Administration in accordance with this section, not later than 9 months after the date of enactment of the `Space Leadership Preservation Act of 2012'. ``(b) Membership and Appointment.--The Board shall consist of 11 members to be appointed as follows: ``(1) Three members shall be appointed by the President. ``(2) Three members shall be appointed by the president pro tempore of the Senate. ``(3) One member shall be appointed by the minority leader of the Senate. ``(4) Three members shall be appointed by the Speaker of the House of Representatives. ``(5) One member shall be appointed by the minority leader of the House of Representatives. In addition to the members appointed under paragraphs (1) through (5), the Administrator shall be an ex officio, nonvoting member of the Board. ``(c) Qualifications.--The persons appointed as members of the Board shall be-- ``(1) former astronauts or scientists or engineers eminent in the fields of human spaceflight, planetary science, space science, Earth science, and aeronautics, or other scientific, engineering, business, and social science disciplines related to space and aeronautics; ``(2) selected on the basis of established records of distinguished service; and ``(3) so selected as to provide representation of the views of engineering, science, and aerospace leaders in all areas of the Nation. ``(d) Limitation on Members.--An individual employed by or representing an organization with which the Administration has a contract is not eligible to serve on the Board, except for scientists employed by or representing colleges, universities, and other not-for- profit organizations. Additionally, a former Board member may not take employment with or represent an organization with which the Administration has a contract, or which is seeking such a contract, for a period of 2 years following completion of service on the Board. ``(e) Terms.--The term of office of each member of the Board shall be 3 years, except that any member appointed to fill a vacancy occurring prior to the expiration of the term for which his predecessor was appointed shall be appointed for the remainder of such term. Any person who has been a member of the Board for 12 consecutive years shall thereafter be ineligible for appointment during the 2-year period following the expiration of such 12th year. ``(f) Travel Expenses.--Each member of the Board shall receive travel expenses, including per diem in lieu of subsistence, in accordance with applicable provisions under subchapter I of chapter 57 of title 5, United States Code. ``(g) Meetings.--The Board shall meet quarterly and at such other times as the Chairman may determine, but the Chairman shall also call a meeting whenever one-third of the members so request in writing. The Board shall adopt procedures governing the conduct of its meetings, including delivery of notice and a definition of a quorum, which in no case shall be less than one-half plus one of the members of the Board. ``(h) Chairman and Vice Chairman.--The election of the Chairman and Vice Chairman of the Board shall take place at each first quarter meeting occurring in an even-numbered year. The Vice Chairman shall perform the duties of the Chairman in his absence. In case a vacancy occurs in the chairmanship or vice chairmanship, the Board shall elect a member to fill such vacancy. ``(i) Staff.--The Board may, with the concurrence of a majority of its members, permit the appointment of a staff consisting of professional staff members, technical and professional personnel on leave of absence from academic, industrial, or research institutions for a limited term, and such operations and support staff members as may be necessary. Such staff shall be appointed by the Chairman and assigned at the direction of the Board. The professional members and limited term technical and professional personnel of such staff may be appointed without regard to the provisions of title 5, United States Code, governing appointments in the competitive service, and the provisions of chapter 51 of such title relating to classification, and shall be compensated at a rate not exceeding the maximum rate payable under section 5376 of such title, as may be necessary to provide for the performance of such duties as may be prescribed by the Board in connection with the exercise of its powers and functions under this section. ``(j) Special Commissions.--The Board is authorized to establish such special commissions as it may from time to time deem necessary for the purposes of this section. ``(k) Committees.--The Board is also authorized to appoint from among its members such committees as it deems necessary, and to assign to committees so appointed such survey and advisory functions as the Board deems appropriate to assist it in exercising its powers and functions under this section. ``(l) Functions.-- ``(1) Budget proposal.--Not later than November 15 of each year, the Board shall provide to the President, and to the Committee on Appropriations and the Committee on Science, Space, and Technology of the House of Representatives and the Committee on Appropriations and the Committee on Commerce, Science, and Transportation of the Senate, a proposed budget for the National Aeronautics and Space Administration for the next fiscal year. Such budget shall-- ``(A) carry out the purpose described in section 20102(h); ``(B) be based on-- ``(i) the best professional judgement of the Board; ``(ii) recommendations from the scientific, engineering, and other technical experts communities; and ``(iii) the recommendations of the most recent National Research Council decadal surveys; and ``(C) follow such decadal survey's recommended decision rules regarding program implementation, including a strict adherence to the recommendation that the National Aeronautics and Space Administration include in a balanced program a flagship class mission, which may be executed in cooperation with one or more international partners. ``(2) Nominees for administrator, deputy administrator, and chief financial officer.--The Board shall provide to the President-- ``(A) a list of 3 nominees from which the President shall appoint an Administrator pursuant to section 20111(a); ``(B) a list of 3 nominees from which the President shall appoint a Deputy Administrator pursuant to section 20111(b); and ``(C) a list of 3 nominees from which the President shall appoint a Chief Financial Officer pursuant to section 205(a) of the Chief Financial Officers Act (31 U.S.C. 901(a)). The Board shall provide the first set of nominees under this paragraph not later than 15 months after the date of enactment of the `Space Leadership Preservation Act of 2012'. ``(3) Reports.-- ``(A) Annual infrastructure, capabilities, and workforce assessment.--The Board shall provide to the President and the Congress annually a report assessing the status of United States spaceflight infrastructure, unique space capabilities, and the health of the United States workforce necessary to maintain such infrastructure and capabilities. The assessment shall also identify areas of concern, gaps in capability compared to foreign spaceflight capabilities, and recommendations on how to strengthen or improve United States capabilities and workforce. ``(B) Specific policy matter reports.--The Board shall provide to the President and the Congress reports on specific, individual policy matters within the authority of the Administration (or otherwise as requested by the Congress or the President) related to human space flight, planetary science, earth science, aeronautics, and science, technology, engineering, and mathematics education, as the Board, the President, or the Congress determines the need for such reports. ``(4) Quadrennial review.--The Board shall provide to the President and the Congress, not later than the later of 180 days after the establishment of the Board or the third quarterly meeting of the Board, and once every 4 years thereafter, a quadrennial review of current space programs and a vision for future space exploration. ``(5) Removal of administrator for cause.--The Board may provide to the President and the Congress a report recommending the removal of the Administrator for cause. Any such report shall include the reasons for such recommendation. ``(m) Budget Meetings.--Portions of Board meetings in which the Board considers the budget proposal required under subsection (l)(1) for a particular fiscal year may be closed to the public until the Board submits the proposal to the President and the Congress. ``(n) Financial Disclosure.--Members of the Board shall be required to file a financial disclosure report under title II of the Ethics in Government Act of 1978 (5 U.S.C. App. 92 Stat. 1836), except that such reports shall be held confidential and exempt from any law otherwise requiring their public disclosure.''. (b) Table of Sections.--The table of sections for chapter 201 of title 51, United States Code, is amended by adding at the end of the items for subchapter II the following new item: ``20118. Board of Directors.''. SEC. 4. BUDGET PROPOSAL. Section 30103 of title 51, United States Code, is amended by adding at the end the following new subsection: ``(e) Board of Directors Proposal.-- ``(1) Inclusion in president's proposed budget.--The proposed budget for the Administration submitted to the Congress by the President for each fiscal year shall include a description of, and a detailed justification for, any differences between the President's proposed budget and the budget provided by the Board of Directors under section 20118(l)(1). ``(2) Elements of budget proposal.--Subsections (a) through (d) of this section shall apply to the proposed budget provided by the Board of Directors under section 20118(l)(1).''. SEC. 5. LONG TERM CONTRACTING. (a) Amendments.--Section 20142 of title 51, United States Code, is amended-- (1) in the section heading, by striking ``Contracts regarding expendable launch vehicles'' and inserting ``Long term contracting''; (2) in subsection (a), by-- (A) striking ``expendable launch vehicle services'' and inserting ``rocket propulsion systems and manned and unmanned space transportation vehicles and payloads, including expendable launch vehicles, and any other infrastructure intended for placement or operation in space or on celestial bodies, and services related thereto,''; and (B) striking ``related to launch'' and inserting ``related to''; and (3) in subsection (b), by striking ``launch services'' and inserting ``the goods and services to have been provided under the contract''. (b) Table of Sections Amendment.--The item relating to section 20142 in the table of sections for chapter 201 of title 51, United States Code, is amended to read as follows: ``20142. Long term contracting.''.

Space Leadership Preservation Act of 2012 - Establishes a Board of Directors for the National Aeronautics and Space Administration (NASA). Sets forth Board membership and appointment criteria. Directs the President to appoint the NASA Administrator and Deputy Administrator from among a list of nominees provided by the Board. Requires the Board to provide: (1) NASA's proposed annual budget; (2) annual reports on spaceflight infrastructure, unique space capabilities, and the workforce necessary to maintain such infrastructure and capabilities; (3) reports on specific policy matters; and (4) quadrennial reviews of current space programs and a vision for future space exploration. Authorizes the Administrator to enter into contracts for rocket propulsion systems and manned and unmanned space transportation vehicles and payloads.

the prevalence of type 2 diabetes ( t2 dm ) is increasing globally with approximately 3.2 million patients in the uk alone , plus a further 630,000 patients undiagnosed . the leading cause of mortality in such patients is cardiovascular disease ( cvd ) , with t2 dm patients suffering a threefold increase in cvd mortality over those without diabetes . insulin resistance is a feature of prediabetes , a silent condition that is difficult to diagnose early due to compensatory hyperinsulinaemia that can maintain glycaemia and delay diagnosis of the disease . accordingly , over 30% of newly diagnosed t2 dm patients present with cardiovascular complications the treatment of which places a significant burden and inevitable impact on healthcare costs . hyperglycaemia is the hallmark of diabetes and clinical trials have revealed that intensive glycaemic control can ameliorate the microvascular complications of t2 dm . however , macrovascular complications persist at least in the medium term , particularly in patients with active coronary heart disease [ 5 , 6 ] , suggesting that factors other than glycaemia may contribute to persistent vascular dysfunction . t2 dm patients frequently present with a variety of metabolic disturbances such as hyperinsulinaemia , inflammation ( elevated inflammatory cytokines such as tumor necrosis factor alpha ; tnf- ) , and disturbed lipid profile ( elevated free fatty acids , e.g. , palmitate ) that may have a cumulative effect and impart persistent pathological changes on ec that are not easy to reverse . the endothelium is a highly metabolic monolayer of cells that lines the luminal surface of all blood vessels and is a principal moderator of vascular health ( reviewed in ) . however , endothelial dysfunction is perceived to precede the development of overt cvd . in health , however , in prediabetic patients with insulin resistance this balance is disturbed and favours prothrombotic and vasoconstrictive effects . endothelial dysfunction predisposes patients to atherosclerosis and coronary artery disease ; thus revascularisation procedures are almost a requirement in diabetic patients [ 8 , 9 ] . the principal method of revascularisation is coronary artery bypass grafting ( cabg ) , frequently performed using the autologous long saphenous vein ( sv ) to bypass diseased coronary arteries . during sv harvesting , the endothelial layer is damaged ; therefore the ability of endothelial cells ( ec ) to proliferate and migrate is essential to restore homeostasis . migration of ec is also vital for angiogenesis and the formation of collateral blood vessels , which provide alternate pathways of blood flow in the damaged coronary circulation . whilst premature coronary artery disease is evident in t2 dm patients , these individuals also suffer inferior outcomes post - cabg [ 10 , 11 ] . one particular study showed that failure of sv grafts occurred in 9.7% of nondiabetic patients 1-year post - cabg , which increased to 14.4% in the diabetic group . it is likely that the impaired capacity of ec to proliferate and migrate is at least partly due to metabolic disturbances in these patients . the aims of this study were twofold ; firstly , to examine the in vitro phenotype and function of sv - ec from patients with or without t2 dm , and secondly to investigate the effects of candidate diabetic stimuli on nondiabetic ( nd ) endothelial function . samples of undistended sv were collected from patients undergoing coronary artery bypass grafting at the leeds general infirmary . local ethical committee approval and informed patient consent were obtained . sv - ec were isolated using worthington type ii collagenase digestion ( 1 mg / ml , lorne laboratories , berkshire , uk ) as we described previously . cells were maintained in m199 medium ( sigma - aldrich , dorset , uk ) supplemented with 20% foetal calf serum ( fcs ; labtech international , sussex , uk ) , 1% l - glutamine , 1% antibiotic , 20 mm hepes ( all life technologies , paisley , uk ) , 15 g / ml endothelial cell growth supplement , 1 m pyruvate ( both sigma - aldrich ) , and 5 u / ml heparin ( leo laboratories ltd . , hurley , uk ) in a humidified atmosphere of 5% co2 in air at 37c and passaged using trypsin / edta ( life technologies ) as necessary . all experiments were performed on early passage cells ( p37 ) from patients with ( t2dm - ec ) or without ( nd - ec ) diabetes . subconfluent sv - ec monolayers were imaged at 100 magnification and spread cell areas measured from 50 cells per patient population as previously described . in addition , cell circularity was measured using imagej software ( http://imagej.nih.gov/ij/ ) and expressed relative to a perfect circle with a value of 1.0 . sv - ec were seeded at a density of 2 10 cells per well in 12-well plates and proliferation assays performed essentially as previously described [ 15 , 16 ] . following overnight quiescence in minimal medium ( mm ; containing 1% fcs ) , cells were reexposed to medium containing 20% fcs ( designated day 0 ) for up to 5 days , with medium replenished on day 3 . viable cells were counted on days 0 , 3 , and 5 using a haemocytometer and trypan blue ( sigma - aldrich ) . further experiments were performed using a range of fcs concentrations ( 520% ) and all cell counts made on day 5 . data were expressed as both a percentage increase in cell number ( where day 0 counts = 100% ) and area under curve ( auc ) . to examine sv - ec proliferation / death in real time , time - lapse ptychography was used . cells were seeded at a density of 7.5 10 cells per well in glass - bottomed 6-well plates . after overnight quiescence in mm , cells were reexposed to medium containing 20% fcs for 3 d and maintained in a humidified environment of 5% co2 in air at 37c in an incubator surrounding a phase focus virtual lens ( pfvl21 ) microscope . a 20x objective ( na 0.4 ) and a 635 nm illumination were used to obtain a 0.2 mm region at the centre of the dish . images were acquired every ~30 min for 3 d and used to create a time - lapse video . finally , these cells were trypsinised and viability was measured using a beckman coulter vi - cell . migration was analysed using a linear scratch wound model essentially as we previously described [ 15 , 16 ] . briefly , confluent sv - ec monolayers were quiesced in mm for 24 h , wounded with a sterile 10 ml pipette tip to generate a cell free area , imaged , and treated with medium containing fcs ( 120% ) for 24 h after which the number of cells migrated into the wounded area was quantified . data are represented as percentage increase in migration ( versus 1% fcs media ( mm ) = 100% ) . cells were quiesced in mm for 16 hours before preparing whole cell lysates and immunoblotting as previously described . antibodies were used at the following concentrations : phospho - enos ( ser1177 , bd biosciences , 1 : 800 ) , phospho - akt ( ser473 , cell signaling technology , 1 : 500 ) , phospho - erk1/2 ( thr202 and tyr204 , cell signaling technology , 1 : 800 ) , total akt ( cell signaling technology , 1 : 500 ) , total erk ( cell signaling technology , 1 : 1000 ) , and glyceraldehyde 3-phosphate dehydrogenase ( gapdh ; abcam , 1 : 4000 ) . films were scanned using an epson perfection 4490 flatbed scanner and densitometry analysis performed using imagej software ( http://imagej.nih.gov/ij/ ) . lysate ( designated as 100% ) that was loaded on all membranes to allow comparison between experiments . in additional experiments , cells were stimulated with 100 nm insulin ( sigma - aldrich ) for 5 min and lysates were immunoblotted for p - akt and p - erk . in vitro angiogenesis was investigated using matrigel ( vwr international , lutterworth , uk ) tube - forming assays . briefly , 1 10 sv - ec were seeded in mm in duplicate wells onto polymerised matrigel 24-well plates . plates were incubated at 37c in a humidified chamber with 5% co2 in air for up to 24 h. the number of intact tubes was counted in ten random 100 fields by two independent observers . in further experiments , sv - ec were pretreated with either akt inhibitor ly294002 ( 1 m ; merck - millipore , watford , uk ) , enos inhibitor ( l - n - nitroarginine methyl ester , l - name ; 500 m ; sigma - aldrich ) , high glucose ( 25 mm ; sigma - aldrich ) , tnf- ( 1 ng / ml ; life technologies ) , palmitate ( 100 m ; sigma - aldrich ) , or appropriate control vehicle for 24 h prior to angiogenesis assays . cells were incorporated into assays without replenishment of the stimulus / inhibitor and tube formation was quantified after 8 h. in selected experiments , time - lapse ptychography was performed in order to visualise any differences in nd and t2 dm tube dynamics , for example , the rate of formation or breakdown . in those experiments , cells were plated on matrigel - coated glass - bottomed 35 mm dishes and maintained in a humidified environment in 5% co2 ( in air ) at 37c by an incubator surrounding the pfvl21 microscope . images were acquired as described previously ; briefly a 10x objective ( na 0.3 ) and a 635 nm illumination were used to obtain a 5.88 mm region at the centre of the dish . image acquisition began 2 h after seeding of the cells , taken every 10 min for a total period of 24 h and used to create a time - lapse video such that tube formation and degradation could be monitored . sv - ec were seeded in gelatin - coated chamber slides at a density of 1 10 cells per well , cultured for 72 h in complete growth medium then fixed in 4% paraformaldehyde . to determine effects of diabetic stimuli , cells were quiesced in mm and then incubated in medium containing 5% fcs , either alone or supplemented with high glucose ( 25 mm ) , tnf- ( 1 ng / ml ) , palmitate ( 100 m ) , or appropriate controls for 24 h before fixing . the f - actin cytoskeleton was visualised using fluorescent rhodamine phalloidin ( life technologies ) as previously described . all images were captured on a zeiss axio imager z1 epifluorescence microscope at 200 and 400 magnification . all data are expressed as mean sem , with n representing the number of experiments on cells from different patients . data were analysed using standard or ratio ( log transformed ) two - way anova or mann - whitney t - test as appropriate , using graphpad software ( www.graphpad.com ) , with p < 0.05 considered statistically significant . experiments were performed on endothelial cells from a total of 44 patients . the mean age of nd and t2 dm patients was not significantly different : nd ( n = 27 , 85% male ) , 64.5 1.6 ( range 5080 ) years versus t2 dm ( n = 17 , 82% male ) , and 67.0 2.1 ( range 4878 ) years ; p = 0.35 . all t2 dm patients were receiving oral therapy ( metformin / sulfonylureas / gliptins ) , and 30% of these were also receiving insulin . routine cardiovascular medications ( statins , -blockers , angiotensin modulating agents , anticoagulation therapies , and diuretics ) were similar in both cohorts as we have reported previously . in contrast to the distinct morphological and proliferative changes we have previously observed in sv smooth muscle cells ( sv - smc ) from t2 dm patients [ 14 , 21 , 22 ] , there were no distinct differences in morphology between nd and t2dm - ec , with all cells exhibiting a typical ec cobblestone appearance and no consistent difference in f - actin organisation ( figure 1(a ) ) . whilst there was inherent variability in cell size between patients , this neither did circularity vary between the two populations ( figure 1(c ) ) . although cell number of t2 dm ec was ~70% of nd - ec cell number at day 5 , this did not reach statistical significance ( figure 1(d ) ) . area under curve analysis for each cell population , whilst suggesting a trend towards reduced proliferation in the t2 dm cells , did not reach statistical significance ( figure 1(e ) ) . a similar degree of t2dm - ec proliferative impairment was visible across a range of concentrations of fcs ( figure 1(f ) ) . ptychography is a novel label - free methodology that generates high quality / contrast phase images of living cells with no invasive labelling protocols or requirement for high energy illumination . the ability to digitally focus images after acquisition prevents loss of data due to focal drift of the microscope . nd and t2dm - ec were monitored for 3 d and a quantitative parameter related to cellular dry mass was calculated at each time point as a measure of proliferation . growth profiles of the 3 cell populations for both nd and t2 dm cells over time are represented in figure 1(g ) ( left panel ) . video data ( suppl . files 1 and 2 in supplementary material available online at http://dx.doi.org/10.1155/2015/409432 ) show that any reduction in dry mass was due to cells moving out of the field of view and not to increased cell death . two populations ( one each of nd and t2dm - ec ) did not proliferate readily , highlighting the inherent interpatient variability as shown by direct cell counting ( figures 1(d)1(f ) ) . importantly , the viability of all cell populations was similar between nd and t2 dm patients ( 96.2% and 96.8% , resp . ; figure 1(h ) ) suggesting that the trend towards reduced proliferation in t2dm - ec was not a result of increased cell death . indeed , time - lapse imaging showed multiple proliferation events and a lack of cell death events ( figure 1(g ) , right panel and suppl . ec motility was assessed using a scratch wound model where sv - ec migration into a denuded area over 24 h ( figure 2(c ) ) was evaluated . fcs - induced migration in both nd and t2dm - ec was concentration dependent , although the response in t2dm - ec was blunted ( figure 2(a ) ) . accordingly , in 10% fcs , t2dm - ec migration was reduced by > 30% compared to nd - ec ( figures 2(b ) and 2(c ) ) . we therefore explored the concept that basal differences in two principal insulin - stimulated signalling pathways , akt and erk ( figure 3(f ) ) , may be evident between nd and t2 dm sv - ec . cells were cultured in mm and phosphorylation of akt , enos , and erk quantified using western blotting . basal phosphorylation states of both akt ( figure 3(a ) ) and enos ( figure 3(b ) ) were significantly lower in t2dm - ec ( 56% and 73% of nd - ec , resp . ) . in contrast , phosphorylation of erk was similar in each population ( figure 3(c ) ) . diminished akt phosphorylation in t2 dm cells was maintained in response to stimulation with insulin ( figure 3(d ) ) whilst levels of erk phosphorylation were similar between populations ( figure 3(e ) ) . patients with t2 dm have impaired ability to form collateral blood vessels ; it is likely that the reduced migratory capacity is a factor contributing to inferior angiogenesis . using in vitro tube - forming assays , time courses were performed , revealing that the temporal profile of tube formation was similar in nd - ec and t2dm - ec . however , whilst each sv - ec population exhibited a similar temporal profile of tube formation which was maximal after 8 h , the number of tubes was significantly fewer in the t2 dm group ( ~60% nd ) ( figures 4(a ) and 4(b ) ) . to explore the kinetics of tube formation , we performed time - lapse ptychography over a 24 h interval . the establishment of tube - like networks was evident in both nd - ec and t2dm - ec after 2 h , the earliest time point at which the technique could detect all cells within the same plane . in nd - ec , tubes gradually expanded over the 24 h and formed stable , robust walls comprised of multiple cell layers ( denoted by red bars in figure 4(c ) ; also see suppl . file 3 ) . in t2dm - ec tubes appeared to expand more rapidly than nd - ec ( suppl . file 4 ) but tube walls appeared fragile ( generally only one cell thick ) and there were frequent broken / incomplete tubes ( illustrated by asterisks in figure 4(c ) ) . t2dm - ec exhibited marked reduction in basal levels of akt and enos phosphorylation ( figure 3 ) . to determine whether inhibiting akt or enos activity modulated in vitro angiogenesis , we treated nd - ec with appropriate inhibitors ( ly294002 and l - name , resp . ) prior to tube - forming assays . exposure to 1 m ly294002 for 24 h resulted in a reduction in akt phosphorylation confirming the efficacy of the inhibitor in these experiments ( figure 4(d ) ) . akt inhibition significantly impaired tube forming by 36% ( figure 4(e ) ) ; however the effect of l - name was inconsistent between cells from different patients ( figure 4(e ) ) . nd - ec were cultured under conditions designed to mimic the in vivo environment of t2 dm and the impact on angiogenesis assays was evaluated . we also examined the f - actin cytoskeleton due to its important role in migration and intercellular communication . surprisingly , 25 mm glucose had no impact on tube formation or the cytoskeleton ( figures 5(a ) and 5(b ) ) . in contrast , both the proinflammatory cytokine tnf- and free fatty acid palmitate significantly impaired angiogenesis , by 27% and 43% , respectively ( figures 5(c ) and 5(e ) ) . there was reduced f - actin staining intensity and reorganisation from peripheral fibres in control cells to more centrally aligned stress fibres in the tnf--treated cells ( figure 5(d ) ) . in palmitate treated cells a similar reduction in staining intensity was observed and although peripheral localisation was maintained , fibres in the body of the cell appeared more disorganised ( figure 5(f ) ) . a key strength of this study was the use of the exact cells whose dysfunction underlies failure or complications following bypass grafting in t2 dm patients , namely , sv - ec . during harvesting and grafting for cabg the endothelium is inevitably denuded and hence ec regeneration through both proliferation and migration is pivotal to restore a functional monolayer . in contrast to sv - smc [ 14 , 21 , 22 ] , gross sv - ec morphology was indistinguishable between nd and t2 dm patients ; although this does not rule out the possibility of subcellular alterations . instead , we focused on differences in cellular function that would be viewed as key to cardiovascular health . importantly , vital functions were persistently impaired , namely , migration , tube forming , and , to a lesser degree , proliferation . previously described a significant inhibition of proliferation in t2dm - ec isolated from human sv . indeed , the difference between the nd and t2 dm cells in our study appears more distinct at later time points and extending the study beyond 5 days would potentially answer this question . importantly , the modest reduction in t2dm - ec proliferation was not a result of increased cell death . previous studies have demonstrated impaired migration in bovine and human aortic ec under conditions of hyperglycaemia , suggesting that the diabetic milieu may harm the migratory capacity of resident cells . studies in a murine model of t2 dm also reported impaired ec migration in the db / db mouse . in human studies , reduced migration of endothelial progenitor cells from t2 dm patients was impaired relative to nd patients . accordingly we observed a significant impairment in migration of native t2dm - ec relative to nd - ec . importantly this divergence was observed under normoglycaemic conditions ( 5.5 mm glucose ) , lending credence to the notion of a persistent ec phenotype imprinted in vivo and that does not reverse easily in culture . insulin signals through the insulin receptor via two main arms , triggering the akt and erk pathways ( figure 3(f ) ) . it is perceived that in t2 dm patients the akt pathway is impaired with signalling preferentially stimulating the erk pathway . to our knowledge this is the first direct demonstration of divergent akt and erk signalling , both basally and following insulin stimulation , in human sv - ec , another feature maintained in culture . this is in agreement with evidence in animal models of diabetes and human skeletal muscle . since activation of akt leads to enos phosphorylation ( figure 3(f ) ) , it is perhaps not surprising that enos phosphorylation was also diminished in t2dm - ec . previous studies have revealed reduced akt and enos phosphorylation in atrial biopsies from t2 dm patients which concurs with the data presented here ; however phosphorylation of enos was reportedly elevated in venous ec from t2 dm patients ' forearms . this highlights the importance of evaluating the strengths and weaknesses of different experimental models and advocates the use of an appropriate cellular model ( i.e. , sv - ec to explore dysfunction with respect to graft failure ) . an alternative compensatory pathway of restoring blood flow in arteries diseased by atherosclerosis is the formation of collateral blood vessels through angiogenic mechanisms . these small , new vessels help to revascularise the myocardium and bypass the occlusion . given the increased prevalence of cvd in t2 dm patients this is an important mechanism ; however it is well recognised that such patients suffer from impaired coronary collateral formation which in turn increases the need for coronary revascularisation . animal models of diabetes exhibit reduced angiogenic capacity in vivo [ 35 , 36 ] . in our study we used a well validated in vitro model to study sv - ec angiogenesis and believe this is the first demonstration of impaired angiogenic capacity in human t2dm - ec versus nd - ec . ptychography was used to monitor tube formation dynamics without damaging or altering the cells , for example , by using fluorescent labels that potentially interfere with cell behaviour . this revealed that the initial establishment of tubes was not different between nd and t2dm - ec ; however t2dm - ec tubes expanded rapidly once established and exhibited thin , fragile walls that started to degenerate after 8 h. combining this knowledge with the reduced total number of tubes observed at 8 h , it is likely that t2dm - ec tubes are less stable than nd - ec . ptychography may be a useful technique to distinguish between the absolute capacity to form and maintain robust tubes and the ability to monitor degeneration . moreover , the absence of a requirement for cell labelling of any kind , together with a diffuse , low - powered 635 nm illumination , provides confidence that the cell has not been modified by such markers . having observed reduced akt and enos phosphorylation in native t2dm - ec , we explored whether akt and/or enos inhibition impaired angiogenesis in ec of nondiabetic origin . whilst akt inhibition significantly reduced tube formation , the response to enos inhibition was inconsistent ; four out of six cell populations showing reduced tube formation to varying degrees . other downstream effectors of akt , for example , vascular endothelial growth factor , may additionally be necessary in order to elicit a significant and robust inhibition . hyperglycaemia reportedly impairs ec migration [ 26 , 27 ] and inhibits angiogenesis in human microvascular ec and huvec . somewhat unexpectedly we observed no effect of consistent high glucose on angiogenesis in sv - ec , possibly reflecting differences in the sources of ec . microvascular and macrovascular ec are phenotypically distinct , and huvecs express a foetal gene pattern which is divergent from sv - ec . another possible explanation is that variability in glycaemic control is more deleterious to endothelial cells than persistent hyperglycaemia . for example , some previous studies reported that fluctuating or intermittent high glucose increased expression of adhesion molecules icam-1 , vcam-1 , and e - selectin , augmented apoptosis , and downregulated no production . no studies have investigated hyperglycaemia per se on human sv - ec angiogenesis but the failure of intensive glycaemic control to normalise macrovascular complications in t2 dm in the medium term ( accord , advance , and vadt clinical trials [ 5 , 6 ] ) suggests involvement of other factors . circulating levels of tnf- are elevated in t2 dm patients but reports of its effects on angiogenesis are contradictory . duration of exposure to tnf- is reportedly key to its pro- or antiangiogenic effects , and dysfunctional angiogenesis has been attributed to attenuated enos activity and modification of rho gtpase activity ; the latter potentially associated with disturbed f - actin dynamics as observed in the present study and previously noted by others . raised plasma levels of free fatty acids are associated with metabolic syndrome . palmitate is proapoptotic to ec [ 53 , 54 ] although its effect on angiogenesis is not clear . in our study , in vitro tube - forming was markedly impaired with comparatively low ( 100 m ) concentrations of palmitate and could be attributable to inhibition of enos phosphorylation . our data also indicate reduced staining intensity of f - actin and disorganisation of identifiable fibres in palmitate - treated cells . palmitate was shown to reduce f - actin content in l6 myotubes , reportedly via accumulation of membrane cholesterol ; it is therefore possible that this mechanism exists in sv - ec . multiple cytokines and chemokines relevant to diabetic complications are induced by hyperglycaemia , including interleukin-1 beta ( il-1 ) . indeed , hyperglycaemia - induced il-1 expression in retinal endothelial cells is believed to underlie diabetic retinopathy . interestingly , a very recent study demonstrated that monocytes exposed to palmitate secreted il-1 , which in turn , induced ec adhesion molecule expression , an effect abolished by il-1 receptor antagonism . il-1 clearly plays an important role , both directly and indirectly via effects on other pathways . the maintenance of a persistent aberrant t2dm - ec phenotype under culture conditions is perhaps indicative of the phenomenon of metabolic memory ; that is , the concept that prior exposure to hyperglycaemia and/or other metabolic insults in vivo can lead to maintained cellular effects in vitro . this is likely to involve epigenetic mechanisms such as micrornas , histone modifications and/or dna methylation ( reviewed in ) . indeed , transient exposure to hyperglycaemia in human and bovine ec imparted persistent changes in the nuclear factor kappa b ( nfb ) signalling pathway that were retained even when cells were returned to normoglycaemia [ 60 , 61 ] . micrornas ( mirs ) are short , noncoding rnas that negatively regulate target gene expression and have been proposed as biomarkers for cardiovascular disease and diabetes . for example , mir-21 , widely expressed in the vasculature , has been reported to inhibit proliferation , migration , and angiogenesis in huvec . it is entirely possible that similar mechanisms exist in human sv - ec and studies to investigate this hypothesis are currently in progress . to our knowledge , this study is the first to demonstrate divergent migration and tube forming capacity in sv - ec cultured from patients with and without t2 dm . there was a nonsignificant trend towards impaired proliferation . importantly we provide direct evidence for selective impairment of the akt , but not erk signalling pathway in these clinically relevant cells . this t2 dm phenotype persisted throughout culture and passaging , suggestive of epigenetic changes inflicted in vivo and not easily reversed . nd - ec exposed to diabetic stimuli adopted a t2dm - ec phenotype , suggesting the importance of factors other than hyperglycaemia in promoting endothelial dysfunction in t2 dm . in conclusion , the blunted functionality of sv - ec from t2 dm patients in our study , together with our demonstration that diabetic stimuli can impair aspects of nd - ec behavior , may translate into an inadequate or delayed ability to reendothelialise , significantly impacting the homeostatic capabilities of the endothelium and predisposing to graft failure .

type 2 diabetes ( t2 dm ) confers increased risk of endothelial dysfunction , coronary heart disease , and vulnerability to vein graft failure after bypass grafting , despite glycaemic control . this study explored the concept that endothelial cells ( ec ) cultured from t2 dm and nondiabetic ( nd ) patients are phenotypically and functionally distinct . cultured human saphenous vein- ( sv- ) ec were compared between t2 dm and nd patients in parallel . proliferation , migration , and in vitro angiogenesis assays were performed ; western blotting was used to quantify phosphorylation of akt , erk , and enos . the ability of diabetic stimuli ( hyperglycaemia , tnf- , and palmitate ) to modulate angiogenic potential of nd - ec was also explored . t2dm - ec displayed reduced migration ( ~30% ) and angiogenesis ( ~40% ) compared with nd - ec and a modest , nonsignificant trend to reduced proliferation . significant inhibition of akt and enos , but not erk phosphorylation , was observed in t2 dm cells . hyperglycaemia did not modify nd - ec function , but tnf- and palmitate significantly reduced angiogenic capacity ( by 27% and 43% , resp . ) , effects mimicked by akt inhibition . aberrancies of ec function may help to explain the increased risk of sv graft failure in t2 dm patients . this study highlights the importance of other potentially contributing factors in addition to hyperglycaemia that may inflict injury and long - term dysfunction to the homeostatic capacity of the endothelium .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Proliferation Prevention Enhancement Act of 1999''. SEC. 2. MANDATORY USE OF THE AUTOMATED EXPORT SYSTEM FOR FILING CERTAIN SHIPPERS' EXPORT DECLARATIONS. (a) Authority.--Section 301 of title 13, United States Code, is amended by adding at the end the following new subsection: ``(h) The Secretary is authorized to require the filing of Shippers' Export Declarations under this chapter through an automated and electronic system for the filing of export information established by the Department of the Treasury.''. (b) Implementing Regulations.-- (1) In general.--Not later than 90 days after the date of enactment of this Act, the Secretary of the Treasury, in consultation with the Secretary of Commerce and the Secretary of State, shall publish regulations in the Federal Register to require that, upon the effective date of those regulations, exporters (or their agents) who are required to file Shippers' Export Declarations under chapter 9 of title 13, United States Code, file such Declarations through the Automated Export System with respect to exports of items on the United States Munitions List or the Commerce Control List. (2) Elements of the regulations.--The regulations referred to in paragraph (1) shall include at a minimum-- (A) provision for the establishment of online assistance services to be available for those individuals who must use the Automated Export System; (B) provision for ensuring that an individual who is required to use the Automated Export System is able to print out from the System a validated record of the individual's submission, including the date of the submission and a serial number or other unique identifier for the export transaction; and (C) a requirement that the Department of Commerce print out and maintain on file a paper copy or other acceptable back-up record of the individual's submission at a location selected by the Secretary of Commerce. (c) Effective Date.--The amendment made by subsection (a) and the regulations described in subsection (b) shall take effect 180 days after the Secretary of Commerce, the Secretary of the Treasury, and the Director of the National Institute of Standards and Technology jointly certify, by publishing in the Federal Register a notice, that a secure, Internet-based Automated Export System that is capable of handling the expected volume of information required to be filed under subsection (b), plus the anticipated volume from voluntary use of the Automated Export System, has been successfully implemented and tested. SEC. 3. VOLUNTARY USE OF THE AUTOMATED EXPORT SYSTEM. It is the sense of Congress that exporters (or their agents) who are required to file Shippers' Export Declarations under chapter 9 of title 13, United States Code, but who are not required under section 2(b) to file such Declarations using the Automated Export System, should do so. SEC. 4. REPORT TO CONGRESS. Not later than 180 days after the date of enactment of this Act, the Secretary of Commerce, in coordination with the Secretary of State, the Secretary of Defense, the Secretary of the Treasury, the Secretary of Energy, and the Director of Central Intelligence, shall submit a report to Congress setting forth-- (1) the advisability and feasibility of mandating electronic filing through the Automated Export System for all Shippers' Export Declarations; (2) the manner in which data gathered through the Automated Export System can most effectively be used by other automated licensing systems administered by Federal agencies, including-- (A) the Defense Trade Application System of the Department of State; (B) the Export Control Automated Support System of the Department of Commerce; (C) the Foreign Disclosure and Technology Information System of the Department of Defense; (D) the Proliferation Information Network System of the Department of Energy; (E) the Enforcement Communication System of the Department of the Treasury; and (F) the Export Control System of the Central Intelligence Agency; and (3) a proposed timetable for any expansion of information required to be filed through the Automated Export System. SEC. 5. DEFINITIONS. In this Act: (1) Automated export system.--The term ``Automated Export System'' means the automated and electronic system for filing export information established under chapter 9 of title 13, United States Code, on June 19, 1995 (60 Federal Register 32040). (2) Commerce control list.--The term ``Commerce Control List'' has the meaning given the term in section 774.1 of title 15, Code of Federal Regulations. (3) Shippers' export declaration.--The term ``Shippers' Export Declaration'' means the export information filed under chapter 9 of title 13, United States Code, as described in part 30 of title 15, Code of Federal Regulations. (4) United states munitions list.--The term ``United States Munitions List'' means the list of items controlled under section 38 of the Arms Export Control Act (22 U.S.C. 2778).

Expresses the sense of Congress urging exporters (or their agents) who are required to file Shippers' Export Declarations, but are not required under this Act to file them using the Automated Export System, to do so anyway.

nearby dark clouds like taurus and perseus contain dozens of dense molecular cores where stars like our sun are currently forming or have done so in the recent past ( myers 1995 ) . their large number , together with their proximity and simple structure , make cores unique targets to study the complex physics involved in the formation of a star . dense cores that have not yet formed stars , the so called starless or pre - stellar cores , inform us of the initial conditions of star formation , and their study can help us elucidate the process by which pockets of cloud material condense and become gravitationally unstable . cores with deeply embedded young stellar objects ( `` protostellar cores '' ) are unique targets to study the complex motions that occur during the period of accretion , when a combination of infall , outflow , and rotation is necessary to assemble the star and redistribute the gas angular momentum . finally , evolved cores are primary targets to study the interaction between the newly born star and its environment . these feedback effects are responsible for the transition of the protostar from embedded to visible , and may be important determining the final mass of the star and stabilizing the nearby gas via turbulence generation . the observational study of dense cores has advanced enormously over the last decade thanks to the increase in resolution provided by the new millimeter and submillimeter interferometers , and also due to the systematic combination of observations of dust and molecular tracers ( e.g. , bergin & tafalla 2007 ) . this brief review summarizes some new results from dense cores studies and presents a number of current issues that will greatly benefit from alma observations . the limited space of this article makes any attempt to review the field necessarily incomplete , and the reader is referred for further information to the other contributions on star formation in these proceedings , in particular to those by van dishoeck , andr , shepherd , aikawa , wilner , johnstone , and crutcher . despite significant recent progress , our understanding of the structure and evolution of dense cores is still incomplete due in part to limitations in the resolution and sensitivity of the available observations . even the highest resolution data of nearby dense cores can not discern details finer than about 100 au , which is still insufficient to disentangle the complex kinematics of infall and outflow motions in the vicinity of a protostar . probably more important , the low temperatures of the gas and the dust in cores ( @xmath0 k ) make the emission of any core tracer intrinsically weak , so any increase in the resolution needs to be accompanied by a parallel increase in the sensitivity , or the observations will not achieve enough s / n to provide useful information . this is particularly important when using weak , optically thin tracers to sample the innermost gas in the core . these tracers , in addition , often present extended emission , which poses a problem to the current generation of interferometers that cover sparsely the @xmath1 plane and therefore suffer systematically from missing flux . the high resolution and collecting area afforded by alma , combined with its great sensitivity to extended emission , promises to revolutionize the field of dense cores studies . on the one hand , alma will allow studying the dense cores of nearby clouds with the greatest detail , achieving subarcsecond resolution with high sensitivity . on the other hand , alma will permit the systematic study of dense cores in more distant clouds , enlarging the sample of available targets from the current set of the nearest clouds to cores at distances of at least 1 kpc . the earliest phase of a core , the so - called starless or pre - stellar stage , is characterized by the lack of a point - like object at its center ( e.g. , di francesco et al . 2007 ) . this characterization is of course dependent on the current sensitivity limits of the observations , and is therefore susceptible of misclassifying a core with an embedded source of very low luminosity ( see the case of vellos below ) . still , the significant number of dense cores with no pointlike source detected even after deep spitzer space telescope observations suggests that a population of truly starless cores exists in nearby clouds like taurus ( werner et al . 2006 ) . starless cores present systematically a close to constant density of @xmath2-@xmath3 @xmath4 over the central 5000 - 10000 au followed by an almost power - law drop at large distances . this central flattening of the density profile has been observed in a number of cores using different observational techniques , like millimeter dust continuum emission ( ward - thompson et al . 1999 ) , mir absorption ( bacmann et al . 2000 ) , and nir extinction ( alves et al . 2001 ) , and therefore constitutes a robust result of recent core studies . the presence of a density flattening provides further evidence that starless cores have not yet developed a central singularity , and that they are of pre - stellar nature . the physical origin of the flattening , however , is still a matter of debate , as a number of interpretations are consistent with it . the most natural one is that the profile results from an equilibrium configuration in which the pressure of an isothermal gas balances its gravitational attraction , the so called bonnor - ebert profile ( e.g. , alves et al . 2001 ) . indeed , the gas temperature in a core is typically close to constant ( @xmath0 k ) , and the associated thermal pressure dominates the turbulent component by a factor of several ( e.g. , tafalla et al . the bonnor - ebert interpretation , however , seems in conflict with the non - spherical shape of most cores ( typical axial ratio is 2:1 , myers et al . 1991 ) , and with the fact that the density contrast observed in cores often exceeds the factor of 14 limit for stability of the bonnor - ebert analysis ( bacmann et al . 2000 ) . additional magnetic field support could be responsible for these deviations from the theoretical expectation , but unfortunately , the observation of this magnetic component is extremely hard to make ( see contribution from crutcher in this volume ) . even the apparently `` simple '' structure of the cores still eludes our understanding . when the density distribution of a core , as inferred from dust measurements , is compared with the observed emission from most molecular tracers , it is commonly found that they disagree significantly . as illustrated in fig . 1 for l1498 in taurus , the dust emission of a core often appears centrally concentrated ( with of course a relative flattening at the center ) , while all molecular species but nh@xmath5 and n@xmath6h@xmath7 present ring - like distributions around the continuum peak . radiative transfer analysis of the molecular emission indicates that the abundance of most species drops by at least a factor of 10 towards the high density peak of the molecular core ( caselli et al . 1999 , bergin et al . 2002 , tafalla et al . 2002 ) . such strong abundance decrease is suffered by all the c - bearing molecules as well as other species ( like so ) , while it does not affect significantly nh@xmath5 or n@xmath6h@xmath7 ( see di francesco et al . 2007 and bergin & tafalla 2007 for reviews ) . nh@xmath5 seems in fact to be enhanced toward the center of most cores ( tafalla et al . 2002 ) , while the n@xmath6h@xmath7 abundance tends to have a constant value or may drop at the very center of some cores ( bergin et al . 2002 , pagani et al . 2005 ) . cores therefore have a differentiated ( onion - like ) molecular composition , with a center rich in nh@xmath5 and n@xmath6h@xmath7 and a series of outer layers containing c - bearing species . the inhomogeneous composition of the starless dense cores most likely results from the freeze out of the main molecular species onto the cold dust grains at the center ( bergin & langer 1997 , aikawa et al . 2005 ) . the high densities and low temperatures typical of dense core centers make the freeze out time ( @xmath8 yr ) become much shorter than the core dynamical scale ( @xmath9 1 myr ) , and as a consequence , species like co disappear rapidly from the gas phase . other molecular species suffer the same fate as co , but more importantly , the original chemical balance , characterized by a relative large co abundance ( @xmath10 ) , is changed dramatically by freeze out . a new chemical balance emerges , and it is characterized by the enhancement of certain n - bearing species , like n@xmath6h@xmath7 , which are daughter products of n@xmath6 and whose abundance is controlled by the amount of co in the gas phase ( co is the main destroyer of n@xmath6h@xmath7 ) . even as n@xmath6 freezes out on the dust grains with a similar binding energy as co ( berg et al . 2005 ) , the n@xmath6h@xmath7 abundance can increase relatively from its value in the diffuse cloud ( where co is undepleted ) and give rise to the relatively `` high '' abundances ( few 10@xmath11 ) typical of dense cores . nh@xmath5 can then form from n@xmath6h@xmath7 via dissociative recombination ( geppert et al . 2004 ) , giving rise to the observed central enhancement ( aikawa et al . 2005 ) . another effect of the co depletion in cores is the enhancement of deuterated species . deuteration at the low ( 10 k ) temperature of dense cores occurs via the enhancement of h@xmath6d@xmath7 , which then passes the deuterium atom to other species via ion - molecule reactions ( dalgarno & lepp 1984 ) . as h@xmath6d@xmath7 is mainly destroyed by co , the depletion of co further enhances the h@xmath6d@xmath7 abundance , which in turn enriches in deuterium a number of additional species . high abundance of h@xmath6d@xmath7 has in fact been observed in the heavily co - depleted dense core l1544 ( caselli et al . 2003 ) , and a correlation of co depletion and high deuteration has been reported by bacmann et al . ( 2003 ) and crapsi et al . this deuteration in the cold and dense pre - stellar phase is responsible for the extreme deuteration values of species like h@xmath6co , ch@xmath5oh , and nh@xmath5 seen toward protostellar cores ( ceccarelli et al . 1998 , roueff et al . 2000 , van der tak et al . as cores evolve , they are expected to become more and more centrally concentrated until they reach the point of gravitational instability . one of the most pressing issues in star formation studies is to understand whether this process of concentration is driven by the loss of magnetic field support via ambipolar diffusion ( e.g. , shu et al . 1987 , mouschovias & ciolek 1999 ) or by the dissipation of turbulence via shocks ( e.g. , maclow & klessen 2004 ) . observations of dense cores can not yet distinguish between these scenarios , but do show a systematic correlation between central concentration and other indicators of evolution , like co depletion and deuterium fractionation ( crapsi et al . 2005 ) . evidence for inward motions also seems correlated with central concentration , and this suggests that some cores that we see now as starless have already begun collapsing to form stars . one of the best candidates for such a collapsing system is the l1544 core in taurus , whose pattern of inward motions has been studied in a number of molecules ( tafalla et al . 1998 , williams et al . 1999 , caselli et al . the l1544 dense core is characterized by a high central density and concentration ( ward - thompson et al . 1999 , tafalla et al . 2002 ) , a high degree of co depletion and deuterium fractionation ( caselli et al . 1999 , 2002 ) , and seems starless despite deep spitzer space telescope observations in the ir ( bourke , private communication ) . clearly this core , an similar objects , will be prime targets for alma observations . cores more evolved than l1544 are expected to contain already a luminous object surrounded by an envelope of accreting material . the little observable difference between the pre and proto - stellar phases of a core is illustrated by the case of l1521f , a core initially thought from molecular data to be an almost twin of l1544 ( crapsi et al . 2004 ) and later found with spitzer observations to have a luminous central star ( bourke et al . the central object in l1521f has a luminosity close to 0.1 l@xmath12 , and is characteristic of a new group of objects identified by the spitzer telescope and usually referred as vellos ( very low luminosity objects ) . these vellos seem associated with very weak nir nebulosity and low velocity bipolar outflows ( bourke et al . 2005 ) , and their status in the evolutionary sequence of protostars is still unclear . although some vellos could represent precursors of substellar objects ( proto brown dwarfs ) , it seems more likely that in the case of l1521f we are witnessing the very first moments of accretion , when the central source has an extremely low mass . the proto brown dwarf alternative is unlikely in this case because the dense core has about 5 m@xmath12 of mass ( crapsi et al . 2004 ) , and no clear perturbation seems stopping the accretion ( the outflow has too little mechanical power ) . the pristine nature of vellos makes them ideal candidates to study star - forming infall motions . the study of these motions has a long and rich tradition , and is plagued by difficulties as illustrated by the case of b335 . this dense core harbors a very young ( class 0 ) object whose inward motions were first characterized by zhou et al . these authors found that the spectral signatures from this core are in good agreement with the expectation from the inside - out collapse model of shu ( 1977 ) . high resolution observations with the plateau de bure interferometer by wilner et al . ( 2000 ) , however , have shown that some of the signatures of `` infall '' ( like the high velocity wings in the cs lines ) arise in fact from outflow acceleration , and not from an increase in velocity of the infalling material as it approaches the central object . a revisit of b335 ( and similar objects ) making use of alma s high angular resolution and selecting appropriate ( i.e. , depletion resistant ) tracers is therefore needed to clarify the still confusing picture of star - forming infall motions . the clean appearance of some vellos , together with their weaker outflow emission , offers an interesting alternative to the more evolved ( and massive ) objects like b335 , that have fully developed outflows . because of their lower mass , vellos may present weaker signatures of infall and may be tracing the very first moments of collapse . the combined study of vellos and more luminous class 0 and class i sources should therefore allow us to reconstruct the sequence of star - forming accretion as a function of time . the presence of a protostar at the center of a core affects not only the gas kinematics but its chemistry . the newly born star heats up the nearby gas and dust introducing a temperature gradient in its vicinity . in the @xmath13 au region where the dust temperature exceeds the co evaporation temperature ( @xmath14 - 30 k ) , this molecule returns to the gas phase and undoes part of the chemical processing that occurred during the pre - stellar phase ( jrgensen et al . 2004 , jrgensen 2004 ) . closer to the protostar ( @xmath15 au ) , the dust temperature reaches the 90 - 100 k value at which water evaporates from the grains , further enriching the chemistry . observations of some very young protostellar objects , like iras 16293 - 2422 , show that these very small regions have extreme abundance of a number of complex molecules like hcooh , hcooch@xmath5 , and ch@xmath5och@xmath5 ( cazaux et al . 2003 , bottinelli et al . 2004 ) . the chemical richness of these regions rivals that of the hot cores around massive protostars , justifying their common denomination as `` hot corinos '' ( ceccarelli et al . the exact origin of the complex molecules in these regions , however , is still not fully understood . one possibility is that they result from direct evaporation of species trapped in the water ice , while an alternative is that they result from the processing of simpler evaporated molecules . even the geometry of hot corinos remains unknown , with the innermost part of the envelope or a more stable disk - like distribution as the most likely locations . despite these temporary uncertainties , hot corinos offer a unique opportunity to study the innermost vicinity of low - mass protostars . their distinctive chemical composition makes them highly selective tracers of the most complex and interesting region of the protostar , where inflow , outflow , and rotation motions play comparable roles , and angular momentum is transfered between different gas components . hot corino studies with alma will surely constitute some of the first scientific projects of the instrument . at the same time that protostars accrete material , they eject powerful bipolar outflows of supersonic speed . co observations of these outflows reveal masses that are too large to originate directly from the central protostar , and indicate that most of the moving gas is core ambient material accelerated by a collimated stellar wind ( lada 1985 ) . the lobes of bipolar outflows , in addition , commonly coincide with evacuated cavities seen via scattered light from the protostar , further illustrating how the outflow phenomenon represents a major disruption in the core internal structure ( padgett et al . 1999 ) . despite more than two decades of intense outflow research , a number of outstanding problems remain , and alma observations represent our current best hope to solve them ( see also contribution by d. shepherd in this volume ) . the properties of the underlying wind , for example , are not yet understood , and several alternative models have been proposed over the years . the two main types of models that attempt to fit the observations are the jet - driven outflow and the wind - driven shell , each of them with a number of flavors ( see bachiller 1996 for a review ) . despite significant successes , however , neither type of model can reproduce the rich variety of kinematic properties found by observations , so each of of them is necessarily incomplete ( lee et al . 2002 ) . in the jet driven model , a highly collimated agent shocks and sweeps cloud material along an almost straight line . this model succeeds in explaining the highly collimated co outflows often found toward class 0 objects , but fails to reproduce observations of less collimated flows ( usually powered by class i sources ) , where the co emission arises from gas along limb - brightened shells ( like l1551 , see moriarty - schieven et al . 1987 ) . to fit these less collimated systems , the jet models need to broaden the outflow path , and this has been done by either invoking jet precession/wandering ( masson & chernin 1993 ) or large - scale bow shocks ( raga & cabrit 1993 ) . none of these elements however seems consistent with observations ( see arce et al . 2007 for more details ) , and this leaves the jet models limited to fitting the youngest , and admittedly more spectacular , bipolar outflows . wind - driven models , on the other hand , naturally produce shell - like structures thanks to a wide - angle agent that sweeps ambient material ( shu et al . these models , unfortunately , do not reproduce the appearance of the highly collimated outflows or the mass - velocity distribution commonly observed even in the poorly collimated flows ( masson & chernin 1992 ) . a combination of high resolution observations and new developments in outflow modeling are starting to show a possible solution to the current impasse . interferometer mapping of the outflow powered by the very young source iras 04166 + 2706 in taurus shows both jet and shell features simultaneously ( see fig . 2 and poster contribution by santiago - garca et al . the jet - like feature in this outflow , seen in both co and sio emission , is extremely rectilinear , appears only at the highest velocities ( between 30 and 50 km s@xmath16 ) , and shows no evidence for precession or wandering . the shell - like part appears at low velocities ( 2 to 10 km s@xmath16 ) and seems to delineate two opposed cavities with the iras source at their vertex . this cavity interpretation is supported by the fact that the blue outflow shell coincides with the walls of a nir scattering nebula seen in spitzer images , as expected from its more favorable projection . in addition , the high velocity jet runs along the axis of the two cavities showing a remarkable degree of symmetry ( see poster contribution for further details ) . the data from iras 04166 + 2706 , therefore , leads to the inevitable conclusion that , at least in some cases , both highly collimated and wide - angle components coexist in the outflow driving agent , and that a model that considers both components simultaneously is needed to explain the observations . interestingly enough , recent realistic modeling of the interaction between the x - wind of shu et al . ( 1994 ) and a toroidal core shows that both jet and shell components should be observed simultaneously in very young outflows ( shang et al . this so - called `` unified '' model of bipolar flows shows in fact a remarkable likeness with the iras 04166 + 2706 observations , both in geometry and kinematics ( compare fig . 2 and the models in shang et al . 2006 ) . the unified outflow model not only unifies the jet and wide - angle aspects of the outflows , but also brings together the evolution of flows and the dense cores , two elements often treated separately . evidence for outflow - core interaction has been reported in a number of systems ( e.g. , tafalla & myers 1997 , arce & sargent 2006 ) , but no unified framework of how this interaction happens or how outflows and cores evolve in parallel exists yet . the beautiful simulations of shang et al . ( 2006 ) illustrate how the most important elements of this interaction occur inside the central 1000 au region , which corresponds to less than @xmath17 even towards the most nearby clouds . high angular resolution observations with alma are clearly needed to sample the complex geometry and kinematics inside this critical region , and thus compare real outflows with their simulated counterparts . producing a unified picture of the different and interacting processes occurring during the formation of a solar - type star can be one of most significant achievements of alma .

dense cores are the simplest star - forming sites that we know , but despite their simplicity , they still hold a number of mysteries that limit our understanding of how solar - type stars form . alma promises to revolutionize our knowledge of every stage in the life of a core , from the pre - stellar phase to the final disruption by the newly born star . this contribution presents a brief review of the evolution of dense cores and illustrates particular questions that will greatly benefit from the increase in resolution and sensitivity expected from alma .

Section 1. This Act may be cited as the ``Immigration Reform Transition Act of 1997''. Sec. 2. (a) Section 240A, subsection (e), of the Immigration and Nationality Act is amended-- (1) in the first sentence, by striking ``this section'' and inserting in lieu thereof ``section 240A(b)(1)''; (2) by striking ``, nor suspend the deportation and adjust the status under section 244(a) (as in effect before the enactment of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996),''; and (3) by striking the last sentence in the subsection and inserting in lieu thereof ``The previous sentence shall apply only to removal cases commenced on or after April 1, 1997, including cases where the Attorney General exercises authority pursuant to paragraphs (2) or (3) of section 309(c) of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (Public Law 104-208, Division C, 110 Stat. 3009).''. (b) Section 309, subsection (c), of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (Public Law 104-208, Division C, 110 Stat. 3009) is amended by striking paragraphs (5) and (7). (c) Section 240A of the Immigration and Nationality Act is amended-- (1) in subsection (b), paragraph (3), by striking ``(1) or (2)'' in the first and third sentences of that paragraph and inserting in lieu thereof ``(1), (2), or (3)''; (2) in subsection (b), by redesignating paragraph (3) as paragraph (4); (3) in subsection (d), paragraph (1), by striking ``this section.'' and inserting in lieu thereof ``subsections (a), (b)(1), and (b)(2).''; (4) in subsection (b), by adding after paragraph (2) the following new paragraph-- ``(3) Special rule for certain aliens covered by the settlement agreement in american baptist churches et al. v. thornburgh (abc), 760 f. supp. 796 (n.d. cal. 1991).-- ``(A) The Attorney General may, in his or her discretion, cancel removal and adjust the status from such cancellation in the case of an alien who is removable from the United States if the alien demonstrates that-- ``(i) the alien has not been convicted at any time of an aggravated felony, and ``(I) was not apprehended after December 19, 1990, at the time of entry, and is either-- ``(aa) a Salvadoran national who first entered the United States on or before September 19, 1990, who registered for benefits pursuant to the ABC settlement agreement on or before October 31, 1991, or applied for Temporary Protected Status on or before October 31, 1991; or ``(bb) a Guatemalan national who first entered the United States on or before October 1, 1990, and who registered for benefits pursuant to the ABC settlement agreement by December 31, 1991; or ``(cc) the spouse or unmarried son or daughter of an alien described in (aa) who entered the United States on or before September 19, 1990, or the spouse or unmarried son or daughter of an alien described in (bb) who entered the United States on or before October 1, 1990; or ``(II) is a Nicaraguan, Guatemalan, or Salvadoran who filed an application for asylum with the Immigration and Naturalization Service before April 1, 1990, and the Immigration and Naturalization Service had not granted, denied, or referred that application as of April 1, 1997; and ``(ii) the alien is not described in paragraph (4) of section 237(a) or paragraph (3) of section 212(a) of the Act; and ``(iii) the alien-- ``(I) is removable under any law of the United States except the provisions specified in subclause (II) of this clause, has been physically present in the United States for a continuous period of not less than seven years immediately preceding the date of such application, and proves that during all of such period he was and is a person of good moral character, and is a person whose removal would, in the opinion of the Attorney General, result in extreme hardship to the alien or to his spouse, parent, or child, who is a citizen of the United States or an alien lawfully admitted for permanent residence; or ``(II) is removable under paragraph (2) (other than section 237(a)(2)(A)(iii)) of section 237(a), paragraph (3) of section 237(a), or paragraph (2) of section 212(a), has been physically present in the United States for a continuous period of not less than 10 years immediately following the commission of an act, or the assumption of a status, constituting a ground for deportation, and proves that during all of such period he has been and is a person of good moral character, and is a person whose removal would, in the opinion of the Attorney General, result in exceptional and extremely unusual hardship to the alien or to his spouse, parent or child, who is a citizen of the United States, or an alien lawfully admitted for permanent residence. ``(B) Subsection (d) of this section shall not apply to determinations under this paragraph, and an alien shall not be considered to have failed to maintain continuous physical presence in the United States under clause (A)(iii) of this paragraph if the alien demonstrates that the absence from the United States was brief, casual, and innocent, and did not meaningfully interrupt the continuous physical presence. ``(C) The determination by the Attorney General whether an alien meets the requirements of subparagraph (A) or (B) of this paragraph is final and shall not be subject to review by any court. Nothing in the preceding sentence shall be construed as limiting the application of subparagraph (B) of section 242(a)(2) to other eligibility determinations pertaining to discretionary relief under this Act.''. (d) The amendments made by this section shall be effective as if included in Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (Public Law 104-208, Division C, 110 Stat. 3009). Sec. 3. Any alien who has become eligible for suspension of deportation or cancellation of removal as a result of the amendments made by section 2, may, notwithstanding any other limitations on motions to reopen imposed by the Immigration and Nationality Act or by regulation, file one motion to reopen to apply for suspension of deportation or cancellation of removal. The Attorney General shall designate a specific time period in which all such motions to reopen must be filed. The period must begin no later than 120 days after the date of enactment of this Act and shall extend for a period of 180 days.

Immigration Reform Transition Act of 1997 - Amends the Immigration and Nationality Act (and the Illegal Immigration and Immigrant Responsibility Act of 1996) to authorize the Attorney General to cancel the removal and adjust the status of certain Central American aliens.

Pope Benedict XVI marked the holiest night of the year for Christians by stressing that humanity isn't a random product of evolution. Faithful gather in St. Peter's Basilica during the Easter Vigil mass celebrated by Pope Benedict XVI, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting... (Associated Press) Pope Benedict XVI holds a candle as he celebrates the Easter Vigil mass, in St. Peter's Basilica, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting a candle... (Associated Press) Faithful gather in St. Peter's Basilica during the Easter Vigil mass celebrated by Pope Benedict XVI, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting... (Associated Press) Pope Benedict XVI holds the pastoral staff as he celebrates the Easter Vigil mass, in St. Peter's Basilica, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting... (Associated Press) Pope Benedict XVI holds a candle as he celebrates the Easter Vigil mass, in St. Peter's Basilica, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting a candle... (Associated Press) Pope Benedict XVI holds up the book of the Gospels during the Easter Vigil mass, in St. Peter's Basilica, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting... (Associated Press) Pope Benedict XVI holds a candle as he celebrates the Easter Vigil mass, in St. Peter's Basilica, at the Vatican, Saturday, April 23, 2011. The pontif began Saturday night's ceremony by lighting a candle... (Associated Press) Benedict emphasized the Biblical account of creation in his Easter Vigil homily Saturday, saying it was wrong to think at some point "in some tiny corner of the cosmos there evolved randomly some species of living being capable of reasoning and of trying to find rationality within creation, or to bring rationality into it." "If man were merely a random product of evolution in some place on the margins of the universe, then his life would make no sense or might even be a chance of nature," he said. "But no, reason is there at the beginning: creative, divine reason." Church teaching holds that Roman Catholicism and evolutionary theory are not necessarily at odds: A Christian can, for example, accept the theory of evolution to help explain developments, but is taught to believe that God, not random chance, is the origin of the world. The Vatican, however, warns against creationism, or the overly literal interpretation of the Bibilical account of creation. Benedict's voice was hoarse and he coughed several times during the three-hour service, which ended after midnight. It was the second late night in a row for the 84-year-old pontiff following his participation in the Good Friday Way of the Cross procession at Rome's Colosseum, which commemorates Jesus' death. On Sunday, he celebrates Easter Mass in St. Peter's Square and gives his traditional Easter greetings in dozens of languages _ his last major celebration before next week's beatification of Pope John Paul II. The Easter Vigil is the most important liturgy on the church's calendar, when the faithful mark the passage from Christ's death to his resurrection on Easter Sunday. It is rich with symbols: fire and light signifying Jesus' resurrection, and the water used to baptize people into the faith. On Saturday night, Benedict baptized six adults from Switzerland, Albania, Russia, Peru, Singapore and China, pouring water over their heads as he prayed. Benedict began the service by lighting a candle and walking down a darkened central aisle of St. Peter's Basilica in silence, while hundreds of faithful in the pews shared the flame from candle to candle until the entire basilica twinkled. This year, students of the Legion of Christ, the conservative order undergoing a major Vatican-mandated overhaul, provided the liturgical service at the vigil. The Vatican took over the Legion last May 1 after confirming its founder was a pedophile. ||||| We celebrate this day as the origin and the goal of our existence. 'The first day of the week was the third day after Jesus' death. It was the day when he showed himself to his disciples as the Risen Lord. In truth, this encounter had something unsettling about it. The world had changed. This man who had died was now living with a life that was no longer threatened by any death. A new form of life had been inaugurated, a new dimension of creation', Pope Benedict proclaimed to the faithful. VATICAN CITY (Catholic Online) - The long 40 days of Lent now ended, the Great Triduum brings us to the Easter Vigil. The Vicar of Christ and Successor of the Apostle Peter, Pope Benedict XVI, gave this wonderful homily to the faithful who gathered in St. Peters Basilica. We share it in its entirety with our readers around the globe. (Editor in Chief, Deacon Keith Fournier): ***** 2011 Easter Vigil Homily of Pope Benedict XVI Dear Brothers and Sisters, The liturgical celebration of the Easter Vigil makes use of two eloquent signs. First there is the fire that becomes light. As the procession makes its way through the church, shrouded in the darkness of the night, the light of the Paschal Candle becomes a wave of lights, and it speaks to us of Christ as the true morning star that never sets - the Risen Lord in whom light has conquered darkness. The second sign is water. On the one hand, it recalls the waters of the Red Sea, decline and death, the mystery of the Cross. But now it is presented to us as spring water, a life-giving element amid the dryness. Thus it becomes the image of the sacrament of baptism, through which we become sharers in the death and resurrection of Jesus Christ. Yet these great signs of creation, light and water, are not the only constituent elements of the liturgy of the Easter Vigil. Another essential feature is the ample encounter with the words of sacred Scripture that it provides. Before the liturgical reform there were twelve Old Testament readings and two from the New Testament. The New Testament readings have been retained. The number of Old Testament readings has been fixed at seven, but depending upon the local situation, they may be reduced to three. The Church wishes to offer us a panoramic view of whole trajectory of salvation history, starting with creation, passing through the election and the liberation of Israel to the testimony of the prophets by which this entire history is directed ever more clearly towards Jesus Christ. In the liturgical tradition all these readings were called prophecies. Even when they are not directly foretelling future events, they have a prophetic character, they show us the inner foundation and orientation of history. They cause creation and history to become transparent to what is essential. In this way they take us by the hand and lead us towards Christ, they show us the true Light. At the Easter Vigil, the journey along the paths of sacred Scripture begins with the account of creation. This is the liturgy's way of telling us that the creation story is itself a prophecy. It is not information about the external processes by which the cosmos and man himself came into being. The Fathers of the Church were well aware of this. They did not interpret the story as an account of the process of the origins of things, but rather as a pointer towards the essential, towards the true beginning and end of our being. Now, one might ask: is it really important to speak also of creation during the Easter Vigil? Could we not begin with the events in which God calls man, forms a people for himself and creates his history with men upon the earth? The answer has to be: no. To omit the creation would be to misunderstand the very history of God with men, to diminish it, to lose sight of its true order of greatness. The sweep of history established by God reaches back to the origins, back to creation. Our profession of faith begins with the words: "We believe in God, the Father Almighty, Creator of heaven and earth". If we omit the beginning of the Credo, the whole history of salvation becomes too limited and too small. The Church is not some kind of association that concerns itself with man's religious needs but is limited to that objective. No, she brings man into contact with God and thus with the source of all things. Therefore we relate to God as Creator, and so we have a responsibility for creation. Our responsibility extends as far as creation because it comes from the Creator. Only because God created everything can he give us life and direct our lives. Life in the Church's faith involves more than a set of feelings and sentiments and perhaps moral obligations. It embraces man in his entirety, from his origins to his eternal destiny. Only because creation belongs to God can we place ourselves completely in his hands. And only because he is the Creator can he give us life for ever. Joy over creation, thanksgiving for creation and responsibility for it all belong together. The central message of the creation account can be defined more precisely still. In the opening words of his Gospel, Saint John sums up the essential meaning of that account in this single statement: "In the beginning was the Word". In effect, the creation account that we listened to earlier is characterized by the regularly recurring phrase: "And God said ." The world is a product of the Word, of the Logos, as Saint John expresses it, using a key term from the Greek language. "Logos" means "reason", "sense", "word". It is not reason pure and simple, but creative Reason, that speaks and communicates itself. It is Reason that both is and creates sense. The creation account tells us, then, that the world is a product of creative Reason. Hence it tells us that, far from there being an absence of reason and freedom at the origin of all things, the source of everything is creative Reason, love, and freedom. Here we are faced with the ultimate alternative that is at stake in the dispute between faith and unbelief: are irrationality, lack of freedom and pure chance the origin of everything, or are reason, freedom and love at the origin of being? Does the primacy belong to unreason or to reason? This is what everything hinges upon in the final analysis. As believers we answer, with the creation account and with John, that in the beginning is reason. In the beginning is freedom. Hence it is good to be a human person. It is not the case that in the expanding universe, at a late stage, in some tiny corner of the cosmos, there evolved randomly some species of living being capable of reasoning and of trying to find rationality within creation, or to bring rationality into it. If man were merely a random product of evolution in some place on the margins of the universe, then his life would make no sense or might even be a chance of nature. But no, Reason is there at the beginning: creative, divine Reason. And because it is Reason, it also created freedom; and because freedom can be abused, there also exist forces harmful to creation. Hence a thick black line, so to speak, has been drawn across the structure of the universe and across the nature of man. But despite this contradiction, creation itself remains good, life remains good, because at the beginning is good Reason, God's creative love. Hence the world can be saved. Hence we can and must place ourselves on the side of reason, freedom and love - on the side of God who loves us so much that he suffered for us, that from his death there might emerge a new, definitive and healed life. The Old Testament account of creation that we listened to clearly indicates this order of realities. But it leads us a further step forward. It has structured the process of creation within the framework of a week leading up to the Sabbath, in which it finds its completion. For Israel, the Sabbath was the day on which all could participate in God's rest, in which man and animal, master and slave, great and small were united in God's freedom. Thus the Sabbath was an expression of the Covenant between God and man and creation. In this way, communion between God and man does not appear as something extra, something added later to a world already fully created. The Covenant, communion between God and man, is inbuilt at the deepest level of creation. Yes, the Covenant is the inner ground of creation, just as creation is the external presupposition of the Covenant. God made the world so that there could be a space where he might communicate his love, and from which the response of love might come back to him. From God's perspective, the heart of the man who responds to him is greater and more important than the whole immense material cosmos, for all that the latter allows us to glimpse something of God's grandeur. Easter and the paschal experience of Christians, however, now require us to take a further step. The Sabbath is the seventh day of the week. After six days in which man in some sense participates in God's work of creation, the Sabbath is the day of rest. But something quite unprecedented happened in the nascent Church: the place of the Sabbath, the seventh day, was taken by the first day. As the day of the liturgical assembly, it is the day for encounter with God through Jesus Christ who as the Risen Lord encountered his followers on the first day, Sunday, after they had found the tomb empty. The structure of the week is overturned. No longer does it point towards the seventh day, as the time to participate in God's rest. It sets out from the first day as the day of encounter with the Risen Lord. This encounter happens afresh at every celebration of the Eucharist, when the Lord enters anew into the midst of his disciples and gives himself to them, allows himself, so to speak, to be touched by them, sits down at table with them. This change is utterly extraordinary, considering that the Sabbath, the seventh day seen as the day of encounter with God, is so profoundly rooted in the Old Testament. If we also bear in mind how much the movement from work towards the rest-day corresponds to a natural rhythm, the dramatic nature of this change is even more striking. This revolutionary development that occurred at the very the beginning of the Church's history can be explained only by the fact that something utterly new happened that day. The first day of the week was the third day after Jesus' death. It was the day when he showed himself to his disciples as the Risen Lord. In truth, this encounter had something unsettling about it. The world had changed. This man who had died was now living with a life that was no longer threatened by any death. A new form of life had been inaugurated, a new dimension of creation. The first day, according to the Genesis account, is the day on which creation begins. Now it was the day of creation in a new way, it had become the day of the new creation. We celebrate the first day. And in so doing we celebrate God the Creator and his creation. Yes, we believe in God, the Creator of heaven and earth. And we celebrate the God who was made man, who suffered, died, was buried and rose again. We celebrate the definitive victory of the Creator and of his creation. We celebrate this day as the origin and the goal of our existence. We celebrate it because now, thanks to the risen Lord, it is definitively established that reason is stronger than unreason, truth stronger than lies, love stronger than death. We celebrate the first day because we know that the black line drawn across creation does not last for ever. We celebrate it because we know that those words from the end of the creation account have now been definitively fulfilled: "God saw everything that he had made, and behold, it was very good" (Gen 1:31). Amen. --- Copyright 2016 - Distributed by THE CALIFORNIA NETWORKSports: That sports may be an opportunity for friendly encounters between peoples and may contribute to peace in the world.Living the Gospel: That Christians may live the Gospel, giving witness to faith, honesty, and love of neighbor.

– There is "divine reason" behind creation and humanity, said Pope Benedict XVI in his Easter Vigil homily yesterday. "Are irrationality, lack of freedom, and pure chance the origin of everything, or are reason, freedom, and love at the origin of being?" he asked. "If man were merely a random product of evolution in some place on the margins of the universe, then his life would make no sense or might even be a chance of nature. But no, reason is there at the beginning: creative, divine reason. " The 84-year-old Benedict coughed several times and his voice sounded sore, according to the AP report of the three-hour service, the most important liturgy on the Catholic church's calendar. The liturgical service was provided by students from the Legion of Christ, a conservative order being restructured after its was found last year to be embroiled in a sexual abuse scandal. You can check out Benedict's homily in its entirety here.

the anomalous magnetic moment of the muon @xmath3 is among the most precisely known quantities in the standard model ( sm ) , and therefore , provides us with a sensitive probe of new physics beyond the sm ( bsm ) @xcite . there is a long - standing @xmath4 discrepancy between the sm prediction @xcite and the measured value of @xmath5 @xcite : @xmath6 the uncertainties in the experimental measurement , which come from the e821 experiment at bnl @xcite , can be reduced by about a factor of four in the upcoming muon @xmath7 experiment at fermilab @xcite . if comparable progress can be made in reducing the uncertainties of the sm prediction @xcite , we will have a definite answer to the question whether or not @xmath8 is evidence for bsm physics . thus from a theoretical point of view , it is worthwhile investigating simple bsm scenarios which can account for the @xmath0 anomaly , should this endure , and at the same time , have complementary tests in other ongoing and near future experiments . with this motivation , we discuss here a simple @xmath9 interpretation of the @xmath0 anomaly . a sufficiently muonphilic @xmath9 can address the @xmath0 discrepancy @xcite ; however , in order to avoid stringent bounds from the charged lepton sector , while being consistent with a sizable contribution to @xmath0 , the @xmath9 coupling must violate lepton universality . decays at the lhcb @xcite , in @xmath10 decays at babar @xcite , belle @xcite and lhcb @xcite , and in the @xmath11 decay at both cms @xcite and atlas @xcite ( which however seems to have disappeared in the early run - ii lhc data @xcite ) . see e.g. refs . @xcite for the most recent attempts to explain some of these anomalies . in this work we concentrate on @xmath0 and only comment on @xmath11 . ] for instance , a sizable @xmath9 coupling to electrons is strongly constrained over a large range of @xmath9 masses from @xmath12 measurements at lep @xcite , electroweak precision tests @xcite , @xmath13 ( with @xmath14 ) at babar @xcite , @xmath15 at na48/2 @xcite , the @xmath7 of the electron @xcite , and neutrino - neutrino scattering in supernova cores @xcite . similarly , a sizable flavor - diagonal @xmath1 coupling to muons is strongly constrained from neutrino trident production @xmath16 @xcite using the ccfr data @xcite . in addition , charged lepton flavor - violating ( lfv ) processes , such as @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 , @xmath22 , constrain all the lepton - flavor - diagonal couplings of the @xmath9 , as well as the flavor off - diagonal couplings to electrons and muons @xcite . there also exist stringent lhc constraints from di - lepton resonance searches : @xmath23 @xcite , @xmath24 @xcite and @xmath25 @xcite . all these constraints require the flavor - diagonal @xmath1 couplings , as well as the flavor off - diagonal couplings involving electrons to be very small , or equivalently , push the @xmath9 mass scale to above multi - tev range @xcite . we propose a simplified leptophilic @xmath9 scenario with _ only _ a flavor off - diagonal coupling to the muon and tau sector [ see eq . below ] , which trivially satisfies all the above - mentioned constraints , and moreover , can be justified from symmetry arguments , as discussed below . in such a scenario , we find that the most relevant constraints come from leptonic @xmath26 decays in low - energy precision experiments , and to some extent , from the leptonic decays of the sm @xmath27 boson at the lhc . in particular , we show that the @xmath0 anomaly can be accounted for only with @xmath28 and by allowing a larger @xmath9 coupling to the right - handed charged - leptons than to the left - handed ones , whereas the lighter @xmath1 scenario ( with @xmath29 ) is ruled out completely from searches for @xmath30+invisible decays . we emphasize that the entire allowed range can likely be tested in future low - energy precision measurements of lepton flavor universality in @xmath26 decays at belle 2 , as well as in the leptonic decay of the @xmath27 boson at the lhc . a striking four - lepton collider signature consisting of like - sign di - muons and like - sign di - taus can be probed at the high luminosity phase of the lhc ( hl - lhc ) as well as at a future electron - positron collider running at the @xmath31 pole . we also point out an interesting possibility for the detection of our flavor - violating @xmath9 scenario by the scattering of ultra - high energy neutrinos off lower - energy neutrinos , which leads to characteristic spectral absorption features that might be observable in large volume neutrino telescopes like icecube and km3net . the rest of the paper is organized as follows : in section [ sec : model ] , we present our phenomenological model lagrangian , which can be justified in a concrete bsm scenario . in section [ sec : gm2 ] , we show how the @xmath0 anomaly can be resolved in our lfv @xmath1 scenario . section [ sec : lfv ] discusses the lepton flavor universality violating tau decays for @xmath1 masses larger than the tau mass . section [ sec:2body ] discusses the two - body tau decays for a light @xmath1 . in section [ sec : lhc ] , we derive the lhc constraints on our model from leptonic @xmath27 decays . section [ sec : lep ] derives the lep constraints from @xmath31-decay measurements . section [ sec:4lepton ] presents a sensitivity study for the new collider signature of this model . section [ sec : icecube ] discusses some observational prospects of the @xmath1 effects in neutrino telescopes . our conclusions are given in section [ sec : concl ] . our simplified model lagrangian for the @xmath1 coupling exclusively to the muon and tau sector of the sm is given by @xmath32 where @xmath33 are the chirality projection operators . due to @xmath34 invariance , the couplings of the left - handed neutrinos and charged leptons are identical , whereas we do not introduce right - handed neutrinos in order to keep the model minimal . the left - handed and right - handed couplings @xmath35 and @xmath36 could in principle contain @xmath37 violating phases . we will take into account the complex nature of these couplings in all the equations below ; in our numerical analysis however , we will take them to be real for simplicity . we allow different lfv couplings of the @xmath1 to left- and right - handed charged leptons , which will be crucial for the @xmath0 explanation . we assume the @xmath1 can acquire mass from the spontaneous breaking of some extra @xmath38 symmetry , under which it is charged . the details of the mechanism that generates the @xmath9 mass are irrelevant for our phenomenological purposes , and we treat @xmath39 as a free parameter in the following . since @xmath40 is the only flavor - blind @xmath41 symmetry that is anomaly - free with the sm field content , the advantage of the extra @xmath38 is that the associated @xmath1 can couple differently to different sm fermion families . as mentioned above , most of the existing experimental constraints involve first generation fermions , which may be regarded as more ` fundamental ' in the sense that these comprise ordinary matter around us . thus , we assume that the couplings of the @xmath9 to the first generation fermions are vanishingly small or non - existent @xcite , so that all these stringent experimental constraints are readily avoided . symmetry @xcite , which is in fact the only anomaly - free @xmath41 group with nonzero charge assignments to sm neutrinos that can lead to an experimentally viable light @xmath1 without requiring the addition of any exotic fermions . another possibility is a @xmath41 group charged under only muon or tau number , but this requires new chiral fermions charged under both @xmath34 and @xmath40 , as well as under the new @xmath42 or @xmath43 group . ] if the @xmath1 does not couple universally to quarks , there will be no glashow - iliopoulos - maiani ( gim ) suppression of the flavor changing neutral current ( fcnc ) processes in the quark sector , and the current experimental bounds on neutral meson mixing , such as @xmath44 @xcite , as well as fcnc decays of the top , bottom and strange quarks @xcite will force the @xmath1 couplings to be rather small . therefore , we will assume that the @xmath1 in our case is leptophilic , and more specifically , couples only to second and third generation leptons . the phenomenological lagrangian in eq . can then be justified by imposing an exact discrete symmetry under which @xcite @xmath45 where @xmath46 and @xmath47 are respectively the usual @xmath34 lepton doublets and singlets in the sm in the gauge eigenstate basis and @xmath48 is the @xmath40 gauge field . phenomenology discussed here . ] since the @xmath48 gauge field , and hence , the photon and @xmath31 fields are even under the discrete symmetry , we can forbid kinetic @xmath49 mixing and @xmath50 mixing to all orders , thus removing a few more stringent experimental constraints , e.g. from neutrino - electron scattering @xcite and beam dump experiments @xcite . the flavor - violating @xmath9 coupling in eq . gives rise to a new contribution to @xmath0 , as shown in fig . [ fig:1 ] , and is given by the general expression @xcite @xmath51\nonumber \\ & \times \big[m_\mu^2 x^2+m_{z'}^2(1-x)+x(m_\tau^2-m_\mu^2)\big]^{-1 } \ , , \label{gm2}\end{aligned}\ ] ] where @xmath52 and @xmath53 in the notation of eq . . for @xmath54 , this reduces to @xmath55 \ , , \label{eq : g-2}\ ] ] note that in the presence of both left - handed and right - handed couplings , the contributions of the flavor changing @xmath9 are enhanced by a factor @xmath56 . this is in contrast to contributions from flavor - blind new physics , that do not enjoy such an enhancement . moreover , a purely left - handed or right - handed coupling would lead to a negative contribution to @xmath5 , thus making the @xmath8 discrepancy worse than in the sm . contribution to the anomalous magnetic moment of the muon in our model.,width=151 ] vs. @xmath57 plane for @xmath58 gev . the green band is preferred at @xmath59 by the @xmath0 anomaly , whereas the gray region is disfavored at @xmath60 ( see section [ sec : gm2 ] ) . the red region is excluded by lepton flavor universality in tau decays ( see section [ sec : lfv ] ) . the dashed red contours show values of constant lepton flavor universality violation in tau decays . the black dashed curve shows the 95% cl lhc exclusion from searches for leptonic @xmath27 decays ( see section [ sec : lhc ] ) and the purple dashed curve shows the 95% cl lep exclusion from @xmath31 coupling measurements ( see section [ sec : lep ] ) . the orange dotted curve shows the expected @xmath61 sensitivity to the process @xmath62 at the high - luminosity lhc ( see section [ sec:4lepton]).,scaledwidth=46.0% ] in figs . [ fig:2 ] and [ fig:3 ] we show regions of parameter space that allow to address the @xmath0 discrepancy . the plot in fig . [ fig:2 ] shows the @xmath35 vs. @xmath36 plane for a fixed @xmath9 mass @xmath58 gev ; the plots in fig . [ fig:3 ] show the @xmath63 vs. @xmath36 plane for two choices of @xmath35 , namely , @xmath64 ( left ) and @xmath65 ( right ) . the green bands correspond to the @xmath66 preferred region from eq . ( [ eq : gm2 ] ) . in the gray regions , the discrepancy is larger than @xmath67 which we consider to be excluded . note that both left - handed and right - handed couplings are required to explain the anomaly . pure left - handed or pure right - handed couplings of the @xmath9 necessarily enlarge the discrepancy in @xmath0 , as seen from eq . , and hence , are not entertained here . other constraints shown in figs . [ fig:2 ] and [ fig:3 ] are explained below . constraints on our flavor violating @xmath9 scenario can be derived from leptonic tau decays . in the sm , the leptonic decays of the tau , @xmath68 and @xmath69 , are mediated by the tree - level exchange of a @xmath27 boson . integrating out the @xmath27 , we arrive at the following effective hamiltonian describing the decays : @xmath70 where @xmath71 is the @xmath34 gauge coupling . due to lepton flavor universality of the weak interactions , the ratio of the branching ratios of the leptonic tau decays is close to unity . in the sm , the ratio can be predicted with extremely high accuracy @xcite : @xmath72 where the deviation from unity is almost entirely due to phase space effects . on the experimental side , the most precise measurement of this ratio comes from babar @xcite . the pdg average @xcite also includes less precise determinations from cleo @xcite and argus @xcite : @xmath73 we observe a slight tension with the sm prediction at the level of @xmath74 . combining eqs . ( [ eq : tausm ] ) and ( [ eq : tauexp ] ) we find @xmath75 the tree level exchange of the considered flavor violating @xmath9 can not affect the @xmath76 decay . however , it does give additional contributions to the @xmath77 decay and induces the new tau decay mode @xmath78 , as shown in fig . [ fig:4 ] . the decay @xmath78 is absent in the sm , but has exactly the same experimental signature as @xmath77 . in the following we will therefore consider the sum of the two decay modes that we denote with @xmath79 . as long as @xmath54 the treatment of the @xmath9 effect in terms of an effective hamiltonian is valid and we find @xmath80 the hamiltonian in eq . leads to the following correction to the lepton flavor universality ratio @xmath81 : @xmath82 note that our model can only increase the ratio @xmath81 compared to the sm prediction . thus , the result in eq . ( [ eq : taubound ] ) gives strong constraints on the @xmath9 parameter space . if we neglect the term that contains the right - handed @xmath9 coupling , we find the following approximate constraint at the @xmath66 level @xmath83 note that in the absence of @xmath35 , the @xmath9 does not couple to neutrinos and the constraint from lepton flavor universality in tau decays can be avoided . contribution to the lepton flavor universality violating tau decay.,width=188 ] the constraint ( [ eq : taubound ] ) is shown in fig . [ fig:2 ] in the @xmath35@xmath57 plane in red , for a fixed @xmath9 mass of @xmath58 gev . large values of @xmath35 are strongly constrained , leaving a compact region of @xmath35-@xmath36 parameter space , where the @xmath0 anomaly can be explained . the dashed red lines show values of constant lepton flavor universality violation , i.e. @xmath84 . probing lepton flavor universality violation in tau decays down to a level of @xmath85 would allow us to conclusively test the entire remaining parameter space relevant for our explanation of the @xmath0 anomaly . this should be possible to achieve at belle 2 @xcite with 50 ab@xmath86 luminosity , assuming that systematic uncertainties can be kept under control . for @xmath9 masses of the order of the tau mass , the momentum transfer along the @xmath9 propagator in fig . [ fig:4 ] has to be taken into account . in this case we find @xmath87 with the functions @xmath88 \ , , \nonumber \\ g(z ) & = & \frac{2}{z^4 } \left [ - z^3 -3z^2 + 6z + 6(1-z)\log(1-z ) \right ] \ , . \nonumber\end{aligned}\ ] ] in the limit @xmath54 , we have @xmath89 , @xmath90 and then eq . reduces to eq . ( [ eq : heavyzp ] ) . note that in the above expression we still neglected the muon mass . once the @xmath9 mass comes close to the tau mass , such that @xmath91 also the muon can no longer be treated massless . in our numerical analysis we take into account the muon mass . in fig . [ fig:3 ] we show in red the regions in the @xmath63@xmath57 plane that are excluded by the current experimental measurement of @xmath81 , for two choices of @xmath35 . as expected , the constraint is strongest for large values of @xmath35 . for a heavy @xmath9 the constraint agrees well with the approximate bound in eq . ( [ eq : mzpbound ] ) . we observe that in the case @xmath64 , the tau decays exclude entirely our explanation of the @xmath0 anomaly for any @xmath9 mass larger than @xmath92 . in the tau rest frame in the presence of a light @xmath1 with the indicated masses.,scaledwidth=46.0% ] a light @xmath9 of the order of the tau mass not only affects the overall rate of the @xmath77 decay , but also modifies the muon energy spectrum . in fig . [ fig:5 ] we show the muon energy spectrum in the tau rest frame for various choices of the @xmath9 mass . we set @xmath93 and choose @xmath36 such that the @xmath9 leads to a 10% increase of the @xmath77 decay rate , i.e. @xmath94 . for a @xmath1 mass close to the tau mass , the @xmath9 exchange leads to muons that tend to be slightly softer compared to that from the sm . we caution the reader that a possible impact of the modified muon spectrum is not taken into account when deriving the bound in fig . [ fig:3 ] . a careful analysis of the experimental acceptances and efficiencies would be required to ascertain the robustness of the bound shown in the parameter region @xmath95 few gev ( shown by the dotted red curve ) , which is beyond the scope of this work . a more detailed study of the @xmath1 effect might include a michel parameter analysis for tau decays @xcite . moreover , a study of the tau polarization via its decays may be useful to probe differences from the sm , induced by the @xmath1 effect . if the @xmath9 mass is smaller than the difference of tau and muon mass , @xmath96 the two body decay @xmath97 opens up kinematically . this is illustrated for the two cases @xmath98 gev and @xmath99 gev by the peaks in the muon energy spectrum shown in fig . [ fig:5 ] . in this region of parameter space the only available decay mode of the @xmath9 is into neutrinos . direct searches for the decay @xmath100missing energy can then be used to constrain the @xmath9 parameter space . the @xmath97 decay width reads @xmath101 \nonumber \\ & \times \sqrt{\left ( 1 - \frac{m_{z^\prime}^2}{m_\tau^2 } \right)^2 - \frac{m_\mu^2}{m_\tau^2 } \left ( 2 + \frac{2m_{z^\prime}^2}{m_\tau^2 } -\frac{m_\mu^2}{m_\tau^2}\right ) } \ , . \label{eq : muzp}\end{aligned}\ ] ] neglecting terms that are suppressed by the muon mass , this can be simplified to @xmath102 in our numerical analysis we keep muon mass effects and use eq . . searches for the two body decay @xmath103 by argus @xcite , where @xmath104 is an unobservable particle , directly apply to our case ; they give bounds on the corresponding branching ratio for masses up to @xmath105 gev . the region of @xmath9 parameter space that is excluded by this search is shown in fig . [ fig:3 ] in blue . the bound from @xmath97 is remarkably strong , and as a result , our explanation of the @xmath0 is entirely excluded for @xmath106 by orders of magnitude , independent of the relative size of @xmath35 and @xmath36 . the direct lhc constraints on @xmath1 from simple resonance searches like @xmath107 and @xmath108 are not applicable in our case , since the @xmath1 does not couple to quarks at the tree level . moreover , the flavor - violating @xmath1 searches at the lhc have only focused on the @xmath25 channel so far @xcite . nevertheless , we can derive lhc constraints on the @xmath109 coupling from the leptonic decays of the @xmath27 boson , since @xmath110 will also get a contribution from @xmath111 , followed by the @xmath1-mediated decay of tau , as shown in fig . [ fig:4 ] . this will lead to an isolated muon and three neutrinos in the final state , where the neutrinos will be registered in the lhc detectors simply as missing energy , without any information on their number or flavor content . so we can use the constraints derived from this channel in our case , as long as the missing energy criterion @xmath112 gev used in the corresponding @xmath113 search at @xmath114 tev lhc @xcite is satisfied . to check this , we implemented our model lagrangian into madgraph5 @xcite for event generation with ct14nnlo pdfs @xcite , used pythia 6.4 @xcite for showering and hadronization , and delphes 3 @xcite for a fast detector simulation . we find that most of our @xmath115 signal events pass the event selection cuts of ref . @xcite for a wide range of @xmath1 masses of interest . here we have used the narrow - width approximation and have written down the @xmath1-induced cross section as @xmath116 for @xmath117 , we use the following expression for the width of the 3-body decay @xmath118 : @xmath119 where @xmath120 and we included both channels @xmath121 and @xmath122 . for @xmath123 , we use the 2-body decay formula as in eq . . comparing the measured value of the @xmath110 cross section @xmath124 nb @xcite with the sm nnlo prediction @xcite @xmath125 nb obtained using ct14nnlo pdfs @xcite , we derive 95% cl upper limits on the @xmath1 couplings , as shown in figs . [ fig:2 ] and [ fig:3 ] by the black dashed curves . we find that the lhc constraints are weaker than the low - energy constraints directly derived from @xmath26 decay . future run - ii lhc data , as well as the high - luminosity phase @xcite and/or a future 100 tev collider @xcite will perhaps be able to probe a large portion of the allowed parameter space in figure [ fig:3 ] , if the systematics and the sm theory uncertainty could be improved . while our @xmath1 does not couple to electrons and quarks at tree level , it can contribute , however , to the processes @xmath126 , and @xmath127 via one - loop diagrams involving @xmath1 , as shown in fig . [ fig : lep ] . measurements of the sm @xmath31 couplings @xcite to muons , taus and neutrinos can therefore be used to set constraints on the @xmath1 parameter space . we find the following modifications of the @xmath31 couplings due to the @xmath1 loop : @xmath128 with the loop function @xmath129 @xcite @xmath130 \ , , \label{loop}\end{aligned}\ ] ] where @xmath131 is the di - logarithm . in the above expressions , we use the electron couplings @xmath132 and @xmath133 as convenient normalization , as they are not affected by @xmath1 loops . -decay vertex due to lfv @xmath1 interactions.,width=188 ] the combined experimental results for the @xmath31 couplings from lep and sld read @xcite @xmath134 with the error correlation matrix @xmath135 to derive bounds on the @xmath1 couplings and mass we perform a simple @xmath136 fit , setting the electron couplings @xmath132 and @xmath133 to the measured values . the resulting constraint is shown in the plots of figs . [ fig:2 ] and [ fig:3 ] as dashed purple curves . above the curves @xmath137 , corresponding to a @xmath138 cl exclusion . the constraint vanishes around @xmath139 gev , where the loop function has a zero crossing . we observe that the lep constraint is generically weaker than the constraint obtained from the tree - level leptonic tau decays . similarly , the constraints obtained from the modifications to the @xmath27 and @xmath31 total widths due to the @xmath1 effects @xcite are weaker than those in the whole parameter space of interest , and therefore , are not shown in fig . [ fig:3 ] . this is applicable to both lepton and hadron colliders ( depending on whether the initial state fermion @xmath140 is a sm charged lepton or quark ) . there exists a similar diagram with an intermediate muon , which is not shown here , but included in our calculation.,width=188 ] the leptophilic @xmath1 scenarios have characteristic multi - lepton signatures at both lepton and hadron colliders @xcite . a particularly interesting signal in our lfv @xmath1 scenario is the 4-lepton final state with two same - sign muons and taus at the lhc , i.e. @xmath141 as shown in fig . [ fig : col ] . this signal is very clean and effectively background - free . through this process , one might also be able to determine the @xmath9 mass for @xmath142 , when the @xmath1 in fig . [ fig : col ] goes on - shell and one of the @xmath109 pairs will have an invariant mass at @xmath39 . although the tau reconstruction poses some practical challenges , eq . could provide a ` smoking gun ' signal for our @xmath1 scenario at the lhc . we simulate the process to estimate the sensitivity reach at the @xmath143 tev lhc . the parton level events are generated using madgraph5 @xcite , which are then fed to pythia 6.4 @xcite for showering and hadronization , and delphes 3 @xcite for a fast detector simulation . we impose the basic trigger cuts following a previous analysis for light @xmath1 searches in the @xmath144 channel @xcite : * the leading lepton must satisfy the transverse momentum cut @xmath145 gev , while the sub - leading leptons are required to satisfy a milder cut @xmath146 gev ; * all the four leptons must satisfy the pseudo - rapidity @xmath147 and the isolation cut @xmath148 . these values are set to be as inclusive as possible for an optimistic analysis . since we are interested in the final states with same - sign muon pairs , we select the hadronic decay mode of the taus . in the sm , each tau decays hadronically with a probability of @xmath149 65% , producing a tau - jet mostly containing neutral and charged pions . in our case with a pair of taus in the final state , 42% of the events will contain two tau - jets . the hadronic tau decays have low charged track multiplicity ( one or three prongs ) and a relevant fraction of the electromagnetic energy deposition due to photons coming from the decay of neutral pions . moreover , when the momentum of the tau is large compared to its mass , the tau - jets will be highly collimated and produce localized energy deposit in the electromagnetic and hadronic calorimeters . these characteristics can be exploited to enhance the identification of hadronic tau decays @xcite . we have assumed an optimistic value of 70% for the tau - tagging efficiency in our analysis . since the sm background is negligible for the same - sign di - lepton pairs @xmath150 , we can simply estimate the signal sensitivity as @xmath151 , where @xmath152 is the integrated luminosity and @xmath153 is the signal cross section times efficiency , as obtained from our detector simulation . our results for the @xmath154 sensitivity reach ( corresponding to @xmath155 ) in the high - luminosity phase of the lhc with 3 ab@xmath86 integrated luminosity are shown in figs . [ fig:2 ] and [ fig:3 ] by the orange curves . the lhc sensitivity gets weaker for a very light @xmath9 with mass @xmath156 , since both the intermediate tau as well as @xmath1 in fig . [ fig : col ] are off - shell in this case . the small bump around @xmath31-mass is because the @xmath31 also becomes off - shell for @xmath157 . overall , we find that for @xmath142 , the hl - lhc has good sensitivity to large parts of the @xmath0-favored region . the lhc sensitivity again becomes weaker for a very heavy @xmath158 tev or so , simply due to the kinematic suppression . a future @xmath159 tev @xmath160 collider could extend our lfv @xmath1 sensitivity reach to the multi - tev range . the collider sensitivity can be further improved for @xmath161 by considering a lepton collider operating at the @xmath31-pole , i.e. with @xmath162 . as an example , we consider a next generation @xmath163 @xmath31 factory such as the fcc - ee , and simulate the process ( cf . [ fig : col ] ) @xmath164 for @xmath161 using the procedure outlined above . our results are shown in fig . [ fig:3 ] by the blue curves for the maximum achievable integrated luminosity of 2.6 ab@xmath86 at fcc - ee @xcite . we find that the sensitivity can be improved by a factor of 2 - 3 , thus covering almost the entire @xmath0-favored region for @xmath161 . our @xmath1 scenario can in principle also affect the sm higgs decays . first of all , the @xmath165 decay will receive a one - loop correction due to the lfv @xmath1 interactions . although it is enhanced by the tau yukawa coupling , due to the loop suppression factor , and given that br@xmath166 in the sm @xcite , the deviation due to the @xmath1-loop correction is extremely difficult to be observed at the hl - lhc or even at a dedicated higgs factory . the @xmath1 interactions could also induce a lfv decay of @xmath167 , where the @xmath1 goes undetected for a sufficiently small @xmath39 . however , for the allowed range of masses and couplings in fig . [ fig:3 ] , this effect is again small and easily compatible with the lhc searches for @xmath168 that imply br@xmath169 @xcite . contributions to the charged - current neutrino - nucleon interactions . similar diagrams for incident neutrinos of muon flavor , as well as for antineutrinos and also for neutral - current interactions , are not shown here.,title="fig:",width=151 ] contributions to the charged - current neutrino - nucleon interactions . similar diagrams for incident neutrinos of muon flavor , as well as for antineutrinos and also for neutral - current interactions , are not shown here.,title="fig:",width=151 ] in this section , we briefly discuss a complementary way to test our lfv @xmath1 hypothesis using ultra - high energy ( uhe ) neutrinos in large volume neutrino telescopes like icecube and km3net . first , we note that the @xmath1 interactions in our model induce new channels for the neutrino - nucleon interactions , as illustrated in fig . [ fig:6 ] for the charged - current ( cc ) process . for @xmath170 , they could potentially give rise to a novel signature with simultaneous muon and tau events coming from the @xmath171 decay . however , it turns out that in presence of both left and right - handed @xmath1 couplings to charged leptons , as required for the @xmath0 explanation , there is a destructive interference between the two diagrams in fig . [ fig:6 ] , which leads to a cross section too small to be ever observed . moreover , the stringent limits on the @xmath1 couplings from tau decays ( cf . figs . [ fig:2 ] and [ fig:3 ] ) necessarily imply that even if we disregard the @xmath0 favored region by taking @xmath172 , the total cross section for the processes in fig . [ fig:6 ] is still small , as compared to that of the sm cc interaction . to give an example , for a benchmark point with @xmath173 gev , @xmath174 and @xmath175 which satisfies the @xmath176 constraint , we find the total cross section for the processes shown in fig . [ fig:6 ] ( including the antineutrino initial states ) for an incoming neutrino energy @xmath177 pev to be @xmath178 , as compared to the corresponding sm cc cross section of @xmath179 , both calculated using the ct14nnlo pdfs @xcite . it is difficult to measure such a small cross section at icecube even with large statistics , since it will be overshadowed by various uncertainties in the incoming neutrino flux , flavor composition , and parton distribution functions ( see e.g. @xcite ) . a better possibility to detect a light @xmath1 at icecube might be through its effect on neutrino - neutrino scattering due to on - shell @xmath1 production . in fact , the resonant absorption of uhe neutrinos by the cosmic neutrino background ( c@xmath180b ) @xcite in the presence of a light mediator has been invoked @xcite to explain the apparent energy gap in the icecube neutrino data @xcite just below the pev deposited energy bin . however , this scenario works only for an mev - scale @xmath1 , which is unfortunately ruled out in our model due to the @xmath181 constraint . for a higher @xmath1 mass , the incoming neutrino energy required to observe a resonance feature at the icecube will be shifted upwards : @xmath182 where @xmath183 is the redshift parameter at which the scattering occurs ( typically taken to be the source redshift ) , in eq . is due to the fact that the energy @xmath184 of the cosmic neutrino @xmath185 at the source position @xmath183 is @xmath186 times the energy @xmath187 measured at icecube in an expanding universe . ] @xmath188 is the mass of the target c@xmath180b , which is assumed to be larger than the effective temperature of the thermal distribution of the c@xmath180b , @xmath189 ev . in eq . should be replaced with the thermally averaged momentum @xmath190 . ] the total cross section for @xmath191 , where @xmath192 and @xmath193 or @xmath194 ( with @xmath195 ) , is given by @xmath196 where @xmath197 is the squared center of mass energy and @xmath198 is the total width of the @xmath1 . here we have ignored the @xmath199-channel contribution for the @xmath200 final state , as it is highly suppressed relative to the @xmath197-channel resonance . also we have assumed @xmath201 . for @xmath142 , there are two decay modes of @xmath202 , with the corresponding decay widths given by @xmath203 \ , , \end{aligned}\ ] ] where @xmath204 , @xmath205 and @xmath206 are defined below eq . . the total decay width of @xmath1 is then given by @xmath207 , taking into account two possibilities for each decay mode . as a function of the energy of one of the initial state neutrinos . for the second neutrino @xmath208 , we consider two cases : c@xmath180b ( red solid curve ) and supernova neutrinos with mev energy ( blue solid and dashed curves ) . the numbers above the peaks show the @xmath1 mass . for comparison , we also show the sm neutrino - nucleon cc and @xmath209 cross sections.,width=302 ] the cross section is plotted in fig . [ fig:7 ] as a function of the energy of the incoming uhe neutrino @xmath185 for three different cases , depending on the energy of the other neutrino @xmath208 . first , we consider the c@xmath180b for which the effective temperature @xmath210 is smaller than at least two of the light neutrino masses , so @xmath211 . from eq . , it is clear that for @xmath39 above the tau mass , the resonance will occur at very high energies well beyond the energy scale currently being probed at the icecube . for an illustration , we choose a benchmark point from fig . [ fig:3 ] ( right panel ) satisfying all the constraints : @xmath212 gev , @xmath213 , and @xmath214 and take the light neutrino mass @xmath215 ev and a typical source redshift @xmath216 . for this benchmark , we find the resonance energy to be at @xmath217 gev , resonance occurs at @xmath218 gev for @xmath216 . ] as shown by the red solid curve in fig . [ fig:7 ] . the other two light neutrino mass eigenstates will induce similar peaks at different energies , depending on their mass hierarchy . for comparison , we also show the sm neutrino - nucleon cc and @xmath209 cross sections , with the latter having the glashow resonance @xcite at 6.3 pev . in spite of the resonance enhancement , the @xmath200 cross section turns out to be much smaller than the sm @xmath219 cross section . in order to check the condition under which the uhe neutrinos @xmath185 will likely have at least one interaction with the c@xmath180b during their entire journey from the source to earth , we calculate their mean free path ( mfp ) , given by @xmath220^{-1 } \nonumber \\ & \ = \ \frac{1}{n_\nu \sigma(e_\nu ) } \ , , \end{aligned}\ ] ] where @xmath221 is the number density of the c@xmath180b ( for each flavor ) and @xmath222 is given by eq . . the mfp will be the minimum at the resonance energy which corresponds to the maximum cross section . the survival rate of the high - energy neutrino @xmath185 travelling from the source at @xmath183 to earth ( at @xmath223 ) is then given by @xmath224 } \ , , \end{aligned}\ ] ] where @xmath225 , @xmath226 is the speed of light in vacuum , and the present best - fit values of the cosmological parameters in a @xmath227cdm universe are @xmath228 with @xmath229 , the matter energy density @xmath230 and the dark energy density @xmath231 @xcite . thus , if the traveling distance of the uhe neutrinos is larger than the mfp , they will be attenuated by the @xmath232b and their survival rate will have a ` dip ' at the resonance energy . this will lead to a characteristic absorption feature in the uhe neutrino energy spectrum . for the benchmark discussed above , we find @xmath233 kpc , which means that all extragalactic sources like gamma - ray bursts and active galactic nuclei ( with typical distances of mpc or larger ) or even far - away galactic sources like supernova remnants could in principle show an absorption feature in their neutrino spectrum due to the presence of a light @xmath1 . the resonance energy could be lowered significantly if we consider interactions of the high - energy neutrinos with other relativistic neutrinos naturally available , e.g. supernovae neutrinos ( after they have oscillated into muon and tau flavors ) which have a typical energy @xmath234 in the mev range @xcite . in this case , the center - of - mass energy of the system is @xmath235 , and the resonance condition gets modified to @xmath236 , independent of the light neutrino mass , thus lowering the resonance energy down to the tev scale . this is illustrated in fig . [ fig:7 ] for two choices of @xmath212 gev ( blue solid curve ) and 10 gev ( blue dashed curve ) . below the tev scale , it will be difficult to observe the resonance feature , since it will be swamped by the atmospheric neutrino background . the neutrino number density at the supernova core surface is much larger , e.g. @xmath237 for sn1987a @xcite . hence , the mfp can be much smaller , thus allowing for the possibility of observing the absorption feature from both galactic and extragalactic sources , provided the incoming high - energy neutrinos encounter a supernova core collapse en route to earth . the likelihood of such an arrangement somewhat depends on the origin of the high - energy neutrino source , and can not be excluded at the moment . the lfv interactions could also alter the ratio of astrophysical neutrino flavors at detection on earth from the standard expectation of @xmath238 . the detailed predictions for the event rate and the track - to - shower ratio will depend on many parameters , including the source neutrino flux normalization and spectral index , redshift , as well as the pdf uncertainties , but in spite of all these uncertainties , the anomalous features could plausibly be measured @xcite by icecube or next generation neutrino telescopes like icecube - gen2 , thereby opening a new era of ` cosmic neutrino spectroscopy ' . we have discussed a simple new physics interpretation of the long - standing anomaly in the muon anomalous magnetic moment in terms of a purely flavor off - diagonal @xmath1 coupling only to the muon and tau sector of the sm . we have discussed the relevant constraints from lepton flavor universality violating tau decays for @xmath239 and from @xmath240 invisibles decay for @xmath241 , as well as the latest lhc constraints from @xmath242 searches . we find that for a @xmath1 lighter than the tau , the low - energy tau decay constraints rule out the entire @xmath0 allowed region by many orders of magnitude . however , a heavier @xmath1 solution to the @xmath0 puzzle is still allowed , provided the @xmath1 coupling to the charged leptons has both left- and right - handed components , and the right - handed component is larger than the left - handed one . the deviations from lepton flavor universality in the tau decays predicted in this model can be probed at belle 2 , while a large part of the @xmath0 allowed region can be accessed at future colliders such as the high - luminosity lhc and/or an @xmath163 @xmath31-factory such as fcc - ee . the on - shell production of @xmath1 in high - energy neutrino interactions with either cosmic neutrino background or with other natural neutrino sources such as supernova neutrinos could lead to characteristic absorption features in the neutrino spectrum , which might be measured in neutrino telescopes . w.a . acknowledges discussions with stefania gori and financial support by the university of cincinnati . the work of c .- y.c . is supported by nserc , canada . research at the perimeter institute is supported in part by the government of canada through nserc and by the province of ontario through medt . the work of b.d . is supported by the dfg grant no . ro 2516/5 - 1 . b.d . also acknowledges partial support from the tum university foundation fellowship , the dfg cluster of excellence origin and structure of the universe " , and the munich institute for astro- and particle physics ( miapp ) during various stages of this work . the work of a.s . is supported in part by the us doe contract no . de - 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we discuss a minimal solution to the long - standing @xmath0 anomaly in a simple extension of the standard model with an extra @xmath1 vector boson that has only flavor off - diagonal couplings to the second and third generation of leptons , i.e. @xmath2 and their antiparticles . a simplified model realization , as well as various collider and low - energy constraints on this model , are discussed . we find that the @xmath0-favored region for a @xmath1 lighter than the tau lepton is totally excluded , while a heavier @xmath1 solution is still allowed . some testable implications of this scenario in future experiments , such as lepton - flavor universality - violating tau decays at belle 2 , and a new four - lepton signature involving same - sign di - muons and di - taus at hl - lhc and fcc - ee , are pointed out . a characteristic resonant absorption feature in the high - energy neutrino spectrum might also be observed by neutrino telescopes like icecube and km3net .

38 shot — 9 fatally — in weekend gun violence across Chicago Nine people were killed and at least 29 others were wounded in weekend shootings in Chicago. Shootings across the city wounded 12-year-old boy on the Far South Side, and wounded a woman who tried to break up a fight in University Village, from 5 p.m. Friday to 5 a.m. Monday. In the weekend’s last shooting, two women were shot by a man they were arguing with in Englewood on the South Side, Chicago Police said. Among the fatalities was 39-year-old Tyrone White, who was killed in a shooting that wounded five others the West Woodlawn neighborhood on the South Side. About 1:10 a.m. Sunday, White and the others were gathered outside in the 6400 block of South Eberhart when someone fired shots from inside a passing vehicle, police and the Cook County Medical Examiner’s Office said. Six people were taken to University of Chicago Medical Center, where White was pronounced dead, authorities said. The five other victims included a 24-year-old man shot in his leg; a 21-year-old man grazed in the head; a 24-year-old woman shot in her arm; a 21-year-old man shot in his leg and a 19-year-old man shot in the back. Their conditions had stabilized. Shortly after the shooting, police taped off the entire block of 6400 South Eberhart. Several cars on the street had bullet holes. One smelled strongly of leaking gasoline. At the emergency room, a group of women walked outside. “He didn’t make it,” screamed one of the women. “That’s bogus as hell. They won’t let me go and see my son again.” Another woman in the group was sobbing. The last fatal shooting of the weekend happened about 5 p.m. Sunday in the South Side Back of the Yards neighborhood. Gregory Jodie, 26, was sitting on a porch when someone walked through a gangway in the 5400 block of South Winchester and opened fire, authorities said. Jodie was struck once in the chest and three times in the back, and was pronounced dead at a hospital. The shooter drove away in a silver car. Jodie lived in Englewood. A 24-year-old man was fatally shot about 3:20 a.m. Sunday in the Englewood neighborhood. Cornelius Bell was outside in the 800 block of West 59th Street when someone in a passing car shot him multiple times, authorities said. Bell was shot in the chest, stomach, back and arms. He later died at University of Chicago Medical Center. Hours earlier, a man was shot to death on the border of the Back of the Yards and Englewood neighborhoods. Devane Williams, 29, was sitting in a vehicle about 1:15 a.m. in the 1900 block of West Garfield Boulevard when someone walked up and shot him in the abdomen, according to authorities. Walker drove himself down the street and then crashed into a parked vehicle near a gas station on Damen Avenue. He died later at a hospital. Saturday night, a 40-year-old man was fatally shot about 8:30 p.m. in the South Side Chatham neighborhood. The man was in the 7600 block of South Rhodes when another male got out of a dark-colored vehicle and fired shots, striking him multiple times in his head and body, according to police. The shooter then got back into the vehicle and drove off. The man later died at University of Chicago Medical Center. The medical examiner’s office hasn’t released details about his death. Earlier Saturday morning, a man was shot to death in the South Side Bronzeville neighborhood. About 6:10 a.m., officers responded to an unresponsive person in the 4500 block of South Champlain Avenue and found 30-year-old David Thomas with multiple gunshot wounds, authorities said. He was pronounced dead at the scene. He lived in the Roseland neighborhood. The first fatal shooting Saturday happened in the Marquette Park neighborhood on the Southwest Side. Two men, both 25, were standing about 1:40 a.m. in the 7200 block of South Western Avenue when they heard gunfire and realized they’d been shot. Scott S. Strahan suffered a gunshot wound to his right hip, while the other man was shot in the left arm and back, authorities said. They were taken to Christ Medical Center in Oak Lawn, where Strahan was pronounced dead. On Friday, a man was fatally shot in South Chicago. About 10 p.m., 25-year-old man was shot in the head and leg in the 7900 block of South Muskegon Avenue, police said. He was pronounced dead on the scene. The medical examiner’s office hasn’t released details about the death. Area South detectives were conducting a homicide investigation. Hours earlier, 30-year-old Kennedy Blount was shot to death in the Lawndale neighborhood on the Southwest Side. About 7 p.m., Blount was walking in the 1600 block of South Homan Avenue when someone got out of a gray Jaguar and opened fire, authorities said. He was shot in the head and right arm and later died at Mount Sinai Hospital. The shooter got back into the Jaguar and drove south on Homan. No one was in custody Friday night as Area Central detectives investigated. Blount lived in the Austin neighborhood. Shootings on Sunday killed four people and wounded 18 others. Saturday shootings left three people dead and seven wounded. Last weekend, 30 people were wounded and one was killed in gun violence. ||||| 2 women shot by man they were arguing with in West Englewood Two women were shot early Monday in the West Englewood neighborhood on the South Side. About 2 a.m., the women, ages 31 and 33, were arguing with a man they knew outside in the 6500 block of South Oakley Avenue, according to Chicago Police. The man then pulled out a handgun and shot the women in their legs, police said. The older woman was taken to University of Chicago Medical Center with a gunshot wound to her left leg. The younger woman was taken to Christ Medical Center in Oak Lawn with a gunshot wound to her right leg. Their conditions had stabilized. Area Central detectives were investigating the shooting. ||||| A 12-year-old boy hit by a stray bullet from a shootout on the Far South Side and six people at an outdoor party in West Woodlawn were among 19 people shot Saturday and early Sunday in Chicago, including three who died from their injuries, according to police. The party in the 6400 block of Eberhart Avenue was cut short when one or more shooters opened fire. A 39-year-old man shot multiple times in the abdomen and leg was pronounced dead at the University of Chicago Medical Center. Police said five others were stable at the same hospital, though further information about their conditions was not released. They included a 24-year-old man shot in the leg; a 21-year-old man grazed in the head; a 24-year-old woman shot in the arm; a 21-year-old man shot in the leg; and a 19-year-old man shot in the back. Police cars and yellow tape created a large crime scene. Witnesses said the shooting lasted a long time, what seemed like a couple minutes. One man said he was talking outside a friend’s car when he heard gunshots. He couldn’t tell where they were coming from, so he took cover inside the car and waited it out, he said. The man said he was afraid for his name to be published in part because of how snitches are often handled. He said he hates the way shooters don’t seem to care about the lives of innocent people they hurt. “If they cared, they wouldn’t shoot,” he said. “People just want a lick back [revenge].” Standing outside the hospital with the older brother of the woman shot, the man said going to shooting scenes or hospitals had become like a form of entertainment for too many people. “It happens so much… it becomes like a routine,” he said. About two dozen people had gathered in smaller groups outside the emergency room, where at least 10 police officers lined up outside the entrance and police cars blocked off the street leading up to it. The 12-year-old boy was shot in the leg shortly before 4:20 p.m. in the 300 block of East 130th Street in the Riverdale area. He was taken in good condition to Comer Children's Hospital. Police said the boy was an unintended target who happened to be standing outside when two other people began shooting at each other. Not quite four hours later in the Near West Side, a 45-year-old man was shot. Just after 8 p.m., police said the man was standing in the 2100 block of West Jackson Boulevard when two people got out of a light sedan and started shooting at him, hitting his body multiple times, then fled the area. Police initially said the man was shot in the leg. He showed up at Stroger Hospital, where police said he is in good condition. About 20 minutes later, a 40-year-old man was killed in Chatham. The shooter got out of a dark car and started shooting at the man about 8:20 p.m. Saturday in the 7600 block of South Rhodes Avenue, then got back in the car and drove away, police said. The man was taken to the University of Chicago Medical Center, where he was pronounced dead. In other shootings: About 8:30 p.m. Saturday in the 200 block of North Keeler Avenue in West Garfield Park, two people were hit in a drive-by shooting. The pair was in a vehicle when someone in a passing car shot at them, hitting the 19-year-old woman in her abdomen and a 24-year-old man in his face, police said. The woman was stable at Mount Sinai Hospital, while the man was in serious condition at Stroger Hospital. A car fleeing the scene hit a pole in the 1500 block of North Pulaski, causing no reported injuries, and four people were taken into custody, police said. About 1:15 a.m. in the 1900 block of West Garfield Boulevard in Back of the Yards, a 29-year-old man was shot while sitting in his car. Someone walked up and shot him in the abdomen. police said. The man drove a short distance, then crashed into a parked car. He was taken to University of Chicago Medical Center in serious condition. About 1:05 a.m. in the 1000 block of North Kildare Avenue in West Humboldt Park, a 32-year-old man was shot twice in the abdomen and once in his shoulder after two people got out of a black vehicle and fired at him, then left the area. An ambulance took the man to West Suburban Hospital, where police said he was in critical condition. A 25-year-old man was shot in the leg about 3 a.m. in the first block of West 110th Street in Roseland. Police said he was uncooperative, providing no information about the shooting or shooter. He is stable at Roseland Hospital, police said. About 3:15 a.m. in the 1300 block of South Loomis Street in University Village/Little Italy, a 24-year-old woman was shot while trying to intervene in a dispute between a relative and another person, who got upset and shot the woman, hitting her face and stomach, police said. She self-transported to the University of Illinois Chicago Hospital and is stable, police said. A 24-year-old man was killed in a shooting that took place shortly after 3:20 a.m. in the 800 block of West 59th Street in Englewood. Witnesses said a green car sped away from the area of the shooting, according to police. The man, who was on foot when he was shot, had gunshot wounds in his chest, stomach and back, police said. He was pronounced dead at the University of Chicago Medical Center. About 6:42 a.m. in the 7800 block of South Ashland Avenue in Gresham, three men were shot. They walked into a Chicago firehouse seeking medical attention for multiple gunshot wounds, according to police. A 27-year-old man with an unspecified gunshot wound is stable at Christ Hospital, while another 27-year-old man who was hit in his right leg is in serious condition at Christ Hospital, police said. A 19-year-old-man, who was hit in the thigh, is in serious condition at University of Chicago Hospital, according to police. A 12-year-old boy hit by a stray bullet from a shootout on the Far South Side and six people at an outdoor party in West Woodlawn were among 16 people shot Saturday and early Sunday in Chicago, including three who died from their injuries, according to police. 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– At least 38 people were shot over the weekend in Chicago, nine of them fatally, the Chicago Sun-Times reports. Those injured included a 12-year-old boy hit by a stray bullet during a shootout on the Far South Side, the Chicago Tribune reports. Six people were shot at an outdoor party on the South Side, including a 39-year-old man who died of his injuries. Two women were arguing with a man they knew when he took out a gun and shot them in their legs; they were in stable condition. A woman who tried to break up a fight between a relative and another person was shot when the second person got upset and fired at her; she was also in stable condition. The newspapers have more details on many more of the shootings and fatalities.

radiation therapy is a key component of breast conservation therapy for in situ or invasive breast cancers . fisher 's landmark nsabp b-06 study showed at twenty - year follow - up a significant decrease in ipsilateral breast tumor recurrence from 39.2% to 14.3% ( p < 0.001 ) when lumpectomy patients were treated postoperatively with whole breast irradiation . the early breast cancer trialists ' collaborative group 's meta - analysis of 7300 women treated with breast - conserving surgery and postoperative radiotherapy also showed a decrease in ipsilateral breast tumor recurrence over 5 years from 26% without radiotherapy to 7% with radiotherapy ( p = 0.0002 ) . in contrast to the nsabp trial , this study also showed a 15-year breast cancer mortality risk reduction from 35.9% without radiation to 30.5% with radiation ( p = 0.005 ) . therefore , the necessity of radiation in association with breast conservation surgery is widely accepted . radiation causes dna damage through the formation of free radicals which cause irreparable damage to cancer cells . browman and colleagues showed that head and neck cancer patients who continued to smoke during radiation therapy had lower rates of response and shorter disease free survival and overall survival than patients who did not smoke during radiation . however , this phenomenon has never been studied in patients undergoing radiation therapy for breast cancer . the purpose of this study was to compare the recurrence rates for patients who smoked or did not smoke during radiation therapy after breast conservation surgery . after institutional review board approval , the prospectively collected database at the breast center smilow cancer hospital at yale new haven was queried to capture cases of in situ and invasive breast cancers diagnosed between the years 2002 and 2010 treated with partial mastectomy followed by radiation therapy . patient demographics , tumor characteristics , further treatment including adjuvant systemic and radiation therapy , recurrence , and survival were obtained from both the database and the hospital tumor registry . patient charts were then reviewed to ascertain smoking status from the patient 's intake history form or from physician - documented histories or initial consultations . patient smoking history was categorized as never , former , current , or not available . former smokers were defined by the provider or patient through subjective history and the duration since last tobacco use was unknown . patients were treated in standard fashion with partial mastectomy and postoperative whole breast , external beam radiation therapy . treatment of the axillary field was at the discretion of the radiation oncologist and varied on a case - by - case basis depending on the burden of lymph node disease . the majority of patients were treated with standard 2-tangent whole breast irradiation if less than 4 lymph nodes were involved or 4 field , if more than 4 lymph nodes were involved . of 1166 charts reviewed on patients undergoing partial mastectomy , 624 had information regarding smoking status and follow - up documented and were included in this study . five of the included patients had follow - up at other institutions and were known to have had recurrence but it was not known whether the recurrence was local or distant . all cases of ductal intraepithelial neoplasia ( din ) were included , except for grade 1 din less than 2 mm in size , which is considered atypical ductal hyperplasia ( adh ) . categorical data were compared using chi - square tests and kaplan - meier curves were constructed and compared with log rank ( mantel - cox ) tests for recurrence - free survival . of the 624 patients in the study , 52 ( 8.3% ) were current smokers at the time of diagnosis , 196 ( 31.4% ) were former smokers , and 376 ( 60.3% ) were never smokers . smoking status was associated with race , patient age , and tumor stage , but not with grade , histology , or receptor status . african american women were significantly more likely to be current smokers than other racial / ethnic groups , and current smokers were significantly younger than nonsmokers . current smokers were more likely to have stage 0 disease ( dcis ) or stage 2 disease , whereas never smokers were most likely to have stage 1 disease . there was a trend for current smokers to have less infiltrating lobular cancer , but this was not statistically significant . there was no difference in estrogen receptor , progesterone receptor , or her2/neu receptor expression ( or any molecular subtype combination such as er / pr , her2 + , or triple negative ) by smoking history . at the time of analysis , the mean follow - up was 45 months and the median follow - up was 40 months ( range 5130 ) . there were 22 total recurrences ; the type of recurrence by smoking history is shown in table 2 . there were too few cases to analyze the type of recurrence , but any recurrence was significantly more frequent in current smokers than in never smokers ( p = 0.039 ) . current smokers tended to recur sooner than never smokers , and prior smokers were intermediate between the two ( p = 0.003 by log rank ) . multivariable cox regression models were constructed using race , age , stage , and smoking status and , as shown in table 3 , both stage and smoking status remained significantly associated with recurrence . when adjusted for race , age , and tumor stage , current smokers were 6.7 times more likely to develop a recurrence than never smokers ( 95% ci : 2.022.4 ) . there was no statistically significant difference , however , in overall survival by smoking status . this is the first study to show that , among breast cancer patients treated with partial mastectomy and radiation therapy , current smokers have a significantly higher recurrence rate than prior smokers or never smokers . although the numbers are small , almost 10% of current smokers had a documented recurrence at a mean follow - up of 45 months , compared with less than 4% for never and former smokers ( 2.7 and 3.6% , resp . ) . there was a tendency for current smokers to have more stage 2 disease whereas never smokers had more stage 1 disease . in a multivariable model , however , the key mechanism of action of radiation involves direct dna damage through formation of free radicals which cause irreparable damage , slowing the growth of cancers or causing direct cell death . as cancer cells are usually dividing at a faster rate than normal cells , they are more directly affected by radiation damage . when cancer cells are in a hypoxic milieu , they are thought to be less susceptible to radiation - induced damage . the results of the current study would seem to support the hypothesis of browman and colleagues who showed similar results for head and neck cancer patients who continued to smoke through radiation therapy . a review by holmes and colleagues of the nurses ' health study in 2007 found on multivariate analysis that current smokers had a 43% increase in adjusted relative risk of death from any cause . current and past smokers had higher rates of death from lung cancer , copd , and other lung diseases , but no direct increase in mortality from breast cancer . however , holmes ' study evaluated all methods of treatment for breast cancer in this diverse patient population of 5,056 patients . there was no significant difference in mortality among smokers compared with nonsmokers either with or without radiation . with regard to breast cancer and smoking status , prior studies have shown a decreased overall survival of smokers . calle and colleagues ' 1994 epidemiological study followed 676,530 female volunteers prospectively from 1982 to 1988 as part of the cancer prevention study ii through the american cancer society . during the study period , they found 880 deaths from breast cancer with an increased relative risk of death for current smokers ( rr = 1.26 ; 95% ci : 1.051.50 ) . furthermore , breast cancer mortality increased with total number of years smoked and number of cigarettes per day ( p = 0.0096 and p = 0.0003 , resp . ) . types of treatment , including surgery , drug therapy , and radiation therapy , were not included in this study . . followed 792 women diagnosed with breast cancer in sweden from 1977 to 1986 . relative risk of mortality from breast cancer compared with never smokers was 1.44 for current smokers ( 95% ci : 1.01 to 2.06 ) and 1.13 ( 95% ci : 0.66 to 1.94 ) for prior smokers . all - cause mortality adjusted for age was 1.46 for smokers ( 95% ci : 1.15 to 1.86 ) compared to never smokers . data from 12,989 female patients in memorial sloan - kettering cancer center 's tumor registry was analyzed by yu and colleagues in 1997 , and a history of smoking carried a risk ratio of 1.43 for all - cause mortality . this effect was seen not only for breast cancer , but also for oral and pancreatic cancers . it is interesting to speculate whether the results of the current study may have implications for breast cancer on a population level . a major epidemiologic problem has been to explain the increased mortality from breast cancer among african american women . most studies have focused either on reason for later stage of diagnosis or on biological factors leading to aggressive tumor behavior [ 10 , 11 ] . however , the finding that african american women are more likely to be smokers , and that this may be detrimental , opens up a new avenue for investigation . prior epidemiologic studies have shown interesting molecular changes associated with african american race , smoking status , and breast cancer development . current smokers have also been shown to have increased rates of p53 mutations , independent of stage at diagnosis , which has been shown on multivariate analysis to be a predictor of poor prognosis . limitations of this study include the small number of current smokers and the uncertain location of recurrence in five patients as documented by the tumor registry . follow - up or smoking status was not available for 542 patients of the initial 1166 lumpectomy patients identified in our database , because the patient intake form was incomplete or because some patients only had consultations or part of their care provided at our center . in addition , it is unknown whether some patients may have stopped smoking after the diagnosis was made . future directions would include looking at a larger study population , examining postmastectomy radiation patients to see if they had similar outcomes and examining other concomitant epigenetic and environmental factors that may be confounding the data , such as bmi and socioeconomic status . if the results are really due to tissue hypoxia during radiation , one would expect this to primarily affect local and not distant recurrence . it is unclear at this time whether the results of this study should influence our treatment of breast cancer . although other factors could be confounding the findings , the results would suggest that smokers should be actively counseled to quit smoking at least through the duration of therapy . this could potentially even raise the question of not offering breast conservation therapy to active smokers , as they may be less likely to benefit from the effects of radiation therapy .

background . prior studies have shown earlier recurrence and decreased survival in patients with head and neck cancer who smoked while undergoing radiation therapy . the purpose of the current study was to determine whether smoking status at the time of partial mastectomy and radiation therapy for breast cancer affected recurrence or survival . method . a single institution retrospective chart review was performed to correlate smoking status with patient demographics , tumor characteristics , and outcomes for patients undergoing partial mastectomy and radiation therapy . results . there were 624 patients who underwent breast conservation surgery between 2002 and 2010 for whom smoking history and follow - up data were available . smoking status was associated with race , patient age , and tumor stage , but not with grade , histology , or receptor status . african american women were more likely to be current smokers ( 22% versus 7% , p < 0.001 ) . with a mean follow - up of 45 months , recurrence was significantly higher in current smokers compared to former or never smokers ( p = 0.039 ) . in a multivariate model adjusted for race and tumor stage , recurrence among current smokers was 6.7 times that of never smokers ( ci 2.022.4 ) . conclusions . although the numbers are small , this study suggests that smoking may negatively influence recurrence rates after partial mastectomy and radiation therapy . a larger study is needed to confirm these observations .

although genomic dna contains genetic information that should be error - free for proper cellular function , it is continually subjected to ubiquitous dna - damaging agents of both environmental and endogenous origins , such as uv and ionizing radiation and reactive oxygen species ( ros ) [ 13 ] . to maintain genomic integrity , cells possess several repair pathways , including nucleotide excision repair ( ner ) , base excision repair ( ber ) , and recombination repair , to cope with the various resulting lesions . however , some lesions are not repaired and are encountered by the replication machinery . during dna replication , these lesions block high - fidelity replicative dna polymerases , and if not processed correctly , eventually lead to mutagenesis , carcinogenesis , or cell death . to avoid such catastrophic consequences , cells have a translesion dna synthesis ( tls ) mechanism that allows efficient and accurate dna synthesis past lesions [ 46 ] . the importance of tls in humans has been indicated by studies of an inherited human disease called xeroderma pigmentosum variant ( xp - v ) , which is characterized by the hypersensitivity of skin to sunlight and the high incidence of sunlight - induced skin cancer [ 7 , 8 ] . the xpv gene encodes human dna polymerase ( hspol ) , a 713 amino acid protein that is a member of the y - family dna polymerases that includes human dna polymerases , , and rev1 [ 6 , 9 , 10 ] . cells from xp - v patients are defective in the replication of damaged dna and show hypermutability after exposure to uv radiation or dna - damaging agents . these results indicate that hspol is at least involved in the accurate translesion pathway to avoid mutations by uv - induced lesions in vivo . consistent with these observations , biochemical studies revealed that hspol , unlike the replicative pol and pol , was able to catalyze efficient and accurate tls past a uv - induced cis - syn cyclobutane pyrimidine dimer ( cpd ) . in contrast , dna containing other uv - induced lesions , such as the pyrimidine(64)pyrimidone photoproduct ( 64 pp ) and its dewar valence isomer ( dewar ) , which are efficiently repaired by ner in vivo [ 11 , 12 ] , is not replicated by hspol [ 13 , 42 ] . furthermore , this enzyme was reportedly able to bypass not only uv - induced lesions but also various other lesions induced by both environmental and endogenous reactive oxygen species . for instance , hspol bypasses 7,8-dihydro-8-oxoguanine ( 8-oxog ) , 5r - thymine glycol ( 5r - tg ) , and 5s - thymine glycol ( 5s - tg ) , but not an apurinic / apyrimidinic ( ap ) site [ 1319 ] , although these lesions , which have small alterations in their chemical structures , are mainly repaired by ber in vivo . thus , these findings indicate that hspol also plays an important function in the replication of dna containing ros - induced lesions in vivo . in addition to its role in tls , hspol can extend dna synthesis from d - loop recombination intermediates , and its activity is stimulated by rad51 recombinase . moreover , pol-disrupted dt40 cells show significant decreases in the frequencies of both immunoglobulin - variable gene conversion and double - strand break - induced homologous recombination . taken together , these reports indicate that pol is involved in homologous recombination repair , and thus , pol seems to be important for dna damage tolerance in living cells . alvinella pompejana is a polychaetous annelid that inhabits active deep - sea hydrothermal vent sites along the east pacific rise , where it colonizes the walls of actively venting high - temperature chimneys . the average temperature is about 68c , with spikes up to 81c , and thus exceeds the predicted 55c limit for the survival of eukaryotes [ 22 , 23 ] . the ability of this worm to survive in such an extreme environment suggests that a. pompejana may contain highly stable proteins that can be used for biology , biotechnology , and industry . several proteins have been characterized from a. pompejana and the analyses have revealed the proteins have enhanced thermostability [ 2426 ] , which include a. pompejana superoxide dismutase ( sod ) and u2af65 , which are more stable than their human homologs . in this study , we cloned an a. pompejana gene with homology to the hspol gene . characterization of appol revealed that it had the ability to bypass cpd , 8-oxog , 5r - tg , and 5s - tg , but did not bypass either 64 pp , dewar , or an ap site analog . this substrate specificity is similar to that of the hspol , yet appol is comparatively more thermostable than hspol and retains activity in the presence of organic solvents . therefore , appol is a robust human - like pol that is useful to complement and expand ideas on tls mechanisms by virtue of its eukaryotic origin and enhanced stability . recombinant hspol tagged with ( his)6 at its c - terminal end was produced in sf9 insect cells using the baculovirus expression system and was purified by sequential column chromatography on hitrap q , ni - nta agarose , and monos , as described previously . klenow fragment 35 exonuclease minus ( kf ) and t7 dna polymerase were purchased from new england biolabs and usb , respectively . oligonucleotides containing cpd , 64 pp , dewar , 5r - tg , and 5s - tg were synthesized on an applied biosystems 3400 dna synthesizer , as described , and those containing 8-oxog and the ap site analog ( dspacer ) were synthesized using phosphoramidite building blocks purchased from glen research . full - length appol cdna was isolated by race pcr , using cdna prepared with the generacer kit ( invitrogen ) from total rna isolated from frozen whole worm samples . a 2.5 cm frozen section of the posterior end of a. pompejana collected with the dsv alvin submersible was ground using a mortar and pestle in liquid nitrogen . the ground tissue was aliquoted into eppendorf tubes , and after the addition of trizol ( invitrogen ) ( 1.4 ml ) , the mixture was incubated at room temperature for 10 minutes . after centrifugation at 12,000 g for 10 minutes , the supernatant ( 1 ml ) was mixed with chloroform ( 250 l ) , and was incubated at room temperature for 2 minutes . the samples were then centrifuged at 12,000 g for 15 minutes to separate the total rna into the aqueous layer . the rna was then precipitated by adding isopropanol ( 500 l ) to the aqueous solution ( 600 l ) , and was incubated at 4c for 1.5 hours . after centrifugation at 12,000 g for 10 minutes at 4c , the pellet was washed with 75% ethanol ( 1.4 ml ) and then stored in 75% ethanol ( 1 ml ) at 80c . the stored rna was pelleted by centrifugation and resuspended in diethylpyrocarbonate - treated water ( 20 l ) , and the concentration was determined by measuring the absorbance at 280 nm . a 5 g portion of the total rna was used to prepare cdna using the generacer kit ( invitrogen ) , according to the manufacturer 's instructions . in brief , total rna was dephosphorylated using calf intestinal alkaline phosphatase , extracted with phenol - chloroform , and precipitated with ethanol . the rna was decapped using tobacco acid pyrophosphatase , extracted , and precipitated , and then the generacer 5 oligo was ligated to the 5 ends . finally , the rna was subjected to the reverse transcription reaction using a poly - t primer containing the generacer 3 oligo sequence , to generate a single - stranded cdna library with known 5 and 3 sequences . the amino acid sequence of hspol was used for a in - house tblastn search of a translated a. pompejana expressed sequence tag ( est ) database comprised of sequences derived from collaborations with the joint genome institute ( walnut creek , ca ) and genome therapeutics ( waltham , ma ) . a positive hit at the 5 end of the gene was identified on est caga3172 . the 3 sequence was determined from the prepared a. pompejana generacer cdna library by 3 race pcr , using a gene specific primer ( alvixpvf1 5gg gac tgg tct gtg ctg gcc gtg gaa at 3 ) and the generacer 3 oligo primer , together with the touchdown pcr strategy and kod polymerase ( novagen ) . the pcr product was topo cloned into the pcr2.1 vector ( invitrogen ) and was analyzed by restriction enzyme digestion and sequencing . the full - length appol gene was amplified from the cdna library , using two gene - specific primers , alvixpvf1 ( the above sequence ) and alvixpvr2 ( 5 ggg atg att cta cac ttt gct gaa aaa tct atc ca 3 ) , and kod polymerase under the standard pcr conditions . the 2.2 kb product was gel - purified and topo cloned into the pcr4 vector ( invitrogen ) and was analyzed by restriction enzyme digestion and sequencing . restriction sites were added to the ends by a subsequent round of pcr and topo cloning . the full - length appol cdna was then subcloned into pet21a ( novagen ) , using the nde i and eco ri restriction nucleases and t4 dna ligase , and was analyzed by restriction enzyme digestion and sequencing . recombinant appol gene was expressed in e. coli rosetta2 ( de3 ) ( novagen ) . the cells were grown at 37c to an absorbance at 600 nm of 0.6 . the cultures were placed in an ice slurry for 20 minutes , and then isopropyl--d - thiogalactopyranoside was added to a final concentration of 0.5 mm . after the cultures were incubated at 12c for 40 hours , the cells were collected by centrifugation , rinsed with buffer a containing 10 mm sodium phosphate ( ph 7.4 ) , 10% glycerol , and 300 mm nacl , and resuspended in buffer a containing p - amidinophenylmethanesulfonyl fluoride hydrochloride and a protease inhibitor cocktail ( complete , edta free ( roche ) ) . the lysate mixtures were mixed with powdered lysozyme at a final concentration of 2 mg / ml for 10 minutes on ice , and then were subjected to ultrasonicationn . the lysates were centrifuged , and the supernatants were mixed with talon resin ( clontech ) ( 50% w / v , equilibrated with lysis buffer containing 10 mm sodium phosphate ( ph 7.4 ) , 10% glycerol , 300 mm nacl , and 5 mm imidazole ) . the resin was washed with the same buffer , and the bound proteins were eluted with eluate buffer ( lysis buffer containing 300 mm imidazole ) . the eluate was diluted and applied to a hitrap heparin hp column ( ge healthcare ) equilibrated with buffer b ( 50 mm sodium phosphate ( ph 7.4 ) , 1 mm edta , 1 mm -mercaptoethanol , and 0.01% triton x-100 ) containing 0.1 m nacl . elution was performed by a stepwise gradient of 0.2 m to 0.6 m nacl in buffer b. the peak fractions containing appol eluted at 0.5 m nacl , and were stored at 80c . the 5-p - labeled primer - template was prepared by mixing a 16-mer primer labeled at its 5 end with each of the 30-mer templates , at a molar ratio of 1 : 1 . hcl ( ph 8.0 ) , 1 mm mgcl2 , 100 mm dntps , 10 mm dtt , 0.24 mg / ml bsa , 60 mm kcl , 2.5% glycerol , 40 nm 5-p - labeled primer - template , and purified appol , were incubated at 37c . the reaction times and the enzyme amounts are indicated in the figure legends . the reactions were terminated by the addition of stop solution ( 8 l ) , containing 95% formamide , 20 mm edta , 0.025% bromophenol blue , and 0.025% xylene cyanol . the protein was denatured by boiling , and the products were separated by electrophoresis on a denaturing 16% polyacrylamide gel . the relative thermostabilities of appol and hspol were compared by heating each enzyme to temperatures ranging between 37c and 58c for 5 minutes . an aliquot of each enzyme was then used for the standard 20 minutes tls reaction at 37c to measure the incorporation of a single nucleotide , dcmp , opposite the template g residue ( see the tls reactions described above ) . the enzyme concentrations used in the reactions were initially determined by making serial dilutions of each enzyme and identifying the concentration necessary to give the same extension level of the labeled primer . the ability of each enzyme to extend the primer was quantified with multigauge software ( fujifilm ) , and the specific activity , compared to the activity of each enzyme heated to 37c , was calculated . the specific activity was plotted as a function of the temperature to which the enzyme was exposed . a cdna sequence with homology to that of hspol was cloned from an a. pompejana cdna library by race pcr . the open reading frame encoded a predicted product of 745 amino acid residues , with a calculated molecular mass of 83 kda . alignment of the amino acid sequence against hspol revealed 38.1% identity and 57.6% similarity overall ( identities = 283/708 ( 39% ) , positives = 414/708 ( 58% ) , gaps = 68/708 ( 9% ) ) . the alignment ( figure 1(a ) ) also indicated the high conservation within the n - terminal region and the presence of the four structural domains ( finger , palm , thumb , and little finger ) that are the hallmarks of the y - family translesion dna polymerases [ 32 , 33 ] . ubiquitin ( ub)-binding domains [ 3436 ] and a proliferating cell nuclear antigen ( pcna)-binding domain [ 37 , 38 ] , located in the c - terminal region of pol , were identified in the appol amino acid sequence , suggesting that ub and/or pcna regulate this protein . the y - family dna polymerases ( pol ) and ( pol ) and the b - family dna polymerase ( pol ) are known to share sequence homology with the y - family hspol. to analyze the relationship between this a. pompejana protein and other translesion dna polymerases , a phylogenetic tree was produced on the basis of the amino acid sequences of these dna polymerases , by the unweighted pair group method with arithmetic mean ( upgma ) . the tree revealed that this protein was not related to pol , pol , or pol , but was more closely related to pol ( figure 1(b ) ) . therefore , we concluded that this protein is a member of the dna polymerase group , and thus referred to the protein as a. pompejana dna polymerase . to examine the biological activities of the protein encoded by the appol cdna , we prepared the recombinant appol protein with a c - terminal ( his)6 tag in e. coli . the extract was first fractionated on talon beads , and then purified on a heparin column . the recombinant protein was eluted by a step gradient of nacl ( figure 2(a ) ) . as expected from the calculated relative molecular mass , the purified recombinant appol bearing the ( his)6 tag migrated as a single band of approximately 85 kda in the sds - page analysis ( figure 2(b ) ) , and exhibited dna polymerase activity ( figure 3(a ) ) . the recombinant human y - family polymerases , for example , pol , pol , and pol , are usually prepared from baculovirus - infected insect cells , as reported previously [ 13 , 17 , 39 , 40 ] . in the present study , the incubation of the cultures at a low temperature after induction enabled the production of full - length appol in e. coli , as was also reported by hoffman et al . for pol from other species . the yield of the purified protein was 15.5 g per liter of the culture . uv irradiation induces the formation of pyrimidine dimers , namely , cpd and 64 pp . the latter is isomerized to dewar by exposure to uva / b . hspol catalyzed efficient and accurate tls past cpd , but not 64 pp and dewar ( unpublished results ) . to examine whether appol possessed tls activity for uv - induced lesions , 30-mer oligonucleotide templates containing a single lesion were hybridized to a 5-p - labeled 16-mer oligonucleotide primer , and these duplexes were employed for the tls reactions ( figure 3 ) . klenow fragment ( kf ) inserted one nucleotide opposite cpd , but did not elongate the primer ( figure 3(b ) , lane 1 ) , whereas appol could efficiently elongate the primer up to the end of the 30-mer , in an enzyme concentration - dependent manner ( figure 3(b ) , lanes 37 ) . similar experiments were performed with other uv - induced lesions , 64 pp and dewar . appol could insert one nucleotide opposite these lesions , but elongation of the primers was not observed ( figures 3(c ) and 3(d ) ) , in a manner similar to hspol [ 13 , 42 ] . to examine the preference for nucleotide incorporation opposite the lesion by appol , the polymerization reactions were performed in the presence of only a single deoxyribonucleoside triphosphate ( figure 4 ) . although hspol replicates undamaged dna with low fidelity [ 43 , 44 ] , it can accurately incorporate datp opposite the tt sequence of cpd . on the undamaged template , appol preferred to incorporate datp correctly , and dgtp was incorporated less frequently ( figure 4(a ) ) , indicating that appol , like hspol , replicates undamaged dna with low fidelity . when the template contained cpd , appol incorporated datp exclusively ( figure 4(b ) , lane 4 ) , indicating that appol , like hspol , can accurately perform tls past cpd . for both 64 pp and dewar , primers that were elongated with damp and dgmp by appol were detected , although the elongation efficiency was very low ( figures 4(c ) and 4(d ) ) . while we are able to test these activities biochemically , establishing the biological roles of appol would require additional assays such as genetic complementation , however these results were also similar to those obtained for hspol. since a. pompejana inhabits deep sea thermal vent regions that are in excess of 1.5 km under the ocean surface where uv - rays from the sun do not penetrate [ 45 , 46 ] , we thought that cpd containing dna may not be a major template for appol. other candidates were assumed to be oxidative lesions , because the high temperature and the solutes at the hydrothermal vent sites might induce oxidative stress . tg is one of the major dna lesions produced by ros , and two isomeric forms , 5r - tg and 5s - tg , are produced in dna . tg often blocks dna replication by replicative dna polymerases , but rarely induces mutation . however , hspol can catalyze efficient and accurate tls past each tg isomer . using the 30-mer oligonucleotides containing a single lesion at the 17th nucleotide from its 3 end as templates , we examined the ability of appol to replicate dna past 5r - tg and 5s - tg . at both lesions , the replicative t7 dna polymerase was blocked completely ( figures 5(a ) and 5(b ) , lane 1 ) , but appol efficiently catalyzed the replication reaction ( figures 5(a ) and 5(b ) , lanes 37 ) . to examine the preference of nucleotide incorporation opposite each tg isomer , the polymerization reactions were tested in the presence of only a single deoxyribonucleoside triphosphate ( figures 6(a ) and 6(b ) ) . appol preferred to incorporate datp ( figures 6(a ) and 6(b ) , lane 4 ) . although dgtp was incorporated in the absence of the other nucleotides ( lane 6 ) , this product , which exhibited slightly slower migration in the page analysis , was not detected when the four nucleotides were added ( lane 3 ) . these results indicated that appol had the ability to catalyze tls accurately past both 5r - tg and 5s - tg . another major oxidative dna lesion induced by ros is 8-oxog , which is an important promutagen in vivo and in vitro . no insertion of any nucleotide opposite the lesion by t7 dna polymerase was observed ( figure 5(d ) , lane 1 ) , whereas appol could bypass 8-oxog efficiently ( figure 5(d ) , lanes 37 ) . for the nucleotide preference , appol preferred to incorporate the correct dctp opposite the undamaged template g ( figure 6(c ) ) , whereas it mainly incorporated the incorrect datp opposite 8-oxog ( figure 6(d ) ) . thus , this enzyme replicates dna containing 8-oxog efficiently but incorrectly , leading to frequent gc to ta transversions . in addition , we investigated whether appol has tls activity on a template containing the ap site analog . however , like the other y - family dna polymerases , this enzyme was unable to catalyze tls past this lesion ( data not shown ) . as a. pompejana colonizes the walls of actively venting high - temperature chimneys [ 23 , 45 , 46 ] , we hypothesized that its enzymes may be more thermostable than those found in mesophilic organisms , as shown for other tls polymerases derived from single cellular hyperthermophilic organisms such as sulfolobus solfataricus dna polymerase 4 ( dpo4 ) [ 47 , 48 ] . to test this possibility , we compared the activity of appol along with that of hspol after heating both enzymes to various temperatures for 5 minutes . after this treatment , we tested the ability of both enzymes to incorporate a single dcmp opposite a template g. as shown in figure 7 , appol retained the activity even after it was heated to 49c . in contrast , the activity of hspol diminished rapidly after heating to temperatures higher than 43c . therefore , appol is relatively more thermostable than hspol. as a further test of appol stability , we tested the ability of appol to incorporate dcmp opposite a template g in the presence of various organic solvents . in these assays , dimethyl sulfoxide ( dmso ) , ethanol , and isopropanol ( ipa ) similar experiments were performed in a study on tls past a benzo[a]pyrene adduct by another thermostable y - family dna polymerase , archaeal dpo4 , although the organic solvents were added to stabilize the benzo[a]pyrene moiety in the major groove , rather than to test the protein stability . as shown in figure 8(a ) , appol exhibited higher activity than hspol in the presence of all of the solvents used in this study , although ipa greatly reduced the enzyme activity . in the presence of dmso , appol retained the full activity , even when the reaction mixture contained this solvent at a concentration of 20% ( figure 8(b ) ) . these results support our conclusion that the full - length appol protein is more stable than its human homolog . in this study , we cloned the cdna encoding the novel thermostable dna polymerase from a. pompejana , which colonizes deep - sea hydrothermal vents . this enzyme was produced in e. coli , and was purified as a full - length recombinant protein ( 85 kda ) bearing a ( his)6 tag . this enzyme catalyzed tls past cpd , 5r - tg , 5s - tg , and 8-oxog , but not past 64 pp , dewar , or the ap site analog , in a similar manner to hspol ( table 1 ) . we also demonstrated that appol was more stable than hspol. despite the fact that a. pompejana inhabits the deep sea , where uv - rays do not penetrate , the uv - induced cpd was found to be an excellent template for appol. considering that a genetic defect in the hspol gene results in the xp - v syndrome , and that xp - v patients are sensitive to sunlight and highly prone to cancer development , the critical role of hspol is thought to be error - free tls across cpd in human cells . as a. pompejana 's environment is significantly less subject to uv radiation produced by the sun , we speculate that the inclusion of the tls polymerase system within the organism may arise from specific environmental adaptations . evidence for photosynthetic events at hydrothermal vent sites has been noted , where energy for the reactions may arise from vent activity . moreover , the vent area is sporadically subject to periods of intense volcanic and geothermal activity that may cause production of bulky dna lesions within these organisms . the presence of appol may also play a role in protecting developing embryos , as embryos pass through a period of developmental arrest when passing from one colony site to another before renewed growth . in these cases , they may experience periods of geothermal light during passage and during their development at their new colonization site . thus , these pol proteins may protect the embryo until it becomes more self - motile and can build its housing tube . here , we also showed that this polymerase catalyzes efficient and accurate tls past both 5r - tg and 5s - tg , which are generated by ros . since tg can block dna replication by replicative dna polymerases and also induces cell death , the critical role of appol might be error - free tls across tg in a. pompejana cells . since a. pompejana inhabits hydrothermal vent sites at temperatures that often measure within the representative classifications for thermophilic ( 4060c ) and hyperthermophilic organisms ( 60c and higher ) in agreement with these expectations , we found that appol was more thermostable than hspol ( figure 7 ) , but less stable than an archaeal dinb - like polymerase from the hyperthermophile s. solfataricus p2 [ 47 , 51 ] which lives at higher temperatures ( > 75c ) than a. pompejana . since the appol used in this study was produced in e. coli , the measured thermostability was that without eukaryotic post - translational modifications . we expected that this enzyme may be modified in insect cells , which are more closely related to a. pompejana cells than to e. coli cells , and thus might gain higher thermostability . the appol protein produced in sf9 cells could catalyze dna synthesis at 37c , but lacked translesion activity after it was heated to 55c ( data not shown ) . ( 1 ) it has been reported that pol functions in a replication complex during tls [ 37 , 38 , 52 ] . thus , it is possible that appol becomes more heat resistant with the help of other thermostable replication proteins in a. pompejana cells . in fact , appol has a pcna binding motif ( figure 1(a ) ) , indicating that appol may exist in a replication complex with pcna . ( 2 ) y - family dna polymerases replicate undamaged dna in an error - prone manner [ 3436 , 38 ] . hence , to maintain genetic integrity , it might not be favorable for cells to have an extremely stable mutator polymerase . the present study is the starting point for the elucidation of the temperature preference of each a. pompejana enzyme and its biological significance , which will further our understanding of the ecology of this unique living organism . appol could be useful for in vitro studies as a new paradigm system to understand tls mechanisms and also could be a starting material for the development of a more stable eukaryotic - like tls polymerase by directed evolution . such an enzyme will enable us to amplify heavily damaged dna , such as ancient dna , by pcr - like methods . in this study , we cloned an a. pompejana gene with homology to the hspol gene . the primary structure of the protein indicated the conservation of the pcna binding domain and the ubiquitin - binding zinc finger motif . the encoded full - length recombinant protein , appol , was readily produced in escherichia coli and purified . we demonstrated that appol could bypass cpd , 8-oxog , 5r - tg , and 5s - tg , but not 64 pp , dewar , or any ap site analog revealing a similar spectrum of activities to those of the human homolog . appol 's properties of higher stability with human - like activities offer advantages over other known eukaryotic tls polymerases for future basic and practical applications .

human dna polymerase ( hspol ) plays an important role in translesion synthesis ( tls ) , which allows for replication past dna damage such as uv - induced cis - syn cyclobutane pyrimidine dimers ( cpds ) . here , we characterized appol from the thermophilic worm alvinella pompejana , which inhabits deep - sea hydrothermal vent chimneys . appol shares sequence homology with hspol and contains domains for binding ubiquitin and proliferating cell nuclear antigen . sun - induced uv does not penetrate alvinella 's environment ; however , this novel dna polymerase catalyzed efficient and accurate tls past cpd , as well as 7,8-dihydro-8-oxoguanine and isomers of thymine glycol induced by reactive oxygen species . in addition , we found that appol is more thermostable than hspol , as expected from its habitat temperature . moreover , the activity of this enzyme was retained in the presence of a higher concentration of organic solvents . therefore , appol provides a robust , human - like pol that is more active after exposure to high temperatures and organic solvents .

since the 1935 famous publication by einstein , podolsky , and rosen ( epr ) @xcite , which posed the problem in its clearest form , the quantum theory has repeatedly eluded any simple realistic interpretation . although epr actually aimed at demonstrating quantum theory incompleteness , the subsequent celebrated bell s theorem showed that no possible theory assuming additional `` hidden variables '' in order to describe the underlying reality could be in agreement with quantum predictions , provided one also made the very plausible assumption of `` locality '' @xcite for the behavior of such hidden variables . the difference between the predictions of quantum theory and those of all possible local realistic theories could be quantified in well defined `` inequalities '' concerning measurement outcome probabilities @xcite , and hence could be tested in actual experiments , which systematically confirmed the validity of quantum predictions ( see , e.g. , ref . @xcite and references therein ) . later , bell s and epr assumption of locality has been linked to the more general concept of `` non - contextuality '' . the latter is the assumption that measurement results ( even individual results , not only probabilities ) for a given observable are independent of the choice of other compatible observables that are measured at ( about ) the same time @xcite . the importance of this generalization was highlighted by the kochen - specker ( ks ) theorem @xcite , stating that for any physical system , prepared in any possible state ( including separable states showing no special correlations , unlike epr states ) , there exist a finite set of observables such that it is impossible to pre - assign them noncontextual results ( i.e. , independent of which other compatible observables are jointly measured ) respecting the predictions of quantum theory . the thought experiment ideated by hardy in 1993 @xcite `` one of the strangest and most beautiful gems yet to be found in the extraordinary soil of quantum mechanics '' , in the words of david mermin @xcite provides yet another way to highlight the conflict between the predictions of quantum mechanics and any non - contextual realistic interpretation . like the greenberger , horne , and zeilinger ( ghz ) proposal @xcite , hardy s paradox ideally relies only on testing a set of certainty or impossibility ( `` all versus nothing '' ) statements , as opposed to the quantitative assessment of probabilities needed for testing the original bell s theorem , thus providing a form of `` bell s theorem without inequalities '' . on the other hand , hardy s paradox has some advantages with respect to the ghz one : only two , instead of three , compatible observables are required and only a partial , as opposed to maximal , degree of entanglement is needed . in fact , hardy s paradox can be considered to be intermediate between the epr - like paradoxes ( including ghz one ) , requiring a maximally entangled state , and the ks paradox , which applies to any state , including separable ones @xcite . a number of experimental tests of hardy s paradox have been carried out hitherto @xcite , adopting different approaches , but all based on measuring properties of two separated particles ( usually photons ) . therefore , these tests mainly emphasized nonlocality , similarly to the experiments testing bell - like inequalities . if we instead choose to focus on the more general concept of contextuality , we may also carry out experiments involving different degrees of freedom of a same particle . this approach has been taken already several times in the past , for experimentally testing the epr , ghz or ks paradoxes ( see , e.g. , @xcite ) , but to our knowledge it has not been applied before to hardy s paradox . here , we carry out a single - particle experimental test of hardy s paradox by measuring two compatible degrees of freedom of the same photon , namely its spin angular momentum ( sam ) and its orbital angular momentum ( oam ) . as for other experiments involving different degrees of freedom of a same particle , we can not use locality to logically enforce non - contextuality , which must therefore be assumed , based only on the observables compatibility ( which might be tested with separate experiments ) . on the other hand , a single - photon experiment such as ours is simpler to implement and may allow much larger detection efficiencies than typical two - photon ones . this paper is organized as follows . section ii recalls the basic idea of hardy s paradox and illustrates its implementation in a spin - orbit four - dimensional hilbert space of a single photon . our experiment and its results are then described in section iii . brief conclusions follow in section iv . in addition , an appendix is included with a proof of the statistical inequality that can be used to extend hardy s paradox to the case in which experimental noise and imperfections preclude an all - versus - nothing test . hardy s paradox in our specific single - photon implementation can be sketched as follows . alice and bob must measure the properties of the photon and they agree on splitting the work : alice will measure the photon polarization state and bob its oam . however , alice can choose between two different polarization measurement setups , providing either one of two mutually incompatible observables that we will define in detail further on : for the time being , let us just call them @xmath0 and @xmath1 . in practice , alice makes her setup choice by rotating a set of birefringent plates placed before a polarizing beam splitter ( pbs ) . similarly , bob can choose between two different oam measurement setups , providing either one of the two mutually incompatible observables @xmath2 and @xmath3 . bob s choice is performed by selecting different hologram patterns visualized on a spatial light modulator ( slm ) . for both alice and bob , all observable measurements have only two possible outcomes , which will conventionally be labeled with the values @xmath4 . observable choice is supposed not to affect in any way bob s measurement and vice versa , because the experimental procedures act on independent degrees of freedom of the photon . this corresponds to saying that @xmath0 and @xmath1 are compatible with @xmath2 and @xmath3 . alice and bob carry out a large number of measurements over an ensemble of identically prepared photons , choosing every time at random the observable to be measured for each degree of freedom . in this way , they estimate from the experimental frequencies the probabilities @xmath5 of different pairs of properties for the photon . in particular , they observe the following properties in their results : 1 . [ eq : p1 ] : the outcome @xmath6 and @xmath7 never occurs , that is @xmath8 2 . [ eq : p2 ] : the outcome @xmath9 and @xmath10 never occurs , that is @xmath11 3 . [ eq : p3 ] : the outcome @xmath12 and @xmath13 never occurs , that is @xmath14 as we shall prove further below , for any realistic non - contextual model , these three properties should logically imply the validity of the following fourth property : 1 . [ eq : p4 ] : the outcome @xmath12 and @xmath10 never occurs , that is @xmath15 in contrast , alice and bob find that , in a sizable fraction of their measurements , the outcome @xmath12 and @xmath10 is indeed obtained , thus contradicting p4 . this is hardy s paradox . the proof of [ eq : p4 ] from [ eq : p1]-[eq : p3 ] is very simple . in a realistic non - contextual model , alice s and bob s measurement outcome events can be represented as venn diagrams , which may be drawn on a plane that spans the underlying ( hidden ) reality determining all observable results . the venn sets associated to the outcomes @xmath16 , and @xmath10 are shown in fig . [ fig : venn ] . from property [ eq : p2 ] we infer that each time bob measures @xmath3 , finding @xmath10 , then if alice measures @xmath0 , she would certainly find @xmath6 . in other words , the event @xmath10 implies the event @xmath6 which is represented by the fact that the venn set for the event @xmath10 is internal to that for the event @xmath9 , as shown in fig . [ fig : venn ] . similarly , from [ eq : p3 ] we infer that the event @xmath12 implies the event @xmath7 , that is , the venn set of the event @xmath12 is internal to that of the event @xmath7 . venn diagrams for the events @xmath16 , and @xmath10 , satisfying conditions [ eq : p1 ] , [ eq : p2 ] , [ eq : p3 ] . the sets @xmath12 and @xmath10 being internal to disjoint sets can not intersect , so that [ eq : p4 ] follows immediately.,width=264 ] now property [ eq : p1 ] implies that the venn sets of the events @xmath6 and @xmath7 have no intersection , as shown in fig . [ fig : venn ] . it is now evident from the figure that the sets of the events @xmath12 and @xmath10 can not intersect as well , from which we deduce property [ eq : p4 ] . it should be noted that the simultaneous presence of venn sets for the results of incompatible observables , such as for example @xmath0 and @xmath1 , reveals a counterfactual aspect of the presented reasoning , because no single event can yield results for both observables , since they require different setups . however , we are actually assuming that , even when not measured , all observables values have a definite probability in each event . let us now illustrate the quantum mechanical description of the experiment and , based on that , we shall also specify the details of the state preparation and observable definitions to be used . indeed , for a proper choice of states and observables , quantum mechanics can satisfy [ eq : p1 ] , [ eq : p2 ] , and [ eq : p3 ] and violate [ eq : p4 ] , in agreement with observations and in contradiction with a non - contextual realistic interpretation . to start with , the photon must be prepared in the following partially entangled spin - orbit quantum state : @xmath17 where the @xmath18 and @xmath19 subscripts denote the polarization and oam hilbert spaces @xmath20 and @xmath21 , respectively , @xmath22 and @xmath23 denote the left - handed and right - handed circular polarization states , corresponding also to the eigenstates of the sam operator @xmath24 with eigenvalues @xmath4 ( in units of @xmath25 ) , and @xmath26 are the eigenstates of the oam operator @xmath27 with eigenvalue @xmath28 ( also in units of @xmath25 ) , where @xmath28 is any integer . the angle @xmath29 controls the degree of entanglement between the polarization and oam degrees of freedom . the oam hilbert space is infinite - dimensional , but in this paper we shall restrict our attention to a two - dimensional subspace of @xmath21 spanned by @xmath30 . in this way , @xmath20 and @xmath21 are isomorphic to each other and describe two standard qubit spaces , defined in separate degrees of freedom of the photon . we may think of state ( [ eq : psi ] ) as a generic state in the four - dimensional spin - orbit hilbert space @xmath31 , up to `` local '' unitary operations acting separately on the polarization and oam degrees of freedom . only separable states ( corresponding to @xmath32 , with @xmath33 any integer ) and maximally entangled states ( @xmath34 ) can not be used for implementing the hardy paradox , as we shall see . in particular , in the following we shall restrict @xmath29 to the range @xmath35 . let us now define the observables to be measured by alice and bob . in two - dimensional hilbert spaces , all observables can be defined by giving a pair of orthogonal states that form a basis . so , let us first introduce the following four states in each qubit hilbert subspace : @xmath36 where @xmath37 and @xmath38 , and @xmath39 . the observable operators are then defined as follows : @xmath40 these definitions correspond to saying that in order to measure , for example , @xmath0 , alice must project the photon state onto @xmath41 and @xmath42 . if the first projection ( which is actually a filtering operation , in the experiment ) succeeds , then the observable value is @xmath43 , otherwise it is @xmath44 . similar procedures apply to all other observables . let us now calculate the quantum predictions for the four probabilities appearing in properties [ eq : p1][eq : p4 ] . they are given by expressions such as @xmath45 and similar ones . a simple calculation shows that the probabilities appearing in [ eq : p1 ] , [ eq : p2 ] , [ eq : p3 ] are indeed zero , but that the probability in [ eq : p4 ] is given by @xmath46 ^ 2,\ ] ] which is nonzero for the range @xmath35 ( hence , for all partially entangled states , excluding only separable and maximally entangled ones ) . in particular , the probability ( [ eq : pnonzero ] ) is maximized for @xmath47 , for which @xmath48^{-5}\approx9\%$ ] . hence , this is the best working point to test the paradox experimentally . the state given in eq . ( [ eq : psi ] ) with this choice for @xmath29 can be represented by the vector drawn on the spin - orbit poincar sphere @xcite , shown in fig . [ fig : state]a together with the transverse structure of the corresponding optical mode . the polarization and oam states appearing in eqs . ( [ eq : plusminus ] ) are shown in fig . [ fig : state]b , as vectors in the poincar ( or bloch ) spheres representing the corresponding qubit hilbert subspaces . the full layout of the experimental apparatus of our experiment is shown in fig . [ fig : setup ] . the pump pulses are emitted at 82 mhz repetition rate by a ti : sapphire mode - locked laser , centered at the wavelength @xmath49 nm . the pulses are frequency - doubled by second - harmonic generation ( shg ) in a first @xmath50-barium borate ( bbo ) nonlinear crystal , cut for type i phase matching , and then used to generate photon pairs by spontaneous parametric down conversion ( spdc ) in a second bbo nonlinear crystal , cut for type ii degenerate phase matching . the photons were coupled to a single - mode optical fiber to clean the spatial mode and sent to the main apparatus . after compensating for the polarization rotations induced by the fiber , the photons are split by a pbs , and one photon is detected by a silicon avalanche photodiode ( ad ) and used as trigger . the other photon is used for the hardy s test , in a heralded single - photon regime . ) and the heralded photon one ( d@xmath51 ) were sent to a coincidence box , for recording the number of photon coincidences occurring in a given time window . legend : c - box - coincidence box ; d@xmath52 - single photon detector ; dm - dichroic mirror ; f - lens ; h - half - wave plate ; if - bandpass interference filter ; m - mirror ; q - quarter - wave plate ; qp - q - plate ; p - polarizer ; slm - spatial light modulator.,width=340 ] in order to prepare the photon input state , we used the q - plate technology @xcite , which provides a simple and convenient method for entangling polarization and oam degrees of freedom @xcite . in this work , for the first time we exploit a q - plate with @xmath53 to generate partially entangled states , rather than maximally entangled ones . a q - plate , tuned electrically to maximal conversion efficiency @xcite , operates the spin - orbit optical transformations @xmath54 and @xmath55 . hence , in order to generate the state ( [ eq : psi ] ) , we need only to prepare the input photon in the zero oam mode , as obtained after passing through a single - mode fiber , and with elliptical polarization @xmath56 and then pass it through the q - plate . the parameter @xmath29 , fixing the degree of entanglement in the final state , was adjusted using a sequence of birefringent wave plates : a half - wave plate , with optical axis rotated at the angle @xmath57 from the direction of the input polarization , a quarter - wave plate , with the axis set at @xmath58 , and another half - wave plate at @xmath59 ( see fig . [ fig : setup ] ) . we checked the quality of the prepared state by carrying out a full quantum tomography , based on projecting ( filtering ) the state on a set of mutually unbiased bases in both polarization and oam hilbert spaces and then using a standard maximal likelihood estimator for best fit . the polarization filtering was carried out by using a second set of birefringent wave plates followed by a polarizer . the oam filtering was based on a standard holographic method @xcite , by diffracting the photons on a set of computer - generated holograms ( optimized for fidelity @xcite ) visualized on a slm and then filtering the zero oam component within the first - order diffracted photons . [ fig : tomography](a - c ) shows the experimentally reconstructed density matrix @xmath60 of the generated spin - orbit state ( [ eq : psi ] ) for @xmath61 , @xmath62 , and @xmath63 . the corresponding concurrence , as a measure of the degree of entanglement @xcite , was also determined for seven values of @xmath29 and the results are shown in fig . [ fig : tomography](d ) . ) . ( a - c ) experimental reconstructed density matrix for three different values of the entanglement parameter @xmath29 : ( a ) @xmath61 , ( b ) @xmath62 , ( c ) @xmath63 . the associated state fidelities are @xmath64 , @xmath65 , and @xmath66 , respectively . ( d ) concurrence value of schmidt s state as a function of @xmath29 . the red points are the experimental data and the red solid line is an interpolating function used as a guide for the eye , while the solid blue line is from theory . the concurrence value for the hardy state at the optimal angle @xmath67 , is equal to 0.36.,width=302 ] for carrying out the hardy test , we then set @xmath67 in order to maximize the probability ( [ eq : pnonzero ] ) , as explained above . while heralded photons prepared in this state are sent in the main apparatus , we made a series of projective measurements of the observables @xmath68 in the polarization subspace and @xmath69 in the oam subspace . in particular , the probabilities of detecting specified spin - orbit states were assessed experimentally by counting the number of photon coincidences between the test photon and the trigger one in a given time window of 100 s. we first measured the probabilities of the four spin - orbit basis states @xmath70 , which are eigenstates of @xmath24 and @xmath27 . the results are shown in fig . [ fig : paradox]a and are in reasonable agreement with the quantum predictions obtained from state ( [ eq : psi ] ) . more precisely , while the counts for states @xmath71 and @xmath72 were consistent with theory within experimental uncertainties , the counts for state @xmath73 were about 25% smaller than theory and there was a 3% fraction of counts for state @xmath74 , which in theory should have vanishing probability . next , we measured the four probabilities appearing in properties [ eq : p1]-[eq : p4 ] entering hardy s paradox , by performing a projective measurement on the four states @xmath75 , and @xmath76 . the experimental results are given in fig . [ fig : paradox]b . the count frequency of state @xmath76 was found to be @xmath77% ( specified errors are estimated as standard deviations computed assuming poissonian statistics and ignoring other possible sources of errors ) , against a quantum prediction of 9% . the other states presented much smaller , but nonvanishing count frequencies : @xmath78% , @xmath79% , and @xmath80% , respectively for states @xmath81 , and @xmath82 . this outcome , probably due to an imperfect state preparation and/or to some residual cross - talk in the oam and polarization measurements , makes it not possible to apply the simple all - versus - nothing reasoning presented above for hardy s paradox . but this is normal for an experimental test , as no experimental result can be perfectly zero , because of the unavoidable noise and other experimental imperfections . ) for the input photon with @xmath67 . ( a ) coincidence count rates for the four spin - orbit basis states . the measurement time window was of 100 s and the mean total number of coincidences was of @xmath83 , corresponding to the rate @xmath84 coincidences / s . ( b ) coincidence count rates for the measurement of spin - orbit states ( [ eq : plusminus ] ) , which define the observables @xmath85 , and @xmath3 . the ratio of the reported coincidence rate values with @xmath86 gives the experimental frequencies and the estimates of the probabilities for the photon to be in the corresponding state.,width=302 ] to take into account experimental imperfections , one must replace the all - versus - nothing paradox with a bell - like inequality , as for example discussed by mermin @xcite ( on this issue , see also @xcite ) . more precisely , the inequality arising in hardy s paradox is the following one ( see appendix a for a proof ) : @xmath87 this inequality should hold true in any non - contextual realistic model and is trivially satisfied in the ideal noiseless case given by properties [ eq : p1][eq : p4 ] . but it is violated by quantum predictions . our results reported above also violate the inequality by over seven standard deviations , thus confirming the contextual behavior of quantum mechanics . in synthesis , we have demonstrated generation of partially entangled spin - orbit states of single photons and have exploited such states to carry out an experimental test of hardy s paradox . although ideally hardy s paradox is an all - versus - nothing statement , so that a single event could be enough to prove that its assumptions must be wrong , in practice experimental noise forces the use of an inequality and of a statistical verification , similar to the case of a bell inequality test . in our experiment , we verified that the inequality was violated with high statistical confidence . this proves that a non - contextual realistic model of the system can not be true . non - contextuality in our single particle experiment was assumed based on the observable compatibility , and not on their spatial separation . while this is a conceptual limitation of our test , the use of a single particle demonstrated in our approach has some other advantages . the first is that the experiment is much simpler to implement . we used a heralded photon regime , but a similar demonstration could be based on an attenuated light source , thus making it even simpler . simple - to - perform experiments testing the conceptual paradoxes of quantum mechanics may have a strong educational value . a second advantage is that the quantum detection efficiency for a single - photon detection can be made significantly larger than for the two - photon case . this , in turn , could be exploited in the future to carry out hardy - like tests that are free from other assumptions , such as the fair sampling hypothesis , or other detection - related loopholes that may undermine their validity , similarly to the case of bell inequalities ( on this issue see , e.g. , refs . this work was supported by the 7th framework programme of the european commission , within the future emerging technologies program , under grant no . 255914 , phorbitech . we derive here the inequality ( [ eq : inequality ] ) , which is to be satisfied by any realistic and non - contextual statistical model for hardy s paradox . realism of the model means that we can assign probabilities to the set of elementary events corresponding to each possible result of the measurement of the observables @xmath88 , even when they are not measured . because each measurement can have only the two results @xmath89 , we have sixteen probabilities associated to each event . the difference between a realistic statistical model and quantum mechanics stems from the fact that , in the former , probabilities can be assigned to any @xmath90-algebra of the elementary events , while this is impossible in quantum mechanics in general . for example , any realistic statistical model assigns values ( eventually zero or one ) to all 16 probabilities @xmath91 @xmath92 of the four - fold joint measurements of @xmath0 , @xmath1 , @xmath2 , and @xmath3 , as reported in table [ tab:1 ] , which is impossible in quantum mechanics , because the primed observables do not commute with the unprimed ones . besides realism , the model non - contextuality corresponds to the assumption that the results of a measurements on a given observable are independent of possible joint measurements carried out on other compatible observables . this means that each probability @xmath91 depends on the observables pertaining the system under study and not on the context in which the measurements are performed . in particular , the @xmath91 can not depend on parameters characterizing the measurement apparatus or the environment . non - contextuality is always assumed in classical physics and it is implicit in the probabilities @xmath91 in table [ tab:1 ] , independently of their actual values . from the probabilities @xmath91 , we may easily calculate the probabilities defining properties [ eq : p1][eq : p4 ] , relevant for hardy s paradox . we obtain @xmath93 observing that all probabilities on the right of the last of eqs . ( [ eq : p1p4 ] ) are already present on the right of the first three equations , we find inequality ( [ eq : inequality ] ) . the compatibility of two observables @xmath94 and @xmath95 can be operationally defined by the observed independence of their measurement results from the order by which we measure them and the possible measurement repetition . for example , if @xmath94 and @xmath95 are two compatible observables , we can perform the measurement sequences @xmath96 , @xmath97 , @xmath98 , @xmath99 , etc . and we would always obtain the same results for the values of @xmath94 and @xmath95 . in the quantum formalism , observables are compatible if and only if their associated operators commute . the concurrence of a generic state @xmath100 of a bipartite quantum system is defined as @xmath101 , where@xmath102 are the square roots of the eigenvalues of @xmath103 where @xmath104 with @xmath105 pauli matrix .

we test experimentally the quantum `` paradox '' proposed by lucien hardy in 1993 by using single photons instead of photon pairs . this is achieved by addressing two compatible degrees of freedom of the same particle , namely its spin angular momentum , determined by the photon polarization , and its orbital angular momentum , a property related to the optical transverse mode . because our experiment involves a single particle , we can not use locality to logically enforce non - contextuality , which must therefore be assumed based only on the observables compatibility . on the other hand , our single - particle experiment can be implemented more simply and allows larger detection efficiencies than typical two - particle ones , with a potential future advantage in terms of closing the detection loopholes .

the diagnosis of mpd can be made by histopathological evaluation . according to the extent of tumor invasion , mpd is classified into two types : carcinoma in situ ( tis ) and pagetoid carcinoma . we performed immunohistochemical studies of epithelial keratins in intraductal carcinoma in situ ( idcis ) in mpd . a 57-year - old japanese woman first noticed erosion on the right nipple ( fig . 1 ) 8 years ago . magnetic resonance imaging ( mri ) showed thickened epidermis suggesting an intraductal invasion in the breast duct . histopathological findings on the excised specimens showed intraductal invasion with paget cells in breast duct . toker cells , clear cells in the epidermis , are possible precursor cells of paget cells . keratins are important markers in evaluating the origin of epithelial tumors , and are dependent on the stage of differentiation and prognosis of the carcinoma . in the normal mammary gland , luminal cells express k1 , k8 , k15 , k16 , k18 and k19 , whereas basal ( myoepithelial ) cells express k5 , k14 and k17 . toker cells , k7 positive , are observed in 10% of men and women in the nipple . we performed immunohistochemical studies of epithelial keratins ( k1 , k7 , k8 , k10 , k14 , k15 , k16 , k17 , k18 , k19 and k20 ) in mpd . the results showed k7 , k8 , k18 and k19 were expressed in intraepidermal nests containing paget cells ( fig . tumor cells were negative for k17 . in the breast ducts , k7 ( fig . 3d ) . to our interest , k17 was positive in some tumor cells ( fig . the other keratins were negative . k7 , k8 , k18 and k20 are expressed in situ in mpd . k7 , k8 , k18 and k19 are expressed in the intraepidermal nests with paget cells in our study as well as in extramammary paget 's disease ( empd ) . in mpd , k7 , k8 , k18 and k20 are positive in paget cells in situ in the epidermis . k7 , k8 , k18 and k19 are positive in intraepidermal nests in mpd and in empd . interestingly , k17 , which is a hyperproliferative keratin , was detected in intraductal invasion in the breast duct . k17 is induced in wound healing , tumor invasion , epithelial proliferation and tumor growth . keratin expression in intraductal invasion and in situ in the epidermis in mpd may differ and vary according to the invasive pattern of tumor cells . based on the observed pattern of keratin expression , the intraductal invasion in mpd may correlate with the presence of k17 , hyperproliferative keratin and absence of k19 .

we performed immunohistochemical studies of epithelial keratins in intraductal carcinoma in situ ( idcis ) in mammary paget 's disease ( mpd ) . k7 , k8 and k18 were expressed in idcis in mpd . however , k19 was not expressed in idcis in mpd . interestingly , k17 was expressed in some tumor cells in idcis . k17 , a hyperproliferative keratin , may suggest ductal invasion and poor prognosis in mpd .

ST. PAUL, Minn. (AP) — A slain military sniper whose memoir sparked a lawsuit from former Minnesota Gov. Jesse Ventura admitted before his death that he removed Ventura's name from the book because he was afraid of being sued, jurors in Ventura's defamation lawsuit heard Wednesday. Former Minnesota Gov. Jesse Ventura, right, made his way back into Warren E. Burger Federal Building during the first day of jury selection in a defamation lawsuit, Tuesday, July 8, 2014 in St. Paul,... (Associated Press) Taya Kyle, the widow of former Navy SEAL Chris Kyle, arrives with her attorneys at the federal courthouse Tuesday, July 8, 2014 in St. Paul, Minn., for the start of a trial in a lawsuit filed by former... (Associated Press) Former Minnesota Gov. Jesse Ventura makes his way back into Warren E. Burger Federal Building during the first day of jury selection in a defamation lawsuit, Tuesday, July 8, 2014 in St. Paul, Minn. Ventura... (Associated Press) Ventura claims "American Sniper" author Chris Kyle, a former Navy SEAL who was fatally shot last year at a Texas gun range, invented a story in his best-selling autobiography about decking Ventura outside a California bar in 2006. Kyle had said Ventura made loud disparaging comments about SEALs while Kyle was attending a wake for a fellow SEAL killed in battle. Kyle gave a video deposition in November 2012 that jurors saw Wednesday. Near the start, Kyle told Ventura's attorney, David Bradley Olson, that he wasn't concerned about the lawsuit. Asked why, he replied: "You can't defeat the truth." But later on Kyle, who's regarded as the deadliest sniper in U.S. military history, acknowledged he was indeed afraid of being sued. He said his co-authors, Jim DeFelice and Scott McEwen, included Ventura's name in early drafts of the subchapter on the alleged incident — even calling him Jesse "The Body" Ventura, his name from his pro wrestling days. Kyle said he was acting on the advice of a friend who was a Dallas police officer. "He said if you put something in the book that's not true you're probably liable," Kyle recalled, even as he insisted everything in the book was accurate to the best of his knowledge. But he said it took some work to convince them that Ventura's name should come out. The three-page passage ultimately referred to Ventura as "Scruff Face." Kyle's retelling was consistent with his published version of what happened at the bar near Kyle's base at the time in Coronado, California. He stood by his claim that Ventura told him "you deserve to lose a few (SEALs)," saying in the videotape, "Those are his exact words." He said he then punched Ventura because he believed Ventura was fixing to hit him. But Kyle acknowledged he had no direct knowledge of some of the details described in the story, such as an allegation that he gave Ventura a black eye. He said he heard them from witnesses, but he couldn't remember who. "I was told it. I believed it," he said. Kyle also said some details his friends told DeFelice — that he knocked out Ventura, threw him across tables or choked him — definitely weren't true. They didn't make it into print, however. Olson asked Kyle if he was familiar with Ventura before the alleged confrontation. Kyle responded that he'd never met Ventura before, but that he was familiar with Ventura's service as a SEAL and his subsequent career as a wrestler, actor and politician. "Back then we thought that he was a pretty cool dude," Kyle said. Ventura, who was Minnesota governor from 1999-2003, pursued his lawsuit even after Kyle was killed in February 2013, saying it was important to clear his name. Ventura, who has hosted several cable TV shows since his single term ended, has said his job offers dried up after the book came out because of the harm to his reputation. Legal experts have said Ventura must prove that Kyle made up the story, or at least acted with reckless disregard for the truth. Earlier Wednesday, Kyle's widow, Taya Kyle, testified they never intended to keep the money from the book. A key claim Ventura must prove is that the Kyles profited from a made-up story. In often tearful testimony, she said they wanted to donate money to other veterans but found themselves limited by gift tax laws that prevented them from donating more than $13,000 each to two families last year. Olson challenged that assertion, suggesting by his questions that they could have given more away and just paid the taxes. The book has earned more than $3 million in royalties. The judge ruled earlier that any profits from an upcoming movie based on Kyle's book could be subject to damages. Taya Kyle testified Wednesday that the alleged incident won't be part of the movie, which is being directed by Clint Eastwood. Kyle said she had been told by a screenwriter that there wasn't enough room for it. ||||| In this April 6, 2012, photo, former Navy SEAL Chris Kyle poses in Midlothian, Texas. The estate of Kyle, who was fatally shot on a gun range in 2013, faces a lawsuit from former Minnesota Gov. Jesse Ventura, who alleges Kyle fabricated a bar brawl between them. (AP Photo/The Fort Worth Star-Telegram, Paul Moseley) It was Sept. 29, 2006, when Master at Arms 2nd Class Michael Monsoor smothered a grenade in Ramadi, Iraq, to shield other Navy SEALs and Iraqi soldiers they were working with from harm. His actions immediately became the stuff of military legend, and resulted in a posthumous Medal of Honor in 2008. The resulting wake the following month spawned another story that, in turn, led to a high-profile defamation suit being heard in court this week. Fellow SEAL Chris Kyle said in his bestselling 2012 book “American Sniper” that he punched out a celebrity in a bar while mourning Monsoor’s death with other SEALs after the individual “started running his mouth about the war and everything and anything he could connect to it.” That included President George W. Bush and deployed SEALs, who “were doing the wrong thing, killing men and women and children and murdering,” the man said, according to Kyle’s book. Kyle, who was shot to death in 2013, said in his book that he tried to get the man — identified only as “Mr. Scruff Face” — to keep it down, and he responded by saying the the SEALs in the bar “deserve to a lose a few.” The man eventually took a swing at him, Kyle alleged, and all hell broke loose. “Being level-headed and calm can last only so long,” Kyle said in his book. “I laid him out. Tables flew. Stuff happened. Scruff Face ended up on the floor.” Kyle concluded: “I have no way of knowing for sure, but rumor has it he showed up at the [SEAL] graduation with a black eye.” It’s far from the only dramatic part in Kyle’s book — at one point, he accuses his commanding officer during the March 2003 invasion of Iraq of being a coward for failing to involve them in more combat. But it’s the “Scruff Face” passage that now has Kyle’s widow in court facing Jesse Ventura, the former governor of Minnesota, WWF wrestler and Vietnam War era veteran. Ventura sued Kyle in 2012 after the sniper said in media interviews like this one that the individual in question was Ventura, and that Kyle punched him in the face. Disclaimer: There’s some rough language in this radio interview Kyle did with the “Opie and Anthony Show,” but it’s believed to be the first place he named Ventura as “Scruff Face”: The whole mess is in court now, as a Hollywood film version of Kyle’s book makes its way through production with a planned 2015 release. It will star Bradley Cooper as Kyle, and is directed by Clint Eastwood. Other Navy SEALs will reportedly have roles in the film. Former Minnesota Gov. Jesse Ventura, right, makes his way into the Warren E. Burger Federal Building on Tuesday in St. Paul, Minn., during the first day of jury selection in his defamation lawsuit against the estate of former Navy SEAL sniper Chris Kyle. (AP Photo/The Star Tribune, Elizabeth Flores) Ventura pursued the defamation lawsuit against Kyle even after police said the sniper was shot to death by a fellow veteran on a Texas gun range in February 2013. Ventura says the incident never happened, and that it is important for him to clear his name. But critics have pointed out that he is doing so as the profits from “American Sniper” continue to pour in — they’re reportedly over $3 million. Ventura has said that he was worried about looking like a traitor, considering his own ties to the Navy and its Underwater Demolition Teams, which were merged with modern SEAL teams in the 1980s, after he served. It will be a tough case for Ventura to win. As a public figure, he must prove to the jury that Kyle knew the story was false, or that he told it without regard for the truth. Kyle’s widow, Taya, said in court Wednesday that her husband doesn’t lie, and that he planned to donate the proceeds from his book to charity. The trial is expected to take about three weeks. UPDATE: July 9, 10:45 a.m.: This post has been updated to clarify the relationship between the Navy’s UDT units and modern SEAL teams. UPDATE: July 11, 3:15 p.m.: The excellent special operations website SOFREP.com takes on the controversy over whether Ventura should be allowed to call himself a SEAL veteran. The opinion of Brandon Webb, a SEAL veteran himself: “Like it or not, Jesse Ventura is a Navy SEAL. He did the pushups and put up with the cold water, just like the rest of us.”

– A truly strange court proceeding kicked off in Minnesota this week, as former governor/professional wrestler Jesse Ventura brought his defamation suit against murdered American Sniper author Chris Kyle. The Washington Post has a great recap of the dispute, which stems from Kyle's 2012 book. In it, Kyle writes that he punched out a celebrity in a bar for saying that the SEALS "deserve to lose a few" for their actions overseas. Kyle refers to the celebrity only as "Mr. Scruff Face" in the book, but later identified him as Ventura. Ventura pursued the suit even after Kyle's death, because he says the incident didn't happen and he has to clear his name. In his opening statement, his lawyer said Ventura would testify that Kyle "made the whole story up." Yesterday saw Kyle testify from beyond the grave, with a 2012 video deposition in which he said he left Ventura's name out of the book because—you guessed it—he was afraid of being sued, the AP reports.

nocturia is defined as waking one or more times to void during the period between going to bed with the intention of sleeping and waking with the intention of arising ( 1 , 2 ) . recent multinational population - based , cross - sectional survey ( epic ) of adults aged 18 yr using 2002 international continence society ( ics ) definitions showed overall prevalence of any lower urinary tract symptoms ( luts ) was 62.5% in men and 66.6% in women and nocturia ( 2 times / night ) was the most commonly reported storage symptom for both men ( 20.9% ) and women ( 24.0% ) ( 3 ) . similarly , the epidemiological data in adult korean aged 40 - 89 yr national community showed that of 2005 subjects interviewed , 33.5% reported voiding once per night and 48.2% twice or more per night and in addition , the impact of nocturia on daily life was reported by 14.6% of subjects ( 4 ) . nocturia is associated with sleep disruption and consequently impairs the quality of life ( qol ) and potentially increases mortality ( 5 , 6 ) . although this condition should be evaluated and treated , it has only recently been recognized as a clinical entity in its own right , rather than just one of the features of luts . relatively few patients with nocturia seek medical care because of a lack of awareness or misconceptions about nocturia . furthermore , there is a general lack of knowledge about treatment options for nocturia ( 4 , 7 , 8) . because the pathophysiology of nocturia is multifactorial and complex , it is important to adopt a systematic approach to identify the possible causal factors of nocturia and to treat them accordingly . patients with nocturia can be categorized as having one of the following three disorders : ( 1 ) nocturnal polyuria ( np ) in which the voided urine volume during the hours of sleep exceeds 33% of the 24-hr output ( 2 ) , decreased nocturnal bladder capacity ( nbc ) , which results in a nocturnal urinary volume greater than the maximum voided volume ( mvv ) , ( 3 ) or mixed nocturia , a combination of the preceding two categories ( 9 , 10 ) . in one retrospective study of 194 patients with nocturia , 13 ( 7% ) had pure np , 111 ( 57% ) had diminished nbc , and 70 ( 36% ) had a combination of the two ( 9 , 11 ) . desmopressin is a synthetic analogue of arginine vasopressin ( avp ) , but desmopressin has a more potent antidiuretic effect than avp . desmopressin has been shown to be an effective treatment for nocturia with np by decreasing night - time urine production ( 12 - 16 ) . however , a patient with a significantly decreased nocturnal bladder capacity index ( nbci ) > 2 may have bladder outlet obstruction , detrusor overactivity ( do ) , sensory urgency , and/or primary bladder disorders such as infection , or malignancy ( 16 ) . specific treatment of the underlying urological condition would therefore be expected to have a mitigating effect on decreased nbc as a component of nocturia . although clinicians usually treat nocturia patients with decreased nbc based on their personal experience and use anticholinergic and hypnotic agents as well as desmopressin , these treatments have not been studied extensively clinically . in the present study , we investigated the safety and efficacy of oral desmopressin for the treatment of mixed nocturia in patients with both np and a decreased nbc . patients aged 18 yr with mixed nocturia ( 2 voids / night , nocturnal polyuria index [ npi ] > 33% and nbci > 1 ) were enrolled in this open label , prospective , seven - center study . the formula for calculating npi is simply nocturnal urine volume ( nuv ) divided by 24-hr urine volume , and nbci , more complicated formula that addresses voids at night in patients with decreased nbc , is defined as the difference between the predicted number of nightly voids ( pnv ) and the actual number of nightly voids ( anv ) . pnv is derived by calculating ( nuv / mvv ) and subtracting 1 ( 17 ) . the following exclusion criteria were used : nocturia due to other defined causes of increased urinary frequency , primary polydipsia ( > 40 ml / kg/24 h ) , neurogenic bladder dysfunction , urge incontinence , continued post - voiding residual urine > 150 ml , serum sodium levels < 135 mm / l , uncontrolled hypertension , congestive heart failure , use of diuretics , and actual or planned pregnancy . the study was performed in accordance with the international conference on harmonization good clinical practice guidelines , and the principles of the declaration of helsinki . the study protocol received ethical committee approval at each study site and written informed consent was obtained from all patients before recruitment into the study . the study included the following periods : screening ( 1-week ) , dose titration ( 1 - 3 weeks ) , and treatment ( 4 weeks ) ( fig . 1 ) . the patients that fulfilled the primary inclusion criteria entered the dose titration phase . during an open - label dose - titration period of up to 3 weeks , the patients ' optimum oral desmopressin dose ( 0.1 , 0.2 , or 0.4 mg ) was determined as the dose that decreased the number of nocturnal voids by 50% or decreased nuv by 20% without hyponatremia . if the patients did not meet the above criteria during the dose titration period , they received the maximum tolerable dose instead of the optimum dose . in addition , if the patients complained the adverse effects in spite of good responses to desmopressin during the dose titration period , they received the just lower dose instead of the optimum dose . then , eligible patients were treated with the determined optimum desmopressin dose for 4 weeks . all patients kept 3-day frequency - volume charts ( fvc ) , recorded bedtime and sleep disruption , and answered a sleep questionnaire at baseline and after treatment . the sleep questionnaire included items about the duration of sleep until the first nocturnal void , the frequency of > 5 hr of undisturbed sleep , and the patient 's overall impression about his / her quality of sleep expressed as feeling fresh in the morning or feeling tired in the morning . clinical and laboratory assessments including body weight , blood and urine analysis , serum sodium monitoring , and adverse event reports were recorded at baseline and after 4 weeks of treatment . the patients with serum sodium levels < 125 mm / l , symptomatic hyponatremia , or intolerable adverse effects were withdrawn from the study . the efficacy assessments were based on data from the patients ' fvc and answers to the sleep questionnaire after the 4-week treatment period . the primary efficacy endpoint was the proportion of patients with a 50% or greater reduction in the mean number of nocturnal voids compared with baseline levels after the 4-week treatment phase . secondary endpoints included changes in the mean number of nocturnal voids , changes in the mean duration of the period from bedtime to the first nocturnal void ( first sleep interval ) , and the proportion of patients that felt they had a good sleep experience . the safety of oral desmopressin was evaluated based on the collected adverse events , body weight gain , and laboratory data with an emphasis on serum sodium levels . the significance of the results obtained was tested with a paired t - test or wilcoxon 's signed rank test according to the normality of the data . binary variables such as the quality of sleep were analyzed using generalized estimating equations ( gee ) ( p value < 0.001 ) . a p value of < 0.05 was considered statistically significant and the statistical software package spss version 17.0 was used for data management and analysis . the study was performed in accordance with the international conference on harmonization good clinical practice guidelines , and the principles of the declaration of helsinki . the study protocol , patient information and informed consent forms were reviewed and approved by independent review board at each study and all patients were informed of the nature and purpose of the study ( irb no . the study was performed in accordance with the international conference on harmonization good clinical practice guidelines , and the principles of the declaration of helsinki . the study protocol , patient information and informed consent forms were reviewed and approved by independent review board at each study and all patients were informed of the nature and purpose of the study ( irb no . among 103 patients enrolled in the dose - titration phase , 9 ( 8.7% ) withdrew due to informed consent withdrawal ( n=3 ) and protocol violation ( n=6 ) during the dose - titration period ( fig . a total of 94 patients received the optimal desmopressin dose , and 90 ( 95.7% ) patients completed the study . four patients withdrew due to neck stiffness ( n=1 ) or loss to follow - up ( n=3 ) . the study population included 79 men ( 84% ) and 15 women ( 16% ) with a median age of 64.2 yr ( 39 - 86 yr ) ; their baseline characteristics are summarized in table 1 . the efficacy analysis included 94 patients that received at least one dose of the study drug during the dose - titration period , had baseline data before the study , and at least one post - baseline efficacy measurement . during the 4 weeks of active treatment , 44% ( n=41 ) of patients received 0.1 mg oral desmopressin , 33% ( n=31 ) received 0.2 mg of desmopressin , and 23% ( n=22 ) received 0.4 mg of desmopressin . overall patient compliance was high ; 84 ( 89.7% ) patients took 80% of the prescribed medication during the treatment period . the mean number of nocturnal voids / night was reduced in at least 50% compared with baseline levels . in 72% of the patients ( n=68 ) ( 95% ci , 0.63 - 0.81 ) ( p<0.001 ) , the mean number of nocturnal voids decreased significantly from 3.20 to 1.34 after the 4-week treatment with oral desmopressin ( table 1 ) . furthermore , the total number of voids/24 hr decreased significantly after treatment ( 11.18 vs 9.15 , p<0.001 ) ; however , the number of mean daytime voids before and after treatment was not significantly different ( 7.97 vs 7.82 , p=0.38 ) . moreover , the factors associated with nocturnal urine production including the mean nuv , npi , and nocturnal diuresis all decreased significantly after desmopressin treatment . oral desmopressin treatment was also associated with improved nocturnal bladder capacity as evidenced by decreases in both the nocturia index ( ni ) and nbci ( both p<0.001 ) . the mean duration of sleep until the first nocturnal void increased from 118.444.1 to 220.390.7 min ( p<0.001 ) ( fig . 3a ) , and 17 ( 18% ) patients had more than 5 hr of undisturbed initial sleep per night after treatment compared to none at baseline ( fig . 3b ) . the overall impression of patients about their quality of sleep was improved quality ; the number of patients who reported a good night of sleep increased significantly from 19.8% to 78.7% after desmopressin treatment for 4 weeks ( p<0.001 ) ( fig . no significant serum sodium changes ( 141.8 to 141.5 mm / l , p=0.41 ) or changes in serum creatine ( p=0.85 ) , potassium ( p=0.68 ) , or body weight ( p=0.43 ) were observed in the safety analysis compared with baseline . one 74-yr - old man treated with 0.1 mg desmopressin for 4 weeks showed significant hyponatremia ( 132.4 mm / l ) , but was asymptomatic . although adverse events occurred in a total of 6 ( 6.4% ) patients treated with a demopressin dose of 0.2 mg , the symptoms were generally mild ( headache , facial edema , anorexia ) . nocturia can be a symptom of several medical disorders other than lower urinary tract abnormalities , and is also a condition in its own right . therefore , it is important that urologists identify the precise type and causes of nocturia to treat it effectively . for example , in one study , the type of nocturia was classified into three groups based on the voiding diaries and the results of urodynamic study ( uds ) : pure np in which the voided urine volume during the hours of sleep is more than 35% of the 24-hr urine volume , do defined as existing uninhibited contraction on filling cystometrogram , and mixed ( np with do ) . they reported that the proportion of np , do and mixed type were 50.0% , 7.9% , and 17.1% respectively ( 18 ) . in general , nocturia can be categorized into three types : np , decreased nbc , mixed nocturia with a combination of np and decreased nbc , or global polyuria which refers to urine overproduction over a 24-hr period ( 19 ) . pharmacological options that could be considered include the cautious use of loop diuretics in the afternoon , anti - muscarinics for decreased nbc , and desmopressin for nocturia caused by np . because the number of patients with mixed nocturia has been underestimated and few results about the effect of desmopressin on mixed nocturia have been reported , we analyzed the clinical effects of oral desmopressin on patients with mixed nocturia by evaluating the improvements in both np and nbc . the results of our study showed that treatment with desmopressin for 4 weeks resulted in a significant improvement in the parameters associated with np including nuv ( 41.7% reduction ) , npi ( 31.3% reduction ) , and nocturnal diuresis ( 39.9% reduction ) . np is believed to be responsible for at least 50 - 65% of nocturia cases ( 9 , 20 ) . the hormone avp is normally released into the circulation following the diurnal pattern linked to the wake - sleep cycle , and decreases urine production by promoting osmotic re - absorption of solute - free water in the collecting tubules ( 21 ) . oral desmopressin , is effective against np because it compensates for loss of circadian rhythm - related adh secretion and furthermore , it causes slight changes in drinking habits . in one randomized , double - blind , placebo - controlled study for men 18 yr with verified nocturia and ni > 1 , the decrease in the mean number of nocturnal voids ( from 3.0 to 1.7 ) , mean nocturnal diuresis ( from 1.5 to 0.9 ml / min ) , and mean ratio of night/24-hr urine volume ( 23% ) were significantly different between the desmopressin and placebo groups ( all p<0.001 ) ( 15 ) . ( 22 ) also found in a short - term study that desmopressin treatment reduced the mean number of nocturnal voids and there was a reduction of 20% in nocturnal diuresis in 58 patients ( 82% ) and of 50% in 31 ( 44% ) . the effects of desmopressin on the np component of nocturia in patients with mixed nocturia in the present study are similar to those reported in previous studies which inclusion criteria were not limited to mixed nocturia . however , the use of desmopressin for the treatment of nocturia with decreased nbc has not been thoroughly evaluated , and a standard treatment protocol aimed at improving the decrease in nbc has not been developed to date . our results suggest that oral desmopressin improves nocturia by increasing nbc as well as decreasing nuv , which is reflected by improved ni ( 38.9% reduction ) and nbci ( 54.9% reduction ) . type e2 neurons in and around the micturition center directly regulate the activity of the bladder , and type e1 and type i neurons modulate the activity of type e2 neurons by excitatory and inhibitory effects ( 23 ) . moreover , ureterovesical flow has been demonstrated to trigger local and general detrusor activity in an unstable bladder by distension of detrusor muscle bundles around the ureteric hiatus detrusor activity in a pig model ( 24 ) . based on these findings , desmopressin treatment would improve the decreased nbc seen in mixed nocturia patients by suppressing detrusor activity and inhibiting neuron - associated bladder contraction and the ureterovesical flow rate during sleep . the mean duration of the time until the first nocturnal void in patients with mixed nocturia was prolonged by desmopressin and the patients ' overall impression about their quality of sleep improved due to a decrease in the frequency of nocturnal voids in the present study . similarly , van kerrebroeck et al . showed that the duration of the first sleep period was prolonged by 108 min ( placebo group : 41 min , p<0.001 ) and an average of > 5 hr of unbroken first sleep period per night was experienced by 27% of desmopressin - treated patients ( placebo group : 9% ) , resulting in a highly significant between - group difference ( 25 ) . these authors reported that two questions concerning the quality of sleep and tiredness favored desmopressin over the placebo ( p=0.02 ) . among the physiological theories associated with nocturnal urine output , elderly people with frequent awakenings have a larger part of their 24-hr urine output at night than those with fewer awakenings ( 26 ) . the ability to sleep without waking is more indicative of quality sleep than interrupted longer periods of total sleep time during the night . it seems that not only spontaneous sleep , but also less fragmented sleep with undisturbed sleep duration , and deep stages of sleep with a decreased nocturnal voiding frequency improve after desmopressin treatment as a result of the effects of endogenous in vivo adh secretion on nu . however , in another study to investigate the effects of long - term oral desmopressin on baseline adh secretion in elderly patients with nocturia , administration of desmopressin for 1 yr in elderly patients did not affect baseline adh secretion in spite of significantly decreasing nocturnal urine output and the number of nocturia episodes ( p<0.01 ) ( 27 ) . the practical importance of the increase in endogenous adh with regard to the treatment of np requires further investigation . finally , the safety analysis of desmopressin in the present study confirmed that adverse events associated with treatment are infrequent and usually mild . significant hyponatremia occurred in only one case , and this particular patient was asymptomatic . in addition , other side effects such as body weight gain and electrolyte imbalance including sodium abnormalities and decreased renal function did not occur . in a meta - analysis of the risk of hyponatremia in older adults using desmopressin for treatment of nocturia , hyponatremia was found to be a relatively common adverse event with a frequency of 7.6% ( 28 ) . however , other studies have suggested that desmopressin has antidiuretic activity for one night or less ; a daytime pause in treatment may therefore be sufficient to maintain water and electrolyte balance ( 29 , 30 ) . in addition , at least a 10-fold higher - thanrecommended dose did not cause changes in the serum sodium concentration . in conclusion , oral desmopressin treatment results in a significant improvement in the number of mixed nocturia episodes by reducing nuv and increasing nbc . this drug improves the quality of sleep by prolonging the period of sleep until the first void , and is shown to have an acceptable safety profile .

to investigate the efficacy and safety of desmopressin in patients with mixed nocturia , patients aged 18 yr with mixed nocturia ( 2 voids / night and a nocturnal polyuria index [ npi ] > 33% and a nocturnal bladder capacity index [ nbci ] > 1 ) were recruited . the optimum dose of oral desmopressin was determined during a 3-week dose - titration period and the determined dose was maintained for 4 weeks . the efficacy was assessed by the frequency - volume charts and the sleep questionnaire . the primary endpoint was the proportion of patients with a 50% or greater reduction in the number of nocturnal voids ( nv ) compared with baseline . among 103 patients enrolled , 94 ( 79 men and 15 women ) were included in the analysis . the proportion of patients with a 50% or greater reduction in nv was 68 ( 72% ) . the mean number of nv decreased significantly ( 3.20 to 1.34 ) and the mean nocturnal urine volume , nocturia index , npi , and nbci decreased significantly . the mean duration of sleep until the first nv was prolonged from 118.444.1 to 220.390.7 min ( p<0.001 ) . the overall impression of patients about their quality of sleep improved . adverse events occurred in 6 patients , including one asymptomatic hyponatremia . desmopressin is an effective and well - tolerated treatment for mixed nocturia .

fundamental concepts in psychology and philosophy of the mind are the notion of sensation and perception . when a stimulus produces an effect on different sensory receptors it induces sensation . subsequent interpretation and organization of this sensory stimulus produce a meaningful experience of the world and of one 's perception . although in most cases perception is conscious , perception without awareness does exist , that is , the interpretation of semantic stimuli . normally wakefulness and awareness are related ; one has to be awake ; that is , there has to be a certain level of consciousness to be aware of something ; that is , there is content in consciousness . in states of deep sleep , anesthesia , and coma there is little or no wakefulness and hence no awareness . in drowsiness and light sleep however , in certain states , dissociations exist between wakefulness and awareness , such as in the vegetative state , when there is wakefulness presumably without awareness ( eyes open , brain shut ) . in the dream state there is awareness ( content in consciousness ) with decreased wakefulness ( level of consciousness ) . dreams are succession of images , ideas , emotions , and perceptions without sensations that occur involuntarily in the mind predominantly during rapid eye movement ( rem ) sleep . nonpulsatile subjective tinnitus is considered a phantom perception , the conscious awareness of a percept in the absence of an external stimulus . it is characterized by the perception that the phantom sound comes from an external sound source , even though the sound might be pulled from memory [ 1 , 6 , 7 ] . this is reminiscent of a dream state , when there is awareness , with stimuli attributed to the external world but generated internally . whereas tinnitus can be considered a simple phantom percept , dreams could be considered complex phantom percepts , like hallucinations and hallucinosis [ 9 , 10 ] . however , in contrast to hallucinations and hallucinosis that occur during wakefulness , dreams occur during certain stages of sleep . stimulus - evoked auditory cortical activation does not necessarily produce conscious auditory perception , and auditory perception is possible in the absence of auditory input : more than 80% of people with normal hearing perceive phantom sounds when placed in a soundproof room . likewise , after limb amputation almost all people experience a phantom limb , whereas 70% suffer from severe phantom pain . a clear clinical analogy exists between phantom pain and disabling tinnitus [ 1 , 14 , 15 ] . there are also parallels between the pathophysiology of tinnitus and pain , as well as in the treatment [ 16 , 17 ] . however , there are also differences between tinnitus and pain . while physiological pain is mediated via nociceptive pathways , this could explain why commonly available analgesics that suppress acute physiological body pain are inefficient in ameliorating tinnitus . also , medications such as antiepileptics and antidepressants , which are effective in the treatment of neuropathic pain , tend to be ineffective for tinnitus . many to most ( 33100% ) patients who suffer from phantom limb percepts do not experience phantom limb percepts in a dream state [ 2023 ] . this has been explained as follows [ 8 , 21 , 23 ] : neural representation of the body derives from sensory and proprioceptive feedback from the body . during sleep , when the brain / mind is actively kept offline , this sensory feedback is lacking . moreover , during rem sleep and in the absence of external inputs , dreaming could activate a set of innate or early life spatial - temporal categories . so if rem sleep is a state of protoconsciousness , that is , a contextually emergent property of self - sustaining systems , the self as it appears in rem sleep dreams is no longer affected by waking experiences because it feeds from an embodied and functionally intact body scheme [ 8 , 21 ] . in view of the pathophysiological analogy between tinnitus and pain , it can be hypothesized that tinnitus is absent in the dream state as well . we therefore explored this in a group of 78 consecutive tinnitus patients attending the multidisciplinary tinnitus research initiative clinic at the university of antwerp . a recently proposed pathophysiological model of phantom sound based on a predictive brain concept with bayesian updating might explain why tinnitus is not perceived during dreaming . seventy - eight patients ( 57 males and 21 females ) with chronic , nonpulsatile tinnitus were included in this study with an average age of 48.78 years ( sd = 12.87 ) and an average tinnitus duration of 5.74 years ( sd = 6.96 ) . thirty - five patients perceive noise - like tinnitus , while 43 patients experience pure tone tinnitus . forty - three patients had bilateral tinnitus ; 12 patients perceive tinnitus holocranially , 12 on the left side and 11 on the right side . the first question asked whether the tinnitus patient recalled if they dreamed during the night ( 1 ) , followed by the question whether in their dreams they perceive tinnitus ( 2 ) . of the 78 participating patients only 2 ( 2.56% ) declared that they do not recall their dreams , while 76 ( 97.44% ) do . of those 76 patients that do recall their dreams 74 ( 97.73% ) state that they do not perceive tinnitus while dreaming or are not aware of having tinnitus during sleep . people with tinnitus do not perceive tinnitus in their dreams analogous to what is reported for many phantom limb perceptions [ 21 , 25 ] . dreams and wakefulness are both associated with awareness , but in one state of awareness there is no tinnitus ( dreams ) , whereas in the other ( wakefulness ) there is tinnitus . the reason why patients with tinnitus do not perceive tinnitus in their dream state can be theoretically explained by the bayesian brain model which has been used as an explanation for the development of tinnitus in relation to auditory deafferentation . this bayesian brain model is founded on an extension of a predictive brain model ( see figure 1(a ) ) . whereas other models ( see for an overview ) can explain the tinnitus in the presence of deafferentation the bayesian model is compatible with both the deafferentation and noise - cancelling models and provides a rationale why tinnitus develops in a wake state and not in a dream state . physiologically the brain can be conceptualized as a helmholtz machine that constantly makes one or possibly multiple predictions about the world . since the examples given to the learner are unlabeled , there is no error or reward signal to evaluate a potential solution ; in other words , there is no updating of the predictions . a bayesian brain however updates predictions based on what it actively explores in the environment by means of the senses [ 24 , 29 , 30 ] . bayesian inference can therefore be conceptualized in a way that would be familiar to john hughlings - jackson as using sensory information from the environment to update memory - based expectations ( held before acquiring sensory inputs ) to produce posterior beliefs represented as percepts . this mechanism permits decision making based on predictions updated by actively sampling the environment for confirmation or rejection of expectations ( see figure 1(b ) ) . auditory deafferentation limits the amount of information the brain can acquire to make sense of the world . the topographically specific deafferentation induces a topographically specific prediction error hypothetically based on temporal incongruity . in other words , it is inconsistent with what is stored in memory and should be updated . the model hypothesizes that deprived auditory information depends on the amount ( bandwidth ) of deafferented auditory channels . limited damage to auditory receptors causes loss of functional surround inhibition in the cortex , unmasking of latent inputs , and significantly altered neural coding . this suggests that the missing information can be obtained via access of overlapping tuning curves of the neighboring cortical cells . if the deafferentation is somewhat larger , a widening of auditory receptive fields will permit pulling the missing information from the auditory cortical neighborhood . if this is insufficient , due to a still larger deafferentation , dendritic and axonal rewiring can occur . if this is still insufficient , the missing auditory information can be pulled from ( para)hippocampal memory . when we dream , we create an image of the world that is entirely detached from sensory feedback ; that is , it can not be updated . aminergic activity is highest during waking , declines during nrem sleep , and is lowest during rem sleep . this means that the discrepancy between top - down predictions and ( the absence of ) sensory signals received will not be registered , and the auditory deafferentation will not be filled in , resulting in the absence of tinnitus in the dream state ( see figures 2(a ) and 2(b ) ) . it has been argued that the cerebellum is involved in motor , sensory , and cognitive predictions . it is therefore possible that auditory predictions are made in the paraflocculus , as removing this cerebellar structure can prevent tinnitus from arising and arrest the presence of tinnitus in animals . this conceptually suggests that removing the prediction can prevent or abolish tinnitus , which is in accordance with the concept that tinnitus could be a malprediction . however , apart from its theoretical implications , the data might also help to find the neural correlates of tinnitus . the putative on / off switch for tinnitus is to be found in these areas that differ between waking and rem state , that is , the ventrolateral prefrontal cortex / frontopolar - inferior parietal - cerebellar - parahippocampal network . these areas overlap with a recent meta - analysis of pet studies in tinnitus and provide a framework for zooming in on the pathophysiology of this enigmatic symptom . in addition to its evident benefit for tinnitus research , it could also provide clues for consciousness research , by delineating the core areas involved in the neural correlates of consciousness ; that is , minimal assembly of brain areas required for consciousness per se [ 38 , 39 ] . other potential explanations for the absence of tinnitus in the dream state have to be considered . it is possible that during the dream state there is an attention shift from the tinnitus to the dream , analogous to what is noted in patients who do not perceive their tinnitus when intensely engaged in a task . in conclusion , this report demonstrates that tinnitus perception is switched off during dream sleep even though there is awareness , like in wakefulness . this suggests that it is theoretically possible to find the neural correlates of phantom sound and thereby find a potential avenue for suppressing this enigmatic symptom .

there are pathophysiological , clinical , and treatment analogies between phantom limb pain and phantom sound ( i.e. , tinnitus ) . phantom limb pain commonly is absent in dreams , and the question arises whether this is also the case for tinnitus . a questionnaire was given to 78 consecutive tinnitus patients seen at a specialized tinnitus clinic . seventy - six patients remembered their dreams and of these 74 claim not to perceive tinnitus during their dreams ( 97% ) . this can be most easily explained by a predictive bayesian brain model . that is , during the awake state the brain constantly makes predictions about the environment . tinnitus is hypothesized to be the result of a prediction error due to deafferentation , and missing input is filled in by the brain . the heuristic explanation then is that in the dream state there is no interaction with the environment and therefore no updating of the prediction error , resulting in the absence of tinnitus .

primary hyperparathyroidism ( phpt ) is a condition caused by excessive and uncontrolled secretion of parathyroid hormone by the abnormal parathyroid gland(s ) . in the west , this condition is common between the fifth to seventh decades of life with female : male ratio of 3 : 1 . incidence of phpt was estimated to be 20 per 100,000 [ 1 , 2 ] and more than 80% of phpt cases is asymptomatic at the time of diagnosis [ 35 ] . the first sign of phpt is elevated serum calcium on a routine biochemical evaluation . on the contrary , phpt is relatively rare disease in thailand . most of phpt patients in thailand presented with multiple somatic signs and symptoms of many systems including skeletal system ( bone pain , osteitis fibrosa cystica , pathological fracture , and proximal muscle weakness ) , renal system ( recurrent nephrolithiasis , renal failure ) , nervous system ( psychosis , mental state change ) , gi system ( peptic ulcer , constipation , and pancreatitis ) , and hypertension . understanding the clinical presentation and its course of phpt in thai populations would benefit in future detection and management of phpt in thailand . in addition , we can compare these information to other asian countries where screening of hypercalcemia is not the general practice . a retrospective descriptive study of patients with phpt who underwent parathyroidectomy at department of surgery , siriraj hospital during january 1997 and december 2007 was carried out . the study was approved by the institutional review board with the exemption of informed consent . all related medical data including demographic data , clinical presentations , comorbidities , localizations of abnormal parathyroid glands , operations and their findings , and pathology and complications were reviewed . clinical presentations were divided into different physiological systems as skeletal , renal , neuromuscular , neuropsychiatric , gastrointestinal systems , and other nonspecifics symptoms . data on blood chemistry included preoperative and postoperative serum calcium ( total and ionized ) , phosphate , alkaline phosphatase , creatinine , and parathyroid hormone . imaging modalities for localization and their accuracy when comparing to operative findings were noted . all data were prepared and analyzed statistically using the statistical package for the social sciences program version 13.0 for windows ( spss inc , chicago , il , usa ) . 45 new cases of phpt underwent parathyroidectomy at siriraj hospital between january 1997 and december 2007 . the age ranged from 15 to 89 years ( average 49 years ) with female : male ratio of 3 : 1 . mean follow - up period was 3 years ( range 6 months to 7 years ) . in this study , there was only 1 asymptomatic patient ( 2.2% ) at the time of diagnosis . the majority of 44 patients ( 97.8% ) were presented with various symptoms . in this group the most common presentation was skeletal symptoms ( 30 patients , 66.7% ) with one - fifth of all patients had pathological fracture . the second most common clinical features were in renal system . in 21 patients ( 46.7% ) who had renal symptoms , 7 patients ( 15.6% ) had renal function impairment . the only one patient who presented with a neck mass was one of four of parathyroid carcinoma . details of clinical presenting symptoms were shown in table 2 . in this study , median serum calcium at the time of diagnosis was 13.1 mg / dl ( range 8.122 ) . median parathyroid hormone level was 341 pg / ml ( range 1072490 pg / ml ) . it was noted that the highest level of serum parathyroid hormone detected was 2490 pg / ml and was found in patient with parathyroid adenoma not carcinoma . elevated alkaline phosphatase was documented in 36 patients ( 80% ) with the median of 453 unit / l ( range 603 unit / l ) . as in this study there was a high proportion of parathyroid cancer , we also presented the figures of blood chemistry of all cases and cases excluding carcinoma to be compared ( table 3 ) . preoperative localization with the parathyroid scan ( tc-99 m pertechnetate / tc-99 m mibi subtraction and dual phase tc-99 m mibi and spect ) was selected as a primary investigation in 42 patients ( 93.3% ) . of three patients who did not have parathyroid scan , two had ultrasound scan and one had no preoperative imaging for localization . one patient who had negative parathyroid scan had disease gland localized by mri scan . median sternotomy was performed due to location of the disease gland in the mediastinum in one patient . pathological examination revealed single adenoma in 79.5% ( n = 35 ) , hyperplasia 11% ( n = 5 ) , and parathyroid carcinoma 9% ( n = 4 ) . on the postoperative course , 10 patients ( 22% ) had severe and prolonged hypocalcemia , known as hungry bone syndrome . this condition was well related to preoperatively high level of alkaline phosphatase ( median 606 unit / l , range 3203384 in addition , hungry bone syndrome was also found in patients who had severe skeletal symptoms and signs . there was no report of recurrent laryngeal nerve injury , postoperative bleeding , and wound infection . all patients with pathological fracture ( n = 9 ) had significant clinical improvement demonstrated by well union of the fracture sites within 520 months postoperatively . most of the patients with preoperative renal failure ( serum creatinine > 2 ) also did not get benefit on the renal function after parathyroidectomy . phpt was traditionally described with classical symptoms and signs as painful bones , renal stones , abdominal groans , and psychic moan . however , after measurement of serum calcium levels was included in the routine check - up program in many developed countries , number of asymptomatic cases has been increasing , therefore symptomatic ptht has become the minority . in many asian countries , routine testing of serum calcium is still not in a general practice . clinical reports from india and taiwan show all higher percentage of symptomatic phpt compared to the west [ 79 ] . in thailand serum calcium monitoring is also not a routinely practice , therefore our study documented only 2.2% of asymptomatic presentation in phpt . however , we believed that ptht is definitely underdiagnosed and delay detected in thailand . age distribution of phpt in our study seems to expand in every age group ( 1589 years ) which is similar to india but not taiwan . to design a screening age group of phpt for skeletal - and - renal related symptoms were the leading clinical presentation of symptomatic phpt . in this study these clinical features represented the late diagnosis and showed similar pattern of symptoms to other asian countries . although all fractures were reunioned after parathyroidectomy , the period of treatment was relatively longer than in healthy bone ( 520 months ) . anyhow , the renal consequences such as renal calculi and impairment may not improve after parathyroidectomy . interestingly , on analysis without patients with parathyroid cancer , the blood chemistry on diagnosis showed no significant different . these may also refer that late diagnosis of phpt could mimic the clinical pictures of parathyroid carcinoma . other findings of high number of symptomatic cases lead us to quest that there may be many more hidden asymptomatic cases in thai population . first , asymptomatic cases in thai were distributed in all age group , this situation made screening protocol difficult due to varied target group and low cost - effectiveness . the second situation , if asymptomatic cases in thai were clustered in age group 5575 years . the next question was that do screening and parathyroidectomy in those patients really reduced consequences of phpt , as some of the symptomatic cases were young and will be excluded in screening protocol . however , authors believed that in unknown situation , screening serum calcium in female age > 55 or menopausal age group would gain some benefits . thus , we encourage addition of serum calcium screening for female age > 55 who will have routine blood check up for other purposes . localization method with parathyroid scan had been reported with accuracy 5090% . in this study , bilateral exploration was still the operation of choice due to not very high volume of phpt in our experience . with bilateral exploration , there was still one case where the abnormal parathyroid gland could not be identified . finally , pathological findings of the abnormal parathyroid gland in this study were revealed single adenoma in 79.5% ( n = 35 ) , hyperplasia 11% ( n = 5 ) , and parathyroid carcinoma 9% ( n = 4 ) . this high proportion of parathyroid cancer may lead us to think of possibility of many undiagnosed benign cases in the population . in taiwan study , with screening of serum calcium in 4359 healthy individuals aged 2194 years , at least 4 cases were diagnosed with phpt , representing a minimum estimated prevalence of 92 per 100,000 . our experience with phpt from a single institute in thailand was likely the late diagnosis phpt with various severe symptoms . anyway to improve our detection will definitely benefit the patient in duration of treatment and prevention of permanent damage to major organs . clinical features of late diagnosis of benign phpt may also mimic the presentation of parathyroid carcinoma . according to our findings the guideline for screening serum calcium in order to diagnose phpt in thai populations would need further information to develop .

primary hyperparathyroidism ( phpt ) is not an uncommon disease in the western countries . in thailand , on the contrary , phpt was a rare condition with various clinical presentations . all 45 phpt patients who underwent parathyroidectomy at the department of surgery , siriraj hospital during january 1997 and december 2007 were retrospectively reviewed . demographic data , clinical presentation , localizations imaging , operative procedures , findings , complications , and pathological reports were analyzed . median age was 49 years ( range 1589 years ) with female : male ratio of 3 : 1 . only one patient ( 2.2% ) was asymptomatic phpt . of all symptomatic cases , 30 ( 66.7% ) had skeletal symptoms , 7 ( 15.6% ) had renal impairment , and 39 ( 86.7% ) had mixed symptoms . 42 patients ( 93.3% ) had parathyroid scan and all had bilateral exploration of the neck . postoperative hungry bone syndrome was noted in 10 patients ( 22% ) . on followup , skeletal and neuropsychiatric symptoms were improved but the renal impairment was remained . the s small number of asymptomatic phpt in our study may refer to large number of underdiagnosed phpt in general population . the guideline for screening serum calcium for diagnosis of phpt in thai populations will improve the long - term consequence of the disease but will need further information to identify the target group .

the ability to fabricate freestanding graphene , a single atomic layer of graphite , has raised interesting questions with regard to its surface electronic structure . due to the fact that this system exhibits a mirror plane with two surfaces , the eigenstates of this system must be either a symmetric or antisymmetric superposition of the electronic states of each surface . this applies also to image - potential states , a class of intrinsic surface states that exist at all solid surfaces due to the interaction of an electron in the vacuum with the polarizable surface . this interaction can be described by the classical image - potential which gives rise to a hydrogen - like rydberg series of electronic surface states and resonances @xcite . consequently , it has been predicted that freestanding graphene should possess a double rydberg - like series of image - potential states of even and odd symmetry @xcite . however , there are no experiments so far on freestanding graphene that provide clear evidence for these two series . image - potential states have been observed when graphene forms an interface on metal or semiconductor surfaces where it can be grown with remarkable high quality and long - range order @xcite . experiments on graphene / sic(0001 ) using scanning - tunneling spectroscopy ( sts ) @xcite and two - photon photoemission spectroscopy ( 2ppe ) @xcite have revealed a splitting at least of the first @xmath2 image - potential state . it has been argued that these states are remnants of the first even and odd state of freestanding graphene even if its mirror symmetry is in fact broken due to the presence of the substrate . in contrast to these findings , only a single series of image - potential states has been observed on weakly interacting graphene / metal systems @xcite . for other metals , like ni , pd , rh , and ru , the interaction between graphene and the metal can be much stronger . together with the lattice mismatch , this typically leads to a pronounced buckling of the graphene layer forming a moir superstructure with large periodicity @xcite . graphene / ni(111 ) represents an exception with an almost vanishing lattice mismatch . despite the strong interaction , this results in the growth of a flat graphene layer at a distance of @xmath3 @xcite . for g / ru(0001 ) , on the other hand , the corrugation is particularly pronounced and the hexagonal moir superlattice is divided into strongly interacting valley ( _ l _ ) areas with a distance of @xmath4 and weakly interacting hill ( _ h _ ) areas with @xmath5 @xcite . the observation of field - emission resonances with different energies in the _ l _ and _ h _ areas by sts raised a controversial debate about the assignment of the lowest members of the series of stark - shifted image - potential states @xcite . time and angle - resolved 2ppe experiments @xcite support the general assignment of borca _ et al . based on the 2ppe results , it has been suggested that the series of image - potential states is slightly decoupled from the ru substrate in the _ areas , whereas the first @xmath6 image - potential state in the _ h _ areas has a substantial amplitude below the graphene hills . this explains the larger binding energy , shorter lifetime , and higher effective mass of this interfacial state which is closely related to the interlayer state of graphite and of other layered materials @xcite . different model potentials have been developed for the description of image - potential states of freestanding graphene and graphene / metal systems . ab initio _ approaches are not suited for this purpose because the accurate description of the long - range image force is too costly . constructed a hybrid potential for freestanding graphene , which combines a potential , derived from a self - consistent local density ( lda ) calculation for the description of the short - range properties and an image - potential tail for the proper description of the asymptotic long - range properties @xcite . de andres _ etal . _ used an alternative approach that is based on the dielectric response of the graphene and requires only a minimal set of free parameters @xcite . for the description of graphene / metal systems , however , either the metal @xcite , the graphene layer @xcite or both @xcite has been represented only by simple effective barriers characterized by empirical parameters that are fitted to the experimental results on the binding energies of the specific system . here , we present an analytical one - dimensional model - potential that makes it possible to calculate wave functions and binding energies of image - potential states at the @xmath0-point for different graphene / metal systems that are characterized by specific graphene - metal distances . for this purpose we combine potentials for a realistic description of the projected metal band gap , the image - potential of the metal , and the potential of the graphene for an arbitrary graphene - metal distance . furthermore , we include the doping of the graphene layer by considering the work function difference between graphene and the metal as well as corrections due to higher - order image - charges . all parameters of the model potential are determined from the properties of the bare metal surfaces and the freestanding graphene and no free parameters are used for the calculations at different graphene - metal distances . this distance has a strong impact on the properties of the image - potential states . we show how the double rydberg - like series of freestanding graphene evolves to a single series when a flat graphene layer approaches the metal surface as realized for the weakly interacting g / ir(111 ) and the strongly interacting g / ni(111 ) , which exhibit distinct different graphene - metal separations . the observation of two series can be explained for corrugated graphene layers with different local graphene - metal separations as demonstrated for g / ru(0001 ) . the wave functions of the two series of this system are found to show significant differences in their symmetry , binding energy and probability density close to the ru(0001 ) surface . the latter determines the electronic coupling to the metal bulk and can be connected to the experimentally observed difference of the inelastic lifetimes of the corresponding states with the same quantum number in the _ l _ and _ h _ areas . for the description of the graphene / metal interface we have constructed a one - dimensional model - potential @xmath7 which is composed of a metal potential @xmath8 and a graphene potential @xmath9 , where @xmath10 is the spatial separation of the graphene layer in the @xmath11-direction with respect to the position of the last metal surface atom at @xmath12 . @xmath13 and @xmath14 are corrections which consider the work function difference between graphene and the metal and the influence of higher - order image - charges , respectively . we note that our potential does not contain any free parameters for the fitting to experimental binding energies of the combined system . for the modeling of the metal , we use the well - established one - dimensional analytical potential introduced by chulkov _ this potential describes the bulk by the two - band model of nearly free electrons and matches the asymptotic image - potential in order to achieve a total potential @xmath8 that is continuously differentiable for all @xmath11 . its free parameters [ see [ sec_m_pot ] ] are fitted to experimental data on the size and position of the projected band gap as well as on the binding energies of the image - potential states of the clean metal . the limitations of the two - band model for the description of the d - bands in metals like ru , ir , and ni are not important in the framework of the present work because the properties of the image - potential states are most sensitively dependent on the surface - projected bulk band structure in the vicinity of the vacuum level @xmath15 . the graphene layer is modeled by a parameterized analytical potential @xmath9 which has been fitted to the numerically calculated `` lda+image tail '' hybrid potential developed for the description of freestanding graphene by silkin _ the binding energies of the image - potential states for freestanding graphene , which we obtain by using our analytical potential , agree well with those obtained with the use of the `` lda+image tail '' hybrid potential [ see [ sec_g_pot ] ] . although it is known that the @xmath16 and @xmath17 bands of graphene are considerably shifted for strongly interacting graphene / metal systems @xcite , we neglect this change of the electronic structure by using the same potential for all graphene - metal distances since this change has only a minor influence on the image - potential states at the @xmath0-point , where the @xmath16 and @xmath17 bands are far from the vacuum energy @xcite . @xmath14 describes the effect of higher - order image charges which arise at @xmath18 due to infinite multiple reflections of the primary image charges at the metal surface and the graphene layer . the latter can be regarded as metallic because of the efficient screening of lateral electric fields by the _ _ sp__@xmath19 layer @xcite . the classical image - potential between two metal surfaces with distance @xmath10 is given by @xmath20 the first two terms in represent the image - potential in atomic units caused by of the primary image - charges from each metallic surface . the following terms result from subsequent multiple reflections . by reordering , the latter can by written as @xmath21 this series converges to a net repulsive contribution . it increases the potential maximum in the center between the graphene layer and the metal surface ( ) from @xmath22 to @xmath23 , which is the classic value of the self - energy of a charged particle located in the gap between two metals @xcite . for decreasing distance @xmath10 , the potential maximum is lowered . however , even at @xmath4 , as found in _ l _ areas of g / ru(0001 ) , @xmath24 ev remains above the fermi level . a simplified description of the potential between metal and graphene by an effective quantum well with a large depth of 4.8 ev _ below _ the fermi level , as proposed by zhang _ @xcite , thus results in unrealistically large binding energies of the image - potential states . this is the main origin of the discrepancy in the identification of the first field - emission resonance observed in the sts spectra @xcite . the correction @xmath13 considers the charge transfer between metal and graphene . it is approximated by a linear interpolation of the work function difference @xmath25 between the clean metal surface and the combined system : @xmath26 on the basis of the model potential @xmath27 , which is depicted for the example g / ru(0001 ) at a graphene separation @xmath28 in , the wave function of the image - potential states and the corresponding binding energies @xmath29 with respect to the vacuum level @xmath15 have been obtained by solving the one - dimensional schrdinger equation numerically by numerov s method . by extending the model potential to more than @xmath30 into the metal bulk and to more than @xmath31 into the vacuum , we made sure that the results do not depend on the system s extension . even if we halve these intervals , the binding energies of the image - potential states with quantum numbers @xmath32 change by much less than @xmath33 mev . summarizes the calculated and experimental binding energies @xmath34 with respect to @xmath15 of the first two image - potential states for graphene on ru(0001 ) , ir(111 ) , and ni(111 ) . it shows that our model achieves a very good quantitative agreement with the experimentally observed binding energies which have been obtained by 2ppe for g / r(0001 ) @xcite and g / ir(111 ) @xcite . in particular , the distinct binding energies of the ( @xmath1 ) state in the _ l _ and _ h _ areas of g / ru(0001 ) can be reproduced . together with the predicted values for g / ni(111 ) , this data suggests that the binding energies of the image - potential states are strongly correlated with the graphene - metal separation @xmath10 . in order to emphasize this correlation , we will discuss in this section the systematics of the formation of image - potential states at different graphene - metal separations for the example of the strongly corrugated g / ru(0001 ) because its _ l _ and _ h _ areas exhibit distinct graphene - metal separations , that are typical for strongly and weakly interacting graphene / metal systems , respectively @xcite . & & & + & & & + & & & & & + g / ru(0001 ) h @xcite & 3.7 & 0.95 & 0.24 & @xmath35 & @xmath36 + g / ru(0001 ) l @xcite & 2.2 & 0.47 & 0.16 & @xmath37 & @xmath36 + g / ir(111 ) @xcite & 3.4 & 0.88 & 0.23 & @xmath38 & @xmath39 + g / ni(111 ) & 2.1 & 0.41 & 0.15 + the _ l _ and _ h _ areas of g / ru(0001 ) form a hexagonal moir - superlattice with a lateral edge length of approximately @xmath40 of its @xmath41-subunits @xcite . within our one - dimensional model we can treat both areas separately because the lateral confinement due to the finite size of each area will reduce the binding energy of the image - potential states only slightly , as can be estimated from the area size of a half subunit @xmath42 @xmath19 to @xmath43 mev , where @xmath44 with respect to the free electron mass @xmath45 @xcite . since charge - transfer between the metal and graphene leads to a doping of graphene @xcite , we model the work function of g / ru(0001 ) as an empirical function of the graphene - ru separation @xmath10 by @xmath46 , which makes it possible to vary @xmath47 systematically for the model calculations . setting @xmath48 ev matches the work function @xmath49 ev in the _ h _ areas @xcite as well as the @xmath50 ev lower value in the _ areas @xcite . for large separation , it converges to @xmath51 ev @xcite of freestanding graphene . shows the calculated probability densities of the image - potential states for different separations @xmath10 between the graphene layer and the ru(0001 ) surface as well as for the separate systems . the corresponding binding energies are depicted in . for freestanding graphene , the two series with even ( @xmath52 ) and odd ( @xmath53 ) symmetry can clearly be assigned from the amplitude of their wave functions at @xmath54 where the odd states have a node , whereas the even states have an antinode . the presence of the metal substrate breaks the mirror symmetry of the freestanding graphene and the parity of the image - potential is , in principle , no longer a good quantum number . at a graphene - metal separation as large as @xmath55 , however , the influence of the substrate on the lowest members ( @xmath56 ) of the image - potential states is still weak due to the rather small spatial extent of their wave functions perpendicular to the surface . therefore , their probability densities almost resemble those of freestanding graphene . we point out , that even for large @xmath10 , only image - potential states that originate from graphene and no states that are bound in the potential well formed by the image - potential of the metal and its surface barrier are found . this is related to the large difference in work function between graphene and ru(0001 ) ( @xmath57 ev @xcite ) , which results in an additional repulsion from the ru surface . this contributes to a reduction of the binding energies with respect to those of freestanding graphene . the latter are depicted by dashed lines in . the same argument applies for the ir(111 ) ( @xmath58 ev @xcite ) and the ni(111 ) ( @xmath59 ev @xcite ) surface . beside the work function difference , the repulsion due to the surface barrier of the metal contributes additionally to a reduction of the binding energies with respect to freestanding graphene . at @xmath55 , this applies particularly to the higher members ( @xmath60 , @xmath61 , ) because of their more extended wave functions , which are already considerably perturbed by the repulsion due to the surface barrier . this also results in an asymmetry and phase shift of the wave functions with respect to those of freestanding graphene . the wave function of the state labeled as @xmath62 at @xmath55 , for example , has now almost an antinode at @xmath54 and more closely resembles the wave function of the ( @xmath63)-state of freestanding graphene as denoted by the corresponding symbol in . at intermediate separations , the properties of the image - potential states start to be governed by the image - potentials of both surfaces , and the attractive image - potential of the metal partly compensates for the repulsion due to the surface barrier and the work function difference . the attraction of the metal leads to a maximum of the binding energy of each state at specific separations as can be seen in . this is also reflected by the form of the wave functions shown in . at @xmath64 , for example , the symmetric ( @xmath65)-state is still almost unaffected while the more extended wave function of the ( @xmath66)-state is slightly attracted towards the metal surface which results in an increase of the probability density in between the metal surface and the graphene layer compared to larger separations . for comparison we have also made simplified calculations ( not shown ) where we described the metal as a simple barrier without an image - potential similar to the model used in @xcite . in this case , we do not observe this attraction and all image - potential states are always repelled when the graphene layer approaches the metal surface . at small graphene - metal separations ( @xmath67 ) , the repulsion due to the surface barrier of the metal dominates and also the phase of the ( @xmath66 ) wave function shifts and the latter starts to resemble that of the higher - lying ( @xmath68)-state of freestanding graphene . in particular at a separation of @xmath5 , which corresponds to the _ h _ areas of g / ru(0001 ) , the vacuum part ( @xmath69 ) of all wave functions almost resembles the corresponding part of the symmetric series of freestanding graphene . this can be regarded as a transition from the double series of image - potential states of freestanding graphene to one single series , omitting the differentiation with regard to the parity . since only the former ( @xmath65)-state maintains a certain similarity to the corresponding state on freestanding graphene , we denote this fact by writing @xmath52 in parentheses in the _ h _ areas . at a separation of @xmath4 , which corresponds to the _ l _ areas of g / ru(0001 ) , all wave functions are further repelled from the metal surface . even if the phase of the wave functions now correspond to the phase of the odd series of states on free standing graphene , the mirror symmetry has completely vanished , which is indicated by omitting the parity for the whole series . now , all wave functions almost resemble the form of those on the clean ru surface with one layer of atoms atop , as can be seen by comparing ( e ) and ( f ) . in comparison to the clean ru surface , however , the spatial extent of the wave functions in the vacuum is larger , which indicates a stronger decoupling from the surface . in the _ h _ areas , on the other hand , a considerable amount of the ( @xmath70 ) wave function still fits in between the graphene and the ru surface and is therefore more strongly coupled to ru as compared to the _ l _ areas . this state is closely related to the interlayer state of graphite @xcite . as depicted by the different symbols in , the change of the wave function s character upon approaching the graphene layer to the metal surface is also reflected by the change of the binding energy with respect to the vacuum level . whenever the binding energy of the image - potential states of the entire system becomes smaller compared to the next energetic adjacent state of freestanding graphene , the local symmetry at @xmath54 is closer to the latter . at @xmath55 , for example , the binding energies of the first , second , and third state of the entire system are larger compared to the second , third , and fourth state of freestanding graphene . consequently , their local symmetry at @xmath54 is still close to that of the first ( @xmath65 ) , second ( @xmath66 ) , and third ( @xmath68 ) state of freestanding graphene . the energy of the fourth state of the entire system , however , is already smaller compared to the fifth state ( @xmath63 ) of freestanding graphene . its local symmetry at @xmath54 more closely resembles the symmetry of that state and not of the fourth state ( @xmath62 ) of freestanding graphene . the energy of this state is therefore drawn as a closed symbol which denotes states of even ( local ) symmetry . for decreasing graphene - metal separation , the binding energies of the image - potential states increase slightly at first due to the attractive image - potential of the metal . at separations found in real graphene / metal systems ( @xmath71 ) , however , the repulsion due to the surface barrier of the metal dominates and results in a rapid decrease of the binding energies upon further approach . the sequence of the relative energy spacings is , however , rather insensitive towards @xmath10 and resembles a scaled rydberg series with decreasing energy separation for increasing quantum number for all @xmath10 . the absolute change of the binding energy as a function of @xmath47 is most pronounced for the first image - potential state . it decreases from more than 1.4 ev at large @xmath10 to 0.95 ev at the separation found in the _ h _ areas of g / ru(0001 ) and finally to 0.47 ev at the separation found in the _ the difference between the binding energies with respect to @xmath72 in the _ h _ and _ l _ areas of 0.48 ev is twice as large as the difference between the local work functions of 0.24 ev @xcite . the first image - potential state in the _ h _ areas has therefore a smaller energy with respect to the fermi level @xmath73 when compared to the the corresponding state in the _ l _ areas . this confirms the assignment of the peaks in the 2ppe spectrum of @xcite which is reproduced in the inset of . this assignment is also in agreement with density functional theory ( dft ) calculations by borca _ @xcite which shows that the results of our model calculations are robust also for small distances where dft can explicitly describe the chemical interaction between graphene and the metal . for large distances and higher quantum numbers the evolution of the binding energies with distance depicted in @xcite considerably differs from our results which we attribute to the fact that dft can not properly consider the long - range image - force . for the second image - potential state , the calculated difference between binding energies with respect to @xmath15 in the _ h _ and _ l _ areas is in the order of the difference in the local work function , which explains that these two states could not be resolved separately in the 2ppe spectra . the red horizontal lines in depict the experimental results from @xcite under consideration of the local work functions in the _ h _ and _ l _ areas , and help visualize the very good agreement between experiment and model calculation . the small deviation for the binding energy of the lowest image - potential state energy in the _ h _ areas is reduced if one considers the additional reduction of the calculated binding energy due to the lateral localization as discussed above . the localization of this state should be stronger in the _ h _ areas as deduced from the effective mass which has been found to be twice as large as the free electron mass @xcite . the results of our model calculation make it also possible to qualitatively interpret the experimentally observed decay dynamics of electrons in these states , as has been investigated by time - resolved 2ppe @xcite . as shown in ( e ) , the probability densities of all image - potential states in the _ areas mostly resemble those of the clean ru(0001 ) surface but with some degree of decoupling , i.e. the center of gravity of the probability density is located further away from the metal into the vacuum . at first glance , this similarity to the clean ru surface seems to be surprising . the graphene - metal separation in the _ l _ areas is , however , almost identical to the ru - layer spacing ( @xmath74 @xcite ) . the ru surface covered by one metallic - like graphene overlayer therefore has similar properties with respect to the image - potential states as the extension of the ru crystal by one more layer of ru atoms . at the clean ru(0001 ) surface , the lifetimes of electrons in the first two image - potential states of @xmath75 fs and @xmath76 fs @xcite are comparably short because the decay by inelastic scattering with bulk electrons is very efficient due to the high density of states of the ru 4d bands just below the fermi level @xcite . thus , the slightly enhanced experimental lifetimes of @xmath77 fs and @xmath78 fs @xcite are a direct indication for a certain degree of decoupling in the _ l _ areas . in the _ h _ areas , a considerable part of the probability density of the ( @xmath70)-state fits below the graphene layer close to the ru surface . this enhances the electronic coupling to the ru bulk states as is reflected by the shorter lifetime of @xmath79 fs @xcite , which is identical to the value found on clean ru(0001 ) . by adapting @xmath8 , our model can be easily applied to the description of graphene layers on other metal substrates . with ir(111 ) and ni(111 ) we chose two examples that represent limiting cases of weak and strong interaction with the graphene layer , respectively . it has been shown that g / ir(111 ) grows with a rather large and homogeneous separation of @xmath80 @xcite which is very similar to the separation found in the _ h _ areas of g / ru(0001 ) . graphene and ni(111 ) have almost no lattice mismatch . this results in the growth of a flat graphene layer on ni(111 ) , despite the strong interaction @xcite . the resulting separation of about @xmath81 is very similar to that found in the _ l _ areas of g / ru(0001 ) . binding energies and lifetimes of the image - potential states on g / ir(111 ) have been measured by 2ppe @xcite and can be directly compared with the results of our model calculations . no experimental data on g / ni(111 ) are available , but 2ppe results on the binding energies for the clean ni(111 ) surface @xcite make it possible to properly adjust the parameter of the metal potential and to predict the binding energies for the graphene covered surface . the ferromagnetic coupling of ni results in a spin - split surface - projected band structure which is reflected by an exchange - splitting of the image - potential states . the observed splitting of @xmath82 mev is , however , small compared to the linewidth and can only be observed with spin - resolved detection @xcite . we therefore neglect the exchange - splitting here and use a spin - integrated surface - projected band gap extracted from @xcite for our model calculations . because the size and position of the surface - projected bulk band gap do not differ much between ru(0001 ) , ir(111 ) , and ni(111 ) , the calculated binding energies depend most sensitively on the graphene - metal separation @xmath10 . consequently , the binding energies for g / ir(111 ) , as well as for g / ni(111 ) , are very similar to the results for g / ru(0001 ) at the corresponding separations . as shown in , the results of our model calculation for the binding energies on g / ir(111 ) are in excellent agreement with the experimental data . for g / ni(111 ) we predict much smaller binding energies compared to g / ir(111 ) . this is due to the stronger repulsion of the image - potential states at the smaller separations . the binding energies on g / ni(111 ) are on the other hand comparable to those on the _ l _ areas of g / ru(111 ) in correspondence to the similar separation @xmath10 . finally , we would like to comment on the formation of image - potential states at the interface of graphene / sic , even if our model is not directly applicable to this semiconducting substrate . although graphene might possess only a weak interaction to sic , our results generally show that the shape of the image - potential states is very sensitive to the substrate induced symmetry break even for large separations due to their large spatial extent . in another 2ppe experiment on graphene / sic(0001 ) , shearer _ et al . _ @xcite indeed observed a single series of sharp symmetric peaks of image - potential states in agreement with data shown in @xcite . therefore , it seems rather unlikely that the experimentally found splitting of the first image - potential state on graphene / sic @xcite can be interpreted as a remnant of the mirror symmetry of freestanding graphene with a small energy separation between these two states . the latter is particularly hard to understand because the approach of a flat graphene layer towards a substrate with a surface barrier does not change the relative energy spacing of adjacent states , i.e. the energy spacing between the lowest two states is always larger than the subsequent spacing because the energy sequence of the rydberg series is at all distances dominated by the long - range image - potential . on the basis of an analytical , one - dimensional potential , we can quantitatively describe the formation of image - potential states at the interface between a graphene layer and a metal surface by means of model calculations . by systematic variation of the graphene - metal separation , we have shown how the double rydberg - like series of even and odd image - potential states of freestanding graphene evolves towards a single series of the compound system when a flat graphene layer is located at a distance to the metal as found in real graphene / metal systems . this transition is driven by the repulsion from the metal substrate , which increasingly reduces the mirror symmetry of freestanding graphene with decreasing separation . even for separations found in weakly interacting systems , we find no remnant of the distinction between states of even and odd symmetry . at these intermediate separations , the first image - potential state is partly trapped between the metal and the graphene layer . it attains properties of an interfacial state . at distances found in strongly interacting systems , on the other hand , the wave functions almost resemble those of image - potential states on a clean metal surface but with a higher degree of decoupling . the repulsion of the image - potential states from the metal surface is also responsible for a strong reduction of their binding energies with decreasing graphene - metal separation . this explains the distinct differences of the experimentally observed binding energies of the first ( @xmath1 ) image - potential states in the _ h _ and _ l _ areas of strongly corrugated g / ru(0001 ) . according to the respective similar separations on weakly interacting g / ir(111 ) and strongly interacting g / ni(111 ) , we find respective comparable binding energies which are in excellent agreement with available experimental data for g / ir(111 ) . we thank richard hfer for valuable contributions to the multiple - reflection correction of the image - potential and gratefully acknowledge funding by the deutsche forschungsgemeinschaft through sfb 1083 _ structure and dynamics of internal interfaces _ project , b6 . for the metal part @xmath8 of our model potential we used the well - established one - dimensional potential introduced by chulkov _ _ @xcite . this parameterized potential is piecewise defined along the surface normal @xmath11 by : @xmath83 & $ z_{1 } < z \leq z_{\rm im}$\\ \;\;\,\frac{\exp[-\lambda(z - z_{\rm im})]-1}{4(z - z_{\rm i m } ) } & $ z_{\rm i m } < z$ } \label{eq_mpot}\ ] ] here @xmath84 is the layer spacing and @xmath12 corresponds to the position of the surface atom . by requiring that @xmath8 and its first derivative to be continuous at the matching points @xmath85 and @xmath86 , only four of the ten parameters @xmath87 , @xmath88 , @xmath89 , @xmath90 , @xmath91 , @xmath92 , @xmath93 , @xmath94 , @xmath95 , @xmath86 are the independent of each other . it is feasible to choose the offset @xmath87 and the amplitude @xmath88 in order to reproduce the energetic position and width of the surface - projected band gap . for ru(0001 ) , ir(111 ) and ni(111 ) ( spin averaged ) these have been extracted from @xcite , @xcite and @xcite , respectively . the parameters @xmath89 and @xmath93 have been used to reproduce the experimental binding energies @xmath34 of the image - potential states . for ru(0001 ) we have fitted these parameters to the experimental binding energies @xmath96 ev and @xmath97 ev reported by gahl _ _ @xcite . for ni(111 ) we have used data reported by andres _ @xcite . due to the lack of experimental data on the image - potential states of clean ir(111 ) , we have estimated the binding energies by using the rydberg formula @xmath98 where @xmath99 is the quantum defect . for a @xmath100-inverted band gap , the latter can be determined from the position of the vacuum energy @xmath15 within the projected band gap @xcite . this results in @xmath101 ev and @xmath102 ev . & @xmath84 & @xmath103 & @xmath88 & @xmath87 & @xmath89 & @xmath93 + ru(0001 ) & 2.138 @xcite & 5.51 @xcite & 7.436 & 9.400 & 12.70 & 4.3464 + ir(111 ) & 2.217 @xcite & 5.79 @xcite & 9.511 & 6.188 & 6.50 & 4.6068 + ni(111 ) & 2.035 @xcite & 5.27 @xcite & 11.259 & 6.503 & 4.91 & 2.3070 + the parameter sets used for modelling ru(0001 ) , ir(111 ) , and ni(111 ) are collected in . our analytical approximation of the `` lda+image tail '' hybrid potential of silkin _ et al . _ @xcite for the description of freestanding graphene is inspired by the definition of the metal potential with omission of the bulk part : @xmath104 & $ |z_{1}| < |z| \leq |z_{2}|$\\ -g_{3}\exp[-\alpha(|z|-|z_{2}| ) ] & $ |z_{2}| < |z| \leq |z_{\rm im}|$\\ \;\;\,\frac{\exp[-\lambda(|z|-|z_{\rm im}|)]-1}{4(|z|-|z_{\rm im}| ) } & $ |z_{\rm im}| < |z|$. } \label{eq_g_pot}\ ] ] as shown in , @xmath9 is symmetric in the @xmath11-direction with respect to the graphene layer at @xmath12 and converges to the classical image - potential for large distances @xmath105 . again , only four of the twelve parameters @xmath95 , @xmath106 , @xmath107 , @xmath108 , @xmath109 , @xmath110 , @xmath111 , @xmath112 , @xmath113 , @xmath114 , @xmath92 , and @xmath94 are independent if we require @xmath9 to be continuously differentiable at the matching points @xmath95 , @xmath106 , and @xmath86 . we choose the potential offset @xmath115 , the amplitude @xmath108 , and the inverse widths @xmath113 and @xmath114 to fit @xmath9 to the `` lda+image tail '' hybrid potential for a matching point between lda potential and image - tail of @xmath116 a.u . the best fit is shown as solid line in . it has been achieved with @xmath117 ev , @xmath118 , @xmath119 and @xmath120 . the binding energies @xmath121 of the symmetric and antisymmetric image - potential states calculated with these parameters are listed in . they agree well with those calculated using the `` lda+image tail '' hybrid potential for @xmath116 a.u . @xcite the two equivalent positions of the image - planes of @xmath122 , which result from the chosen parameters , are almost coincident with the spatial extent of the polarizable conjugated @xmath17-system @xcite . & @xmath123 & @xmath124 & @xmath125 & @xmath126 + 1d - potential & 1.46 & 0.60 & 0.28 & 0.18 + lda+image tail & 1.47 & 0.72 & 0.25 & 0.19 + the screening of electric fields by the metal as well as the graphene layer is taken into account by cutting the corresponding image tail of @xmath8 and @xmath9 at the respective opposite surface ( @xmath127 for @xmath69 and @xmath128 for @xmath129 ) . together with the corrections @xmath14 and @xmath13 , this results in a discontinuity of the total model potential @xmath27 at @xmath12 and @xmath54 . the discontinuity is compensated by increasing the amplitudes of the respective cosine oscillation of the metal potential @xmath130 and the graphene potential @xmath131 . 10 echenique p m and pendry j b 1978 _ j. phys . c _ * 11 * 2065

the formation of image - potential states at the interface between a graphene layer and a metal surface is studied by means of model calculations . an analytical one - dimensional model - potential for the combined system is constructed and used to calculate energies and wave functions of the image - potential states at the @xmath0-point as a function of the graphene - metal distance . it is demonstrated how the double series of image - potential states of free - standing graphene evolves into interfacial states that interact with both surfaces at intermediate distances , and finally into a single series of states resembling those of a clean metal surface covered by a monoatomic spacer layer . the model quantitatively reproduces experimental data available for graphene / ir(111 ) and graphene / ru(0001 ) , systems which strongly differ in interaction strength and therefore adsorption distance . moreover , it provides a clear physical explanation for the different binding energies and lifetimes of the first ( @xmath1 ) image - potential state in the valley and hill areas of the strongly corrugated moir superlattice of graphene / ru(0001 ) . _ keywords _ : image - potential states , graphene , metal surfaces , electronic structure +

Sixteen people were shot -- one fatally -- inside of a Cincinnati nightclub Sunday morning. O'Bryan Spikes, 27, died in the shooting. At least 16 others were shot. Advertisement Related Content FOP: Officers had to literally step over victims to aid others in worse condition The shooting was reported just after 1 a.m. at Cameo nightclub on Kellogg Avenue in Linwood. Police believe that multiple people fired shots. No arrests have been made. Spikes' family told WLWT News 5 that they were in shock over the man's death. Spikes was a father and junior college student who came to the club often, they said. "The bar was very crowded, approximately a couple hundred people," Isaac said. "Several local men got into some type of a dispute inside the bar, and it escalated into shots being fired from several individuals." "This is a tragedy that has struck other communities, and now it has struck Cincinnati," Mayor John Cranley said. "I'm confident that while our hearts are broken, that our spirit is not." Why the dispute ended with gunfire in a crowded club remains unclear. A look into Cameo during the day post-shooting "There's no reason that anyone should ever feel like they could go into a club, shoot a club up, because they're upset with someone who disrespected them or otherwise hurt them earlier in the day," Cincinnati Councilwoman Yvette Simpson said. "So I continue to say, yes, guns kill people, but people kill people." Related: 'Horrific:' Cincinnati leaders weigh in on Cameo shooting “We are in the middle of a very horrific situation that occurred at the nightclub with multiple victims,” Assistant Police Chief Paul Neudigate said. University of Cincinnati Medical Center treated a total of nine shooting victims. Two victims remain in critical condition, three are listed as stable. Four victims have been treated and released. Christ Hospital and Bethesda North Hospital each treated two victims with minor injuries, who were able to leave on Sunday. One victim walked in to Mercy Health Hospital, Anderson with a gunshot wound. A single victim also walked into Mercy Health Hospital, West with a minor injury, not a gunshot wound. Both victims have been discharged, according to Mercy Health. City officials have asked anyone who knows anything about the shooting inside Cameo nightclub to step forward and share what they know. "We can't let the bad guys win," Cranley said. "We can't let the evil who pull out a gun in a crowded club and start shooting innocent people to not be punished for their crimes. ... You have innocent people shot, just for going out to have a good time. That's totally unacceptable. It's totally evil." One witness told WLWT News 5 that he heard the club's DJ call for security about 10 minutes before the shooting. FULL NEWS CONFERENCE: 17 shot, 1 fatally, in Cincinnati nightclub shooting Surveillance cameras were inside the club at the time of the shooting, police said, and investigators are viewing the tapes. Neudigate added that Sunday morning’s shooting was one of the largest shooting cases that he has worked in his 27-plus years with the department. Cameo nightclub has had several issues in the past, authorities said. The club allows admission to anyone over the age of 18 on certain days, and is open until 4 a.m. on Saturdays. “We are aware of it. It has had some challenges in the past,” Neudigate said. Police said there were two shootings at the nightclub in 2015: one on New Year's Day, when someone was shot in the foot, and another in September, when a shooting victim was found in the parking lot. Isaac said Cameo is a large establishment, and it employs off-duty police officers to patrol the parking lot. Photos: Mass shooting at Cincinnati's Cameo Night Club “It is my understanding that they do wand individuals and pat them down,” Isaac said of the club’s security measures. “However, what we know at this point, several firearms were able to be brought inside the bar.” Dan Hils, president of Cincinnati's Fraternal Order of Police, said the situation could have been worse if not for the four off-duty police officers keeping an eye on the club's parking lot. "People are running away because they have the natural fear, because shots are being fired," Hils said. "Our people are running in. And that makes you very, very proud." The Bureau of Alcohol, Tobacco and Firearms is helping Cincinnati police with the investigation. Cincinnati restaurateur Jeff Ruby is offering a $10,000 reward for information leading to the arrest and conviction of the person responsible for the shooting death, he tweeted Sunday. The next scheduled press briefing will be Monday morning in Council Chambers. Anyone with information about the shooting is asked to contact Crime Stoppers at (513) 352-3040 or on their website. AlertMe ||||| CINCINNATI (AP) — At least two people opened fire inside a crowded nightclub early Sunday morning, killing one person and wounding more than a dozen others in what authorities described as a chaotic scene. It was not clear what prompted the shooting at the Cameo club about 1:30 a.m., and authorities didn't immediately have any suspects. "Saturday night, it is a very young crowd. We have had incidents here in the past, but this is by far the worst," Capt. Kim Williams said. Several officers were working security detail at the club and performed first aid and tried to revive the person that died, Williams said. Fifteen people were shot. Some of them drove themselves to area hospitals and others were taken by ambulance. Authorities are interviewing several witnesses, but Williams said a lot of the club goers had left. "The biggest problem when you have a large crowd like this and the shots ring out, a lot of the witnesses disappear," she said. Authorities were asking anyone with information to come forward. Williams said investigators are checking to see if surveillance cameras were working. WLWT reported (http://bit.ly/2mDfUV3 ) that at least one person was in critical condition at University of Cincinnati Medical Center.

– At least two people opened fire inside a crowded nightclub early Sunday, killing one person and wounding more than a dozen others in what authorities described as a chaotic scene, reports the AP. It was not clear what prompted the shooting at the Cameo club about 1:30am, and authorities didn't immediately have any suspects. "Saturday night, it is a very young crowd. We have had incidents here in the past, but this is by far the worst," Capt. Kim Williams said. Several officers were working security detail at the club and performed first aid and tried to revive the person that died, Williams said. Fifteen people were shot. Some of them drove themselves to area hospitals and others were taken by ambulance. Authorities are interviewing several witnesses, but Williams said a lot of the club goers had left. "The biggest problem when you have a large crowd like this and the shots ring out, a lot of the witnesses disappear," she said. Authorities were asking anyone with information to come forward. Williams said investigators are checking to see if surveillance cameras were working. WLWT reported that at least one person was in critical condition at University of Cincinnati Medical Center.

'Bones' Star Emily Deschanel Gets Married Email This Emily Deschanel's rep confirms that the TV actress tied the knot on Saturday night in her hometown of Los Angeles with writer-actor David Hornsby, according to a People.com report. The 'Bones' star, 33, and her groom married in a "quiet evening ceremony" attended by friends and relatives. Almost exactly a year ago, Emily Deschanel's younger sister, '(500) Days of Summer' star Zooey Deschanel, Emily Deschanel's rep confirms that the TV actress tied the knot on Saturday night in her hometown of Los Angeles with writer-actor David Hornsby, according to a People.com report.The 'Bones' star, 33, and her groom married in a "quiet evening ceremony" attended by friends and relatives.Almost exactly a year ago, Emily Deschanel's younger sister, '(500) Days of Summer' star Zooey Deschanel, wed Death Cab for Cutie frontman Ben Gibbard on Sept. 20, 2009. http://xml.channel.aol.com/xmlpublisher/fetch.v2.xml?option=expand_relative_urls&dataUrlNodes=uiConfig,feedConfig,entry&id=879491&pid=879490&uts=1273503952 http://www.popeater.com/mm_track/popeater/tv/?s_channel=us.tvpop&s_account=aolpopeater,aolsvc&omni=1&ke=1 http://cdn.channel.aol.com/cs_feed_v1_6/csfeedwrapper.swf Stars in Love Colin Hanks and Samantha Bryant Married Hanks tied the knot with publicist Samantha Bryant on Saturday, May 8 in Los Angeles at sunset on the roof of the London Hotel in West Hollywood. Neilson Barnard, Getty Images Neilson Barnard, Getty Images Stars in Love Hornsby is known to fans of the FX comedy 'It's Always Sunny in Philadelphia' as Sweet Dee's not-so-secret admirer, Rickety Cricket. His new bride is shooting season 6 of 'Bones' (starring opposite David Boreanz and earning a producer credit behind the scenes), and she'll reportedly make her directorial debut on the series next year.Congrats to the happy couple! ||||| Emily Deschanel Weds or leave a comment of your own See what other readers have to say about this story – Actress Emily Deschaneland writer-actor David Hornsby tied the knot in a quiet evening ceremony in front of family and friends in the Pacific Palisades area of Los Angeles on Saturday, her rep confirms to PEOPLE.The bride wore a pair of matching diamond and platinum scroll hair pins and drop earrings by Neil Lane.Deschanel, 33, is currently starring in the sixth season of Bones, while Hornsby is best known for his work on It's Always Sunny in Philadelphia.

– "Bones" has finally tied the knot, and not to fictional FBI agent Seeley Booth. Emily Deschanel, star of the hit TV series about a brainiac forensic anthropologist, married long-time writer-actor beau David Hornsby of It's Always Sunny in Philadelphia. They wed in a private evening ceremony overlooking the Pacific Palisades in Los Angeles, reports People, almost exactly one year after sis/fellow actress Zooey tied the knot. Click here for more.

a considerable number of attempts have been made at clarifying the phase structure of the surface model of helfrich , polyakov , and kleinert @xcite ; henceforce we will refer to this as the hpk model . tethered surface models are defined on triangulated fixed connectivity surfaces representing polymerized biological membranes or membranes in the gel phase @xcite , and they are classified into a major class of the hpk model @xcite . fluid surface models are considered a different class of the hpk model defined on dynamically triangulated surfaces representing these biological membranes in the fluid phase , however , we will not discuss the fluid surface model in this paper @xcite . an interesting problem that remains unanswered at present is whether the tethered self - intersecting ( or phantom ) surface model undergoes a continuous transition or a discontinuous one . the model is expected to undergo a phase transition separating the smooth phase in the limit @xmath0 from the crumpled one in the limit @xmath1 . the mean field analysis predicts that the model undergoes a discontinuous phase transition @xcite , whereas the large-@xmath2 expansion predicts a continuous transition @xcite . biological membranes including artificial vesicles were thought to undergo the crumpling transition . however , we currently have no experimental evidence for such a transition in biological membranes , except for an investigation on artificial vesicles @xcite . in a recent numerical study , it was reported that the tethered model of hpk undergoes a first - order phase transition on spherical surfaces relatively larger than those used so far @xcite . the bending energy and the gaussian term used in @xcite are those widely accepted as standard discrete hamiltonians in numerical studies on the hpk model . the bending energy is of the form @xmath3 , where @xmath4 is the unit normal vector of the triangle @xmath5 . the gaussian term is given by the sum of bond length squares . however , it has not yet been clarified whether the order of phase transition depends on the discretization of the hamiltonian . if the order of phase transition changes depending on the choice of the discretization , the phase transition might be seen only in the lattice models , and as a consequence we can obtain no information on the phase transition of the continuous model by using the numerical simulations . hence , it is natural to consider that the order of the transition depends on the discretization of hamiltonian . therefore , it is worthwhile to investigate further the tethered model defined by hamiltonian which is different from the above - mentioned bending energy and gaussian term . in this paper , we studied three types of tethered models on triangulated spherical surfaces , which are obtained by dividing the icosahedron as in @xcite . the hamiltonian of the first model contains the ordinary gaussian energy and a bending energy , which is defined by the normal vector of vertices . hence , the discretization of the bending energy in the first model is slightly different from that of the standard bending energy . it was previously reported that the first model undergoes a discontinuous transition on voronoi lattices @xcite . however , it remains unclear whether the discontinuous transition can be seen on any other lattices . thus , we can also check that the discontinuous transition is independent of the lattice structure by investigating the first model defined on lattices constructed from the icosahedron . the second model is called the nambu - goto surface model @xcite . at present , it is unclear whether the nambu - goto model undergoes a discontinuous phase transition when the model is defined on surfaces with extrinsic curvature . the area energy , which is given by the sum of the area of the triangles , corresponds to the gaussian energy in the first ( hpk ) model . it is well - known that the nambu - goto model without the bending energy term is not well - defined due to the lack of the smooth phase and the appearance of spikes on the surface @xcite . the area term imposes a constraint only on the area of the triangles , and hence allows the appearance of spiky configurations made up of oblong triangles . on the contrary , some additional terms in the hamiltonian can make the model well - defined . in fact , it was reported recently that the nambu - goto model with a deficit angle term , which is an intrinsic curvature , is well - defined and undergoes a discontinuous transition between the smooth phase and a tubular phase @xcite . the second model in this paper is also well - defined @xcite , because the hamiltonian includes a bending energy , which is an extrinsic curvature defined according to the dual lattice formulation of the discrete mechanics by lee @xcite . the third model is a tensionless model whose hamiltonian contains the standard bending energy and a hard - wall potential which gives an upper bound on the bond length . there is no gaussian term in the hamiltonian . the bending energy of the model is identical to the one in @xcite . therefore , the discretization of the third model is the same as in @xcite . however , it is not yet clear whether a tensionless tethered model undergoes a discontinuous transition . it is nontrivial whether those three discrete models lead to the same result on the order of the transition . the standard bending energy for the hpk model is not equivalent to the above mentioned bending energy for the nambu - goto surface model . in fact , the nambu - goto model with the standard bending energy is ill - defined because of the lack of the smooth phase and the appearance of spikes in the whole region of the bending rigidity @xcite . thus , it is worthwhile to study numerically whether these three models have the same continuous limit for the order of the transition . we will see that the three models undergo a discontinuous transition on spherical surfaces relatively larger than those used to date , and then we will understand that the discontinuous transition of the model is independent of the discretization of the hamiltonian . therefore , the results obtained in this paper together with those in @xcite lead us to conclude that a first - order phase transition can be observed in a spherical tethered surface model defined by hamiltonian that includes a bending energy term . this means that the first - order transition of triangulated surfaces is universal in the sense that the order of the transition is independent of discretization of the hamiltonian . the partition function of the models is defined by @xmath6,\ ] ] where @xmath7 is the total number of vertices , @xmath8 is hamiltonian of the model . the center of the surface is fixed to remove the translational zero - mode . the self - avoiding interaction is not assumed in the hamiltonian , hence the surface is considered to be phantom . we investigate three types of model which differ from each other in energy terms included in the hamiltonian @xmath8 . the first model denoted by _ model 1 _ is defined by @xmath9 , \quad ( { \rm model \;1})\end{aligned}\ ] ] where @xmath10 is the bending rigidity , @xmath11 is the unit normal of the triangle @xmath12 meeting at the vertex @xmath5 . the symbol @xmath13 in eq . ( [ s1s2-model-1 ] ) is a normal vector of the vertex @xmath5 , and it is defined by @xmath14 where @xmath15 denotes the summation over triangles @xmath12 linked to the vertex @xmath5 , and @xmath16 is the area of @xmath12 . model 1 is considered a hpk model as mentioned in the introduction . the second model denoted by _ model 2 _ is defined by @xmath17 where @xmath18 is the area of the triangle @xmath19 , @xmath20 is the edge length of @xmath19 , and @xmath21 is the angle between the triangles attaching to the edge @xmath20 . in eq . ( [ s1s2-model-2 ] ) is the area of the shaded traiangle in ( b ) , and @xmath20 is the edge length of the triangle.,width=321 ] figures [ fig-1](a ) , ( b ) show the triangles whose normal vectors are interacting with one of the shaded triangles corresponding to model 1 and model 2 , respectively . @xmath18 in eq . ( [ s1s2-model-2 ] ) is the area of the shaded triangle in fig . [ fig-1](b ) , and @xmath20 in eq . ( [ s1s2-model-2 ] ) is the edge length of the triangle . it should be noted that the nambu - goto model is considered a classical analogue of the polyakov string model . in fact , the polyakov string model reduces to the nambu - goto model if the metric , which is a dynamical variable of the polyakov string , is fixed to the induced metric @xcite . the third model denoted by _ model 3 _ is defined by the hamiltonian @xmath22 @xmath23 in @xmath8 of eq . ( [ s2v - model-3 ] ) is the bending energy , which was already introduced in the introduction , and @xmath24 is a hard - wall potential , which gives an upper bound on the bond length . @xmath25 in @xmath24 denotes the sum over bonds @xmath26 connecting the vertices @xmath5 and @xmath27 , and @xmath28 in @xmath23 is the sum over triangles @xmath29 sharing a common bond . the symbol @xmath4 in @xmath23 denotes the unit normal vector of the triangle @xmath5 . the range of interaction of @xmath4 in @xmath23 is identical to that of model 2 , shown in fig . [ fig-1](b ) . the symbol @xmath30 in eq . ( [ s2v - model-3 ] ) is the potential between the vertices @xmath5 and @xmath27 , and is defined by @xmath31 the value of @xmath32 in the right hand side of eq . ( [ v ] ) is fixed to @xmath33 . then we have @xmath34 , which is satisfied when the gaussian term @xmath35 is included in the hamiltonian without the hard - wall potential @xmath24 . if it were not for the constraint @xmath36 , the size of the surface grows larger and larger in the mc simulations . thus the constraint @xmath36 is necessary for the bond length to have a well - defined value when the gaussian term @xmath37 is not included in the hamiltonian . we note that the model seems to depend on a hidden length scale introduced by @xmath32 , and as a consequence the model appears to be ill - defined . however , we checked in ref . @xcite that there is no @xmath32-dependence on the results . this is a consequence of the scale invariant property of the model , which will be mentioned in the next section . therefore , we use @xmath33 in the mc simulations . we should comment on a relationship between the discrete bending energy @xmath23 in eqs . ( [ s1s2-model-1 ] ) , ( [ s1s2-model-2 ] ) , and ( [ s2v - model-3 ] ) and the continuous one of the polyakov - kleinert string model . the functional action of the polyakov - kleinert string in @xmath38 is defined by @xmath39 where @xmath40 is the first fundamental form ( or the metric tensor ) of the surface @xmath41 . the @xmath42 is defined by @xmath43 , where @xmath44 is the second fundamental form ( or the extrinsic curvature tensor ) on @xmath41 in @xmath38 @xcite . in @xmath45 , @xmath46 denotes a mapping from the surface @xmath41 to @xmath38 , where the image @xmath47 is the membrane . it is easy to see that @xmath48 in the second term of @xmath45 in eq . ( [ cont - s1s2 ] ) is equivalent to @xmath23 in eqs . ( [ s1s2-model-1 ] ) , ( [ s1s2-model-2 ] ) , and ( [ s2v - model-3 ] ) if the metric tensor @xmath40 is given by the induced one ; @xmath49 . in fact , the second fundamental form @xmath44 can be expressed by @xmath50 , where @xmath51 is the unit normal vector of the surface . then by using this relation and the induced metric , the second term in @xmath45 can be expressed by @xmath52 . this action is identical to the one of the @xmath53-model , and hence a natural discretization of this term is given by @xmath23 in eqs . ( [ s1s2-model-1 ] ) , ( [ s1s2-model-2 ] ) , and ( [ s2v - model-3 ] ) . the canonical monte carlo ( mc ) technique is used to update the variable @xmath46 . the new position @xmath54 of the vertex @xmath5 is given by @xmath55 , where @xmath56 is chosen randomly in a small sphere for model 1 and model 2 . the radius of the small sphere is chosen at the start of the mc simulations to maintain about @xmath57 acceptance rate . the new position @xmath54 is accepted with the probability @xmath58 $ ] , where @xmath59 is given by @xmath60 . under the constraint of eq.([v ] ) for the edge length for model 3 , the new position @xmath54 is accepted with the probability @xmath58 $ ] ; namely the metropolis accept / reject procedure is applied only for @xmath54 satisfying the constraint of eq.([v ] ) . this constraint for the edge length is imposed by @xmath61 as described in the previous section . the rate of acceptance for the constraint of eq . ( [ v ] ) is about @xmath57 . a random number called mersenne twister @xcite is used in the mc simulations . we use two - sequences of random numbers ; one for the 3-dimensional move of vertices @xmath46 and the other for the metropolis accept / reject in the update of @xmath46 . for model 1 and model 2 , the minimum bond length is not assumed , while the minimum area of triangle is assumed to be @xmath62 , where @xmath63 is the mean area of triangles computed at every 250 mcs ( monte carlo sweeps ) and is almost constant throughout the mc simulations . the area of almost all triangles generated in the simulations is larger than the lower bound @xmath62 . for model 3 , the minimum area of triangle is assumed to be @xmath64 . the area of almost all triangles generated in the mc simulations is larger than the lower bound @xmath64 . the minimum bond length is assumed to be @xmath64 , however , we find no bond whose length is less than the lower bound @xmath64 in the mc simulations . this means that no constraint is imposed on the lower bound of the bond length . the hamiltonians in eqs . ( [ s1s2-model-1 ] ) , ( [ s1s2-model-2 ] ) , and ( [ s2v - model-3 ] ) are defined on the surfaces which are constructed uniformly by the co - ordination number . they are obtained by dividing the icosahedron . by dividing every edge of the icosahedron into @xmath65-pieces of the same length , we have a triangulated lattice of size @xmath66 . these lattices are characterized by @xmath67 and @xmath68 , where @xmath69 is the total number of vertices with co - ordination number @xmath70 ; thus we have lattices in which 12 vertices are of @xmath71 , and all other vertices @xmath72 . we comment on the unit of physical quantities in the model . the scale of length in the model can be arbitrarily chosen because of the scale invariant property of the partition function in eq . ( [ part - func ] ) . then , by letting @xmath73 be a length unit in the model , we can express all quantities with unit of length in terms of @xmath73 . hence , the unit of @xmath37 is @xmath74 . let @xmath75 be the surface tension coefficient , then @xmath76 in eqs . ( [ s1s2-model-1 ] ) , ( [ s1s2-model-2 ] ) for model 1 , model 2 can be written as @xmath77 . thus , the unit of @xmath75 can be written as @xmath78 , where @xmath79 is the boltzmann constant , @xmath80 is the temperature . the unit of @xmath10 is therefore expressed by @xmath81 . the coefficient @xmath75 is assumed to be @xmath82 in this paper . this is always possible because of the scale invariant property of the partition function of the model . the unit of @xmath75 can be influenced by the length unit @xmath73 of the model , and the value of @xmath75 varies depending on @xmath73 . however , @xmath75 can always be fixed to @xmath82 . this is the reason why the length unit @xmath73 is arbitrary chosen in the model . note also that varying the temperature @xmath80 is effectively identical to varying @xmath10 in the model . the dependence of @xmath75 on @xmath80 can be absorbed into a redefinition of @xmath75 , which can be fixed to @xmath82 due to the scale invariant property as stated above . the parameter @xmath32 in eq . ( [ v ] ) plays a role in the length unit @xmath73 of model 3 . first , we summarize the total number of mcs iterated in the simulations . at the transition point of model 1 , @xmath83 , @xmath83 , and @xmath84 mcs were iterated on the surfaces of @xmath85 , @xmath86 , and @xmath87 , respectively . at the transition point of model 2 , @xmath88 , @xmath89 , and @xmath90 mcs were iterated on the surfaces of @xmath91 , @xmath92 , and @xmath93 , respectively . for model 3 , the total number of mcs at the transition point was about @xmath94 , @xmath95 , and @xmath96 for the surfaces of @xmath93 , @xmath97 , and @xmath98 , respectively . a relatively small number of mcs were performed at @xmath10 which is not the transition point on each surface . the mean square size @xmath99 is defined by @xmath100 where @xmath101 is the center of the surface . of @xmath99 for model 1 on the @xmath86 surface at @xmath102 , and ( b ) the variation of @xmath99 against mcs . ( c ) @xmath103 , and ( d ) the variation of @xmath99 obtained on the @xmath85 surface at @xmath104 . two distinct peaks on each @xmath103 imply that the size of surfaces in one phase is very different from that in the other phase at the transition point of model 1 . , width=321 ] figure [ fig-2](a ) is a normalized distribution @xmath103 ( or the histogram ) of @xmath99 for model 1 on the surface of size @xmath86 at the transition point @xmath102 . the variation of @xmath99 against mcs is plotted in fig . [ fig-2](b ) . figures [ fig-2](c ) and [ fig-2](d ) are those obtained on the surface of @xmath85 at @xmath104 . two distinct peaks visible in @xmath103 imply that the size of surfaces in one phase is very different from that in the other phase at the transition point . of @xmath99 for model 2 on the @xmath92 surface at @xmath105 , and ( b ) the variation of @xmath99 against mcs , ( c ) @xmath103 and ( d ) the variation of @xmath99 obtained on the @xmath91 surface at @xmath105 . , width=321 ] figure [ fig-3](a ) is a normalized histogram @xmath103 of @xmath99 for model 2 on the surface of size @xmath92 at the transition point @xmath105 . the variation of @xmath99 against mcs is plotted in fig . [ fig-3](b ) . figures [ fig-3](c ) and [ fig-3](d ) are those obtained on the surface of @xmath91 at @xmath105 . of @xmath99 for model 3 on the @xmath97 surface at @xmath106 , and ( b ) the variation of @xmath99 against mcs , ( c ) @xmath103 and ( d ) the variation of @xmath99 obtained on the @xmath98 surface at @xmath107 . , width=321 ] figure [ fig-4](a ) is a normalized histogram @xmath103 of @xmath99 for model 3 on the surface of size @xmath97 at the transition point @xmath106 . the variation of @xmath99 against mcs is plotted in fig . [ fig-4](b ) . figures [ fig-4](c ) and [ fig-4](d ) are those obtained on the surface of @xmath98 at @xmath107 . in order to obtain the hausdorff dimensions @xmath108 ( @xmath109 ) in the smooth ( crumpled ) phase close to the transition point , the mean value of @xmath99 was obtained by averaging @xmath99 over a small region at each peak of @xmath103 . for model 1 , we assumed the region : @xmath110 and @xmath111 at @xmath112 on the @xmath113 surface , @xmath114 and @xmath115 at @xmath116 on the @xmath87 surface , @xmath117 and @xmath118 at @xmath102 on the @xmath119 surface , and @xmath120 and @xmath121 at @xmath104 on the @xmath85 surface . for model 2 , we assumed the region : @xmath122 and @xmath123 at @xmath124 on the @xmath87 surface , @xmath125 and @xmath126 at @xmath127 on the @xmath93 surface , @xmath128 and @xmath129 at @xmath105 on the @xmath92 surface , and @xmath130 and @xmath131 at @xmath105 on the @xmath91 surface . for model 3 , we assumed the region : @xmath132 and @xmath133 at @xmath134 on the surface of @xmath87 , @xmath135 and @xmath136 at @xmath137 on @xmath93 , @xmath138 and @xmath139 at @xmath106 on @xmath97 , and @xmath140 and @xmath141 at @xmath107 on the surface of @xmath98 . against @xmath7 obtained in the smooth phase and in the crumpled phase close to the transition point for ( a ) model 1 , ( b ) model 2 , and ( c ) model 3 . the error bars on the data represent the standard deviations . , width=453 ] figures [ fig-5](a),(b),(c ) are log - log plots of @xmath99 against @xmath7 for model 1 , model 2 , and model 3 respectively , where the values of @xmath99 are obtained by averaging @xmath99 in the regions described above . error bars on the data represent the standard deviations . the straight lines are drawn by fitting the data @xmath99 to @xmath142 then we have @xmath143 where @xmath5 in @xmath144 denotes the model @xmath145 , and smo ( cru ) denotes the smooth ( crumpled ) phase . @xmath146 , @xmath147 , and @xmath148 in eq . ( [ h - model ] ) are comparable to the topological dimension @xmath149 within the errors . this data indicates that the surfaces are smooth in the smooth phase at the transition point for the three models . @xmath150 in eq.([h - model ] ) is less than the physical bound @xmath151 . this implies that the surface is not completely crumpled but relatively smooth in the crumpled phase at the transition point of model 2 . a similar phenomenon occurs for the standard tethered model @xcite . note also that @xmath150 in eq . ( [ h - model ] ) is comparable to the theoretical prediction @xmath152 within the error , which corresponds to the scaling exponent @xmath153 @xcite where @xmath154 . on the contrary , we got @xmath155 in the crumpled phase at the transition point of model 1 by fitting the data to eq . ( [ hausdorff - scale ] ) . however , it seems that @xmath156 is not well - defined because of the large error . the logarithmic divergence @xcite ; @xmath157 , is also expected for @xmath99 in the crumpled phase . in fact , the residual sum of squares rss is @xmath158 for the log - log fit of @xmath99 in the crumpled phase at the transition point , whereas the linear - log fit gives @xmath159 for these @xmath99 , where @xmath160 is defined by @xmath161 ^ 2 $ ] . the fact that the linear - log fit is better than the log - log fit indicates that @xmath99 scales according to the logarithmic divergence and that @xmath155 is not well - defined . we also have @xmath162 by fitting @xmath99 in the crumpled phase at the transition point of model 3 . the dashed line in fig . [ fig-5](c ) is drawn by using this @xmath163 , and indicates that @xmath163 is ill - defined for the same reason as for @xmath156 . in fact , we have @xmath164 for the linear - log fit and @xmath165 for the log - log fit in fig . [ fig-5](c ) . thus , the linear - log fit is better than the log - log fit for @xmath99 in the crumpled phase of model 3 . this allowed us to conclude that @xmath162 is an ill - defined value . we understand also that a choice of discretization of the hamiltonian influences the scaling property of @xmath99 in the crumpled phase at the transition point . of @xmath166 , and ( b ) the variation of @xmath166 against mcs , on the @xmath86 surface at @xmath102 , ( c ) @xmath167 and ( d ) the variation of @xmath166 on the @xmath85 surface at @xmath104 . @xmath168 . , width=321 ] figure [ fig-6](a ) is a normalized histogram @xmath167 of @xmath166 obtained on the surface of size @xmath86 at the transition point @xmath102 , where @xmath169 denotes @xmath168 , and @xmath170 is the total number of bonds given by @xmath171 . the bending energy @xmath23 of model 1 is divided by @xmath169 so that @xmath166 can be regarded as @xmath172 . two peaks can be seen clearly in @xmath167 . the variation of @xmath23 against mcs is plotted in fig . [ fig-6](b ) . figures [ fig-6](c ) and [ fig-6](d ) show @xmath167 and the variations of @xmath23 obtained on the surface of @xmath85 at @xmath104 . we also find two distinct peaks in @xmath167 in figs . [ fig-6](c ) . these two peaks in figs . [ fig-6](a ) and [ fig-6](c ) obviously show that model 1 undergoes a first - order phase transition . note also that the discontinuous transition is independent of the lattice structure . it was reported in @xcite that the same model undergoes a discontinuous transition on voronoi triangulated spherical surfaces , which are different from those used in this paper . of @xmath173 , and ( b ) the variation of @xmath173 against mcs , on the @xmath92 surface at @xmath105 , ( c ) @xmath167 and ( d ) the variation of @xmath173 on the @xmath91 surface at @xmath105 . , width=321 ] figure [ fig-7](a ) is a normalized histogram @xmath167 of @xmath173 obtained on the @xmath92 surface at the transition point @xmath105 , where @xmath175 denotes the total number of triangles given by @xmath174 . the variation of @xmath23 against mcs is plotted in fig . [ fig-7](b ) . figures [ fig-7](c ) and [ fig-7](d ) show @xmath167 and the variations of @xmath23 obtained on the @xmath91 surface at @xmath105 . the double peak structures of @xmath167 in figs . [ fig-7](a ) and [ fig-7](c ) obviously show that model 2 undergoes a first - order phase transition . of @xmath176 , and ( b ) the variation of @xmath176 against mcs , on the @xmath97 surface at @xmath106 , ( c ) @xmath167 and ( d ) the variation of @xmath173 on the @xmath98 surface at @xmath107 . @xmath177 . , width=321 ] figure [ fig-8](a ) is a normalized histogram @xmath167 of @xmath176 obtained on the @xmath97 surface at the transition point @xmath106 . the variation of @xmath23 against mcs is plotted in fig . [ fig-8](b ) . figures [ fig-8](c ) and [ fig-8](d ) show @xmath167 and the variations of @xmath23 obtained on the @xmath178 surface at @xmath107 . the double peak structures in @xmath167 in figs . [ fig-8](a ) and [ fig-8](c ) obviously show that model 3 undergoes a first - order phase transition . against the bending rigidity @xmath10 of ( a ) model 1 , ( b ) model 2 , ( c ) model 3 , and the bending energy ( d ) @xmath166 against @xmath10 of model 1 , ( e ) @xmath173 against @xmath10 of model 2 , ( f ) @xmath179 against @xmath10 of model 3 . @xmath169 is twice that of @xmath170 the total number of bonds and @xmath175 is the total number of triangles . , width=453 ] figures [ fig-9](a ) , ( b ) , ( c ) show @xmath99 against @xmath10 obtained in model 1 , model 2 , and model 3 , respectively . figure [ fig-9](d ) shows the bending energy @xmath166 against @xmath10 obtained in model 1 . figure [ fig-9](e ) shows @xmath99 and @xmath173 against @xmath10 obtained in model 2 , and fig . [ fig-9](f ) shows @xmath99 and @xmath176 against @xmath10 obtained in model 3 . note that the value for @xmath23 of model 2 is very different from that for model 1 or model 3 . the reason for this is because @xmath173 can not be regarded as @xmath172 , which can be demonstrated in eq . ( [ s1s2-model-2 ] ) . @xmath99 , @xmath166 , and @xmath173 in figs . [ fig-9](a ) , ( b ) , ( d ) , ( e ) are almost smooth , and no discontinuous change is seen for intermediate bending rigidity @xmath10 . the reason for those smooth behaviors is because the surface size is relatively small for model 1 and model 2 . we expect that the discontinuous changes can be seen in those quantities obtained on large surfaces . however , we consider that the sizes @xmath85 and @xmath91 are sufficiently large , because the discontinuous nature of the transition is obvious from the double peak in @xmath167 in figs . [ fig-6 ] and [ fig-7 ] . on the contrary , we see discontinuous changes in @xmath99 , @xmath179 shown in figs . [ fig-9](c ) , ( f ) for model 3 . surface size @xmath98 seems sufficiently large for model 3 showing the discontinuity of @xmath99 , @xmath179 . against the bending rigidity @xmath10 of ( a ) model 1 , ( b ) model 2 , and ( c ) model 3 . log - log plot of the peak values @xmath180 against @xmath7 of ( d ) model 1 , ( e ) model 2 , and ( f ) model 1 . the straight lines in ( d ) and ( e ) are drawn by fitting the largest three @xmath180 to eq . ( [ sigma - fitting ] ) . the solid ( dashed ) line in ( f ) is drawn by fitting the largest ( smallest ) four @xmath180 to eq . ( [ sigma - fitting ] ) . , width=453 ] the specific heat @xmath181 is defined by @xmath182 figure [ fig-10](a ) shows @xmath181 of model 1 on the surfaces of size @xmath85 , @xmath86 , and @xmath87 . sharp peaks in fig . [ fig-10](a ) indicate that model 1 undergoes a discontinuous transition . figure [ fig-10](b ) shows @xmath181 of model 2 on the surfaces of @xmath91 , @xmath92 , and @xmath87 , and fig . [ fig-10](c ) shows @xmath181 of model 3 on the surfaces of @xmath98 , @xmath97 , @xmath93 , and @xmath87 . figure [ fig-10](d ) is a log - log plot of the peak value @xmath180 against @xmath7 including the results obtained on the @xmath113 surface for model 1 . the peaks @xmath180 are plotted in fig . [ fig-10](e ) and in fig . [ fig-10](f ) for model 2 and model 3 , respectively . the straight lines in figs . [ fig-10](d ) , ( e ) were drawn by fitting the largest three @xmath180 to @xmath183 where @xmath53 is a critical exponent of the transition . the straight line denoted by _ large four _ ( _ small four _ ) in fig . [ fig-10](f ) were drawn by fitting the largest ( smallest ) four @xmath180 to eq . ( [ sigma - fitting ] ) . thus , we have @xmath184 and @xmath185 for model 3 . the exponents @xmath186 , @xmath187 , @xmath188 in eq . ( [ sigma - result ] ) indicates that the phase transition is of the first order in all three models . on the contrary , @xmath189 for @xmath190 indicates that model 3 appears to undergo a continuous transition on small - sized surfaces of @xmath191 . the result @xmath189 is almost comparable to @xmath192 of the model on voronoi triangulated spherical surfaces of size up to @xmath193 in @xcite . two different behaviors for @xmath180 against @xmath7 shown in fig . [ fig-10](f ) are consistent with the fact that two distinct peaks in @xmath167 are observed only on large ( @xmath194 ) surfaces . of @xmath99 obtained on ( a ) the model 1 surface of @xmath92 at @xmath195 , @xmath196 , and @xmath197 , ( b ) the model 2 surface of @xmath91 at @xmath198 , @xmath199 , and @xmath200 , and ( c ) the model 3 surface @xmath98 at @xmath201 , @xmath202 , and @xmath203 . , width=453 ] figures [ fig-11](a),(b),(c ) are the autocorrelation coefficient @xmath204 of @xmath99 defined by @xmath205 ^ 2 } , \quad \tau_{i+1 } = \tau_i + n \times 500 , \;(n=1,2,\cdots),\ ] ] from which we can see the convergence speed of @xmath99 in the simulations . @xmath204 in fig . [ fig-11](a ) are obtained on the model 1 surface of @xmath92 at @xmath206 , @xmath104 , and @xmath207 , and those in fig . [ fig-11](b ) are obtained on the model 2 surface of @xmath91 at @xmath208 , @xmath105 , and @xmath209 . figure [ fig-11](c ) shows @xmath204 obtained on the model 3 surface @xmath98 at @xmath210 , @xmath107 , and @xmath211 . in these figures , we find the phenomenon of critical slowing down , which reflects the transition . the horizontal axes in figs . [ fig-11](a),(b),(c ) represent @xmath212-mcs , which is a sampling - sweep between the samples @xmath213 and @xmath214 . the critical slowing down is clearly seen in the figures . the reason for this critical slowing down is because the volume of phase space ( @xmath215 ) for @xmath46 at the transition point becomes larger than those at the crumpled phase and at the smooth phase . it is remarkable that the phase space volume in the smooth phase seems comparable to that in the crumpled phase , despite the fact that the surfaces in the smooth phase extend to large regions in @xmath38 . this can also be seen in a tethered model with intrinsic curvature on a sphere @xcite and in a tethered model on a torus @xcite . on the surface of @xmath92 . , width=359 ] figure [ fig-12](a ) is a snapshot of model 1 surface of @xmath92 in the crumpled phase at @xmath104 , and fig . [ fig-12](b ) is the one in the smooth phase at the same @xmath10 . the sections of the surface shown in figs . [ fig-12](a ) and [ fig-12](b ) are depicted in figs . [ fig-12](c ) and [ fig-12](d ) , respectively . snapshots were drawn at the same scale . on the surface of @xmath91 . , width=359 ] figure [ fig-13](a ) is a snapshot of model 2 surface of @xmath91 in the crumpled phase at @xmath105 , and fig . [ fig-13](b ) is the one in the smooth phase at the same @xmath10 . the sections of the surface shown in figs . [ fig-13](a ) and [ fig-13](b ) are depicted in figs . [ fig-13](c ) and [ fig-13](d ) , respectively . snapshots were drawn at the same scale . on the surface of @xmath98 . , width=359 ] figure [ fig-14](a ) is a snapshot of the @xmath98 surface in the crumpled phase at @xmath107 , and fig . [ fig-8](b ) is the one in the smooth phase at the same @xmath10 . the mean square size is about @xmath216 and @xmath217 in figs . [ fig-14](a ) and [ fig-14](b ) , respectively . the sections of the surface in figs . [ fig-14](a ) and [ fig-14](b ) are depicted in figs . [ fig-14](c ) and [ fig-14](d ) , respectively . surfaces are rough at short scales even for the smooth phase shown in figs . [ fig-12](b ) , [ fig-13](b ) , [ fig-14](b ) , whereas they are smooth at the long range scale . surfaces rough at short scales can also be seen deep in the smooth phase . only a spherical monolayer surface is apparent in the smooth phase . none of non - spherical surfaces ; such as oblong surfaces , linear ones , and branched - polymer like ones , were observed . the surfaces in the crumpled phase at the transition point are completely collapsed in both model 1 and model 3 . these crumpled surfaces are in contrast to those in model 2 and those in @xcite , where the crumpled state at the transition point seems not completely crumpled and seems to be characterized by a hausdorff dimension less than the physical bound @xmath151 . this paper aimed to show that the first - order transition of the tethered surface model for biological membranes is independent of the discretization of the hamiltonian . three types of tethered surface models were investigated . the first model ( model 1 ) is a discrete model of helfrich and polyakov - kleinert , the second ( model 2 ) is that of nambu - goto , and the third ( model 3 ) is a tensionless model of helfrich and polyakov - kleinert . the first and the second models are closely related to each other in the context of the string model . the canonical mc simulations were carried out on spherical surfaces of size up to @xmath85 for model 1 , @xmath91 for model 2 , and @xmath98 for model 3 , where the lattices were constructed by dividing the icosahedron . a discrete form of the hamiltonian of model 1 is a linear combination of the gaussian term and a bending energy term , which is defined by using a normal vector of vertices . the hamiltonian of model 2 contains an area term and a bending energy term , which makes the model well - defined . the hamiltonian of model 3 contains a bending energy term and a hard - wall potential , which gives an upper bound on the bond length . the first - order transition of models 1 , 2 , and 3 were observed on lattices of size @xmath218 , @xmath219 , and @xmath220 , respectively . we have shown in this paper that the first - order crumpling transition is universal on spherical surfaces of the extrinsic curvature models for biological membranes . in fact , we have found that the first - order transition is independent of a choice of hamiltonian of the tethered surface model , if it is discretized on a sphere . therefore , the results obtained in this paper together with those in @xcite lead us to conclude that a first - order phase transition can be observed in a spherical tethered surface model whose hamiltonian includes a bending energy term . it is also found that the hausdorff dimension @xmath221 in the smooth phase at the transition point is almost identical to the topological dimension @xmath149 and is also independent of the discretization of the hamiltonian . on the contrary , a choice of discretization of the hamiltonian influences the scaling property of @xmath99 in the crumpled phase at the transition point . nevertheless , we consider that the crumpled state of the model is not a phantom one but a real physical one , because the hausdorff dimension of the crumpled phase in model 2 is @xmath222 , which is less than the physical bound and is also comparable to the result in @xcite . finally , we emphasize that our results suggest that biological membranes can exhibit the crumpling transition . experimental investigations on the crumpling transition are expected . further numerical studies on the transition should also be performed on larger surfaces . m. bowick , s. catterall , m. falcioni , g. thorleifsson , and k. anagnostopoulos , j. phys . i france 6 ( 1996 ) 1321 ; + m. bowick , s. catterall , m. falcioni , g. thorleifsson , and k. anagnostopoulos , nucl . 47 ( 1996 ) 838 ; + m. bowick , s. catterall , m. falcioni , g. thorleifsson , and k. anagnostopoulos , nucl . 53 ( 1997 ) 746 . h. koibuchi , phys . lett . a 300 ( 2002 ) 582 ; + h. koibuchi , n. kusano , a. nidaira , k. suzuki , and m.yamada , phys . lett . a 319 ( 2003 ) 44 ; + h. koibuchi , n. kusano , a. nidaira , and k. suzuki , phys . lett . a 332 ( 2004 ) 141 . m. matsumoto and t. nishimura , `` mersenne twister : a 623-dimensionally equidistributed uniform pseudorandom number generator '' , acm trans . on modeling and computer simulation vol . 1 , january ( 1998 ) pp.3 - 30 .

we found that three types of tethered surface model undergo a first - order phase transition between the smooth and the crumpled phase . the first and the third are discrete models of helfrich , polyakov , and kleinert , and the second is that of nambu and goto . these are curvature models for biological membranes including artificial vesicles . the results obtained in this paper indicate that the first - order phase transition is universal in the sense that the order of the transition is independent of discretization of the hamiltonian for the tethered surface model . and crumpling transition , first - order transition , bending energy , surface model 64.60.-i , 68.60.-p , 87.16.dg

SECTION 1. SHORT TITLE. This Act may be cited as the ``ADA Education and Reform Act of 2015''. SEC. 2. COMPLIANCE THROUGH EDUCATION. Based on existing funding, the Disability Rights Section of the Department of Justice shall, in consultation with property owners and representatives of the disability rights community, develop a program to educate State and local governments and property owners on effective and efficient strategies for promoting access to public accommodations for persons with a disability (as defined in section 3 of the Americans with Disabilities Act (42 U.S.C. 12102)). Such program may include training for professionals such as Certified Access Specialists to provide a guidance of remediation for potential violations of the Americans with Disabilities Act. SEC. 3. UNFAIR AND DECEPTIVE ACTS AND PRACTICES RELATING TO ADA COMPLIANCE DEMAND LETTERS. It shall be unlawful for any person to send or otherwise transmit a demand letter or other form of pre-suit notification alleging a violation of section 302 or 303 of the Americans with Disabilities Act of 1990 (29 U.S.C. 12182; 12183) if such letter or communication does not specify in detail the circumstances under which an individual was actually denied access to a public accommodation, including the address of property, the specific sections of the Americans with Disabilities Act alleged to have been violated, whether a request for assistance in removing an architectural barrier to access was made, and whether the barrier to access was a permanent or temporary barrier. Any person who violates this section shall be fined under title 18, United States Code. SEC. 4. NOTICE AND CURE PERIOD. Paragraph (1) of section 308(a) of the Americans with Disabilities Act of 1990 (42 U.S.C. 12188(a)(1)) is amended to read as follows: ``(1) Availability of remedies and procedures.-- ``(A) In general.--Subject to subparagraph (B), the remedies and procedures set forth in section 204(a) of the Civil Rights Act of 1964 (42 U.S.C. 2000a-3(a)) are the remedies and procedures this title provides to any person who is being subjected to discrimination on the basis of disability in violation of this title or who has reasonable grounds for believing that such person is about to be subjected to discrimination in violation of section 303. Nothing in this section shall require a person with a disability to engage in a futile gesture if such person has actual notice that a person or organization covered by this title does not intend to comply with its provisions. ``(B) Barriers to access to existing public accommodations.--A civil action under section 302 or 303 based on the failure to remove an architectural barrier to access into an existing public accommodation may not be commenced by a person aggrieved by such failure unless-- ``(i) that person has provided to the owner or operator of the accommodation a written notice specific enough to allow such owner or operator to identify the barrier; and ``(ii)(I) during the period beginning on the date the notice is received and ending 60 days after that date, the owner or operator fails to provide to that person a written description outlining improvements that will be made to remove the barrier; or ``(II) if the owner or operator provides the written description under subclause (I), the owner or operator fails to remove the barrier or to make substantial progress in removing the barrier during the period beginning on the date the description is provided and ending 120 days after that date.''. SEC. 5. MEDIATION FOR ADA ACTIONS RELATED TO ARCHITECTURAL BARRIERS. The Judicial Conference of the United States shall, under rule 16 of the Federal Rules of Civil Procedure or any other applicable law, in consultation with property owners and representatives of the disability rights community, develop a model program to promote the use of alternative dispute resolution mechanisms, including a stay of discovery during mediation, to resolve claims of architectural barriers to access for public accommodations. To the extent practical, the Federal Judicial Center should provide a public comment period on any such proposal. The goal of the model program shall be to promote access quickly and efficiently without the need for costly litigation. The model program should include an expedited method for determining the relevant facts related to such barriers to access and steps taken before the commencement of litigation to resolve any issues related to access. SEC. 6. EFFECTIVE DATE. This Act and the amendments made by this Act take effect 30 days after the date of the enactment of this Act.

ADA Education and Reform Act of 2015 This bill requires the Disability Rights Section of the Department of Justice to develop a program to educate state and local governments and property owners on strategies for promoting access to public accommodations for persons with a disability. The program may include training for professionals to provide a guidance of remediation for potential violations of the Americans with Disabilities Act of 1990 (ADA). The bill prohibits persons from, and subjects violators to a criminal fine for, sending demand letters or other pre-suit notifications alleging a violation of ADA public accommodation requirements if the notification does not specify the circumstances under which an individual was actually denied access. The notification must specify: (1) the address of property, (2) the specific ADA sections alleged to have been violated, (3) whether a request for assistance in removing an architectural barrier was made, and (4) whether the barrier was permanent or temporary. The bill also prohibits commencement of civil action based on the failure to remove an architectural barrier to access into an existing public accommodation unless: (1) the aggrieved person has provided to the owners or operators a written notice specific enough to identify the barrier, and (2) the owners or operators fail to provide the person with a written description outlining improvements that will be made to improve the barrier or they fail to remove the barrier or make substantial progress after providing such a description. The Judicial Conference of the United States must develop a model program to promote alternative dispute resolution mechanisms to resolve such claims. The model program should include an expedited method for determining relevant facts related to such barriers and steps to resolve accessibility issues before litigation.

SECTION 1. SHORT TITLE. This Act may be cited as the ``Livestock Ownership Fairness Act of 2002''. TITLE I--LIVESTOCK OWNERSHIP AND FEEDING PROHIBITION SEC. 101. PROHIBITION ON PACKERS OWNING OR FEEDING LIVESTOCK FOR EXTENDED PERIOD. (a) Prohibition; Exceptions.--The Packers and Stockyards Act, 1921, is amended by inserting after section 202 (7 U.S.C. 192) the following new section: ``SEC. 202A. PROHIBITION ON PACKERS OWNING OR FEEDING LIVESTOCK FOR EXTENDED PERIOD. ``(a) Prohibition.--It shall be unlawful for any packer with respect to livestock, meats, meat food products, or livestock products in unmanufactured form to own or feed livestock intended for slaughter for more than 14 days prior to slaughter. The prohibition applies regardless of whether the ownership or feeding of the livestock is by the packer directly or through a subsidiary or an arrangement described in subsection (b). ``(b) Covered Arrangements.--The arrangements referred to in subsection (a) mean arrangements that give a packer operational, managerial, or supervisory control over livestock or over a farming operation that produces livestock to such an extent that the actual producer of the livestock is no longer materially participating (as such term is defined in section 469(h) of the Internal Revenue Code of 1986) in the management of the farming operation with respect to the production of the livestock. ``(c) Exceptions.--Subsection (a) does not apply to the following: ``(1) Forward contracting arrangements, executed in advance of slaughter and used by packers for the purchase of livestock, so long as the producer retains operational, managerial, and supervisory control over the livestock until their delivery for slaughter and over the farming operation that produces the livestock. ``(2) A cooperative, if a majority of the ownership interest in the cooperative is held by active cooperative members that-- ``(A) own or feed livestock; and ``(B) provide the livestock to the cooperative for slaughter. ``(3) A packer that is owned or controlled by producers of a type of livestock, if, during the previous calendar year, the packer slaughtered less than 2 percent of the total number of that type of livestock slaughtered in the United States. ``(d) Conspiracy.--It shall also be unlawful for any packer to conspire, combine, agree, or arrange with any other person to do, or aid or abet the doing of, any act made unlawful by subsection (a).''. (b) Effective Date.-- (1) In general.--Subject to paragraph (2), section 202A of the Packers and Stockyards Act, 1921, as added by subsection (a), takes effect on the date of the enactment of this Act. (2) Transition rules.--In the case of a packer that, as of the date of the enactment of this Act, owns or feeds livestock in violation of section 202A of the Packers and Stockyards Act, 1921, the prohibitions in subsections (a) and (d) of such section shall apply to the packer-- (A) in the case of a packer of swine, beginning 540 days after the date of the enactment of this Act; and (B) in the case of a packer of any other type of livestock, beginning as soon as practicable, but not later than 180 days, after the date of the enactment of this Act, as determined by the Secretary of Agriculture. TITLE II--AGRICULTURAL ANTITRUST PROVISIONS SEC. 201. PREMERGER NOTICE REQUIREMENT. (a) Notice.--Whenever a person in the business of purchasing livestock, poultry, or a basic agricultural commodity for wholesale resale either unprocessed or processed, files a notification under section 7A of the Clayton Act (15 U.S.C. 18a), such person shall file simultaneously with the Secretary a notice in accordance with rules issued by the Secretary, that such person has filed such notification. (b) Public Comments.--The Secretary shall-- (1) publish promptly in the Federal Register a copy of each notice received under subsection (a), (2) accept public comments on the proposed merger described in such notice, and (3) consider as part of the review required by subsection (c), such comments timely received. (c) Review.--Not later than 30 days after receiving a notice filed under subsection (a), the Secretary shall-- (1) review the proposed acquisition described in such notice; (2) determine-- (A) the probable effects such acquisition would have on the prices paid to producers of any livestock, poultry, or basic agricultural commodities who sell to, buy from, or bargain with 1 or more of the persons involved in the proposed acquisition; and (B) whether such acquisition would-- (i) result in significantly increased market power for any of such persons; and (ii) increase the potential for anticompetitive or predatory pricing conduct by any of such persons; (3) prepare a report containing-- (A) the detailed findings made by the Secretary as a result of such review and such determination; and (B) an economic analysis of the Secretary regarding whether such acquisition may substantially lessen competition or tend to create a monopoly; and (4) transmit to the Office of Special Counsel for Agriculture, and shall publish in the Federal Register, simultaneously, a copy of such report. SEC. 202. SPECIAL COUNSEL FOR AGRICULTURE. (a) Establishment of Office.--The Attorney General shall establish in the Department of Justice an Office of Special Counsel for Agriculture that shall handle agricultural antitrust issues and related matters, as determined by the Attorney General. (b) Appointment.--The Special Counsel for Agriculture may be appointed by the Attorney General only after the expiration of the 30- day period beginning on the date the Attorney General publishes in the Federal Register the name of the individual proposed to be appointed and requests public comment with respect to the appointment of such individual. SEC. 203. DEFINITIONS. For purposes of this title-- (1) the term ``antitrust laws'' has the meaning given such term in subsection (a) of the 1st section of the Clayton Act (15 U.S.C. 12(a)), (2) the term ``basic agricultural commodity'' means corn, wheat, or soybeans, (3) the term ``livestock'' means cattle, sheep, goats, swine, or equine animals used for food or in the production of food, (4) the term ``person'' has the meaning given such term in subsection (a) of the 1st section of the Clayton Act (15 U.S.C. 12(a)), (5) the term ``poultry'' means chickens, turkeys, ducks, geese, or other domestic fowl used for food or in the production of food, and (6) the term ``Secretary'' means the Secretary of Agriculture.

Livestock Ownership Fairness Act of 2002 - Amends the Packers and Stockyards Act, 1921 to prohibit livestock packers directly or through a subsidiary, from conspiring to, or owning or feeding livestock to such an extent that the producer no longer materially participates in the management of the operation, with respect to livestock held for more than 14 days prior to slaughter. Exempts from such prohibition certain: (1) forward contracting arrangements under which the producer retains pre-delivery operational control of the livestock; (2) cooperatives that own, or feed livestock and provide such livestock for slaughter; or (3) certain small producer-owned or-controlled packers.Directs the Attorney General to establish in the Department of Justice an Office of Special Counsel for Agriculture to handle agricultural antitrust and related matters.Requires: (1) a person in the business of purchasing livestock, poultry, or a basic agricultural commodity for wholesale resale who files a premerger notice under the Clayton Act to file simultaneously a premerger notice with the Secretary of Agriculture; and (2) the Secretary to review the proposed merger and report to the Office of Special Counsel for Agriculture..

SECTION 1. SHORT TITLE. This Act may be cited as the ``Pre-K for USA Act.'' SEC. 2. FINDINGS. Congress makes the following findings: (1) The United States ranks 25th in early learning enrollment with fewer than 3 out of 10 four-year-olds enrolled in high-quality prekindergarten programs. (2) Studies show that children with access to high-quality prekindergarten programs are less likely to repeat a grade or drop out of high school, and more likely to succeed in their careers. (3) Every public dollar spent on high-quality prekindergarten programs returns $7 through a reduced need for spending on other services such as remedial education, grade repetition, and special education. (4) Children who attended prekindergarten are less likely to develop drug problems, commit a felony, and go to prison, and are half as likely to be arrested. (5) Children who attended prekindergarten usually have higher grade point averages and are more likely to attend a four-year college. (6) About 40 percent of school districts do not offer prekindergarten programs. (7) Over half of school districts that have pre- kindergarten programs offer only part-day programs. (8) Texas missed out on up to $118.48 million in Federal funding to expand prekindergarten programs. (9) Reports showed that in 2011 the Texas legislature cut approximately $5.4 billion in education funding and eliminated the $200 million in grants it offered to schools to expand prekindergarten programs from half-day to full-day. (10) In response to the State of Texas' education funding cuts, certain local governments took it upon themselves to fund full-day prekindergarten programs. (11) For these reasons, certain localities, including local governments and local educational agencies would benefit from direct application prekindergarten Federal program funding. SEC. 3. PREKINDERGARTEN DEVELOPMENT GRANTS. (a) In General.--The Secretary of Education, in consultation with the Secretary of Health and Human Services, shall award competitive grants to States, local educational agencies, or other local government entities that wish to increase their capacity and build the infrastructure within the State to offer high-quality prekindergarten programs. (b) Grant Duration.--The Secretary shall award grants under this Act for a period of not more than 3 years. Such grants shall not be renewed. (c) Application.-- (1) In general.--A Governor, or chief executive officer of a State, a local educational agency, or another local government entity that desires to receive a grant under this Act shall submit an application to the Secretary of Education at such time, in such manner, and accompanied by such information as the Secretary may reasonably require. (2) Development of state application.--In developing an application for a grant under this Act, a State shall consult with the State Advisory Council on Early Childhood Education and Care and incorporate their recommendations, where applicable. (d) Matching Requirement.-- (1) In general.--To be eligible to receive a grant under this Act, a State, local educational agency, or other local government entity shall contribute for the activities for which the grant was awarded non-Federal matching funds in an amount equal to not less than 20 percent of the amount of the grant. (2) Non-federal funds.--To satisfy the requirement of paragraph (1), a State, local educational agency, or other local government entity may use-- (A) non-Federal resources in the form of State funding, local funding, or contributions from philanthropy or other private sources, or a combination of such resources; or (B) in-kind contributions. (3) Financial hardship waiver.--The Secretary may waive paragraph (1) or reduce the amount of matching funds required under that paragraph for a State, local educational agency, or other local government entity that has submitted an application for a grant under this subsection if the State, local educational agency, or other local government entity demonstrates, in the application, a need for such a waiver or reduction due to extreme financial hardship, as determined by the Secretary. (e) Subgrants.-- (1) In general.--A State, local educational agency, or other local government entity awarded a grant under this subtitle may use the grant funds to award subgrants to eligible local entities, to carry out the activities under the grant. (2) Subgrantees.--An eligible local entity awarded a subgrant under paragraph (1) shall comply with the requirements of this Act relating to grantees, as appropriate. (f) Double-Dipping Prevention.--The Secretary may not award a subgrant to a local educational agency or other local government entity under subsection (e) for a program in a fiscal year if the State, agency, or entity received funding for the program in such fiscal year. (g) Authorization of Appropriations.--There are authorized to be appropriated to carry out this section-- (1) $750,000,000 for fiscal year 2016; and (2) such sums as may be necessary for each of fiscal years 2017 through 2025. SEC. 4. DEFINITIONS. In this Act: (1) Eligible local entity.--The term ``eligible local entity'' means-- (A) a local educational agency, including a charter school or a charter management organization that acts as a local educational agency, or an educational service agency in partnership with a local educational agency; (B) an entity (including a Head Start program or licensed child care setting) that carries out, administers, or supports an early childhood education program; or (C) a consortium of entities described under subparagraph (A) or (B). (2) Full-day.--The term ``full-day'' means a day that is-- (A) equivalent to a full school day at the public elementary schools in the State; and (B) not less than 5 hours. (3) High-quality prekindergarten program.--The term ``high- quality prekindergarten program'' means a prekindergarten program supported by an eligible local entity that includes, at a minimum, the following elements based on nationally recognized standards: (A) Serves children who-- (i) are age 4 or children who are age 3 or 4, by the eligibility determination date (including children who turn age 5 while attending the program); or (ii) have attained the legal age for State- funded prekindergarten. (B) Requires high staff qualifications, including that teachers meet the requirements of 1 of the following clauses: (i) The teacher has a bachelor's degree in early childhood education or a related field with coursework that demonstrates competence in early childhood education; (ii) The teacher-- (I) has a bachelor's degree in any field; (II) has demonstrated knowledge of early childhood education through passage of a State-approved assessment in early childhood education; (III) engages in ongoing professional development in early childhood education for not less than 2 years; and (IV) is enrolled in a State- approved educator preparation program in which the teacher receives ongoing training and support in early childhood education and is making progress toward the completion of the program in not more than 3 years; or (iii) The teacher has a bachelor's degree in any field with a credential, license, or endorsement that demonstrates competence in early childhood education. (C) Maintains a maximum class size of 20 children. (D) Maintains a child to instructional staff ratio that does not exceed 10 to 1. (E) Offers a full-day program. (F) Provides developmentally appropriate learning environments and evidence-based curricula that are aligned with the State's early learning and development standards. (G) Offers instructional staff salaries comparable to kindergarten through grade 12 teaching staff. (H) Provides for ongoing monitoring and program evaluation to ensure continuous improvement. (I) Offers accessible comprehensive services for children that-- (i) include, at a minimum-- (I) screenings for vision, dental, health (including mental health), and development and referrals, and assistance obtaining services, when appropriate; (II) family engagement opportunities (taking into account home language), such as parent conferences (including parent input about their child's development) and support services, such as parent education and family literacy services; (III) nutrition services, including nutritious meals and snack options aligned with requirements set by the most recent Child and Adult Care Food Program guidelines promulgated by the Department of Agriculture as well as regular, age-appropriate, nutrition education for children and their families; (IV) programs coordinated with local educational agencies and entities providing programs authorized under section 619 and part C of the Individuals with Disabilities Education Act (20 U.S.C. 1419 and 1431 et seq.); (V) physical activity programs aligned with evidence-based guidelines, such as those recommended by the Institute of Medicine, and that take into account and accommodate children with disabilities; and (VI) additional support services, as appropriate, based on the findings of a needs analysis; and (ii) are provided on-site, to the maximum extent feasible. (J) Provides high-quality professional development for staff, including regular in-class observation for teachers and teacher assistants by individuals trained in observation and which may include evidence-based coaching. (K) Meets the education performance standards in effect under section 641A(a)(1)(B) of the Head Start Act (42 U.S.C. 9836a(a)(1)(B)). (L) Maintains evidence-based health and safety standards. (4) ESEA terms.--The terms ``local educational agency'' and ``State'' have the meanings given the terms in section 9101 of the Elementary and Secondary Education Act of 1965 (20 U.S.C. 7801). (5) Secretary.--The term ``Secretary'' means the Secretary of Education.

Pre-K for USA Act This bill requires the Department of Education (ED) to award high-quality prekindergarten (pre-K) program development grants on a competitive basis to states, local education agencies, or other local government entities. A grant recipient may use the grant funds to award subgrants to local entities, provided that the entity did not receive pre-K program&nbsp;funding within the same fiscal year. Grants are nonrenewable and shall be awarded for a period of no more than three years. Unless granted a financial hardship waiver by ED,&nbsp;a grant recipient shall contribute matching funds equal to at least 20% of the grant amount.

the past decade has seen unprecedented growth in the number of new , often high - cost , health technologies and consumer demand for access to them . it has also seen increased public awareness and scrutiny of decisions about which technologies to include in the basket of publicly insured services.13 to improve the legitimacy of such decisions and optimize health outcomes through the effective use of increasingly strained health care resources , many payers , particularly those in europe , have established centralized systems for determining the reimbursement status of new health technologies.4,5 in this invited review , we compare these systems across selected countries in northern , southern , western , eastern , and central europe , examining : their mandate , authority , organizational structure , and policy optionsmechanisms for identifying , selecting , and evaluating technologiesclinical and economic evidence expectationsreview committee composition , procedures , and key factors considered during deliberationsuse of conditional reimbursement options for enabling access to promising new technologies around which considerable uncertainty related to clinical and/or economic value existsthe role of manufacturers in steps comprising the reimbursement review process . their mandate , authority , organizational structure , and policy options mechanisms for identifying , selecting , and evaluating technologies clinical and economic evidence expectations review committee composition , procedures , and key factors considered during deliberations use of conditional reimbursement options for enabling access to promising new technologies around which considerable uncertainty related to clinical and/or economic value exists the role of manufacturers in steps comprising the reimbursement review process . this review is based upon findings from a comprehensive search for publicly available information on centralized reimbursement systems in selected european countries . peer - reviewed literature published in english over the past decade ( ending in january 2011 ) was located using a structured search strategy that combined relevant controlled vocabulary terms , ie , mesh and emtree ( eg , technology , medical , reimbursement mechanisms , decision - making , technology assessment , health policy ) and free text terms ( eg , pharmaceuticals , medical devices , coverage , funding , centralized review , health technology assessment , and reimbursement , the full search strategy being available from the authors ) . such terms were identified through an analysis of words used to index references familiar to the authors . the strategy was applied to several health - related electronic bibliographic databases , including pubmed , medline , embase , healthstar , cinahl , econlit , pascal , scopus , international pharmaceutical abstracts , web of science , and the uk centre for reviews and dissemination databases ( database of abstracts of reviews of effects , national health service economic evaluation database , and health technology assessment ) . for comprehensiveness , reference lists of retrieved papers and the most recent issues of health policy - related journals were hand - searched . a search for gray ( unpublished ) literature ( eg , working papers , conference abstracts , reports , presentations , government documents ) was also performed using the google search engine and terms from the main search strategy . in addition , the following dedicated gray literature databases were scanned : the new york academy of medicine s gray literature database , knowledge utilization database , systematic reviews for management and policy making , and national health service evidence in health and social care . separate searches for information on centralized reimbursement processes within health care systems of the top 30 european countries ranked according to gross domestic product per capita by the world bank were also conducted . this number was considered sufficient to capture the full spectrum of such processes . for each country , the websites of relevant ministries ( eg , health , social affairs , economics ) , translated into english with google translate , were scanned for documents describing legislation and other policies and processes for making reimbursement decisions on new health technologies , including pharmaceuticals , medical devices , diagnostic tests , and procedures . published papers unrelated to the introduction of individual health technologies ( eg , those on macrolevel priority setting ) were excluded . because the purpose of this review was to examine current actual processes , papers proposing specific decision - making tools or discussing one component of decision - making were also excluded . information on process - related characteristics of the centralized reimbursement systems , including perceived strengths and weaknesses , was extracted using a standardized , pretested data abstraction form . to ensure it reflected the current policy environment , the following individuals were consulted : corresponding authors of published papers , contacts listed on organizations websites , and european policy experts with whom the authors were already acquainted . extracted information was tabulated to facilitate the identification of patterns or trends across country - specific reimbursement processes , and subsequently analyzed qualitatively using content analysis and constant comparison techniques . of the 30 european countries initially identified for the review , information on centralized reimbursement processes could only be found for 23 . therefore , the review included the following 23 countries : austria , belgium , czech republic , denmark , estonia , finland , france , germany , greece , hungary , ireland , italy , norway , poland , portugal , scotland , slovakia , spain , sweden , switzerland , the netherlands , the united kingdom , and wales . the majority ( 18/23 ) of countries have established centralized reimbursement processes to support coverage decision - making for either pharmaceuticals or pharmaceuticals and devices needed for their delivery . in general , eligible pharmaceuticals comprise those requiring a prescription . two - thirds of such processes review both inpatient and outpatient pharmaceuticals ( 12/18 ) , while one - third ( 6/18 ) considers those administered in outpatient settings only ( table 1 ) . the remaining five countries have invested in centralized reimbursement systems that span medical devices , procedures , and pharmaceuticals ( table 1 ) . despite differences in the scope of technologies included , such processes share a similar mandate to determine the reimbursement status of new technologies . in most of the countries , this amounts to a decision on whether to add the technology to a positive list . however , a small proportion of the countries also maintain a negative list ( ie , a list of nonreimbursable services ) , broadening the mandate of their centralized reimbursement systems to include decisions resulting in active exclusion of some technologies from the benefit plan ( table 1 ) . in legislation governing most systems ( 13/23 ) , decisions are authoritative ( ie , must be implemented ) , rather than advisory ( ie , recommendations ) . given that the price of a technology can significantly influence assessments of value for money and affordability , many of the countries have also incorporated pricing into the mandates of such systems ( discussed in detail later ) . finally , all consider at least three funding decision options , ie , provide , do not provide , and provide with restrictions or conditions ( ie , restrict use to specific providers or patients meeting certain criteria , table 1 ) . in addition , approximately one - third have introduced a fourth option , ie , provide while additional evidence is collected . the latter comprises a provisional funding arrangement in which the technology is reimbursed in the interim while information needed to reduce uncertainties in existing evidence is collected to support a definitive decision . approaches to the identification of technologies for review by centralized reimbursement systems vary across countries ( table 2 ) . broadly , there are three strategies : technologies may be submitted by manufacturers seeking coverage for newly licensed pharmaceuticals ( 13/23 ) ; they may be referred by potential payers ( eg , government , sickness funds ) or users ( eg , hospitals , providers , patients ) , as well as manufacturers ( 8/23 ) ; or they may be identified by payers or users only ( 2/23 ) . systems limited to consideration of reimbursement applications from manufacturers alone typically review submissions in order of receipt , unless a technology is eligible for fast tracking , which moves it to the front of the queue . in countries with such mechanisms ( eg , the netherlands ) , eligibility criteria include technologies ( mainly pharmaceuticals ) used to treat rare or life - threatening conditions for which no alternatives beyond best supportive care exist . some countries ( eg , scotland and norway ) have more closely linked centralized regulatory and reimbursement processes in order to reduce overall inefficiencies in technology policy . specifically , pharmaceuticals are automatically sent to the centralized reimbursement system for review upon market approval . in systems that accept referrals from multiple stakeholders , technology selection and/or prioritization criteria for example , germany s federal joint committee , which determines which technologies to review , takes into account clinical relevance , cost implications , and potential risks related to the technology and its introduction into the health care system.6 in the uk , the topic selection panel of the national institute of health and clinical excellence , whose members include health care providers and patient representatives , formulate recommendations following consideration of : the burden of disease for which the technology targets ; anticipated clinical impact ( ie , whether the technology represents a significant medical advance that could yield substantial health benefits ) ; potential impact on national health service costs and resources ; alignment of the technology with broader government priority areas ; concerns over appropriateness of use in practice ; and potential for national guidance to add value.7 recommendations are forwarded to the department of health , which makes the final decision . across centralized reimbursement systems , technology identification and selection is followed by some form of health technology assessment ( table 2 ) . this involves collection and synthesis of evidence ( clinical and , in most cases , economic ) , the findings of which are presented in an assessment report , and critical appraisal of the relevance , quality , and generalizability of that evidence . responsibility for the preparation of these reports varies . in systems where a manufacturer s submission initiates the reimbursement review process , most systems have developed a standard template / structure for the report and submission guidelines to which manufacturers must adhere . these guidelines largely include content / information requirements and internationally accepted methods for synthesizing and analyzing evidence . in two of the countries , responsibility for the assessment depends upon the type of review ( appraisal ) . both france and the uk have created single technology appraisal and multiple technology appraisal processes . single technology appraisals compare the candidate technology with a limited number of alternatives for a specific , well - defined indication ( eg , disease stage ) . their scope most closely resembles processes based upon manufacturers submissions . multiple technology appraisals consider either several indications for a candidate technology or several technologies ( along with the candidate technology ) for a condition at one or more points in its course , taking a disease management approach . the assessment report for a single technology appraisal is prepared by the manufacturer . for a multiple technology appraisal , the report is drafted either internally with support from external content and methodological experts ( france ) or by an independent academic group ( the uk ) . finally , in some countries , technical staff of a dedicated health technology assessment body or the centralized reimbursement system itself undertake the assessment report , regardless of the scope ( eg , germany ) . with one exception ( the uk ) , responsibility for preparing the evaluation report that accompanies each assessment also lies with technical staff and , if necessary , external experts . the national institute of health and clinical excellence commissions independent academic groups to evaluate assessments submitted by manufacturers as part of its single technology appraisal process . centralized reimbursement systems have issued their own guidelines or endorsed internationally recognized published ones specifying clinical and economic evidence requirements for assessment reports ( tables 3 and 4 ) . these guidelines state topics to be addressed and the types of information accepted for addressing them . in most cases ( 16/23 ) , specified clinically - related topics are similar and include : burden of illness and/or characteristics of the target patient population ; therapeutic claim of the candidate technology ; safety ; efficacy ; and effectiveness ( preferably comparative effectiveness ) across relevant patient subgroups ( table 3 ) . additionally , several require information on current management or the place of the candidate technology within existing treatment pathways ( eg , france and the uk ) , and its proposed frequency and duration of use ( eg , austria ) . across systems and where reported , there is a shared preference for information on health outcomes that represent final clinical endpoints related to mortality , morbidity , and quality of life . this may be explained by the fact that a prerequisite for reimbursement review is typically regulatory approval . therefore , systems may view reconsideration of adverse events , which relate to the safety of a technology , unnecessary . in systems proposing or stipulating the use of quality - adjusted life - years ( 7/23 ) , change in health - related quality of life is to be measured in patients and then valued in the public or general population ( eg , the uk ) . surrogate outcomes are discouraged or not accepted unless well validated ( eg , germany ) . lastly , some systems elicit the views of patients and or carers in identifying topic specific outcomes and their relative importance ( eg , germany ) . in general , centralized reimbursement systems state a preference for head - to - head randomized controlled trials comparing the candidate technology with standard care , no active treatment / best supportive care , or placebo ( if no alternatives exist , table 3 ) . however , increased interest in evidence of comparative effectiveness over comparative efficacy among most reimbursement systems has led to requests for inclusion of head - to - head randomized controlled trials conducted in naturalistic settings ( ie , pragmatic trials , in the uk ) and other direct comparative studies ( observational and experimental in design ) , the collective findings of which may offer a more accurate prediction of the behavior of the technology in general clinical practice ( eg , france , germany , and sweden ) . also , there appears to be emerging recognition of the need for flexibility in evidence expectations under certain circumstances . recently , germany s institute for quality and efficiency in health care , which conducts health technology assessments and makes reimbursement recommendations on selected health technologies to the federal joint committee , issued methodological guidelines suggesting that when no active alternative treatment exists , well designed case series would be deemed adequate.8 while across systems , the preferred source of such clinical evidence is published , peer - reviewed studies , many encourage , and in several cases require if available , inclusion of unpublished or ongoing studies ( eg , austria , belgium , norway , poland , slovakia , sweden , the netherlands , and the uk ) , commercial in - confidence data ( eg , austria , france , sweden , and the uk ) and/or current national and international clinical practice guidelines ( eg , france ) in assessment reports . in recent years , some systems have incorporated submissions from patient and/or carer organizations into their processes ( eg , scotland , sweden , and the uk ) . such submissions are increasingly viewed as an important source of information regarding the relative value of outcome measures employed in clinical studies and the meaningfulness or significance of findings to patients and carers . finally , while systems tend not to explicitly exclude sources of information , belgium s drug reimbursement committee states that abstracts are not accepted.9 most centralized reimbursement systems ( 20/23 ) have made mandatory the inclusion of a formal economic evaluation / analysis for either some ( ie , those for which alternative(s ) exist(s ) , eg , germany , or those offering added therapeutic value , eg , austria and belgium , or all candidate technologies to inform deliberations around in the latter case , the type of evaluation is rarely stipulated , because options available depend , in part , on the magnitude of the incremental benefit of the technology over its comparators . however , a rationale must be presented , and methods adopted must comply with economic guidelines developed or endorsed by the centralized reimbursement system ( table 4 ) . for technologies that appear to offer added therapeutic value ( ie , are more effective ) , some systems indicate a preference for certain types of evaluations , such as cost - utility analysis by ireland s health service executive.10 others state explicitly which types will not be accepted , such as cost - benefit analysis by belgium s drug reimbursement committee.11 in addition to a formal economic evaluation , the institute for quality and efficiency in health care in germany requires an efficiency frontier analysis , which assesses the relative value of different technologies within a given therapeutic area.12 regarding the perspective to be taken for the economic evaluation , the proportion of systems adopting a payer , societal , or both payer and societal perspective is similar . among systems considering a payer s perspective only , costs to be captured are often restricted to those directly related to care associated with the use of the candidate technology throughout the course of a disease or condition ( ie , direct costs to the health care system ) . one exception is the national institute of health and clinical excellence , which specifies inclusion of direct and indirect costs to the national health service and personal social services.13 in systems requiring a societal perspective , costs specified comprise direct costs to not only the health care system , but also services beyond health care and indirect ( lost productivity ) costs . however , they must be reported separately ( eg , finland , portugal , and the netherlands ) . in sweden , the dental and pharmaceutical benefits board has taken a wider view on indirect costs , requesting that time lost by patients and carers be considered , along with lost productivity.14,15 thus , its methods broadly resemble those of holistic economic analysis , a technique initially developed for economic evaluations of public programs , the costs and benefits of which are often complex . nevertheless , considerable debate over the valuation of items such as time lost within academic and policy communities remains . this may be why other systems employing a societal perspective have assumed a narrower position on eligible indirect costs . with respect to the choice of comparator for the economic evaluation , almost all systems specify use of one of the following : standard care , the most commonly used alternative , or france also requires separate analyses with two additional comparators , ie , the most recently reimbursed alternative and the least expensive alternative.16 in belgium , if the candidate technology represents an addon treatment , the comparator must constitute current treatment without the candidate technology.17 further , the use of offlabel treatments as the comparator is not permitted.11 all systems rely upon sensitivity analyses to assess the stability of estimates generated through the economic evaluation , but few stipulate the type . among those that do , probabilistic sensitivity analysis is the most commonly prescribed ( eg , belgium , germany , scotland , slovakia , the uk , and wales ) . in recent years , affordability has become an increasingly important consideration for centralized reimbursement systems , with almost all of those included in this review ( where information could be found ) requiring a budget impact analysis ( table 4 ) . however , some waive this analysis in certain circumstances , eg , when no alternative treatment exists ( belgium).17 although information describing the specific costs to be included appears scarce , based on that available , they mirror those for the economic evaluation of the same technology . specifically , if the economic evaluation is limited to direct costs , so must the budget impact analysis , eg , hungary and ireland . in most of the centralized reimbursement systems , the assessment and evaluation reports are sent to and scrutinized by a review committee ( sometimes referred to as an appraisal committee ) . while the composition of this committee varies across systems , it is usually multidisciplinary , with members representing payers , administrators , health care providers , and academia ( eg , health economists , table 5 ) . approximately one - third have also appointed patient representatives to their respective committees ( eg , sweden , switzerland , and the uk ) , although not always as voting members ( germany),18,19 and one - fifth include manufacturers ( belgium , switzerland , the uk , and wales ) . in most systems , the authority of the review committee is advisory ( ie , makes recommendations ) . aside from lists of factors / criteria considered ( table 6 ) , publicly available procedural information on committee deliberations is often limited to conditions under which presentations / testimonials from external experts ( including patients ) are sought or accepted and whether an incremental cost - effectiveness ratio threshold is employed . among the exceptions there , review committees ( the commission devaluation des medicaments ( cem ) , followed by the transparency commission ) adhere to a two stage process . i representing major medical benefit and v representing insufficient to justify reimbursement.16,2023 upon approval of the score by the minister , the cem then compares the technology with already reimbursed alternatives in order to formulate an opinion on the improvement in medical benefit or six possible levels exist , ranging from i ( major innovation ) to vi ( negative opinion regarding inclusion on the benefit list ) . therefore , innovativeness is viewed as the size of the incremental clinical benefit achieved by the candidate technology . the opinion of the cem is forwarded to the transparency commission , who makes a formal recommendation on the asmr classification . this classification is , in turn , used to negotiate price and reimbursement rate . in germany , the innovativeness of a technology is also based on whether it offers added therapeutic value . moreover , it plays an important role in determining the content of subsequent committee deliberations , because cost - benefit analyses are only taken into account when a technology has been deemed innovative.1824 the review committee of the italian medicines agency , ie , the technical scientific committee , explicitly weighs both the availability of existing treatments and the extent of clinical benefit in its assessment of a new pharmaceutical s innovativeness . the two attributes are scored separately and then combined to determine whether it represents an important , moderate , or modest innovation.25 this rating , along with the category of clinical value to which the pharmaceutical has been assigned , is sent to a second review committee , ie , the pricing and reimbursement committee , which negotiates price and reimbursement status with the manufacturer.26,27 regardless of the reimbursement system , one of the main goals of the review committee is to determine the broadly , its assessment combines consideration of clinical benefit with that of clinical need , taking into account key factors related to each dimension . for clinical need , they comprise , at a minimum , burden of illness ( prevalence of severity ) of the target condition and availability of alternatives . for clinical benefit , they include at least safety ( risk benefit ratio ) and efficacy / effectiveness , on the basis of which an overall estimate of the ratio of the benefits to harms of a candidate technology is estimated ( table 6 ) . while a further goal shared by most review committees is to formulate an opinion on whether the candidate technology represents value for money or an efficient use of resources , their approach to accomplishing this differs . approximately one - third are guided by , but not compelled to adhere to , a predefined incremental cost - effectiveness threshold or threshold range.28,29 typically , if the incremental cost - effectiveness for a candidate technology lies below the threshold , it is deemed cost - effective or good value for money . if it lies above the threshold , additional factors are taken into account when judging acceptability ( eg , uncertainties in estimates of outcomes , the severity of condition , and wider societal benefits).30,31 across systems whose committees do not refer to an incremental cost - effectiveness threshold , approaches to operationalizing value or money appear vague , with information largely limited to statements such as reasonableness of cost relative to therapeutic value ( table 6).32 similarly , although all but one of the systems ( sweden21 ) list affordability or impact of the candidate technology on health system resources among factors / criteria considered by their respective review committees , no information describing processes for deciding whether or not a technology is affordable could be found . equity or ethical implications comprise decision - making factors / criteria ( explicitly or implicitly ) in one - third of systems . for example , sweden s dental and pharmaceutical benefits board stipulates two principles that decisions must reflect , ie , the need and solidarity principle ( patients in the greatest need or the norwegian medicines agency explicitly takes into account equity , as do review committees in hungary and poland.26,3436 however , the way in which this is accomplished during deliberations is not clear . committees using an incremental cost - effectiveness threshold to guide decisions implicitly incorporate equity by virtue of the assumptions underpinning the incremental cost - effectiveness calculation ( ie , each quality - adjusted life - year [ qaly ] carries the same weight , regardless of the characteristics of the patients receiving it ( eg , age , gender , social status , income ) . consideration of additional , often competing ethical principles by these committees is operationalized through exception conditions under which the normal efficiency expectations do not need to be met ( eg , last chance therapies , orphan technologies , life - extending , end - of - life treatments).37 under such conditions , not all qalys are deemed equal . rather , a form of solidarity premium is applied , where , for example , qalys gained in the later stages of disease are given greater weight . while there is little disagreement over the importance of instituting exception conditions as a means of ensuring that reimbursement decisions embody the broader values of the population , considerable debate around definitions / qualifiers ( eg , what constitutes last chance ? or by what period of time must a technology lengthen survival in order to be regarded as life - extending ? ) remains . finally , the following factors are simply listed as criteria / factors by a small proportion of committees : alignment with government priorities ; feasibility ; and/or risk of off - label use of the technology ( table 6 ) . in general , systems aim to complete single technology reviews within 180 days of submission / identification of candidate technology , the time period prescribed by the european union transparency directive . based on tracking data , the actual time required appears to depend primarily on whether the assessment report accompanies a reimbursement application ( eg , belgium ) or is undertaken ( internally or externally ) by the system once a technology is identified for review ( eg , the uk , table 5 ) . in the latter case , review times can be 90 days or less ( eg , denmark and france).20,38 the majority of systems have established mechanisms for appealing recommendations or decisions . briefly , there are two main types of disputes , ie , those related to process and those amounting to disagreements over the interpretation of the evidence . in approximately one - third of systems , acceptable grounds for appeals are those of the first type only ( failed to act in accordance with processes39 ) . for the most part , appeals are heard by an expert panel appointed by the respective health care organization or payer alternatively , they must be filed in an administrative court ( eg , germany and sweden ) . increasingly , reimbursement systems are expressing interest in and/or implementing reimbursement policy options that extend beyond the traditional yes , no , or yes with restrictions such policy options take the form of provisional reimbursement arrangements , in which funding for a technology is provided in the interim while evidence needed to make a definitive decision is collected.40 collectively referred to as access with evidence development ( aed ) schemes , they have emerged in response to calls for mechanisms that balance access to new technologies with the need to ensure their safe , effective , and efficient introduction and use in the health care system . in recent years , these calls have heightened , as tension between payers and manufacturers , patients , and providers has intensified . many new high - cost technologies are supported by limited , albeit promising , evidence . therefore , reimbursement decisions are made under conditions of considerable uncertainty , with significant risks and consequences of getting it wrong aed schemes attempt to reduce such risks through managed entry of new technologies into everyday clinical practice . there are three main types , ie , coverage linked to an outcomes guarantee , coverage as part of a study , and automatic reassessment ( table 7 ) . often referred to as risk - sharing schemes , patient access schemes , and payment by results , the first type consists of contractual arrangements between payers and manufacturers , where payment is tied to the achievement of an outcome , be it financial or health - related.41,42 such schemes have been employed in approximately one - third of the systems in this review ( table 7 ) . they include financially - based price - volume agreements , where manufacturers must pay back the cost of sales exceeding those forecasted ( eg , belgium , france , germany , hungary , portugal),41,43,44 and expenditure caps , in which manufacturers cover the cost of treatment in patients for whom costs over a fixed time period exceed a prespecified amount ( eg , italy , the uk).41,45 health - related risk sharing arrangements , also called no cure no pay schemes , have been implemented by a smaller proportion of systems ( belgium , denmark , italy , the uk).41,4547 under such schemes , continued reimbursement of a technology ( usually a pharmaceutical for a rare disorder or cancer ) requires evidence of a predefined treatment effect . the second type , coverage as part of a study , involves provision of interim funding by payers in order to conduct studies designed to collect specific information needed to fill key evidence gaps . typically , such evidence gaps relate to the effectiveness and/or cost implications of the technology in real world settings . funding may be partial ( costs of the technology and/or health care associated with its use ) or full ( all health care and research costs ) . this type of scheme constitutes a policy option in approximately one quarter of the reimbursement systems , the majority of which have mandates that span pharmaceutical and nonpharmaceutical technologies ( eg , france , germany , the uk , table 7 ) . eligible technologies vary across systems , but often include those defined as innovative ( eg , granted an innovation pass in the uk ) and those anticipated to significantly impact health care organization budgets ( eg , the netherlands).25,48 the third type of aed scheme , automatic reassessment , comprises a programmed review of a reimbursement decision following a fixed period on the benefit list or when additional evidence is available.4951 it has become a part of the policy framework in half of the reimbursement systems included in this review , with most requiring reassessments of all technologies within their decision - making scope ( table 7 ) . despite the appeal of aed schemes , evidence of their effectiveness is both limited and mixed . recent reviews have highlighted the challenges involved in both their design and implementation.52,53 such challenges primarily stem from the need to reach consensus among stakeholders on the terms of the scheme . often , considerable time and resources have been required to resolve disagreements over elements such as the value proposition , outcomes to be measured and for what period , how the scheme should be funded , and to whom its oversight should be handed . further , negotiations have , in some cases , resulted in complex arrangements that failed to generate the evidence needed to support a policy decision and/or created a significant administrative burden on payers and providers involved in its implementation . in an effort to address these issues , guidelines for conducting aed schemes , derived from international experiences to date , were recently published.53,54 moreover , some systems have proposed alternative approaches to dealing with decision uncertainties . for example , earlier this year , national institute of health and clinical excellence announced a new form of value - based reimbursement termed flexible pricing.4548 under this approach , manufacturers adjust the price of a technology ( pharmaceutical ) in response to additional evidence of actual benefit to patients as it emerges . the national institute of health and clinical excellence subsequently assess this evidence , along with the proposed price , and determines whether the technology represents if a negative opinion is reached , the national institute of health and clinical excellence may veto the proposed price . given the potential benefits of such an approach ( eg , reduced administrative burden and system resource requirements ) it has already sparked interest among the national institute of health and clinical excellence s counterparts across europe . few reimbursement systems have established roles for manufacturers beyond referral of a technology for review and the opportunity to comment on draft reports and/or preliminary recommendations ( table 8) . processes exist and assessment reports are commissioned or undertaken by the reimbursement system , manufacturers may participate in defining the scope or protocol of the assessment ( france , germany , the uk ) or submit information to the group preparing such reports ( germany , ireland , spain , the uk ) . among systems that prepare the evaluation report only , about half invite manufacturers to contribute information ( scotland , italy , sweden , the uk , wales ) . involvement of manufacturers otherwise appears limited to single examples , eg , able to participate in consultations during the assessment ( france ) or attend review committee meetings ( wales ) . the majority ( 18/23 ) of countries have established centralized reimbursement processes to support coverage decision - making for either pharmaceuticals or pharmaceuticals and devices needed for their delivery . in general , eligible pharmaceuticals comprise those requiring a prescription . two - thirds of such processes review both inpatient and outpatient pharmaceuticals ( 12/18 ) , while one - third ( 6/18 ) considers those administered in outpatient settings only ( table 1 ) . the remaining five countries have invested in centralized reimbursement systems that span medical devices , procedures , and pharmaceuticals ( table 1 ) . despite differences in the scope of technologies included , such processes share a similar mandate to determine the reimbursement status of new technologies . in most of the countries , this amounts to a decision on whether to add the technology to a positive list . however , a small proportion of the countries also maintain a negative list ( ie , a list of nonreimbursable services ) , broadening the mandate of their centralized reimbursement systems to include decisions resulting in active exclusion of some technologies from the benefit plan ( table 1 ) . in legislation governing most systems ( 13/23 ) , decisions are authoritative ( ie , must be implemented ) , rather than advisory ( ie , recommendations ) . given that the price of a technology can significantly influence assessments of value for money and affordability , many of the countries have also incorporated pricing into the mandates of such systems ( discussed in detail later ) . finally , all consider at least three funding decision options , ie , provide , do not provide , and provide with restrictions or conditions ( ie , restrict use to specific providers or patients meeting certain criteria , table 1 ) . in addition , approximately one - third have introduced a fourth option , ie , provide while additional evidence is collected . the latter comprises a provisional funding arrangement in which the technology is reimbursed in the interim while information needed to reduce uncertainties in existing evidence is collected to support a definitive decision . approaches to the identification of technologies for review by centralized reimbursement systems vary across countries ( table 2 ) . broadly , there are three strategies : technologies may be submitted by manufacturers seeking coverage for newly licensed pharmaceuticals ( 13/23 ) ; they may be referred by potential payers ( eg , government , sickness funds ) or users ( eg , hospitals , providers , patients ) , as well as manufacturers ( 8/23 ) ; or they may be identified by payers or users only ( 2/23 ) . systems limited to consideration of reimbursement applications from manufacturers alone typically review submissions in order of receipt , unless a technology is eligible for fast tracking , which moves it to the front of the queue . in countries with such mechanisms ( eg , the netherlands ) , eligibility criteria include technologies ( mainly pharmaceuticals ) used to treat rare or life - threatening conditions for which no alternatives beyond best supportive care exist . some countries ( eg , scotland and norway ) have more closely linked centralized regulatory and reimbursement processes in order to reduce overall inefficiencies in technology policy . specifically , pharmaceuticals are automatically sent to the centralized reimbursement system for review upon market approval . in systems that accept referrals from multiple stakeholders , technology selection and/or prioritization criteria for example , germany s federal joint committee , which determines which technologies to review , takes into account clinical relevance , cost implications , and potential risks related to the technology and its introduction into the health care system.6 in the uk , the topic selection panel of the national institute of health and clinical excellence , whose members include health care providers and patient representatives , formulate recommendations following consideration of : the burden of disease for which the technology targets ; anticipated clinical impact ( ie , whether the technology represents a significant medical advance that could yield substantial health benefits ) ; potential impact on national health service costs and resources ; alignment of the technology with broader government priority areas ; concerns over appropriateness of use in practice ; and potential for national guidance to add value.7 recommendations are forwarded to the department of health , which makes the final decision . across centralized reimbursement systems , technology identification and selection is followed by some form of health technology assessment ( table 2 ) . this involves collection and synthesis of evidence ( clinical and , in most cases , economic ) , the findings of which are presented in an assessment report , and critical appraisal of the relevance , quality , and generalizability of that evidence . responsibility for the preparation of these reports varies . in systems where a manufacturer s submission initiates the reimbursement review process , most systems have developed a standard template / structure for the report and submission guidelines to which manufacturers must adhere . these guidelines largely include content / information requirements and internationally accepted methods for synthesizing and analyzing evidence . in two of the countries , responsibility for the assessment depends upon the type of review ( appraisal ) . both france and the uk have created single technology appraisal and multiple technology appraisal processes . single technology appraisals compare the candidate technology with a limited number of alternatives for a specific , well - defined indication ( eg , disease stage ) . their scope most closely resembles processes based upon manufacturers submissions . multiple technology appraisals consider either several indications for a candidate technology or several technologies ( along with the candidate technology ) for a condition at one or more points in its course , taking a disease management approach . the assessment report for a single technology appraisal is drafted either internally with support from external content and methodological experts ( france ) or by an independent academic group ( the uk ) . finally , in some countries , technical staff of a dedicated health technology assessment body or the centralized reimbursement system itself undertake the assessment report , regardless of the scope ( eg , germany ) . with one exception ( the uk ) , responsibility for preparing the evaluation report that accompanies each assessment also lies with technical staff and , if necessary , external experts . the national institute of health and clinical excellence commissions independent academic groups to evaluate assessments submitted by manufacturers as part of its single technology appraisal process . centralized reimbursement systems have issued their own guidelines or endorsed internationally recognized published ones specifying clinical and economic evidence requirements for assessment reports ( tables 3 and 4 ) . these guidelines state topics to be addressed and the types of information accepted for addressing them . in most cases ( 16/23 ) , specified clinically - related topics are similar and include : burden of illness and/or characteristics of the target patient population ; therapeutic claim of the candidate technology ; safety ; efficacy ; and effectiveness ( preferably comparative effectiveness ) across relevant patient subgroups ( table 3 ) . additionally , several require information on current management or the place of the candidate technology within existing treatment pathways ( eg , france and the uk ) , and its proposed frequency and duration of use ( eg , austria ) . across systems and where reported , there is a shared preference for information on health outcomes that represent final clinical endpoints related to mortality , morbidity , and quality of life . this may be explained by the fact that a prerequisite for reimbursement review is typically regulatory approval . therefore , systems may view reconsideration of adverse events , which relate to the safety of a technology , unnecessary . in systems proposing or stipulating the use of quality - adjusted life - years ( 7/23 ) , change in health - related quality of life is to be measured in patients and then valued in the public or general population ( eg , the uk ) . surrogate outcomes are discouraged or not accepted unless well validated ( eg , germany ) . lastly , some systems elicit the views of patients and or carers in identifying topic specific outcomes and their relative importance ( eg , germany ) . in general , centralized reimbursement systems state a preference for head - to - head randomized controlled trials comparing the candidate technology with standard care , no active treatment / best supportive care , or placebo ( if no alternatives exist , table 3 ) . however , increased interest in evidence of comparative effectiveness over comparative efficacy among most reimbursement systems has led to requests for inclusion of head - to - head randomized controlled trials conducted in naturalistic settings ( ie , pragmatic trials , in the uk ) and other direct comparative studies ( observational and experimental in design ) , the collective findings of which may offer a more accurate prediction of the behavior of the technology in general clinical practice ( eg , france , germany , and sweden ) . also , there appears to be emerging recognition of the need for flexibility in evidence expectations under certain circumstances . recently , germany s institute for quality and efficiency in health care , which conducts health technology assessments and makes reimbursement recommendations on selected health technologies to the federal joint committee , issued methodological guidelines suggesting that when no active alternative treatment exists , well designed case series would be deemed adequate.8 while across systems , the preferred source of such clinical evidence is published , peer - reviewed studies , many encourage , and in several cases require if available , inclusion of unpublished or ongoing studies ( eg , austria , belgium , norway , poland , slovakia , sweden , the netherlands , and the uk ) , commercial in - confidence data ( eg , austria , france , sweden , and the uk ) and/or current national and international clinical practice guidelines ( eg , france ) in assessment reports . in recent years , some systems have incorporated submissions from patient and/or carer organizations into their processes ( eg , scotland , sweden , and the uk ) . such submissions are increasingly viewed as an important source of information regarding the relative value of outcome measures employed in clinical studies and the meaningfulness or significance of findings to patients and carers . finally , while systems tend not to explicitly exclude sources of information , belgium s drug reimbursement committee states that abstracts are not accepted.9 most centralized reimbursement systems ( 20/23 ) have made mandatory the inclusion of a formal economic evaluation / analysis for either some ( ie , those for which alternative(s ) exist(s ) , eg , germany , or those offering added therapeutic value , eg , austria and belgium , or all candidate technologies to inform deliberations around in the latter case , the type of evaluation is rarely stipulated , because options available depend , in part , on the magnitude of the incremental benefit of the technology over its comparators . however , a rationale must be presented , and methods adopted must comply with economic guidelines developed or endorsed by the centralized reimbursement system ( table 4 ) . for technologies that appear to offer added therapeutic value ( ie , are more effective ) , some systems indicate a preference for certain types of evaluations , such as cost - utility analysis by ireland s health service executive.10 others state explicitly which types will not be accepted , such as cost - benefit analysis by belgium s drug reimbursement committee.11 in addition to a formal economic evaluation , the institute for quality and efficiency in health care in germany requires an efficiency frontier analysis , which assesses the relative value of different technologies within a given therapeutic area.12 regarding the perspective to be taken for the economic evaluation , the proportion of systems adopting a payer , societal , or both payer and societal perspective is similar . among systems considering a payer s perspective only , costs to be captured are often restricted to those directly related to care associated with the use of the candidate technology throughout the course of a disease or condition ( ie , direct costs to the health care system ) . one exception is the national institute of health and clinical excellence , which specifies inclusion of direct and indirect costs to the national health service and personal social services.13 in systems requiring a societal perspective , costs specified comprise direct costs to not only the health care system , but also services beyond health care and indirect ( lost productivity ) costs . however , they must be reported separately ( eg , finland , portugal , and the netherlands ) . in sweden , the dental and pharmaceutical benefits board has taken a wider view on indirect costs , requesting that time lost by patients and carers be considered , along with lost productivity.14,15 thus , its methods broadly resemble those of holistic economic analysis , a technique initially developed for economic evaluations of public programs , the costs and benefits of which are often complex . nevertheless , considerable debate over the valuation of items such as time lost within academic and policy communities remains . this may be why other systems employing a societal perspective have assumed a narrower position on eligible indirect costs . with respect to the choice of comparator for the economic evaluation , almost all systems specify use of one of the following : standard care , the most commonly used alternative , or france also requires separate analyses with two additional comparators , ie , the most recently reimbursed alternative and the least expensive alternative.16 in belgium , if the candidate technology represents an addon treatment , the comparator must constitute current treatment without the candidate technology.17 further , the use of offlabel treatments as the comparator is not permitted.11 all systems rely upon sensitivity analyses to assess the stability of estimates generated through the economic evaluation , but few stipulate the type . among those that do , probabilistic sensitivity analysis is the most commonly prescribed ( eg , belgium , germany , scotland , slovakia , the uk , and wales ) . in recent years , affordability has become an increasingly important consideration for centralized reimbursement systems , with almost all of those included in this review ( where information could be found ) requiring a budget impact analysis ( table 4 ) . however , some waive this analysis in certain circumstances , eg , when no alternative treatment exists ( belgium).17 although information describing the specific costs to be included appears scarce , based on that available , they mirror those for the economic evaluation of the same technology . specifically , if the economic evaluation is limited to direct costs , so must the budget impact analysis , eg , hungary and ireland . in most of the centralized reimbursement systems , the assessment and evaluation reports are sent to and scrutinized by a review committee ( sometimes referred to as an appraisal committee ) . while the composition of this committee varies across systems , it is usually multidisciplinary , with members representing payers , administrators , health care providers , and academia ( eg , health economists , table 5 ) . approximately one - third have also appointed patient representatives to their respective committees ( eg , sweden , switzerland , and the uk ) , although not always as voting members ( germany),18,19 and one - fifth include manufacturers ( belgium , switzerland , the uk , and wales ) . in most systems , the authority of the review committee is advisory ( ie , makes recommendations ) . aside from lists of factors / criteria considered ( table 6 ) , publicly available procedural information on committee deliberations is often limited to conditions under which presentations / testimonials from external experts ( including patients ) are sought or accepted and whether an incremental cost - effectiveness ratio threshold is employed . among the exceptions there , review committees ( the commission devaluation des medicaments ( cem ) , followed by the transparency commission ) adhere to a two stage process . i representing major medical benefit and v representing insufficient to justify reimbursement.16,2023 upon approval of the score by the minister , the cem then compares the technology with already reimbursed alternatives in order to formulate an opinion on the improvement in medical benefit or six possible levels exist , ranging from i ( major innovation ) to vi ( negative opinion regarding inclusion on the benefit list ) . therefore , innovativeness is viewed as the size of the incremental clinical benefit achieved by the candidate technology . the opinion of the cem is forwarded to the transparency commission , who makes a formal recommendation on the asmr classification . this classification is , in turn , used to negotiate price and reimbursement rate . in germany , the innovativeness of a technology is also based on whether it offers added therapeutic value . moreover , it plays an important role in determining the content of subsequent committee deliberations , because cost - benefit analyses are only taken into account when a technology has been deemed innovative.1824 the review committee of the italian medicines agency , ie , the technical scientific committee , explicitly weighs both the availability of existing treatments and the extent of clinical benefit in its assessment of a new pharmaceutical s innovativeness . the two attributes are scored separately and then combined to determine whether it represents an important , moderate , or innovation.25 this rating , along with the category of clinical value to which the pharmaceutical has been assigned , is sent to a second review committee , ie , the pricing and reimbursement committee , which negotiates price and reimbursement status with the manufacturer.26,27 regardless of the reimbursement system , one of the main goals of the review committee is to determine the broadly , its assessment combines consideration of clinical benefit with that of clinical need , taking into account key factors related to each dimension . for clinical need , they comprise , at a minimum , burden of illness ( prevalence of severity ) of the target condition and availability of alternatives . for clinical benefit , they include at least safety ( risk benefit ratio ) and efficacy / effectiveness , on the basis of which an overall estimate of the ratio of the benefits to harms of a candidate technology is estimated ( table 6 ) . while a further goal shared by most review committees is to formulate an opinion on whether the candidate technology represents value for money or an efficient use of resources , their approach to accomplishing this differs . approximately one - third are guided by , but not compelled to adhere to , a predefined incremental cost - effectiveness threshold or threshold range.28,29 typically , if the incremental cost - effectiveness for a candidate technology lies below the threshold , it is deemed cost - effective or good value for money . if it lies above the threshold , additional factors are taken into account when judging acceptability ( eg , uncertainties in estimates of outcomes , the severity of condition , and wider societal benefits).30,31 across systems whose committees do not refer to an incremental cost - effectiveness threshold , approaches to operationalizing value or money appear vague , with information largely limited to statements such as reasonableness of cost relative to therapeutic value ( table 6).32 similarly , although all but one of the systems ( sweden21 ) list affordability or impact of the candidate technology on health system resources among factors / criteria considered by their respective review committees , no information describing processes for deciding whether or not a technology is affordable could be found . equity or ethical implications comprise decision - making factors / criteria ( explicitly or implicitly ) in one - third of systems . for example , sweden s dental and pharmaceutical benefits board stipulates two principles that decisions must reflect , ie , the need and solidarity principle ( patients in the greatest need or worse off must be given priority ) and the human value principle ( sociodemographic characteristics of patient populations can not influence decisions).21,33 along with solidarity , the norwegian medicines agency explicitly takes into account equity , as do review committees in hungary and poland.26,3436 however , the way in which this is accomplished during deliberations is not clear . committees using an incremental cost - effectiveness threshold to guide decisions implicitly incorporate equity by virtue of the assumptions underpinning the incremental cost - effectiveness calculation ( ie , each quality - adjusted life - year [ qaly ] carries the same weight , regardless of the characteristics of the patients receiving it ( eg , age , gender , social status , income ) . consideration of additional , often competing ethical principles by these committees is operationalized through exception conditions under which the normal efficiency expectations do not need to be met ( eg , last chance therapies , orphan technologies , life - extending , end - of - life treatments).37 under such conditions , not all qalys are deemed equal . rather , a form of solidarity premium is applied , where , for example , qalys gained in the later stages of disease are given greater weight . while there is little disagreement over the importance of instituting exception conditions as a means of ensuring that reimbursement decisions embody the broader values of the population , considerable debate around definitions / qualifiers ( eg , what constitutes last chance ? or by what period of time must a technology lengthen survival in order to be regarded as life - extending ? ) remains . finally , the following factors are simply listed as criteria / factors by a small proportion of committees : alignment with government priorities ; feasibility ; and/or risk of off - label use of the technology ( table 6 ) . in general , systems aim to complete single technology reviews within 180 days of submission / identification of candidate technology , the time period prescribed by the european union transparency directive . based on tracking data , the actual time required appears to depend primarily on whether the assessment report accompanies a reimbursement application ( eg , belgium ) or is undertaken ( internally or externally ) by the system once a technology is identified for review ( eg , the uk , table 5 ) . in the latter case , review times can be 90 days or less ( eg , denmark and france).20,38 the majority of systems have established mechanisms for appealing recommendations or decisions . briefly , there are two main types of disputes , ie , those related to process and those amounting to disagreements over the interpretation of the evidence . in approximately one - third of systems , acceptable grounds for appeals are those of the first type only ( failed to act in accordance with processes39 ) . for the most part , appeals are heard by an expert panel appointed by the respective health care organization or payer ( eg , ministry of health , table 5 ) . alternatively , they must be filed in an administrative court ( eg , germany and sweden ) . increasingly , reimbursement systems are expressing interest in and/or implementing reimbursement policy options that extend beyond the traditional yes , such policy options take the form of provisional reimbursement arrangements , in which funding for a technology is provided in the interim while evidence needed to make a definitive decision is collected.40 collectively referred to as access with evidence development ( aed ) schemes , they have emerged in response to calls for mechanisms that balance access to new technologies with the need to ensure their safe , effective , and efficient introduction and use in the health care system . in recent years , these calls have heightened , as tension between payers and manufacturers , patients , and providers has intensified . many new high - cost technologies are supported by limited , albeit promising , evidence . therefore , reimbursement decisions are made under conditions of considerable uncertainty , with significant risks and consequences of getting it wrong aed schemes attempt to reduce such risks through managed entry of new technologies into everyday clinical practice . there are three main types , ie , coverage linked to an outcomes guarantee , coverage as part of a study , and automatic reassessment ( table 7 ) schemes , patient access schemes , and payment by results , the first type consists of contractual arrangements between payers and manufacturers , where payment is tied to the achievement of an outcome , be it financial or health - related.41,42 such schemes have been employed in approximately one - third of the systems in this review ( table 7 ) . they include financially - based price - volume agreements , where manufacturers must pay back the cost of sales exceeding those forecasted ( eg , belgium , france , germany , hungary , portugal),41,43,44 and expenditure caps , in which manufacturers cover the cost of treatment in patients for whom costs over a fixed time period exceed a prespecified amount ( eg , italy , the uk).41,45 health - related risk sharing arrangements , also called no cure no pay schemes , have been implemented by a smaller proportion of systems ( belgium , denmark , italy , the uk).41,4547 under such schemes , continued reimbursement of a technology ( usually a pharmaceutical for a rare disorder or cancer ) requires evidence of a predefined treatment effect . the second type , coverage as part of a study , involves provision of interim funding by payers in order to conduct studies designed to collect specific information needed to fill key evidence gaps . typically , such evidence gaps relate to the effectiveness and/or cost implications of the technology in real world settings . funding may be partial ( costs of the technology and/or health care associated with its use ) or full ( all health care and research costs ) . this type of scheme constitutes a policy option in approximately one quarter of the reimbursement systems , the majority of which have mandates that span pharmaceutical and nonpharmaceutical technologies ( eg , france , germany , the uk , table 7 ) . eligible technologies vary across systems , but often include those defined as innovative ( eg , granted an innovation pass in the uk ) and those anticipated to significantly impact health care organization budgets ( eg , the netherlands).25,48 the third type of aed scheme , automatic reassessment , comprises a programmed review of a reimbursement decision following a fixed period on the benefit list or when additional evidence is available.4951 it has become a part of the policy framework in half of the reimbursement systems included in this review , with most requiring reassessments of all technologies within their decision - making scope ( table 7 ) . despite the appeal of aed schemes , evidence of their effectiveness is both limited and mixed . recent reviews have highlighted the challenges involved in both their design and implementation.52,53 such challenges primarily stem from the need to reach consensus among stakeholders on the terms of the scheme . often , considerable time and resources have been required to resolve disagreements over elements such as the value proposition , outcomes to be measured and for what period , how the scheme should be funded , and to whom its oversight should be handed . further , negotiations have , in some cases , resulted in complex arrangements that failed to generate the evidence needed to support a policy decision and/or created a significant administrative burden on payers and providers involved in its implementation . in an effort to address these issues , guidelines for conducting aed schemes , derived from international experiences to date , were recently published.53,54 moreover , some systems have proposed alternative approaches to dealing with decision uncertainties . for example , earlier this year , national institute of health and clinical excellence announced a new form of value - based reimbursement termed flexible pricing.4548 under this approach , manufacturers adjust the price of a technology ( pharmaceutical ) in response to additional evidence of actual benefit to patients as it emerges . the national institute of health and clinical excellence subsequently assess this evidence , along with the proposed price , and determines whether the technology represents if a negative opinion is reached , the national institute of health and clinical excellence may veto the proposed price . given the potential benefits of such an approach ( eg , reduced administrative burden and system resource requirements ) it has already sparked interest among the national institute of health and clinical excellence s counterparts across europe . few reimbursement systems have established roles for manufacturers beyond referral of a technology for review and the opportunity to comment on draft reports and/or preliminary recommendations ( table 8) . processes exist and assessment reports are commissioned or undertaken by the reimbursement system , manufacturers may participate in defining the scope or protocol of the assessment ( france , germany , the uk ) or submit information to the group preparing such reports ( germany , ireland , spain , the uk ) . among systems that prepare the evaluation report only , about half invite manufacturers to contribute information ( scotland , italy , sweden , the uk , wales ) . involvement of manufacturers otherwise appears limited to single examples , eg , able to participate in consultations during the assessment ( france ) or attend review committee meetings ( wales ) . their introduction has , inarguably , brought greater consistency to processes and an improved sense of legitimacy to decisions . nevertheless , there remains a lack of transparency around critical elements , such as how multiple factors or criteria are weighed during committee deliberations . further , empirical studies evaluating the extent to which centralized reimbursement systems with advisory as opposed to decision - making authority are able to reduce inequities in access to new technologies within jurisdictions appear sparse . given the rapid pace with which new technologies that appear promising are now entering the market and the need to work alongside broader government industrial policies for encouraging innovation in an economic climate that demands prudent use of strained health care resources , the adoption of aed schemes by reimbursement systems seems inevitable . however , until more information on the outcomes of initiatives such as flexible pricing in the uk becomes available , their implementation should be approached with caution .

background : the purpose of this study was to compare centralized reimbursement / coverage decision - making processes for health technologies in 23 european countries , according to : mandate , authority , structure , and policy options ; mechanisms for identifying , selecting , and evaluating technologies ; clinical and economic evidence expectations ; committee composition , procedures , and factors considered ; available conditional reimbursement options for promising new technologies ; and the manufacturers roles in the process.methods:a comprehensive review of publicly available information from peer - reviewed literature ( using a variety of bibliographic databases ) and gray literature ( eg , working papers , committee reports , presentations , and government documents ) was conducted . policy experts in each of the 23 countries were also contacted . all information collected was reviewed by two independent researchers.results:most european countries have established centralized reimbursement systems for making decisions on health technologies . however , the scope of technologies considered , as well as processes for identifying , selecting , and reviewing them varies . all systems include an assessment of clinical evidence , compiled in accordance with their own guidelines or internationally recognized published ones . in addition , most systems require an economic evaluation . the quality of such information is typically assessed by content and methodological experts . committees responsible for formulating recommendations or decisions are multidisciplinary . while criteria used by committees appear transparent , how they are operationalized during deliberations remains unclear . increasingly , reimbursement systems are expressing interest in and/or implementing reimbursement policy options that extend beyond the traditional yes , no , or yes with restrictions options . such options typically require greater involvement of manufacturers which , to date , has been limited.conclusion:centralized reimbursement systems have become an important policy tool in many european countries . nevertheless , there remains a lack of transparency around critical elements , such as how multiple factors or criteria are weighed during committee deliberations .

INDIO, CA - Trial proceedings were expected to get underway starting Monday for an Indio man accused of murdering his girlfriend and dumping her body at an Indio golf course. Michael John Franco, 45, faces life without the possibility of parole for the alleged murder of Jill Grant, 41, a popular Palm Desert High School math teacher whose body was found at the Golf Club at Terra Lago in the early morning hours of Dec. 23, 2013. In addition to murder, Franco faces special circumstance allegations of inflicting torture on Grant and committing the murder in the commission of a felony, initially making him eligible for the death penalty. In August 2015, prosecutors decided not to pursue capital punishment against him. Franco also faces one felony count each of being a convicted felon in possession of a firearm and carrying a loaded firearm, and sentence-enhancing allegations of using a deadly weapon in the commission of a felony. Grant's body was found by golf course employees, who told Indio police that an SUV sped off from the scene, leaving tire marks along the course. Grant was found with numerous injuries; the criminal complaint lists a Toyota Prius and a box cutter as weapons used in the killing. Investigators said a search conducted the following day at Grant's residence in the 84-400 block of Onda Drive in Indio revealed blood on several items throughout the house and shoe prints consistent with impressions found at the crime scene, according to court records. Franco was taken into custody on Dec. 24, 2013 in Palm Desert. Police said in court documents that Franco had to be Tased before being taken into custody following "a short scuffle" and told police that he was trying to get to Mexico before they caught him. Franco remains held in lieu of $5 million bail. According to the criminal complaint, he was convicted of felony robbery in Alameda County in June 1990, but has no felony convictions in Riverside County. - City News Service / Image via Shutterstock ||||| Indio Police Department Indio Police Department INDIO, Calif. - A 44-year-old ex-con pleaded not guilty Thursday to murdering his girlfriend, a Coachella Valley native and popular Palm Desert High School math teacher. The body of Jill Grant, 41, was discovered in a dirt area near Golf Center Parkway and Avenue 42 in Indio on Dec. 23, 2013, and Michael John Franco of Indio was arrested in Palm Desert the following day. In addition to murder, Franco faces one felony count each of being a convicted felon in possession of a firearm and carrying a loaded firearm, and sentence-enhancing allegations of using a deadly weapon in the commission of a felony. He is scheduled to return to court for a trial-readiness conference on Feb. 2. Franco, who's being held in lieu of $5 million bail, was ordered to stand trial on Dec 3. Investigators found evidence at Grant's residence in the 84400 block of Onda Drive in Indio that linked her boyfriend to her death, an Indio Police Department spokesman alleged at the time of the defendant's arrest. Grant suffered multiple injuries; the criminal complaint lists a Toyota Prius and a box cutter as weapons used in the killing. Sherry Johnstone, assistant superintendent for personnel at the Desert Sands Unified School District, said in 2013 that Grant was ``a beloved teacher and part of the Desert Sands family for many years.'' ``We are grief-stricken -- students, faculty, staff ... Everyone loved Jill and this is a horrible tragedy,'' she said. Grant grew up in the Santa Rosa Mountains above Palm Springs and attended Palm Desert Middle School and Palm Desert High School, graduating in 1990. She attended College of the Desert, then transferred to Cal State San Bernardino, where she majored in mathematics. She taught math at Palm Springs High School for three years, starting in 1995, then began teaching at her alma mater in 1998. According to the criminal complaint, Franco was convicted of felony robbery in Alameda County in June 1990.

– Jill Grant and her boyfriend Michael Franco had planned to throw a party on Dec. 23, 2013. But when guests showed up to their gated neighborhood in Indio, Calif., they couldn't get in, and Franco told them the party was off. Grant's brother called police—who by that time had already recovered Grant's body. Prosecutors say Franco killed the 41-year-old high school math teacher, and the Desert Sun now reports that an inadvertent voicemail may have captured the final desperate moments of her life. Prosecutors allege Franco first cut his girlfriend's throat, then ran her over with a car and deposited her body at a nearby golf course; KESQ reports a box cutter and Toyota Prius are listed as the weapons used in the criminal complaint. The voicemail in question is one left by Franco's phone to a friend's number in an apparent butt dial, per court documents. Though the Desert Sun reports it's largely inaudible, Grant is heard saying this: "What if I drive the car someplace and call [911] myself and say I was attacked? Would that work? But we can think of something to say like (inaudible) ... What do you want me to say?" Among the other alleged evidence against Franco, who has pleaded not guilty: Franco took money out of an ATM using Grant's card on the night of her death, and when apprehended by police reportedly told them he was trying to flee to Mexico. A cell mate claims Franco confessed to him, saying Franco said he ran her over when she tried to get away from him. Palm Desert Patch reports he faces life without parole. (This man died after his 911 call was dismissed as a butt dial.)

dimension - free harnack inequality has been extensively studied ( see @xcite ) . it is first introduced by wang @xcite for diffusions on riemannian manifolds with curvature bounded below , then it is considered by aida and kawabi @xcite for some infinite dimensional diffusion processes ; rckner and wang @xcite for generalized mehler semigroup ; arnaudon et al . @xcite for diffusions on riemannian manifolds with curvature unbounded below ; wang @xcite for stochastic porous media equations ; da prato et al . @xcite for singular stochastic equations on hilbert spaces ; and the author et al . @xcite for ornstein - uhnelbeck processes with jumps in infinite dimensional spaces etc .. for the applications of harnack inequalities , we refer to @xcite for contractivity properties and functional inequalities ; @xcite for short time heat kernel estimates of infinite dimensional diffusions ; @xcite for regularizing properties ; and @xcite for heat kernel estimates etc .. in @xcite etc . harnack inequalities were proved via gradient estimate . in @xcite the method of coupling and giranov transformation ( @xcite ) was introduced . this method has been applied in @xcite etc .. in this paper , we adopt this method to establish harnack inequality for multivalued stochastic evolution equations which are generalization of the single valued and multivalued linear case considered respectively in @xcite . multivalued equations attracted the interest of many researchers recently . see kre @xcite , cpa @xcite , bensoussan and rascanu @xcite , cpa and lpingle @xcite , and zhang @xcite etc . and references therein . we prove harnack inequalities ( see theorem [ thm : msee ] ) and strong feller property ( see theorem [ thm : strongfeller ] ) of the invariant measure for the transition semigroup associated with the multivalued stochastic evolution equations in banach spaces in the framework of @xcite . as applications of the harnack inequalities , we prove the invariant measure is fully supported on the domain of the underlying multivalued maximal monotone operator ; and we study the hyperboundedness , ultraboundedness and compactness for the transition semigroup . we also get a log - harnack inequality and an entropy - cost inequality . we refer to theorem [ thm : application ] and theorem [ entropy_cost : loghi : msee ] for details . zhang ( * ? ? ? * theorem 5.8 ) has proved finiteness of the second moment of the invariant measure of the transition semigroup associated with evolution equations . we obtain stronger concentration properties of the invariant measure . see theorem [ thm : concentration : msee ] . the organization of this paper follows . we introduce the multivalued stochastic evolution equation in section [ sec : msee ] ; study the concentration property of the invariant measure in section [ sec : concentration : msee ] ; and prove harnack inequalities in section [ subsec : msee : hi ] ; then present the applications in section [ subsec : application : msee ] . we first recall the definition of multivalued maximal monotone operator . see for instance brzis @xcite for more details . denote by @xmath1 for the set of all subsets of @xmath2 . let @xmath3 be a set - valued operator . define the domain of @xmath4 by @xmath5 the multivalued operator @xmath4 is characterized by its graph defined by @xmath6 1 . a multivalued operator @xmath4 on @xmath2 is called monotone if @xmath7 2 . a monotone operator @xmath4 is called maximal monotone if it must be @xmath8 for any @xmath9 satisfying @xmath10 that is , @xmath4 is maximal monotone if its graph @xmath11 is not contained in the graph of any other monotone operator let @xmath12 be a separable and reflexive banach space which is continuously and densely embedded in a separable hilbert space @xmath2 . then we have an evolution triplet @xmath13 satisfying @xmath14 where @xmath15 is the dual space of @xmath12 and we identify @xmath2 with its own dual @xmath16 . denote by @xmath17 , @xmath18 , @xmath19 the norms in @xmath12 , @xmath2 and @xmath15 respectively ; by @xmath20 the inner product in , and @xmath21 the dual relation between @xmath12 and @xmath15 . in particular , if @xmath22 and @xmath23 , then @xmath24 let @xmath4 be a multivalued maximal monotone operator on @xmath2 . we introduce two sets for every @xmath25 : 1 . @xmath26 : the set of all @xmath2-valued functions of finite variation on @xmath27 $ ] . @xmath28 : the space of all @xmath29 $ ] such that @xmath30 ; \overline{d(a)})$ ] , @xmath31 with @xmath32 , and for all @xmath33,{\ensuremath{\mathds{h}}\xspace})$ ] satisfying @xmath34 , the measure @xmath35 let @xmath36 be a cylindrical wiener process on @xmath2 with respect to a filtered probability space @xmath37 . let @xmath38 be a single valued operator from @xmath12 to @xmath15 ; and @xmath39 an operator from @xmath40 to @xmath41 . consider the following multivalued stochastic evolution equation@xmath42 [ def : sol : mssee ] a pair of @xmath43-adapted random processes @xmath44 is called a solution of equation if 1 . @xmath45\in \mathscr{a}_{t}$ ] for almost all @xmath46 ; 2 . for some @xmath47 , @xmath48 ; { \ensuremath{\mathds{v}}\xspace})$ ] for almost all @xmath46 it holds for all @xmath49 $ ] almost surely @xmath50 the following theorem on the existence and uniqueness of the equation is due to zhang ( * ? ? ? * theorem 4.6 ) . [ msee : solution : existence ] assume the following conditions . ( h1 ) : : ( h2 ) : : ( h3 ) : : ( h4 ) : : ( h5 ) : : ( h6 ) : : then there exists a unique solution to equation in the sense of definition [ def : sol : mssee ] . the following proposition will play an important role . see zhang ( * ? ? * proposition 3.3 ) for a proof . [ hi : msee : crucialprop ] let @xmath51 , [ \tilde{u},\widetilde{k}]\in \mathscr{a}_{t}$ ] . then the measure @xmath52 .\ ] ] suppose that conditions hold . by theorem [ msee : solution : existence ] , equation has a unique solution @xmath53 . define @xmath54 for every @xmath55 $ ] , @xmath56 . let @xmath39 be deterministic and time independent . then @xmath57 is a markov semigroup ( see ( * ? ? ? * theorem 5.5 ) ) . zhang ( * ? ? ? * theorem 5.8 ) has studied the the existence , uniqueness of the invariant measure associated with @xmath57 . he also proved that the invariant measure @xmath58 satisfies @xmath59 we prove a stronger concentration properties . [ thm : concentration : msee ] assume that hold with @xmath60 . let @xmath39 be deterministic and independent of time . assume further that @xmath12 is compactly embedded in @xmath2 . if @xmath61 , then suppose in addition that @xmath39 is uniformly bounded and @xmath62 , where @xmath63 is the constant such that @xmath64 . then there exist an invariant measure associated with @xmath57 in the sense that @xmath65 moreover , @xmath66 if @xmath39 is uniformly bounded , then for every @xmath60 , there exist some @xmath67 such that @xmath68 \(1 ) the existence of the invariant measures has been proved in ( * ? ? ? * theorem 5.8 ( i ) ) for the case @xmath69 . the extension to the case @xmath61 is not hard . we skip the proof here since the main technique can be found below . \(2 ) from ( h3 ) we know for all @xmath70 , @xmath71 if @xmath61 , then @xmath72 if @xmath69 , then by young s inequality , @xmath73 hold for every @xmath74 , where @xmath75 satisfying @xmath76 . use the estimate and in for @xmath61 and @xmath69 ( by taking @xmath77 small enough in this case ) respectively , we know there are constants @xmath78 such that @xmath79 by young s inequality again , we know for any @xmath80 , @xmath81 where @xmath82 . therefore , we deduce from and by taking @xmath83 small enough to get @xmath84 for some constant @xmath85 . now we fix a @xmath86 . let @xmath87 be the solution to the multivalued stochastic evolution equation . by definition , we have @xmath88 by it s formula , using and and young s inequality again , we obtain @xmath89 where @xmath90 are some constants . in the calculation of we also used young s inequality to get control from @xmath91 if @xmath92 is strictly greater than 2 . if @xmath61 , we use the assumption that @xmath39 uniformly bounded . therefore , by , we get @xmath93 consequently we have @xmath94 hence we obtain @xmath95 this proves . \(3 ) for every @xmath67 , by we have @xmath96 for some constant @xmath97 and some local martingale @xmath98 . since @xmath64 , for small enough @xmath99 , we have @xmath100 let us focus at the drift of the right hand of . by the fact @xmath64 and young s inequality , @xmath101 for some constant @xmath102 . now let @xmath103 note that on @xmath104 , both @xmath105 and @xmath106 are bounded . therefore @xmath107 for some constant @xmath108 . hence from and , we can get an estimate of the drift of the right hand side of . that is , @xmath109 by integrating the inequality from 0 to @xmath110 , we get @xmath111 then we take expectation for both side of with respect to @xmath112 , we get @xmath113 it follows that @xmath114 where @xmath115 note that @xmath58 is the weak limit of @xmath116 ( refer to the proof of @xcite ) , we can deduce from to get @xmath117 this proves . in the following we assume conditions in theorem [ msee : solution : existence ] and instead of we suppose that ( h6@xmath118 ) : : for every @xmath119 , define @xmath120 the distance associated with @xmath121 is called the intrinsic distance induced by @xmath122 . we are going to prove the following harnack inequality for the semigroup @xmath57 associated with the solution process of equation . [ thm : msee ] assume and . suppose that there exists some nonnegative constant @xmath123 , and some strictly positive continuous function @xmath124 on @xmath125 such that @xmath126 holds on @xmath127 . then for every @xmath25 , @xmath128 , @xmath129 and @xmath130 , the following inequality holds @xmath131 where @xmath132 with @xmath133 assume the diffusion coefficient @xmath39 is independent of @xmath134 and the function @xmath124 in is taken as constant @xmath135 . then holds with @xmath136 replaced by @xmath137^{-\frac{4+r}{2+r}}.\ ] ] the proof is divided into six steps . we outline the main procedure of the proof of in the first step and then realize the idea in the next four steps . the simplification from to is obtained in the last step . \(1 ) _ main idea_. consider the following coupled multivalued stochastic evolution equation [ coupledequ : msee1 ] dx_t - ax_tdt + bx_tdt+(t)dw_t- u_tdt , [ coupledequ : msee11 ] + dy_t - ay_tdt + by_tdt+ ( t)dw_t[coupledequ : msee12 ] with initial conditions @xmath138 and the drift @xmath139 in is of the following form @xmath140 where the stopping time @xmath141 in is the coupling time of @xmath53 and @xmath142 defined by @xmath143 the power @xmath144 in is a constant in @xmath145 ( see ) and @xmath146 is a deterministic function on @xmath125 . both @xmath144 and @xmath146 in will be specified later such that the following two crucial conditions @xmath147 and @xmath148 are satisfied . let @xmath149 by we know @xmath150_t \right ) , \quad t\in[0,t]\ ] ] is a martingale on @xmath151 . then we can define a new probability measure @xmath152 on @xmath153 by setting @xmath154 by girsanov s theorem , @xmath155 is still a cylindrical wiener process on @xmath156 . hence equation can be rewritten in the following way @xmath157 with initial condition @xmath158 . by the uniqueness of the solution , the transition law of @xmath159}$ ] under @xmath152 is the same with the transition law of @xmath160}$ ] under @xmath161 . so by the fact which will be verified , we have @xmath162 note that we also have @xmath163 therefore by applying hlder s inequality to , we get @xmath164 then the proof is completed by estimating @xmath165 . \(2 ) _ existence of the solution of the coupled equation _ . note that the function @xmath166 satisfies the monotone condition off the diagonal ( see ( * ? ? ? * appendix a ) ) . by applying theorem [ msee : solution : existence ] we see the coupled equation has a solution up to the coupling time @xmath141 . so there exists continuous processes @xmath167 and @xmath168 such that for all @xmath169 , [ integralcoupledequ : msee ] x_t = x - k_t+_0^t bx_sds + _ 0^t(s ) dw_s-_0^t u_sds , [ integralcoupledequ : mseea ] + y_t = y-_t+_0^t by_sds + _ 0^t(s ) dw_s . [ integralcoupledequ : mseeb ] on the other hand , it is obvious that the solution of equation ( or equivalently , equation ) can be extended to be a solution for all time @xmath55 $ ] . let @xmath170 solves equation . now we get solution of equation ( or ) by defining @xmath171 , @xmath172 for all @xmath173 . \(3 ) _ verify _ . apply it s formula ( see e.g. @xcite ) or zhang ( * ? ? ? * theorem a.1 ) etc . ) to @xmath174 and then let @xmath175 , by using condition ( h4 ) we have for @xmath169 @xmath176 by proposition [ hi : msee : crucialprop ] , for all @xmath169 we have @xmath177 then @xmath178 hence by we get @xmath179 we take @xmath180 with @xmath181 it must be @xmath182 and hence @xmath183 . otherwise , if @xmath184 , by taking integral from 0 to @xmath185 for both sides of the inequality , we can obtain @xmath186 by the right hand side of equals to 0 . so we can conclude @xmath183 from . but this is contradict with the assumption that @xmath184 . \(4 ) _ verify _ . from and the assumption we can get for all @xmath187 @xmath188 let @xmath144 be defined as in . then from we get @xmath189 according to , we have @xmath190 . now by integrating both sides of the inequality from @xmath191 to @xmath185 , we get ( note that @xmath183 ) @xmath192 by hlder s inequality , we have @xmath193 note that @xmath194 we obtain @xmath195 now it is clear that holds . \(5 ) _ estimate of @xmath196_. denote @xmath197 . since @xmath198 is a @xmath161-martingale , for any @xmath199 with @xmath200 , we have @xmath201_t\right ) \exp\left(\frac{1}{2}\beta(\beta p-1)[n]_t\right)\\ \leq & \left[\e_{\p}\exp\left(p\beta n_t-\frac{1}{2}p^2\beta^2[n]_t\right)\right]^{1/p}\cdot \left[\e_{\p}\exp\left(\frac{1}{2}\beta q(\beta p-1)[n]_t\right)\right]^{1/q}\\ = & \left[\e_{\p}\exp\left(\frac{1}{2}\beta q(\beta p-1)[n]_t\right)\right]^{1/q}. \end{split}\ ] ] hence we get by using the estimate and letting @xmath202 go to 1 . \(6 ) suppose that @xmath39 is independent of @xmath134 . and we take @xmath124 in as a constant @xmath135 . then we can simplify @xmath136 as follows . @xmath203^{-\frac{4+r}{2+r } } \\ = & 4\delta^{-1 } \gamma^{-\frac{2}{2+r } } \zeta^{-\frac{4}{2+r } } \left[\omega^{-1}(1-\operatorname{e}^{-\delta \omega t } ) \right]^{-\frac{4+r}{2+r } } = \widetilde{\theta}_{t } \end{aligned}\ ] ] we refer to ( * ? ? ? * corollary 1.3 ) for sufficient conditions for . consider the following multivalued stochastic differential equation on @xmath204 @xmath205 where @xmath4 is a maximal monotone operator on @xmath206 with @xmath207 , @xmath36 is a wiener process on a filtered probability space @xmath208 , @xmath209 is a continuous function such that there exists some @xmath210 @xmath211 then by ( * ? ? ? * thorem 2.8 ) , the solution @xmath53 exists . for the transition semigroup @xmath212 associated with @xmath213 , we have @xmath214 for every @xmath215 , @xmath128 , @xmath129 and @xmath130 . the proof is similar to the proof of theorem [ thm : msee ] except that we choose another simpler drift . that is , instead of , we consider the following coupled equations [ hi : msde : couple : monotonic ] dx_t+ax_tdt dw_t+b(x_t)dt- _ t |x - y| _ \{t < } dt , [ hi : msde : couple : monotonic1 ] + dy_t+ay_tdt dw_t+b(y_t)dt , [ hi : msde : couple : monotonic2 ] with initial data @xmath158 and @xmath216 , where @xmath141 is the coupling time of @xmath53 and @xmath142 and @xmath217 zhang ( * ? ? ? * corollary 5.3 ) studied feller property of @xmath57 . we prove strong feller property for @xmath57 under additional conditions . [ thm : strongfeller ] assume , and with @xmath218 . then the semigroup @xmath57 is strongly feller and the following estimate holds @xmath219 for every @xmath215 , @xmath220 and @xmath221 . moreover , if the invariant measure @xmath58 exist , then for every @xmath222 in @xmath223 with @xmath224 , @xmath225 is continuous on @xmath226 . the last statement follows directly from the harnack inequality by applying ( * ? ? ? * proposition 4.1 ) . we only need to show the estimate . we follow the notation in the proof of theorem [ thm : msee ] . by , we see @xmath227 it is clear @xmath228 by , we know @xmath229 using the elementary inequality @xmath230 , @xmath231 , we can deduce from and to get @xmath232 substitute the estimate above into we can obtain . [ thm : application ] assume , , , @xmath39 is independent of @xmath134 and the invariant measure @xmath58 of the semigroup @xmath57 exist . then 1 . the invariant measure @xmath58 is fully supported on @xmath233 . 2 . for every @xmath234 , @xmath215 , the transition density @xmath235 ( with respect to @xmath58 ) exist and for every @xmath128 @xmath236^{-(\alpha-1)/\alpha}.\ ] ] 3 . suppose @xmath237 . 1 . if @xmath61 and @xmath62 , where @xmath63 is the constant such that @xmath64 , then @xmath57 is hyperbounded . 2 . if @xmath69 , then @xmath57 is ultrabounded . more precisely , there exist some constant @xmath238 such that @xmath239 + consequently , @xmath57 is compact for large @xmath215 for both cases . \(1 ) if @xmath240 , then there exists some @xmath241 and @xmath242 such that @xmath243 , where @xmath244 . applying to the function @xmath245 for @xmath246 and @xmath247 , we have @xmath248 hence , by integrating both sides of with respect to @xmath249 , we obtain @xmath250 this implies @xmath251 for all @xmath247 . therefore , @xmath252 where @xmath253 denotes the solution to with @xmath254 . since @xmath53 is continuous on @xmath2 , by letting @xmath255 in , we have @xmath256 but obviously this is impossible . so it must be @xmath257 . \(2 ) we refer to @xcite or @xcite for the idea of the proof . \(3 ) since @xmath237 , for any @xmath258 , we know @xmath259 therefore , by theorem [ thm : msee ] , there exist some constant @xmath260 such that for every @xmath261 and @xmath262 , @xmath263 where @xmath264 with @xmath265 . by integrating both sides of with respect to @xmath249 over @xmath266 , we see for every @xmath267 and @xmath262 , @xmath268 \(i ) if @xmath61 , then by taking square and integration with respect to @xmath269 for both sides of the equation , and using theorem [ thm : concentration : msee ] , we have @xmath270 for @xmath215 big enough . this proves @xmath271 for sufficiently big @xmath215 . that is , @xmath57 is hyperbounded . \(ii ) assume @xmath69 . then the inequality implies @xmath272 for some constant @xmath273 . let @xmath274 be the solution to the following equation @xmath275^{\frac{2(q-1)}{q } } \right ) \,dt\ ] ] with @xmath276 . by the comparison theorem , we have @xmath277 for some constant @xmath278 . by inequality we have @xmath279\ ] ] for some constants @xmath280 . by using young s inequality , we see @xmath281 \leq \varepsilon \cdot |x_{t/2}^{x}|_{{\ensuremath{\mathds{h}}\xspace}}^{q } + \varepsilon ' t^{-\frac{q}{q-2}}\ ] ] for arbitrary @xmath74 . by considering small enough @xmath74 , it follows from the inequality above and and we can obtain . this proves that @xmath57 is ultrabounded . since @xmath57 has transition density with respect to @xmath58 , we know @xmath57 is compact in @xmath282 for large @xmath215 for these two cases ( @xmath61 or @xmath69 ) by ( * ? ? ? * lemma 3.1 ) . by ( * ? ? ? * section 2 ) , we can get some heat kernel inequalities from harnack inequality . especially we have the following log - harnack inequality and an entropy - cost type inequality . [ entropy_cost : loghi : msee ] assume , and with @xmath218 . then 1 . for every @xmath25 , @xmath129 , @xmath283 , and @xmath284 @xmath285 2 . for every @xmath25 , @xmath286 such that @xmath287 , @xmath288 where @xmath289 denotes all the coupling of @xmath58 and @xmath290 . inequality follows as ( * ? ? ? * proposition 2.2 ) . integrating both sides of with respect to @xmath291 , and minimizing in @xmath292 , we get @xmath293 now we obtain by noting @xmath294 due to the fact that @xmath58 is invariant for @xmath212 and @xmath295 . this work was supported in part by the dfg through the international graduate college stochastics and real world models " . the author would like to thank the encouragement of professors michael rckner and feng - yu wang . s. aida , h. kawabi , short time asymptotics of a certain infinite dimensional diffusion process , in : l. desreusefond , b. ksendal , a. s. stnel ( eds . ) , stochastic analysis and related topics , vii ( kusadasi , 1998 ) , vol . 48 of progr . birkhuser boston , boston , ma , 2001 , pp . 77124 . h. brzis , oprateurs maximaux monotones et semi - groupes de contractions dans les espaces de hilbert , north - holland publishing co. , amsterdam , 1973 , north - holland mathematics studies , no . 5 . notas de matemtica ( 50 ) . n.v . krylov , b. l. rozovskii , stochastic evolution equations , in : stochastic differential equations : theory and applications , vol . 2 of interdiscip . sci . , world sci . publ . , hackensack , nj , 2007 , pp . 169 . ouyang , harnack inequalities and applications for stochastic equations , ph.d . thesis , bielefeld university , 2009 , available on http://bieson.ub.uni- bielefeld.de / volltexte/2009/1463/pdf / ouyang.pdf[http://bieson.ub.uni- bielefeld.de/volltexte/2009/1463/pdf/ouyang.pdf ] .

by the method of coupling and girsanov transformation , harnack inequalities [ f .- y . wang , 1997 ] and strong feller property are proved for the transition semigroup associated with the multivalued stochastic evolution equation on a gelfand triple . the concentration property of the invariant measure for the semigroup is investigated . as applications of harnack inequalities , explicit upper bounds of the @xmath0-norm of the density , contractivity , compactness and entropy - cost inequality for the semigroup are also presented . * ams subject classification ( 2000 ) * : 60h15 , 47d07 , 37l40 * keywords * : harnack inequality , multivalued stochastic evolution equation , invariant measure , contractivity

there is a growing number of deterministic models of quantum mechanical objects which are based on conjectured fundamental information loss or dissipation mechanisms @xcite . these studies are largely motivated by the unresolved issues surrounding `` quantum gravity '' , i.e. , by the conflict between quantum mechanics necessitating an external time and diffeomorphism invariance in general relativity , for example , which defies its existence . furthermore , despite its great successes in describing the statistical aspects of experiments , quantum theory itself presents problems of interpretation , which arise from its indeterministic features and which are clearly seen , for example , in the unresolved measurement problem ( also `` wave function collapse '' or `` objective reduction '' ) . thus , concerning the foundations of quantum mechanics , there is an increasing impetus to try to reconstruct and to better understand the emergence of quantum mechanics from simpler structures beneath . so far , the construction of models has proceeded case by case . it is guided by the idea that quantum states may actually represent large equivalence classes of deterministically evolving `` classical '' states which become indistinguishable when affected by the conjectured information loss or dissipative process @xcite . furthermore , t hooft s existence theorem @xcite shows that generally the evolution of all quantum mechanical objects that are characterized by a finite dimensional hilbert space can be captured by a dissipative process . this has recently been generalized for objects which are described by a set of mutually commuting hermitian operators @xcite , i.e. , for the case of a finite set of _ beables _ @xcite . for completeness , we review these results in the appendix . however , it has not been shown before how to complement the existence theorem by a dynamical theory . in order to describe the quantum mechanical world around us , such a theory has to deal with interacting as well as approximately isolated objects that exist throughout a large range of length and energy scales . we make a step in this direction , by showing that familiar aspects of quantum mechanics can be generated by an attractor mechanism , which is obtained by a generalization of the classical liouville equation . this will lead us to emerging quantum states which evolve according to the schrdinger picture embodied in the vonneumann equation , to the born rule , and to the randall - sundrum energy - parity symmetry , which may protect the cosmological constant against far too large corrections , which otherwise should be determined by particle physics scales @xcite . for simplicity , we consider objects with a single continuous degree of freedom . however , it is straightforward to repeat the following derivations for interacting few - body systems and fields . to begin with , we assume that there are only conservative forces and that hamilton s equations are determined by the generic hamiltonian function : @xmath0 defined in terms of generalized coordinate @xmath1 and momentum @xmath2 , and where @xmath3 denotes the potential . an ensemble of such objects , for example , following trajectories with different initial conditions , is described by a distribution function @xmath4 in phase space , i.e. , by the probability @xmath5 to find a member of the ensemble in an infinitesimal volume at point @xmath6 . this distribution evolves according to the liouville equation : @xmath7 with @xmath8 . a fourier transformation , @xmath9 , replaces the liouville equation by : @xmath10 without changing the symbol for the distribution function , whenever changing variables . thus , momentum is eliminated in favour of _ doubling _ the number of coordinates . finally , with the transformation : @xmath11 we obtain the liouville equation in the form : @xmath12 \label{hx } \hat h_\chi & : = & -\frac{1}{2}\partial_\chi ^{\;2}+v(\chi ) \;\ ; , \;\;\;\mbox{for}\;\;\chi = q , q \;\ ; , \\ [ 1ex ] \label{i } \delta ( q , q)&:=&(q - q)v'(\frac{q+q}{2 } ) -v(q)+v(q)\;=\;-\delta ( q , q ) \;\;. \end{aligned}\ ] ] several comments are in order here : * the presented reformulation of classical dynamics is rather independent of the number of degrees of freedom . it applies to matrix valued as well as to grassmann valued variables , representing the `` pseudoclassical '' fermion fields introduced by casalbuoni and by berezin and marinov . field theories require the classical functional formalism employed previously in a related context @xcite . gauge theories or , generally , theories with constraints have to be examined carefully . + * the eq.([schroed ] ) appears as the _ vonneumann equation _ for a density operator @xmath13 , considering @xmath14 as its matrix elements . however , a crucial difference is found in the interaction @xmath15 between the _ bra- _ and _ ket- _ states . the related hilbert space and its dual , therefore are coupled , unlike the case of quantum mechanics . + * alternatively , the eq.([schroed ] ) might be read as the _ schrdinger equation _ for two identical ( sets of ) degrees of freedom . however , their respective hamilton operators , @xmath16 , contribute with opposite sign . since their interaction @xmath15 is antisymmetric under @xmath17 , the complete ( liouville ) operator on the right - hand side of eq.([schroed ] ) has a symmetric spectrum with respect to zero and , generically , will not be bounded below . this _ kaplan - sundrum energy parity symmetry _ has been invoked before as a protection for a ( near ) zero cosmological constant which , otherwise , is threatened by many orders of magnitude too large zeropoint energies @xcite . only for free particle or harmonic oscillator @xmath15 vanishes . generally , with a coupling of the hilbert space and its dual , or without a stable ground state , our reformulation of hamiltonian dynamics does not qualify as a quantum theory . the problem of a missing ground state , sometimes in disguise , has been the stumbling block in previous attempts at deterministic model building for quantum objects and has been overcome only in individual examples @xcite . based on hamilton s equations , we have seen that deterministic ensemble theories imply the absence of a lowest energy state , when suitably rewritten in the form of a schrdinger equation ( or functional schrdinger equation for field theories ) . on the other hand , a dissipative process was of paramount importance in the proof of existence of deterministic models for quantum mechanical objects , as reviewed in the appendix . in the following , we shall make use of these hints . we propose an attractor mechanism that turns deterministic evolution , described by an ensemble theory as in section2 . , into the schrdinger evolution of quantum states , based on a stable ground state . our construction refers particularly to two assumptions : + ( a ) _ the emergence of quantum states originates from a microscopic process beneath which applies to all physical objects . _ + ( b ) _ the statistical interpretation of quantum states ( born rule ) originates from the classical ensemble theory . _ we begin with the normalization of the classical probability distribution : @xmath18 incorporating the transformations of section2 . consider a complete set of orthonormal eigenfunctions of the operator @xmath19 of eq.([hx ] ) , defined by @xmath20 and @xmath21 , respectively , with a discrete spectrum , for simplicity . then , we may expand @xmath4 : @xmath22 employing this , the normalization condition ( [ clnorm ] ) can be stated as : @xmath23 since the classical phase space distribution is real , the expansion coefficients form a hermitean matrix , @xmath24 , which we also denote by @xmath25 . the _ classical _ expectation values are calculated as follows : @xmath26 \label{xexpect1 } & = : & \mbox{tr}\;\big ( \hat x\hat f(t)\big ) \;\ ; , \\ [ 1ex ] \label{pexpect } \langle p\rangle : = \int\frac{\mbox{d}x\mbox{d}p}{2\pi}\;pf(x , p;t ) & = & \int\mbox{d}q\mbox{d}q\;\delta ( q - q)(-i)\frac{\partial_q-\partial_q}{2}f(q , q;t ) \;\ ; , \\ [ 1ex ] \label{pexpect1 } & = : & \mbox{tr}\;\big ( \hat p\hat f(t)\big ) \;\ ; , \end{aligned}\ ] ] introducing the operators @xmath27 and @xmath28 , with matrix elements @xmath29 and @xmath30 ( derivatives act left or right , as indicated ) . eliminating one of the two integrations in the above equations with the help of the @xmath31-functions and suitable partial integrations , these operators are recognized as the coordinate and momentum operators of quantum theory . we also find , for example : @xmath32 where the cancelling imaginary terms stem from the first and second term on the left - hand side , respectively , which both contribute equally to the integral . operators appear here strictly by rewriting classical statistical formulae and _ not by a quantization rule _ , such as replacing @xmath1 and @xmath2 by operators @xmath27 and @xmath28 , with @xmath33=i$ ] , acting on a hilbert space ( not necessarily related to phase space ) . furthermore , the eqs.([clnorm ] ) , ( [ xexpect])([noncommops ] ) are in accordance with the interpretation of @xmath14 as matrix elements of a density operator @xmath13 . however , there is an important _ caveat _ : the eigenvalues of normalized quantum mechanical density operators are usually constrained to lie between zero and one , corresponding to the interpretation as standard probabilities . this is not necessarily the case with the operator @xmath25 obtained from a classical probability distribution . similarly , the wigner distribution obtained from the matrix elements of a quantum mechanical density operator by applying the transformations leading from @xmath34 to @xmath35 in reverse generally , is not positive semi - definite on phase space , even though its marginal distributions are . therefore , it does not necessarily qualify as a classical probability density . the discussion of negative or larger - than - one probabilities is beyond the scope of the present article ; we refer to the literature for arguments that make sense of them , see , for example , refs . however , we anticipate that the proper quantum mechanical aspects of the states shall emerge dynamically , see section3.3 . we will point out in the following , where the restriction to probabilities that lie in the interval @xmath36 $ ] arises . thus , the application of operators here , together with the density operator in particular , constitute examples for the _ born rule _ , once they are complemented by a suitable dynamical framework . we will propose a generalization of the conservative classical dynamics described by eqs.([schroed])([i ] ) that incorporates dissipation as well as diffusion . for sufficiently long times , the evolving density operator should be attracted to solutions of the quantum mechanical vonneumann equation : @xmath37 \;\;.\ ] ] equivalently , the expansion coefficients @xmath38 in eq.([fexpans ] ) should become constants . employing this expansion , generally , the eq.([schroed ] ) can be rewritten as matrix equation for the coefficients : @xmath39 with the interaction double matrix @xmath40 defined by : @xmath41 employing the antisymmetry of @xmath15 , eq.([i ] ) . consequently , @xmath42 maps a hermitean matrix , such as @xmath25 , to a hermitean matrix . this map produces zero when taking the trace , @xmath43 , for any matrix @xmath44 , since : @xmath45 by definition ( [ deltamatrix ] ) , completeness , and eq.([i ] ) . for example , the solution of eq.([schroedcoeff ] ) , @xmath46 , conserves the normalization of @xmath25 , eq.([clnorm1 ] ) . the interaction @xmath15 presents the unfamiliar coupling between hilbert space and its dual , which prevented us from considering eq.([schroed ] ) as a truly quantum mechanical equation . we will now present some heuristic considerations which entail important modifications of the deterministic ensemble theory . for very small intervals , spacetime itself may be thought to have atomistic structure and dynamics , as discussed , for example , in terms of classical _ causal sets_. such a locally finite ordered set evolves by sequential growth , i.e. , by the random ( `` sprinkling '' ) appearance of new set elements @xcite . consider a `` hypersurface '' formed by the set elements that have no successors i.e. , which do not precede any other set elements , according to the causal order relation at a certain stage of the evolution . furthermore , consider the probability distribution @xmath4 of our coarse grained phase space picture and , in particular , the amount of probability that resides in the volume @xmath47 corresponding to @xmath48 arbitrarily chosen elements in this hypersurface . following further growth , with a sufficiently large number of new elements added to the causal set , we pick those @xmath49 elements from the evolved hypersurface that either have ancestors among the previously chosen @xmath48 elements or that are among the previously chosen elements and have not become ancestor to any new element . if @xmath50 , this induces a change of probability density , if the amount of probability is conserved , as the volume evolves correspondingly , @xmath51 . comparing two different choices of the @xmath48 elements , say subsets @xmath52 and @xmath53 of the considered hypersurface , the corresponding values @xmath54 and @xmath55 , generally , will differ , due to the random growth of the causal set . this induces random fluctuations in the probability density . we represent the induced fluctuations by a homogeneous stochastic term @xmath56 contributing to the right - hand side of eq.([liouvilleeq ] ) . we shall see shortly that it leads to _ relatively , such fluctuations become less important , i.e. , typical fluctuations decrease , as the discrete spacetime associated with the growing causal set continues to evolve , supposedly towards a continuum limit . accordingly , we treat @xmath57 as a random variable , with distribution @xmath58 and @xmath59 an energy scale . variability ( `` aging '' ) of @xmath59 , incorporating an initial cut - off of the width , for example , is neglected . furthermore , the evolution of @xmath4 must be modified by _ diffusion _ , caused by the randomly growing structure beneath @xcite . somehow reminding of _ galton s board _ , additional causal set elements keep appearing on which a moving phase space distribution `` scatters '' and , thus , spreads into different microscopic evolutionary paths . asymptotically , diffusion and dissipation may balance each other in such a way that probability is conserved , resulting in a hermitian matrix @xmath60 , with unit trace , to which @xmath25 must be attracted . these effects are incorporated in our minimalist model : @xmath61 which generalizes eq.([schroedcoeff ] ) . the dissipative term stems from @xmath62 entering the right - hand side of eq.([schroed ] ) , which means adding @xmath63 in eq.([schroedcoeff ] ) . together with its prefactors , the matrix @xmath60 enters as a source term here . the solution of the linear first order eq.([schroedcoeff1 ] ) is : @xmath64 averaging over the gaussian fluctuations @xmath57 gives : @xmath65 \label{fdisssol1 } & = & \hat g(t)+\mbox{e}^{-i(\hat\delta -i\epsilon ) t}\big ( \hat f(0)-\hat g(0)\big ) -\int_0^t\mbox{d}s\;\mbox{e}^{-i(\hat\delta -i\epsilon ) ( t - s)}\partial_s\hat g(s ) \;\ ; , \end{aligned}\ ] ] which shows the nonunitary dissipative decay caused by the fluctuations . taking the trace of eq.([fdisssol ] ) or ( [ fdisssol1 ] ) , with the help of eq.([trzero ] ) and with @xmath66 , however , we find that probability is conserved , i.e. , the normalization @xmath67 , provided that @xmath68 . thus , the source term compensates the dissipative loss . furthermore , if @xmath69 becomes constant sufficiently fast , for large @xmath70 , then @xmath71 , asymptotically . in this limit , dissipation effectively eliminates the coupling @xmath15 and our simplistic account of dissipation / diffusion leads to constant matrix elements @xmath72 . via eq.([fexpans ] ) , this implies that the vonneumann eq.([vonneumann ] ) becomes a valid approximation for sufficiently large @xmath73 ; i.e. , in this limit _ quantum theory _ will be recovered . however , we still need a relation between the matrices @xmath69 and @xmath13 , in order to complete the dynamical model and to take into account that the properties of common quantum mechanical objects are highly reproducible . the minimalist model of eq.([schroedcoeff1 ] ) is completed by a nonlinear equation for the source matrix @xmath60 : @xmath74 with @xmath75 a time scale and @xmath76 . this equation is structurally similar to nonlinear wave equations that have been considered as extensions of the schrdinger equation , incorporating dissipation or measurement processes into quantum mechanics @xcite . however , presently we consider it as a phenomenological description of how following a measurement or state preparation the source evolves . the diffusive effects , alluded to before , are assumed to result in a source term which reflects the initial condition of the classical theory , represented by @xmath77 . the solution of eq.([nonling ] ) is given simply by : @xmath78 this implies @xmath68 , as needed for the conservation of probability . for all times , the matrix @xmath69 can be diagonalized by the unitary transformation which diagonalizes the hermitian matrix @xmath77 , @xmath79 . furthermore , for _ all _ finite initial @xmath77 , the eigenvalues of the matrix @xmath69 are positive and , by its unit trace , constrained to lie in @xmath36 $ ] . in particular , note that initially @xmath80 , i.e. , the matrix starts out with a homogeneous distribution of eigenvalues ( with a regularization to be implemented ) . this gives no preference to any energy eigenstate , recalling that we are working with the basis of eigenstates of the operator @xmath19 , cf . section3.1 . however , for sufficiently large times , the diagonalized matrix @xmath81 approaches exponentially fast an onedimensional _ projector _ @xmath28 : @xmath82 \label{projector1 } & \longrightarrow&\;\;\mbox{diag}\left ( 0,\;\dots , 1,0,\;\dots\ ; \right ) \;=:\hat p \;\ ; , \end{aligned}\ ] ] where the only novanishing entry appears in the position of the largest eigenvalue of @xmath83 , @xmath84 , assuming that it is not degenerate , for simplicity . this particular position is indicated by @xmath85 , for example , in @xmath86 . we recall from the previous section3.2 . that the time dependent matrix @xmath25 of expansion coefficients of eq.([fexpans ] ) is attracted to the asymptotic value of the source matrix @xmath60 , for sufficiently large @xmath73 . undoing the diagonalizing transformation , which depends on @xmath77 , we obtain : @xmath87 thus , if @xmath77 is diagonal , corresponding to @xmath88 , then the distribution @xmath4 of eq.([fexpans ] ) is attracted to become a _ density matrix representing a stationary state _ : @xmath89 which presents a solution of the vonneumann equation ( [ vonneumann ] ) with @xmath90 . all diagonal @xmath77 that have their largest eigenvalue in the same position ( refering to the chosen basis ) , and which are related to classical phase space distributions via eq.([fexpans ] ) , lead to the same density matrix . in this precise sense , a stationary _ quantum state represents a large equivalence class of classical distributions_. more generally , if @xmath77 is not diagonal , corresponding to @xmath91 , then the distribution @xmath4 is attracted to become a _ density matrix representing a pure state _ : @xmath92 also a solution of eq.([vonneumann ] ) , this includes superpositions of stationary states , which are again seen as representing large equivalence classes of classical distributions . finally , mixed states are formed by ensembles of pure states . thus , the quantum states emerge asymtotically , exponentially fast . they are represented by properly normalized density matrices with eigenvalues in @xmath36 $ ] , which agrees with the standard probability interpretation . however , this does not exclude initial phase space distributions @xmath4 which assume nonstandard values according to the underlying ensemble theory , cf . here we share a pragmatic point of view : due to the normalization of a phase space distribution @xmath4 , any negative or larger - than - one probability must be compensated so that the sum over all alternatives of events , to which probabilities are assigned , equals one . therefore , it must be possible to perform a coarse graining , i.e. , a re - partitioning of the set of alternatives , such that nonstandard probabilities are avoided altogether . this amounts to a partitioning of the space of events , e.g. , phase space , corresponding to independent alternatives which , in principle , are the ones that can be explored experimentally @xcite . in order to address such issues in detail , a microscopic theory is needed of dissipation and diffusion , due to spacetime fluctuations , and an understanding of how a measurement or state preparation fixes an initial @xmath77 or an equivalence class of such initial state matrices . this may lead to new insights concerning the measurement problem . its solution must transcend quantum theory , in its usual formulation , as is well known . in particular , the stochastic nature of measurement results might be related to the fact that quantum states represent large equivalence classes of classical phase space distributions , as we have seen , rather than ontological `` elements of reality '' . we have generalized liouville s phase space equation for hamiltonian systems by incorporating an attractor mechanism , comprising a homogeneous stochastic term and a source term . the latter compensates dynamically the dissipative loss of information induced by the former . for suitably chosen variables , this classical model can be cast into the form of eqs.([schroedcoeff1 ] ) and ( [ nonling ] ) . its solutions are attracted to density matrices which solve the vonneumann equation . with respect to the classical ensemble theory , these quantum states are recognized as large equivalence classes of states with varying initial conditions . motivated by the assumption of an atomistic structure of spacetime such as represented by a causal set our model reflects the question : does quantum mechanics originate , as a phenomenon of coarse graining , from fluctuations which are induced by the growth of discrete spacetime beneath ? it is a pleasure to thank a.khrennikov and v. manko for discussions and m.genovese for the invitation to present this work at the 4th workshop ad memoriam of carlo novero _ `` advances in foundations of quantum mechanics and quantum information with atoms and photons '' _ ( torino , may 2008 ) . having mentioned individual cases of deterministic dynamical models of quantum objects in section1 , we review here statements about their existence in general . the existence theorem of thooft concerns the schrdinger equation for a quantum system with a @xmath93-dimensional hilbert space @xcite : @xmath94 where @xmath95 denotes the hamiltonian , a @xmath96 matrix here . as it turns out , the dynamics of eq.([g1 ] ) is reproduced in a _ deterministic system _ with two degrees of freedom , one periodic variable , @xmath97 , and another real variable , @xmath98 , which evolve according to the classical equations of motion : @xmath99 \label{g3 } & & \frac{\mbox{d}\omega ( t)}{\mbox{d}t}=-\kappa f(\omega ) f'(\omega ) \;\;,\;\;\ ; f(\omega ) : = \det\;(\hat h-\omega ) \;\ ; , \end{aligned}\ ] ] where @xmath100 is a parameter . it is easy to see that @xmath98 moves exponentially fast towards one of the eigenvalues of @xmath95 , since multiplying @xmath4 by minus one times its derivative @xmath101 makes all corresponding zeros attractive ( see figure1 of ref . for an illustration ) . the initial condition for eq.([g3 ] ) determines which eigenvalue @xmath102 is approached , resulting in a limit cycle for @xmath103 with period @xmath104 . it is useful to introduce two auxiliary operators : @xmath105 which are _ not _ related to classical observables . we also define : @xmath106 with @xmath107 . this operator generates the evolution described by the classical equations of motion ( [ g2])([g3 ] ) . indeed , we can rewrite them as : @xmath108 \;\ ; , \\ [ 1ex ] \label{g31 } & & \frac{\mbox{d}\omega ( t)}{\mbox{d}t}=-i[\omega ( t),\hat h ] \;\ ; , \end{aligned}\ ] ] with @xmath109:=xy - yx$ ] . thus , the operator formalism , which is familiar in quantum theory , turns out to be useful in this classical context as well . the generator @xmath110 is hermitian , despite the dissipative character of the equations motion . the hilbert space on which these operators act is composed of elements which we call _ prequantum states_. they can be employed as usual , in order to calculate the observable properties of the classical system , which are functions @xmath111 . let us consider the evolution of those prequantum states @xmath112 which describe the trajectory of the classical system for an arbitrary but fixed initial condition : @xmath113 \label{prequ1 } & \stackrel{t\rightarrow\infty}{\longrightarrow } & \sum_n e^{in(\varphi -\omega_it)}\psi_n ( \omega_i;0 ) \;\ ; , \end{aligned}\ ] ] where @xmath114 is the particular fixed point to which @xmath115 is attracted , depending on its initial condition ; the fourier transformation takes periodicity in the angular variable into account . then , in a _ superselection _ sector where the absolutely conserved `` quantum number '' @xmath116 is fixed to a particular value @xmath117 , the prequantum states are directly related to the energy eigenstates of the quantum system described by eq.([g1 ] ) : @xmath118 evolving in the usual way , with @xmath119 . probabilistic superpositions of prequantum states with different @xmath114 can be formed and result in pure quantum states showing interference . next , we consider quantum mechanical objects that require , for a complete characterization of their state , a set of simultaneous eigenvalues of a number of linearly independent and mutually commuting hermitian operators , @xmath120 , collectively denoted by @xmath121 , which are the _ beables _ @xcite . these operators , with eigenvalues denoted by @xmath122 , act linearly on a finite dimensional hilbert space , corresponding to a finite number of degrees of freedom . while a particular @xmath123 _ symmetry of beables _ @xcite has been useful in generalizing the previous existence theorem for the case at hand , we assume here for simplicity that the set of beables is fixed . then , the proof of existence of a _ deterministic model accounting for a finite number of beables _ @xcite is analogous to the previous one , eqs.([g2])([psie ] ) . the model here comprises @xmath48 real degrees of freedom which are periodic , @xmath124 , @xmath125 , and evolve according to the classical equation of motion : @xmath126 involving a second set of @xmath48 real degrees of freedom , @xmath127 . while eq.([phivec ] ) replaces eq.([g2 ] ) , presently the vector @xmath128 evolves according to the classical equation : @xmath129 with @xmath100 . this equation determines @xmath128 , once its initial value @xmath130 is supplied and the function @xmath131 is given by : @xmath132 where the sum is over the components of the vector inside @xmath133 and the determinant refers to the hilbert space on which the operators act that are collected in @xmath134 . we remark that operators and hilbert space have only been introduced for convenient book keeping . essentially needed , so far , are the real numbers @xmath135 which parametrize @xmath131 , in analogy to the energy eigenvalues entering eqs.([g3 ] ) . an important property of beables is that related eigenvalues are invariant under unitary transformations in hilbert space . therefore , the function @xmath131 had to be a scalar under such transformations . other symmetry aspects are discussed in ref . . furthermore , the sum of squares of determinants in eq.([finit ] ) is zero , if and only if the @xmath48-dimensional vector @xmath128 corresponds to one of the points of the @xmath48-dimensional finite lattice defined by @xmath136 numbers @xmath135 , i.e. , by the @xmath93 eigenvalues of each one of the @xmath48 operators @xmath134 . in this way , the eqs.([fbc])([finit ] ) generalize the eqs.([g3 ] ) . as in the previous case , the zeros of @xmath131 are attractive . thus , the vector @xmath128 is attracted to a fixed vector with components determined by eigenvalues of the operators @xmath137 : @xmath138 which particular eigenvalues contribute , indexed by @xmath139 , depends on the arbitrary initial condition for @xmath128 . finally , the considerations of eqs.([prequ])([psie ] ) are easily generalized . we consider prequantum states @xmath112 which describe the trajectory of the deterministic system : @xmath140 where the fixed point @xmath141 for a given initial condition and periodicity in @xmath142 are taken into account . all components of the vector @xmath141 contribute to the phase of the evolving state , i.e. , all @xmath48 hermitian operators @xmath137 contribute , each with one of its set of @xmath93 eigenvalues @xmath135 . the states fall into superselection sectors that can be classified by the absolutely conserved vector @xmath143 . three qualitatively different situations may arise . first , the model universe may find itself in a state where all components of @xmath143 are equal , denoted by @xmath144 . here , the emergent hamiltonian must be identified as : @xmath145 with an eigenvalue @xmath146 corresponding to a particular initial condition for the deterministic trajectory . the quantum states are related to the prequantum states by : @xmath147 with @xmath119 , cf . eq.([psie ] ) . one of the beables , corresponding to @xmath148 , for example , could be eliminated in favour of the hamiltonian and @xmath149 , respectively , such that the above relation becomes @xmath150 . thus , we find degenerate energy eigenstates , which are further resolved by the eigenvalues of the @xmath151 remaining beables , i.e. , by the values of @xmath152 . second , assuming that all @xmath153 are of the same order of magnitude , one of the components of the superselection vector @xmath143 , say @xmath154 , may be very much larger than all others . in this case , we consider the hamiltonian : @xmath155 with eigenvalues @xmath156 , which presents a valid approximation , as long as only sufficiently small eigenvalues @xmath157 have to be taken into account . in this case : @xmath158 with @xmath159 . that is , one contribution to the phase is dominant ; this leads to degenerate energy eigenstates , to be resolved as before . there will be only accidental degeneracies , if any , in the third case , when all beables possibly contribute : @xmath160 with eigenvalues of the form @xmath161 . here , we obtain : @xmath162 one of the eigenvalues @xmath163 could be replaced by @xmath164 , provided @xmath165 . thus , in this most general case , there still exist a unique hamiltonian and a related energy variable , which govern the evolution of the emergent states . this completes our review of the existence theorems @xcite . they do not present constructive theorems , since spectral information is needed as input . in the main part of this article , we aim for a constructive theory instead . g.thooft , _ a mathematical theory for deterministic quantum mechanics _ , j. phys . : conf . ser . * 67 * ( 2007 ) 012015 ; arxiv : quant - ph/0604008 ; _ dito _ , int * 42 * ( 2003 ) 355 - 361 ; _ dito _ , class . * 16 * ( 1999 ) 3263 - 3279 . h .- t.elze , _ deterministic models of quantum fields _ , j. phys . ser . * 33 * ( 2006 ) 399 - 404 ; arxiv : gr - qc/0512016 ; _ dito _ , braz . j. phys . * 35 * ( 2005 ) 343 - 350 ; _ dito _ , phys . lett . * a310 * ( 2003 ) 110 - 118 . m.blasone , p.jizba and h.kleinert , _ quantum behavior of deterministic systems with information loss . path integral approach _ , ann . phys . * 320 * ( 2005 ) 468 - 486 ; arxiv : quant - ph/0504200 ; _ dito _ , braz . j. phys . * 35 * ( 2005 ) 497 - 502 ; _ dito _ , phys . _ a71 _ ( 2005 ) 052507 . f.dowker , _ causal sets and the deep structure of spacetime _ in : `` 100 years of relativity - space - time structure : einstein and beyond '' , a.ashtekar ( ed . ) ( world scientific , singapore 2005 ) , arxiv : gr - qc/0508109 .

the dissipative dynamics anticipated in the proof of t hooft s existence theorem _ `` for any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization '' _ is constructed here explicitly . we propose a generalization of liouville s classical phase space equation , incorporating dissipation and diffusion , and demonstrate that it describes the emergence of quantum states and their dynamics in the schrdinger picture . asymptotically , there is a stable ground state and two decoupled sets of degrees of freedom , which transform into each other under the energy - parity symmetry of kaplan and sundrum . they recover the familiar hilbert space and its dual . expectations of observables are shown to agree with the born rule , which is not imposed _ a priori_. this attractor mechanism is applicable in the presence of interactions , to few - body or field theories in particular . # 1#1 :

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"Dear John" is meant to be a star-making role for Channing Tatum, who plays a U.S. Army Special Forces soldier named John Tyree. Starting in the spring of 2001, we follow him off to various war zones as he uses handwritten letters (they didn't have e-mail back then) to stay connected to Savannah, the blond, green-eyed love of his life. The movie takes place over seven years, starting with the couple's star-crossed romance on the beaches of South Carolina. Savannah (Amanda Seyfried) is a big-hearted rich kid with snobby parents. John is a former ruffian raised by an autistic father (the great Richard Jenkins, an Oscar nominee for 2008's "The Visitor"). Their attraction is instant. Seyfried, of HBO's "Big Love," attacks her role with gooey determination. "Two weeks together, that's all it took," Savannah says of her love for John. Cue acoustic love song. One problem: The Sept. 11 terrorist attacks, which send a patriotic tidal wave through the ranks, carry John off to re-enlistment. "Tell me everything," Savannah says. A rousing montage of letter writing ensues, cutting back and forth between Savannah daydreaming in class and John dodging Taliban bullets. If we've learned anything from Sparks adaptations, it's to be prepared for a barrage of sappy plot twists. One, concerning John's dad, actually contains some welcome earnestness. But it's quickly brushed aside for more Sparksian schmaltz. ||||| Critic's Rating: ** stars Novelist Nicholas Sparks says that his novel "Dear John," following his bestselling romances "The Notebook" and "Nights in Rodanthe," was inspired by the classic screen romance "Casablanca." The movie version of "Dear John" - starring Channing Tatum and Amanda Seyfried as star-crossed lovers in a different prewar world, America before Sept. 11 - does have whirlwind romance, heartbreak and second chances. But Bogart and Bergman it's not. Tatum plays John Tyree, a former bad boy turned Special Forces soldier back home in Charlotte, S.C., on leave, during the summer of 2001. He meets Savannah Curtis (Seyfried), a beautiful and privileged college student home for the summer, when he rescues her bag from the surf while they're at the beach. The photogenic duo dive into a two-week, end-of-summer romance, complete with rain-soaked make-out sessions, montages set against breathtaking scenery and the obligatory home-construction sequence. One of the cardinal rules for big-screen romances: If he's handy, he's a keeper! Typical of Sparks' storytelling, when circumstances separate the lovelorn duo - he's got a year of active duty to complete before he can leave the Army; she's due back at school, where she's studying to be a special-education teacher - they agree to correspond via written letter, even though e-mail would be a more convenient, efficient and timely way to connect from around the world. After the Sept. 11 terrorist attacks, John's plan to leave the Army changes, and when Savannah doesn't hear from him for a couple of months after two-plus years of regular correspondence, he gets the letter no man ever wants to get: She is about to marry someone else. Director Lasse Hallström ("The Cider House Rules," "Chocolat") coaxes some nice rising-star performances from Tatum and Seyfried, and some solid supporting work from Henry Thomas as a longtime friend of Savannah's raising his special-needs child on his own and Richard Jenkins as John's regimented father. But with one too many Lifetime cable movie markings, "Dear John" not only wears its saccharin heart on its sleeve, it casts a big spotlight on it, just to make sure you can't miss it. Dear John ** Cast: Channing Tatum, Amanda Seyfried, Richard Jenkins, Henry Thomas, Scott Porter, Keith Robinson, D.J. Cotrona, Cullen Moss, Gavin McCulley Behind the scenes: Produced by Marty Bowen, Wyck Godfrey and Ryan Kavanaugh. Written by Jamie Linden. Directed by Lasse Hallström. Rated: PG-13; some sensuality, war-related violence Approximate running time: 105 minutes ||||| Amanda Seyfried and Channing Tatum can do little to save 'Dear John.' SUPPLIED PHOTO Dear John (out of 4) Starring Channing Tatum, Amanda Seyfried and Richard Jenkins. Directed by Lasse Hallström. 105 minutes. At major theatres. PG Much has been made of Hollywood's seemingly endless capacity to make movies targeted at 17-year-old boys. Dear John is a flick directed squarely at adolescent girls – a sappy version of the old letters-from-the-trenches weepers of the 1940s that hobbles along despite the best effort of its cast and a director who ought to know better. Lasse Hallström (The Shipping News; Chocolat) gives Dear John its beautiful look, making the most of the gorgeous Spanish moss-strewn Charleston location. But the flaccid backbone of the piece, the sappy story by Nicholas Sparks (The Notebook; Nights in Rodanthe), can't hold up the picture, which melts into a gooey, directionless puddle before the first reel is out. Channing Tatum plays John, a brooding U.S. soldier home on leave in 2000 when he meets gorgeous Savannah (Amanda Seyfried), a sweet girl whose only flaw seems to be cursing – in her head. The two fall for each other during his two weeks home. He even takes her to meet his dad (Six Feet Under's Richard Jenkins), an obsessive, child-like coin collector with a touch of Rain Man about him. Jenkins is far and away the best thing about Dear John, delivering a moving performance as a man trapped inside himself and terrified to be there. John and Savannah's mostly chaste love blossoms until he's shipped out to a series of anonymous outposts. Far away from WiFi and BlackBerrys, the couple gets the job of keeping in touch done the old-fashioned way – they write letters. But world events extend their separation as 9/11 means John feels an obligation to extend his tour of duty. Savannah keeps the home fires burning in a variety of ways. John gets a whole bunch of letters that begin, "Dear John." Montages pass the time, while a teen-friendly soundtrack from Snow Patrol helps nudge along a movie with no discernable plot. Seyfried, who has a recurring role on HBO's Big Love and held her own with a big-name cast in Mamma Mia!, fares better than Tatum in this formula flick. If this moping, tense dude is the best she can do, better Savannah throw away her pen. The movie relies heavily on pretty scenes and messages about altruism designed to turn on tear ducts, leading up to a weepy scene in a hospital corridor that will have the romantics reaching for their hankies yet again. But the only eyeball action Dear John got out of me involved rolling.

– Dear John, the latest Nicholas Sparks film adaptation, works familiar territory: ooey-gooey love. Critics aren't falling for the tale of long-distance romance between an American soldier stationed in the Middle East (Channing Tatum) and his dream girl back home (Amanda Seyfried). Tom Horgen of the Minneapolis Star Tribune decries the movie's "Sparksian schmaltz," panning director Lasse Hallstrom for leaving the audience with "a giggle-worthy mess." Linda Barnard of the Toronto Star says it's "a sappy version of the old letters-from-the-trenches weepers of the 1940s that hobbles along despite the best effort of its cast and a director who ought to know better." "The uneasy combination of the World Trade Center, Sparks and schmaltzmeister director Lasse Hallstrom pushed me perilously close to nausea and diabetic shock, not to mention deep sleep," moans Lou Lumenick of the New York Post. "Bogart and Bergman it's not," writes Mack Bates for the Milwaukee Journal Sentinel.

Sir Young may have hated to say that he was a rapist, but he couldn't deny it, either. "That's rape," he said in a recorded interview with a Dallas police detective, describing his encounter with a 14-year-old girl. Young was 18 at the time. They were both students at Booker T. Washington High School for the Performing and Visual Arts. "I hate to have that on my plate. But that's rape." Now 20, Young pleaded guilty to sexual assault of a child. He could have spent up to twenty years in prison. But instead, Dallas County District Judge Jeanine Howard decided to give him a nice break during his sentencing last week. Young will spend a short stint of just 45 days in jail, Judge Howard ruled. And when he's out, the sentence says, "the defendant is to start 250 hours of Community Service at the Rape Crisis Center." Oh no he won't, says the rape crisis center. Apparently, rape victims don't like turning to rapists in times of crisis. "We all read it [the sentence] and we're like, wait a minute," Bobbie Villareal, Executive Director of the Dallas Area Rape Crisis Center, tells Unfair Park. The center accepts volunteers, but not people completing community service hours. Volunteers all have to undergo a criminal background check. "You cannot in any form or fashion have anything on your record," Villareal says. "The fact that she would order 250 hours at a rape crisis center just surprised us." Curious, Villareal has been waiting to see if Young ever calls the center about completing his community service there. (If the call comes in, the answer is still no). The only other rape crisis center in Dallas is at Parkland. And they don't use any volunteers at all, a hospital spokesman tells Unfair Park. It seems then that Young has little chance of spending 250 hours assisting rape victims. Informed of this, the judge's court coordinator told Unfair Park that she'll change the sentence slightly. "She's going go back and modify those conditions and give him community service hours somewhere else, but she hasn't determined where yet," Court Coordinator Jerry Barker says. The judge's office otherwise declined to comment on the sentence. Hopefully, the new volunteer spot will not be a place involves direct contact with sexual assault victims or children. ||||| Rape crisis center scolds Texas judge after she sentences rapist to work with victims there By David Edwards Thursday, May 1, 2014 11:39 EDT A Texas judge who ordered a rapist to serve community service at a rape crisis center has been forced to reconsider the sentence. In a police interview, Sir Young admitted that he had raped a 14-year-old girl in 2011 at Booker T. Washington High School for the Performing and Visual Arts when he was 18. “I hate to have that on my plate. But that’s rape,” he told police. According to The Dallas Observer, Young could have served 20 years in jail, but Dallas County District Judge Jeanine Howard showed him leniency during last week’s sentencing. Howard ruled that Young would only have to spend 45 days in jail, but it was the “250 hours of community service at a rape crisis center” that shocked victim advocates. “I’m sure she probably thought that it was his way of giving back perhaps,” Dallas Area Rape Crisis Center Executive Director Bobbie Villareal told WFAA. “But it’s just not an appropriate place for him to do his community supervision,” “There’s just so many problems with that,” she pointed out. “First of all, we would worry about our client safety and well-being, the appropriateness of them having any kind of contact with survivors — even if it was a past victimization. Just having a criminal defendant in the office could be a triggering effect for many of our clients.” So when the probation office called to arrange Young’s community service, Villareal answered with a firm “no.” “[We] had a really nice conversation with them, but told them — first of all — that we have a strict policy on our volunteers,” she explained. “They can have no criminal backgrounds whatsoever.” Jerry Barker, the court coordinator, said that Judge Howard would find another place for Young to serve out his sentence. “The judge and the probation department are modifying his conditions,” Barker told WFAA. “They’re working on it right now. They’re going to come up with a different order for him to do his community service somewhere else.” Villareal noted that the rest of Howard’s sentence was also an insult to rape survivors. “It is a deterrent to all survivors when you see a very lenient sentence like this passed down,” Villareal observed. “It sends a devastating message to survivors of sexual assault. That victim’s family definitely didn’t feel like there was justice for her and for other survivors of sexual assault.” Judge Howard has refused to comment while the case was still pending. Watch the video below from WFAA, broadcast April 30, 2014.

– Dallas County District Judge Jeanine Howard is known for handing out unusual sentences, but her latest "shocked and disturbed," reports WFAA. Sir Young, 20, pleaded guilty to raping a 14-year-old girl at Booker T. Washington High School; he was an 18-year-old student there at the time. He faced 20 years behind bars, but was last week handed 45 days in jail and an order to do 250 hours of community service ... at a rape crisis center. Outcry ensued, with the executive director of the Dallas Area Rape Crisis Center calling the decision inappropriate. Bobbie Villareal told the probation department as much on Tuesday when it called to ask if Young could complete his required hours there. Setting aside the fact that the clinic's volunteers aren't permitted to have criminal backgrounds, "we would worry about our client safety and well-being, the appropriateness of (Young) having any kind of contact with survivors," says Villareal. Now, the judge and the department are "modifying his conditions" so that Young logs the hours elsewhere, a rep for the court tells the Dallas Observer. But WFAA points out another part of his sentence is drawing complaints: five years of deferred adjudication; that's a kind of probation that will result in his case essentially being dismissed if he completes the requirements of his sentence. (Another rape case is grabbing headlines for much the same reason.)

the study of metals on semiconductors dates back to the nineteenth century and has seen a vigorous recent revival due to tremendous interest in nanotechnology . our ability to manipulate atoms , placing them at will on different surface sites to create exotic artificial structures , has led to further investigations @xcite of electronic and transport properties of free and supported nanowires . the placement of trivalent atoms ( al , ga and in ) on si(001 ) can lead to the formation of low - dimensional structures , exhibiting significant new electronic properties . one can easily compute the electronic properties of free standing nanowires . for this , one must first compute the total energy and determine the possible stable structures . such calculations have indeed been carried out for nanowires @xcite consisting of a wide variety of atoms , _ e.g. _ , k , al , cu , ni , au and si . a general finding is that a zigzag structure in the form of an equilateral triangle is the most stable @xcite . this can be understood as arising primarily due to the maximization of coordination number for each atom in a quasi 1d structure . another structure which also has a local minimum , but not terribly stable , is a wide angle isosceles triangle which somehow is reminiscent of the bulk environment . for example , si which is a four fold coordinated in the bulk ( tetrahedral angle @xmath1 ) shows @xcite a local minimum at an angle of @xmath2 . in general , free standing nanowires tend to be metallic ( have bands crossing the fermi level ) but these nanowires in practice are to be supported . silicon is the most widely used substrate for practical applications and the low index surfaces , si(001 ) is the surface of choice . with the downward spiral toward nano devices , it is desirable to study the metallic properties at the lowest possible coverages . it is in this context that the study of metals like al , ga and in at submonolayer coverages on si(001 ) take on the added importance . the interaction of metal nanowires with substrate can significantly alter the electronic properties . low - energy - electron - diffraction ( leed ) , auger electron spectroscopy ( aes ) and scanning tunneling microscopy ( stm ) studies have provided much informations about the interaction of al , ga and in overlayers on the si(001 ) surface at different coverages and at different temperatures @xcite . ide et al . @xcite observed 2@xmath32 , 2@xmath33 , 4@xmath35 , and 1@xmath37 structures depending on the coverages less than 1 monolayer ( ml ) of al on si(001 ) and the substrate temperature in their leed and aes experiments . however , the 2@xmath32 and 2@xmath33 phases were observed around 0.5 and 1/3 ml coverages respectively at low temperatures . sakamoto and kawanami @xcite performed reflection high energy electron diffraction experiments and established the existence of phases with various symmetries ( 2 @xmath3 3 , 2 @xmath35 , 2@xmath32 and 8@xmath31 ) for ga coverages less than 1 ml and at temperatures @xmath4 350@xmath5 c. later , bourguignon et al . @xcite examined the evolution of 1ml of ga on si(001 ) with leed and observed all the above mentioned phases and in addition they also observed 1@xmath32 phase at 1 ml coverage . nogami et al . @xcite did stm studies and observed 2@xmath32 at and below 0.5 ml coverage of al , ga and in on si(001 ) . knall et al . @xcite performed experiment for in adsorption on si(001 ) using rhed , leed , aes and stm and observed transition from 2@xmath32 to 2@xmath31 structure of in as coverage increased . all the experimental results @xcite point to the fact that at low temperatures al , ga and in form 2@xmath32 structure on the si(001 ) surface at 0.5 ml coverage . at higher metal coverage , nagomi et al . @xcite observed 3d island formation of al on si(001 ) around 1 ml coverage while ordered structures were observed for ga and in on si(001 ) at 1 ml coverage without any island formation @xcite . in particular , a 1@xmath32 structure was observed for ga , and 2@xmath32 , 2@xmath31 structures were observed for in on si(001 ) . since ga does not form islands at 1ml coverage and it has been argued that al forming islands at 1 ml coverage is unusual , we present a complete theoretical study for al / si(001 ) at 1 ml coverage . note that several experimental results were explained @xcite in terms of metal dimers oriented parallel to the si dimer rows _ i.e. _ metal dimers were assumed to be directed perpendicular to the si dimers in the reconstructed surface . this orientation of metal dimers is named as ` ortho ' dimers . electronic structural calculations were done by batra @xcite for al on si(001 ) at 0.5 ml coverage and he explained the experimentally observed patterns in terms of these ` ortho ' dimers . later , northrup et al . @xcite did theoretical calculations on the same system and showed that the orientation of metal dimers parallel to the si dimers was most favorable . these dimers orientated parallel to the si dimers are called as ` para ' dimers . a series of experiments @xcite performed recently for the structural configuration of metal dimers on the si(001 ) surface indeed confirm the findings of northrup et al . @xcite at 0.5 ml coverage . to the best of our knowledge , there is hardly any detailed theoretical study at higher coverages ( 1 ml ) for these systems . in this paper , we put significant effort to perform zero temperature electronic structural calculations for both 0.5 ml and 1 ml coverages of al , ga and in on the si(001 ) surface and compare our results with the experimental and theoretical findings where available . we attempt to put the work in perspective and fill the holes by presenting new results . in particular , we find that our calculations at 0.5 ml give results in accord with northrup s predictions and also with the recent experimental results obtained by sakama et al @xcite . more significantly , we obtain an orientational transition ( ` para ' to ` ortho ' ) for al dimers as we go from 0.5 ml to 1 ml coverage . our calculations also reveal that the reconstruction of si(001 ) is completely lifted at 1 ml coverage of al . we find that in and ga interacts differently with the surface ; for these metals the reconstruction is not lifted at 1 ml coverage . one finds the staggered mixed ( ` ortho ' and ` para ' ) dimers to be the lowest energy structure for in while the mixed dimers are non - staggered for ga . the important conclusion is that the ` ortho ' dimers , which are energetically unfavorable at 0.5 ml coverage , become viable at higher coverage facilitating ` para ' to ` ortho ' transition as a function of coverage . also , a previously reported semi - metallic phase of supported zigzag al nanowire is found to be stable against a dimerizing peierls transition unlike @xmath0 . the soliton @xcite formation in the supported nanowire is argued to be improbable . the paper is organized as follows . the calculational parameters are given in sec . ii and the results and discussions are presented in sec . iii followed by a summary of our findings in sec . first principle total energy calculations were carried out within density functional theory at zero temperature using the vasp code @xcite . the wave functions are expressed by plane waves with the cutoff energy @xmath6 ev . the brillouin zone ( bz ) integrations are performed by using the monkhorst - pack scheme with 4@xmath34@xmath31 @xmath7-point meshes for 2@xmath32 primitive cells . ions are represented by ultra - soft vanderbilt type pseudopotentials and results for fully relaxed atomic structures are obtained using the generalized gradient approximation ( gga ) . the preconditioned conjugate gradient method is used for the wave function optimization and the conjugate gradient method for ionic relaxation . the si(001 ) surface is represented by a repeated slab geometry . each slab contains five si atomic planes with hydrogen atoms passivating the si atoms at the bottom of the slab . consecutive slabs are separated by a vacuum space of 9 . the si atoms on the top four layer of the slab are allowed to relax while those in the bottom layer of the slab and the passivating hydrogen atoms are kept fixed to simulate the bulk like termination . the convergence with respect to the energy cutoff and the number of @xmath7 points for similar structures has been established @xcite . we have performed total energy calculations using the above parameters for both the ideal and the reconstructed si ( 001 ) surfaces . for the ideal case , the si atoms on the surface are arranged in a square pattern of side 3.84 . for the reconstructed surface the si atoms rearrange in such a way that the top layer si atoms form dimer rows along the @xmath8 [ 1@xmath90 ] direction but the atoms move along the @xmath10 [ 110 ] direction to form dimers . here we consider 2@xmath32 supercell for our calculations . at the 0.5 ml coverage of al , ga and in we start only with the reconstructed surface and at 1 ml coverage we start with both the ideal and reconstructed surfaces . here we consider various structural arrangements of metal atoms on the si(001 ) surface . the @xmath11 primitive cell contains two metal atoms which corresponds to 0.5 ml coverage . the results for al / si(001 ) are elaborated here and the results for ga and in are briefly discussed . two metal atoms in the cell may be placed in various ways on the surface . we consider several configurations to identify energetically the most favorable configuration . the configurations considered here are shown in the fig . 1 . 2 cells closed by thick borders are shown for different configurations of metal atoms at 0.5 ml coverage . the unfilled circles represent the top layer si atoms and the filled circles represent the metal atoms . ] the metallic dimers configurations on reconstructed si(001 ) shown in figs . 1(a ) , 1(b ) and 1(c ) were considered by batra @xcite . he found that the configuration in fig . 1(b ) was the most stable one followed by the configuration in fig . 1(c ) . the configurations in figs . 1(c ) and 1(f ) were considered by northrup et al @xcite and they concluded that configuration in 1(f ) was energetically the most favorable one . the arrangement in 1(c ) is referred to as the ` ortho ' orientation of metal dimers and that in 1(f ) is the ` para ' orientation of metal dimers as described earlier by the northrup et al @xcite . in addition we consider two more configurations and they are shown in figs . 1(d ) and 1(e ) respectively . the relative energies and the distance between the neighbor atoms for all the configurations are given in table i. all the energies are measured with respect to the reference energy which at 0.5 ml coverage of metal atoms correspond to the configuration shown in fig . for calculating the reference energy , all the si atoms are held fixed and the metal atoms are allowed to relax along the [ 001 ] direction . the reference energies for the cases of al , ga , and in are -131.625 ev , -130.714 ev , and -130.255 ev . respectively . it is clear from table i that the configuration shown in 1(f ) _ i.e. _ , al dimer placed between the si dimer rows with ` para ' orientation has the lowest energy and hence the most favorable configuration . our results support the calculations first made by northrup et al @xcite and later by brocks et al@xcite . we also observe that the next most favorable configuration is that shown in 1(e ) which also has ` para ' orientation of al dimer but the dimer is placed within a si dimer row . however , the energy difference between these two configurations with ` para ' orientation of metal dimers is @xmath4 1 ev . this is because the dimer within the si row [ 1(e ) ] has to reside at much higher position compared to that placed between the dimer rows [ 1(f ) ] and hence has a weaker binding . we also note that the energy difference between the ` para ' and ` ortho ' orientation of dimers is even larger , the ` para ' being more stable @xmath4 1.3 ev . to calculate the potential energy variation of the system as a function of the al dimer orientation , we place the al dimer between the si dimer rows at a fixed height and rotate about the [ 001 ] direction . the result is shown in fig . 3 . this shows two minima at ` ortho ' and ` para ' orientations respectively and there is a small barrier as one goes from ` ortho ' to ` para ' orientation . therefore , the al dimers take ` para ' orientation which is strongly more favorable compared to the ` ortho ' orientation . this result also agrees with the observation in a recent experiment by sakama et al @xcite . we note that though the si dimers are stretched by 0.26 the reconstruction of the si surface is not lifted at 0.5 ml of coverage . we have also done similar calculations for ga and in adsorption on the reconstructed si(001 ) surface and found that the ` para ' orientation of ga and in dimers are also favored with relative energies -3.29 ev and -2.90 ev respectively . the results for ga and in also agree with recent experimental results obtained by sakama et al @xcite . the surface pattern at 0.5 ml coverage is 2@xmath32 . it is also clear that all the patterns observed at low temperatures and below 0.5 ml coverage of al , ga and in on the reconstructed si(001 ) can be explained by the ` para ' dimers as proposed by northrup @xcite , but contrary to the earlier proposal by batra @xcite . 2 reconstructed cell as the al dimer is rotated from ` ortho ' to ` para ' orientation . the al dimer is placed between the si dimer rows of the reconstructed si(001 ) surface . ] one focus of batra s work @xcite , however , was to find a stable metallic configuration for al . he reported a zigzag nano - structure shown in fig . 1(b ) which he labeled as @xmath12 , as being stable with a local minimum in energy . our present calculations support this finding except that we get @xmath13 in contrast to batra s value of @xmath14 . this overlayer structure of al atoms is reminiscent of a uniform bond @xmath0 structure with the important difference that there is no direct al - al bond . the nearest neighbor al - al distance ( @xmath4 4 ) in the overlayer is much longer than the bulk al - al distance ( @xmath4 2.8 ) and they see " each other only through the delocalized electrons in the @xmath15-orbitals . in @xmath0 , c - c atoms are not only coupled through @xmath16-electrons but they also form strong uniform @xmath17-bonds leading to a semi - metallic structure . this structure becomes semi - conducting upon undergoing a bond alternation peierls like transition to double ( d ) , single ( s ) , ds , ds ... repeating pattern of bonds . it supports the soliton @xcite formation by creating a defective structure of the type .. ds , ds , sd , sd .. by having two single bonds adjacent to each other . the al overlayer structure@xcite has two electrons of each al atom tied to a surface si atom in an @xmath18 like fashion while the third electron of al is in a free electron like state along the nanowire ( @xmath8-direction ) . here x represents a surface si atom which nominally has a single electron in a dangling @xmath15-orbital available for bonding with al . interatomic distance between al and surface si atoms , d(al - x ) @xmath19 2.4 , implies a strong bond . the delocalized @xmath15 electron ( one per al atom ) creates a one dimensional semi - metallic system . naturally , under such situation metallic wires may be realized and it will be conducting under small bias conditions . but then the standard peierls distortion may come into play depending upon the strength of the surface bonds . within the error of our calculations ( estimated at @xmath4 7 mev ) we did not find any lowering of the total energy upon dimerization , unlike @xmath20 . in fact we noted that a dimerization of al atoms in the zigzag structure by an amount @xmath21 raised the total energy by @xmath4 0.1 ev . thus the surface bonds formed by supported nanowires can lock the metallic structure in place . there is no possibility of a soliton formation in the al overlayer structure because of the large al - al distance . however , it will be interesting to look for soliton behavior in other overlayers . we consider the adsorption of four metal atoms on the si(001 ) surface of a 2@xmath32 unit cell which corresponds to 1 ml coverage . results for al , ga , and in on si(001 ) are presented here . various possible configurations considered are shown in fig . calculations are done for both the ideal and the reconstructed si surfaces to find energetically the most favorable configuration . the 2@xmath32 unit cells are bordered by thick lines in fig . 4 . the configurations considereed include para - para and ortho - ortho metal dimers on reconstructed ( figs . 4(a ) - 4(d ) ) and ideal ( figs . 4(e ) - 4(h ) ) on si(001 ) surface . in addition , we also consider mixed dimers ( ortho and para ) on reconstructed surfaces ( figs . 4(i ) - 4(l ) ) . mixed dimers on ideal si surface were not stable and readily caused the silicon surface to reconstruct . 2 cells closed by thick borders are shown for different configurations metal atoms at 1 ml coverage . the unfilled circles represent the top layer si atoms and the filled atoms represent the metal atoms ( al or ga or in ) . ] the relative energies for the relaxed structures of al , ga and in on the reconstructed surfaces are given in table ii for four possible configurations and the same on the ideal surfaces are shown in table iii . the energies for the configurations with mixed dimers are given in table iv . the reference energies at 1 ml coverage of metal atoms are obtained for the configuration shown in fig . 2(b ) where all si atoms are held fixed the metal atoms are allowed to relax along the ( 001 ) direction . the reference energies for the cases of al , ga and in are -137.963 ev , -136.485 ev and -136.044 ev respectively . a general conclusion is that with increasing coverage beyond 0.5 ml , ` ortho ' dimers become part of the low energy configurations leading towards a ` para ' to ` ortho ' transition at 1 ml coverage . for in , mixed staggered dimers ( ` ortho ' and ` para ' ) give the lowest energy configuration . for ga , mixed dimers are non - staggered , while for al ` para ' to ` ortho ' transition of dimers is complete . this is an important conclusion because at or below 0.5 ml ` ortho ' dimers were not favorable . also , the puzzle that ` ortho ' and ` para ' dimers are both seen is resolved due to the preponderance of ` ortho ' dimers at increasing coverages . let us first consider the structure consisting of al dimers with ` para ' orientation as it was the most favorable structure at 0.5 ml coverage . two configurations are possible with ` para ' orientation of al dimers : ( i ) the configurations shown in figs . 4(a ) and 4(e ) on the reconstructed and ideal surfaces respectively and ( ii ) the configurations shown in figs . 4(b ) and 4(f ) on the reconstructed and ideal surfaces respectively . after complete relaxation , we note that the final low energy structure is independent of the initial surface pattern ( reconstructed /ideal ) . when we start from an ideal surface , the si atoms dimerize and the low energy structure is the one with reconstructed si surface . same final structure is achieved when we start form the reconstructed surface . also note that the relaxed system with the staggered dimers configuration in 4(b ) consisting of parallel dimers on the reconstructed surface is less favorable compared to that on the same reconstructed surface with the configuration in 4(a ) . comparing 4(b ) and 4(f ) we find that the final energies of the systems differ by a large amount : staggered dimers on the ideal surface are least favorable . next we consider the configurations in 4(c ) and 4(d ) . these structures are obtained by just rotating the al dimers in 4(a ) and 4(b ) by 90 degree ( _ i.e. _ , dimers now take ` ortho ' orientation ) . from table ii it is clear that these configurations are more favorable compared to those in 4(a ) and 4(b ) . we find that after complete relaxation , the total energies and the structures of these two configurations become independent of the initial surface pattern . in addition , we consider the configurations consisting of mixed dimers ( ` ortho ' and ` para ' ) as shown in figs . 4(i ) - 4(l ) . similar configurations on ideal surface are unstable , the si surface reconstructs itself and eventually leads to the configurations 4(i ) , 4(j ) and 4(k ) . again for al , the configurations 4(j ) and 4(l ) are unstable . from table iv we see that the configuration with mixed al dimers shown in fig . 4(i ) has a deep local minumum . this configuration is more favorable compared to the configurations consisting of only ` para ' orientation of al dimers ( i.e. , figs . 4(a ) and 4(f ) ) . however , comparing the energies for configurations 4(i ) and 4(g ) we find that the lowest energy structure is the one shown in fig . 4(g ) where the reconstruction is completely lifted . all the si bonds are saturated here . since the reconstruction is completely lifted at 1 ml coverage , we conclude that the breaking of si dimer bonds is initiated just beyond 0.5 ml of coverage . most interestingly we note that an orientational transition for the al dimers takes place as one goes from 0.5 ml coverage to 1 ml coverage : the al dimers change their orientation from ` para ' to ` ortho ' after breaking the si dimer bonds . this is also supported by the charge density plot for the lowest energy configurations at 0.5 and 1 ml coverage as shown in figs . 5(a ) and 5(b ) respectively . earlier , it was argued that at 0.5 ml coverage all si bonds are saturated and therefore beyond 0.5 ml coverage al atoms may reside on top of each other and form 3d island . one experimental study observed the 3d island formation beyond 0.5 ml of al coverage @xcite . our calculation , however , suggests that for al an orientational transition can take place at 1 ml coverage and the surface structure becomes regular having a 1@xmath22 pattern where all bonds of si and al are saturated due to removal of the reconstruction of the si surface . this leads us to speculate that further experiments on al may seek out 1@xmath32 pattern at 1 ml coverage . furthermore , at coverages between 0.5 ml and 1 ml both the ` para ' and ` ortho ' al dimers may coexist . this also clarifies why experiments at times have reported both ` para ' & ` ortho ' dimers because precise coverage is a difficult parameter to quantify . now we consider the ga adsorption at 1 ml coverage . if we start with the reconstructed surface we find that the configuration in fig . 4(i ) with mixed dimers leads to the lowest energy structure where the reconstruction of the si surface is not lifted during the relaxation process . the next best configuration is shown in fig . 4(g ) and consists of only ` ortho ' dimers . the structure remains ideal even after complete ionic relaxation . the configurations in figs . 4(j ) and 4(l ) are unstable . comparing final energies for various configurations on ideal and reconstructed surfaces we observe that the configuration in 4(i ) is energetically the most favorable structure . experiments indicate observing the 1@xmath32 structure shown in 4(g ) @xcite . here the reconstruction of the si surface is lifted , ga dimers prefer ` ortho ' orientation leading to a 1@xmath32 patten . our calculations suggest that mixed dimers ( fig . 4(i ) ) and ` ortho ' dimers ( fig . 4(g ) ) as two contenders for the energy favored structures . for the case of in we find that energetically the most favorable configuration is given in fig . this configuration corresponds to a 2@xmath32 surface pattern . the configurations in figs . 4(i ) and 4(l ) are unstable . more significantly , we note that the reconstruction of the surface is not lifted . we also find that the configurations consisting of ` para ' dimers ( i.e. , figs . 4(a ) and a(b ) ) are degenerate and energetically next favorable structures . the configurations in figs . 4(a ) and 4(b ) correspond to the 2@xmath31 and 2@xmath32 surface structures respectively . experimental results indicate the existence of both the 2@xmath32 and 2@xmath31 surface structures near 1 ml coverage of in . the most and the next favorable structures from our calculations are consistent with the experimentally observed 2@xmath32 and 2@xmath31 surface structures respectively . to understand the bonding of ga and in atoms on si(001 ) , the charge density distributions are plotted on the plane of metal atoms for the most favorable configurations at 1ml coverage of ga and in and they are shown in figs . 6(a ) and 6(b ) respectively . we observe that to a first approximation metal atoms display strong intra - plane bondings amongst themselves leaving the substrate in reconstructed state . the charge distribution in fig . 6(b ) also helps us to understand why the configuration 4(i ) is unstable for in . in being larger in size , the in atoms in ` ortho ' orientation of configuration 4(i ) are pushed away from each other to have a suitable coupling among in atoms and thus favoring the configuration 4(j ) with ( mixed ) staggered dimers . it is worth mentioning that one usually ends up with semi - metallic or non - metallic nanowires when supported on substrates as we saw above for the group iii metals on si(001 ) . very recently , there have been several important studies @xcite of monovalent au chains on various high indexed si surfaces dealing with metallicity , peierls distortion , charge density instability , fractional band fillings , and possibility of a spin charge separation due to the luttinger - liquid phase . in fact , himpsel and his group showed that au nanowire supported on si(553 ) is stable and it shows metallic behavior @xcite . we have done extensive total energy calculations for al , ga and in adsorption on the si(001 ) surface at 0.5 and 1 ml coverages . the ` para ' orientation of dimers is the most stable orientation at 0.5 ml coverage for al , ga and in , which supports the results of northrup et al and also agrees with the recent experimental observations . all the patterns observed in various experiments at low temperature and below 0.5 ml coverages can be explained by the ` para ' orientation of metal dimers . an interesting zigzag semi - metallic structure similar to @xmath0 is formed at 0.5 ml but is not the lowest energy structure . soliton formation in overlayers is a fundamental topic for further study . at 1 ml coverage a tendency towards the ` ortho ' orientation of dimers is noted . thus we predict an orientational transition from ` para ' to ` ortho ' as we go from 0.5 ml to 1 ml coverage for al and possibly ga on the si 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extensive electronic structure calculations are performed to obtain the stable geometries of metals like al , ga and in on the si(001 ) surface at 0.5 ml and 1 ml coverages . our results coupled with previous theoretical findings explain the recent experimental data in a comprehensive fashion . at low coverages , as shown by previous works , ` para ' dimers give the lowest energy structure . with increasing coverage beyond 0.5 ml , ` ortho ' dimers become part of low energy configurations leading toward a ` para ' to ` ortho ' transition at 1 ml coverage . for in mixed staggered dimers ( ` ortho ' and ` para ' ) give the lowest energy configuration . for ga , mixed dimers are non - staggered , while for al ` para ' to ` ortho ' transition of dimers is complete . thus at intermediate coverages between 0.5 and 1 ml , the ` ortho ' and ` para ' dimers may coexist on the surface . consequently , this may be an explanation of the fact that the experimental observations can be successfully interpreted using either orientation . a supported zigzag structure at 0.5 ml , which resembles @xmath0 , does not undergo a dimerization transition , and hence stays semi - metallic . also , unlike @xmath0 the soliton formation is ruled out for this structure . -0.25 in -0.2 in 0.2 in

fungal rhinosinusitis ( frs ) has been a known medical entity for several hundred years but only in more recent times the entity has been further defined . frs comprises a variety of different disease processes which vary in presentation , histologic appearances , and clinical significance . disease is most commonly classified as being non - invasive or invasive based on whether the fungi have invaded into the sinonasal submucosal tissue resulting in tissue necrosis and destruction [ 13 ] . entities which are considered non - invasive frs include fungal ball ( fb ( an entangled mass of fungus without significant surrounding sinonasal inflammatory reaction ) and allergic fungal rhinosinusitis ( afrs ) ( a complex entity characterized by the presence of allergic mucin with histologic similarities to those reported in allergic bronchopulmonary aspergillosis ) . invasive disease is characterized as either acute or chronic based on the length the time symptoms are present before presentation . patients with acute invasive disease ( aifrs ) are usually immunosuppressed and , by definition , present with symptoms of less than one - month duration . this entity is characterized by the presence of fungal forms invading into the sinonasal submucosal with frequent angioinvasion and rapid intervention is necessary . two forms of chronic invasive disease , chronic invasive frs ( cifrs ) , and chronic granulomatous frs ( cgfrs ) , have been described and like aifrs both are also serious , often requiring surgical and medical therapy . in the current study , we evaluate the histopathologic and microbiologic classification of a large population of frs patients in a large quaternary care university medical center in the northeastern united states . the study took place at the hospital of the university of pennsylvania , a 725-bed academic quaternary care center . following approval from the university of pennsylvania institutional review board , the surgical pathology archives were searched for patients with a diagnosis of frs between the years 1991 and 2008 . the patients were classified as non - invasive ( fb ; afrs and mixed fb / afrs ) , invasive ( aifrs , cifrs , and cgfrs ) , or mixed invasive / non - invasive based on known clinical and histologic criteria ( table 1 ) . results of fungal cultures , if available , were reviewed and correlated with the histopathologic findings . 87.25% had non - invasive disease including 40.25% fb , 45.0% afrs , and 2.0% combined fb and afrs , and 12.5% had invasive disease , including 11.0% aifrs , 1.0% cifrs , and 0.5% cgfrs . one patient had combined non - invasive ( fb ) and invasive disease ( cgfrs ) ( 0.25% ) . overall the mean patient age was 50 ( range 1890 ) with a male to female ratio of 1.2 : 1 . histologically , fb was characterized by the presence of entangled masses of fungal forms ( figure 1 ) [ 3 , 4 ] . in many cases , fibrinopurulent material was seen surrounding the mass of fungi and the fungal organisms were identified embedded in acute inflammation and fibrinous exudate and only visible with histochemical stains ( grocott silver stain ) for fungal organisms . in other cases , the fungal organisms were clearly visible on hematoxylin and eosin stains without significant surrounding inflammatory reaction . by definition , no tissue invasion or granulomatous reaction the average patient age was 55 ( range 1890 ) , and there was a female to male ratio of 2 : 1 . the disease was localized to one sinus in 97% of cases with no laterality predominance and was bilateral in 3% of cases . seventy percent of cases involved the maxillary sinus and 27% involved the sphenoid / ethmoid sinuses . fifteen patients had known sinus surgery 1 month to 14 years prior to diagnosis and an additional 14 subjects were immunosuppressed either by a malignancy or organ transplantation . two patients showed recurrence of an fb , one at 6 months and the other at 7 years following the initial surgery . one hundred seven patients had fungal culture results available for review ( table 4 ) . the remaining culture positive cases grew dematiaceous species as well as a variety of other fungi . seven patients grew multiple fungal isolates in culture with 5 of 7 showing dematiaceous species in combination with other fungal organisms ( table 4 ) . the diagnosis of afrs was established using pathologic criteria by either the presence of eosinophilic mucin ( em ) containing fungal forms on histologic examination using a grocott silver stain or the presence of em without histologic evidence of fungi but with positive fungal cultures [ 57 ] . histologically , em was characterized by the presence of lamellated mucinous material with the presence of eosinophils , eosinophilic debris , and charcot - leyden crystals ( figure 2 ) . in order to identify all potential cases of afrs , all sinus contents specimens with histologically evident three - hundred fifty - three patients with em were identified , 134 of which had fungal forms by histology . of the 219 patients without histologic fungus , 46 had positive fungal cultures for an overall total of 180 presumed afrs patients . the remaining 173 patients with em either had negative fungal cultures ( 100 patients ) or unknown culture results ( 73 patients ) and these patients were considered to have insufficient evidence for a pathologic diagnosis of afrs although since more sensitive techniques for fungal detection such as pcr were not performed on this population , they may still actually have afrs . the average patient age was 45 ( range 1888 ) and there was a female - to - male ratio of 1.2 : 1 . thirty percent of patients presented up to 10 years prior to afrs diagnosis with specimens showing chronic sinusitis with eosinophilia and/or the presence of em without fungal organisms . fungal culture results were available in 142 patients , 79% of which were positive ( table 5 ) . sixty - five percent of the culture - positive patients grew a single fungal isolate while 35% grew more than one fungal organism . ( 34% ) with a. fumigatus , a. flavus , and a. niger most frequent and dematiaceous species ( 30% ) with alternaria sp . specimens from the remaining 36% of patients grew a variety of other fungi including paecilomyces sp . , fusarium sp . , scedosporium sp . , c. albicans , and penicillium sp . of the patients whose cultures revealed multiple fungal isolates , 34% grew a single dematiaceous species combined with a nonaspergillus sp . , 23% grew a single dematiaceous species combined with aspergillus sp . with or without another fungal species , 16% grew multiple aspergillus sp . with or without a non - dematiaceous species , forty - eight percent of patients with multiple isolates grew them at different points in time . one patient grew nine different fungal types in multiple specimens cultured over a three year time period . there were noticeable differences between the fungi isolated in patients with em containing fungal forms histologically and those patients with em without histologically identifiable fungi but positive fungal cultures ( tables 6 and 7 ) . in those afrs cases with histologic fungi and positive fungal cultures , 36% dematiaceous species , and 13% other including fusarium sp . and scedosporium sp . ) ; however fungal cultures in afrs patients with positive cultures and em without fungal forms showed a single isolate in only 63% of cases ( 24% aspergillus sp , 10% dematiaceous species , 66% non - aspergillus / non - dematiaceous species including c. albicans , penicillium sp , and yeast not further specified ) . six of these patients had evidence of entangled masses of fungus with extensive surrounding em . cultures were positive in four of these patients ( a. niger , a. flavus , alternaria sp . and an additional , patient had an initial diagnosis of afrs with negative fungal cultures with multiple subsequent surgeries showing em but no fungal forms and cultures that were either negative or positive for alternaria sp , a. flavus and a. niger . she then developed a fb 15 years subsequent to the initial surgery with fungal cultures positive for a. flavus . similarly another patient had a diagnosis of afrs with negative cultures and developed a fb culture positive for a. niger three years following the initial diagnosis of afrs . one of the cgfrs patients was a 50-year - old sudanese female with an over 20-year history of cgfrs whose cultures grew a. flavus . the other cgfrs patient was a 66-year - old male with a long - standing history of non - insulin - dependent diabetes mellitus who presented with symptoms attributable to chronic rhinosinusitis . histologically , both specimens showed fibrosis , granulomatous inflammation , and chronic inflammation composed of lymphocytes and plasma cell without significant eosinophils ( figure 3 ) . two patients ( ages 21 and 41 ) presented with long - standing nasal septal perforation of unknown etiology . both of these patients showed mucosal ulceration with evidence of acute and chronic inflammation , fibrosis and submucosal invasive fungal forms without angioinvasion . the remaining two patients ( ages 63 and 65 ) presented with a history of presumed chronic rhinosinusitis and no known risk factors for fungal sinusitis . both of these patients showed chronic inflammation and associated mucosal ulceration with submucosal invasive fungal forms without angioinvasion ( figure 4 ) . one patient showed evidence of a fb with areas of underlying tissue invasion of fungal forms with the presence of granulomatous inflammation . this patient was a 72-year - old male who presented with long - standing diplopia , proptosis , and a left orbital mass . histologically , the specimen consisted of a matted mass of fungal forms consistent with fb which was associated with the presence chronic inflammation with areas of submucosal fibrosis and focally granulomatous inflammation with fungal forms invading into the submucosal tissue without histologic evidence of angioinvasion . eighty - four percent had a hematologic disorder with or without bone marrow transplantation due most commonly to acute leukemia ( 32 patients ) , non - hodgkin lymphoma ( 3 patients ) , and multiple myeloma ( 2 patients ) . the remaining seven patients had either treatment or conditions that led to immunosuppression including solid organ transplantation ( 2 liver and 1 kidney ) , systemic necrotizing vasculitis ( 1 patient ) , ulcerative colitis ( 1 patient ) and non - insulin - dependent diabetes mellitus ( 2 patients ) . patient ages ranged from 24 and 82 with a male - to - female ratio of 1.5 : 1 . fungal culture results were available in 27 patients with the most common cultured organism being aspergillus sp . followed by rhizopus sp . other fungi isolated included one case each of alternaria sp . , paecilomyces sp . , and fusarium sp . histologically all patients showed necrotic sinonasal mucosa with the presence of angioinvasive fungal forms ( figure 5 ) . clinically , frs can be acute ( aggressive ) and chronic ( indolent ) [ 13 ] . the pathologic spectrum encompasses a variety of different entities which are classified as either invasive or non - invasive and then into specific pathologic categories which are descriptive of clinical and histologic disease processes . in the current study , we present a cohort of 400 patients with frs observed in a large quaternary care medical center that receives numerous referrals for surgical treatment of rhinosinusitis , in particular those with symptoms of chronic rhinosinusitis . as such , the majority of the patients that we observed were those with non - invasive disease with an almost equal distribution of afrs and fb with incidences of 45% and 40% , respectively . in our experience , invasive frs was rare with acute disease representing almost 90% of those with invasive disease . chronic invasive disease was only rarely noted in our population and most likely reflects the referral population to our medical center . relatively similar distributions have been seen in other studies performed in the united states . in a study from houston , tx , granville et al . reported non - invasive disease in > 90% of patients with 72% afrs , 23% fb , and 2.1% each of aifrs and cgfrs . in addition , taxy observed non - invasive disease in over 80% of frs patients in the chicago area with an equal incidence of afrs and fb and an 8% incidence of aifrs . overall it appears , at least in these studies , that non - invasive frs predominates in the united states population . however , studies performed in other countries such as india show significantly fewer fb cases and more cgfrs cases compared to these other studies . das et al . observed non - invasive frs in 60% of 284 patients ( afrs 56% ; fb 4% ) and invasive frs in 36% of patients ( aifrs 17% , cifrs 1% , and cgfrs 17% ) . . michael et al . observed a prevalence of 63% afrs and 24% aifrs similar to das et al .. however , the incidence of cifrs was higher ( 10% ) and cgfrs significantly lower ( < 1% ) than seen in das et al . ' study . on the other hand , while panda et al . observed a 60% incidence of non - invasive disease , they most commonly encountered fb in their series of 178 patients . observed a much lower incidence of non - invasive frs ( 25% ) versus invasive disease ( 75% ) with a 30% incidence of cgfrs . this geographic diversity may be due to different climates and environmental factors , as well as different means of fungal exposure and variation in frs terminology and definitions ; however , the reasons for variations in frs presentations are not understood . panda et al . and dufour et al . noted that fb was the most common form of frs in their patients in india and france respectively , although several other studies as noted above have observed this form of frs to be the least common [ 814 ] . the patient population we observed shared many features to those described in dufour et al . with an increased incidence in elderly females , location in the maxillary sinus and the predominance of a. fumigatus on fungal cultures . however , our incidence of positive fungal culture was higher ( 51% versus 30% ) than seen in their study and , in our patient population , we had only rare cases associated with scedosporium sp . afrs was seen in 45% of patients in this study . afrs was diagnosed as either the presence of em containing fungal forms on histology ( despite culture results ) or the presence of em without histologic fungi but positive fungal cultures . this latter group is probably the most problematic in the current study since it is difficult to ascertain without other clinical criteria that these patients should be truly considered as having afrs . the diagnosis in this group was based on the presence of em with positive fungal cultures ; however , fungal cultures in this patient group commonly grew neither aspergillus sp . nor dematiaceous fungi , two of the most common agents isolated in patients with afrs , indicating that the fungi isolated may be unrelated to the em and could be potential contaminants . it is possible that some of the patients with em without fungi but positive cultures are not truly afrs patients and that a positive fungal culture alone is not sufficient to make a diagnosis of afrs without other clinical findings . the other problematic aspect of this study is that patients with em but with no fungi on histology and negative fungal cultures were excluded . more sensitive fungal cultures , pcr , or other molecular techniques may have identified fungi in this patient group but , based on the current material available , a classification of these patients as having afrs was not possible . since this was a retrospective study , there was no way to control whether the em material was preserved in a fashion to allow for more sensitive culturing techniques . there has been recent controversy over the role of fungi in the development of chronic rhinosinusitis , an entity often treated with antibiotic therapy . in a study by ponikau et al . using a sensitive fungal culturing technique , positive fungal cultures were seen in almost 100% of chronic sinusitis patients ( although control subjects also had positive fungal cultures ) . while the finding of positive fungal cultures in most patients with chronic sinusitis is controversial in nature and not universally accepted , there is belief that chronic sinusitis may be related to inflammatory reaction to fungi [ 1618 ] . of note , almost 30% of the afrs patients in this study initially presented with chronic sinusitis with eosinophils but no histologic evidence of fungus . fungi isolated in frs , while showing geographic variation , are often similar in the particular forms of this disease . aspergillus sp . particularly a. fumigatus and a. flavus appears to consistently be the most common agents isolated in patients with fb in a variety of different geographic locations including our current study [ 1014 ] . other fungal isolates including scedosporium sp . , fusarium sp . , and dematiaceous fungi have also been rarely associated with this entity . other rare fungi such as fusarium sp . and dematiaceous species may also be isolated in aifrs . chronic invasive disease either cifrs or cgfrs are also usually associated with aspergillus sp , particularly a. flavus [ 1013 ] . dematiaceous species are isolated but the species of fungi vary significantly from study to study . in studies performed in india as well as saudi arabia , a. flavus appears to be the most common fungal organism cultured in afrs [ 1013 , 19 ] . in the united states , particularly in the south and southwest , in granville et al . 's study , almost 70% of afrs cases grew dematiaceous fungi and their group showed no cases with aspergillus sp . by culture . schubert and goetz observed that > 80% afrs cases were associated with dematiaceous fungi with almost 70% due to bipolaris sp . and only 9% due to aspergillus sp . . , in the chicago area , taxy reported an equal incidence of alternaria sp . and aspergillus sp . in their patients with afrs . in the current study , both dematiaceous fungi and aspergillus sp . , curvularia sp . , a. fumigatus , a. flavus , and a. niger being the most common single isolates in patients with histologically confirmed em with fungal organisms . we also observed several patients with multiple different fungal isolates either at one time or multiple times during the disease process , . in 16% of patients with em and histologic fungal forms , more than one fungal isolate was identified either at a single or at multiple time points , most commonly aspergillus sp . this indicates that some patients may be predisposed to develop a reaction to more than one type of fungus including both dematiaceous and aspergillus sp . this study did not control for the fact that the aspergillus sp . may grow faster in culture than other organisms and that , even though aspergillus sp . may have grown as an isolate in many afrs patients , other types of fungi may also be present . interestingly , in more recent studies , using in situ hybridization and immunohistochemistry , we have confirmed the presence of aspergillus sp . in aspergillus in fact , two patients originally presented with afrs and on subsequent surgery up to 9 years later developed a fungal ball . the other patients had classic em with fungal organisms as well as an entangled mass of fungi consistent with fb . in addition , one patient in this study had combined fb and cgfs . about 4% of patients presented by das et al . had combined frs with either afrs , fb , or aifrs combined with cgfs . manning and holman in a study from the southwestern united states observed combined afrs and cgfs in 1.5% of their patient population . in summary , in this retrospective study , we present 400 patients with frs . non - invasive frs was more frequently encountered in our patient population . invasive disease , while less common in our group , was more commonly acute in nature . while a variety of fungi are isolated in patients with frs , aspergillus sp . still appears to be a common isolate in our patient population .

fungal rhinosinusitis ( frs ) is a well known entity , but only in more recent times have the types of frs been more fully defined . in this study , we evaluate the diagnosis of frs in a single medical center . cases were divided into 2 main categories , non - invasive and invasive . non - invasive frs included fungus ball ( fb ) and allergic fungal rhinosinusitis ( afrs ) . invasive frs included acute invasive fungal rhinosinusitis ( aifrs ) , chronic invasive fungal rhinosinusitis ( cifrs ) , and chronic invasive granulomatous fungal rhinosinusitis ( cgfrs ) . fungal culture data , if available was reviewed . 400 patients with frs were identified . 87.25% were non - invasive ( 45% afrs , 40% fb , and 2% combined afrs and fb and 12.5% were invasive 11% aifrs 1.2% cifrs 0.5% cgfrs . one patient ( 0.25% ) had combined fb / cgfrs . aspergillus sp . or dematiaceous species were the most common fungi isolated in afs while aspergillus sp . was most common in fb and aifrs . in our experience , most frs is non - invasive . in our patient population , invasive frs is rare with aifrs representing > 90% of cases . culture data supports that a variety of fungal agents are responsible for frs , but aspergillus sp . appears to be one of the most common organisms in patients with frs .

extended thermal x - ray emission from the hot ( @xmath0 k ) interstellar medium ( ism ) in giant elliptical galaxies is usually interpreted in terms of a ` cooling flow ' scenario [ see loewenstein for a recent review ] . it implies that radiative cooling of optically thin hot plasma drives a subsonic inflow towards the centre of a potential well formed by the stellar component and a massive dark halo . galactic cooling flows and cooling flows in clusters of galaxies are essentially different owing to a difference in the origin of the two media . the intracluster medium is mostly primordial , cools from its high virial temperature and is accreted by the central galaxy , which provides a focus for the flow . in contrast , the ism in elliptical galaxies is constantly replenished by mass loss from evolved stars . this gas must be thermalized in the galaxy s gravity field and heated to x - ray temperatures from which it may cool down again . thus , in hydrodynamic terms , galactic cooling flows are defined as systems where the mass flux is dominated by source terms as opposed to ` boundary terms ' as in cluster cooling flows @xcite . several potential heat sources have been considered to counterbalance radiative cooling of the hot ism in ellipticals . the energy supplied with normal stellar mass loss is limited by the value of the stellar velocity dispersion and may only provide temperatures a factor of @xmath1 lower than the ism temperatures @xcite . in contrast , gravitational energy liberated in case of gas _ inflow _ would provide too much heat to the central regions [ thomas and references therein ] . heating by supernovae ( sn ) type ia remains a controversial issue . on the one hand , the sn rate is not very well constrained . its value varies from @xmath2 snu , suggested by van den bergh & tammann , the uncertainty being a factor of the order of 1.5 , to @xmath3 snu derived by cappellaro , evans & turatto . is the hubble constant in units of @xmath4 km s@xmath5mpc@xmath5 ; 1 snu = 1 supernova per century per @xmath6 solar bolometric luminosities . ] on the other hand , the low iron content of the diffuse hot gas in ellipticals estimated from high - quality broad band x - ray spectra provided by asca for a single - temperature plasma model @xcite suggests a very low efficiency of ism enrichment by type ia sne . this implies either that the sn rate is lower than @xmath7 snu @xcite or that sn ejecta do not mix with the hot ism @xcite . however , the multi - parametric analysis of x - ray spectra is a complex procedure based on iron l line diagnostic tools , and requires accurate atomic physics data @xcite . the procedure is also model - dependent . using two - temperature multi - phase plasma models buote obtained substantially better spectral fits for the same data sets with iron abundances of @xmath8 solar and relative element abundances fixed at their solar values . his results are consistent with the type ia sn rate being up to a factor of @xmath1 lower than reported by cappellaro et al . . clearly , better quality data are required to determine the type ia sn heating rate more precisely . all of the above mentioned energy sources may be described as being continuously distributed within a galaxy and their local rates depending on the stellar mass density and velocity dispersion , the gas inflow velocity profile , and the shape of the gravitational potential . there is a ` global problem ' @xcite of balancing heating and cooling both in the centre and in the outer regions , since the source terms depend in different ways on physical characteristics which vary with radius . however , empirical scaling laws for ellipticals and the physics of radiative cooling and thermal instability imply certain restrictions on the radial dependences . one possible solution to this problem is a hydrostatic hot gas recycling model @xcite for hot coronae of elliptical galaxies . in the hydrostatic gas configuration all that remains of the gas dynamical equations are the algebraic source terms which balance to zero . in this model two equilibrium conditions are simultaneously satisfied : ( 1 ) the stellar mass loss rate exactly balances the rate that mass cools locally from the flow ( dropout ) and ( 2 ) the rate that thermal energy is radiated away is exactly balanced by the energy input from stars and supernovae . the recycling model can be used as a tool to distinguish between inflow and outflow regimes for a given set of galaxy parameters ( kritsuk , bhringer & mller 1998 ) . periods of sporadic activity can drastically change the thermal state of the ism in the inner ` cooling flow ' region of a cluster or of an elliptical on a time scale of @xmath9 yr . there are numerous observations of an interaction between radio sources and the hot gas both in central cluster galaxies and other ellipticals @xcite . it is this complex central region that is most sensitive to any imbalance in the energy budget of the ism . since the ` thermal ' time scale is shorter there , the core of a few kpc in radius is the first to reach a new equilibrium state corresponding to the current status of heating . high spatial and spectral resolution x - ray observations of these central regions are critical to distinguish among the various heat sources and flow regimes in the core . the response of a cooling flow to energy injection by the central black hole that is fed by the cooling flow was simulated by binney & tabor ( 1995 ) . in their spherically symmetric numerical models the black hole heats the central kiloparsec of the ism as soon as it begins to swallow gas from the ism . the resulting expansion of the heated gas eliminates the cusped density profile and establishes a core that is roughly 2 kpc in radius . after the central heat source has switched off , the core again cools catastrophically within 0.5 gyr . among several limitations of the model ( which include a peculiar feedback mechanism ) the authors particularly note the restriction of spherical symmetry . both the jet and the ensuing convective instabilities can not be properly modelled due to this symmetry restriction . in this paper we analyze the hot gas flow regimes , which develop in elliptical galaxies in response to a small imbalance in the energy budget caused by a global instability of the equilibrium recycling model @xcite . we use multi - dimensional numerical simulations to investigate compact cooling inflows and subsonic convection two alternative saturated nonlinear regimes for a slightly disturbed thermal equilibrium in the core . here , we restrict ourselves to spherically symmetric ( on the average ) convective flows , which have not been studied before . the symmetry restriction will be relaxed in a subsequent paper which more closely addresses the astrophysical aspects of the problem . the analysis presented here provides a basis for a better understanding of more complex convective flows and allows for a direct comparison with one - dimensional models . a short description of our basic model is given in section 2 . section 3 describes the numerical method . the results of numerical experiments are presented in section 4 together with the detailed properties of the inner convective cores . in section 5 we summarize the results and discuss effects to be expected for the dynamical state of the hot gas in ellipticals from a larger imbalance between cooling and heating . our numerical experiments are based on a physical model , which has been described in kritsuk et al . . we refer the reader to that paper and references therein for a more detailed description than given below . we assume that the local mass budget of the hot ism inside the galaxy is determined exclusively by mass supply from the old stellar population of the galaxy [ in the form of stellar winds , planetary nebulae , supernova explosions , etc . ; a detailed discussion can be found in mathews and mathews & brighenti ] , and by gas condensation to a warm phase due to thermal instabilities . our motivation for including mass dropout is based on the fact that the assumed mass supply mechanisms inevitably cause nonlinear small scale perturbations in the hot phase , which can trigger thermal instabilities . the rate of mass dropout is assumed to be a function of local conditions in the hot ism , and given by the expression @xmath10 , where @xmath11 is the density of the hot phase . the spectrum of the initial small - scale perturbations in the gas and , in particular , its modification by heat conduction are described by a single parameter @xmath12 $ ] . the heaviside function @xmath13 and the linear instability growth rate @xmath14 are defined as @xmath15 @xmath16 here @xmath17 is the hot gas temperature , @xmath18 is the nonequilibrium zero field radiative cooling function for solar composition and complete ionization of the plasma @xcite , and @xmath19 is the specific heat at constant pressure . the first term in the _ rhs _ of equation ( [ growthrate ] ) coincides with field s instability criterion , and the second one describes stabilization due to stellar mass loss @xcite , @xmath20 is the specific stellar mass loss rate , and @xmath21 is the local stellar mass density . here we assume @xmath22 @xcite . since we are interested in relatively short evolutionary time scales ( @xmath23 gyr ) , we assume @xmath20 to be a constant . the local energy budget of the hot ism is determined by radiative losses and energy supply from stars ( via sn type ia explosions and via thermalization of the kinetic energy of orbital motion for the gas shed by stars ) . radiative cooling comprises two energy sinks due to ( i ) direct radiative cooling of the hot phase and ( ii ) due to radiative losses by the condensing material . finally , the hydrodynamic description for the hot phase is based upon the assumption that the sources are homogeneously distributed . note that this assumption is fulfilled as long as the numerical resolution is not excessively high . the set of conservation laws for mass , momentum , and energy of the hot phase can then be written as follows : @xmath24 @xmath25 @xmath26 = } \nonumber \\ & & \alpha\rho _ * e _ * -\dot\rho_{{\mathrm { ti}}}(e+p)/\rho-\rho^2\lambda + \rho \bmath{v\cdot\nabla}\phi . \label{energy}\end{aligned}\ ] ] here @xmath27 is the velocity vector , @xmath28 is the pressure , @xmath29 is the adiabatic index , @xmath30 is the specific internal energy , and @xmath31 is the characteristic specific energy of the heat source of temperature @xmath32 . the energy density @xmath33 . we define a spherically symmetric gravitational potential @xmath34 to be that of a two - component isothermal sphere , which includes stars and a massive dark halo @xcite . the galaxy model is characterized by four parameters : the stellar velocity dispersion @xmath35 , the characteristic radius of the stellar mass distribution @xmath36 the ratio of the stellar and dark matter ( dm ) velocity dispersions @xmath37 and the ratio of the dark matter mass density and the stellar mass density at the centre of the galaxy @xmath38 for the prototype galaxy ngc 4472 , we set @xmath39 km s@xmath5 , @xmath40 kpc , @xmath41 , @xmath42 , which allows us to reproduce its surface brightness profiles both in the optical and in x - rays with a reasonable accuracy . in this case sinks and sources of mass and energy for the hot phase are locally compensated everywhere in the galaxy if the parameters @xmath20 , @xmath43 , and @xmath44 are constant . hydrostatic equilibrium requires an adjustment of the temperature of the hot gas @xmath45 and of the stellar velocity dispersion @xmath35 . this is achieved by additional restrictions applied to the values of @xmath43 and @xmath32 coupled by @xmath46 where @xmath47 is the gas constant and the mean molecular weight @xmath48 [ see @xcite for more detail ] . for a specific stellar mass loss rate @xmath49 s@xmath5 @xcite , hydrostatic equilibrium is achieved with a reasonable mass deposition efficiency of @xmath50 and a characteristic temperature of the heat source of @xmath51 k. this temperature is lower than the @xmath52 k corresponding to a sn type ia rate of @xmath53 snu @xcite , but it is higher than the @xmath54 k obtained for a supernova rate of @xmath55 snu @xcite . note , that we do not claim ngc 4472 to be a _ perfect _ galaxy with an isothermal hot ism , an isothermal stellar system and an isothermal dark halo . rather we construct a simple model whose physical properties are based on observations of ngc 4472 . the use of a restricted set of control parameters allows us to investigate in which way(s ) our model differs from the real object . the evolutionary equations are solved by means of the amra code @xcite , which is based on the direct eulerian version of the ppm method of colella & woodward on an adaptively refined hierarchical system of completely nested grids @xcite . for the present 1d and 2d axisymmetric simulations we use spherical coordinates . the computational domain extends from @xmath56pc ( @xmath57pc in 1-d simulations ) to @xmath58kpc in radius and covers ( in 2d simulations ) the wedge @xmath59 . periodic boundary conditions are imposed in the angular direction . in the radial direction hydrostatic equilibrium is assumed at @xmath60 and at @xmath61 , i.e. the radial ( and theta ) velocity is set to zero and the boundary pressure is defined in such a way that the pressure gradient at the boundary is equal to the hydrostatic one . we allow for up to 4 levels of refinement with density and pressure jumps of 10 per cent used as refinement criteria . with refinement ratios of 4 and 2 in radius and angle , respectively , the resolution of our 2-d models is equivalent to that of a uniform grid run with @xmath62 zones ( @xmath63pc and @xmath64 ) . the source terms are calculated explicitly @xcite using the operator split approach . in the presence of heat conduction the equilibrium recycling model for the hot gas in giant ellipticals is meta - stable @xcite . it means that , while arbitrary infinitesimal perturbations do not grow , perturbations of a finite amplitude can switch the system to a different equilibrium state or to a nonequilibrium catastrophic evolutionary regime . since we are mostly interested in studying thermal effects and since the characteristic thermal time scale is usually longer than the dynamical time , it is quite natural to examine the response of the system to a class of perturbations , which do not disturb the hydrostatic equilibrium . in general , the system can be perturbed in a number of different ways . however , the approximation of spherical symmetry , which allows us to reduce the problem to 1-d , is rather restrictive . the simplest perturbation of this class is a global density perturbation @xmath65 which , at first sight , may seem to be unphysical because of its global nature . however , due to stratification of the hot gas , the thermal time scale depends strongly on radius , i.e. for a time scale of a few @xmath66 yr the perturbation only affects the inner region because the rest of the hot gas has not enough time to react . hence , for a sufficiently short time interval the global perturbation is equivalent to a more local one . we have computed a series of spherically symmetric solutions with initial global density perturbation amplitudes @xmath67 and 0.2 , and compared the results obtained with different spatial resolution in the central cooling region . left and right panels of fig . [ inflow ] illustrate our results for @xmath67 . the left panel shows distributions of density temperature and velocity at @xmath68 , 50 , 100 , 150 , 200 , 250 , and 300 myr for our intermediate resolution run with a radial spacing of 12 pc . the heavy lines indicate the initial conditions . the quasi - steady regime is already established at @xmath69 myr after having passed through the linear growth regime which covers most of the earlier epochs . then , for a very short time , a transient dynamic inflow occurs . afterwards the flow remains quasi - steady . the gas temperature in the cooling core drops below the equilibrium value @xmath70 by a factor of @xmath71 . the density distribution shows a central cusp @xmath72 with a power index @xmath73 . hence , this model predicts a compact central peak in the x - ray surface brightness . this peak can be observed if the instrument has sufficient angular resolution , and if finite optical depth effects in the inflowing dense core will not render the approximation of an optically thin plasma invalid . note , that heat conduction and/or magnetic pressure support can modify the stability of the initial equilibrium model and even suppress the formation of the cooling core @xcite . the right panel shows the flow variables at @xmath74 myr soon after a compact cooling inflow has been established in the core region of @xmath75 kpc in radius . the effects of the finite grid resolution are most evident in the velocity plot . changes in the grid resolution effectively modify the position of the inner boundary thus determining the lowest velocity and temperature , and the highest density values attained on the grid . at the coarsest grid spacing of 48 pc the compact inflow region ( @xmath76 pc ) is covered by less than 10 grid zones and hence remains unresolved . steep gradients of dependent variables introduce interpolation errors , and errors due to explicit calculation of the source terms . these errors caused by the finite difference scheme are amplified by the physical thermal instability and , as a result , for @xmath77 the numerical solution displays high frequency noise in the temperature distribution for @xmath78myr . using the same spatial resolution but doubling the size of the initial perturbation ( @xmath79 ) makes the inflow even more dynamic and the noise amplitude becomes so large that the numerical solution eventually switches from the inflow to the outflow regime ( see fig . [ sketch ] ) . grid resolution determines the amount of numerical dissipation of ppm . although ppm does not utilize artificial viscosity explicitely , its interpolation scheme introduces some amount of dissipation , which depends on grid resolution . when increasing the resolution by a factor of 16 to @xmath80 pc the decreased numerical dissipation is found to be too small to prevent the development of small scale condensations due to the physical thermal instability inherent to flows with radiative cooling [ see , e.g. , hunter , binney & tabor ] . as a result , a quasi - steady inflow solution is obtained ( solid lines in the right panel of fig . [ inflow ] ) , which becomes unstable soon after @xmath81 myr causing the breakup of the central density enhancement into multiple spherical condensation fronts . at an intermediate spatial resolution of 12 pc ( left panels and dashed lines in the right panels of fig . [ inflow ] ) the cooling inflow region is well resolved by @xmath82 grid zones . the numerical solution remains stable for at least 500 myr beyond the initial relaxation to a steady state inflow at @xmath83 myr . note that at higher spatial resolution ( solid lines ; right panels ) the profiles are smoother than at lower grid resolution ( left panels ) . the ripples present at lower resolution can be eliminated , for instance , by including a small phenomenological diffusion term in the equations , as in binney & tabor , or by taking into account thermal conductivity [ kritsuk et al . ] . the numerical experiments discussed below are all performed with a minimum radial grid spacing of 12 pc . at a much coarser grid important hydrodynamic scales remain unresolved , whereas a much finer grid is no longer consistent with our basic assumption that the sinks and sources of mass and energy are distributed continuously . preliminary results obtained in two dimensions assuming axial symmetry indicate that cooling inflows are stable against random small velocity perturbations . the stability is maintained due to advection of linear perturbations towards the inner boundary by the accelerating gas inflow . as an alternative to quasi - steady cooling inflows we have studied a class of subsonic outflow solutions , which can be obtained through negative global perturbations added to the equilibrium density . in such a case heating and mass supply from evolved stars in the galaxy overtake cooling and mass dropout , and instead of a compact cooling core a hot bubble develops in the centre ( fig . [ sketch ] ) . [ outflow ] shows an example of a subsonic outflow solution at @xmath68 , 100 , 200 , and 300 myr for @xmath84 . in addition to the density , temperature , and velocity distributions we also show the entropy , which is defined here as @xmath85 numerical values for the entropy @xmath86 are given assuming @xmath87 . as the gas in the hot bubble expands it compresses the ambient medium and thus creates a leading spherical quasi - isobaric condensation wave . the wave front is clearly seen as a peak in density and as a sharp minimum in the temperature profiles . the gas temperature in the bubble is a factor of @xmath1 higher than the equilibrium temperature @xmath70 . it eventaully saturates at a value of about @xmath88 k which is fixed by the heating rate at the centre . typical expansion velocities in the bubble are about 10 km s@xmath5 . the maximum velocity continuously grows as the bubble expands while less and less dense outer layers of the hydrostatic corona start to feel the energy imbalance due to the initial global density perturbation . the bubble will expand beyond 300 myr ( the state shown in fig . [ outflow ] ) because of the special form of the initial perturbation . thus , the solution will not tend towards a steady galactic wind . since on a timescale of a few gyrs the heating rate and stellar mass loss vary , such steady wind solutions are unrealistic , anyway . negative velocities observed at @xmath89 kpc are related to a sound wave , which is triggered at the beginning of the simulation by small deviations of the initial model from an exact hydrostatic state . the outflow solution is rayleigh - taylor unstable since the initially stable entropy stratification is modified by the expanding bubble . in particular , one may expect that the unstable local entropy inversion associated with the forming condensation front will be smeared out by convective motion , if the restriction of spherical symmetry of the flow is relaxed , and , thus , such a sharp front will never form in reality . in order to initialize the flow in the axisymmetric case we impose besides a @xmath84 global density perturbation also a small random velocity perturbation with an amplitude of @xmath90 of the adiabatic sound speed . this additional axisymmetric perturbation helps us to initiate two - dimensional flow . in the central region , @xmath91kpc , the grid resolution is @xmath92 zones . the evolution has been followed for 300 myr . convection starts to develop after @xmath93 myr from the beginning of the simulation in the form of small - scale vertical finger - like structures . the fingers originate the central region of unstable entropy inversion . high entropy material flows upwards and low entropy material downwards , restoring a marginally stable stratification with an adiabatic temperature gradient @xmath94 as the fingers flowing in opposite directions accelerate , kelvin - helmholtz roll - up transforms them into mushroom - like structures typical for the developing convective pattern ( * ? ? ? * section 6 ) . by @xmath95 myr a convective core with a radius of @xmath75 kpc forms and large scale structures become dominant . at that time the radial velocities of the convective motion reach @xmath96 km s@xmath5 , and convection approaches a quasi - stationary regime . still later , when the outer gas layers start to feel the imbalance of mass and energy gains and losses due to the global initial density perturbation , these layers become involved into the convective motion , too . as the temperature in the hot bubble grows and the convective core expands , large scale convective structures with higher flow velocities appear . at @xmath97 myr the linear size of the largest mushroom is about 3 kpc and typical flow velocities are @xmath98 km s@xmath5 . a little bit earlier , at @xmath99 myr , the maximum mach number of 0.54 is recorded for a stream of upflowing hot gas . thus , the convection driven by initially small ergs s@xmath5 . a conservative estimate of @xmath100 ergs s@xmath5 for the typical power supplied by agns in the form of mechanical energy of jets is much larger than this value ( see , e.g. , owen , eilek & kassim ) . the typical power required to sustain radio core sources in elliptical galaxies is about @xmath101 ergs s@xmath5 . our simulations show that a smaller ( @xmath102 ) initial density perturbation develops a convective core with a radius of @xmath103 kpc by 300 myr . ] ( @xmath104 ) deviations from local thermodynamic equilibrium remains subsonic . in a realistic 3-d situation one could expect even lower convective velocities due to the extra dimension available for a redistribution of the kinetic energy . snapshots of the temperature , entropy and vorticity distributions for the inner 4 kpc are shown in figs [ temperature][vorticity ] . the temperature maps clearly exhibit the expansion of the hot bubble and the distorted analogue of the spherically symmetric leading condensation front , which is formed by the uppermost parts of the mushroom caps . the mushrooms are best seen in the entropy maps owing to the formation of an entropy ` plateau ' in the core . the mean value of the entropy in the core steadily grows . consequently , the convective pattern changes from blue via green and yellow to red . the vorticity maps highlight small scale structures in the velocity field and help in tracing the mushroom clouds as counter - rotating eddies forming the caps ( fig . [ vorticity ] ) . the convective core as a whole has a well defined sharp outer boundary defined by the largest mushroom caps . the global maximum of the hot gas density is typically slightly off centre . for further details on the flow evolution we refer to a set of computer animations available at http://www.mpa-garching.mpg.de/hydro . analysis of the angular averages of the hydrodynamic variables allows one to compare the properties of the new equilibrium , the flow evolves slowly on a time scale of hundreds of myrs which is longer than the typical life span of a convective element ( see sections [ fourier ] , [ integral ] ) . ] established in the convective core with those of the hydrostatic recycling model , and those of the outflow solution . [ meanflow ] shows angular averages at 300 myr for the central 4 kpc region . convection has smeared out the condensation front , which forms in the spherically symmetric case . as a result , the averaged convective solution falls in between the equilibrium model and the 1-d outflow . the gas density near the very centre is by a factor of @xmath105 smaller than in the equilibrium , but still larger by a factor of @xmath106 than in the 1-d case . unlike in a compact inflow , there will be no sharp peak in the x - ray brightness in the central 1 kpc in this case ( see also the emissivity distribution in the upper panel of fig . [ meansrc ] ) . an observation with sub - arcsec resolution of a nearby elliptical galaxy , like ngc 4472 , would be a critical experiment to distinguish between the compact inflow and convective outflow realizations in the core . the relatively small density fluctuations about the mean indicate that compressibility is not very important , which is consistent with a subsonic convection regime . the average temperature grows by a factor of @xmath1 in the central 1 kpc and has a shallow minimum at the position of the condensation front . local relative temperature variations in the convective flow are about @xmath107 , mainly at the interface between the convective core and the ambient hydrostatic gas . the average pressure profile shows clear deviations from the hydrostatic stratification . local pressure fluctuations are @xmath108 per cent , and hence imply a quasi - isobaric regime of convection . the angular averaged entropy distribution is almost flat within a 2 kpc core and rises further outwards . there is no entropy inversion as in the 1-d case , i.e. the system has settled to a new equilibrium state via nonlinear saturation of the convective instability . both vertical and horizontal gas velocities are quite high compared to typical cooling flow values of about @xmath109 km s@xmath5 . however , the mean radial velocity at @xmath97 myr lies in the range @xmath110kms@xmath5 , which is similar to the 1-d case , where @xmath111kms@xmath5 . thus , there is no considerable mass flux in the radial direction . in order to assess the efficiency of radiative cooling in the turbulent core , we define the volume emissivity @xmath112 as @xmath113 the two terms on the _ rhs _ in the above equation describe radiative losses from the cooling condensations and direct radiative cooling of the hot gas phase , respectively . the upper panel in fig . [ meansrc ] shows the distribution of the emissivity with radius for the inner 4 kpc . the peak central emissivity in the convective core is an order of magnitude lower than in hydrostatic equilibrium . for @xmath114kpc the emissivity distribution roughly follows the one of the recycling model . local variations of the emissivity by a factor of @xmath115 are detected in the condensation front region between 2 and 3.5 kpc . the lower panel in fig.[meansrc ] shows the relative rates of mass supply from stellar winds and mass deposition due to local thermal instabilities . notice that for @xmath116kpc the mass sink is switched off due to a stabilization by intensive sn - heating ( see equation [ growthrate ] ) . mass dropout dominates on average at radii from 2 to 3 kpc . the oscillations of the mass dropout rate are rather intense between 2 and 3.5 kpc , where the convective flow turns over . all of the best x - ray observations of elliptical galaxy x - ray halos show positive temperature gradients in the central @xmath11710 kpc @xcite . xmm-_newton _ observations of m87 and its x - ray halo report @xmath118 kev in the central circle of @xmath119 ( @xmath120 kpc ) in radius , a ` steep ' temperature rise to @xmath121 kev at @xmath122 ( @xmath123 kpc ) , and a shallow rise to @xmath124 kev in the range from @xmath125 to @xmath126 @xcite . yet the measured temperature gradients do not give us much information about the temperature distribution within the central kpc . only the latter would help us to verify the model assumptions concerning the thermal balance of the hot gas near the centre . the measured gradients can rather point to a slight non - isothermality of the underlying gravitational potential , which traces the transition from the dark matter halo / cluster dominated outer region to the stellar core of m87 @xcite . at the same time , the flat ( on the average ) entropy distribution in the core region of our model is supported by the assumed spherical symmetry of the underlying gravitational potential , average gas density distribution , and the net heat source . as we mention in the introduction , this assumption is restrictive . even a small asymmetry , e.g. , in the central heating efficiency would create a hybrid in / out - flow with a more stable ( on the average ) entropy stratification , i.e. with a mild positive average temperature gradient . as soon as the asymmetric heating is sufficient and , still , centrally concentrated ( as in the case of agn heating ) , such a flow would not necessarily display a central density / x - ray brightness cusp . observationally , one can expect to see convection in the form of uprising hot bubbles interacting with a background flow of cooling gas . it is possible , that flows of this kind are observed in x - rays by _ chandra _ and in radio on vla in ngc 1275 @xcite and in m87 @xcite . such flows seem to be largely subsonic , and the interface of a hot bubble with the background flow does not imply shock waves unlike in the model of heinz , reynolds & begelman . rather , it would be physically similar to the interface of our convective core with the surrounding hydrostatic corona , displaying lower temperatures , larger mass deposition rates and a higher x - ray surface brightness . we shall consider such flows in detail elsewhere . a spectral decomposition of a flow helps to reveal information which is not apparent otherwise , like the distribution of energy over length scales and effects of the finite grid resolution . in order to reveal this information we have computed one - dimensional fourier transforms along the @xmath127-coordinate direction at various radii . strong gravitational stratification of the gas density and the lack of periodicity in the radial direction would dominate the spectrum in the radial direction , and thus would complicate the analysis . for a scalar quantity of interest , @xmath128 , we define the horizontal fourier transform to be @xmath129 which is a function of time , radius , and the horizontal wavenumber @xmath130 . here @xmath131 is the horizontal periodic length . the power spectrum is the square of the modulus of its complex fourier transform , namely @xmath132 . we have used simple periodograms [ see , e.g. , press , teukolsky , vetterling & flannery ] as the power spectra estimates for discrete data sets given on the finest level grid covering the inner convective region of the computational domain . for the spectral analysis we have used the velocity field . when the density is constant , the power spectrum of the velocity field is similar to a kinetic energy spectrum . as the gas density varies only slightly about its mean value with angle at a given radius ( see @xmath133 and @xmath134 envelopes in fig . [ meanflow ] ) , the density factor is always negligible . however , since radial modes are ignored in our 1d analysis , the sum of the power spectra of the velocity components is not expected to be a measure of the total kinetic energy . since instantaneous power spectra are noisy and since they fluctuate considerably in time , we use temporal averages to estimate the typical power distribution with wavenumber . the convective core expands as the source terms associated with the stellar system drive the hot bubble at the centre . hence , we had to take averages over a period of time shorter than the expansion time scale ( @xmath9 yr ) but longer than the lifetime of the largest mushroom - like structures in our convective flow ( @xmath135 myr , see section [ integral ] ) . averaging over a time interval 25 myr sufficiently suppresses the oscillations in the mean spectra at small wavenumbers . we use angle brackets @xmath136 in the following to denote the computed temporal averages . [ power ] shows the power spectra of the two velocity components at radii of 0.71 , 1.32 , 1.93 , 2.54 , and 3.15 kpc , respectively . obviously , the power is concentrated towards the large scales , as already mentioned in section [ flowevol ] when discussing the settling of the convective regime . the spectra do not show any significant radial dependence . the mean slope @xmath137 of the spectra @xmath138 is @xmath139 . following the work of porter & woodward , who investigated the numerical dissipation of the ppm scheme , we estimate that in our simulations numerical dissipation starts to become important for @xmath140 , i.e. for structures smaller than about 16 angular zones . batchelor ( 1969 ) in his paper on two - dimensional isotropic turbulence derived an analogue of the kolmogorov energy spectrum . for 2d flows the spectrum of vorticity is universal . if @xmath141 is the vorticity spectrum , then @xmath142 is the analogue of kolmogorov s power law . for the energy spectrum of 2d flows one has @xmath143 . from our fourier analysis we obtain as expected @xmath144 and @xmath145 in the interval @xmath146 $ ] . this explains the transition from small scale to large scale mushrooms when convection sets in . the characteristics of the convective flow in the inner region can also be examined by calculating the angular averaged energy and a set of energy fluxes , which we define below following hurlburt , toomre & massaguer . the angular integrated total energy equation ( [ energy ] ) can be expressed as @xmath147 with @xmath148 where @xmath149 is the heat flux due to a spherically symmetric expansion or contraction of the model , @xmath150 is the ` enthalpy ' or convective heat flux , @xmath151 is the kinetic heat flux , and @xmath152 is the net energy source term . these fluxes and the source term are defined as @xmath153 @xmath154 @xmath155 @xmath156 \:r^2\sin{\theta}\:d\theta.\ ] ] the above definitions involve spatially fluctuating variables @xmath157 , where @xmath158 is the angular mean value and @xmath159 is the fluctuation about that mean value . they allow us to discuss correlations between the radial velocity and a number of fluctuating quantities . such correlations provide useful insights into energy generation and energy transport mechanisms in the convective interior of the hot ism . we further define a total energy flux @xmath160 . in a steady state with @xmath161 the total flux does not depend on radius @xmath162 . if a convective flow achieves a statistically steady state , then for sufficiently long time averages the average total energy flux @xmath163 does not dependent on radius as well , while the individual contributing fluxes may vary considerably with @xmath162 . before turning to the fluctuations let us consider the inner 4kpc region where convective motion occurs in a mean ` background ' flow after the onset of the instability . fig.[initialfluxes ] shows the radial dependence of the total energy flux @xmath164 and net source @xmath152 at four representative moments of time before and shortly after the instability sets in . at these times the total flux is directed outwards and increases from zero at @xmath165 to values around @xmath166erg / s at @xmath167kpc mainly due to a slow overall expansion of the gas . this expansion is stimulated partly by an outgoing weak sound wave generated by the initially imperfect hydrostatic equilibrium , and also by the increasing source terms blowing a hot bubble at the centre . since the flow is spherically symmetric for @xmath168 myr , the major contribution to the total flux is due to gas expansion in an external gravity field , i.e. @xmath169 . the small wrinkles visible at @xmath170kpc in the flux diagram at @xmath171myr hint towards a contribution from fluctuations of the developing convective flow , but still @xmath172 . by @xmath97 myr , when the convective flow already covers the whole inner region ( @xmath173 kpc ) , the global expansion driven by the action of the source terms remains the dominant contributor to the total energy flux ( fig . [ fluxes ] ) . note that the mean energy flux carried away from the inner region at @xmath174 myr amounts to about 7 per cent of the luminosity of the hot gas in the whole computational domain @xmath175 kpc ( see fig . [ integral ] ) . our analysis indicates that the fluctuations play only a secondary role for the energy transport . the mean angular integrated convective flux , @xmath176 , is positive everywhere except for the region around @xmath177 kpc , where the mean source @xmath178 attains its minimum , yielding an upward convective transport of thermal energy . like in case of an incompressible fluid a positive flux value corresponds to motions where hot fluid parcels rise and cold ones sink . the depression in @xmath176 at @xmath179 kpc spans the same range in radius as the condensation front smeared by convection . in this region mass dropout due to thermal instabilities dominates over mass supply from stellar winds , and the enthalpy flux , carried by fluctuations from the inner region , decreases . the mean kinetic flux @xmath180 steadily grows in absolute value , as the convective core becomes more extended giving rise to larger convective structures with higher velocities . the kinetic flux is positive ( i.e. directed outwards ) at @xmath181 kpc and weakly negative further out in the region where convective motions overshoot through the condensation front . the sign of @xmath151 is related to differences in strength and filling factor between upward and downward directed motions . in our two - dimensional simulations upflows are considerably faster than downflows in the interior of the convective core and there is no apparent asymmetry in the filling factors ( see the angular velocity diagram in fig . [ meanflow ] ) . in order to follow the evolution of global characteristics of the flow we computed the total hot gas luminosity @xmath182 and the net mass deposition rate @xmath183 as integrals over the whole computational domain ( fig.[integral ] ) . the computed total luminosity is close to the x - ray luminosity @xmath184 erg s@xmath5 of ngc 4472 at a distance of 17 mpc . there is a mild tendency for the luminosity to grow with time as the gas shed by stars in the galaxy slowly accumulates in the convective core . low amplitude oscillations in the luminosity on a time scale of @xmath185myr correspond to a life cycle of the largest convective structures . assuming a linear scale of @xmath186kpc and @xmath187myr , one can estimate a characteristic velocity @xmath188kms@xmath5 . this value is typical for the convective core which developed in the simulations by @xmath189myr ( see fig . [ meanflow ] ) . a time scale of 25myr is also a reasonable choice for the time averaging interval to be used when computing mean power spectra . the net mass deposition rate @xmath183 , given by the volume integral @xmath190 is initially positive , since a negative global density perturbation @xmath191 breaks the balance between the mass supply to the hot phase from stellar winds and mass loss from the hot phase due to local thermal instabilities . the mass supply from stars always dominates , and @xmath183 grows from 0.5 to 0.75m@xmath192yr@xmath5 ( fig.[integral ] ) since the system evolves further away from hydrostatic equilibrium . for our model galaxy with a stellar mass @xmath193m@xmath192 the rate of steady supply of gas from stars , @xmath194m@xmath192yr@xmath5 , implies that the gas condensation rate varies from 0.7 at @xmath68 to @xmath195m@xmath192 yr@xmath5 at 300myr . as one can see in fig . [ integral ] , @xmath183 slightly oscillates in phase with the x - ray luminosity . maxima of @xmath183 record moments when streams of rising hot material form new large scale mushroom - like structures . in this paper we have studied hot gas flows originating in the central few kpc of hot galactic coronae in response to a slight energy supply imbalance in a model initially in equilibrium . it is shown that a negative energy budget drives a quasi - steady compact cooling inflow , which is stable to small perturbations . excessive heating creates an isentropic ( on average ) convective core in the vicinity of the galaxy centre . provided the net energy gain in the core is not too high , the convection remains subsonic with typical flow velocities ( both , radial and angular ) of the order of @xmath196kms@xmath5 . the characteristic convective pattern consists of a manifold of mushroom - like structures of different scales . the power spectra of the velocity components are dominated by the largest - scale mushrooms . the emission weighted gas temperature in the core is slightly rising towards the centre . unlike in the case of a cooling inflow , the x - ray surface brightness of a convective core does not display a sharp maximum at the centre . the inner parts of the convective core are dominated by mass supply from evolved stars , while in the colder outer shell mass drop out dominates the mass budget . large - scale mushrooms ( mainly their caps ) can probably be marginally detected by high resolution x - ray images with good photon statistics , as their volume emissivity is about a factor of 2 higher than that of the surrounding gas . we have considered an idealized case with a spherically symmetric heat source and small deviations from ` thermal ' equilibrium near the centre . however , we can extrapolate our results to a more realistic hydrodynamic picture . first , stronger heating in the vicinity of the centre can drive a supersonic convection with velocities in excess of 400kms@xmath5 and produce a much larger ( here 3 - 4kpc ) convective region . second , a type ia sn heating rate which is lower all over the galaxy , and an excessive heating by an agn in the central region will create a hybrid flow with an inner convective core and an outer ` cooling flow ' , which will vanish in convection when the inflow velocity is very subsonic . our preliminary results indicate that such a hybrid dynamic flow can be stable and can last as long as the central source is active . third , a low type ia sn heating rate without extra energy supply near the centre will drive a more extended massive cooling inflow with an even more pronounced central surface brightness peak . it would be harder to turn such a dynamic inflow into an outflow by a strong perturbation ( e.g. , a burst of agn activity , or a merger ) than a weaker compact inflow . finally , we expect that an asymmetric central heat source in excess of the equilibrium value would create bubble(s ) filled with a ( mean ) isentropic convective flow with properties similar to the ones described above . _ chandra _ , _ newton _ and future x - ray missions will teach us more about the hydrodynamics of ` cooling flows ' . ak was partly supported by the russian foundation for basic research ( project 98 - 02 - 19670 ) and by the federal targeted programme _ integration _ ( project a 0145 ) . tp was partly supported by grant 2p03d.014.19 from the polish committee for scientific research . the simulations were performed on the risc cluster of the mpa , and on the sgi power challenge at the interdisciplinary centre for computational modelling in warsaw .

we use hydrodynamic simulations with adaptive grid refinement to study the dependence of hot gas flows in x - ray luminous giant elliptical galaxies on the efficiency of heat supply to the gas . we consider a number of potential heating mechanisms including type ia supernovae and sporadic nuclear activity of a central super - massive black hole . as a starting point for this research we use an equilibrium hydrostatic recycling model @xcite . we show that a compact cooling inflow develops , if the heating is slightly insufficient to counterbalance radiative cooling of the hot gas in the central few kiloparsecs . an excessive heating in the centre , instead , drives a convectively unstable outflow . we model the onset of the instability and a quasi - steady convective regime in the core of the galaxy in two - dimensions assuming axial symmetry . provided the power of net energy supply in the core is not too high , the convection remains subsonic . the convective pattern is dominated by buoyancy driven large - scale mushroom - like structures . unlike in the case of a cooling inflow , the x - ray surface brightness of an ( on average ) isentropic convective core does not display a sharp maximum at the centre . a hybrid model , which combines a subsonic peripheral cooling inflow with an inner convective core , appears to be stable . we also discuss observational implications of these results . [ firstpage ] hydrodynamics instabilities cooling flows galaxies : ism ism dark matter

SECTION 1. SHORT TITLE. This Act may be cited as the ``Vacancies Clarification Act of 1998''. SEC. 2. FINDINGS. Congress finds that-- (1) Congress enacted the Act entitled ``An Act to authorize the temporary supplying of vacancies in the executive departments'', approved July 23, 1868 (commonly referred to as the ``Vacancies Act''), to-- (A) preclude the extended filling of a vacancy in an office of an executive or military department subject to Senate confirmation, without the submission of a Presidential nomination; (B) provide an exclusive means to temporarily fill such a vacancy; and (C) clarify the role of the Senate in the exercise of the Senate's constitutional advice and consent powers in the Presidential appointment of certain officers; (2) subchapter III of chapter 33 of title 5, United States Code, includes a codification of the Vacancies Act, and (pursuant to an amendment on August 17, 1988, to section 3345 of such title) specifically applies such vacancy provisions to all Executive agencies, including the Department of Justice; (3) the legislative history accompanying the 1988 amendment makes clear in the controlling committee report that the general administrative authorizing provisions for the Executive agencies, which include sections 509 and 510 of title 28, United States Code, regarding the Department of Justice, do not supersede the specific vacancy provisions in title 5, United States Code; (4) there are statutory provisions of general administrative authority applicable to every Executive department and other Executive agencies that are similar to sections 509 and 510 of title 28, United States Code, relating to the Department of Justice; (5) despite the clear intent of Congress, the Attorney General of the United States has continued to interpret the provisions granting general administrative authority to the Attorney General under sections 509 and 510 of title 28, United States Code, to supersede the specific vacancy provisions in title 5, United States Code; (6) the interpretation of the Attorney General would-- (A) virtually nullify the vacancy provisions under subchapter III of chapter 33 of title 5, United States Code; (B) circumvent the clear intention of Congress to preclude the extended filling of certain vacancies and provide for the temporary filling of such vacancies; and (C) subvert the constitutional authority and responsibility of the Senate to advise and consent in certain appointments; (7) it is necessary to further clarify the intention of Congress to reject the interpretation of the Attorney General by modernizing the intricate language of the long-standing Vacancies Act; and (8) to ensure compliance by the executive branch with the Vacancies Act, the Act needs an express enforcement mechanism. SEC. 3. FEDERAL VACANCIES. (a) In General.--Chapter 33 of title 5, United States Code, is amended by striking sections 3345 through 3349 and inserting the following: ``Sec. 3345. Acting officer ``(a)(1) If an officer of an Executive agency (other than the General Accounting Office) whose appointment to office is by the President, by and with the advice and consent of the Senate, dies, resigns, or is otherwise unable to perform the functions of the office, the President may direct a person described under paragraph (2) to perform the functions and duties of the office temporarily in an acting capacity, subject to the time limitations of section 3346. ``(2) The person referred to under paragraph (1) is any person who on the date of death, resignation, or the beginning of inability to perform serves-- ``(A) in the position of first assistant to the officer who dies, resigns, or is otherwise unable to perform; or ``(B) in an office for which appointment by the President, by and with the advice and consent of the Senate is required. ``(b) With respect to the office of the Attorney General of the United States, the provisions of section 508 of title 28 shall be applicable. ``Sec. 3346. Time limitation ``(a) The person serving as an acting officer as described under section 3345 may serve in the office-- ``(1) for no longer than 120 days; or ``(2) if any nomination for the office is submitted to the Senate within the 120-day period beginning on the date the vacancy occurs, for the period that the nomination is pending in the Senate. ``(b)(1) If the nomination for the office is rejected by the Senate or withdrawn, the person may continue to serve as the acting officer for no more than 120 days after the date of such rejection or withdrawal. ``(2) Notwithstanding paragraph (1), if a second nomination for the office is submitted to the Senate during the 120-day period after the rejection or withdrawal of the first nomination, the person serving as the acting officer may continue to serve-- ``(A) until the second nomination is confirmed; or ``(B) for no more than 120 days after the second nomination is rejected or withdrawn. ``(c) If a person begins serving as an acting officer during an adjournment of the Congress sine die, the 120-day period under subsection (a) shall begin on the date that the Senate first reconvenes. ``Sec. 3347. Application ``Sections 3345 and 3346 are applicable to any office of an Executive agency (other than the General Accounting Office) for which appointment by the President, by and with the advice and consent of the Senate, is required, unless-- ``(1) another statutory provision expressly provides that such provision supersedes sections 3345 and 3346; or ``(2) the President makes an appointment to fill a vacancy in such office during a recess of the Senate. ``Sec. 3348. Vacant office ``Subject to section 3347, if an office is not temporarily filled under sections 3345 and 3346 within 120 days after the date on which a vacancy occurs, the office shall remain vacant until a person is appointed by the President, by and with the advice and consent of the Senate. ``Sec. 3349. Enforcement ``(a)(1) An acting officer who serves in a position in violation of section 3345 or 3346 may not receive pay for any day of service in violation of section 3345 or 3346. ``(2) Pay not received under paragraph (1) shall be forfeited and may not be paid as backpay. ``(3) Notwithstanding section 1342 of title 31, paragraph (1) shall apply regardless of whether such acting officer is performing the duties of another office or position in addition to performing the duties of the vacant office. ``(b) The head of an affected Executive agency (other than the General Accounting Office) shall submit to the Comptroller General of the United States and to each House of Congress-- ``(1) notification of a vacancy and the date such vacancy occurred immediately upon the occurrence of the vacancy; ``(2) the name of any person serving in an acting capacity and the date such service began immediately upon the designation; ``(3) the name of any person nominated to the Senate to fill the vacancy and the date such nomination is submitted immediately upon the submission of the nomination; and ``(4) the date of a rejection or withdrawal of any nomination immediately upon such rejection or withdrawal. ``(c) If the Comptroller General of the United States makes a determination that an officer is serving longer than the 120-day period including the applicable exceptions to such period as provided under section 3346, the Comptroller General shall report such determination to each House of Congress, the President, the Secretary of the Treasury, and the Office of Personnel Management.''. (b) Technical and Conforming Amendment.--The table of sections for chapter 33 of title 5, United States Code, is amended by striking the items relating to sections 3345 through 3349 and inserting the following: ``3345. Acting officer. ``3346. Time limitation. ``3347. Application. ``3348. Vacant office. ``3349. Enforcement.''. SEC. 4. EFFECTIVE DATE AND APPLICATION. This Act shall take effect on the date of enactment of this Act and shall apply to any office that-- (1) becomes vacant after such date; and (2) is vacant on such date, except sections 3345 through 3349 of title 5, United States Code (as amended by this Act), shall apply as though such office first became vacant on such date.

Vacancies Clarification Act of 1998 - Revises provisions regarding the filling of Federal vacancies to authorize the President, if an appointed officer of an executive agency (other than the General Accounting Office (GAO)) dies, resigns, or is otherwise unable to perform office functions, to direct a person described by this Act to perform such functions temporarily in an acting capacity, subject to specified time limitations. Describes a person authorized to perform such functions as one: (1) in the position of first assistant to the officer unable to perform; or (2) in an office for which appointment by the President, with the advice and consent of the Senate, is required. Applies vacancy provisions of the Federal judicial code with respect to the office of the Attorney General. Retains existing time limitations on temporary appointments. Makes vacancy and time limitation provisions applicable to any affected office for which an advice and consent appointment is required unless: (1) another statutory provision expressly supersedes such provisions; or (2) the President makes an appointment to fill a vacancy during a Senate recess. Requires an office to remain vacant until a person is appointed if not temporarily filled within 120 days after the date the vacancy occurs. Prohibits acting officers serving in violation of vacancy or time limitation provisions from receiving pay. Requires pay not received to be forfeited and prohibits backpay. Directs the heads of affected executive agencies to submit to the Comptroller General and to the Congress: (1) notification of a vacancy and the date such vacancy occurred immediately upon occurrence of the vacancy; (2) the name of the person serving in an acting capacity and the date such service began immediately upon the designation; (3) the name of any person nominated to fill the vacancy and the date such nomination is submitted immediately upon submission; and (4) the date of a rejection or withdrawal of any nomination immediately upon such action. Requires the Comptroller General to report to the Congress, President, Secretary of the Treasury, and the Office of Personnel Management any determination that an officer is serving longer than the prescribed 120-day period, including exceptions to such period.

Kevin Collins case: SFPD looking at man Kevin Collins 1982 mug shot of Dan Therrien, identified by San Francisco police on Feb. 6, 2013, as a "person of interest" in the disappearance of 10-year-old Kevin Collins. The boy vanished in February 1984. 1982 mug shot of Dan Therrien, identified by San Francisco police on Feb. 6, 2013, as a "person of interest" in the disappearance of 10-year-old Kevin Collins. The boy vanished in February 1984. Photo: Photo From San Francisco Police, San Francisco Police Photo: Photo From San Francisco Police, San Francisco Police Image 1 of / 7 Caption Close Kevin Collins case: SFPD looking at man 1 / 7 Back to Gallery (02-07) 09:16 PST SAN FRANCISCO -- San Francisco police probing the 1984 disappearance of a 10-year-old boy sought the public's help Wednesday in providing information about a man with a history of kidnapping and molestation in Canada and San Francisco who died five years ago. "This is a case that haunts the San Francisco Police Department and the city of San Francisco," Chief Greg Suhr said at a press conference at which investigators identified a person of interest in the long-cold case of Kevin Collins' disappearance. "We carry it with us every day." The man on whom police are focused was last known as Dan Leonard Therrien, but also used at least four other names in his life. He was living in a Masonic Avenue home in 1984 not far from where Kevin was last seen near the Panhandle. Police working the renewed investigation into the boy's disappearance searched the home last week, but found only what are believed to be dog bones. Therrien matched the description of a 6-foot-tall man who was sitting on steps when he was talking to Kevin shortly before the boy was last seen Feb. 10, 1984, at Masonic and Oak Street, police said. Kevin was waiting for a bus after leaving basketball practice at nearby St. Agnes School. The man had a large, black dog, witnesses said. Therrien had such a dog, but two witnesses who were shown pictures of Therrien could not identify him as the person they had seen talking to Kevin, police said. "They saw him just in passing, so they might not remember his face well enough," homicide Inspector Joe Toomey said. Therrien allowed police to search the Masonic Avenue home in 1984, but authorities found nothing, Suhr said. Authorities knew then that Therrien had been arrested in San Francisco under the name of Wayne D. Jackson in April 1981 in connection with an incident in which a 7-year-old boy had been kidnapped at Fisherman's Wharf and molested, police said. Therrien jumped bail but was caught in March 1982 at the home on Masonic, where he was living under the name Kelly Sean Stewart. Therrien was sentenced under the name of Jackson to six months in jail and three years' probation for felony lewd acts on a child, court records show. Although investigators looking into Kevin's disappearance were aware of that case, they did not know that Therrien had also been accused of kidnapping and molesting two 13-year-old boys in 1973 in Canada, because he had been arrested under the name Raymond William Stewart. Therrien fled to the United States after being released on bail. He was never prosecuted for the crime, "in part because of the multiple identities he used," homicide Lt. Tim Plyer said at the press conference. He died under the name of Therrien in February 2008 in San Francisco. He was listed as 51 under that name, but ages he gave with other aliases would have made him 61. In addition to searching the home where he once lived, police showed a photo of Therrien to Kevin's mother, Ann Collins of Concord, Suhr said. She could not be reached for comment Wednesday. Suhr said Therrien's multiple aliases had contributed to the "rather winding road getting to this guy." "What we're looking for now is anybody that saw this guy back in 1984, anybody who talked to this guy back in 1984, anybody who talked to somebody who talked to this guy back in 1984," the chief said. "We would love to find out the whereabouts of that little boy." ||||| A man known as Dan Leonard Therrien (top), and Wayne Jackson (bottom) is seen in these photographs released by the San Francisco Police Department February 6, 2013. Dan Leonard Therrien, also known as Wayne Jackson and three other names, is seen in this California drivers license photograph taken April 26, 1999 and released by the San Francisco Police Department February 6, 2013. Wayne Jackson, who was known to go by four other names, is seen in this police booking photograph taken June 18, 1982 and released by the San Francisco Police Department February 6, 2013. SAN FRANCISCO Police using cadaver dogs and jack hammers have renewed their probe into the fate of a young San Francisco boy who became a national symbol for abducted children three decades ago, and they publicly identified their prime suspect for the first time on Wednesday. San Francisco police held a news conference to enlist the public's help in learning more about a man investigators had questioned in the disappearance of 10-year-old Kevin Collins just days after he vanished in 1984. The suspect, Wayne Jackson, who was known to go by four other names, lived across the street from the Catholic grammar school that Kevin attended in the Haight-Ashbury District. He had a history of sex crimes against children and died in 2008, police said. The American public came to know Kevin after he was among the first missing children to have his picture printed on milk cartons distributed throughout the nation. Newsweek magazine ran his photograph on its cover under the headline "Stolen Children." "This is a case that haunts the San Francisco Police Department and the city of San Francisco," police Chief Greg Suhr said. Kevin was last seen at a bus stop following a school basketball practice on February 10, 1984. Normally, Kevin traveled to and from school with his brother, but his sibling was home sick that day. The last two people known to have seen Kevin alive said the boy with the gap-toothed smile had been talking to a blond, 6-foot-tall man with a large dog. Jackson, who listed his birth date as between 1947 and 1956, fit the description and had a dog like the one the witnesses described. Police also learned then that he had been arrested in 1981 for kidnapping a 7-year-old boy and attempting a sex act with the child. After skipping bail, Jackson was re-arrested and ended up serving six months in jail, police said. After Kevin's disappearance, police searched Jackson's home but found nothing. The two witnesses who reported seeing Kevin talking with a tall blond man failed to identify Jackson in a photo lineup, and the lead seemed to die there -- until last month. A new group of cold-case detectives decided in recent days to try turning up fresh clues with cadaver dogs, and two dogs were brought in for a first-ever search of the basement and garage of Jackson's old home last week. Both dogs independently responded to the same spot in the garage, and a city crew jack-hammered through the concrete and unearthed fragmentary skeletal remains last Tuesday. So far, however, the bones appear to be from an animal. Additional tests are continuing in a state crime lab. Meanwhile, investigators recently learned that Jackson had been arrested in 1973 in Canada on charges he kidnapped two 13 year olds but fled Canada before that case could be resolved, police said. Kevin's disappearance tore up his family. His parents divorced, and his father dedicated himself to finding his son and other missing children by starting the Kevin Collins Foundation for Missing Children. On the 10th anniversary of Kevin's disappearance, when the boy on the milk carton would have been 20, his parents and his eight brothers and sisters held a private memorial service at Holy Cross Cemetery in Colma, south of San Francisco. There they dedicated a bench to him inscribed with his name, a cross and the words, "Forever in our hearts." (Reporting and writing by Ronnie Cohen; Editing by Steve Gorman and Lisa Shumaker)

– San Francisco police have reopened a 29-year-old abduction case, renewing the search for the body of Kevin Collins, who disappeared in 1984 when he was 10 years old, and publicly naming a suspect for the first time. That suspect, who was last known as Dan Leonard Therrien but has gone by at least four names, died in 2008, the San Francisco Chronicle reports. Therrien had a history of pedophilia, and matched the description of a 6-foot-tall man seen with Kevin shortly before his disappearance. Investigators searched Therrien's home back in 1984 and found nothing. But in recent days, police used cadaver dogs and jackhammers to search his property, Reuters reports. They quickly found bones buried in the garage, but initial testing seems to indicate that they're from an animal. Kevin was one of the first missing children ever put on a milk carton. "This is a case that haunts the San Francisco Police Department," the police chief said. "We carry it with us every day."

the study of dynamics of opinion formation is nowadays a hot topic in the statistical physics of complex systems , with a considerable amount of papers published in the last years ( see @xcite and references therein ) . even simple models can exhibit an interesting collective behavior that emerges from the microscopic interaction among individuals or agents in a given social network . usually those models exhibit nonequilibrium phase transitions and rich critical phenomena , which justifies the interest of physicists in the study of opinion dynamics @xcite . in the last few years , a recent attention has been done to the kinetic exchange opinion models ( keom ) @xcite , inspired in models of wealth exchange @xcite . the lccc model was the first one to consider kinetic exchanges among pairs of agents that present continuous states ( opinions ) @xcite . in this case , the model presents a continuous symmetry - breaking phase transition . after that , some extensions were analyzed for continuous and discrete opinions . for example , the inclusion of competitive interactions @xcite , three - agents interactions @xcite , dynamic self - confidence @xcite , presence of inflexible agents @xcite , and others , similarly to was done previously in other opinion dynamics , like the galam s models @xcite . in all these extensions the critical behavior of the system was extensively analyzed . dynamics of decision - making has been treated in several works in psychology @xcite and neuroscience @xcite . for the dynamics of opinion formation , we find many models by physicists dedicated to explain the decision - making process or the exchange of opinion through interactions among agents @xcite . the mechanisms consider kinetic exchanges ( keom @xcite ) , imitation ( voter model @xcite , sznajd model @xcite ) or the power of local majorities ( majority - rule model @xcite , majority - vote model @xcite ) , among others . nevertheless , the inclusion of noise and disorder can be considered in such models @xcite . usually discrete opinion models consider two distinct positions or opinions @xmath5 ( yes or no , democrat or republican , candidate a or candidate b ) . they can be enriched with the inclusion of a third state , @xmath6 , representing neutral state or indecision . indecision is a current and rising phenomenon which affects both recent and consolidated democracies @xcite . many reasons can lead an individual to become neutral or undecided , for example it can be associated to an anticonformism / nonconformism to the proposals on both sides of the debate . the impact of indecision / neutrality was considered recently in many works @xcite . in this work we consider a discrete keom in the presence of noise and disorder . in addition to pairwise random interactions , we introduce an indecision noise that significantly affects the dynamics of the system . our aim is to analyze the critical behavior of the model . in this case , based on analytical and numerical results , we found three distinct phase transitions , namely the usual ferro - paramagnetic transition , and two distinct transitions to an absorbing state : from the ferromagnetic state and from the paramagnetic one . we considered a keom @xcite with competitive positive / negative interactions . our artificial society is represented by @xmath7 individuals in a fully - connected graph . each agent @xmath8 can be in one of three possible opinions at each time step @xmath9 , i.e. , @xmath10 or @xmath2 . this general scheme can represent a public debate with two distinct choices , for example _ yes _ and _ no _ , and also including the undecided / neutral state . the following microscopic rules control our model : 1 . we choose two agents at random , say @xmath8 and @xmath11 , in a way that @xmath11 will try to persuade @xmath8 ; 2 . with probability @xmath12 , the opinion of agent @xmath8 in the next step @xmath13 is updated according to the kinetic rule @xmath14 $ ] ; 3 . with probability @xmath4 , the agent @xmath8 spontaneously change to the neutral state , i.e. , @xmath15 . in the above dynamic rule , sgn(x ) is the signal function defined such that sgn(0)=0 . this is usual in keom , in order to keep all the agents opinions in one the three possible ones , @xmath0 , @xmath1 or @xmath2 @xcite . the pairwise couplings @xmath16 are quenched random variables does not affect our results , they can also be considered as annealed variables . ] that follows the discrete probability distribution @xmath17 . in other words , the parameter @xmath3 stands for the fraction of negative interactions . as discussed in previous works @xcite , the consideration of such negative interactions produces an effect similiar to the introduction of galam s contrarians in the population @xcite . in addition , competitive interactions were also considered for the modelling of coalition forming @xcite . the probability @xmath4 acts as a noise in the system , and it allows an autonomous decision of an individual to become neutral @xcite . it can be viewed as the volatility of some individuals , who tend to spontaneously change their choices . in a two - candidate election , if a given individual does not agree with the arguments of supporters of both sides , he / she can decide to not vote for any candidate , and in this case he / she becomes neutral . in this case , this indecision noise must be differentiated / disassociated from other usual kinds of noises because , unlike the others , it privileges only the neutral opinion . as a recent example , in the 2012 usa election barack obama and mitt romney disputed for the election for president as the main candidates . it was reported that two months out from election day , nearly a quarter of all registered voters are either undecided about the presidential race or iffy in their support for a candidate , as indicated by polls @xcite . for @xmath18 , i.e. , in the absence of noise , the model undergoes a nonequilibrium order - disorder ( or ferro - paramagnetic ) transition at a critical fraction @xmath19 @xcite . in the ordered ferromagnetic phase , one of the extreme opinions @xmath0 or @xmath1 dominates the population , whereas in the disordered paramagnetic phase the three opinions coexist with equal fractions ( @xmath20 ) . at this point , some definitions are necessary . the order parameter of the system can be defined as @xmath21 that is the `` magnetization per spin '' of the system , and @xmath22 stands for average over disorder or configurations , computed at the steady states . let us also define @xmath23 and @xmath24 as the stationary fractions or densities of opinions @xmath25 and @xmath2 , respectively . one can start considering the probabilities that contribute to increase and decrease the order parameter . following @xcite , one can obtain the master equation for @xmath26 , @xmath27 - \\ \nonumber & & \mbox{}- qf_1 -(1-q ) [ ( 1-p)f_1 f_{-1 } + pf_{1}^{2 } + ( 1-p)f_0 f_{-1 } + \\ & & \mbox{}+ pf_0 f_{1 } ] = 0 ~.\end{aligned}\ ] ] in the stationary state @xmath28 . using the normalization condition @xmath29 , we obtain two solutions for eq . ( [ eq2 ] ) in the stationary state , namely @xmath30 , which implies in @xmath31 ( disordered solution ) , or @xmath32 in this case , eq . ( [ eq3 ] ) is valid in the ferromagnetic phase . we emphasize that @xmath18 leads to @xmath33 , which agrees with the result of ref . one can obtain another equation for @xmath24 considering the fluxes into and out of the neutral state @xmath6 . in this case , the master equation for @xmath24 is given by @xmath34 considering the disordered phase , where @xmath31 , eq . ( [ eq4 ] ) gives us in the stationary state ( where @xmath35 ) @xmath36\left(\frac{1-f_{0}}{2}\right ) ~,\ ] ] which gives us two solutions , namely @xmath37 which can be ignored by considering the steady state of the other two fractions @xmath38 and @xmath39 @xcite , or @xmath40 in this case , eq . ( [ eq6 ] ) is valid in the paramagnetic phase . the above equations ( [ eq3 ] ) and ( [ eq6 ] ) are both valid at the critical point , and we can equate them to obtain @xmath41 these critical noises separate the ferromagnetic and the paramagnetic phases . as discussed above , in the ferromagnetic phase one of the extreme opinions @xmath0 or @xmath1 dominates the population ( one of the sides wins the debate ) , whereas in the paramagnetic phase the two extreme opinions coexist ( @xmath42 , i.e. , there is no decision ) . notice that we recover @xmath43 in eq . ( [ eq6 ] ) and @xmath19 in eq . ( [ eq7 ] ) for @xmath18 , in agreement with @xcite . in order to obtain an analytical expression for the order parameter , one can consider the fluxes into and out of the state @xmath44 . the master equation for @xmath38 is then @xmath45 - ( 1-q)\left[pf_{1}^{2 } + ( 1-p)f_{1 } f_{-1}\right ] - \\ & & \mbox{}-qf_{1 } ~.\end{aligned}\ ] ] considering the normalization condition and the expression for @xmath24 valid in the ferromagnetic phase , eq . ( [ eq3 ] ) , we obtain for @xmath38 in the stationary state ( where @xmath46 ) @xmath47 \pm \sqrt{\delta}}{2(1-p)(2p-1 ) } ~,\ ] ] where @xmath48[1 - 2(2p+q - pq ) ] ~.\ ] ] eq . ( [ eq9 ] ) is plotted in fig . [ fig1 ] as a function of @xmath4 for typical values of @xmath3 . as eq . ( [ eq9 ] ) predicts two solutions ( see the @xmath49 signals ) , one has two curves for each value of @xmath3 since @xmath50 , where @xmath51 is given by eq . ( [ eq7 ] ) . when @xmath52 assumes one of these values consequently @xmath39 takes the other one . the curve labeled as @xmath42 is the disordered paramagnetic solution for the stationary fractions @xmath38 and @xmath39 this solution signals the limit of validity of eq . ( [ eq9 ] ) , and it will be discussed in the following . the order parameter can be given by @xmath53 . considering eqs . ( [ eq3 ] ) and ( [ eq9 ] ) for @xmath24 and @xmath38 , respectively , one obtains @xmath54 \left [ 1 - 2(2p+q - pq)\right ] } } { ( 1-p)(1-q ) \sqrt{1 - 2p } } ~.\ ] ] one can see from eq . ( [ eq11 ] ) that consensus is reached only for @xmath55 , i.e. , in the absence of negative interactions and noise all agents of the system will share one of the extreme opinions , @xmath0 or @xmath1 . in order to obtain the critical exponent @xmath56 that governs the order parameter in the vicinity of the order - disorder phase transition , one can simplify eq . ( [ eq11 ] ) using eqs . ( [ eq3 ] ) and ( [ eq7 ] ) . in this case , we have @xmath57 where @xmath24 is given by eq . ( [ eq3 ] ) , i.e. , the solution valid in the ferromagnetic phase . in other words , one can write the order parameter in the usual form @xmath58 , where @xmath59 , a typical ising mean - field exponent in a ferro - paramagnetic phase transition , suggesting that our model is in the same universality class of the mean - field ising model , as expected due to the mean - field character of the interactions . on the other hand , the case @xmath60 presents a distinct behavior . putting @xmath60 in eq . ( [ eq3 ] ) , one obtains @xmath61 using this result , @xmath62 obtained from eq . ( [ eq7 ] ) and putting @xmath60 in eq . ( [ eq13 ] ) , the order parameter can be written as @xmath63 and thus @xmath64 , where @xmath65 and @xmath66 . furthermore , using @xmath67 in eq . ( [ eq14 ] ) , we have @xmath37 , which implies in @xmath68 due to the normalization condition . this result implies that for @xmath69 and @xmath60 all agents will be in the neutral state @xmath6 . a look to the microscopic rules that define our model shows that the system will remain in this state forever , indicating an absorbing state . thus , we have for @xmath60 an active - absorbing ( ferromagnetic - absorbing ) phase transition , i.e. , the critical behavior is affected and the system can be mapped in the universality class of mean - field directed percolation ( or contact process ) @xcite . as previous discussed , if @xmath70 the order parameter goes to zero with @xmath59 , signaling a ferromagnetic - paramagnetic phase transition at critical points @xmath51 given by eq . ( [ eq7 ] ) . for @xmath71 the ferromagnetic solution for @xmath72 , eq . ( [ eq3 ] ) is not valid anymore . in this case the valid solution for @xmath24 is given by eq . ( [ eq6 ] ) , the solution in the paramagnetic phase . considering eq . ( [ eq6 ] ) and that in the paramagnetic phase we have @xmath31 , one obtains @xmath73 that is the above - mentioned solution for @xmath42 in the paramagnetic phase , see fig . [ fig1 ] . from eq . ( [ eq16 ] ) , one can see that @xmath74 and @xmath75 for @xmath76 . these solutions are not physically acceptable , and thus the valid solution for @xmath76 is @xmath68 and @xmath37 . in addition , as @xmath77 in the paramagnetic phase , we can use another order parameter to analyze the system in the vicinity of @xmath78 , namely @xmath79 where we used eq . ( [ eq6 ] ) . in this case , we have @xmath80 in the absorbing phase ( where @xmath37 ) and @xmath81 in the paramagnetic phase ( where @xmath82 ) . one can rewrite eq . ( [ eq17 ] ) as @xmath83 where @xmath84 and @xmath85 . thus , for @xmath86 the system is always in an absorbing phase with all individuals sharing the neutral state @xmath6 ( or in other words @xmath37 ) , independent of @xmath3 . thus , the transition may be of active - absorbing type for @xmath60 , or paramagnetic - absorbing for @xmath87 , both occurring at @xmath88 and belonging to the directed percolation universality class ( critical exponent @xmath65 ) @xcite . for the best of our knowledge , it is the first time that the para - absorbing transition appears in a keom . to complement our results , we performed numerical simulations for a population size @xmath89 . we computed the order parameter @xmath26 by eq . ( [ eq1 ] ) . in fig . [ fig2 ] we exhibit the numerical results for @xmath26 versus @xmath4 and typical values of @xmath3 , together with the analytical result given by eq . ( [ eq11 ] ) . one can observe transitions at different points @xmath90 that depend on @xmath3 , with the usual finite - size effects for @xmath91 , @xmath92 and @xmath93 ( see the inset ) . moreover , we can also see in the inset that the order parameter goes exactly to zero for @xmath94 , independent of the value of @xmath3 , confirming the transition to the absorbing state , as analytically predicted . finally , we performed simulations in order to obtain estimates of the other critical exponents , since our analytical results give us only the critical points and the exponent @xmath56 . for the ferro - paramagnetic transition , we considered the usual finite - size scaling ( fss ) relations , @xmath95 that are validy in the vicinity of the transition . in addition , for the transitions to the absorbing state ( ferro - absorbing and para - absorbing ) , we considered the dynamic fss relations @xcite @xmath96 in fig . [ fig3 ] we exhibit as an example results for @xmath91 . in pannel ( a ) we show the data collapse for the susceptibility @xmath97 , near the ferro - paramagnetic transition , where we obtained the usual mean - field ising exponents @xmath98 and @xmath99 , that are the standard exponents of keom @xcite . in fig . [ fig3 ] ( b ) we show the time relaxation of the order parameter ( in the inset ) in the vicinity of the para - absorbing transition , as well as the data collapse ( main figure ) , for values near the transition point @xmath88 . our estimates for the critical exponents @xmath100 and @xmath101 are in agreement with the values for the directed percolation ( and contact process ) , @xmath102 and @xmath103 @xcite . to summarize , in fig . [ fig4 ] we exhibit the phase diagram of the model in the plane @xmath4 versus @xmath3 . the line separating the ferromagnetic and paramagnetic phases are given by eq . ( [ eq7 ] ) , valid in the region @xmath104 and @xmath105 . the region for @xmath86 represents the absorbing phase , for all values of @xmath3 , and we also see the ferro - absorbing transition in the @xmath60 axis . in this work we have studied how the inclusion of negative pairwise interactions ( disorder ) and indecision ( noise ) affect the critical behavior of a kinetic exchange opinion model . the agents can be in one of three possible states ( opinions ) , represented by discrete variables @xmath106 and @xmath2 . the topology of the society is a fully - connected network . the disorder is ruled by a parameter @xmath3 , representing the fraction of negative interactions , and the noise is controlled by a parameter @xmath4 , representing the probability of a spontaneous change to the neutral state . we analyzed the critical behavior of the system in the stationary states . the consensus regarding one of the extreme opinions @xmath0 or @xmath1 , a macroscopic collective behavior representing a total agreement , is only reached when the two ingredients , disorder and noise , are completely absent ( @xmath55 ) . for suitable values of @xmath3 and @xmath4 , the system is in an ordered ferromagnetic phase , where one of the two extreme opinions @xmath0 or @xmath1 are shared by the majority of the population . this state mimics the situation where one of the two topics under debate is winner , and presents an order parameter @xmath107 . we also found critical values @xmath51 that separate the ordered ferromagnetic phase from a disordered paramagnetic one . in this last phase , the fractions of extreme opinions are equal and we have a null order parameter , @xmath77 . in this case , the debate does not present a winner side . the critical exponent associated with the order parameter was found analytically to be @xmath108 , and we estimated through monte carlo simulations that the other exponents are @xmath109 and @xmath99 , typical mean - field exponents belonging to the ising model universality class . in this case , our numerical results show the typical finite - size effects for the order parameter when the system undergoes the order - disorder transition . on the other hand , for @xmath60 , i.e. , in the absence of negative interactions , the system is governed only by the noise @xmath4 . in this case , our analytical and numerical calculations showed that there is a critical point @xmath62 above which the system is in an absorbing state . in this state , all agents become neutral , and the dynamics does not evolve anymore , characterizing a typical noise - induced absorbing phase transition . in this case , the order parameter is identically null , and it does not present the usual finite - size effects of order - disorder transitions ( the `` tails '' of the order parameter ) . in this case , we considered the dynamic fss relations for transitions to absorbing states . our analytical results predicted an exponent @xmath65 for the order parameter in the vicinity of the transition , and numerically we found estimates for other exponents , namely @xmath102 and @xmath103 . these exponents are the typical ones for the mean - field directed percolation , a prototype of a nonequilibrium phase transition to an absorbing state @xcite . finally , considering the case @xmath110 and @xmath111 , when the system is in a paramagnetic state , we observed another transition . in this case , for @xmath69 the system is always in the absorbing state , @xmath112 . this phase is the same observed for the case @xmath60 , but now the system goes from a paramagnetic phase with null order parameter to an absorbing phase also with @xmath77 . in this case , in order to calculate the critical exponent @xmath56 , we defined another order parameter based on the stationary fraction @xmath24 of neutral agents , namely @xmath113 . in this case , we have @xmath114 in the paramagnetic phase , where the extreme opinions @xmath0 and @xmath1 coexist with the neutral state @xmath2 , and we have @xmath80 in the absorbing phase , where @xmath37 . in this case , we also observed an exponent @xmath65 , and the paramagnetic - absorbing transition also belongs to the directed percolation universality class . for the best of our knowledge , it is the first time that this para - absorbing transition appears in a keom . all our analysis was done considering the new parameter @xmath4 as the control parameter , but the exponents do not depend on that , the another parameter @xmath3 can be considered as well , and the same critical exponents are found . the universality of the exponents is expected due to the mean - field character of the model . as extensions of this work , it can be considered the inclusion of local or global mass media effects @xcite , as well as the inclusion of a neighborhood ( lattice , network ) . the authors acknowledge financial support from the brazilian funding agency cnpq . fox news , _ poll : key fraction of voters remain undecided , unexcited ahead of election _ , available on - line at http://www.foxnews.com/politics/2012/08/25/poll-large-fraction-voters-remain-undecided-unexcited-ahead-election.html

in this work we study a 3-state ( @xmath0 , @xmath1 , @xmath2 ) opinion model in the presence of noise and disorder . we consider pairwise competitive interactions , with a fraction @xmath3 of those interactions being negative ( disorder ) . moreover , there is a noise @xmath4 that represents the probability of an individual spontaneously change his opinion to the neutral state . our aim is to study how the increase / decrease of the fraction of neutral agents affects the critical behavior of the system and the evolution of opinions . we derive analytical expressions for the order parameter of the model , as well as for the stationary fraction of each opinion , and we show that there are distinct phase transitions . one is the usual ferro - paramagnetic transition , that is in the ising universality class . in addition , there are para - absorbing and ferro - absorbing transitions , presenting the directed percolation universality class . our results are complemented by numerical simulations . keywords : dynamics of social systems , collective phenomena , phase transitions , universality classes

pheochromocytoma ( pheo ) and paraganglioma ( pgl ) are neural - crest derived neoplasms , primarily found in the adrenal gland with a prevalence of 0.1% to 0.6% in patients affected by hypertension . tumors of adrenal medulla predominantly secrete norepinephrine over epinephrine , instead adrenal medulla normally secretes 80% of epinephrine . hypertension , either paroxysmal or sustained , is the most consistent finding in neoplasms , and the classical triad of symptoms ( headache , palpitations , and diaphoresis ) is present in more than 50% of patients . in severe cases , a patient can present with myocardial infarction , heart failure , pulmonary oedema , arrhythmias , or intrachranial hemorrhage . the coexistence of pheo and parkinson 's disease or parkinsonism is very rare , with only 3 cases reported in literature . a 70-year - old man with history of parkinsonism and diabetes mellitus presented to the specialized center of secondary hypertension , university of rome la sapienza , rome , italy for an evaluation of hypertension and an adrenal incidentaloma that was detected on abdomen ultrasonography ( us ) and confirmed by magnetic resonance imaging ( mri ) ( 3 2 cm round mass with the presence of necrotic areas ; fig . ( a ) magnetic resonance imaging ( mri ) : mass in the right adrenal gland ( 3 2 cm ) with the presence of necrotic areas . ( b ) thorax scintiscan with 123-i metaiodio benzilguanidine ( 123-i - mibg ) showed a severely reduced mibg cardiac uptake , with a heart to mediastinum ( hm ) ratio of 1.38 . ( c ) scintiscan with 123-i metaiodio benzilguanidine ( 123-i - mibg ) shows raised activity within the right adrenal gland . at the age of 67 years the patient begun to exhibit gait deficits and bradykinesia of the left lower limb , followed by stiffness of the trunk and amimica facies and limitation in upward gaze . an 123-i - fp - cit ( dat - scan)-spect showed a reduction in the physiological concentration in brain presynaptic dopamine transporters with consequent reduction of the striatal structures . levodopa and benserazide therapy was started , subsequently replaced with levodopa and carbidopa at a dose of 750 mg per daily . after starting treatment with levodopa and carbidopa , he did not report any complaints of episodic headaches , palpitations , sweating , and chest pain . on examination , patient 's pulse rate was 67 beats min , blood pressure ( bp ) was 160/100 mm hg , with postural drop ( 140/80 mm hg ) . his height was 181 cm , and his weight was 75 kg , with a body mass index of 22.8 kg m. no cardiac murmurs or abdominal bruits were revealed . his average 24-hr - ambulatory - bp ( abpm ) was 130/90 mm hg , with nondipping profile . the ecg was normal and mild left ventricular concentric remodeling was showed by an echocardiography . the patient was under treatment with irbesartan , nebivolol , metformin , levodopa , and carbidopa . routine blood tests were normal except for fasting blood glucose ( 138 mg dl ; normal range 70100 mg dl ) . after replacing nebivolol and irbesartan with nifedipine ( 60 mg per daily ) and doxazosin ( 8 mg per daily ) bp decreased to normal values ( 135/85 mm hg ) , and biochemical tests to determine functional hormone secretion were performed . investigation for adrenal hormones , including low - dose dexamethasone suppression test , plasma aldosterone levels were normal , while 2 repeated 24-hr - urinary metanephrines measurements were elevated ( 721 and 782 g/24 hr ; normal range 20345 g/24 hr ; table 1 ) . endocrinological data considering the probability of adrenal pheo , a 123-i- metaiodobenzylguanidine ( 123-i - mibg ) spect scintiscan was performed ; 185 mbq of 123 i - mibg was i.v . administered and planar images of thorax were obtained at 20 min and 4 hr , while images of abdomen were obtained at 4 and 24 hr . thorax scan showed a severely reduced mibg cardiac uptake , with a heart to mediastinum ( hm ) ratio of 1.38 ( hm cut off : 2 ) , highly suggestive of a parkinson 's disease ( fig . 1b ) ; whereas , abdomen scan revealed raised activity within the right adrenal gland , concordant with the mass ( fig . a surgical consult was requested , and the patient , now diagnosed with pheo , was to undergo a surgical resection ; however , the surgery was postponed , and the patient was prescribed with 4 mg of doxazosin twice a day , followed by 5 mg of nebivolol daily after testing for the adequacy of the -blockade in order to prevent paroxysmal increases of bp during surgery . one month later , with a bp of 135/80 mm hg , the patient underwent a laparoscopic tumor resection . the patient has been in regular follow - up for the 12 months , and in treatment with levodopa and carbidopa in addition to doxazosin ( 4 mg per daily ) . during the follow - up adrenal hormone tests were run ( table 1 ) . office and abpm showed optimal control of bp ( average systolic and diastolic bp 125/75 mm hg ) , and laboratory analysis showed normal values of fasting glicemia ( 89 mg dl ) without metformin treatment . since the introduction of imaging techniques in medical practice , abnormalities of unknown clinical significance were found more often . pathology of adrenal incidentaloma may vary from simple benign cyst or lipoma to adrenal carcinoma . the differential diagnosis of the adrenal mass includes several conditions , such as adenoma , myelolipoma , cyst , lipoma , pheo , hyperplasia , adrenal cancer , and metastatic cancer . in order to differentiate the adrenal mass detected on abdominal imaging studies , this hormonal evaluation can be difficult with patients with comorbidities , or with patients who are prescribed with interfering medications . in this article , we discuss the case of pheo in parkinsonian patient , in treatment with dopaminergic medications , that presented with an adrenal incidentaloma . the first case reported by metha et al is a 59-year - old american man with a 7-year history of parkinson 's disease , presented episodes of sudden severe headaches with neck pain , tachycardia , sweating , and paleness associated with marked elevation of bp . these symptoms suggested a condition of hypercathecolaminism , and even though further tests revealed normal values of plasma and urinary metanephrines , an 123-i - mibg - single photon ct ( spect ) was positive for increased uptake in the left adrenal region concordant with the nodule showed in the mri scan . the histopathological examination , after laparoscopic adrenalectomy , revealed an adrenal medullary hyperplasia . the second case reported by collier et al is about a 63-year - old american man , with a 5-year history of parkinson 's disease and a left adrenal incidentaloma . the urinary metabolities of catecholamines were elevated , and 123-i - mibg confirmed an increased activity within the left adrenal gland . histological examination following laparoscopic surgical excision showed the presence of a composite pheo / pgl / ganglioneuroma . the third case reported by shimodaira et al is about a 75-year - old japanese man , affected by parkinson 's disease and paroxysmal hypertension associated with vague abdominal symptoms and right adrenal mass showed during abdominal us . urine analysis revealed elevated levels of catecholamines and their metabolites , and 123-i - mibg scintigraphy showed increased uptake in the right adrenal gland concordant with computed tomography ( ct ) . after laparoscopic adrenalectomy , histopathological examination analysis of the mass confirmed the diagnosis of pheo . parkinson 's disease is a chronic neurodegenerative disorder characterized by dopaminergic dysfunction and disturbances in neurotransmitter system with motor system disorders including tremor , rigidity , slowness of movement , and impaired balance or coordination . levodopa is converted peripherally to other cathecolamines , such as norepinephrine , epinephrine , and their metabolites , and medications containing levodopa may cause false - positive results in endocrine testing for pheo . the clinical presentation and biohumoral markers of pheo depend on the capacity of the neoplasm to synthesize , metabolize , and release catecholamines and their metabolites into circulation . initial biochemical tests for pheo , recommended by clinical guidelines subcommittee of endocrine society , should include measurements of plasma - free metanephrines or urinary fractionated metanephrines . in fact , traditional biochemical tests , including measurements of urine and plasma cathecolamines , and urinary vanilmandelic acid , may be unreliable because catecholamine secretion in pheo is often episodic or even negligible in asymptomatic patients . the higher diagnostic accuracy of metanephrines can be attributed to continuous intratumoral production and secretion of metanephrines into circulatory compartment . particularly , the measurements of urine metanephrines by mass spectrometry provide excellent sensitivity ( 97% ) and specificity ( 91% ) for diagnosis of pheo . several factors have to be taken into account in order to attain a correct interpretation of biochemical test results . preanalytical factors may affect the results , such as exercise , posture , food , stress , and medications ; these factors may alter production or disposition of catecholamines and their metabolites . particularly , some drugs ( acetaminophen , labetalol , buspirone , mesalazine , sulfasalazine , tricyclic antidepressants , and levodopa ) can interfere analytically or pharmacodynamically with measurements of plasma and urinary catecholamines and metabolites , which may result in false - positive test results . particularly , levodopa causes falsely elevated urine normetanephrine , and it can also cause mildly raised values of urine metanephrines . regarding our patient , the dopaminergic medications ( levodopa and carbidopa ) may have interfered in the measurement of free urinary metanephrines ; as it was impossible to discontinue these medications , we performed determination of urinary metanephrines only . another important data showed in these case report ( comprised our case ) were that in all parkinsonian patients with suspected diagnosis of pheo and in treatment with dopaminergic drugs the 123-i - mibg was performed . the mibg scintigraphy is based on evidence that norepinephrine and mibg have the same mechanisms for uptake , storage , and release . radiolabeled i - mibg demonstrate high uptake both in normal sympathetically innervated tissues , such as the heart and salivary glands , and in tumors that express the neurohormone transporters , specifically those of neural crest and neuroendocrine origin . currently , 123-i - mibg is considered the gold standard in diagnosing these tumors . particularly , 123-i - mibg scintigraphy is used as a diagnostic tool for the detection of pheo . the sensitivity of 123-i - mibg scintigraphy in pheo is reported to be 95% , whereas the specificity is 80% to 90% . however , tumors smaller than 1.5 cm in diameter and with extensive necrosis or hemorrhage may yield false - negative results due to poor uptake of the tracer . only limited reports of false - positive uptake in other lesions have been published , and 1 major cause of false - positive findings is urinary tract retention , since the reagent is excreted in the urine . recently , jacobson et al , in a recent meta - analysis of 123-mibg , concluded that although results in clinical practice will likely be a few percentages lower , the long history of successful use of this technique and the recent prospective clinical trial support that continued utility of 123-i - mibg imaging in the diagnosis and management of patients with pheo . another finding observed in our parkinsonian patient during i - mibg ( spect ) scan was the reduced cardiac uptake of the ligand , which was consistent with the postganglionic sympathetic denervation which is frequent in parkinson 's disease . in fact , in recent years , cardiac scintigraphy with mibg labeled with iodine ( 123-i ) have been used in parkinson 's disease for evaluating noradrenergic activity of myocardium . this method provides a functional analysis of the sympathetic postganglionic pathway to evaluate in vivo the noradrenergic neurotransmission of the heart . in conclusion , a feature of parkinson 's disease appears to be an inverse correlation with all types of cancer excluding malignant melanoma . interestingly , the melanocytes and the cells of the pheo derived both from the neural crest . moreover , these 2 types of cells and neurons of the substantia nigra , ascribed to the pathogenesis of parkinson 's disease , are all pigmented cells . this is the only association in contrast to the finding that neurodegenerative diseases have a lower risk of developing neoplasms .

abstractto evaluate the diagnostic route of pheochromocytoma ( pheo ) in a patient under dopaminergic treatment.a 70-year - old man with parkinsonism and under treatment with levodopa and carbidopa came to our observation for evaluation of arterial hypertension and right adrenal mass discovered incidentally.to evaluate adrenal hormone levels we performed a dexamethasone suppression test , plasma aldosterone levels and 24-hr urinary metanephrine , which revealed elevated levels of catecholamines metabolities . 123-i - metaiodobenzylguanidine spect scintiscan revealed raised activity within the right adrenal gland concordant with the mass . the diagnosis of pheo was posed and an elective laparoscopic adrenalectomy was performed ; histopathological examination confirmed the pheo diagnosis.recently the coexistence of pheo and parkinsonism is a very rare association of diseases , with only 3 cases reported in literature . in this article , another case is reported and diagnostic procedures are discussed .

in 2009 , the @xmath4 was first observed by the cdf collaboration in the @xmath5 mass spectrum in the @xmath6 decays with a statistical significance in excess of @xmath7 @xcite . in 2011 , the cdf collaboration confirmed the @xmath8 in the @xmath9 decays with a statistical significance greater than @xmath10 , and observed an evidence for the new resonance @xmath11 with an approximate statistical significance of @xmath12 @xcite . in 2013 , the cms collaboration confirmed the @xmath4 in the @xmath5 mass spectrum in the @xmath13 decays , and fitted the structure to an s - wave relativistic breit - wigner line - shape above a three - body phase - space nonresonant component with a statistical significance exceeding @xmath14 @xcite . in the same year , the d0 collaboration confirmed the @xmath4 in the @xmath15 decays with a statistical significance of @xmath12 @xcite . recently , the lhcb collaboration performed the first full amplitude analysis of the @xmath16 decays with @xmath17 , @xmath18 with a data sample of 3 @xmath19 of @xmath20 collision data collected at @xmath21 and @xmath22 with the lhcb detector , confirmed the @xmath4 and @xmath11 in the @xmath23 mass spectrum with statistical significances of @xmath24 and @xmath25 , respectively , and determined the spin - parity to be @xmath26 with statistical significances of @xmath27 and @xmath28 , respectively @xcite . moreover , the lhcb collaboration observed the new particles @xmath1 and @xmath3 in the @xmath23 mass spectrum with statistical significances of @xmath29 and @xmath30 , respectively , and determined the spin - parity to be @xmath31 with statistical significances of @xmath32 and @xmath33 , respectively @xcite . the measured masses and widths are & x(4140 ) : m = 4146.5 4.5 ^+4.6_-2.8 , = 83 21 ^+21_-14 , + & x(4274 ) : m = 4273.3 8.3 ^+17.2_-3.6 , = 56 11 ^+8_-11 , + & x(4500 ) : m = 4506 11 ^+12_-15 , = 92 21 ^+21_-20 , + & x(4700 ) : m = 4704 10 ^+14_-24 , = 120 31 ^+42_-33 . the @xmath4 , @xmath11 , @xmath1 and @xmath3 are all observed in the @xmath5 mass spectrum , if they are tetraquark states , their quark constituents must be @xmath2 . the s - wave @xmath5 systems have the quantum numbers @xmath34 , @xmath35 , @xmath36 , the p - wave @xmath37 systems have the quantum numbers @xmath38 , @xmath39 , @xmath40 , @xmath41 @xcite . we can construct the interpolating currents with @xmath42 and @xmath43 to study the @xmath4 , @xmath11 and @xmath1 , @xmath3 , respectively . in ref.@xcite , we study the masses and pole residues of the @xmath44 hidden charmed tetraquark states with the qcd sum rules . the theoretical predictions support assigning the @xmath45 and @xmath46 to be the @xmath35 and @xmath47 diquark - antidiquark type tetraquark states , respectively . if we take the @xmath4 as the hidden strange cousin of the @xmath45 , then @xmath48 , the @xmath49 breaking effect is about @xmath50 , which is consistent with our naive expectation . however , detailed analysis based on the qcd sum rules indicates that it is unreasonable to assign the @xmath4 to be the diquark - antidiquark type @xmath2 tetraquark state with @xmath42 @xcite . the charged resonances @xmath51 and @xmath52 have analogous decays @xcite , @xmath53 , @xmath54 . the mass gaps are @xmath55 and @xmath56 , so it is natural to assign the @xmath57 to be the first radial excitation of the @xmath46 @xcite . in ref.@xcite , we study the @xmath46 and @xmath57 with the qcd sum rules in details , the theoretical predictions support assigning the @xmath46 and @xmath57 to be the ground state and the first radial excited state of the @xmath47 tetraquark states , respectively . now we can draw the conclusion tentatively that the energy gap between the ground state and the first radial excited state of the tetraquark states is about @xmath58 . in 2004 , the belle collaboration observed the @xmath0 in the @xmath59 mass spectrum in the exclusive @xmath60 decays @xcite . in 2007 , the babar collaboration confirmed the @xmath0 in the @xmath59 mass spectrum in the exclusive @xmath60 decays @xcite . in 2010 , the belle collaboration confirmed the @xmath0 in the two - photon process @xmath61 @xcite . now the @xmath0 is listed in the review of particle physics as the @xmath62 state with the quantum numbers @xmath34 @xcite . in ref.@xcite , lebed and polosa propose that the @xmath0 is the lightest @xmath63 scalar tetraquark state based on lacking of the observed @xmath64 and @xmath65 decay modes , and attribute the single known decay mode @xmath66 to the @xmath67 mixing effect . if the mass gap between the ground state and the first radial excited state of the tetraquark states is about @xmath58 , just like in the case of the @xmath46 and @xmath57 , the @xmath1 can be assigned to be the first radial excited state of the @xmath0 according to the mass gap @xmath68 . the diquarks @xmath69 have five structures in dirac spinor space , where @xmath70 , @xmath71 , @xmath72 , @xmath73 and @xmath74 for the scalar , pseudoscalar , vector , axialvector and tensor diquarks , respectively , the @xmath75 and @xmath76 are color indexes . the attractive interactions of one - gluon exchange favor formation of the diquarks in color antitriplet @xmath77 not in color sextet @xmath78 @xcite , where @xmath79 , the structure constants @xmath80 , the favored configurations are the scalar ( @xmath81 ) and axialvector ( @xmath82 ) diquark states @xcite , the heavy scalar and axialvector diquark states have almost degenerate masses from the qcd sum rules @xcite . we construct the diquark - antidiquark type currents , @xmath83 to study the lowest tetraquark states @xcite , and observe that the @xmath84 type and @xmath85 type hidden charm tetraquark states have almost degenerate masses @xcite . in this article , we choose the @xmath85 type current to study the @xmath0 and @xmath1 together . in calculations , we observe that the lowest tetraquark masses are much larger than @xmath86 , if the @xmath87 type interpolating currents are chosen . the @xmath72 type diquark states are not as stable as the @xmath82 type and @xmath88 type diquark states , the @xmath89 type tetraquark states are expected to have much larger masses than that of the @xmath84 type and @xmath85 type tetraquark states . so in this article , we choose the @xmath89 type current to study the @xmath3 . in this article , we assign the @xmath0 and @xmath1 to be the ground state and the first radial excited state of the @xmath90 type @xmath2 tetraquark states respectively , assign the @xmath3 to be the ground state of the @xmath91 type @xmath2 tetraquark state , and study their masses and pole residues with the qcd sum rules in details . in ref.@xcite , chen et al interpret the @xmath1 and @xmath3 as the d - wave diquark - antidiquark type @xmath2 tetraquark states with @xmath92 , the @xmath4 and @xmath11 as the s - wave diquark - antidiquark type @xmath2 tetraquark states with @xmath93 based on the qcd sum rules . the article is arranged as follows : we derive the qcd sum rules for the masses and pole residues of the @xmath0 , @xmath1 and @xmath3 in section 2 ; in section 3 , we present the numerical results and discussions ; section 4 is reserved for our conclusion . in the following , we write down the two - point correlation functions @xmath94 and @xmath95 in the qcd sum rules , @xmath96 where @xmath97 we choose the currents @xmath98 and @xmath99 to interpolate the @xmath0 , @xmath1 and @xmath3 , respectively . at the phenomenological side , we insert a complete set of intermediate hadronic states with the same quantum numbers as the current operators @xmath98 and @xmath100 into the correlation functions @xmath94 and @xmath101 to obtain the hadronic representation @xcite . after isolating the ground state and the first radial excited state contributions from the pole terms in the @xmath94 , which are supposed to be the tetraquark states @xmath0 and @xmath1 respectively , and isolating the ground state contribution from the pole term in the @xmath95 , which is supposed to be the tetraquark state @xmath3 , we get the following results , @xmath102 where the pole residues or coupling constants @xmath103 are defined by @xmath104 there maybe also exist non - vanishing coupling constants @xmath105 , @xmath106 we can take into account those contributions . in calculations , we observe that the existence of the non - vanishing coupling constants @xmath105 leads to bad qcd sum rules . it is better to neglect them . the tetraquark operators @xmath98 and @xmath100 contain a hidden strange component . if we contract the quark pair @xmath107 in the currents @xmath98 and @xmath100 , and substitute it by the quark condensate @xmath108 , we obtain @xmath109 the scalar currents @xmath110 and @xmath111 couple potentially to the scalar charmonium @xmath112 , @xmath113 where the decay constant @xmath114 from the qcd sum rules @xcite . the coupling constants have the relation @xmath115 , moreover , the @xmath116 and @xmath117 in the currents @xmath98 and @xmath100 are valent quarks , while the @xmath116 and @xmath117 in the currents @xmath110 and @xmath111 are not valent quarks , they are just normalization factors . so the contaminations from the @xmath112 are very small . the diquark - antidiquark type currents couple potentially to tetraquark states , the currents can be re - arranged both in the color and dirac - spinor spaces , and changed to special superpositions of color singlet - singlet type currents , @xmath118 @xmath119 the color singlet - singlet type currents couple potentially to the meson - meson pairs or molecular states . the diquark - antidiquark type tetraquark state can be taken as a special superposition of a series of meson - meson pairs , and embodies the net effects . the component @xmath120 couples potentially to the meson pair @xmath121 , not the scalar charmonium @xmath112 alone , the main component of the @xmath122 is @xmath123 from the qcd sum rules @xcite . the contaminations from the @xmath112 can be neglected safely . in the following , we briefly outline the operator product expansion for the correlation functions @xmath94 and @xmath95 in perturbative qcd . we contract the @xmath116 and @xmath124 quark fields in the correlation functions @xmath94 and @xmath95 with wick theorem , and obtain the results : @xmath125 { \rm tr}\left [ \gamma^{\alpha } c^{n^{\prime}n}(-x)\gamma^{\mu } c s^{m^{\prime}mt}(-x)c\right ] \ , , \\ \pi_5(p)&=&i\varepsilon^{ijk}\varepsilon^{imn}\varepsilon^{i^{\prime}j^{\prime}k^{\prime}}\varepsilon^{i^{\prime}m^{\prime}n^{\prime}}\int d^4x e^{ip \cdot x } \nonumber\\ & & { \rm tr}\left [ \gamma_{\mu}\gamma_5 c^{kk^{\prime}}(x)\gamma_5\gamma_{\alpha } cs^{jj^{\prime}t}(x)c\right ] { \rm tr}\left [ \gamma^{\alpha } \gamma_5c^{n^{\prime}n}(-x)\gamma_5\gamma^{\mu } c s^{m^{\prime}mt}(-x)c\right ] \ , , \end{aligned}\ ] ] where the @xmath126 and @xmath127 are the full @xmath116 and @xmath124 quark propagators , respectively , @xmath128 @xmath129 and @xmath130 , the @xmath131 is the gell - mann matrix , @xmath132 @xcite . then we compute the integrals both in the coordinate space and in the momentum space to obtain the correlation functions @xmath94 and @xmath95 therefore the qcd spectral densities through dispersion relation . in this article , we carry out the operator product expansion to the vacuum condensates up to dimension ( @xmath133 ) 10 and take the assumption of vacuum saturation for the higher dimension vacuum condensates . the condensates @xmath134 , @xmath135 , @xmath136 , @xmath137 and @xmath138 are the vacuum expectations of the operators of the order @xmath139 . we take the truncations @xmath140 and @xmath141 in a consistent way , the operators of the orders @xmath142 with @xmath143 are discarded . finally we can take the quark - hadron duality below the continuum thresholds @xmath144 and perform borel transform with respect to the variable @xmath145 to obtain the qcd sum rules : @xmath146 @xmath147 where @xmath148 the explicit expression of the qcd spectral density @xmath149 is given in the appendix . we differentiate eq.(19 ) with respect to @xmath150 , then eliminate the pole residue @xmath151 , and obtain the qcd sum rule for the mass of the tetraquark state @xmath3 , @xmath152 we take the predicted mass @xmath153 as input parameter , and obtain the pole residue @xmath151 from eq.(19 ) . now we study the masses and pole residues of the @xmath0 and @xmath1 . in ref.@xcite , m. s. maior de sousa and r. rodrigues da silva introduce a new approach to calculate the masses and decay constants of the ground state and the first radial excited state of the conventional @xmath154 , @xmath155 and @xmath156 mesons with the qcd sum rules . we introduce the notations @xmath157 , @xmath158 , and use the subscripts @xmath159 and @xmath160 to denote the ground state @xmath0 and the first radial excited state @xmath1 , respectively , then write the qcd sum rule in eq.(18 ) in the following form , @xmath161 where the subscript @xmath162 denotes the qcd side of the borel transformed correlation function . we differentiate the qcd sum rule with respect to @xmath163 to obtain @xmath164 then we have two equations , it is easy to solve them to obtain the qcd sum rules , @xmath165 where @xmath166 . again we differentiate above qcd sum rules with respect to @xmath163 to obtain @xmath167 the squared masses @xmath168 satisfy the following equation , @xmath169 where @xmath170 @xmath171 , @xmath172 . we solve the equation in eq.(26 ) and obtain the solutions @xmath173 the squared masses @xmath174 and @xmath175 from the qcd sum rules in eqs.(28 - 29 ) are functions of the borel parameter @xmath176 , continuum threshold parameter @xmath177 and energy scale @xmath178 . in ref.@xcite , m. s. maior de sousa and r. rodrigues da silva extract the masses and decay constants of the conventional mesons @xmath179 , @xmath180 , @xmath181 from the qcd spectral densities at the special energy scales @xmath182 , @xmath183 and @xmath184 , respectively , and observe that the theoretical values of the ground state masses are smaller than the experimental values . the new approach has a remarkable shortcoming . in ref.@xcite , we apply the new approach to study the hidden charm tetraquark states @xmath46 and @xmath57 , and use the energy scale formula , @xmath185 to determine the energy scales of the qcd spectral densities so as to overcome the shortcoming , and reproduce the experimental values of the masses @xmath186 and @xmath187 satisfactorily , where the @xmath188 denote the tetraquark states and the @xmath189 is the effective @xmath124-quark mass @xcite . we take the masses @xmath186 and @xmath187 from the bes collaboration and lhcb collaboration respectively as input parameters to determine the optimal energy scales @xmath190 , @xmath191 of the qcd spectral density firstly , then we search for the suitable borel parameter and continuum threshold parameter , and obtain predicted masses @xmath192 and @xmath193 from the qcd sum rules , which happen to coincide with the experimental values @xmath186 and @xmath187 , respectively . on the other hand , we vary the energy scales @xmath178 of the qcd spectral density , and search for the suitable borel parameter and continuum threshold parameter to extract the masses @xmath192 and @xmath193 at each energy scale . in calculations , we observe that the predicted masses @xmath192 and @xmath193 vary with the energy scales @xmath178 , the optimal energy scales @xmath178 satisfy the energy scale formula in eq.(30 ) @xcite . the two routines lead to the same result , we can choose either of them . in this article , we choose the first routine , take the masses @xmath194 , @xmath195 and @xmath153 from the particle data group and lhcb collaboration respectively as input parameters , use the energy scale formula in eq.(30 ) to determine the energy scales of the qcd spectral densities and extract the masses @xmath196 , @xmath197 and @xmath153 from eq.(28 ) , eq.(29 ) and eq.(21 ) , respectively , and examine whether or not they coincide with the experimental values @xmath198 , @xmath199 and @xmath200 respectively , in other words , whether or not the predicted masses satisfy the energy scale formula . the basic input parameters at the qcd side are shown explicitly in table 1 . the quark condensates , mixed quark condensates and @xmath201 masses evolve according to the renormalization group equation , we take into account the energy - scale dependence , @xmath202^{\frac{4}{9}}\ , , \nonumber\\ \langle\bar{s}g_s \sigma gs \rangle(\mu)&=&\langle\bar{s}g_s \sigma gs \rangle(q)\left[\frac{\alpha_{s}(q)}{\alpha_{s}(\mu)}\right]^{\frac{2}{27}}\ , , \nonumber\\ m_c(\mu)&=&m_c(m_c)\left[\frac{\alpha_{s}(\mu)}{\alpha_{s}(m_c)}\right]^{\frac{12}{25 } } \ , , \nonumber\\ m_s(\mu)&=&m_s({\rm 2gev } ) \left[\frac{\alpha_{s}(\mu)}{\alpha_{s}({\rm 2gev})}\right]^{\frac{4}{9 } } \ , , \nonumber\\ \alpha_s(\mu)&=&\frac{1}{b_0t}\left[1-\frac{b_1}{b_0 ^ 2}\frac{\log t}{t } + \frac{b_1 ^ 2(\log^2{t}-\log{t}-1)+b_0b_2}{b_0 ^ 4t^2}\right]\ , , \end{aligned}\ ] ] where @xmath203 , @xmath204 , @xmath205 , @xmath206 , @xmath207 , @xmath208 and @xmath209 for the flavors @xmath210 , @xmath211 and @xmath212 , respectively @xcite . . the basic input parameters in the qcd sum rules [ cols="^,^,^,^",options="header " , ] in refs.@xcite , we study the hidden charm ( bottom ) tetraquark states systematically with the qcd sum rules by calculating the vacuum condensates up to dimension 10 in the operator product expansion in a consistent way , and explore the energy scale dependence of the hidden charm ( bottom ) tetraquark states in details for the first time , and suggest a formula @xmath213 to determine the energy scales of the qcd spectral densities . in refs.@xcite , we obtain the effective mass for the diquark - antidiquark type tetraquark states @xmath214 . later , we re - checked the numerical calculations and found that there exists a small error involving the mixed condensates . we correct the small error , and obtain the optimal value @xmath215 @xcite . the borel windows are modified slightly and the numerical results are also improved slightly . in this article , we choose the updated value @xmath215 . if we assign the @xmath0 and @xmath1 to be the ground state and the first radial excited state of the @xmath216 type tetraquark states , respectively , the optimal energy scales are @xmath217 and @xmath218 for the qcd spectral density in the qcd sum rules for the @xmath0 and @xmath1 , respectively , the shortcoming of the new approach introduced in ref.@xcite is overcome . at the energy scale @xmath217 and @xmath218 , we can obtain the physical values @xmath194 and @xmath195 respectively , the associate values @xmath195 and @xmath194 from the coupled eqs.(28 - 29 ) are not necessary the physical values , and are discarded . on the other hand , if we assign the @xmath3 to be the ground state @xmath219 type tetraquark state , the optimal energy scale is @xmath220 . in the conventional qcd sum rules @xcite , there are two criteria ( pole dominance at the phenomenological side and convergence of the operator product expansion at the qcd side ) for choosing the borel parameters @xmath176 and continuum threshold parameters @xmath221 . now we search for the borel parameters @xmath176 and continuum threshold parameters @xmath144 to satisfy the two criteria . the resulting borel parameters and continuum threshold parameters are @xmath222 the contributions of the pole terms are @xmath223 the pole dominance at the phenomenological side is satisfied . the contributions come from the vacuum condensates of dimension 10 @xmath224 are @xmath225 the operator product expansion at the qcd side is well convergent . so it is reliable to extract the masses and pole residues from the qcd sum rules . now we take into account the uncertainties of all the input parameters , and obtain the values of the masses and pole residues of the @xmath0 , @xmath1 and @xmath3 , @xmath226 at the energy scale @xmath217 , @xmath227 at the energy scale @xmath228 , and @xmath229 at the energy scale @xmath220 . the energy scale formula in eq.(30 ) is well satisfied . . , title="fig:",width=264 ] . , title="fig:",width=264 ] then we take the central values of the predicted masses and pole residues as the input parameters , and obtain the corresponding pole contributions of the @xmath0 and @xmath1 respectively , @xmath230 at the energy scale @xmath217 and @xmath231 at the energy scale @xmath228 . it is more reliable to extract the masses and pole residues from the qcd sum rules with larger pole contributions . the pole contribution of the @xmath0 at @xmath217 is larger than that at @xmath228 , we prefer to extract the mass and pole residue of the @xmath0 at @xmath217 and discard the ones at @xmath228 . on the other hand , the pole contribution of the @xmath1 at @xmath228 is larger than that at @xmath217 , we prefer to extract the mass and pole residue of the @xmath1 at @xmath228 and discard the ones at @xmath217 . in this article , we take the referred values @xmath232 as the physical values . the predicted masses @xmath233 , @xmath234 , @xmath235 satisfy the energy scale formula in eq.(30 ) . the predicted masses @xmath233 , @xmath234 , @xmath235 , which are shown explicitly in fig.1 , are in excellent agreement with the experimental data , the present calculations support assigning the @xmath0 and @xmath1 to be the ground state and the first radial excited state of the @xmath216 type @xmath236 tetraquark states , and assigning the @xmath3 to be the ground state @xmath219 type @xmath236 tetraquark state . now we study the finite width effects on the predicted tetraquark masses . the currents @xmath98 and @xmath99 couple potentially with the scattering states @xmath5 , @xmath237 , @xmath238 , @xmath239 , we take into account the contributions of the intermediate meson - loops to the correlation functions @xmath240 and @xmath241 , @xmath242 where the @xmath243 and @xmath244 are bare quantities to absorb the divergences in the self - energies @xmath245 , @xmath239 . all the renormalized self - energies contribute a finite imaginary part to modify the dispersion relation , @xmath246 we take into account the finite width effects by the following simple replacements of the hadronic spectral densities , @xmath247 where @xmath248 the experimental values of the widths are @xmath249 @xcite , @xmath250 , @xmath251 @xcite . then the phenomenological sides of the qcd sum rules in eqs.(18 - 19 ) undergo the following changes , @xmath252 and @xmath253 where the @xmath254 denotes the borel transformation . so we can absorb the numerical factors @xmath255 and @xmath256 into the pole residues @xmath257 and @xmath151 safely , the intermediate meson - loops can not affect the predicted masses @xmath258 significantly , the zero width approximation in the phenomenological spectral densities works . in this article , we tentatively assign the @xmath0 and @xmath1 to be ground state and the first radial excited state of the @xmath90 type @xmath2 tetraquark states , respectively , assign the @xmath3 to be the ground state @xmath91 type @xmath2 tetraquark state , construct the corresponding interpolating currents , and study their masses and pole residues with the qcd sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in the operator product expansion . moreover , we use the energy scale formula @xmath259 to determine the ideal energy scales of the qcd spectral densities . the numerical results support assigning the @xmath0 and @xmath1 to be the ground state and the first radial excited state of the @xmath90 type @xmath2 tetraquark states , respectively , and assigning the @xmath3 to be the ground state of the @xmath91 type @xmath2 tetraquark state . the explicit expression of the qcd spectral density @xmath149 , @xmath260 @xmath261+(y+z)\left[12\left(2s-\overline{m}_c^2\right)+2\overline{m}_c^4\delta\left(s-\overline{m}_c^2\right ) \right ] \right\ } \nonumber\\ & & -\frac{g_s^2\langle\bar{s}s\rangle^2}{1944\pi^4}\int_{y_i}^{y_f}dy \int_{z_i}^{1-y}dz \ , ( 1-y - z)\left\ { 15\left(\frac{z}{y}+\frac{y}{z } \right)\left(3s-2\overline{m}_c^2 \right)+7\left(\frac{z}{y^2}+\frac{y}{z^2 } \right)\right . \nonumber\\ & & \left.m_c^2\left [ 2+\overline{m}_c^2\delta\left(s-\overline{m}_c^2\right)\right]+(y+z)\left[12\left(2s-\overline{m}_c^2\right ) + 2\overline{m}_c^4\delta\left(s-\overline{m}_c^2\right)\right ] \right\ } \nonumber\\ & & -\frac{m_sm_c \langle\bar{s}s\rangle^2}{12\pi^2}\int_{y_i}^{y_f}dy \left\ { 2+\widetilde{m}_c^2\delta(s-\widetilde{m}_c^2)\right\}\nonumber\\ & & + \frac{m_c^3\langle\bar{s}s\rangle}{144\pi^2 } \langle\frac{\alpha_sgg}{\pi}\rangle\int_{y_i}^{y_f}dy \int_{z_i}^{1-y}dz \left(\frac{y}{z^3}+\frac{z}{y^3}+\frac{1}{y^2}+\frac{1}{z^2}\right)(1-y - z)\nonumber\\ & & \left(1+\frac { \overline{m}_c^2}{t^2}\right ) \delta\left(s-\overline{m}_c^2\right)\nonumber\\ & & -\frac{m_c\langle\bar{s}s\rangle}{48\pi^2}\langle\frac{\alpha_sgg}{\pi}\rangle\int_{y_i}^{y_f}dy \int_{z_i}^{1-y}dz \left(\frac{y}{z^2}+\frac{z}{y^2}\right)(1-y - z ) \left\{2+\overline{m}_c^2\delta\left(s-\overline{m}_c^2\right ) \right\}\nonumber\end{aligned}\ ] ] @xmath262 where @xmath263 , @xmath264 , @xmath265 , @xmath266 , @xmath267 , @xmath268 , @xmath269 , when the @xmath270 functions @xmath271 and @xmath272 appear . this work is supported by national natural science foundation , grant numbers 11375063 , and natural science foundation of hebei province , grant number a2014502017 .

in this article , we tentatively assign the @xmath0 and @xmath1 to be the ground state and the first radial excited state of the axialvector - diquark - axialvector - antidiquark type scalar @xmath2 tetraquark states , respectively , assign the @xmath3 to be the ground state vector - diquark - vector - antidiquark type scalar @xmath2 tetraquark state , and study their masses and pole residues with the qcd sum rules in details by calculating the contributions of the vacuum condensates up to dimension 10 . the numerical results support assigning the @xmath0 and @xmath1 to be the ground state and the first radial excited state of the axialvector - diquark - axialvector - antidiquark type scalar @xmath2 tetraquark states , respectively , and assigning the @xmath3 to be the ground state vector - diquark - vector - antidiquark type scalar @xmath2 tetraquark state . + zhi - gang wang + department of physics , north china electric power university , baoding 071003 , p. r. china pacs number : 12.39.mk , 12.38.lg key words : tetraquark state , qcd sum rules

let us consider the following problem . we have a square chessboard with sides of length @xmath0 and a simple random walk on it . more precisely , think the chessboard as the square lattice box @xmath1 with the simple random walk @xmath2 on @xmath3 . denote by @xmath4 the hitting time of a set @xmath5 for the walk @xmath2 and by @xmath6 the law of @xmath2 starting from @xmath7 . can you find a probability law @xmath8 on the subsets @xmath9 of @xmath3 with cardinality @xmath10 such that @xmath11\right ] \text { does not depend on } x\text { ? } \ ] ] in other words , can you sample @xmath12 `` well distributed points '' among the @xmath13 points of @xmath14 ? in this example , a possible simple answer is the following . take @xmath9 to be the set of either white or black squares of the chessboard with probability @xmath15 . one could then raise the following questions : * what if the random subsets @xmath9 are required to have any other cardinality @xmath16 ? * what if , instead of the chessboard @xmath3 , we consider any other finite weighted ( possibly oriented ) graph ? we notice that the case @xmath17 is trivial , and that in the case @xmath18 , it is known that it suffices to choose the point in @xmath3 according to the stationary measure of the walk ( see e.g. @xcite ) . one of the main goals of this paper is to answer these questions for @xmath19 . in the sequel , we work on a finite oriented weighted graph with the natural irreducible markov chain associated with it . we study a certain probability measure on the set of spanning rooted oriented forests on this graph . it will turn out that the set of roots of the forest sampled from this measure , with conditioning on the number of roots , provides a solution to this problem in full generality . as far as practical sampling issues are concerned , by using an algorithm due to wilson and propp @xcite we can sample this measure without conditioning . furthermore , under the assumption that the generator of the random walk associated with the starting weighted graph has only real eigenvalues , we explain how to get a sample with an approximate prescribed number @xmath20 of roots within an error of order @xmath21 . in section [ setting ] below , we introduce the main framework and notation , and in section [ paper ] we describe the structure of the paper and the results we derive . let @xmath2 be a markov process on a finite state space @xmath3 , with @xmath22 . assume @xmath2 is irreducible with generator given by @xmath23,\quad x\in \mathcal{x},\ ] ] with @xmath24 arbitrary and @xmath25 a given collection of non - negative transition rates . note that such a markov process has variable speed depending on the current state , namely , if the chain is at position @xmath26 , the next jump will be performed after an exponential time of rate @xmath27 the collections of rates induces a structure of oriented weighted graph on @xmath3 . in fact , consider the set of oriented edges @xmath28 then @xmath29 is a weighted oriented graph . the main object of our investigation is a measure on the spanning rooted oriented forests in @xmath30 . let @xmath31 denote the set of spanning forests constituted by oriented rooted trees ( oriented towards their roots ) . for @xmath32 , define the weight of a such a forest by @xmath33 * ( standard forest measure)*[theforest ] denote by @xmath34 the set of roots of a forest @xmath35 , i.e. , the set of points which are the roots of the trees constituting @xmath36 . fix @xmath37 and define on @xmath31 the measure @xmath38 given by @xmath39 by normalizing it via the partition function : @xmath40 we denote the resulting probability measure by @xmath41 we call _ standard measure _ , _ standard partition function _ and _ standard probability measure _ , the objects defined by equations , , and , respectively . * remarks : * there are obvious similarities between the weights appearing in equation ( [ standardforestmeasure ] ) and those of fortuyn - kasteleyn model . we stress here the main differences . fk - percolation is defined on spanning graphs that are not required to be forests . however , in the zero limit of its main parameters , properly rescaled , the model does converge to a measure on spanning forests ( see e.g. @xcite ) . nevertheless , our forests are rooted and this extra structure introduces an entropic factor in comparison ( by projection on unrooted forests ) with this zero limit of fk - percolation . we note that the weights in ( [ forestweight ] ) are those associated by freidlin and wentzell with the so called `` @xmath42-graphs '' @xcite and we will recover some of their results in this paper . our standard forest measure has also been studied in various works . for example to sample points from the stationary measure of the random walk @xcite , or to study in @xcite recurrent configurations of abelian dissipative sandpile introduced in @xcite . this spanning forest measure and other associated objects we will discuss later are actually a variation on the theme of uniform spanning trees and loop - erased random walks . we refer to @xcite and references therein for the vast literature on the subject . as it will become clear , the measure in definition [ theforest ] and the associated partition function encode several information related to the chain @xmath2 . at the occurrence , we will derive several results related with slightly more general measures and partition functions . to this aim , we introduce here some further notation . let us first introduce a natural generalization of the measure in definition [ theforest ] . let @xmath43 be the space of square matrices of size @xmath44 . given a collection of extra weights @xmath45 : \ : x\in\mathcal{x}\}$ ] , let @xmath46 be the diagonal matrix in @xmath43 defined by @xmath47 with @xmath48 for @xmath49 . we anticipate that these extra weights will be interpreted as killing rates for the chain @xmath2 . set @xmath50 and define the measure @xmath51 by @xmath52 by assuming that there is at least one @xmath53 with @xmath54 we can turn @xmath51 into a probability measure on @xmath31 by normalizing it via the partition function : @xmath55 and we denote the resulting probability measure by @xmath56 this is the general form of the probability measure at the core of our investigation . when answering the questions raised in section [ chessboard ] , we need the following special case of the generalized measure in . for a given subset @xmath5 , suppose that the collection of extra weights @xmath45 , x\in\mathcal{x}\}$ ] is such that @xmath57 in this case , @xmath58 , and we write @xmath59 for the measure and the partition function , @xmath60 and @xmath61 , respectively . in particular , for @xmath62 , @xmath63 and @xmath64 . note further that , when @xmath65 , we recover the _ standard _ measure and partition function , @xmath66 and @xmath67 . in the sequel we will denote by @xmath68 a random variable on a probability space @xmath69 with values in @xmath70 and law @xmath71 . to avoid ambiguities , when needed , we write @xmath72 , @xmath73 or @xmath74 in place of @xmath75 . our analysis of the forest measures introduced above will lead us to several results . before describing them and the organization of the paper , we emphasize herein what we consider as our three main results . first , in theorem [ determinantalroots ] we prove that the set of roots @xmath76 sampled from the standard measure in is a determinantal process . more precisely , denoting by @xmath77 , the transition probabilities of the markov chain @xmath2 in observed at independent exponentially distributed times of parameter @xmath78 , we have that @xmath79 with @xmath80 being the determinant of @xmath81 restricted to @xmath82 ( see section [ notation ] below for the notation ) . this echoes burton and pemantle transfer current theorem ( @xcite , thm 1.1 ) . our kernel @xmath81 is however not required to be reversible ( and with possibly complex eigenvalues ) , and we present a direct proof not relying on transfer currents . the second result is an answer to the questions in the introductory section [ chessboard ] . in fact , in theorem [ hittingrootsthm ] we give a formula for the hitting times of random sets constituted by the roots of our standard random forests , with or without conditioning on having a fixed number of roots . in particular , such a formula is independent of the starting point @xmath26 . while wilson and propp algorithm gives a way to sample the unconditioned measure , in section [ hittingtimes ] we explain how to obtain , in absence of complex eigenvalues , a sample with approximately @xmath20 roots , with an error of order @xmath21 , for any @xmath83 . our third result concerns a non - trivial algebraic statement on symmetric matrices derived in @xcite , thm 3.2 therein . this theorem has been used in some recent probabilistic works @xcite to study absorption times of reversible markov chains on general finite graphs , as a key tool to define , in such a general setting , the local equilibria introduced in @xcite . in @xcite , the author motivates the importance of having a probabilistic interpretation of micchelli and willoughby algebraic result . in section [ mw ] we restate their result and give , by means of our standard forest measure , probabilistic insights into their proof . the rest of the paper is organized as follows . * background material : * section [ background ] is a warm - up section where we provide some known background material . in section [ loops ] we prove in a slightly different way a result originally due to marchal @xcite on loop - erased trajectories , proposition [ marchal ] . in section [ wilson ] we recall wilson s algorithm , definition [ wilson ] , and as a corollary of proposition [ marchal ] , following @xcite , we show how to sample our unconditioned measures , corollary [ wilsonprob ] . * results : * section [ main ] is the bulk of this work where we derive our results . each subsection presents some new results related with our forest measures . section [ forroots ] presents the first analysis on the forest measures , in theorem [ partitionthm ] and corollary [ bernoullicity ] therein we show some connection of these measures with the spectrum of the chain @xmath2 . in theorem [ determinantalroots ] we prove that the set of roots is a determinantal process . in section [ hittingtimes ] we prove theorem [ hittingrootsthm ] on the hitting times of the roots set , answering the questions raised in section [ chessboard ] . section [ mw ] concerns a partial probabilistic interpretation of the proof and result by micchelli and willoughby @xcite . in section [ marmelata ] we mention a couple of coalescence and fragmentation processes associated with our measures . one of them is obtained by coupling together all the standard forest measures for different values of @xmath78 . the focus of section [ pietruccia ] is on the ` rooted partitions ' induced by our spanning forests , proposition [ localequilibria ] , and on the cumulants , or truncated correlation functions , of the roots process , section [ cumulants ] . * appendix : * appendix [ appendix ] is devoted to technical known results used along the paper , which we derive in our context in order to have a self - contained work . in appendix [ schur ] , we recall what is the schur complement for block matrices and its probabilistic interpretation , proposition [ schurprob ] . in appendix [ wentzell ] , we give different proofs of two lemmas from freidlin and wentzell ( lemmas 3.2 , 3.3 in @xcite ) on hitting distribution and times of subsets of the graph , again by means of our forest measure . these lemmas are used in section [ hittingtimes ] . appendix [ divideddiff ] concerns the notion of divided differences which are used in section [ mw ] . we state three equivalent definitions and prove a related lemma . to conclude this introductory section and to simplify the reading , we fix here some notation . further notation will be introduced at the occurrence . * _ set theory _ * * * spaces : * @xmath84 will be our reference state space for the markov process @xmath2 . in the sequel , we work with extensions of @xmath84 which will be denoted by @xmath85 or with more general spaces denoted by @xmath86 . * * * subsets : * the symbols @xmath87 and @xmath88 will be used as inclusion and strict inclusion , respectively . subsets will be generally denoted by capital letters : @xmath89 . * * * complement : * unless specified , we always deal with subsets of the space @xmath84 . for a given subset @xmath90 , we denote by @xmath91 the complement of @xmath82 in @xmath84 . * _ graphs _ * * * edges * : @xmath30 introduced in stands for the set of oriented edges on @xmath84 . * * * extreme points of oriented edges : * for an oriented edge @xmath92 , we denote the starting and the ending points of @xmath93 by @xmath94 and @xmath95 , and by @xmath96 the weight associated to it . * * * forest space : * @xmath31 denotes the set of spanning rooted oriented forests on @xmath3 . * * * a given forest : * elements of @xmath31 are denoted by @xmath32 , which can also be seen as subsets of @xmath30 . * * * roots : * given @xmath32 , @xmath76 denotes the set of the roots of the trees constituting @xmath36 . * * * tree associated with a given vertex : * given @xmath26 in @xmath14 and @xmath97 we denote by @xmath98 the unique tree in @xmath36 that covers @xmath26 . we write @xmath99 when @xmath98 is rooted at @xmath26 . * _ matrix _ * * * square matrices space : * the space of square matrices with @xmath44 columns and @xmath44 rows is denoted by @xmath43 . * * * restriction of a matrix : * given a matrix @xmath100 with elements @xmath101 s in @xmath3 , for any subset @xmath82 of @xmath3 , @xmath102_a$ ] stands for the matrix @xmath103 restricted to its elements doubly indexed in @xmath82 . * * * determinants : * @xmath104 will denote the determinant of the matrix obtained from @xmath103 by removing all the lines and columns with indexes outside @xmath105 , i.e. , @xmath106_a)$ ] . * _ random walks _ * * * markov processes and discrete skeletons : * @xmath2 and @xmath107 will denote markov processes on the spaces @xmath3 and @xmath108 , respectively . @xmath109 and @xmath110 will denote some associated discrete - time markov chains . * * * generators : * @xmath111 and @xmath112 denote the generators of the markov processes @xmath2 and @xmath107 respectively . for a given subset @xmath82 of @xmath113 , @xmath114 stands for the generator of the markov process @xmath2 _ restricted _ to the component @xmath82 . while @xmath115 denotes the _ trace _ of the process @xmath107 on some fixed subset @xmath82 of @xmath116 . we introduce here a slightly more general setting than in section [ setting ] . let @xmath107 be a markov process on a finite state space @xmath108 . assume @xmath107 is irreducible with generator given by @xmath117,\quad y\in \mathcal{y},\ ] ] with @xmath118 arbitrary and @xmath119 : \ : ( y , z)\in \mathcal{y}\times \mathcal{y}\}$ ] a given collection of non - negative transition rates . let @xmath120.\ ] ] let @xmath121 be a subset of @xmath108 such that @xmath122 so that , @xmath123 for any @xmath124 , the complement of @xmath121 in @xmath108 . denote by @xmath125 a self - avoiding path of @xmath126 points and length @xmath127 such that @xmath128 for @xmath129 and @xmath130 . for @xmath131 , let @xmath132 the law of the random walk @xmath107 when starting from @xmath133 . denote by @xmath134 a random trajectory obtained from @xmath107 under @xmath132 as follows . stop the walk @xmath107 when it enters the set @xmath121 for the first time and erase all its loops . after this procedure , we are left with a self - avoiding trajectory of variable length . in the next proposition we compute the probability that @xmath134 equals a given trajectory @xmath135 of length @xmath127 . to simplify the proof , we use the discrete skeleton of the markov process @xmath107 on @xmath136 . this justify the following definitions . set @xmath137 and let @xmath138 , with @xmath139 , be the transition matrix identified by the entries @xmath140 such a matrix @xmath141 is a markovian transition matrix for a discrete - time random walk @xmath110 on @xmath86 . in particular , for an arbitrary function @xmath142 , by construction we have that @xmath143 we are in shape to prove the claimed proposition , by using a nice independence argument we learned from laurent tournier @xcite . [ marchal ] * ( marchal @xcite ) * consider the random walk @xmath107 on @xmath108 with generator @xmath112 as in . fix @xmath131 . then , under @xmath132 , @xmath144 with the matrix notation according to section [ notation ] and @xmath145 a self - avoiding path of length @xmath127 such that @xmath128 for @xmath129 and @xmath130 . for the discrete chain @xmath146 , let @xmath147 and @xmath148 be the first return time to @xmath133 and the hitting time of @xmath121 , respectively . more precisely , @xmath149 and @xmath150 . note that by definition of @xmath134 , we have that @xmath151 as a consequence , we can write : @xmath152 it follows from that @xmath153 denote by @xmath154 the local time @xmath146 spends at @xmath133 before entering @xmath121 , and by @xmath155_{b^c}$ ] the matrix @xmath156 restricted to @xmath136 , then @xmath157=\sum_{k\geq 0}[\hat{p}]^k_{b^c}(y_0,y_0)\\ & = ( [ \mathbbm{1}-\hat{p}]_{b^c})^{-1}(y_0,y_0)= \frac{{\rm det}_{b^c\setminus \{y_{0}\}}(\mathbbm{1}-\hat{p})}{{\rm det}_{b^c}(\mathbbm{1}-\hat{p } ) } , \end{aligned}\ ] ] where the last equality follows by cramer s formula for an inverse matrix . on the other hand , for the numerator in the r.h.s . of equation , we can write @xmath158 by plugging and into , and iterating , we have that @xmath159 we introduce here the algorithm due to wilson and propp @xcite which allow us to sample the measure . first , we extend the markov process @xmath2 defined through on @xmath84 to a markov process @xmath160 on the space @xmath161 by interpreting @xmath162 as an absorbing state and by adding some killing rates . consider the space @xmath3 , with @xmath22 . assume a collection of killing rates @xmath45 : \ : x\in\mathcal{x}\}$ ] is given , and let @xmath46 be the diagonal matrix in @xmath43 defined by @xmath47 with @xmath48 for @xmath49 . consider the markov process @xmath160 on the finite state space @xmath85 with generator given by @xmath163,&\mbox { if } x\in \mathcal{x},\\ 0,&\mbox { if } x=\delta . \end{array } \right.\ ] ] with @xmath164 arbitrary , and @xmath111 defined in . in particular , the matrix @xmath165 associated with the generator in satisfies @xmath166 next , we describe the algorithm . for any @xmath167 , note that , due to irreducibility , @xmath168 is a.s . finite . * ( wilson s algorithm ) * 1 . start the process @xmath169 from any point @xmath170 until it reaches the absorbing state @xmath162 . 2 . erase all the loops of the trajectory described by @xmath169 up to time @xmath171 . call @xmath172 this self - avoiding trajectory . ( @xmath172 is such that @xmath173 . ) if @xmath172 covers the whole @xmath174 stop , else pick any point @xmath175 , with @xmath176 denoting the set of points covered by @xmath172 . start the process @xmath169 from @xmath177 until it hits the set @xmath176 . 4 . erase all the loops of the trajectory described by @xmath169 starting from @xmath177 up to time @xmath178 . call @xmath179 this self - avoiding trajectory . 5 . if @xmath180 stop , else pick any point @xmath181 . start the process @xmath169 from @xmath177 until it hits the set @xmath182 . iterate until @xmath174 is covered . denote by @xmath183 the set of spanning oriented trees on @xmath85 rooted at @xmath162 . this algorithm produces in finite time an element @xmath184 of @xmath183 . as a corollary of proposition [ marchal ] , we can easily compute the probability that the algorithm produces a given @xmath185 . [ wilsonprob ] fix a tree @xmath185 . let @xmath186 be the set of edges in @xmath184 connected to the root @xmath162 ( possibly via the edges with infinite rate from @xmath187 to @xmath162 ) . denote by @xmath188 the probability that wilson s algorithm produces the tree @xmath184 . then @xmath189 \left[\displaystyle\prod_{e\in\tau\setminus\partial{\rho(\tau)}}w(e)\right ] } { { \rm det}_{{\cal x } \setminus s}(-\mathcal{l})}.\ ] ] recall the notation in proposition [ marchal ] . set @xmath190 and @xmath191 . start with @xmath192 . by the definition of the algorithm , the proof follows by iterating the formula in equation where at each iteration we set the right @xmath121 according to the given tree @xmath184 . whatever the choice of starting points in wilson algorithm we get the same result . we conclude this section by observing that there exists a natural bijection between @xmath193 and @xmath183 . indeed , given @xmath194 , let @xmath195 be the unique element in @xmath183 obtained from @xmath36 by adding all the edges connecting the roots in @xmath36 to @xmath162 , i.e. add all edges @xmath93 such that @xmath196 and @xmath197 . vice versa , given @xmath185 , by removing all edges @xmath198 we can identify a unique element @xmath194 . this simple observation together with corollary [ wilsonprob ] allow us to sample the measure in using wilson s algorithm . samples from @xmath199 for @xmath200 on the two - dimensional @xmath201 torus with uniform rates equal to 1 between nearest neighbours for the first picture and , for the second picture , with an additional northward drift , such that @xmath202 if @xmath203 is the northern nearest neighbour of @xmath26 and @xmath204 otherwise . the third picture is a sample from @xmath199 for the same @xmath200 on the @xmath205 rectangular grid and for metropolis random walk in a browian sheet potential @xmath206 , i.e. , nearest neighbour rates are given by @xmath207_+\}$ ] with @xmath208 and @xmath206 is the restriction to the grid of a brownian sheet with 0 value on the west and north sides of the box . in each picture different blue levels are assigned to points in different trees , cyan lines separate neighbouring trees , and the forest roots are at the centers of red diamonds . , title="fig : " ] samples from @xmath199 for @xmath200 on the two - dimensional @xmath201 torus with uniform rates equal to 1 between nearest neighbours for the first picture and , for the second picture , with an additional northward drift , such that @xmath202 if @xmath203 is the northern nearest neighbour of @xmath26 and @xmath204 otherwise . the third picture is a sample from @xmath199 for the same @xmath200 on the @xmath205 rectangular grid and for metropolis random walk in a browian sheet potential @xmath206 , i.e. , nearest neighbour rates are given by @xmath207_+\}$ ] with @xmath208 and @xmath206 is the restriction to the grid of a brownian sheet with 0 value on the west and north sides of the box . in each picture different blue levels are assigned to points in different trees , cyan lines separate neighbouring trees , and the forest roots are at the centers of red diamonds . , title="fig : " ] samples from @xmath199 for @xmath200 on the two - dimensional @xmath201 torus with uniform rates equal to 1 between nearest neighbours for the first picture and , for the second picture , with an additional northward drift , such that @xmath202 if @xmath203 is the northern nearest neighbour of @xmath26 and @xmath204 otherwise . the third picture is a sample from @xmath199 for the same @xmath200 on the @xmath205 rectangular grid and for metropolis random walk in a browian sheet potential @xmath206 , i.e. , nearest neighbour rates are given by @xmath207_+\}$ ] with @xmath208 and @xmath206 is the restriction to the grid of a brownian sheet with 0 value on the west and north sides of the box . in each picture different blue levels are assigned to points in different trees , cyan lines separate neighbouring trees , and the forest roots are at the centers of red diamonds . ] this section is the bulk of the paper containing our main theorems . each subsection is devoted to some new results relating the markov chain @xmath2 to the law of the forest at the core of our investigation . we start here to analyze the measure introduced in on the space @xmath31 of spanning rooted oriented forests on @xmath84 . we compute the partition function , we identify the distribution of the number of roots in the standard case and we prove that the roots process is a determinantal one . [ partitionthm ] * ( partition function and spectrum ) * assume a collection of killing rates @xmath45 : \ : x\in\mathcal{x}\}$ ] is given , and let @xmath46 be the diagonal matrix in @xmath43 defined by @xmath47 with @xmath48 for @xmath49 . let @xmath71 the probability measure on @xmath193 in . then @xmath209 and , recalling the notation from section [ wilson ] , @xmath210 in the case @xmath211 , we recover the standard probability measure in , and the standard partition function in satisfies @xmath212 where @xmath213 is the characteristic polynomial of @xmath111 , i.e. @xmath214 where the @xmath215 s are the eigenvalues of @xmath216 ordered by non - decreasing real part . when @xmath217 and @xmath218 , we have that @xmath219_{r^c}}(q)\ ] ] with @xmath220_{r^c}}$ ] being the characteristic polynomial of the sub - markovian generator of the process killed in @xmath9 . * remark : * this kind of results goes back to kirchhoff @xcite . here we include the non - reversible case and stress the dependence in @xmath78 . as observed in the previous section , for each forest @xmath32 there is a unique @xmath221 . by corollary [ wilsonprob ] we then have that @xmath222 \left[\displaystyle\prod_{e\in\tau\setminus\partial{\rho(\tau)}}w(e)\right ] } { { \rm det}_{{\mathcal x}\setminus s}(-\mathcal{l } ) } = \frac{w_q(\phi)}{{\rm det}_{{\cal x } \setminus s}(q - l)}.\ ] ] by summing over all @xmath194 we immediately get . in fact , @xmath223 moreover , if @xmath211 , then @xmath224 and @xmath225=\chi_l(q)$ ] . in the standard case , an immediate consequence of theorem [ partitionthm ] is a characterization of the law of the cardinality of the set of roots . [ bernoullicity ] * ( root number distribution ) * assume the standard case @xmath211 and that @xmath111 has real spectrum . let @xmath226 be a sum of @xmath44 independent bernoulli random variables with parameters @xmath227 . under the probability measure @xmath74 , the random variable @xmath228 counting the number of roots ( or equivalently , of trees ) in @xmath68 has the same law as @xmath226 . observe that the coefficient of degree @xmath229 in @xmath230 is the total weight of the set of forest with exactly @xmath229 roots . since @xmath231 we get , @xmath232}\prod_{i\in i}\lambda_i\\ & = \sum_{i\in \mathcal{p}[n - k]}\left[\prod_{i\in i}\left(\frac{\lambda_i}{q+\lambda_i}\right)\right ] \left[\prod_{j\notin i}\left(\frac{q}{q+\lambda_j}\right)\right]\\ & = \sum_{j\in \mathcal{p}[k ] } \left[\prod_{j\in j}\left(\frac{q}{q+\lambda_j}\right)\right ] \left[\prod_{i\notin j}\left(1-\frac{q}{q+\lambda_i}\right)\right ] , \end{aligned}\ ] ] where @xmath233 $ ] stands for the set of all possible @xmath229 elements of the set @xmath234 . * remark : * when the spectrum of @xmath111 does contain a non - real part , one can still compute the law of @xmath228 and get the same algebraic expressions in terms of the eigenvalues . one can also compute momenta by differentiating with respect to @xmath78 the logarithm of the partition function . in particular , the mean value and the variance are given by @xmath235 = \sum_{i = 0}^{n - 1 } \frac{q}{q + \lambda_i } , \label{swizzera}\\ & { \mathbb v}\!{\rm ar}_q(|\rho(\phi)| ) = \sum_{i = 0}^{n - 1 } \frac{q}{q + \lambda_i } - \left(\frac{q}{q + \lambda_i}\right)^2.\end{aligned}\ ] ] we note however that the contribution of the imaginary part of the eigenvalues can make uneasy the comparison between variance and mean value , at least for small values of @xmath78 . this is the reason why , when dealing with the question of getting samples with a number of roots that approximates a given @xmath83 , we will restrict ourselves to the real spectrum case . next , we prove that under @xmath72 the set of roots @xmath236 is a determinantal process as suggested after @xcite by the previous result . this is the content of theorem [ determinantalroots ] for which we will present an algebraic and a probabilistic proof . let us first show a simple lemma . consider the markov process @xmath160 on @xmath237 defined via its generator in . let @xmath238 be the hitting time of @xmath239 . denote by @xmath240 the last point visited by the process @xmath169 before time @xmath238 . let @xmath81 be the transition matrix defined by @xmath241 this transition kernel can also be expressed in terms of green s functions : [ greenkernel ] for @xmath242 , let @xmath243=(q - l)^{-1}(x , y)\ ] ] be the green s function of the process @xmath169 on the subspace @xmath244 . then @xmath245 we use the notation of section [ marchal ] to work in time . set @xmath246 , @xmath247 , @xmath248 and write @xmath249\frac{q(y)}{\bar{\alpha } } = g_{\delta}(x , y)q(y ) . \end{aligned}\ ] ] note that , in the standard case @xmath211 , we can write @xmath250 with @xmath251 being an independent exponential random variable of parameter @xmath78 . in particular , if @xmath252 $ ] is the green s function up to time @xmath251 , then @xmath253 [ determinantalroots]*(determinantal roots ) * under @xmath71 with finite killing rates ( i.e. @xmath254 ) , the set of roots in @xmath36 is a determinantal process with kernel @xmath81 defined in . equivalently , for any @xmath255 : @xmath256 more generally , if @xmath257 , @xmath236 is still a determinantal process on @xmath258 with kernel @xmath81 , that is : @xmath259 * ( algebraic proof of thm [ determinantalroots ] ) * assume first @xmath254 . consider a set @xmath255 with @xmath260 of the form @xmath261 . by choosing the different points in @xmath82 as starting point at each iteration in wilson s algorithm , by , we get @xmath262\frac{{\rm det}_{a^c}(q - l)}{{\rm det}_{\mathcal{x}}(q - l)}\\ & = \frac{{\rm det}_{a^c}(q - l)}{{\rm det}_{\mathcal{x}}(q - l)}\displaystyle{\rm det}_{a}(q ) . \end{aligned}\ ] ] in case @xmath263 , the claim is straightforward since equation reads @xmath264 and the r.h.s . equals @xmath265 due to lemma [ greenkernel ] . in case @xmath266 , we can use the schur complement ( see in appendix [ schur ] ) to show that @xmath267 therefore , from equation , we have that @xmath268 where the second to the last equality is justified because @xmath46 is a diagonal matrix and the last equality follows from . when @xmath269 , the proof is the same . we just have to subtract from the various considered sets . * ( probabilistic proof of thm [ determinantalroots ] ) * to avoid a heavy notation , we consider only the case @xmath254 . starting from the markov process @xmath2 and the killing rates @xmath270 , we construct two different absorbing states @xmath271 and @xmath272 accessible from the set @xmath82 and @xmath273 , respectively . set @xmath274 . let @xmath107 be the markov process with generator @xmath275\\ & + q(x)\mathbbm{1}_{\{x\in a^c\}}[f(\delta_{a^c})-f(x ) ] , \quad \text { if } x\in \mathcal{x } , \end{aligned}\ ] ] and @xmath276 if @xmath277 with @xmath118 and @xmath111 as in . next , consider the subspace @xmath278 . let @xmath279 be the markov process with state space @xmath280 obtained as the trace of the process @xmath107 on @xmath280 . let us remark two features of wilson s algorithm . first , wilson s algorithm can be extended to the case of a state space with more than one absorbing state . in this case it produces a rooted spanning forest instead of a tree . second , wilson s algorithm is uniquely determined once we fix a state space with some absorbing set and a markov generator . these observations justify the following definitions . let @xmath281 be the set of ending points of the edges starting from @xmath82 after running wilson algorithm on @xmath282 with absorbing state @xmath162 and generator @xmath283 . similarly let @xmath284 associated in the same way with @xmath82 , when wilson s algorithm is run on @xmath285 with absorbing set @xmath286 and generator @xmath287 . observe at this point that @xmath288 and , by using proposition [ marchal ] , compute @xmath289_a\right)^{-1}\right){\rm det}_{a}(q)\\ & = { \rm det}_a\left(g^{\bar{\bar{a}}}_{\{\delta_a,\delta_{a^c}\}}\right){\rm det}_{a}(q ) , \end{aligned}\ ] ] where @xmath290 denotes the green s function of the process @xmath279 stopped when entering the absorbing states @xmath291 . note now that for @xmath292 , @xmath293 with @xmath294 and @xmath295 being the green s function of the process @xmath169 in . finally , since @xmath296 for @xmath297 , the claim follows by combining equations and . on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the one - dimensional torus our determinantal process is distributed like a simple gas of particles with a repulsive `` nearest - neighbour two - body interaction '' that is quite easily detected by comparison with a bernoulli product measure . here are samples of our roots set ( first line of each picture ) and of the product measure ( second line ) with exactly 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 and 60 roots or points , respectively . , title="fig : " ] on the two dimensional torus , the difference between the law of our roots set and that of a bernoulli product measure is far too subtle to be detected on a single sample . walking away from translation invariant models , we can find much more correlations . here are pictures of a sample on the two - dimensional torus with uniform rates equal to 1 and @xmath298 ( on the left ) , and of a sample associated with the metropolis random walk on the square grid in a brownian sheet potential with inverse temperature @xmath299 and extinction rate @xmath300 ( on the right ) . , title="fig : " ] on the two dimensional torus , the difference between the law of our roots set and that of a bernoulli product measure is far too subtle to be detected on a single sample . walking away from translation invariant models , we can find much more correlations . here are pictures of a sample on the two - dimensional torus with uniform rates equal to 1 and @xmath298 ( on the left ) , and of a sample associated with the metropolis random walk on the square grid in a brownian sheet potential with inverse temperature @xmath299 and extinction rate @xmath300 ( on the right ) . , title="fig : " ] in this section we answer the question raised in the introductory section [ chessboard ] . to this end , we focus on hitting times of a given subset @xmath301 , i.e. , @xmath302 . in appendix [ wentzell ] , lemma [ wentzellthm ] , we derive , in terms of our measures , a result originally due to freidlin and wentzell , see lemma 3.3 in @xcite , which allows to give a formula for @xmath303 $ ] . in this section , with the help of lemma [ wentzellthm ] , we compute the expectation @xmath303 $ ] when @xmath9 is the set of roots sampled from @xmath199 , or @xmath304 for any given @xmath20 . [ hittingrootsthm]*(hitting - time formulas ) * let @xmath71 be the forest probability measure defined in . then , for any @xmath305 , @xmath306\right ] = \displaystyle\sum_{y\in\mathcal{x}}\frac{1}{q(y)}\left[{\mathbb p}_q\left(\rho\left(\tau_\phi(x)\right)=\{y\}\right)-{\mathbb p}_q(\rho(\phi)=\{y\})\right],\ ] ] with @xmath307 being the unique tree in @xmath68 containing @xmath26 . in the standard case , @xmath211 , equation reduces to @xmath308\right ] = \frac{1}{q}\left[1-{\mathbb p}_q\left(|\rho(\phi)|=1\right)\right]=\frac{1}{q}\left(1-\prod_{i = 1}^{n - 1 } \frac{\lambda_i}{q + \lambda_i}\right).\ ] ] moreover , for @xmath309 and any @xmath305 , @xmath310\mid \ , |\rho(\phi)|=m\right]=\frac{{\mathbb p}_q(|\rho(\phi)|=m+1)}{q{\mathbb p}_q(|\rho(\phi)|=m)}.\ ] ] * remark : * notice , that the r.h.s . in ( [ conditionedhittingroots ] ) can simply be expressed as the ratio between two successive coefficients of the characteristic polynomial of the generator @xmath111 . observe first that under @xmath71 , the probability of sampling a given set @xmath301 as set of roots can be written as @xmath311 with @xmath312 as in . by using equation together with , we have that @xmath313&= \displaystyle\sum_{r \neq \emptyset}{\mathbb p}_q(\rho(\phi)=r)e_x[t_r]\\ & = \displaystyle\sum_{r \neq \emptyset : \ : r \supset s}\frac{{\rm det}_{r\setminus s}(q)}{z_q } \displaystyle\sum_{y\notin r}\sum _ { \stackrel{\scriptstyle\phi:\rho(\tau_\phi(x))=\{y\ } , } { \scriptstyle\rho(\phi)=r\cup\{y\ } } } w(\phi)\\ & = \frac{1}{z_q } \displaystyle\sum_{y\notin s } \displaystyle\sum _ { \stackrel{\scriptstyle r \neq \emptyset : \ : r \supset s } { r\not\ni y } } \displaystyle\sum _ { \stackrel{\scriptstyle\phi:\rho(\tau_\phi(x))=\{y\ } , } { \scriptstyle\rho(\phi)=r\cup\{y\ } } } \frac{w_q(\phi)}{q(y)}\\ & = \frac{1}{z_q}\displaystyle\sum_{y\notin s}\left[\displaystyle\sum_{\phi:\rho(\tau_\phi(x))=\{y\}}\frac{w_q(\phi)}{q(y ) } -\sum_{\phi:\rho(\phi)=\{y\}}\frac{w_q(\phi)}{q(y)}\right]\\ & = \displaystyle\sum_{y\notin s}\frac{1}{q(y)}\left[{\mathbb p}_q(\rho(\tau_\phi(x))=\{y\})-{\mathbb p}_q(\rho(\phi)=\{y\})\right ] . \end{aligned}\ ] ] the restriction of summing over @xmath314 can be removed , since @xmath315 for @xmath316 . hence holds and readily follows when @xmath211 . the proof of follows by an analogous computation . note that the r.h.s . of and is uniform in the starting point @xmath26 . this latter observation allows to answer the questions in the introduction . in fact , no matter of the geometry of the graph and the weights we are considering , we can take random subsets @xmath317 with law @xmath318 and the formula in equation says that the hitting times do not dependent on the starting point @xmath26 . to practically obtain a sample from @xmath199 with approximately @xmath83 roots when @xmath111 has only real eigenvalues , one can use wilson s algorithm and play with the parameter @xmath78 as follows ( see figure [ yo ] ) . if @xmath78 is such that @xmath319 one has an expected number of @xmath20 roots with fluctuations of order @xmath21 or smaller ( see corollary [ bernoullicity ] ) . in principle one should compute the eigenvalues of @xmath111 , which is in general difficult for large @xmath44 , and then solve equation ( [ albicocca ] ) in @xmath78 . to overcome this obstacle , a possible alternative procedure is the following : 1 . start with any positive @xmath78 and run wilson s algorithm with this parameter to get a sample from @xmath199 with a certain number @xmath320 of roots . 2 . replace @xmath78 by @xmath321 and run again wilson s algorithm with this new parameter to get a new sample with another number of roots , say @xmath320 again . 3 . iterate the previous step until a sample with @xmath320 roots satisfying @xmath322 is obtained . as a matter of fact , @xmath323 rapidly converges to the solution of ( [ albicocca ] ) , hence the algorithm rapidly reaches an end . since we believe this procedure to be quite far from an optimal one , we are only sketchy on this point . we sampled approximatively 100000 , 10000 , 1000 and 100 roots on the @xmath201 grid for the random walk in a brownian sheet potential with inverse temperature @xmath208 by following the procedure described in section [ hittingtimes ] . we obtained 100443 , 10032 , 1042 and 111 roots in 8 , 6 , 6 and 8 iterations , respectively . , title="fig : " ] we sampled approximatively 100000 , 10000 , 1000 and 100 roots on the @xmath201 grid for the random walk in a brownian sheet potential with inverse temperature @xmath208 by following the procedure described in section [ hittingtimes ] . we obtained 100443 , 10032 , 1042 and 111 roots in 8 , 6 , 6 and 8 iterations , respectively . , title="fig : " ] we sampled approximatively 100000 , 10000 , 1000 and 100 roots on the @xmath201 grid for the random walk in a brownian sheet potential with inverse temperature @xmath208 by following the procedure described in section [ hittingtimes ] . we obtained 100443 , 10032 , 1042 and 111 roots in 8 , 6 , 6 and 8 iterations , respectively . , title="fig : " ] we sampled approximatively 100000 , 10000 , 1000 and 100 roots on the @xmath201 grid for the random walk in a brownian sheet potential with inverse temperature @xmath208 by following the procedure described in section [ hittingtimes ] . we obtained 100443 , 10032 , 1042 and 111 roots in 8 , 6 , 6 and 8 iterations , respectively . , title="fig : " ] we conclude this section with an estimate on the mean hitting times above when taking the maximum over the starting points @xmath26 . [ maxhittingrootsthm]*(max hitting - time estimates ) * under the standard measure @xmath199 , the following bound holds @xmath324\right]\leq \frac{1}{q}\left[{\mathbb e_q}\left[|\rho(\phi)|\right]-{\mathbb p_q}(|\rho(\phi)|=1)\right]=\frac{1}{q}\left(\sum_{i = 0}^{n - 1 } \frac{q}{q + \lambda_i } - \prod_{i = 1}^{n - 1 } \frac{\lambda_i}{q + \lambda_i}\right).\ ] ] furthermore , for any @xmath325 , we have the estimate @xmath326\mid \ , |\rho(\phi)|=m\right]\leq \frac { ( m+1){\mathbb p}_q \left ( |\rho(\phi)| = m + 1 \right ) } { q { \mathbb p}_q \left ( |\rho(\phi)| = m \right ) } .\ ] ] as we remarked before , wilson s algorithm works also when considering more than one absorbing state . denote by @xmath327 the running time of wilson s algorithm ( i.e. the total running time of the loop erased random walks needed to cover the whole graph ) when the absorbing states form a non - empty subset @xmath9 of @xmath3 ( this amounts to sample @xmath328 ) . it can be shown ( see e.g. @xcite , proposition 1 ) that the mean running time can be expressed in spectral terms as @xmath329 , with @xmath330 being the eigenvalues of the operator @xmath331_{r^c}$ ] , the sub - markovian generator associated with the process absorbed in @xmath9 when these eigenvalues are real . the same holds in the case of complex eigenvalues by defining `` the sum of exponential variables '' through its laplace transform and the same algebraic formula as in the real case . ] . note at this point that we can overestimate the l.h.s . of by the expectation of @xmath332 . hence , using ( [ lucien ] ) and looking at the coefficient of degree 1 in @xmath333 , @xmath334\right ] & \leq { \mathbb e_q}\left[t^{wil}_{\rho(\phi)}\right]= { \mathbb e_q}\left[\sum_{i=0}^{|\rho(\phi)|-1}\frac{1}{\lambda_{i,\rho(\phi)}}\right ] = \displaystyle\sum_{r \neq \emptyset}\frac{z_{r}(0)}{z(q)}q^{|r|}\sum_{i=0}^{|r|-1}\frac{1}{\lambda_{i , r } } \\&=\frac{1}{z(q)}\displaystyle\sum_{r\neq \emptyset}q^{|r|}\sum_{\phi:\rho(\phi)\supset r , |\rho(\phi)|=|r|+1}\frac{w_{q , r}(\phi)}{q } \\&=\frac{1}{qz(q)}\sum_{k=1}^n\sum_{r : |r|=k}\sum_{\phi:\rho(\phi)\supset r , |\rho(\phi)|=k+1}q^{|r|}w_{q , r}(\phi ) \\&=\frac{1}{qz(q)}\sum_{k=1}^n\sum_{\phi:|\rho(\phi)|=k + 1}w_q(\phi)(k+1 ) \\&=\frac{1}{q}\sum_{\phi:|\rho(\phi)|\geq 2}\frac{w_q(\phi)|\rho(\phi)|}{z(q ) } , \end{aligned}\ ] ] and the latter equals the r.h.s . of . the bounds in follows by a similar argument . * remark : * we expect these estimates to be good either when @xmath78 is very small or very large , or when @xmath20 is close to @xmath335 or @xmath44 . improving them in the intermediate regime seems a challenging problem we were not able to solve . throughout this section we work with the markov process @xmath2 on @xmath3 in , _ under the assumption that @xmath2 is reversible with respect to some probability measure @xmath336 on @xmath3 _ , i.e. , @xmath111 is a self - adjoint operator in @xmath337 endowed with the inner product @xmath338 for @xmath339 , possibly @xmath340 , we turn the points of @xmath9 into `` absorbing points '' by adding infinite weight edges towards a cemetery @xmath162 and we assume the resulting markov process with sub - markovian generator @xmath331_{r^c}$ ] to be irreducible . we denote by @xmath341 , with @xmath342 , the eigenvalues of @xmath343_{r^c}$ ] , and following @xcite , we define , for each @xmath26 in @xmath344 , a sequence of _ local equilibria _ by setting @xmath345_{r^c } + \lambda_{k , r}}{\lambda_{k , r } } , \quad 1 \leq k \leq l - 1 . \label{acqua_di_rosa}\end{aligned}\ ] ] theorem 3.2 in @xcite is a statement on symmetric matrices that in our setting can be stated as follows . * ( micchelli and willoughby @xcite)*[macine ] fix an arbitrary @xmath7 , for all @xmath346 , @xmath347 in equation is a non - negative measure . in this section we give a proof of this theorem following the key steps of micchelli and willoughby s algebraic proof , however , unlike the original proof , we develop probabilistic or combinatorial arguments . before starting the proof we note , following @xcite , that equation ( [ acqua_di_rosa ] ) can be rewritten as @xmath348_{r^c } = \lambda_{k , r } ( \nu_{k - 1 } - \nu_k),\ ] ] which gives the following interpretation . the process leaves the measure , or `` state '' , @xmath347 at rate @xmath349 to be absorbed in @xmath9 or to decay into @xmath350 . provided that @xmath347 and @xmath350 are indeed non - negative measures , this can be turned into a rigorous mathematical statement @xcite . then , by looking at the different decay times up to an exponential time @xmath251 that is independent from the process , and by observing that , by hamilton - cayley theorem , the process leaves the state @xmath351 at rate @xmath352 only to be absorbed in @xmath9 , we get , for all @xmath26 and @xmath203 in @xmath344 , @xmath353 the left hand side in ( [ lampo ] ) is the probability to have @xmath354 when @xmath36 is sampled from @xmath355 . then , multiplying by @xmath356 ( recall ( [ lucien ] ) ) , dividing by @xmath78 , and denoting the result by @xmath357 , we can rewrite as @xmath358_{r^c}^{-1}(x , y ) \label{nodo } \\ & = & \frac{1}{q } \sum _ { \stackrel{\scriptstyle \phi : \ : \rho(\tau_\phi(x ) ) = \{y\ } } { \scriptstyle \rho(\phi ) \supseteq r } } q^{|\rho(\phi)| - |r| } w(\phi ) \label{capello } \\ & = & ( q + \lambda_{0 , r } ) \cdots ( q + \lambda_{l - 2 , r } ) \nu^x_{l - 1}(y ) \nonumber\\ & & + ( q + \lambda_{0 , r } ) \cdots ( q + \lambda_{l - 3 , r } ) \lambda_{l - 1 , r}\nu^x_{l - 2}(y ) \nonumber\\ & & + \cdots + ( q + \lambda_{0 , r } ) \lambda_{l - 1 , r } \lambda_{l - 2 , r}\cdots \lambda_{2 , r } \nu^x_{1}(y ) \nonumber\\ & & + \lambda_{n - 1 , r } \cdots \lambda_{1 , r } \nu^x_0(y ) . \label{capra}\end{aligned}\ ] ] next , by density and continuity , we can restrict ourselves to the case of distinct eigenvalues , and equation suggests , for @xmath346 , the following relation for the divided differences ( see definition [ divdiff3 ] in appendix [ divideddiff ] ) of @xmath359 : @xmath360(x , \cdot ) = \lambda_{l-1 , r } \cdots \lambda_{k + 1 , r } \nu^x_k = \delta_x \prod_{i = k + 1}^{l - 1 } ( [ l]_{r^c } + \lambda_{i , r}),\ ] ] that is @xmath361 = \prod_{i = k + 1}^{l - 1 } ( [ l]_{r^c } + \lambda_{i , r}).\ ] ] we can now start to follow the main steps of micchelli and willoughby s proof . * step 1 : checking equation ( [ cavolo ] ) . * we simply use definition [ divdiff2 ] and spectral decomposition . with @xmath362 being the right eigenvector associated with @xmath363 , and , for any measure @xmath364 , @xmath365 , we have , recalling ( [ nodo ] ) , for any @xmath78 , @xmath366this gives @xmath367 & = \sum_{r=0}^k\frac{\nu w_r(-\lambda_{r , r})}{\prod_{m\neq r}(\lambda_{m , r}-\lambda_{r , r})}= \sum_{r=0}^k \sum_{j=1}^{l-1 } \langle \mu_j,\nu\rangle \frac{\prod_{i\neq j}(\lambda_{i , r}-\lambda_{r , r})\mu_j}{\prod_{m\neq r}(\lambda_{m , r}-\lambda_{r , r})}\\ & = \sum_{r=0}^k \langle \mu_r,\nu\rangle \frac{\prod_{i\neq j}(\lambda_{i , r}-\lambda_{r , r})\mu_r}{\prod_{m\neq r}(\lambda_{m , r}-\lambda_{r , r})}= \sum_{r=0}^k \langle \mu_r,\nu\rangle \prod_{i = k+1}^{l-1}(\lambda_{i , r}-\lambda_{r , r})\mu_r\\ & = \sum_{r=0}^{l-1 } \langle \mu_r,\nu\rangle \prod_{i = k+1}^{l-1}(\lambda_{i , r}-\lambda_{r , r})\mu_r=\nu \prod_{i = k+1}^{l-1}([l]_{r^c}+\lambda_{i , r } ) \end{aligned}\ ] ] and equation readily follows . * step 2 : a combinatorial identity . * the key point of the proof lies in the following lemma . [ mw2 ] for any @xmath368 in @xmath369 , @xmath370 in addition one has @xmath371 let us first consider the case @xmath368 . due to , we have that @xmath372 we also have @xmath373 and @xmath374 next , define for each @xmath36 in ( [ w1 ] ) , @xmath375 if @xmath376 belongs to @xmath36 , and @xmath377 if @xmath26 is connected in @xmath36 to @xmath203 through @xmath378 and @xmath379 ( possibly with @xmath380 ) in such a way that @xmath381 and @xmath382 belong to @xmath36 . finally , by observing that @xmath383 and @xmath384 , is obtained from , and . then , equation ( [ mirtillo ] ) follows from ( [ w1 ] ) for @xmath385 . * step 3 : conclusion by induction with cauchy interlacement theorem . * for @xmath386 , let @xmath387 $ ] be the following statement : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ for all @xmath388 such that @xmath389 , for all @xmath390 , for all @xmath391 such that @xmath392 for all @xmath393 , for all @xmath394 , and for all @xmath395 : @xmath396(x , y ) \geq 0.\ ] ] _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ we can proceed inductively to show that @xmath387 $ ] holds . for @xmath397 , the claim is obvious . fix @xmath398 . in the case @xmath399 , the inductive hypothesis is unnecessary . indeed , from ( [ mirtillo ] ) , one has @xmath396(x , x ) = z_{r \cup \{x\}}[\xi_0 , \dots , \xi_k].\ ] ] then note that , by cauchy interlacement theorem , @xmath392 implies that @xmath400 for @xmath401 , and hence , by lemma [ divdif ] , we get @xmath396(x , x ) \geq 0.\ ] ] when @xmath402 , @xmath387 $ ] follows in the same way by using ( [ wxy ] ) and the inductive hypothesis . we can finally conclude the proof of theorem [ macine ] . it suffices to apply the claim with @xmath403 for all @xmath393 and recall ( [ cavolo ] ) or ( [ bruxelles ] ) . in this section we present two coalescence and fragmentation processes closely related with our forest measures . to build the first process , we couple all the @xmath199 s together for different @xmath78 s . this coupling can be seen as a coalescence and fragmentation process when @xmath78 decreases to @xmath404 and @xmath405 is thought as time . we make use of wilson s original representation of his algorithm with `` site - indexed random paths '' . assume that , to each site of the graph , is attached an infinite list / collection of arrows pointing towards one neighbour , and that these arrows are independently distributed according to the discrete skeleton transition probabilities . in other words , an arrow , pointing towards the neighbour @xmath203 of a site @xmath26 , appears at each level in the list associated with @xmath26 with probability @xmath406 ( in this context , we set @xmath407 , and consider @xmath26 itself as one of its possible neighbours ) . imagine that each list of arrows attached to a site is piled down in such a way that it make sense to talk of an infinite stack with an arrow on the top of this stack . by using this representation , one can generate the random walk on the graph as follows . at each jump time , the random walk steps to the neighbour pointed by the arrow on the top of the stack where the walker is sitting , and the top arrow is erased from the stack . to describe wilson s algorithm one has to introduce a further ingredient : pointers to the absorbing state @xmath162 in each stack . such a pointer should appear with probability @xmath408 at each level in the list . one way to introduce it is by generating independent uniform random variables @xmath409 together with each original arrow in the stack , and by replacing the latter by a pointer to the absorbing state whenever @xmath410 . a possible description of wilson s algorithm is then the following . * start with a particle on each site , particles and sites will be divided into active and frozen particles or sites and , at the beginning , all sites and particles are declared to be active . * choose a particle among all the active ones and look at the arrow at the top of the stack it is seated on . call @xmath26 the site where the particle is seated . * * if the arrow is the pointer towards @xmath162 , declare the particle to be frozen and site @xmath26 as well . * * if the arrow points towards another site @xmath411 , remove the particle and keep the arrow . * * if the arrow points to @xmath26 itself , remove the arrow . * once again , choose a particle among all the active ones , look at the arrow on the top of the stack it is seated on , and call @xmath26 the site where the particle is seated . * * if the arrow points to @xmath162 , the particle is declared to be frozen , and so are declared @xmath26 and all the sites eventually leading to @xmath26 by following discovered top pile arrows paths . * * if the arrow points to a frozen particle or site , remove the particle , keep the arrow , and freeze site @xmath26 as well as any site eventually leading to @xmath26 by following discovered top pile arrows paths . * * if the arrow points to an active , then there are two possibilities . by following the arrows at the top of the stacks , we either reach a different active particle , or runs in a loop back to @xmath26 . in the former case , remove the chosen particle from site @xmath26 and keep the discovered arrow . in the latter , erase all the arrows along the loop and set an active particle on each site of the loop . note that this last case includes the possibility for the discovered arrow of pointing to @xmath26 itself , in which case , we just have to remove the discovered arrow . * iterate the previous steps up to exhaustion of the active particles . the crucial observation is that , no matter of the choice of the particles at the beginning of the steps , when this algorithm stops , the same arrows are erased and the same spanning forest with a frozen particle at each root is obtained . in particular , by choosing at each step the last encountered active particle , or the same as in the previous step when we just erased a loop , we perform a simple loop - erased random walk up to freezing . since @xmath199 is sampled in this way , and the same uniform variables @xmath409 can be used for each @xmath78 , this provides a coupling among all the @xmath199 s . by means of this coupling , one can actually sample @xmath412 starting from a sample of @xmath199 for @xmath413 . let us now explain this fact . note first that , running this algorithm for sampling @xmath412 , one can reach at some point the final configuration obtained for @xmath199 with the only difference that some frozen particles of the final configuration obtained with parameter @xmath78 can still be active at this intermediate step of the algorithm run with @xmath414 . it suffices , indeed , to choose the sequence of active particles in the same way with both parameters . this is possible since each pointer to @xmath162 in the stacks with parameter @xmath414 is associated with a pointer to @xmath162 at the same level in the stacks with parameter @xmath78 . thus we just have to replace some frozen particle of the configuration sampled with @xmath199 and continue the algorithm with parameter @xmath414 to sample @xmath412 . to do so , it suffices to declare active each frozen particle at site @xmath26 with probability @xmath415 then , at the top of the stack set an arrow that points toward @xmath203 with probability @xmath406 , and to keep @xmath26 frozen with probability @xmath416 . when @xmath78 continuously decreases , we obtain a coalescence - fragmentation process @xmath417 such that @xmath418 is distributed according to @xmath419 at all time @xmath420 , and in which each tree can fragment and partially coalesce with the other trees of the forest . when a root of a tree turns active , the tree is eventually fragmented into a forest , some trees of which being possibly grafted " on the previous frozen trees . it is worth noting that , by , the mean number of trees is decreasing along this coalescence process @xmath417 . the previous observations show that we can sample the `` finite dimensional distributions '' of the process , i.e. the law of @xmath421 for any choice of @xmath422 . we can actually sample whole trajectories @xmath423 for any finite @xmath424 . in fact , note first that at each time @xmath425 , the next frozen particle ( or root ) becoming active is uniformly distributed among all the roots , and the time @xmath426 when it wakes up " is such that the variable @xmath427 has the law of the maximum of @xmath20 independent uniform variables on @xmath428 , with @xmath20 being the number of roots at time @xmath420 . since , for all @xmath429 , @xmath430 @xmath206 has the same law as @xmath431 , with @xmath409 uniform on @xmath432 . using ( [ savona ] ) we can then sample @xmath426 by setting @xmath433 summing up , in order to sample the whole trajectory it suffices to proceed as follows once @xmath417 is sampled at a given jump time @xmath420 : * choose uniformly a root @xmath26 . * sample the next jump time @xmath426 from a uniform random variable @xmath409 on @xmath432 , by using ( [ cornice ] ) . * restart the algorithm with parameter @xmath434 by declaring active the particle in @xmath26 and putting an arrow to @xmath203 with probability @xmath435 . snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots of the coalescence and fragmentation process in section [ q_coupling ] associated with a simple random walk on the two - dimensional torus of size @xmath201 at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 . roots are red , non - root vertices at the border of trees are cyan , other vertices are in blue . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] snapshots at times @xmath405 equal to 0 , .5 , 2 , 8 , 32 , 128 , 512 , , 524288 of the coalescence and fragmentation process on the square grid of size @xmath201 for the random walk in a brownian sheet potential with inverse temperature @xmath299 . , title="fig : " ] numbers of trees as a function of time for the coalescence and fragmentation processes in figures [ farfalla ] and [ lampada ] in loglog scale . ] we conclude by observing that @xmath417 crosses " almost surely all the manifolds @xmath436 . indeed , by ( [ swizzera ] ) , it starts from @xmath437 and reaches @xmath438 almost surely , and , each time the number of roots decreases , it does so by only 1 unit : when the activated " tree fragments into trees that coalesce only with the previously frozen ones . with @xmath439 , it is also simple to sample @xmath440 . we note however that @xmath440 is not distributed according to @xmath441 . the other dynamics we want to mention is a simple variant of the tree random walk introduced in @xcite to prove the so called markov chain tree theorem . for fixed @xmath78 , the dynamics we now present is another coalescence and fragmentation process for which the standard measure @xmath199 is the stationary probability measure . remind that for a given forest @xmath32 and @xmath305 , we denote by @xmath442 the unique tree in @xmath36 containing @xmath26 , and note that if @xmath196 then @xmath443 . our dynamics can then be defined as follows . 1 * ( forest dynamics ) * [ rootdynamics ] fix @xmath444 . let @xmath445 be the markov process with state space @xmath31 characterized by the following generator acting on functions @xmath446 : @xmath447,\ ] ] where the transition rate @xmath448 and the new state @xmath449 are defined as follows : 1 . [ add]if @xmath196 and @xmath450 , then @xmath451 and @xmath452 . [ swap]if @xmath196 and @xmath453 , then @xmath451 and @xmath454 , with @xmath455 being the unique edge in @xmath36 such that @xmath456 . 3 . [ remove]if @xmath457 , then @xmath458 and @xmath459 . 4 . @xmath460 else . the rules corresponding to 1 , 2 and 3 can be rephrased by saying that we _ add , swap _ and _ remove _ a bond from the forest @xmath36 , respectively . notice that such a dynamics induces a non - conservative dynamics on the set of roots . in particular , when transition 1 occurs , @xmath461 and two trees merge into one . on the other hand , when transition 3 occurs , @xmath462 and the tree containing @xmath93 is fragmented into two trees where the new appearing root is at @xmath463 . transitions of type 2 produce a rearranging in one of the tree . they leave invariant the cardinality of the set of roots but the location of the root in the modified tree is relocated at the vertex @xmath456 . [ invmeasrootdyn]*(invariance ) * for all @xmath464 the measure @xmath38 in is invariant for @xmath465 in . we need to show that for any @xmath466 @xmath467 indeed , amounts to say that for any @xmath468 @xmath469 \\ & = \sum_{\phi'\in \mathcal{f}}\sum_{\phi\in \mathcal{f}}w_q(\phi ) \sum_{e\in\mathcal{e } : \phi^e= \phi ' } \gamma(\phi , e)f(\phi^e)- \sum_{\phi'\in \mathcal{f}}w_q(\phi')\sum_{e\in\mathcal{e}}\gamma(\phi',e)f(\phi ' ) \\ & = \sum_{\phi'\in \mathcal{f}}\big[\sum_{\phi\in \mathcal{f}}\sum_{e\in\mathcal{e } : \phi^e= \phi ' } w_q(\phi)\gamma(\phi , e)- \sum_{e\in\mathcal{e } } w_q(\phi')\gamma(\phi',e)\big]f(\phi')= 0 . \end{aligned}\ ] ] for a given @xmath466 , we start by splitting the l.h.s . of in the three terms corresponding to the different transitions allowed by the dynamics in definition [ rootdynamics ] whenever @xmath470 . @xmath471 we can rewrite @xmath472 @xmath473 and , denoting , for each @xmath455 such that @xmath474 and @xmath475 , by @xmath93 the unique bond in the only one cycle of @xmath476 such that @xmath477 , with @xmath478 , @xmath479 summing @xmath480 , @xmath481 and @xmath482 together we then get ( [ invcond ] ) . * remark : * when @xmath483 we recover the anantharam and tsoukas dynamics and the proof of the markov chain tree theorem . indeed , the standard forest measure restricted to spanning trees is the invariant measure of the dynamics . starting with a single tree , its roots follows a markovian evolution with generator @xmath111 , so that , at equilibrium , in the long time limit we have @xmath484 with @xmath336 being the stationary distribution associated to @xmath111 . we conclude with two last results concerning static properties of the standard measure @xmath199 . the first one concerns the `` rooted partition '' inherited from a forest sampled from @xmath199 . we show , as a consequence of the markov chain tree theorem , that the roots are distributed according to the restricted measures associated with the sampled partition , these restricted measures being the equilibrium measures of the restricted dynamics inside each component of the partition . our last result concerns the determinantal process @xmath485 : its cumulants are given by a nice formula it is worth to notice . for @xmath36 in @xmath70 with roots @xmath486 , , @xmath487 , let us denote by @xmath488 the partition of @xmath14 where each component @xmath489 is the set of sites spanned by @xmath490 . since each component of the partition comes with a special point corresponding to a root , we call _ rooted partition _ the pair @xmath491 we note that for each @xmath82 in @xmath492 , the _ restricted dynamics _ with generator @xmath493 , \quad f : a \rightarrow { \mathbb r } , \quad x \in a,\ ] ] has only one irreducible component since each @xmath26 in @xmath82 is connected with the root . as a consequence the restricted dynamics has a unique equilibrium measure which we call _ restricted measure _ @xmath494 . note that when @xmath111 has a _ reversible _ equilibrium @xmath495 , then @xmath494 is nothing but the equilibrium measure @xmath336 conditioned on @xmath82 , i.e. @xmath496 . [ localequilibria]*(roots at restricted equilibrium ) * fix @xmath497 , then @xmath498 for any partition @xmath499 of @xmath3 and any @xmath500 , for @xmath501 for each @xmath502 in @xmath503 , let us call @xmath504 the set of spanning trees of @xmath489 . for each @xmath505 in @xmath504 , define @xmath506 and for @xmath507 in @xmath489 , write @xmath508 , if @xmath507 is the root of the tree @xmath509 . compute @xmath510 where the last equality follows by applied to the restricted dynamics . a rooted partition with 50 roots ( at the center of red diamonds ) sampled for the metropolis random walk in a brownian sheet potential on the @xmath205 grid and with inverse temperature @xmath511 . blue levels depend on the potential : the lower the potential , the darker the blue . we see that each root is distributed according to the restricted equilibrium of its own piece of the partition . see also the first two pictures in figure [ mimosa ] . ] * remark : * when @xmath2 is reversible with respect to a measure @xmath336 , this gives a way to build the associated gaussian free field with mass @xmath512 , that is the gaussian process @xmath513 with covariance matrix @xmath514 by successive sampling of the standard measure @xmath199 . start from independent centered random variables @xmath515 with variance @xmath516 , @xmath517 , sample @xmath36 according to @xmath199 , call @xmath518 the set of vertices of @xmath98 and set @xmath519 then the random field @xmath520 has zero mean and covariance matrix @xmath521 and the rescaled partial sum @xmath522 , with @xmath523 , @xmath524 , independent copies of @xmath520 , converges in law to @xmath417 as @xmath44 goes to infinity . indeed , for each @xmath26 and @xmath203 in @xmath3 , @xmath525 and @xmath526 are centered and one computes @xmath527 = \sum_{a\subset\mathcal{x } } \mathbb{p}\left ( a(x ) = a(y ) = a \right ) \frac{1}{\mu(a)^2 } \sum_{z \in a } \frac{\mu(z)}{q } = \sum_{a\ni x , y } \mathbb{p}\left ( a(x ) = a(y ) = a \right ) \frac{1}{q\mu(a ) } .\ ] ] on the other hand , following wilson algorithm , @xmath528 by combining it with , we conclude that @xmath529 = \frac{k(x , y)}{q\mu(y ) } .\ ] ] let us associate with our random forests @xmath68 with law @xmath199 , the random variables @xmath530 note that they completely describe the roots process . for @xmath531 with distinct @xmath101 s , the cumulants of these random variables are defined by @xmath532 \bigg|_{\lambda = 0 } .\ ] ] these quantities are the so - called truncated correlation functions , that can also be recursively defined by @xmath533 = \sum_{\pi \in { \cal p}_a } \prod_{b \in \pi } \kappa_b(\eta),\ ] ] where @xmath534 stands for the set of partitions of @xmath82 . the determinantal nature of the roots process makes its cumulants easy to compute . with @xmath535 and @xmath536 being the permutation group on @xmath82 , one has @xmath537 = { \mathbb p}\left ( a \subset \rho(\phi ) \right ) = { \rm det}_a(k ) = \sum_{\sigma \in { \cal s}_a } ( -1)^{{\rm sgn}(\sigma ) } \prod_{x \in a } k(x , \sigma(x)).\ ] ] making a cycle decomposition of each permutation in this sum and denoting by @xmath538 the set of long cycles on @xmath539 , i.e. the set of cycles of length @xmath540 in @xmath121 , after some simple algebra , we get @xmath537 = \sum_{\pi \in { \cal p}_a } \prod_{b \in \pi } \sum_{\sigma \in { \cal c}_b } ( -1)^{|b| - 1 } \prod_{x \in b } k(x , \sigma(x)).\ ] ] this identifies our cumulants through ( [ luce ] ) and gives the following lemma . for all @xmath535 @xmath541 where @xmath542 stands for the set of cycles of length @xmath543 in @xmath82 . * remark : * we can not help making the following observation . in the case of uniformly equal weights between nearest neighbours , for large @xmath78 , @xmath544 behaves like the natural low temperature partition function associated with an embedded travelling salesman problem . in this regime , on the one hand , wilson s algorithm quickly provides perfect samples of the roots process and , on the other hand , the cumulant is the expected value of some observable for the system made of @xmath44 independent copies of @xmath485 @xcite . this suggests that one could find a practical way to estimate this low temperature partition function and then solve the travelling salesman problem . unfortunately , the corresponding observable has an exponentially small probability to be different from @xmath404 and consequently , it is in reality impossible to estimate its mean in this way . assume we have a markov process @xmath107 on a finite state space @xmath108 , with generator @xmath112 given by @xmath545,\quad y\in \mathcal{y},\ ] ] with @xmath118 arbitrary and @xmath546 a given collection of non - negative and finite transition rates . as in section [ loops ] , let us denote by @xmath110 the discrete skeleton of the random walk @xmath107 with markovian transition matrix @xmath156 . fix a subset @xmath547 with @xmath548 and consider a new markov chain @xmath549 with state space @xmath82 obtained as the trace of the process @xmath110 on @xmath82 . in other words , @xmath549 is the random walk with transition matrix @xmath550 , with entries @xmath551 where @xmath552 denotes the first return time in @xmath82 of the chain @xmath110 . back to the continuous - time setting , denote by @xmath553 be the continuous - time version of @xmath549 with jump times given by exponential random variables of parameter @xmath554 i.e. the process with generator @xmath555 equivalently , @xmath553 is the trace of the markov process @xmath107 on @xmath82 , namely , the process obtained by following the trajectory of @xmath107 at infinite velocity outside @xmath82 and without speeding up inside @xmath82 . [ schurprob]*(schur complement and trace process ) * given the markov process @xmath107 on @xmath108 with generator @xmath112 , fix a subset @xmath547 with @xmath548 . let @xmath115 be the generator of the markov process @xmath553 obtained as the trace of the process @xmath107 on @xmath82 . then , @xmath115 is the schur complement of @xmath556_{a^c}$ ] in @xmath112 , i.e. @xmath557_a-[\mathcal{l}]_{a , a^c}[\mathcal{l}]^{-1}_{a^c}[\mathcal{l}]_{a^c , a},\ ] ] with @xmath556_a$ ] and @xmath556_{a^c}$ ] being the sub - markovian generator of the process killed outside @xmath82 and @xmath273 , respectively . in other words , @xmath556_a$ ] and @xmath556_{a^c}$ ] represent the operators obtained from the matrix representation of @xmath283 , by deleting the row and the columns indexed by sites outside @xmath82 and @xmath273 , respectively . whereas @xmath556_{a , a^c}$ ] and @xmath556_{a^c , a}$ ] are the operators obtained from the matrix representation of @xmath283 , by keeping only those rates from @xmath82 to @xmath273 and @xmath273 to @xmath82 , respectively . denote by @xmath155_a\in \mathcal{m}_{k\times k}$ ] , the sub - markovian matrix @xmath156 restricted to @xmath82 . note that @xmath155_a$ ] is different from @xmath558 . due to , for any @xmath292 , we can write subtracting @xmath560 on both side of , we obtain that @xmath561_a - [ \hat{p}-\mathbbm{1}]_{a , a^c}\left([\hat{p}]_{a^c}-\mathbbm{1}_{a^c}\right)^{-1}[\hat{p}-\mathbbm{1}]_{a^c , a}. \end{aligned}\ ] ] we then get our result by multiplying both sides by @xmath562 . when @xmath563 contains an absorbing set @xmath121 and @xmath564 we can do the same computation with the sub - markovian generator @xmath556_{b^c}$ ] in place of @xmath283 . for any @xmath26 and @xmath203 in @xmath82 the mean local time in @xmath203 starting from @xmath26 and before hitting @xmath121 is the same for @xmath107 and the trace process @xmath553 , i.e. @xmath565 that is @xmath566_{b^c}^{-1 } \right]_a = \left ( [ { \cal l}]_{b^c}^a \right)^{-1 } .\ ] ] more generally , one has the following definition and properties . [ schur]*(schur complement ) * let @xmath103 be a @xmath567 block matrix in @xmath43 of the form @xmath568,\ ] ] where @xmath569 and @xmath570 , for some @xmath325 . the schur complement of @xmath281 in @xmath103 is defined as the matrix @xmath571 one can then check : @xmath572 = \left [ \begin{array}{cc } i_k & bd^{-1 } \\ 0 & i_{n - k } \end{array } \right ] \left [ \begin{array}{cc } s_m(d ) & 0 \\ 0 & d \end{array } \right ] \left [ \begin{array}{cc } i_k & 0 \\ d^{-1}c & i_{n - k } \end{array } \right].\ ] ] it follows that @xmath573 and , as a generalization of ( [ cubo ] ) , @xmath574.\ ] ] in particular , from ( [ inverse ] ) and ( [ detm ] ) , @xmath575 with @xmath576 and @xmath577 . this relation is used in the algebraic proof of theorem [ determinantalroots ] . in this section we use our forest measure analysis to prove two formulas on the hitting distribution and the expectation of hitting times of a given subset of the given graph . this result is originally due to freidlin and wentzell , see lemmas 3.2 and 3.3 in @xcite . [ wentzellthm]*(freidlin and wentzell @xcite ) * fix a non - empty subset @xmath9 of @xmath3 . recall the notation in . consider the markov process @xmath2 on @xmath3 identified by , and let @xmath4 be the hitting time of the set @xmath9 . then , for any @xmath578 and @xmath579 @xmath580 and , for any @xmath578 , @xmath581 = \frac{1}{z_r(0 ) } \sum_{y \not\in r } \sum _ { \stackrel { \scriptstyle \phi:\rho(\phi)=r\cup\{y\ } } { \scriptstyle \rho(\tau_x)=\{y\ } } } w_(\phi).\ ] ] consider the extended space @xmath174 and the extended markov process @xmath169 as in , with the killing rates as in for @xmath483 . equation ( [ wilsonabsorbingset ] ) is simply obtained by considering wilson s algorithm started from @xmath26 . to prove ( [ wentzellformula ] ) we will use the discrete skeleton of section with @xmath582 and @xmath583 . let @xmath584 \quad\text{and}\quad \hat{g}_r(x , y)= e_x[l_y(\hat{t}_r ) ] , \quad x , y \in r^c,\ ] ] be the continuous and the discrete - time green s functions before hitting the set @xmath9 , respectively . since @xmath585=\sum_{y\notin r}g_r(x , y),\ ] ] it suffices to show that @xmath586 since @xmath587 with @xmath588 being the return time to @xmath203 , @xmath589}. \end{aligned}\ ] ] observe that @xmath590 for any @xmath591 , thus using : @xmath592}\\ & = \frac { \frac{1 } { z_{r\cup\{y\}}(0 ) } \sum _ { \stackrel { \scriptstyle \phi:\rho(\phi)=r\cup\{y\ } } { \scriptstyle \rho(\tau_x)=\{y\ } } } w(\phi ) } { \frac{1}{z_{r\cup\{y\}}(0 ) } \sum_{z\neq y } \alpha(y , z ) \sum _ { \stackrel { \scriptstyle \phi:\rho(\phi)=r\cup\{y\ } } { \scriptstyle \rho(\tau_x ) \neq \{y\ } } } w(\phi ) } \\ & = \frac{1}{z_r(0 ) } \sum _ { \displaystyle \stackrel { \scriptstyle \phi:\rho(\phi)=r\cup\{y\ } } { \scriptstyle \rho(\tau_x)=\{y\ } } } w(\phi ) . \end{aligned}\ ] ] in this appendix , we recall three equivalent definitions of the notion of divided differences of a real function . we further give a lemma due to micchelli and willoughby for which we provide an alternative elementary proof which plays with these different definitions . this result is used in section [ mw ] . * ( divided differences 1 ) * we call divided difference of a function @xmath142 at the distinct points @xmath593 , @xmath486 , , @xmath594 , the quantity @xmath595 $ ] recursively defined via @xmath596= \frac{f[x_1,\cdots , x_k]-f[x_0,\cdots , x_{k-1}]}{x_k - x_0},\ ] ] with @xmath597=f(x_i).\ ] ] * ( divided differences 3 ) * for any function @xmath142 and distinct points @xmath593 , @xmath486 , , @xmath598 , @xmath594 , @xmath600+f[x_0,x_1](x - x_0)+f[x_0,x_1,x_2](x - x_0)(x - x_1)\\&+\ldots+f[x_0,\cdots , x_k](x - x_0)\ldots(x - x_{k-1 } ) \end{aligned}\ ] ] is the unique polynomial of degree @xmath229 with @xmath601 , for @xmath602 [ divdif ] * ( micchelli and willoughby @xcite ) * consider a polynomial of degree @xmath44 of the form @xmath603 with @xmath44 distinct real zeros @xmath604 in decreasing order : @xmath605 . let @xmath606 with @xmath607 and such that @xmath608 then , for any @xmath609 , @xmath610\geq 0.\ ] ] we prove the following statement by induction on @xmath611 : @xmath612 \geq 0$. '' } \ ] ] since @xmath142 is a polynomial of degree @xmath44 , ( [ chiocciola ] ) follows from definition [ divdiff3 ] as soon as @xmath613 . also , since the dominant coefficient of @xmath142 is @xmath335 , the same argument shows @xmath614 = 1 $ ] and the claim holds for @xmath615 . fix now @xmath616 , i.e. @xmath617 , and @xmath618 satisfying ( [ beta ] ) . if @xmath619 then @xmath620 - f[\alpha_0 , \alpha_1 , \dots , \alpha_k ] } { \beta_0 - \alpha_0 } & = \frac { f[\beta_0 , \alpha_1 , \dots , \alpha_k ] - f[\alpha_1 , \dots , \alpha_k , \alpha_0 ] } { \beta_0 - \alpha_0 } \label{crema } \\ & = f[\beta_0 , \alpha_1 , \dots , \alpha_k , \alpha_0]\\ & = f[\beta_0 , \alpha_0 , \alpha_1 , \dots , \alpha_k ] . \label{nuvola}\end{aligned}\ ] ] by definition [ divdiff2 ] we have @xmath621 = 0 $ ] and the numerator in the l.h.s . of ( [ crema ] ) is merely equal to @xmath622 $ ] . the denominator is positive from ( [ beta ] ) and so is the r.h.s . of ( [ nuvola ] ) by induction hypothesis . it follows that @xmath623 \geq 0\ ] ] and the same is true when @xmath624 . if @xmath625 , we compute @xmath626 - f[\beta_0 , \alpha_1 , \dots , \alpha_k ] } { \beta_1 - \alpha_1 } = f[\beta_0 , \beta_1 , \alpha_1 , \dots , \alpha_k ] , \ ] ] get then in the same way @xmath627 \geq 0\ ] ] and the same is true when @xmath628 . proceeding similarly we eventually obtain that @xmath629 \geq 0.\ ] ] * acknowledgements : * a.g . thanks laurent tournier for the many fruitful discussions on the matter , and , in particular , the nice independence argument we presented in section [ background ] . he also thanks pablo ferrari , ins armendariz , pablo groisman , leonardo rolla and matthieu jonckheere for their hospitality in buenos aires where all this work started . y. le jan , _ markov paths , loops and fields _ , vol . 2026 of lecture notes in mathematics . springer , heidelberg , 2011 . lectures from the 38th probability summer school held in saint - flour , 2008 , ecole dt de probabilits de saint - flour .

consider a finite weighted oriented graph . we study a probability measure on the set of spanning rooted oriented forests on the graph . we prove that the set of roots sampled from this measure is a determinantal process , characterized by a possibly non - symmetric kernel with complex eigenvalues . we then derive several results relating this measure to the markov process associated with the starting graph , to the spectrum of its generator and to hitting times of subsets of the graph . in particular , the mean hitting time of the set of roots turns out to be independent of the starting point , conditioning or not to a given number of roots . wilson s algorithm provides a way to sample this measure and , in absence of complex eigenvalues of the generator , we explain how to get samples with a number of roots approximating a prescribed integer . we also exploit the properties of this measure to give some probabilistic insight into the proof of an algebraic result due to micchelli and willoughby @xcite . further , we present two different related coalescence and fragmentation processes . _ msc 2010 : _ primary : 05c81,60j20,15a15 ; secondary : 15a18,05c85 . + _ keywords : _ finite networks , spanning forests , determinantal processes , random sets , hitting times , local equilibria , wilson s algorithm , random partitions , coalescence and fragmentation .

quantum statistical physics , such as condensed matter or plasma physics , but also quantum chemistry , heavily depends on effective numerical methods for solving complex few - particle and many particle problems . implementing suitable theoretical concepts for their description on modern supercomputer architectures , nowadays computational physics constitutes , besides experiment and theory , the third pillar of contemporary physics @xcite . numerical techniques become especially important for strongly correlated systems where analytical approaches largely fail . this is due to the absence of small ( coupling ) parameters or , more general , because the relevant energy scales are not well separated , both preventing the application of standard perturbative schemes . common to any numerical method in quantum physics is the requirement to represent the states and operators describing the physical system in the hilbert space in a form that is suited for computations . then , working with a discrete basis of the hilbert space , the computational challenge is the solution of an eigenvalue problem for huge ( sparse ) matrices . for most physical systems the dimension of the hilbert space is much too large in order to perform a full exact diagonalisation of the related hamilton matrix . fortunately some quantities of interest depend on the properties of the ground state or a few excited states only , and therefore may be studied by iterative krylov space techniques such as lanczos diagonalisation @xcite . the quantum dynamics or long time behaviour of correlated systems , however , require , in principle , the knowledge of all eigenstates . the theoretical investigation of quantum dynamics was triggered in recent years by the vast progress of the experimental techniques . nowadays femtosecond laser spectroscopy , for instance , allows for a precise analysis of quantum dynamical processes with extreme time resolution . direct time integration of the schrdinger equation at the cost of a full diagonalisation of the system s hamiltonian ( including the coupling to external fields ) is impractical in such cases because of its computational complexity . the aim of this work is to propose a very efficient chebyshev - based algorithm that allows calculating the dynamics of a quantum system numerically exactly , also for relatively long times , and therefore overcomes the above mentioned problem at least partially . in order to demonstrate the power of our iterative chebyshev expansion approach , we compare the accuracy and computational costs of certain model calculations with those emerging by the use of the more the standard crank - nicholson , wigner - moyal and quantum tomography methods . we start by presenting the basic ideas of the iterative ( chebyshev , crank - nicholson ; sect . [ sect : directmethods ] ) and semiclassical ( wigner - moyal , tomographic ; sect . [ sect : semiclassicalmethods ] ) techniques . afterwards , in sect . [ sect : systems ] , we consider three different problems of increasing complexity : ( i ) the motion of a gaussian wave packet in a 1d geometry ( sec . [ sect : doublewells ] ) , ( ii ) the evolution of a particle in a disordered 2d graphene nanoribbon ( sec . [ sect : grapheneribbon ] ) , and ( iii ) the spatiotemporal evolution of polaron states in finite quantum systems ( sec . [ sect : polaron ] ) . our conclusions will be presented in sect . [ sect : conclusion ] . the time evolution of a quantum state @xmath0 is described by the schrdinger equation @xmath1 if the hamilton operator @xmath2 does not explicitly depend on time @xmath3 we can formally integrate this equation and express the dynamics of a given quantum state @xmath4 in terms of the time evolution operator @xmath5 as @xmath6 , where @xmath7 . exploiting that @xmath5 is diagonal in the eigenbasis of the hamiltonian , we can directly determine the dynamics of the quantum system . for systems with moderate hilbert space dimensions , a full diagonalisation of the hamiltonian permits expression of the quantum dynamics of an initial state @xmath4 as @xmath8 here @xmath9 are the ( time independent ) eigenstates of the system and @xmath10 the corresponding eigenenergies . in this way , the decomposition of an initial state into a linear combination of eigenstates allows for an exact calculation of the quantum state at arbitrary times . as soon as the physical description of the system requires a larger hilbert space dimension , however , this direct calculation is no longer feasible and we have to resort to alternative approaches . _ crank - nicholson scheme . _ one of the standard methods to calculate the quantum time evolution iteratively is the crank - nicholson algorithm @xcite . dividing @xmath11 $ ] into @xmath12 subintervals @xmath13 , the quantum state evolves for each iterative time step @xmath13 from @xmath14 to @xmath15 according to @xmath16 there are two limitations to this scheme . first , in addition to the matrix vector multiplication ( mvm ) on the right hand side of ( [ eq : cn ] ) , each iteration requires the solution of a linear system of equations to obtain @xmath17 . despite the availability of many powerful methods for the solution of large ( sparse ) linear equation systems , this task remains the most time consuming part of the algorithm . using iterative methods for the solution of the linear equation system , the attainable hilbert space dimensions increase substantially as compared to direct methods . second , the crank - nicholson algorithm is accurate only to order @xmath18 , which severely restricts the maximum usable iterative time step . _ chebyshev scheme . _ both limitations can be overcome by an approach where we expand the time evolution operator @xmath19 into a finite series of first - kind chebyshev polynomials of order @xmath20 : @xmath21 . we then obtain @xcite @xmath22 . \label{eq : u_1}\ ] ] prior to the expansion the hamiltonian has to be shifted and rescaled such that the spectrum of @xmath23 is within the definition interval of the chebyshev polynomials , @xmath24 $ ] . the parameters @xmath25 and @xmath26 are calculated from the extreme eigenvalues of @xmath2 as @xmath27 and @xmath28 . here we introduced @xmath29 to ensure the rescaled spectrum @xmath30 lies well inside @xmath24 $ ] . in practice , we use @xmath31 . note that the chebyshev expansion also applies to systems with unbounded spectra . in those cases we truncate the infinite hilbert space to a finite dimension by restricting the model on a discrete space grid or using an energy cutoff . in this way we ensure the finiteness of the extreme eigenvalues . in ( [ eq : u_1 ] ) , the expansion coefficients @xmath32 are given by @xmath33 ( @xmath34 denotes the @xmath20-th order bessel function of the first kind ) . to calculate the evolution of a state @xmath4 from one time grid point to the adjacent one , @xmath35 , we have to accumulate the @xmath32-weighted vectors @xmath36 . since the coefficients @xmath37 depend on the time step but not on time explicitly , we need to calculate them only once . the vectors @xmath38 can be computed iteratively exploiting the recurrence relation of the chebyshev polynomials , @xmath39 with @xmath40 and @xmath41 . evolving the wave function from one time step to the next requires @xmath42 mvms of a given complex vector with the ( sparse ) hamilton matrix of dimension @xmath43 and the summation of the resulting vectors after an appropriate rescaling . the chebyshev expansion may also be applied to systems with time dependent hamiltonians , but there the time variation @xmath44 determines the maximum @xmath45 by which the system may be propagated in a single time step . for time independent @xmath2 , in principle , arbitrary large time steps are possible at the expense of increasing @xmath42 . we may choose @xmath42 such that for @xmath46 the modulus of all expansion coefficients @xmath47 is smaller than a desired accuracy cutoff . this is facilitated by the fast asymptotic decay of the bessel functions , @xmath48 thus , for large @xmath42 , the chebyshev expansion can be considered as quasi - exact , and permits a considerably larger time step than e.g. the crank - nicholson scheme . besides the high accuracy of the method , the linear scaling of computation time with both time step and hilbert space dimension are promising in view of potential applications to more complex systems . in our cases almost all computation time is spent in sparse mvms , which can be efficiently parallelised , allowing for a good speedup on parallel computers . during the last decades , a variety of semiclassical methods have been tailored in order to incorporate certain quantum effects at least partially into classical many - particle simulations . based on the real time ( feynman- ) path integral formulation of quantum mechanics , where action integrals take the center stage , they allow propagation of the ( complex ) wave function of a quantum system in time . within the numerical evaluation of the integrals occurring by monte carlo ( mc ) techniques @xcite , the oscillatory complex valued integrand causes a dynamical sign problem which spoils the efficiency of the mc integration . _ wigner - moyal approach . _ since a quantum system can be described equivalently in terms of real valued quantum phase space distribution functions @xcite , e.g. , the wigner function , the dynamical sign problem may be alleviated @xcite . starting from the von neumann equation we may derive an evolution equation for the wigner function @xmath49 @xcite @xmath50 where @xmath51 is the classical force , and @xmath52 in the classical limit , the right hand side of ( [ eq : eom_wigner ] ) vanishes , leaving us with the liouville equation for the phase space density . then the dynamics can be expressed in terms of the classical propagator @xmath53\\ & \times\delta [ p-\bar{p}(t;p_0,q_0,t_0 ) ] \ , , \end{split}\ ] ] where @xmath54 and @xmath55 are the momentum and coordinate of a trajectory that evolves according to the hamilton equations of motion with initial conditions @xmath56 and @xmath57 . using @xmath58 , we may rewrite ( [ eq : eom_wigner ] ) in form of an integral equation @xcite , @xmath59 and solve it by iteration . here , we consider only the lowest order , which means that the second integral is neglected completely . that is , we propagate classical trajectories @xmath60 in time , after sampling their initial conditions @xmath61 and @xmath62 from the initial wigner function @xmath63 at time @xmath64 by a mc procedure . their superposition at the next time grid point gives @xmath49 . the importance of higher order terms in the iteration series was investigated in refs . . _ quantum tomographic approach . _ as the dynamical sign problem is still present for the wigner function , some years ago the description of quantum states in terms of a strictly positive function , the so called quantum tomogram , has been proposed @xcite . such a description seems promising in view of an effective mc sampling of the trajectories during the propagation . the quantum tomogram @xcite , @xmath65 relates to the wigner function by a class of radon transforms @xcite which are characterised by @xmath66 and @xmath67 . each tomogram contains a density information , and tuning @xmath68 appropriately , we may continuously switch between coordinate and momentum representation . also for the quantum tomogram , an evolution equation can be derived from the von neumann equation @xmath69 \tilde{w } = 0\ , . \label{eq : eom_tom } \end{split}\ ] ] for harmonic potentials , eq . ( [ eq : eom_tom ] ) can be reformulated as a continuity equation and solved by trajectory methods . for potentials of arbitrary shape , the complicated structure prevents a direct evaluation of ( [ eq : eom_tom ] ) in order to get @xmath70 . a possible way out is a local expansion of the potential up to second order @xcite . the identification with the continuity equation then holds locally for each coordinate about which the potential is expanded . since the slope and local curvature of the potential enter the propagator for the trajectories , the efficiency of the tomogram - reconstruction depends crucially on the choice of the potential sampling positions . an intuitive , albeit not unique , choice for those positions are the coordinates of classically evolving particles similar to those in the wigner approach . advantageously , it is not necessary to propagate the whole set of tomograms if one is interested in the tomogram in one reference frame @xmath68 only . instead , it is sufficient to find those trajectories which end up in a given @xmath71 , or equivalently to propagate the desired @xmath72trajectories backward in time : one needs to be aware of the non - uniqueness of the propagator due to the various possible choices of the potential sampling points . we now apply the numerical techniques presented in the preceding section to selected physical systems and situations . as a first step , we calibrate the different approaches by studying a simple double well toy model . detecting the limitations and prospects of the various methods seems to be necessary before applying them to the more complicated problems of current interest . let us point out that the considered implementations of the semiclassical approaches provide an approximate description of quantum mechanics only , i.e. they will clearly not reproduce all the quantum effects . for the finite graphene nanoribbons studied in the second example it is barely possible to determine the full quantum dynamics by means of direct diagonalisation techniques or applying the crank - nicholson scheme . this gives us the opportunity to benchmark their performance in comparison to the chebyshev expansion for a system for which the hamilton matrix is not tridiagonal . the last example has been chosen to demonstrate the applicability of the chebyshev approach to a true many - particle problem , the tunnelling of a polaron . there the hilbert space dimension is so large that neither the direct diagonalisation method nor the crank - nicholson can be applied . as a basic test case we consider the motion of a gaussian wave packet in the 1d double well potential @xmath73 sketched in the top panel of fig . [ fig : doublewell ] . we use @xmath74 , @xmath75 , @xmath76 and @xmath77 , where @xmath78 , @xmath79 , @xmath80 are the reference units for mass , time and length , respectively . the initial gaussian of width @xmath81 is centred at @xmath62 , with centre - of - mass momentum @xmath61 , @xmath82 where we choose @xmath83 , @xmath84 , and @xmath85 . the top panel of fig . [ fig : doublewell ] gives also the real and imaginary part of the wave function , where the baseline indicates the energy of the initial state in relation to @xmath86 . discretising the potential @xmath86 on an equally spaced grid of @xmath87 @xmath88points , we fully diagonalise the hamiltonian to get the exact dynamics as reference . if we choose the iterative time step accordingly , the real and imaginary part of the wave function at @xmath89 is reproduced by both iterative methods with an absolute error less than @xmath90 . for this the maximum allowable time step for the crank - nicholson scheme is @xmath91 . for the chebyshev approach , the accuracy is even better than @xmath92 . here the required time step is related to the order of the chebyshev expansion , i.e. the number of moments @xmath42 . for @xmath93 we may propagate the wave function by @xmath94 . at the expense of calculating a larger number of moments @xmath42 , larger times steps may be chosen without loss of accuracy . this will be demonstrated in the next section . the time evolution of the modulus squared of the wave function is shown in the second panel of fig . [ fig : doublewell ] . while the major part of the wave packet stays in the left well , a sizeable fraction also penetrates the barrier . the rich structure in the density pattern reflects the ( well - known ) presence of strong interference effects . restricting the wigner - moyal scheme to first order , the corresponding data reproduces in essence the overall dynamics , but the fine interference patterns are not resolved within this approximation ( see third panel of fig . [ fig : doublewell ] ) . there are two major parameters which influence the computation time for this approach : ( a ) the number of propagated trajectories and ( b ) the time step necessary for their classical propagation . for the results presented , we have used @xmath95 trajectories and a propagation time step of @xmath96 . the agreement between the exact solution and the tomographic result ( see also the bottom panel of fig . [ fig : doublewell ] ) is even worse as the tunnelling to the right hand side of the barrier is missed almost completely . furthermore , the probability density for large negative values is overestimated , i.e. the effect of the steep anharmonic confinement potential is not accounted for correctly . in tab . [ tab : doublewell ] we summarise the run times @xmath97 on a single xeon 5160 processor required by the different methods in order to follow the time evolution of the system up to @xmath98 . this very basic example already shows that a straightforward use of the wigner - moyal and tomographic approaches only partially accounts for quantum effects . while , in principle , both methods are equivalent with respect to the solution of the time dependent schrdinger equation , an efficient implementation is lacking . for the wigner - moyal formalism there are two prospects . if the accuracy of the first order approximation is satisfactory , i.e. the neglect of the fine interference patterns is tolerable , this method provides an acceptable performance and might show its true virtue for many - particle systems . if one has to include higher terms of the iteration series , however , e.g. because subtle quantum effects are important , the method is not competitive anymore because ( i ) the computational requirements increase drastically and ( ii ) numerical fluctuations amplify strongly during the calculation @xcite . the practical applicability of the tomographic approach to arbitrarily shaped potentials is also questionable , mainly because there is no simple way to construct suitable sampling functions for the coordinate sampling in the potential evaluation . extensions beyond harmonic potentials will suffer crucially from this limitation . apart from the poor accuracy of the results , also the computational requirements were significant higher than for the other methods ( although we used only @xmath99 trajectories in this calculation ) . .time evolution of a wave packet in the double well potential up to @xmath100 . data gives the run times by exact diagonalisation ( ed ) , crank - nicholson ( cn ) , chebyshev ( c ) , wigner - moyal ( wm ) and tomographic ( t ) methods . [ cols="^,^,^,^,^,^",options="header " , ] the cycle of quasiparticle formation is fundamental to many fields of physics . in condensed matter , e.g. , the coupling between a charge carrier and the lattice degrees of freedom may create a new quasiparticle , an electron dressed by an phonon cloud . this composite entity is called polaron . from the basic electron - phonon ( ep ) interaction processes , the absorption / emission of a phonon with a simultaneous change of the electron state , it is clear that the motion of even a single electron in a deformable lattice constitutes a complex many - body problem , in that phonons are excited at various positions , with highly non - trivial dynamics @xcite . polaron transport through finite quantum systems becomes increasingly important for nanotechnology applications . the microscopic structure of polarons is very rich . focusing on polaron formation in systems with short - range non - polar ep interaction and site - dependent potentials , we consider a generalised holstein hamiltonian @xcite @xmath101 where @xmath102 ( @xmath103 ) creates an electron ( phonon ) at site @xmath104 of a 1d lattice . parameters are the electron transfer integral @xmath105 , the ep coupling strength @xmath106^{1/2}$ ] , and the phonon frequency @xmath107 . the potentials @xmath108 can describe a tunnel barrier , disorder , or a voltage basis . how does a bare electron time evolve to become a polaron quasiparticle ? to what extent can a polaron tunnel through a quantum barrier ? having the iterative chebyshev - based time evolution algorithm explained in sec . 2.2 at hand , we can address these questions in the framework of model ( [ eq : ghm ] ) . let us emphasise that our numerical approach , acting in the tensorial product hilbert space of electron and phonons , takes into account the full dynamics of both quantum objects . since the hilbert space associated to the phonons is infinite , we applied a controlled truncation procedure retaining only basis states with at most @xmath109 phonons @xcite . however the truncated hilbert space dimension ( @xmath110 ) is still very large even for small lattices and the dimension of the corresponding sparse matrix problem does limit the physical parameter region attainable . thus , we use a memory saving implementation of the sparse mvm where the non - zero matrix elements are not stored but recomputed in each sparse mvm step , limiting the overall memory consumption of our implementation to five vectors of size @xmath110 . in this context we can access a massively parallel sparse mvm code which has proven to be sufficient to compute the ground state of the model ( [ eq : ghm ] ) up to @xmath111 very efficiently on more than 5000 processor cores @xcite . for the single polaron dynamics presented here , the matrix dimension is @xmath112 and we run the chebyshev approach on 18 processors of a sgi altix4700 compute server accessing a total of approximately 60 gbytes of main memory and consuming less than 500 cpu - hrs to compute the result presented in fig . [ fig : polarondynamics ] . with momentum @xmath113 . moving to the right , a polaron is formed that hits the barrier located at site 12 at about @xmath114 . there complicated reflection and transmission processes of the composite quasiparticle made up of an electron and phonons take place . displayed is the time - evolution of the local particle densities @xmath115 ( solid lines , open circles ) , phonon numbers @xmath116 ( dot - dashed lines , stars ) and ep correlations @xmath117 ( dashed lines ) . open boundary conditions were used at sites 1 and 18 . in the numerics we account for all states with up to @xmath118 phonons and in the ground state the weight of all basis states containing exactly @xmath119 is less than @xmath120 . ] figure [ fig : polarondynamics ] shows snapshots of polaron formation and polaron propagation at intermediate ep coupling @xmath121 in the non - adiabatic regime @xmath122 ( the time and all energies were measured in units of @xmath123 and @xmath105 , respectively ) . at @xmath124 a bare electron wave packet is injected at site 4 and launched to the right . shortly after , the electron is not yet dressed and moves nearly as fast as a free particle . but then the electron emits ( creates ) phonons in the vicinity of the electron s starting point , in order to reduce its energy to near the bottom of the band , and then forms a polaron ( see the panel at @xmath125 ) . one of the most important properties of the polaron is an increased inertial mass , for the reason that some phonons have to travel with the particle ( as indicated by the enhanced on - site ep correlations ) . at the same time we observe a `` backscattered '' current @xcite , evolving to a left moving polaron . when the right - moving polaron reaches the wall at site 12 it will be partly reflected . more importantly , the additional local ep interaction @xmath126 renormalises the on - site adiabatic potential at site 12 , i.e. leads to a local polaron level shift that softens the barrier @xmath127 . as a result a vibration - mediated tunnelling of the particle takes place , whereby some phonons are stripped at the barrier and are recollected by the transferred particle afterwards ( cf the snapshots from @xmath128 to 14 ) . finally , the particle is reflected at the boundary and moves to the left passing the barrier again . note that during the whole run time uncorrelated phonon excitations remain in the system , especially near the injection point . in our opinion this example impressively demonstrates that our approach can be used to monitor the complicated multiple time - scale dynamics of quasiparticle transport in finite quantum structures . to summarise , in this work we compared various numerical approaches to the dynamics of complex quantum systems : expansion into eigenstates , iterative crank - nicholson and chebyshev schemes , as well as semiclassical wigner - moyal and quantum tomography methods . the different methods have been applied to several physical systems and problems , ranging from motion in a simple double - well toy model to questions of current interest such as electron transport in disordered graphene nanoribbons or polaron motion in a finite quantum structure . the wigner - moyal approach , evaluated in first order of the iteration series , essentially reproduces the quantum dynamics . nevertheless important quantum interference effects , appearing in the exact solution , are missed . the successful application of the quantum tomogram to the time evolution of quantum systems crucially depends on a suitable sampling algorithm for the coordinates at which the potential is evaluated . if those are sampled according to trajectories of classically propagated particles , the result for the quantum dynamics is rather poor and fails to describe tunnelling and anharmonicity effects correctly . while the moderate numerical costs of the first order wigner - moyal approach seem appealing for a possible application to more complex systems , the computational resources required by the quantum tomographic approach are high in general . on the side of the exact techniques , the chebyshev approach largely outperforms the standard crank - nicholson scheme , both in computation speed ( usable time step ) and treatable system sizes ( only matrix - vector multiplications were required ) . we conclude that the chebyshev approach represents a very efficient and reliable tool to determine the quantum dynamics even for rather complex interacting many - particle systems . h. fehske , a. alvermann , and g. wellein . in s. wagner , m. steinmetz , a. bode , and m. brehm , editors , _ high performance computing in science and engineering , garching / munich 2007 _ , pages 649668 . springer - verlag , berlin , 2009 .

we examine several numerical techniques for the calculation of the dynamics of quantum systems . in particular , we single out an iterative method which is based on expanding the time evolution operator into a finite series of chebyshev polynomials . the chebyshev approach benefits from two advantages over the standard time - integration crank - nicholson scheme : speedup and efficiency . potential competitors are semiclassical methods such as the wigner - moyal or quantum tomographic approaches . we outline the basic concepts of these techniques and benchmark their performance against the chebyshev approach by monitoring the time evolution of a gaussian wave packet in restricted one - dimensional ( 1d ) geometries . thereby the focus is on tunnelling processes and the motion in anharmonic potentials . finally we apply the prominent chebyshev technique to two highly non - trivial problems of current interest : ( i ) the injection of a particle in a disordered 2d graphene nanoribbon and ( ii ) the spatiotemporal evolution of polaron states in finite quantum systems . here , depending on the disorder / electron - phonon coupling strength and the device dimensions , we observe transmission or localisation of the matter wave .

massive stars are the primary source of radiation , kinetic energy , and chemical enrichment in the interstellar medium , playing a pivotal role in galactic evolution . because of their remote locations , our understanding of their formation has been limited by the lack of high resolution techniques . this challenge has been undertaken by adaptive optics systems at large - aperture telescopes . the present work is part of a coordinated effort to understand the formation of high - mass stars by using state - of - the - art instruments available at the _ vlt _ and other telescopes @xcite . herschel 36 is located in a high - mass star - forming region at a distance of 1.8 kpc from us ( van den anker et al . 1997 ; but see also arias et al . 2006 ) near the center of m 8 . the bright central part of m 8 is called the hourglass . the hourglass is a cavity of ionized gas seen through the gaps between the foreground obscuration @xcite . herschel 36 , an o7v star @xcite , is responsible for the ionization of the gas in the cavity . the inferred dynamical age of the ionized gas and , therefore , the age of the hourglass and herschel 36 , is as small as @xmath25@xmath310@xmath4 yrs @xcite . in the present study a special focus is placed on the infrared source found at a distance of 025 southeast of herschel 36 . the extended source called hereafter her 36 se was first recognized by @xcite by means of lunar occultation measurements . herschel 36 had long been known as a peculiar early - type star with substantial mid - infrared excess @xcite . it is only after her 36 se was spatially resolved that we know that this object is actually the source responsible for the excess infrared emission . after the discovery of @xcite , the possible identity of her 36 se has been discussed , including an externally ionized protoplanetary disk , or , a proplyd , an obscured embedded source , and a leftover circumstellar disk of herschel 36 ; however , no solid conclusion was reached . in the next section , the observations at the _ vlt _ and supplemental spectroscopy at the subaru telescope are described . the direct consequences of the observations are summarized in 3 . in 4 we will further discuss the possible nature of her 36 se as a deeply embedded early - type star under the violent influence of the nearby o - star herschel 36 . is color coded in red , @xmath5 in green , and br@xmath0 in blue before continuum subtraction . her 36 se is the red extended emission at 025 southeast of herschel 36 . her 36 b is an infrared star at 36 north of herschel 36 . the coordinates of herschel 36 are r.a . ( j2000 ) 18@xmath603@xmath740@xmath820 , dec ( j2000 ) @xmath92422430 @xcite . [ lp],scaledwidth=49.0% ] the infrared imaging at @xmath5 ( 3.8 @xmath10 m ) and @xmath11 ( 4.7 @xmath10 m ) was carried out at the _ vlt _ ut4 on 2003 june 11 with the adaptive optics imager naco @xcite . herschel 36 ( @xmath12 9.1 mag ) served as a wavefront reference source for the visible wavefront sensor in the adaptive optics system . a short exposure of 180 ms was repeated 27 times in the @xmath5 imaging at each of the 9 positions of the telescope dithering . imaging at @xmath11 was performed the same way , but with a shorter integration time of 56 ms repeated 89 times . the total on - source integration time is 58 s and 60 s at @xmath5 and @xmath11 , respectively . the observing log is presented in table [ tb1 ] including imaging with other filters and additional spectroscopy . the imaging data were reduced in the standard manner . after sky - subtraction and flat - fielding , images were registered referring to the position of herschel 36 . the size of the isoplanatic patch was measured using more than 40 stars inside the entire field of view of naco ( 27@xmath327 ) . the measurements have been done at 2.2 @xmath10 m , since the isoplanatic patch becomes smaller with the wavelength . the point spread function ( psf ) is found elongated only at the edge of the field of view , and no significant degradation of psf is recognized within the field of view relevant to the following discussion shown in figure [ lp ] . the full width at half maximum ( fwhm ) of point sources are 011 at @xmath5 and 013 at @xmath11 in the fully reduced images . m for her 36 se ( top ) and the flux calibration star hd 169916 ( bottom ) . herschel 36 is no longer visible at this wavelength . while hd 169916 has multiple diffraction rings around , her 36 se is extended with no trace of a point source . right : the radial profile of her 36 se and hd 169916 . the size of the emitting region at her 36 se is 850 au in diameter , after deconvolution with the spatial profile of hd 169916 . [ psf],title="fig:",scaledwidth=21.0% ] m for her 36 se ( top ) and the flux calibration star hd 169916 ( bottom ) . herschel 36 is no longer visible at this wavelength . while hd 169916 has multiple diffraction rings around , her 36 se is extended with no trace of a point source . right : the radial profile of her 36 se and hd 169916 . the size of the emitting region at her 36 se is 850 au in diameter , after deconvolution with the spatial profile of hd 169916 . [ psf],title="fig:",scaledwidth=25.0% ] llccclll[b ] 2003 jun 11 & @xmath5 & 3.80 & 0.62 & _ vlt _ & naco & imaging & + 2003 jun 11 & @xmath11 & 4.78 & 0.59 & _ vlt _ & naco & imaging & + 2003 jun 11 & br@xmath13 & 2.17 & 0.023 & _ vlt _ & naco & imaging & + 2003 jun 11 & ib 218 & 2.18 & 0.060 & _ vlt _ & naco & imaging & + 2004 jun 3 & n8.7 & 8.64 & 1.55 & _ vlt _ & midi & imaging & + 2004 jun 3 & [ ] & 12.8 & 0.39 & _ vlt _ & midi & imaging & + 2004 jul 29 & br@xmath1 & 4.05 & & subaru & ircs / ao & spectroscopy & @xmath14 + the absolute flux calibration was tied to the photometry of herschel 36 as given in the literature . the zero point magnitudes were calculated to be consistent with the photometric magnitudes @xmath15 6.3 mag and @xmath16 3.8 mag in @xcite and @xcite , respectively . the images were convolved with gaussian filter at the zero - point calculation to match the spatial resolution in the previous observations . the photometry of herschel 36 was performed inside a small aperture of 02 to avoid confusion with her 36 se . an aperture correction was applied by using the psf sampled at her 36 b ( see figure [ lp ] ) . the photometry of her 36 se was then performed in a circular aperture of 13 , after the contribution of herschel 36 was removed by subtracting the scaled psf . the primary error source in the photometry is the spatial fluctuation of the background emission in the immediate vicinity of herschel 36 . we restored the flux compensation function with varying outer bounds from 06 to 14 , and found that the amount of aperture correction does not differ more than 15 % . the sky level sampled at different locations at 09 to 26 around the object does not change the net photometry by more than 14 % . we therefore quote 0.2 mag as the photometric accuracy , although the formal error is much smaller ( @xmath170.05 mag ) . the results are presented in table [ tb2 ] with other photometry obtained in this paper . the color composite image of @xmath5 , @xmath11 and the narrow - band image at 2.17 @xmath10 m described in the next section is shown in figure [ lp ] . narrow - band br@xmath0 images ( 2.17 @xmath10 m ) were obtained during the same night together with continuum images at 2.18 @xmath10 m . short exposures of 1 s were repeated 20 times to minimize the saturation of bright stars . the total integration time on source is 100 s. the sky at 30 distance from the field was recorded for background subtraction . the data were processed in the same way as it was the case for broadband imaging . aperture photometry was performed for her 36 se in br@xmath0 and the continuum at 2.18 @xmath10 m . since herschel 36 is saturated , her 36 b was used to establish the correct flux scale of the images ( @xmath18 mag ; ks1 in woodward et al . 1990 , 18006nr766 in bik 2004 ) . the psf sampled from her 36 b was scaled and subtracted from herschel 36 to isolate the extended emission of her 36 se . the total pixel counts were summed up inside a circular aperture of 13 centered on her 36 se . note that the br@xmath0 photometry presented in table [ tb2 ] is before the continuum subtraction . the accuracy of the photometry is @xmath20.1 mag for the images with the underlying continuum emission . the continuum image was scaled and subtracted so that the pixel counts of blue stars ( with respect to their infrared colors ) around herschel 36 are equally canceled in the line - emission image . mid - infrared images in the @xmath19 filter ( 8.7 @xmath10 m ) and in the [ ] filter ( 12.8 @xmath10 m ) were obtained on 2004 june 3 at the _ vlt _ with midi @xcite . the instrument is an interferometer / spectrometer , but was used as mid - infrared camera in the present observation . the tip - tilt corrector strap was used to stabilize the images . these thermal infrared data were recorded by using a chopping throw of 10 . the total on - source integration is 80 s at 8.7 @xmath10 m and 375 s at 12.8 @xmath10 m . the data reduction was carried out using the pipeline provided by the midi consortium . the spatial resolution of the final image is nearly diffraction limited ( fig . [ psf ] ) . the emission from her 36 se is clearly extended both in @xmath19 and [ ] . herschel 36 is no longer visible at mid - infrared wavelengths , as is expected from its photospheric spectral energy distribution ( sed ) . it is clear that the peculiar mid - infrared excess toward herschel 36 @xcite is not from the o - star itself , but is almost entirely attributed to her 36 se . the flux calibration was performed with respect to the photometric standard hd 169916 for which the absolute flux density was taken from @xcite . the photometry was performed inside a 18 aperture centered on her 36 se . the size of the aperture is slightly larger than that is used in the shorter wavelengths . the smaller aperture at the thermal near - infrared is because there seem to be two overlapping emission contributions at her 36 se ; the compact dusty cloud at her 36 se itself , and the filamentary emission more connected to the diffuse emission at 2 southeast of herschel 36 . since we will discuss an internal source inside her 36 se below , the diffuse emission should be excluded not to overestimate its luminosity . on the other hand , the mid - infrared images by midi do not show any clear hints of multiple sources , we therefore use a safe oversized aperture not to lose the mid - infrared flux of her 36 se for later discussion of its energetics . supplemental 4-micron spectroscopy ( @xmath20 10,000 ) was performed at the subaru telescope on 29 july 2004 with ircs @xcite . the slit was oriented along a position angle of 110 counted from north to east to cover herschel 36 and se at the same time . an adaptive optics system was used to attain higher spatial resolution @xcite . the sky at 2 north of herschel 36 was observed for background subtraction after each on - source integration . the spectroscopic flat field was obtained from a halogen lamp exposure at the end of the night . one dimensional spectra of herschel 36 and se were extracted with the aperture - extraction package of iraf after the sky - subtraction , flat - fielding , and the interpolation of the bad pixels were applied . the wavelength calibration was carried out using the atmospheric transmission curve modeled by atran @xcite . the br@xmath1 line - emission was calibrated to the photometry of herschel 36 at @xmath5 . first , to correct the continuum slope , the one - dimensional spectrum of herschel 36 was divided by the spectroscopic standard star hr 7121 ( b2.5v ) , and was multiplied by a blackbody spectrum of the temperature corresponding to the effective temperature of a b2.5v star ( @xmath2119,000 k ; crowther 2005 ) . the spectrum with correct slope was then scaled so that the averaged flux density inside the @xmath5 bandpath ( 3.494.11 @xmath10 m ) is equal to the @xmath5-band photometry of herschel 36 . the same conversion factor was used to calibrate the spectral flux of her 36 se reduced in the same way with herschel 36 . the br@xmath1 luminosity at her 36 se is found to be @xmath22(1.41.6)@xmath23 w at the distance of 1.8 kpc , after the continuum and the surrounding diffuse emission is subtracted . the error interval is given by the difference of the two sequential measurements , although it is subject to the uncounted uncertainty associated to the possible vignetting by the narrow slit of 03 . an unresolved source is detected at the location of her 36 se in the continuum - subtracted image at br@xmath0 ( fig . [ ha ] ) . the diameter of the point - like source is less than 130 au from the diffraction - limited spatial resolution of naco ( 0072 in fwhm at 2.17 @xmath10 m ) . the _ hst_/pc2 image retrieved from the st - ecf archive shows a compact h@xmath1 emission at the same location ( fig . the h@xmath1 emission is unresolved as well . considering the plate scale of pc2 ( 0046 pixel@xmath24 ) , this finding indicates that the source is less than 100 au across . furthermore , radio interferometric observations have been carried out with the _ vla _ at a wavelength of 2 cm ( see stecklum et al . 1998 for the observational detail ) . a compact radio source is found at the same location as the position of the br@xmath0 and h@xmath1 emission . the radio source is unresolved with regard to the synthesized beam size of 016 , which translates to 290 au . another line of evidence for a point - like source comes from the spectroscopy . the two - dimensional spectrogram near br@xmath1 is shown in figure [ bra ] . her 36 se shows distinct line emission in br@xmath1 , slightly blueshifted from ambient nebular emission by 2 km s@xmath24 , with a spatial profile apparently narrower than the continuum emission . the sharp spatial profile is comparable to that of herschel 36 , which corroborates the presence of a point - like source in the hydrogen line emission at the location of her 36 se . on the other hand , her 36 se is clearly extended in the continuum emission at wavelengths from 2 to 13 @xmath10 m . if we use the spatial profile of hd 169916 as the instrumental psf , and deconvolve her 36 se by inverting simple square sum , the extent of the emitting source at her 36 se is reduced to 047 at 12.8 @xmath10 m , which is 850 au in diameter at the distance of the object ( fig . [ psf ] ) . the sed of her 36 se is presented in figure [ sd ] to characterize the extended emission . the color temperature of the continuum source clearly points to the existence of warm dust at the location of her 36 se . like substructure is found in the broad band images of her 36 se that could have corresponded to the unresolved line emission . here we first discuss the identity of the line emission source and its possible ionization mechanism , including external ionization by herschel 36 , an embedded low- to intermediate - mass star in its active accretion phase , and an region internally ionized by an early - type star . the br@xmath0 emission is apparently inside the dusty cloud at her 36 se , since it is spatially more confined than the continuum emission . in addition , there is no hint of rim - ionization detected in br@xmath0 emission at the side of her 36 se where it faces toward herschel 36 . we found no solid evidence that herschel 36 plays a direct role to externally ionize the unresolved source inside her 36 se . the radio flux at 2 cm ( @xmath251.3 mjy ) is probably too high for an accretion signature of an intermediate - mass star at 1.8 kpc away . @xcite have calculated the free - free emission arising from an accretion shock in dependence of ( proto)stellar mass and accretion rate . however , even with their most extreme setup ( @xmath26 = 10 @xmath27 , @xmath28yr@xmath24 ) they just reach a 3.6 cm flux of roughly 3 mjy for a source 100 pc away . extrapolated to @xmath29 cm ( by optimistically assuming that the ionized gas is completely optically thick with @xmath30 ) and scaled to a distance of 1.8 kpc , the expected 2-cm flux would be just some 30 @xmath10jy , around 40 times less than the measured value . it is therefore inferred that a star with an early spectral type exists inside her 36 se that gives rise to a small region responsible for the radio emission . the region is internally ionized , but is kept compact because of the high density of the enshrouding cloud . if we take the _ vla _ beam size as the physical dimension of the region ( @xmath31140 au ) , the number of lyman continuum photons required to maintain the ionized gas is 1.6@xmath310@xmath32 s@xmath24 . the lyman continuum photon - rate is reproducible only by a star earlier than b2 if the star is at the zero - age main sequence @xcite . on the other hand , in order not to create a parsec - scale region , the hydrogen density has to be as high as @xmath33 @xmath34 . lccc & herschel 36 & her 36 se + filter & @xmath35 [ @xmath36 w m@xmath37 @xmath10m@xmath24 ] & @xmath35 [ @xmath36 w m@xmath37 @xmath10m@xmath24 ] & psf in fwhm + br@xmath0 & & 2.2 & 0072 + ib 218 & & 2.0 & 0071 + @xmath39 & 5.1 & 7.9 & 011 + @xmath40 & 5.2 & 21 & 013 + n8.7 & & 54 & 035 + & & 12 & 037 + we use the @xmath41-band extinction toward the hypothetical early - type star to estimate whether the gas density is sufficiently high to confine the region . a b2 star at the zero - age main - sequence should have a relative @xmath41-band brightness of 9.9 mag at the distance of herschel 36 without any attenuation ( @xmath42 mag from ducati et al . the sensitivity of our observation at 2 @xmath10 m is 15.7 mag for a 3 sigma detection at the location of her 36 se . with non - detection of any continuum point source at this wavelength , the dust extinction must be larger than 6 mag at 2 @xmath10 m , which translates to @xmath43 60 mag after correcting @xmath44 5 mag for the foreground extinction toward the herschel 36 region @xcite . the visible extinction can be related to a hydrogen column density ( e.g. , * ? ? ? * ; * ? ? ? . provided that the dusty core of her 36 se is spherical , of constant density , and 850 au across as is measured in the 12.8 @xmath10 m image ; the mass in the obscuration is @xmath45 with @xmath46 @xmath34 . thus , the gas density should be high enough to keep the region spatially unresolved . the lyman photon rate derived from br@xmath1 spectroscopy is also consistent with that of an early b type star . the ionizing flux in an region is obtained from br@xmath1 line flux by scaling the photon number - count proportionally to the recombination coefficients , @xmath47 . if we take @xmath48@xmath49 s@xmath24 and @xmath50@xmath49 s@xmath24 from @xcite for the case b of @xmath51 k and @xmath52@xmath34 , the lyman continuum rate turns out ( 6.98.0 ) @xmath310@xmath53 s@xmath24 , which is reproducible by a b2.5 dwarf @xcite . the correction of the foreground extinction needs caution , since the dust obscuration is increasingly transparent in the longer wavelength @xcite ; but if we use @xmath54 mag as a face value , the intrinsic lyman continuum rate is ( 4.14.8 ) @xmath310@xmath32 s@xmath24 , which is still consistent with the ionizing photon rate of a b1b1.5 dwarf . the infrared luminosity of her 36 se is consistent both with an internal b2 star , and also with external heating by herschel 36 . the infrared luminosity from 2 to 40 @xmath10 m is calculated from the naco and midi photometry with the flux density at the longer wavelength extrapolated as @xmath55 ; where @xmath56 is the distance to the object , and @xmath57 is the computed mass absorption coefficient for the grains without ice mantles coagulated in the protostellar cores @xcite . the total infrared luminosity is @xmath58 at an assumed distance of 1.8 kpc insensitive to the gas density of the core @xmath59 @xmath34 to @xmath60 @xmath34 . it is therefore well reproducible either by the luminosity of a b2 star at the zero - age main - sequence ( @xmath61 ) , or by herschel 36 ( @xmath62 ) while the solid angle subtended by her 36 se is of the order of unity at the location of herschel 36 . the dust emitting temperature is 400 k which should be taken as the upper limit , for the lack of additional photometry at the longer wavelengths . we conclude by comparing her 36 se with two similar cases reported to date in which bright mid - infrared sources are found in the immediate ( projected ) vicinity of o - type stars . the infrared source sc3 has been found at 18 ( 810 au ) west of @xmath63 ori c , the primary illumination source of the orion trapezium cluster @xcite . sc3 is spatially resolved , measuring 15 across , however , despite the apparent proximity to @xmath63 ori c ( o5.5v ) , its appearance is barely distorted , almost with a perfect circular symmetry . it is thus proposed that sc3 is a proplyd seen face - on , located deep behind @xmath63 ori c with the physical separation much larger than the apparent projection @xcite . sc3 is visible in the optical ( e.g. , * ? ? ? * ) , and at near - infrared wavelengths @xcite , which also lends support to its proplyd nature . the infrared appearance of sc3 is in strong contrast to her 36 se . we may use the highly distorted dust emission from her 36 se as circumstantial evidence that the source is actually under the influence of herschel 36 , and that the physical distance to the o star is not significantly larger than it appears . on the other hand , @xmath64 ori irs 1 , found next to @xmath64 orionis , shares a similar morphology with her 36 se . it is a compact infrared source at 1200 au away from the o9.5v star , and features a fan - shaped emission with @xmath64 orionis at the apex @xcite , exactly as herschel 36 is to se . the mid - infrared spectrum of @xmath64 ori irs 1 shows the partly crystalline silicate in emission . the presence of processed silicates suggests significant grain growth which is naturally present in a circumstellar disk . a proplyd is therefore again the most probable cause of @xmath64 ori irs 1 , especially because a central star has been detected recently in the @xmath41-band continuum emission ( b. stecklum , private communication ) . the star - forming region around herschel 36 has many features in common with the orion nebula cluster . the local concentration of massive stars , like her 36 b , together forms a trapezium - like cluster around herschel 36 . the presence of known proplyd nearby at [email protected] @xcite underscores the physical similarity as well . the mid - infrared color of her 36 se , and the close vicinity to an o - type star with a distorted morphology suggestive of radiative influence of it all point toward her 36 se is also a proplyd with a low - mass star at its center , as is the case for sc3 at @xmath63 ori c and @xmath64 ori irs 1 . however , in addition to the radio luminosity hardly accounted for by a low - mass star , and no ionized - front outside the dusty cloud ; a proplyd can not explain the lack of a point source to be detected at the continuum wavelengths that comes from the photospheric emission of the star . in the case of no central star inside , another possibility would be that her 36 se is an evaporating gaseous globule , a failed proplyd without an internal star in formation . these starless cores have been detected in numbers toward m 16 @xcite . however , a hypothetical starless globule conflicts with the presence of the unresolved br@xmath0 emission apparently inside of her 36 se . we therefore propose that her 36 se harbors a relatively massive star of early b - type producing a squeezed region inside the dusty cloud @xcite , but the star itself is completely obscured . the distortion of dust emission as well as the diffuse emission downstream of her 36 se , indicates the close physical interaction of herschel 36 and se . herschel 36 se , now in the process of being blown away , is a showcase for the violent impact of the dominant o - star in a cluster on another early - type star nearby . we thank all the staff and crew of the _ vlt _ and subaru for their valuable assistance in obtaining the data , and thorsten ratzka , elena puga and wolfgang brandner for their indispensable help in reducing data . we appreciate the anonymous referee for many critical comments that are necessary to improve the paper . is supported by japan society for the promotion of science fellowship . crowther , p. a. , massive star birth : a crossroads of astrophysics , international astronomical union . symposium no . 227 , 389 , on may 2005 in italy , eds . r. cesaroni , m. felli , e. churchwell , m. walmsley , cambridge : cambridge university press , astro - ph/0506324 grady , c. a. , woodgate , b. , torres , carlos a. o. , henning , th . , apai , d. , rodmann , j. , wang , hongchi , stecklum , b. , linz , h. , williger , g. m. , brown , a. , wilkinson , e. , harper , g. m. , herczeg , g. j. , danks , a. , vieira , g. l. , malumuth , e. , collins , n. r. , & hill , r. s. 2004 , , 608 , 809 leinert , c. , graser , u. , waters , l. b. f. m. , perrin , g. s. , walter , j. , bruno , l. , przygodda , f. , chesneau , o. , schuller , p. a. , grlazenborg - kluttig , annelie , w. , laun , w. , ligori , s. , meisner , j. a. , wagner , k. , bakker , e. j. , cotton , b. ; de jong , j. , mathar , r. , neumann , u. , & storz , c. 2003 , proc . spie 4838 , 893 rousset , g. , lacombe , f. , puget , p. , gendron , e. , arsenault , r. , kern , p. y. , rabaud , d. , madec , p .- y . , hubin , n. n. , zins , g. , stadler , e. , charton , j. , gigan , p. , feautrier , p. 2000 , proc . spie , 407 , 72

we present high - resolution infrared imaging of the massive star - forming region around the o - star herschel 36 . special emphasis is given to a compact infrared source at 025 southeast of the star . the infrared source , hereafter her 36 se , is extended in the broad band images , but features spatially unresolved br@xmath0 line emission . the line - emission source coincides in position with the previous _ hst _ detections in h@xmath1 and the 2 cm radio continuum emission detected by _ vla _ interferometry . we propose that the infrared source her 36 se harbors an early b - type star , deeply embedded in a dusty cloud . the fan shape of the cloud with herschel 36 at its apex , though , manifests direct and ongoing destructive influence of the o7v star on her 36 se .

quark models predict baryon resonances @xcite that have not yet been observed via strong interactions . these resonances could be detected via electro- and photoproduction of strange mesons . of special interest are the nucleon resonances n@xmath1 which some of them could couple strongly to @xmath2 and @xmath3 @xcite . moreover , higher mass nucleon resonances could favor decaying into @xmath4 , near threshold . using a quark - pair creation model @xcite , a study of n@xmath5 , where @xmath6 is the hyperon , shows that most @xmath7 decay branching ratios are small due to the high thresholds of these channels . only a few low - lying negative - parity states are predicted to be strongly coupled to @xmath4 channels , e.g. n(2070 ) , @xmath8(2140 ) , @xmath8(2145 ) . in addition , vector meson production could be used to investigate below - threshold resonance couplings to @xmath9y . experimental studies of neutral vector mesons used to concentrate on high energy regions that are dominated by the diffractive process and which could be accounted for by a soft pomeron exchange model . only recently , the study of non - diffractive mechanism in the vector meson production , near threshold , has become possible via resonance excitations . vector meson electro- and photoproduction near threshold might provide good knowledge about these resonances , their internal structure , and their couplings to vector mesons . this has been the main motivation for doing experiments to study strange mesons electroproduction off the proton , @xmath10 , @xmath11 much work and publications have been done on the first two channels @xcite . however , the third channel has barely been studied , because of its small cross section and the difficulty of detecting the @xmath9 decay . the availability of the high intensity electron facility and the cebaf large acceptance spectrometer ( clas ) in hall b @xcite at jlab , and other facilities , has made it possible to study this channel and opened new avenues to search for missing resonances " . here , @xmath12 electroproduction results are presented . preliminary results of this reaction are also shown in the thesis of ref . a theoretical model in which a quark model , with an effective lagrangian , approach to vector meson production @xcite , near threshold , has been developed for k@xmath0 production @xcite . it is the first theoretical attempt to study nucleon resonances and to present quark model predictions for the k@xmath0 production . in addition to using common quark model parameters , this model ( i ) uses two free parameters : the vector and tensor couplings for the quark - k@xmath1 interaction . they are the basic parameters in this model and are related to the k@xmath13n@xmath1 couplings that appear in the quark model symmetry limit , and ( ii ) adopted the su(3)-flavor - blind assumption of non - perturbative qcd , which suggests the above two parameters should have values close to those used in the @xmath14 and @xmath15 meson photoproductions . our experimental data should play a rule in tuning these parameters as well as testing and improving this model . the production of k@xmath1 vector mesons is related to other strangeness productions , eq . ( [ eq : electro ] ) , as well as non - strange vector meson production . at the _ hadronic level _ , these reactions are related to each other since one reaction contains the meson production in the other one as the t - channel exchanged particle , and therefore constraining the range of available couplings . this allows k@xmath1 and k production to use the same observables , which are obtained from non - strange vector meson production , @xmath15 and @xmath14 in the resonance region @xcite . at the _ quark level _ , both k and k@xmath1 productions involve the creation of s@xmath16 pair production , from the vacuum , in the su(3 ) quark model . in this model , the s quark couples to the meson in the same way as the u and d quarks , assuming quarks have the same masses , i.e. assumption ( ii ) above the k@xmath0 electroproduction data were extracted frome1b " data set using the clas detector @xcite , at jefferson lab s hall b. clas consists of : ( 1 ) the main torus : six superconducting magnetic coils making regions , or sectors " . their toroidal magnetic field deflects charged particles toward or away from the beam line , while keeping the azimuthal angle unchanged , ( 2 ) a forward - angle electromagnetic calorimeter ( ec ) : it is located in the forward region of each clas sector and covers up to 45@xmath17 of the polar angle . it detects particles moving forward and distinguishes electrons from pions , ( 3 ) cherenkov counter ( cc ) : covers the same angular range above . it is used along with the calorimeter to create a coincidence trigger , ( 4 ) three drift chambers ( dc ) : located in each sector and they determine the trajectories of charged particles from which their momenta are reconstructed . they cover about 80 @xmath18 of the azimuthal angle and a polar range from 8@xmath17 to 142@xmath17 , and ( 5 ) scintillator counters ( sc ) : an array of 288 scintillator counters where the charged particles times of flight and their energies are determined . they cover the same angular range as the dc . in this analysis we took data at 4.056 and 4.247 gev electron beam energies , with a liquid hydrogen target of length 5 cm . all data ( 430 and 610 million triggers , respectively ) were taken in feb . the toroidal coils current was 2250 a , corresponding to a magnetic field at 60% of the maximal field setting . we binned the k@xmath0 electroproduction data in the c.m . energy w , from 2.1 to 2.5 gev , and the 4-momentum transfer q@xmath19 , from 0.75 to 1.5 ( gev / c)@xmath20 , which are determined entirely by the electron kinematics . due to low statistics , the data were binned into large bins : ( i ) 100 mev in w , ( ii ) integrated over the above broad range in q@xmath19 , and ( iii ) integrated over the full angular range of @xmath21 and @xmath22 . in addition to the reaction of interest , @xmath23 , where k@xmath0(892 ) decays immediately into two detected particles , @xmath24 , there are other physics background contributions , from k@xmath25 production , @xmath26 @xmath27 where the @xmath28(1520 ) , eq . ( [ eq : our2 ] ) , decays with 14% probability to @xmath29 . that is , eqs . ( [ eq : our2 ] and [ eq : our3 ] ) are background contributions to our final state , @xmath30 . ( [ eq : our3 ] ) represents physics background from other excited states of @xmath28 family , e.g. @xmath28(1600 ) , @xmath28(1670 ) , @xmath28(1690 ) . these resonances have 3- or 4-star ratings as well as several exited states above 1.8 gev . diagrams of the k@xmath0(892 ) production ( signal ) and the @xmath28(1520 ) production are shown in fig . ( [ fig : fig1_ks_lam ] ) . the detected particles are @xmath31 , @xmath32 , and @xmath33 , while k@xmath0 and @xmath34 are undetected directly . the k@xmath0 was identified from the invariant mass of the k@xmath35 system , which peaks at 0.892 gev , while @xmath34 , from which we obtained the yields , was identified by applying cuts on both k@xmath25 mass and the missing mass of k@xmath0 , as explained below . we have two major background sources : ( i ) from the @xmath36 events , where the @xmath37 is mis - identified as a k@xmath25 , and ( ii ) physics backgrounds from other channels , eq . ( [ eq : our3 ] ) . to remove both background contributions and to identify @xmath34 , we used the side - band technique and applied the following mass cuts on both k@xmath25 and k@xmath0 mass distributions : ( 1 ) a cut on the k@xmath25 mass peak and a side - band cut , ( 2 ) two similar cuts on the k@xmath0 invariant mass distribution . the side - band cuts on both k@xmath25 and k@xmath0 produce the pion background and the physics background , respectively . combinations of the above four cuts produce two @xmath34 peaks shown in fig . ( 2 ) , ( i ) top ( k@xmath0 cut ) : cuts on both k@xmath25 and k@xmath0 peaks give the signal ( upper / green ) , and ( ii ) bottom ( y@xmath0 cut ) : k@xmath25 peak along with the k@xmath0 side - band cuts give the physics background contribution ( lower / red ) . the other two combinations give the pion background shown , in yellow , under each peak . in particular , the background from @xmath28(1520 ) production , eq . ( [ eq : our2 ] ) , was removed by applying a cut on the k@xmath25 missing mass . [ fig : fig2_sigpeak ] [ fig : fig3_norm_yeild ] figure 2 . we subtracted the pion background events from each @xmath34 peak , fig . ( 2 ) , obtaining two yields , one from k@xmath1 cut and the other from y@xmath1 cut . subtracting the latter yields from the former one resulted in the final yields . the yields were then corrected for the clas detector acceptance and normalized by the virtual photon flux . the measurements have been finished and analysis of the data is in progress . preliminary values of the normalized yields are shown in fig . ( [ fig : fig3_norm_yeild ] ) as a function of the center - of - mass energy w. currently , these data are being compared with the theoretical model ( not shown ) . our preliminary results show disagreement between the two beam energies , and further work is needed . however , the disagreement could be due to : ( i ) broad @xmath38 bin : a difference between the two @xmath38 averages , at a particular w value , due to our broad @xmath38 bin , might have contributed to this disagreement , ( ii ) @xmath39 dependence : the virtual photon flux dependence on the polarization constant , @xmath39 , which have different values for the two beam energies , might have contributed to this disagreement too , ( iii ) acceptance : the model from which we calculated the acceptances is still under improvements , sec . improving the model and tuning its free parameters are expected to improve the acceptances , and therefore narrowing the difference between the normalized yields . improving the model and calculating the final cross sections are in progress . n. isgur and g karl , phys * b 72 * , 109 ( 1977 ) ; phys . rev . d 23 , 817 ( 1981 ) . s. capstick and w. roberts , phys d 58 * , 74011(1988 ) . r. feuerbach , ph.d . thesis , carnegie mellon university , 2002 . b. mecking _ . meth . * a 503 * , 513 ( 2003 ) . a. weisberg , m.s . thesis , ohio university , 2001 . q. zhao , z. li and c. bennhold , phys . rev . * c 58 * , 2393 ( 1998 ) . q. zhao , j. al - khalili , and c. bennhold , phys . rev . * c64 * , 052210 ( 2001 ) .

the electroproduction of k@xmath0 mesons using the clas detector is described . data for two electron beam energies , 4.056 and 4.247 gev , were measured and the normalized yields are compared .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Sewage Sludge in Food Production Consumer Notification Act''. SEC. 2. NOTIFICATION TO CONSUMERS OF FOOD PRODUCTS PRODUCED ON LAND ON WHICH SEWAGE SLUDGE HAS BEEN APPLIED. (a) Adulterated Food Under Federal Food, Drug, and Cosmetic Act.-- Section 402 of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 342) is amended by adding at the end the following: ``(j)(1) Effective one year after the date of the enactment of the Sewage Sludge in Food Production Consumer Notification Act, if it is a food (intended for human consumption and offered for sale) that was produced, or contains any ingredient that was produced, on land on which sewage sludge was applied, unless-- ``(A) the application of sewage sludge to the land terminated more than one year before the date on which the production of the food or ingredient on the land commenced; ``(B) the food bears a label that clearly indicates that the food, or an ingredient of the food, was produced on land on which sewage sludge was applied; or ``(C) in the case of a raw agricultural commodity or other food generally offered for sale without labeling, a sign is posted within close proximity of the food to notify consumers that the food, or an ingredient of the food, was produced on land on which sewage sludge was applied. ``(2) In this paragraph, the term `sewage sludge' has the meaning given to such term in section 503.9(w) of title 40, Code of Federal Regulations (or any successor regulations).''. (b) Adulterated Food Under Egg Products Inspection Act.--Section 4 of the Egg Products Inspection Act (21 U.S.C. 1033) is amended-- (1) in paragraph (a)-- (A) by striking ``or'' at the end of subparagraph (7); (B) by striking the period at the end of subparagraph (8) and inserting ``; or''; and (C) by adding at the end the following: ``(9) effective one year after the date of the enactment of the Sewage Sludge in Food Production Consumer Notification Act, if it is derived from poultry that were raised, or that consumed animal feed produced, on land on which sewage sludge was applied, unless-- ``(A) the application of sewage sludge to the land terminated more than one year before the date on which the poultry began to be raised on the land or the date on which the production of the animal feed on the land commenced; or ``(B) the container bears a label that clearly indicates that the egg or egg product was derived from poultry that-- ``(i) were raised on land on which sewage sludge was applied; or ``(ii) consumed animal feed produced on land on which sewage sludge was applied.''; and (2) by adding at the end the following: ``(aa) The term `sewage sludge' has the meaning given to such term in section 402(j)(2) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 342(j)(2)).''. (c) Adulterated Food Under Federal Meat Inspection Act.--Section 1 of the Federal Meat Inspection Act (21 U.S.C. 601) is amended-- (1) in paragraph (m)-- (A) by striking ``or'' at the end of subparagraph (8); (B) by striking the period at the end of subparagraph (9) and inserting ``; or''; and (C) by adding at the end the following: ``(10) effective one year after the date of the enactment of the Sewage Sludge in Food Production Consumer Notification Act, if it is derived from livestock that grazed, or consumed animal feed produced, on land on which sewage sludge was applied, unless-- ``(A) the application of sewage sludge to the land terminated more than one year before the date on which the livestock began grazing on the land or the date on which the production of the animal feed on the land commenced; ``(B) the carcass, part thereof, meat or meat food product bears a label that clearly indicates that the livestock-- ``(i) grazed on land on which sewage sludge was applied; or ``(ii) consumed animal feed produced on land on which sewage sludge was applied; or ``(C) in the case of a carcass, part thereof, meat or meat food product generally offered for sale without labeling, a sign is posted within close proximity of the item to notify consumers that the livestock-- ``(i) grazed on land on which sewage sludge was applied; or ``(ii) consumed animal feed produced on land on which sewage sludge was applied.''; and (2) by adding at the end the following: ``(x) The term `sewage sludge' has the meaning given to such term in section 402(j)(2) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 342(j)(2)).''. (d) Adulterated Food Under Poultry Products Inspection Act.-- Section 4 of the Poultry Products Inspection Act (21 U.S.C. 453) is amended-- (1) in paragraph (g)-- (A) by striking ``or'' at the end of subparagraph (7); (B) by striking the period at the end of subparagraph (8) and inserting ``; or''; and (C) by adding at the end the following: ``(9) effective one year after the date of the enactment of the Sewage Sludge in Food Production Consumer Notification Act, if it is derived from poultry that were raised, or that consumed animal feed produced, on land on which sewage sludge was applied, unless-- ``(A) the application of sewage sludge to the land terminated more than one year before the date on which the poultry began to be raised on the land or the date on which the production of the animal feed on the land commenced; ``(B) the poultry product bears a label that clearly indicates that the poultry contained in the product-- ``(i) were raised on land on which sewage sludge was applied; or ``(ii) consumed animal feed produced on land on which sewage sludge was applied; or ``(C) in the case of a poultry product generally offered for sale without labeling, a sign is posted within close proximity of the item to notify consumers that the poultry contained in the product-- ``(i) were raised on land on which sewage sludge was applied; or ``(ii) consumed animal feed produced on land on which sewage sludge was applied.''; and (2) by adding at the end the following: ``(cc) The term `sewage sludge' has the meaning given to such term in section 402(j)(2) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 342(j)(2)).''. (e) Relation to National Organic Program.-- (1) In general.--Nothing in this section or the amendments made by this section shall be construed to modify the prohibition contained in part 205 of title 7, Code of Federal Regulations, on the use of sewage sludge, including ash, grit, or screenings from the production of sewage sludge, in organic food production under the National Organic Program of the Department of Agriculture. (2) Definition.--In this subsection, the term ``sewage sludge'' has the meaning given to such term in section 503.9(w) of title 40, Code of Federal Regulations (or any successor regulations), except that such term includes ash generated during the firing of sewage sludge in a sewage sludge incinerator or grit and screenings generated during preliminary treatment of domestic sewage in a treatment works.

Sewage Sludge in Food Production Consumer Notification Act This bill amends the Federal Food, Drug, and Cosmetic Act, the Egg Products Inspection Act, the Federal Meat Inspection Act, and the Poultry Products Inspection Act to require consumers to be notified regarding food produced from crops, poultry, or livestock on land in which sewage sludge was applied. Sewage sludge is solid, semi-solid, or liquid residue generated during the treatment of domestic sewage in a treatment works. Under the bill, if consumers are not notified regarding food produced on land on which sewage sludge was applied, the food is considered adulterated food subject to Food and Drug Administration or Department of Agriculture recalls.

the presence and severity of coronary artery calcification ( cac ) is a predictor of an increased probability of serious clinical cardiac events including death [ 14 ] . chronic kidney disease is associated with increased cac , and in general the more advanced the stage of kidney disease , the greater is the amount of cac [ 59 ] . the possible causal linkage between end - stage kidney diseases producing cac that in turn accelerates coronary atherosclerotic events has focused attention on the pathophysiology of cac in end stage renal disease with the objective of determining steps in the process that might be amenable to a suitable intervention to reduce the high mortality seen in patient with chronic kidney disease . while the precise mechanisms producing vascular calcification are still being elucidated , investigators contend that the processes likely involve calcium and phosphorus metabolic dysfunction , changes of vascular cells , especially vascular smooth cells ( vsmc ) , into an osteoblastic phenotype and an imbalance between procalcification and anti - calcification factors . vascular calcification in chronic kidney disease vessels is also strongly associated with vascular smooth muscle cell death resulting from calcium- and phosphate - induced apoptosis [ 11 , 12 ] . vascular calcification induced in aortas cultured in a high phosphate medium occurs concomitantly with cell death of vsmc via apoptosis . calcification can be initiated by the release of membrane - bound matrix vesicles from living vsmc and also by the release of apoptotic bodies from dying cells . vesicles released by vsmc after prolonged exposure to calcium and phosphate not only accelerate vascular calcification but also contain preformed calcium phosphate complexes . hypertension is an important risk factor for cac . indeed , some data suggest that the presence of hypertension is the most important determinant of cac in patients with chronic kidney disease ( ckd ) . the association between lower egfr and higher prevalence of cac in the framingham study was attenuated and of less statistical significance after multivariable adjustment for risk factors including hypertension . amongst the 6749 participants of the multiethnic study of atherosclerosis , hypertension was a major factor accounting for the association of decrements of kidney function and cac after adjustment for age , gender , and race / ethnicity . in a multivariate analysis of patients with ckd , after considering many factors , the severity of hypertension , reflected by the number of antihypertensive drugs taken to control hypertension , was significantly associated with cac with an odds ratio of 2.4 compared to patient 's age that had an odds ratio of 1.1 . two factors that have been implicated in the pathogenesis of hypertension are the angiotensin and endothelin family of peptides . endothelin , an even more potent vasoconstrictor peptide , is released from endothelial as well as other cell types . this paper examines the effect of angiotensin ii ( ang ii ) and endothelin 1 ( et-1 ) on vascular calcification focusing on differences in putative pathways leading to vascular calcification . despite similar effects on blood pressure , cac in chronic kidney disease ( ckd ) has been strongly linked to the hyperphosphatemia in severe ckd [ 1720 ] . predictors of cac are higher serum phosphorus levels , lower egfr levels , and traditional cvd risk factors . each 1-mg / dl increase in serum phosphorus increases the odds ratios for cac by 1.5 ( prevalence ) or 1.6 ( incidence ) . the reduction in cac found in some dialysis patients who received renal transplantation correlated with a decrease in calcium x phosphate product , in the early period after renal transplantation . these data support the contention that increased phosphate transport into vsmc may initiate the process of vascular calcification . vsmc express both high affinity na - dependent and na - independent components of pi transport with similar kinetic behavior . the na - coupled saturable uptake has been explained by the expression of two type iii sodium - dependent phosphate cotransporter proteins , pit1 and pit2 . phosphate uptake into the aorta through pit-1 can lead to vsmc calcification by induction of apoptosis or by phosphate - induced phenotypic changes in vsmc to a cell with the capacity to produce calcification . the influx of phosphate through capillary membranes is mediated by a saturable high - affinity system which is independent of sodium , but presumably , it is cellular phosphate concentration rather than the transporter that regulates cellular calcification . ang ii produces a concentration - dependent reduction in cellular phosphate transport ( figure 2 ) . in some tissues such as isolated bovine capillaries , however , ang ii does not affect phosphate transport suggesting that the effect of ang ii impacts the type iii sodium - dependent phosphate cotransporter . in contrast to ang ii , et-1 has been consistently demonstrated to increase cellular phosphate transport . this has been demonstrated in capillaries , brush border membrane vesicles and mouse calvaria - derived osteoblast - like mc3t3-e1 cells . in mc3t3-e1 osteoblast - like cells , et-1 stimulates sodium - dependent phosphate transport . et1-induced stimulation of pi transport is mediated by pkc activation through both phosphoinositide and phosphatidylcholine hydrolyses . considering the kinetics of phosphate transport , et-1 produces a 42 to 73% increase in vmax , depending on tissue or cell type , in contrast to the 38% reduction in vmax observed in response to ang ii ( figure 3 ) [ 26 , 2830 ] . et-1 may induce vascular calcification through its potential to induce vsmc apoptosis [ 31 , 32 ] . vsmc apoptosis that occurs with increased arterial loading is further accentuated in the presence of et-1 [ 31 , 32 ] . increases in arterial loading conditions increase endothelial prepro - et-1 and vsmc endothelin b receptor expression suggesting that the effects of et-1 on the vasculature can be induced from blood pressure elevation regardless of its cause . the role of ang ii to mediate cell apoptosis is less clear [ 33 , 34 ] . endothelin content and endothelin mrna were increased in the model of vascular calcification in which vsmc are treated with beta - glycerophosphate . in the in vivo model of vascular calcification induced by vitamin d(3 ) plus nicotine , endothelin levels in plasma and aorta as well as et 1-a receptor antagonists significantly regress the vascular calcification that is produced in the warfarin plus vitamin k model of vascular calcification . the ability of an et-1 a receptor antagonist to prevent vascular calcification was much greater than the angiotensin receptor blocker although both agents reduced blood pressure . ang ii increased mgp mrna levels by 20% in neonatal rat cardiac myocytes and 40% in cardiac fibroblasts . in contrast , et-1 decreased mgp mrna levels 30% in myocytes and had no effect in fibroblasts . opg inhibits advanced atherosclerotic plaque progression by preventing an increase in lesion size and lesion calcification . in human aortic smooth muscle cells , a 3-fold increase in suprarenal aortic concentration of opg was observed after chronic ang ii administration in apoe(/ ) mice . opg secreted by explants of vascular tissue from human endarterectomy samples was significantly reduced within 48 hours of incubation with the ang ii receptor blocker irbesartan . fetuin - a inhibits pathologic calcification in both soft tissue and vasculature , even in the setting of atherosclerosis . fetuin uptake and secretion by proliferating and differentiating cells in the arterial wall is a protective mechanism against arterial calcification . circulating fetuin - a concentration decreases in parallel with decline in renal function . during predialysis stage of diabetic nephropathy , there is a direct relationship between serum fetuin - a levels and cac score . the combination of fetuin - a deficiency , high - phosphate diet and ckd in apoe - deficient mice greatly enhances calcification . thus factors that increase phosphate transport into the cell would be expected to enhance vascular calcification in the presence of low fetuin - a levels . multiple regression analysis showed that fetuin - a was significantly inversely associated with et-1 and the relationship was independent of estimated glomerular filtration rate , sex , parathyroid hormone , and the calcium x phosphorus product . the negative correlation of coronary artery calcification scores with serum fetuin - a levels coupled with the inverse relationship between fetuin - a and et-1 suggests that fetuin and et-1 have opposite actions leading to cac . although the role of bone morphogenic protein ( bmp-2 ) in vascular calcification is still being elucidated , there are data that bmp-2 induces osteoblastic differentiation of vsmc through induction of msx-2 or by inducing apoptosis of vsmc . bmp-2 effects may be related to the loss of regulation of the matrix gla protein . in addition , bmp-2 induces runx2 and inhibits sm22 expression , indicating that it promotes osteogenic phenotype transition in these cells . inhibition of phosphate uptake abrogated bmp-2-induced calcification suggesting that phosphate transport via pit-1 is crucial in bmp-2 regulation of vsmc . in the mouse osteoblast - like cell line mc3t3-e1 , the ability of et-1 to induce mitosis and mitogen - activated protein kinase phosphorylation in vsmc were significantly increased in the presence of bmp-2 . in vivo studies showed that tissue calcium content was significantly higher in the group that received both bmp-2 and et-1 than in the group receiving bmp-2 alone . osteopontin ( opn ) , a low - affinity , high - capacity calcium - binding phosphoproteins , colocalizes with dystrophic arterial calcification . in human coronary artery segments , obtained at autopsy , there were high amounts of opn in the outer margins of all diseased segments at each calcification front . et-1 consistently induces opn in a number of different cell types [ 5255 ] . et-1 enhances opn as well as various other factors that induce bone formation such as osteocalcin and bone sialoprotein . et-1 enhanced by approximately twofold the mrna expression of both osteopontin and osteocalcin genes in rat osteoblastic osteosarcoma ros17/2.8 cells . et-1 modulation of the expression of these two gene products of osteoblasts suggests that et-1 plays a role in the regulation of bone metabolism . the effect of angii on opn is mediated by signaling cascades involving g(q/11 ) , the ras - erk axis , p42/44 mapk , and the src kinase family and by the transcription factor , ets-1 [ 57 , 58 ] . the putative effects of ang ii and et-1 on vascular calcification are consistent with their effects on bone formation . et-1 promotes both osteoblastic proliferation and differentiation leading to the formation of bone nodules in osteoblastic progenitor cells . et-1 modulation of the expression of the two phenotype - related gene products of osteoblasts suggests that et-1 modulates osteoblastic functions and plays a role in the regulation of bone metabolism . et may decrease the expression of mrna for osteocalcin , which is a marker protein for the maturation of osteoblastic cells and inhibit the mineralization of osteoblastic cells in vitro under some circumstances . ang ii decreased alkaline phosphatase activity in bone cell populations derived from the periosteum of fetal rat calvariae consistent with reduction in bone formation . ang ii stimulated bone resorption in cocultures of osteoclasts with osteoblastic cells . in bone marrow - derived mononuclear cells , ang ii significantly increased osteoclasts via rankl induction . in a rat ovariectomy model of estrogen deficiency , administration of ang ii accelerated the decrease in bone density and ang ii receptor antagonism attenuated the decrease in bone density . these data strongly point to a role for ang ii as factor that reduces the amount of bone mineralization . in summary , the link between hypertension and coronary artery calcification can be related to an action of the vasoconstrictor peptide et-1 on several processes that have been implicated in the pathogenesis of coronary artery calcification . the ability of et1 to consistently increase phosphate transport into the cell suggests that in conditions of hyperphosphatemia , that may occurs in end - stage chronic kidney disease , there is a heightened entry of phosphate into vascular smooth muscle . an increase in cellular phosphate can increase cellular calcification through at least three different mechanisms an increase in calcium x phosphate product transformation of vsmc to a bone - producing cell phenotype or cell apoptosis that releases procalcific substances . et-1 affects other modulators of calcification in a manner that tips the balance in favor of calcification , namely , inhibiting the inhibitors of calcification , matrix gla as well as osteoprotegerin and perhaps fetuin while enhancing the effects of procalcific factors such as bmp-2 and osteopontin . in contrast , another vasoconstrictor peptide operative in hypertension , angiotensin ii , is highly unlikely to be responsible for coronary artery calcification . ang ii inhibits cellular phosphate transport , and increases the presence of inhibitors of calcification , matrix gla protein and osteoprotegerin .

to understand the relationship between putative neurohormonal factors operative in hypertension and coronary artery calcification ( cac ) , the relevant cellular actions of angiotensin ( ang ii ) and endothelin-1 ( et-1 ) are reviewed . there is compelling evidence to implicate et-1 in cac . et-1 increases phosphate transport with a 42 to 73% increase in vmax . increased cellular phosphate may induce cac through increased ca x phosphate product , transformation of vascular smooth muscle cells into a bone - producing phenotype or cell apoptosis that releases procalcific substances . et-1 is increased in several models of vascular calcification . et-1 inhibits inhibitors of calcification , matrix gla and osteoprotegerin , while enhancing pro - calcific factors such as bmp-2 and osteopontin . in contrast , ang ii inhibits phosphate transport decreasing vmax by 38% and increases matrix gla . ang ii also stimulates bone resorption . vascular calcification is reduced by et-1 a receptor antagonists and to a greater extent than angiotensin receptor blockade although both agents reduce blood pressure .

aortocaval fistula ( acp ) is a rare , life - threatening condition with complicated clinical symptoms and findings requiring urgent diagnosis . of the acp cases , 80% occur due to erosion or rupture of the abdominal aorta into inferior vena cava ( ivc ) . they can present as pseudoaneurysm , occlusion of the visceral aortic branches , or arteriovenous fistula . hemodynamic effects of acp when combined with patient age and other comorbidities impose a life - threatening condition for many patients . open surgery is the conventional method of repair in these cases ; however , surgical complication risk rates are very high . we are reporting a late diagnosed acp case that presented with late onset right heart failure and pulmonary hypertension that had developed due to penetrating abdominal trauma . a 50-year - old male presented to the cardiology department due to edema of the legs , erythema , pain , abdominal swelling , and was hospitalized with pulmonary hypertension , right heart failure , atrial fibrillation , chronic obstructive pulmonary disease , and cellulitis . the patient had a history of appendectomy when he was 20 years old and had been stabbed in the abdomen when he was 35 years old . he had been stabbed twice , and 1 h after the stabbing , he had been successfully treated by general surgery . five years earlier , the patient ( age 45 years ) had presented to the cardiology outpatient service and was diagnosed with new york heart association ( nyha ) class ii shortness of breath . on echocardiography ( echo ) , his right heart cavity dimensions were mildly increased and pulmonary artery systolic pressure was found to be 45 mmhg . after treatment , his complaints regressed completely . three years earlier ( age 47 years ) , he had been admitted to the pulmonology department with abdominal and bilateral leg swelling , and shortness of breath ( nyha class iii ) complaints . but dilated ivc was missed or might have been accepted as secondary dilatation to pulmonary hypertension and right heart failure . his echo findings at that period of time were as follows : left ventricular ejection fraction 65% , grade i diastolic dysfunction , normal left heart cavities , significantly enlarged right heart cavities , pulmonary artery systolic pressure 70 mmhg , and grade 23 tricuspid failure . one year earlier ( age 49 years ) , he had been admitted to the pulmonology department due to newly developed high ventricular rate atrial fibrillation ( 168 bpm ) resulting in significant abdominal ascites , diffuse edema of the lower extremities , and crackles in the middle and lower lung zones ( nyha functional class iv ) . at that period of time , the echo had shown normal left heart cavity dimensions , left ventricular ejection fraction 50% , paradoxical interventricular septal motion , significantly enlarged right heart cavities , pulmonary artery systolic pressure 95 mmhg , and grade 3 tricuspid insufficiency . the patient was started on digoxin 1 1 tb , diltiazem 2 120 mg , and warfarin by the cardiologist . in 1 week , his symptoms regressed to nyha class iii and he was discharged from the hospital . fifteen days later , the patient was admitted to emergency department with symptoms of worsening right heart failure and shortness of breath ; therefore , he was moved to the cardiology department and started on intravenous furosemide , spironolactone 25 mg , clexane 2 0.6 cc ( because of subtherapeutic international normalized ratio ) , and continued on diltiazem and digoxin . according to the dermatologist 's recommendation , he was also started on ampicillin / sulbactam 4 1 g iv . laboratory findings were as follows : blood urea nitrogen 60 mg / dl ( normal range 722 mg / dl ) , creatinine 1.2 mg / dl ( normal range 0.81.3 mg / dl ) , aspartate aminotransferase 40 u / l ( normal range 035 u / l ) , alanine aminotransferase 45 u / l ( normal range 0 35 u / l ) , hemoglobin 12.8 g / dl ( 14.017.4 g / dl ) , white blood cells 14,500/l ( normal range 3,50010,500 l ) . on the second day of admission , cardiopulmonary resuscitation ( cpr ) was initiated , the patient was intubated , and on the 5 minute of cpr , he gained basal rhythm of atrial fibrillation and a blood pressure of 100/60 mmhg . the patient was then transferred to the intensive care unit and placed on a mechanic ventilator . with an initial diagnosis of pulmonary embolism , deep vein thrombosis ( dvt ) protocol ct was not performed . only thorax ct angiography and lower extremity venous doppler ultrasonography the ivc diameter was found to be 19 cm . on cardiologic evaluation , at the tricuspid focus , on the left and right corners , a harsh pansystolic murmur at 45/6 intensity was heard . the liver was palpable 78 cm under the costal arch , and diffuse ascites was detected in the abdomen . on the umbilical region of the abdomen , a continuous thrill and a machine - like murmur were detected [ figure 1 ] . on echo , right cardiac cavities were severely enlarged , and 34 degree of tricuspid failure , pulmonary artery pressure of 7580 mmhg , and normal left heart cavities were detected . on the region of abdominal murmur , the echo probe showed fistula between the abdominal aorta and the ivc on transverse plane [ figure 2a and b ] . ct angiography was performed in order to confirm the acp and to determine its dimensions . right at the lower level of renal artery and bifurcation of the aorta , between ivc and abdominal aorta , a fistula was detected . at the localization of fistula on the lower level of the renal artery [ figure 3a ] , the diameter of the aorta was 22 mm , ivc diameter was 99 mm , and the diameter of the fistula tract was 11 mm . at the localization of fistula on the abdominal aortic bifurcation [ figure 3b ] , the aortic diameter was 25 mm , ivc diameter was 169 mm , and fistula tract diameter was 17 mm . , findings consistent with ct angiography ( two fistulas from the abdominal aorta to the ivc ) were found [ figure 4 ] . oxymetrically calculated left - to - right shunt was 2.8 . on coronary angiography , the coronary arteries were normal and systolic pulmonary artery pressure was 75 mmhg [ figure 5 ] . the patient 's condition was hemodynamically stabile ; however , considering the possible complications , the acp was decided to be closed percutaneously . the procedure was to be performed after the pneumonia secondary to intubation had resolved . despite the antibiotic therapy , 50-year - old male presented with edema of legs , erythema , pain , and abdominal swelling and was later diagnosed with chronic aortocaval fistula . abdominal photograph of patient shows a continuous thrill ( star ) , and a machine - like murmur was detected on the umbilical region of the abdomen . 50-year - old male presented with edema of legs , erythema , pain , and abdominal swelling and was later diagnosed with chronic aortocaval fistula . transesophageal echocardiography ( a ) on transverse plane , ( b ) on the region of abdominal murmur , show fistula between the abdominal aorta and the ivc . 50-year - old male presented with edema of legs , erythema , pain , and abdominal swelling and was later diagnosed with chronic aortocaval fistula . axial contrast - enhanced ct angiography , ( 120/350 cc contrast medium , injection rate 4 cc / sec , scan time 30 . sec ) shows fistula ( black arrow ) at the lower level of renal artery and the bifurcation of the aorta between the abdominal aorta ( yellow arrow ) and the ivc . ( b ) axial contrast - enhanced ct angiography , showed fistula ( black arrow ) at the at the abdominal aortic bifurcation , between the abdominal aorta ( yellow arrow ) and the ivc . 50-year - old male presented with edema of legs , erythema , pain , and abdominal swelling and was later diagnosed with chronic aortocaval fistula . abdominal aortography shows two fistulas ( stars ) between the abdominal aorta and the ivc . 50-year - old male presented with edema of legs , erythema , pain , and abdominal swelling later diagnosed with chronic aortocaval fistula . they may occur as a result of infrarenal abdominal aortic aneurysm erosion or rupturing of the aneurysm into the vena cava inferior . very rarely , the aneurysm may fistulize to the left renal vein . in these cases , the most common cause of acps are penetrating firearm ( piece , fragment ) or stabbing ( knife , skewer ) injuries . iatrogenic injuries during arterial and cardiac catheterizations or during lumbal disc surgeries , and blunt traumas are rarer etiologic factors . most of the patients die at the place of injury or are rushed into the emergency department in serious hypotensive shock accompanied by other injuries . the mortality rate in this group of patients is 4050% . in chronic conditions , however , the presence of acp is detected weeks , months , or years after the injury . , chronic acp may be asymptomatic or at the side of injury , it may show signs of a consistent thrill , pain , peripheral edema , arterial insufficiency , and congestive heart failure . factors determining the severity of compensatory changes are the dimension of the fistula , the diameter of the involved artery or vein , patient 's age , and proximity to the heart . these patients adapt to the hemodynamic changes caused by acps easier as they rarely have cardiac problems . clinical symptoms vary according to the diameter of the fistula , anatomical position ( proximal or distal ) , and time of occurence ( acute or chronic ) . large arteriovenous fistulas have common symptoms and signs such as high - output heart failure , abdominal thrill , hypotensive shock , oliguria , regional venous hypertension , and stasis ( leg edema , hematuria , rectal bleed ) . most common symptoms and findings in chronic acps are high - output cardiac failure ( dyspnea , elevated jugular venous pressure , pulmonary edema , wide pulse pressure ) , abdominal thrill , palpable abdominal aneurysm ( if related to aneurysm ) , oliguria , and regional hypertension findings ( edema of the legs , cyanosis , pulsatile varicose veins , hematuria , rectal bleed ) . shock , abdominal pain , chest pain , lower back pain , scrotal edema , tenesmus , priapism , and weak peripheral pulse are the other symptoms and signs encountered . acp may be closed with conventional open surgery . however , mortality rate in this procedure is 67% , which is very high . massive intraoperative hemorrhages related to enlarged retroperitoneal veins are inevitable , particularly in chronic fistulas due to arterialization of the veins . increased hemorrhage risk may be seen during large arteriovenous fistula repairs due to arterialization of the veins and perivascular inflammation . furthermore , reccurent paradoxal pulmonary embolisms and cardiac decompensation are the other complications encountered . in 1999 , parodini et al . , performed the first endovascular repair of chronic acp . not requiring laparotomy , lower loss of blood , use of local anesthetics instead of general anesthesia , lower related post - operative complications , and reduced costs have made endovascular stent graft procedure more attractive than open surgery . coated stents , abdominal aortic endografts , coil embolization , and patent ductus arteriosus device are the endovascular techniques invented until now . the use of aortic stent grafting has benefits such as faster cardiopulmonary recovery and reduced blood loss . considering the cardiopulmonary condition of the patient presented in the report , the acp was decided to be closed using thoracic graft stent due to the high surgical risks involved . however , given the risk of possibly developing infective endocarditis from the graft , priority had been given to his recovery from pneumonia . despite intensive antibiotic therapy , the pneumonia did not resolve , and the patient developed ards and sepsis , and succumbed due to multiorgan failure . it is clear that if the acp had been detected 5 years earlier during early symptoms , the benefits of endovascular or surgical procedure would have been very high . it should also be considered that in early phase where ivc is not significantly enlarged , and pulmonary hypertension and right heart failure have not developed , interventions would carry much lesser amount of complication risk . thrombotic complications may also be seen as a result of endovascular treatment , causing life - threatening situations and clinical emergencies . acute ivc occlusion ( highly decreased blood flow in highly enlarged ivc due to stasis ) , persistent severe lowere extremity edema , and continuous worsening of the clinical condition are some of these complications . in such cases , compression of the ivc by the aortic aneurysm sack may result in intraluminal thrombus formation . paradoxic pulmonary embolism is one of the reported complications that may occur before , during , or after the treatment . compared to open surgery , endovascular treatment has lower operative and 30-day mortality rates and overall low morbidity rates . early diagnosis and intervention before cardiopulmonary deterioration is important and life saving in these patients .

chronic aortocaval fistula ( acp ) is a rare complication of penetrating trauma to the abdomen . we report a case of traumatic acp presenting with pulmonary hypertension and right heart failure symptoms 15 years after the initial penetrating injury . although symptoms of pulmonary hypertension started 5 years ago , it was wrongly diagnosed and treated as chronic obstructive pulmonary disease . the presence of a continuous abdominal bruit and history of penetrating abdominal trauma gave rise to suspicion of a fistula , which was confirmed by computed tomography and angiography . percutaneous closure of acp was planned , but the patient died of severe pneumonia . the clinical presentation of chronic acp can vary from being asymptomatic to symptoms related to pulmonary hypertension , right heart failure , and pulmonary embolism ; thus , definitive diagnosis can be challenging .

cancer is the leading cause of morbidity and mortality worldwide with 14 million new cases and 8 million cancer - related deaths in 2012.1 furthermore , the international agency for research on cancer estimates the number of new cases to rise by 75% over the next two decades . more than 50% of people diagnosed with cancer will experience physical pain and of those people , more than one - third will experience moderate - to - severe pain levels.2,3 the estimated increase in the incidence and prevalence of cancer supports the prediction of an increase in the number of people with pain caused by the disease and its treatment . historically , the continued prevalence and extreme intensity of cancer pain experienced by patients have been documented via numerous international epidemiologic studies . more than 40 years ago , marks and sachar4 found that 75% of patients experienced cancer pain in spite of analgesics ordered by health care providers . inadequate cancer pain relief was reconfirmed in later studies.58 after recognition of an international problem , the world health organization ( who ) responded by the wide distribution of the who cancer pain relief guidelines in 1986,9 herein , referred to as the who guidelines , and subsequently updated the guidelines a decade later.10 the main element of the who guidelines established medical management of cancer pain with a three - step ladder ( figure 1 ) . the purpose of the ladder was to make pain relief available readily to patients with cancer with advanced disease by using effective and inexpensive drugs administered regularly , orally , and on an individual basis while also focusing on safety.11 in addition , the who guidelines were to facilitate and legitimize the use of strong opioids ( ie , morphine and its derivatives ) in regions of the world where the use of these medications was unacceptable or illegal.11,12 despite multiple translations and broad distribution of the who cancer pain relief guidelines , inadequate pain relief still exists.1316 the effectiveness of these guidelines needs to be evaluated to determine the underlying reason for the continuation of inadequate pain management despite medical advances in the past 28 years . the purpose of this paper is to disseminate the results of a comprehensive , integrative review of studies that evaluate the effectiveness of the who guidelines . a key consideration in the evaluation of these studies is to differentiate between those individuals for whom the guidelines are effective and those for whom they are not . two previous reviews of the effectiveness of the who guidelines were found in the literature.17,18 jadad and browman17 identified eight studies for review in 1995 and ferreira et al18 identified 17 studies in 2006 . there were no randomized clinical trials in the reviews that could provide unbiased estimates of the proportion of patients for whom the who guidelines would be efficacious . indirect measures of effectiveness of pain treatment , however , ranged from 45% to 100% within the two reviews . multiple limitations were identified across the reviews , including small sample sizes , variable or short follow - up periods , and high exclusion or dropout rates . jadad and browman17 also concluded that there was a lack of homogeneous criteria across studies to assess pain and treatment outcomes to compare effectiveness of the who guidelines efficiently and accurately . ferreira et al18 discussed that complete relief of pain is rarely achieved in patients with cancer experiencing cancer pain , but pain intensity or duration can be reduced while using the who guidelines . effectiveness of the who guidelines was recognized , but the extent and predictability of the effectiveness across studies were being questioned.17 this current paper expands what has previously been reviewed evaluating the who guidelines . in addition to critiquing previously published work for effectiveness of the guidelines , this review encompasses other pain measurement scales . this review categorizes adequate treatment effectiveness as the pain intensity being 1 ) less than moderate ; 2 ) a visual analog scale ( vas ) , numerical rating scale ( nrs ) , and verbal rating scale ( vrs ) score 3 on a 010 scale ( or 30 on a 0100 point scale ) ; or 3 ) a decrease in the pain intensity on the vas , nrs , or vrs by 70% or more ; a decrease in the integrated pain score ( ips ) by 70% or more ; or an increase in pain relief by 70% or more . the present paper includes studies that were not evaluated by the previous reviews and includes studies that were published in the past decade . the present study included searching more resources than databases and a manual search of reference lists . this review includes health professional literature published within a 28-year period between 1987 and may 2015 . the timeline reflects the period that began immediately following release of the first guidelines from the who in 1986 . a comprehensive computer search was conducted using cumulative index of nursing and allied health literature ( cinahl ) , medline , proquest , and pubmed . medical subject headings ( mesh ) and text words ( txt ) used in the search included pain [ mesh and text ] and cancer [ txt ] or neoplasms [ mesh ] in combination within the full text : relief [ txt ] , control [ txt ] , prevalence [ mesh and txt ] , intensity [ txt ] , intractable [ txt ] , management [ txt ] , under - medication [ txt ] , palliative care [ mesh and txt ] , analgesia [ mesh and txt ] , analgesic ladder [ txt ] , symptom [ txt ] , validation studies [ mesh ] , and world health organization [ mesh and txt ] . in addition , online indices of individual periodicals were searched using titles and abstracts that were established sources to publish reports of the evaluation of the who guidelines . these included pain , journal of pain and symptom management , cancer nursing , pain management nursing , and oncology nursing forum . the internet was searched using multiple search engines such as google and google scholar , yahoo , bing , webcrawler , and ask.com . multiple pain - related web pages were searched for abstracts and text related to the evaluation of who guidelines including , but not limited to , the who , international association for the study of pain ( iasp ) , american pain society ( aps ) , american society of pain management nurses ( aspmn ) , and the pain and policy studies group ( ppsg ) . finally , a comprehensive review of citations within included research studies were also searched for identification of further studies . research studies of any methodological design were included in this review if they : 1 ) specifically identified treatment of adult patients with cancer with the who guidelines , 2 ) evaluated patients self - reported cancer pain , 3 ) provided information on the instruments used to measure cancer pain relief , 4 ) provided data documenting changes in pain intensity via the vas , nrs , vrs , or ips after treatment or provided data documenting the proportion of patients experiencing adequate pain control / relief after treatment , and 5 ) were written in english . each eligible study available was reviewed and coded for the following information : author(s ) , publication year , title , source , study design , aims , sample population and size , dates of data collection , country of data collection , duration of treatment , definition of adequate pain relief , instruments used to measure pain , methodology , findings related to pain intensity or relief , and whether additional measures for pain control were used other than the who analgesic ladder . the samples of the studies were evaluated for size , randomization , and reasons for termination / exclusion from the study . the quality of the data was evaluated according to the aim(s ) of the study , whether data were collected prospectively or retrospectively from the medical record , and the length of the study follow - up periods . the methodology was evaluated by the description of the target population and setting , demographic data of the sample reported , and presence of a control group . cooper s guide for integrated literature reviews was used.19 quality appraisal was not completed for this review because of a lack of randomized control studies . however , the methodology , bias , and threats to internal and external validity are summarized in the results section . several studies shared the same population samples . according to petitti,20 failure to exclude studies analyzing for example , there were six studies using the same patient sample in germany;2126 only the latest and most inclusive study is included in the review.26 in order to ensure accuracy , communication with authors was completed . for example , according to mercandante , the samples of patients were not the same in studies published in 199227 and 1999.28 ten studies were removed from review due to overlap of population samples . several other studies were excluded as they evaluated the intensity / strength of the analgesic treatment of the patients reported pain using the pain management index ( pmi ) developed by cleeland et al.29 while the pmi is based on the who recommendations for cancer pain relief , the studies using the pmi did not specify whether or not the treatment administered to the patients was based on the who guidelines . without the use of the inclusion criteria language , from the original 48 studies identified , 25 studies fulfilled the inclusion criteria . in reviewing the 25 included studies , all of the studies used convenience samples , while only four of the convenience samples were randomized . the four studies that used randomized samples were for the purposes of evaluating the necessity of step 2 of the who analgesic ladder3032 ( figure 1 ) or the use of mild opiates.33 nineteen of the studies were prospective studies , including six quasiexperimental studies in which four used comparison groups . only two studies had a control group32,34 and one study was double - blind.35 because of the lack of control groups throughout all but two of the 25 studies , meta - analysis was not performed . table 1 chronologically summarizes the individual research studies that measure the effectiveness of the who guidelines . findings from the longitudinal studies were classified into five categories : 1 ) the percentage of patient responses that demonstrated a reduction in the ips , 2 ) the percentage of patient responses for whom the reduction in the vas or nrs was stated or could be calculated , 3 ) the percentage of patient responses that were within the categories created from scores on the vas or nrs that was considered as controlled pain or adequate pain relief , 4 ) the percentage of patient responses on the vrs of pain relief or the vrs of pain intensity that were considered as adequate pain relief , and 5 ) others that did not classify findings into the previous four categories . two studies used the ips.36,37 the ips was designed to take into account both pain intensity and duration when assessing patients pain . it is calculated by multiplying the hours of pain duration per day by the pain intensity using a 10-point vas , nrs , or points assigned to a vrs . thus , scoring of the ips has a range of 0240 possible points . in the first few days of treatment with the who guidelines , wenk et al36 found patients experienced a 70% reduction in the ips,36 while ventafridda et al34 found patients experienced a 57% reduction.34 progressive treatment led to an 81%69% reduction in pain scores , respectively . overall , the reduction in the ips after initiation of treatment ranged from 57% to 81% . several of the studies reviewed used patient responses on either a vas or nrs where the percentage of the pain reduction in the scores after initiation of treatment was stated or could be calculated.28,32,33,3845 an analysis of the study results at one interval of measurement ( 37 days after treatment was initiated ) demonstrated a 20%71% reduction in the vas or nrs from the baseline pain assessment . upon the final interval of measurement , there was a 43%81% reduction in the vas or nrs from the baseline pain assessment . the interval length varied among studies but was > 7 days after initiation of treatment . other studies reported the percentage of the categories considered as adequate pain relief or satisfactory pain intensity by dividing the patients responses for the vas , nrs , or vrs into categories . for example , the pain intensity measured by a vas ( 010 point ) might be divided into categories of none ( 0 points ) , mild likewise , on a four point vrs , the categories of none or mild might be considered as adequate pain relief . results from these studies were reported according to the percentage of patients in each category . mercadante et al27 used a vas and reported that 81% of the patients without incidental pain had no pain or mild pain at the time of their death , but only 50% of the patients who experienced incidental pain had no pain or mild pain at the time of their death . ventafridda et al34 using a vrs reported that 76% in their sample reported none or zech et al,26 in a validation study of the who guidelines using a vrs , reported that 72% of the patients had no pain or mild pain at the time of their death . tsui et al44 reported that 88% of their patients were discharged with a vas of 3 ( 010 scale ) , indicating that the patients experienced no pain or mild pain . bhatnagar et al46 reported that 87% and 90% of patients had good pain relief ( vas <3 ) at 1 month and 6 months , respectively . of the studies that reported the percentage of the categories considered as adequate pain relief or satisfactory pain intensity by dividing the patients responses for the vas , nrs , or vrs into categories , 50%90% of the patients experienced adequate pain relief . similar to other studies that categorized the degree of pain intensity , takeda47 categorized the degree of pain reduction of patients responses on the vas into three levels : complete relief ( no pain ) , acceptable relief ( > 90% relief of pain or reduction of the scores ) , and partial relief ( decrease in severity of pain , but a reduction of < 90% ) . at the end of an unknown duration of treatment , 97% of the sample reported complete ( 86% ) or acceptable ( 11% ) relief from pain . inclusion of the percentage of the categories considered as adequate pain relief determined by takeda47 into the range compiled from the other studies that reported the percentage of the categories considered as adequate pain relief ( none or unlike studies that reported the percentage of vas reduction of pain , minotti et al35 and keskinbora et al31 reported patients mean scores of pain intensity using the vas after treatment only . one of the inclusion criteria for the studies , however , was that patients scores of pain using the vas ( 0100 points ) were > 40 or the nrs > 4 ( 010 points ) . after 7 days of treatment , minotti et al35 reported that the mean of the patients scores using the vas was < 40 . keskinbora et al31 demonstrated graphically that the patients treated with an adjuvant in addition to an opioid experienced a mean pain of < 4 on days 4 and 13 after initiation of treatment with the who guidelines . the reduction in pain was statistically significant between patients who received an opioid and an adjuvant and those patients who received an opioid only for their cancer pain . the percentage of reduction in pain intensity was not provided and could not be calculated from information provided within the two studies . siguan et al48 used a pain reduction scale ( prs ) to survey the patients with cancer pain . with this scale , the respondents had the option of indicating whether they had 0% , 25% , 50% , 75% , or 100% pain relief . at the end of an unreported duration of treatment , 86% of respondents stated that they had at least a 75% pain reduction and 96% had at least a 50% pain reduction . similarly , vielvoye - kerkmeer et al49 had respondents rate the effectiveness of their treatment as poor , moderate , good , or excellent . in their study , 69%71% of patients rated their pain relief as good or zech et al,26 meuser et al,41 and maltoni et al30 used other methods of evaluating effectiveness of treatment with the who guidelines . in addition to reporting the patients mean pain scores of the vas or nsr at baseline and after treatment , the first two studies also categorized pain relief according to the number of days the patient experienced severe pain . thus , if the patient reported their average pain to be severe , very severe , or maximal on < 10% of days , treatment effectiveness was defined as good ; on 10%30% of days as satisfactory ; and on > 30% of days as inadequate . with these categories , meuser et al41 found 86% of the patients and zech et al26 found 88% of the patients experienced good or satisfactory pain relief effectiveness . a third study by maltoni et al30 described the percentage of days with worst pain that was $ 5 on the nrs ( 010 points ) . maltoni et al30 reported that on 9%29% of the days , patients experienced moderate - to - severe pain . using the criteria from zech et al26 and meuser et al,41 100% of the patients in the study by maltoni et al30 experienced the range of the pain relief effectiveness of the three studies ranged from 86% to 100% . in the reviewed studies , the overall effectiveness of the who cancer pain relief guidelines was found to range from 20% to 100% . the broad range of effectiveness is dependent upon many measurement factors , including the intensity of the pain , the pain instrument used , the duration of treatment , and the outcome variable of pain relief / control . the overall literature rating is suggestive of a relationship between the who guidelines and pain relief . evidence from research indicates 20%100% of patients with cancer pain considering their status of treatment or end - of - life care can be provided adequate pain relief with application of the who guidelines , with a majority of studies identifying relief > 50% . a reduction of 57%81% was reported using patient responses with the ips after treatment with the who guidelines . the nrs and vas were reportedly reduced in the range of 20%81% after treatment across levels of severity of pain . studies that placed patients responses into categories that described the pain intensity experienced reported that 50%90% of the patients experienced other studies reported that the mean intensity experienced by patients was < 4 or 40 ( depending on whether scale was based upon 010 points or 0100 points ) , indicating full effectiveness of the who guidelines . other studies reported that 69%86% of the patient responses indicated that patients experienced at least 75% pain relief or felt that their pain control was good or excellent effectiveness of the who guidelines was reported between 86% and 100% for patients who were experiencing severe , very severe , or maximal pain on 0%30% of the treatment days . this review demonstrated that pain could be reduced or eliminated in a great majority of the patients when they receive treatment based on the who guidelines . no other guidelines have had the profound effect on cancer pain as the who guidelines.12,50,51 because only one study met inclusion criteria after 2008 , it is questioned whether this finding indicates recognition of the who guidelines , and hence a decreased need for publications of their effectiveness or the acceptance of the treatment of cancer pain with opioids.32 the timeframe correlates with the publication of the european association for palliative care guidelines52,53 and the american pain society guidelines for cancer pain treatment.54,55 these agency guidelines have recognized the worldwide problem of cancer pain , combined with the increasing availability of different opioids , opioid preparations , and interventional procedures during the last 20 years . these agencies have tried to update the international guidelines on the management of cancer pain while focusing on the role of opioids . the who guidelines , though not as specific in direction , encompass a clear and simple approach that has an educational value and is easily remembered and disseminated . regardless of the age of the who guidelines , they still are the cornerstone for cancer pain treatment worldwide . unfortunately , many practitioners are not using the who guidelines and some do not know what the who guidelines entail.56,57 the clear message resonating from the effectiveness of the who guidelines is that they are an effective and cost - effective means to provide cancer pain relief . in the reviewed studies , it was not always specified whether the who analgesic ladder or the entire who guidelines were being investigated . the language regarding the usage of the ladder or the full guideline was often not stated . five studies treated patients with the ladder only or eliminated the study participants who underwent additional treatment that might affect pain perception . eleven of the reviewed studies included patients who were also being treated with antineoplastic treatment , intrathecal analgesics , neurolytic procedures , or surgical procedures , while others did not specify if the patients underwent additional treatment . as the who guidelines endorse the use of other treatment modalities than the analgesic ladder if needed , the guidelines should be investigated in its entirety . some experts suggest that the who analgesic ladder has a fourth and/or fifth step that may include a step for interventional procedures , including nerve blocks , neurolytic blocks , spinal stimulators , and epidurals11,12,58 or a step for opioid switching that includes both pain and side effects as criteria for switching analgesics.59 it can be argued that having the interventional nerve blocks at a later step implies they should be used last . evidence exists that the nerve blocks may be more effective if considered earlier.60,61 thus , like adjuvant analgesics , they may need to be considered at any step and so may need to be placed alongside the ladder rather than a separate step . summarization of the studies proved to be challenging due to different methods of measuring pain , variations in defining the acceptable levels of treatment effectiveness , and missing data . pain intensity was rated according to ips , vas , nrs , vrs , and prs . particularly , the use of the ips made it very difficult to compare pain treatment effectiveness between studies since a score of 20 may indicate a range of severe pain for 2 hours or mild pain for 20 hours . since duration and intensity were a combined score , this type of scoring made it unfeasible to compare the pain treatment effectiveness with other studies and to determine whether adequate treatment effectiveness was achieved . similarly , reporting pain relief according to the number of days the patient experienced severe or very severe pain made comparisons unrealistic . even the same type of scale may have had multiple interval labeling systems associated with them . the variability in the methods of measuring pain or pain treatment effectiveness made comparisons difficult . moreover , the studies reviewed categorized the results according to various operational definitions of adequate or inadequate pain treatment effectiveness . this review categorizes adequate treatment effectiveness as the pain intensity as being 1 ) less than moderate , 2 ) a vrs or nrs as 3 ( or 30 on a 0100 point scale ) , or 3 ) a decrease in the pain intensity / increase of pain relief by 70% or more . in addition , some data were not reported in the reviewed studies , which may have made comparisons easier . a more accurate comparison could have been made if data from all instruments had been discussed . for instance , in ventafridda et al,34 64% and 31% of the cases in the two groups investigated in the study had to be excluded from the study due to incomplete data collection , incomplete recording of patient assessment , or inappropriate timeliness in the follow - up . incomplete data collection also was problematic in other studies.36,42 given the population studied , some reasons for attrition were death,27,34,36,38,41,48,49 ineffective analgesia,35 intolerable side effects,35,48,49 as well as lost to follow - up,26,28,33,34,36,41,48 pain absence or resolution,33,41 low patient compliance,28,41 change of therapy,35 patient being treated by another practitioner or facility,28,41,48 discharged,36 financial constraints,48 physician error,48 and patient receiving other treatments.35,41 although it can be concluded that management of cancer pain as recommended by who is effective for a majority of patients , the research designs of the studies in the literature review were retrospective , descriptive , and/or quasiexperimental rather than randomized controlled trials ( rct ) . a relationship between these two factors is consistent with the knowledge generated in prior pain relief investigations , as it is a combination of pain management knowledge acquired through multiple sources that is being tested with the who guidelines . although the relationship between who guidelines and pain relief is plausible and likely , the predictive quality of experimental designs with rct is missing , and the subsequent ability to predict the effectiveness of the who guidelines through evidence - based certainty is lacking.11 additional methodological limitations other than design are noted . because of the population , most studies of oncology patients employ convenience samples , and thus , findings are not generalizable . for example , it is possible for patients with cancer who are hospitalized to more likely be experiencing severe pain than those who are not hospitalized . similarly , some studies included patients with severe pain only.27,30,31,49 achieving adequate pain relief may be more difficult in more severe cases . therefore , the studies measuring the effectiveness of the who guidelines in reducing the intensity of cancer pain in hospitalized patients or patients who are only experiencing severe pain can not be generalized to all patients with cancer . many of the samples were drawn from one institution in one country . sampling populations from one institution and generalizing the findings globally are inappropriate as several other factors such as availability of different opioids may affect the adequacy of pain relief . furthermore , many studies included only patients treated by cancer specialists ; patients treated by practitioners without oncology training may be more likely to experience inadequate pain relief . the convenience samples in these studies may produce different findings than a randomized sample from a large , international cancer pain patient population . in the reviewed studies , the sample sizes of persons with cancer pain vary , but many samples are small . the results from this limited sample size , especially with convenience sampling , may differ from the population . as with drawing from one - institution samples , the small samples may allow some variables to affect the results , such as the practitioner , local practices and beliefs , and economic or social influences . with small sample sizes , a few patients who improved dramatically while receiving care utilizing the who guidelines may alter the mean improvement of the group even if other patients perceived little or no benefit with treatment . small sample sizes , especially combined with convenience sampling , render widespread generalizations inappropriate . other methodological problems with measuring cancer pain can be revealed in this review . in longitudinal studies of cancer pain , maturation occurs over time as the disease progresses . it may be difficult to demonstrate an effect of an intervention to decrease incidence and intensity of pain as the pain changes with disease remission or progression . in addition , longitudinal data collection intervals varied greatly . the length of time between data point assessments following implementation of the who guidelines and the length of follow - up varied between having only one additional assessment at 1 week after treatment to recording data until death , which may entail follow - up for several months . testing effects may also be prominent , as many studies did not identify the ability of those who collected the data . overall , the multiple methodological problems identified potentially lead to less accuracy in the individual study results and makes comparisons between studies difficult . in reviewing the literature , several of the studies although complete relief is the goal of cancer pain management ; sometimes , it is not possible . an acceptable level of pain should be below moderate pain . with moderate or greater pain , there are often marked negative changes in physical or emotional functioning that interferes with the patient s quality of life.15,62,63 therefore , the delineation of adequate pain relief should be within the mild or no pain categories . in order to measure pain and compare results more consistently , a well - established difficulty is encountered when comparing various pain intensity measurements as it is unknown whether methods of measuring pain and reporting pain relief affect the results of studies . for example , a difference between an individual s responses on vrs may not correlate with responses on a pain relief scale . additional research also is needed to compare methods of reporting pain relief between those reported from pain intensity scales to pain relief scales . likewise , it is understandable that not only the intensity but also the duration of pain needs to be measured , but placing these two concepts in one index , such as done in the ips , may cause misinterpretation of the effects of the pain experience on the patient . perhaps , reporting the intensity and duration in addition to the ips might be more informative . the number of points on a vrs and the terms used on the scale need to be standardized so that findings between studies can be compared . the standardized vrs should then be correlated with the nrs so the findings with the two different types of scales can be compared more consistently . finally , in order to have more accurate results and be able to compare studies , the patient rather than medical personnel or family should complete the pain measurement instruments . standardization in pain management instrumentation and in its completion would allow more consistent measurement , reporting , and comparison between future studies . new studies using experimental designs with randomized control groups would support the strength of the relationship between the who guidelines and cancer pain relief . according to oxman et al,64 who recommendations are usually not based on systematic reviews of the literature but rely heavily on experts in a particular specialty such as cancer pain management . since the release of the who guidelines , a lack of rigor in studies , especially in methodological design , contributes to limitation in generalizability of the published results.11 debates regarding the effectiveness of the who guidelines remain due to the lack of rcts . although rcts demonstrating a relationship between the who guidelines and cancer pain relief are conspicuously absent , there were no evidence - based alternatives supported by rcts found in the literature that were superior to the who guidelines . the first debate about the effectiveness of the guidelines revolves around the utility of step 2 of the who ladder.11,65 proof of the effectiveness of weak opioids is lacking , especially since a limitation of using weak opioids is that there is a ceiling effect.11 a ceiling effect occurs when an increase in dose does not produce a decrease in pain . in an attempt to avoid using weak opioids , nunes et al32 found that a higher incidence of adverse effects occurred when the second step of the ladder was omitted and patients were administered morphine initially . thus , step 2 may still be warranted , and future research is needed to explore its value . a second debate of step 2 includes the role of nonsteroidal anti - inflammatory drugs.11 these medications may affect the gastrointestinal tract , platelets , and kidneys , resulting in negative side effects and possible toxicity . a third debate of step 2 is the lack of criteria for switching from morphine to another opioid , including equianalgesic dosing and the choice of the subsequent opioid to be used.11,66 a fourth debate is that there are multiple new medications and new formulations of older drugs that need to be investigated that considers their pharmacodynamic and pharmacokinetic properties in patients experiencing cancer pain . finally , adverse effects of these opioids need to be documented within the rcts that explore them . suggesting rigorous rcts challenges researchers , including the who , to optimize and improve the guidelines or develop alternatives to ensure the highest possible proportion of patients with cancer pain experience pain relief . nonetheless , the implementation of rct in studies of cancer pain management is not likely due to ethical and logistic reasons . first , to obtain accessibility to patients with cancer pain , convenience samples are often used . second , the ability to control for extraneous variables in studies among international health care practices makes coordination of standards difficult for group comparisons . third , a humane responsibility exists to provide optimal pain relief to all patients , and this renders a control group as being potentially ethically irresponsible . fourth , given the publication of the who guidelines , it is unlikely that the treatment of a potential control group would not be influenced by the broad dissemination of the guidelines that has already occurred . finally , experts in cancer pain management believe that the effort and expense of experimental studies with control groups is unwarranted.67,68 this is based on the strength of the fundamental knowledge underlying the guidelines and the acceptance of these principles . suggesting experimental designs with control groups is an ideal rather than a practical prospect in the actual environment of cancer pain management . rcts are needed , however , when the effect and differences are smaller such as when comparing various drugs or routes.67 comparison groups , gleaned from those treated in various environments , for example , where certain medications are not readily available , would allow for comparison of groups of patients with cancer . also , data from those treated in the past decade or earlier could be compared to those treated currently . cluster randomization is a possible alternative to overcome some of the challenges in getting rcts regarding cancer pain relief . a cluster randomized controlled trial ( crt ) is a type of rct where groups of subjects and not individuals are randomized . the units of randomization are varied and can be clinics or hospitals , among others . advantages include the ability to compare drugs head - to - head within the same class rather than with placebos.69 crt may relieve issues related to recruitment and self - selection and randomization of patients , thus allowing data collection and availability of results more quickly.69 the disadvantages to crts are the multitude of design choices and stratification of the groups.70 the need for informed consent may be averted if the drug studied is the preferred drug in the cluster formulary , and so , ethical requirements for crts may need to be analyzed and modified.69 several recent studies indicate inadequate cancer pain relief still exists , but these studies also fail to indicate if the who guidelines were being implemented during treatment.15 a review of studies by deandrea et al,71 that used the pmi , demonstrated that 43% of patients with cancer pain are undertreated . the pmi compares the intensity / strength of the analgesic treatment according to the who analgesic ladder with the patients reported pain . all studies demonstrated a negative pmi , indicating that the cancer pain is undertreated a majority of the time . deandrea et al71 identified factors associated with a negative pmi that included publication before 2001 ; studies conducted in europe or asia ; studies conducted in countries whose national income per capita was $ 40,000 per year or less ; and patients being cared for in a general setting rather than a cancer - specific setting . patients being treated by oncology subspecialists , however , have also been inadequately medicated for pain according to the who guidelines.15,45 therefore , the use of the who guidelines in oncology specialty areas and by the oncologists themselves can not be assumed . in future studies , the use of the who guidelines to treat patients with cancer with pain should be clearly stated , consistently applied , and then evaluated with the pmi . the results of the review by deandrea et al71 suggest that the question might be how the who analgesic ladder is put into practice rather than its effectiveness . other methodological considerations would be to increase the sample size , follow a longitudinal design , use multiple institutions / agencies , and use more institution / agencies from within the usa , all of which are lacking . the sample size for future studies evaluating the effectiveness of the who guidelines needs to be increased . five studies in this review had a sample size of < 50 subjects , and 13 additional studies had < 100 subjects . weekly , longitudinal studies until study withdrawal would provide additional data to evaluation the effectiveness of the who guidelines in continued relief of cancer pain upon progression of the disease . other cancer care centers need to be surveyed , especially in understudied countries . in the studies reviewed , for example the studies evaluating the effectiveness of the who guidelines provide valuable information on the course of cancer pain and its treatment . from these findings , it can be concluded that the who guidelines are useful in promoting cancer pain relief . evidence from research indicates at least 20%100% of patients with cancer pain can be provided adequate pain relief across the span of their illness , from treatment- to - demise , with the application of who guidelines . recent studies have reported that patients experiencing cancer pain at moderate or greater levels.2,3 while comparing the results of the recent studies describing the incidence and intensity of cancer pain , it can be assumed that the who guidelines have not been as widely adopted as would be expected since their initial release in 1986 . the who guidelines reflect the knowledge and effectual methods to relieve most cancer pain , but the guidelines are not being adequately employed . part of the explanation for the lack of adoption of the who guidelines is that they may be considered outdated by many because they are not specific to the pharmacological and interventional options used in contemporary pain management practices . the greatest attribute of the who guidelines is its simplicity , whereas , a thorough cancer pain guideline results in a complex document that might not be as useful and easy to disseminate . the conundrum of updating the who guidelines is to encompass the latest pharmacologic and interventional innovations while maintaining its original simplicity . at the same time , the patients who have not had their cancer pain adequately relieved , even when the who guidelines have been employed , need further consideration in future research . the who guidelines have been successful in making pain relief knowledge more globally available , but from a moral and ethical standpoint , these guidelines need to be promoted and examined until adequate pain relief is reported in all possible patients with cancer pain .

inadequate cancer pain relief has been documented extensively across historical records . in response , in 1986 , the world health organization ( who ) developed guidelines for cancer pain treatment . the purpose of this paper is to disseminate the results of a comprehensive , integrative review of studies that evaluate the effectiveness of the who guidelines . studies were included if they : 1 ) identified patients treated with the guidelines , 2 ) evaluated self - reported pain , 3 ) identified instruments used , 4 ) provided data documenting pain relief , and 5 ) were written in english . studies were coded for duration of treatment , definition of pain relief , instruments used , findings related to pain intensity or relief , and whether measures were used other than the who analgesic ladder . twenty - five studies published since 1987 met the inclusion criteria . evidence indicates 20%100% of patients with cancer pain can be provided pain relief with the use of the who guidelines while considering their status of treatment or end - of - life care . due to multiple limitations in included studies , analysis was limited to descriptions . future research to examine the effectiveness of the who guidelines needs to consider recommendations to facilitate study comparisons by standardizing outcome measures . recent studies have reported that patients with cancer experience pain at moderate or greater levels . the who guidelines reflect the knowledge and effectual methods to relieve most cancer pain , but the guidelines are not being adequately employed . part of the explanation for the lack of adoption of the who guidelines is that they may be considered outdated by many because they are not specific to the pharmacological and interventional options used in contemporary pain management practices . the conundrum of updating the who guidelines is to encompass the latest pharmacological and interventional innovations while maintaining its original simplicity .

in this paper , we study site percolation on the triangular planar lattice . recall that this can be viewed as a random coloring of the hexagonal cells of a honeycomb lattice , where the color ( black or white ) of each cell is chosen independently of the others : each of these cells has a probability @xmath6 to be black and @xmath7 to be white , for some parameter @xmath6 between @xmath8 and @xmath9 . in percolation theory , one is interested in the connectivity properties of the set of black hexagons ( or the set of white ones ) . they can be regrouped into connected components ( or clusters ) . the phase transition for percolation on this lattice occurs at @xmath10 . often , it is described mathematically as follows , in terms of almost sure properties of percolation in the infinite lattice : when @xmath11 , there exists with probability @xmath9 no infinite cluster of black sites ( subcritical regime ) and an infinite cluster of white sites , and conversely when @xmath12 , there is an infinite cluster of black sites ( supercritical regime ) but no infinite cluster of white sites . in the critical case where @xmath10 , there exists neither an infinite white cluster , nor an infinite black cluster but if one takes a finite large piece @xmath13 of the lattice , one will see white and black clusters of size comparable to that of @xmath13 . see e.g. @xcite for an introduction to percolation . a lot of progress has been made recently in the understanding of the large - scale behavior of critical percolation : in particular , smirnov @xcite proved conformal invariance of the connection probabilities , which allowed to make the link @xcite with the schramm - loewner evolution ( sle ) with parameter 6 introduced in @xcite , and to use the sle technology and computations @xcite to derive further properties of critical percolation , such as the value of some critical exponents , describing the asymptotic behavior of the probabilities of certain exceptional events ( arm exponents ) @xcite . we refer to @xcite for a survey . one precise relation to sle goes as follows : we consider the large equilateral triangle @xmath14 with even side length @xmath1 on the triangular grid such that the middle of the bottom part is the origin and the top point is the point at distance @xmath15 above the origin . we decide to color all cells on the boundary of the triangle , in white if their @xmath16-coordinate is positive and in black if their @xmath16-coordinate is negative , and we perform critical percolation in the inside of @xmath14 . then , we consider the interface @xmath17 ( viewed as a path on the hexagonal lattice dual to the triangular lattice ) between the set of black sites attached to the left part of the triangle and the set of white sites connected to the right part of the triangle ( see figure [ triangle ] ) . when @xmath18 , the law of the rescaled interface @xmath19 converges ( in an appropriate topology ) to that of the sle(6 ) process from @xmath20 to @xmath21 in the equilateral triangle with unit side length . see @xcite for details , and e.g. @xcite for an introduction to sle . thanks to this convergence result , one is able to deduce properties of critical percolation from the properties of sle . for instance ( and we shall come back to this later ) , one can prove that the typical number of steps of the path @xmath17 is of the order @xmath22 ( more precisely , for each @xmath23 , the probability that the number of steps is between @xmath24 and @xmath25 goes to @xmath9 as @xmath18 ) . and the interface @xmath17 ( sketch).,width=340 ] understanding the behavior of critical percolation allows also to derive some properties of percolation when the parameter @xmath6 is very close to @xmath26 . these are the scaling ( and hyperscaling ) relations that were first developed in the physics literature ( the names of fischer , kadanoff and wilson are often associated to these ideas ) , and later rigorously derived in the case of percolation by kesten @xcite ( see also @xcite ) . before explaining these relations in a little more detail , let us first make a trivial observation to help the newcomer to get a feeling of what goes on . suppose that we consider the percolation interface in the large equilateral triangle as before , but choose @xmath27 in such a way that @xmath28 . then , one can couple it with a critical percolation interface ( i.e. with the case when @xmath10 exactly ) in the same triangle in such a way that the two paths are identical except on an event of probability that goes to @xmath8 as @xmath29 ( this is just because the probability that one of the neighbors of the interface changed its color is bounded by @xmath30 times the number of neighbors of the interface and we have just seen that this number is @xmath31 ) . hence , if one lets @xmath1 go to infinity , the scaling limit of the interface is still sle(6 ) . in particular , the probability that the interface @xmath32 hits the right side of the triangle before the left side of the triangle let us call @xmath33 this probability goes to @xmath26 as @xmath18 . on the other hand , for any fixed @xmath34 , one can define @xmath35 for this choice of @xmath36 , if one looks at the possible limiting behavior of @xmath32 , it is clear that the law can not be exactly sle(6 ) anymore because it will hit the right side of the triangle before the left one with probability at least @xmath37 . it is therefore natural to ask what can happen to the scaling limit of this curve when @xmath18 in this regime , and to see how it is related ( or not ) to sle(6 ) . one can equivalently define the so - called correlation length @xmath38 in such a way that @xmath39 . in other words , for @xmath40 , @xmath41 ( note that for @xmath42 fixed , @xmath43 as @xmath18 ) . kesten @xcite has shown that it is possible to deduce from the arm exponents of critical percolation the behavior of @xmath44 as @xmath45 . this derivation relies on the `` four - arm exponent '' : the crossing probability increases exactly when `` pivotal '' sites are flipped . combining kesten s results with the exponents computed using sle , one gets @xcite that @xmath46 when @xmath47 , for any fixed choice of @xmath34 . this is ( see @xcite ) a crucial step in the rigorous proof of the fact that the `` density '' @xmath48 of the infinite cluster for percolation with parameter @xmath6 decays like @xmath49 as @xmath6 decays to @xmath50 . we shall see ( and this is quite easy ) that in order to get a non - trivial limit for @xmath32 ( i.e. neither sle(6 ) nor a path that just sticks to the boundary of @xmath51 ) , one has to take @xmath52 in such a way that @xmath1 is of the order of the correlation length @xmath44 i.e. that @xmath53 $ ] for some @xmath54 . the terminology to describe this regime depends on the circumstances and the papers : near - critical , off - critical , finite - size scaling . it is also very closely related to the scaling and hyperscaling relations . anyway , it has been the subject of numerous and interesting works , see e.g. @xcite and the references therein . one general rule behind the derivation of these results is that as long as @xmath55 , the behavior remains roughly the same as at criticality . we will remind some related results in the next sections , but for example , the probabilities of existence of crossings of annuli for near - critical percolation are bounded by constant times those at criticality . this implies that the exponents describing critical percolation also describe off - critical percolation and lead to kesten s scaling relations . in @xcite , camia , fontes and newman have suggested that the scaling limit of the near - critical picture could be obtained from that of the critical picture by just opening a poissonian family of `` pivotal '' points . we understand that @xcite have succeeded in proving this fact . a consequence would be that the subsequential limits that we are discussing in the present paper are in fact limits , and that they are all related to each other by scaling . let us also mention that near - critical percolation is closely related to the questions concerning the noise - sensitivity of percolation , such as studied in @xcite . before describing the results of the present paper , let us just emphasize the relevance of such near - critical models for physical applications . suppose for instance that one is considering a percolation model in a large box , and that one `` heats '' progressively the system i.e. that cells become progressively black one after the other ( and independently ) . then , we know that the percolation parameter at which a left - to - right crossing of the big box will appear is ( with a large probability ) close to the critical one . but , if one looks at it more precisely , it is easy to see that the value at which the crossing occurs will be @xmath56 where @xmath57 is a uniform random variable in @xmath58 $ ] . hence , at this moment , the picture and its fine properties are that of near - critical percolation . another example where this near - critical picture appears spontaneously is that of gradient percolation , an inhomogeneous percolation model introduced in @xcite and studied mathematically in @xcite . our focus here will be on the scaling limits of near - critical interfaces . here is a list of results that we shall derive in the present paper . choose a sequence @xmath59 and study the behavior of the law of @xmath32 as @xmath18 : * for any @xmath34 , if we choose @xmath0 in such a way that @xmath0 is close to @xmath60 , then there exist subsequential limits for the law of @xmath32 . * the limiting laws are all singular with respect to the law of sle(6 ) . * the only other possible scaling limits are sle(6 ) itself ( when @xmath0 is too close to @xmath2 ) or a degenerate case where @xmath61 follows ( the right part of ) the boundary of the triangle ( this is when @xmath0 is too large ) . * the critical exponents associated to these non - degenerate scaling limits are the same as those of sle(6 ) . in particular , the hausdorff dimension of the curves is almost surely @xmath5 . and at @xmath62 of figure [ nicepic ] depicted separately.,width=384 ] the first result is a rather direct application of the tightness arguments of aizenman and burchard @xcite and the definition of the correlation length . the last two statements follow from the ideas of kesten s paper @xcite . our main result is probably the second one , the fact that the laws of non - trivial scaling limits are singular with respect to sle(6 ) . one way to explain it is the following . in the off - critical regime , one sees on a macroscopic scale a difference between the law of the interface and that of the critical percolation interface ( i.e. the non - critical interface is more to the `` right '' for instance ) . if one zooms in by a factor @xmath63 , one still sees a difference , but this difference tends to disappear , because one is not looking at a picture of size ca . @xmath44 any more , but at a picture of size @xmath64 . the question is whether this difference disappears sufficiently fast when @xmath65 or not . note that one can show that ( just as for the critical interface ) the number of boxes of size @xmath66 visited by the path is of order @xmath67 when @xmath63 is large ( and @xmath1 very large ) . either this difference vanishes fast with @xmath63 and one is not able to almost surely detect a difference between the two macroscopic interfaces , or the difference between these two behaviors can be detected by averaging them out over the @xmath67 parts of the path . in the end , one has to compare certain critical exponents to decide which scenario is correct and it turns out that it is the second one . a `` flavor '' of supercritical percolation is therefore still present in the scaling limit . we would like to emphasize that we do not really use any complex analytic sle technology to derive our results . our considerations are based on percolation techniques , kesten s scaling ideas and the knowledge of the exact value of the critical exponents ( the derivation of which however used sle ) . this paper will build on earlier results on near - critical percolation , and in particular on kesten s paper @xcite . in this section , we recall some results that we shall use . all these results are stated and derived in @xcite . see also the last section of @xcite for a rough survey . throughout the paper , we will use the notation @xmath68 to say that the ratio between two quantities remains bounded away from @xmath8 and @xmath69 . recall our definition of the correlation length @xmath70 note that @xmath71 is non - increasing with respect to @xmath6 and non - decreasing with respect to @xmath72 . we define the event @xmath73 that there exist four paths of alternating colors ( when ordered clockwise around the origin ) , each of them joining a neighbor of the origin to the circle of radius @xmath74 . similarly , we define the event @xmath75 ( resp . @xmath76 ) that there exist two paths of different colors ( resp . one black path ) from a neighbor of the origin to the circle of radius @xmath74 . we will use the following properties , that hold for any fixed @xmath34 : 1 . the russo - seymour - welsh estimates remain valid below @xmath77 : for all @xmath78 , there exists @xmath79 such that for all @xmath6 , for all @xmath80 , the probability ( for @xmath81 ) that there is a black ( resp . white ) horizontal crossing of a @xmath82 parallelogram is at least @xmath83 . 2 . let @xmath84 denote the event that there exist two arms of different colors joining the circles of radii @xmath85 and @xmath86 . then ( this follows from the `` arm - separation lemmas '' ) , @xmath87 uniformly for @xmath88 and @xmath89 ( this is known as the _ quasi - multiplicativity _ property ) . the same is true for four arms and one arm , _ i.e. _ with @xmath90 or @xmath91 instead of @xmath92 . [ multip ] 3 . it can be used to prove that @xmath93 uniformly for @xmath94 and @xmath95 . [ summation ] 4 . we have @xmath96 uniformly for @xmath94 and @xmath97 . [ arms_near ] 5 . finally , @xmath98 as @xmath47 . [ equiv ] the last property , which holds for each @xmath99 , implies in particular that for any fixed @xmath100 , @xmath101 as @xmath18 , and that @xmath102 as @xmath47 . note that the combination of items [ multip ] . and [ arms_near ] . shows that @xmath103 uniformly for @xmath94 , @xmath104 ( and similarly for @xmath90 ) . recall also @xcite ( see also @xcite ) that for any @xmath105 , @xmath106 as @xmath107 , where @xmath108 and @xmath109 as @xmath110 , which in turn implies that @xmath111 as @xmath107 . analogous statements hold for any number of arms ( see @xcite ) . note that the correlation length introduced here differs slightly from the usual one let us denote it here by @xmath112 that is defined in terms of crossing probabilities of rectangles or rhombi ( the one introduced in @xcite , and used for instance in @xcite ) . using russo - seymour - welsh considerations ( and also the fact that for any @xmath100 , @xmath113 see @xcite ) , these two definitions can easily be shown to be equivalent : for any @xmath99 , @xmath114 . we are thus allowed to use for @xmath71 results established for @xmath115 . alternatively , we could have chosen to work with rhombi instead of triangles and then , we would have used directly the usual definition of correlation length . these two definitions are also known to be equivalent to other `` natural '' correlation lengths , describing for example the mean radius of a finite cluster or the rate of decay of connectivity properties ( see e.g. the discussion in section 2.2 of @xcite ) . for simplicity of presentation , we will stick to the setup that we described in the introduction , even if the shape of the considered domain ( in our case , it is the triangle ) could be chosen arbitrarily . let us describe this setup more precisely . we follow here the definitions of @xcite , and refer the reader to this paper for more details . we consider @xmath51 the ( filled ) equilateral triangle of unit side length , with corners @xmath116 , @xmath117 and @xmath21 . the rescaled interfaces will be elements of @xmath118 , the space of curves in @xmath51 : these are equivalence classes of continuous functions from @xmath119 $ ] to @xmath51 , where two functions @xmath120 and @xmath121 represent the same curve if and only if there exists a continuous increasing bijection @xmath122 \to [ 0 , 1]$ ] such that @xmath123 . we endow this space with the quotient metric : @xmath124 } |f_1 - f_2 | \bigg)\ ] ] where the infimum is over the set of increasing bijections @xmath125 from @xmath126 $ ] onto itself . we call @xmath127 the law of the rescaled interface @xmath128 of percolation with parameter @xmath6 in our triangle ( with mesh size @xmath129 ) : this is a probability measure on @xmath118 . endowed with the previous metric , @xmath118 is a complete separable space , so that tightness and relative compactness are equivalent ( by prohorov s theorem ) . the family @xmath130 , n \ge 1)$ ] is relatively compact in @xmath131 . * let us consider a sequence @xmath132 in this family . our goal is to find a converging subsequence : * by symmetry , we can assume that @xmath133 for all @xmath134 . * if @xmath135 remains bounded along a subsequence , proving convergence of a subsequence of @xmath136 is trivial . * we can therefore restrict ourselves to the case where @xmath137 . suppose that for all @xmath34 , @xmath138 along a subsequence ; then it is easy to check ( using russo - seymour - welsh arguments ) that along that subsequence , @xmath139 converges in law to the concatenation of the two parametrized segments @xmath140 \cup [ 1 / 2 , \sqrt{3 } i / 2]$ ] . * we now suppose that for some @xmath141 , @xmath142 remains bounded . in particular , we get that for some fixed @xmath143 , @xmath144 for all large enough @xmath145 ( indeed , by russo - seymour - welsh , one can increase @xmath71 by at least any constant factor by choosing a larger @xmath146 ) . we can then use the machinery developed by aizenman and burchard ( theorem 1.2 in @xcite ) : russo - seymour - welsh estimates hold uniformly for all @xmath6 and @xmath147 , so that for any annulus @xmath148 , @xmath149 for two universal constants @xmath150 ( traversed means here that it visits the inner and the outer boundary of the annulus ) . the bk inequality ( see e.g. @xcite ) then leads to the fact that @xmath151 which is exactly the hypothesis ( h1 ) of @xcite ( uniform power bounds on the probability of multiple crossings in annuli ) . + for the sake of completeness , let us just sketch why tightness can be derived from this . first , the hypothesis ( h1 ) implies regularity properties ( theorem 1.1 in @xcite ) for the random curves @xmath152 : for any @xmath153 , there is some hlder continuity bound such that for each @xmath145 , there is a probability at least @xmath154 that @xmath152 can be parametrized and satisfy this bound . in particular , we can exhibit some equicontinuous set such that for each @xmath145 , @xmath152 belongs to this set with probability at least @xmath154 . tightness follows ( theorem 1.2 in @xcite ) using ( a slight adaptation of ) arzela - ascoli s characterization of compactness for continuous functions on a compact set . hence , in all cases , one can find a converging subsequence of @xmath155 . in this section , we will study the non - degenerate case where @xmath156 is not too large : we assume that @xmath157 $ ] for some fixed @xmath99 ( note that this includes the critical case ) . we exhibit properties that near - critical interfaces share with critical ones . we will first focus on an estimate for discrete interfaces and then study the scaling limits . the length ( number of edges ) @xmath158 of the discrete interface @xmath17 in the finite - size scaling regime is roughly the same as that of the critical interface : [ proplength ] assume that @xmath157 $ ] . then for any fixed @xmath159 , @xmath160 ) = 0.\ ] ] * proof . * note that the hypothesis on @xmath0 implies in particular that @xmath161 , so that we can use the results on near - critical percolation that we have recalled in the preliminaries . let us first derive the upper bound for @xmath162 : we estimate its expectation . we note that for any edge @xmath163 on the dual hexagonal lattice , @xmath164 if and only if there exist two arms as depicted on figure [ 2arms ] , one black joining a neighbor of @xmath16 to the negative real half - axis , and one white joining a neighbor of @xmath16 to the positive real half - axis . , being on @xmath17 corresponds to the existence of two arms . for the lower bound , we consider semi - annuli @xmath165 and we restrict to the edges at distance at least @xmath166 from the boundary of @xmath167 ( dashed).,width=302 ] in particular , @xmath168 it allows us to get an upper bound on @xmath169 : for each @xmath170 , and for some constants @xmath171 ( using the estimates on near - critical percolation and the fact that there are never more than @xmath172 points at distance @xmath173 from @xmath174 ) , @xmath175 the upper bound for @xmath162 follows immediately by markov s inequality . for the lower bound , we use the standard second moment method . for that purpose , take @xmath176 such that @xmath177 and decompose the triangle @xmath14 into concentric `` semi - annuli '' @xmath178 , @xmath179 . note that the curve @xmath17 has to cross each of these semi - annuli . for any edge @xmath16 in @xmath167 at distance at least @xmath166 from the boundary of @xmath167 , the results that we have recalled together with the `` separation lemmas '' imply that the probability @xmath180 that there exist two paths as before , from @xmath181 to the positive and negative real half - axes , that stay in @xmath167 , satisfies @xmath182 uniformly for such @xmath16 and @xmath183 . such an edge @xmath16 is necessarily on @xmath17 by the previous remark . let @xmath184 denote the number of these edges : we have @xmath185 for large @xmath173 ( and any fixed @xmath153 ) . now , using the quasi - multiplicativity property and then item [ summation ] . we get @xmath186 it follows that for some ( universal ) constant @xmath187 , @xmath188 consider some @xmath189 : since the events @xmath190 for @xmath191 are independent , we get that @xmath192 the lower bound follows readily because @xmath193 and our lower bound for @xmath194 . we now show that scaling limits of near - critical interfaces have the same hausdorff dimension as in the critical regime : assume that the law of the curve @xmath61 is the weak limit of @xmath132 , with @xmath195 and @xmath196 $ ] . then the hausdorff dimension of @xmath61 is almost surely @xmath5 . similar statements for @xmath74-point correlation functions , multiple crossings , multifractral spectrum etc . could be derived in the same way . we leave this to the interested reader ( see the informal discussion at the end of the paper ) and we focus here only on this fractal dimension . we might remark that the a priori estimates for the existence of two or three arms near a half - plane , or for the existence of five arms in the interior of the domain still hold ( uniformly ) for @xmath197 , as these are consequences of the russo - seymour - welsh estimates only . hence , exactly as in the convergence to sle(6 ) case ( e.g. @xcite ) , the discrete hitting probabilities converge to the continuous hitting probabilities . * proof . * the argument goes along similar lines as for the discrete length . for the upper bound , it suffices to prove that for all @xmath153 , the expected number of balls of radius @xmath198 needed to cover @xmath61 is bounded by @xmath199 . but , we know that this expected number is bounded uniformly by this quantity for the discrete paths @xmath200 , and so this also holds in the scaling limit . for the lower bound , we decompose the triangle into concentric semi - annuli , and we exhibit a family @xmath201 of independent events of probability at least @xmath202 , such that on each @xmath203 , the curve @xmath61 has dimension @xmath5 . again , we follow exactly the same idea ( with second moment estimates ) as in the discrete case , using the fact ( noticed in section [ prel ] ) that the discrete estimates for @xmath204 hold uniformly . we now prove that for the scaling limits of percolation interfaces , there are only three main options . [ dichotomy ] suppose that @xmath205 is the weak limit of a sequence @xmath136 when @xmath206 , with @xmath195 and @xmath207 . then : * either @xmath205 is the dirac mass on the concatenation of the two boundary segments @xmath208 $ ] and @xmath209 $ ] , * or @xmath205 is the law of sle(6 ) , * or for some @xmath210 , @xmath211 for all large @xmath145 . * suppose now that @xmath205 is the limiting law of a sequence @xmath212 defined under @xmath213 , where @xmath195 and @xmath214 . * let us first suppose that for each @xmath34 , @xmath215 for all sufficiently large @xmath145 . this implies readily ( by standard russo - seymour - welsh arguments ) that for each fixed @xmath146 , @xmath216 . it follows readily that the probability that there exists a closed cluster of radius greater than any fixed positive @xmath57 for @xmath213 in the rescaled triangle goes to @xmath8 as @xmath206 and the @xmath205 must be supported on the path that goes along the right boundary of the triangle . * let us now suppose that for each @xmath217 , @xmath218 for all sufficiently large @xmath145 . we assume that the law @xmath205 is not the law of an sle(6 ) and try to reach a contradiction . in the discrete setting , it is always possible to couple @xmath219 ( corresponding to @xmath220 ) with a realization of the interface @xmath221 for @xmath222 in such a way that the sites that are black for the realization of @xmath222 are also black for the realization of @xmath223 . in this way , the path @xmath219 is more `` to the right '' than @xmath221 . letting @xmath206 , we see that we can couple a realization @xmath224 of @xmath205 with an sle(6 ) @xmath225 in the triangle @xmath51 with the same property . + it follows from our results on hausdorff dimensions ( in fact the uniform russo - seymour - welsh bounds would suffice ) that @xmath224 is almost surely a continuous curve with zero lebesgue measure . clearly , one can divide the set of connected components of @xmath226 into two parts . intuitively speaking , those `` to the right of @xmath224 '' and those `` to the left of @xmath224 '' . let us call @xmath227 and @xmath228 the respective unions of these components . similarly , we can define @xmath229 and @xmath230 . then , we have that @xmath231 . + the fact that the laws of @xmath224 and @xmath225 are not identical implies that with positive probability the two open sets @xmath230 and @xmath228 are not equal . it follows ( using also the fact that @xmath224 is a curve that does not backtrack on its own past ) that for some @xmath232 with rational coordinates and for some @xmath233 with rational coordinates , if we denote by @xmath234 the disc centered at @xmath235 with radius @xmath236 , @xmath237 we also choose @xmath236 small enough so that the distance between @xmath235 and the boundary of the triangle is at least @xmath238 . from now on , @xmath235 and @xmath236 will be fixed . + the convergence of the discrete interfaces to the continuous ones imply that for some positive constant @xmath239 , @xmath240 for any large @xmath145 , with obvious notation . note that these discrete events do not depend on the state of the sites inside @xmath241 as they imply that neither @xmath219 nor @xmath221 did intersect the disc . so , it follows from the uniform rsw estimates that if we define the event @xmath242 that there exist a white circuit in @xmath243 for @xmath223 and a black circuit for @xmath222 in the same annulus ( where both circuits disconnect @xmath235 from @xmath244 ) , we get that for some absolute positive constant @xmath245 and all sufficiently large @xmath145 , @xmath246 + it follows readily that if one increases continuously @xmath6 from @xmath2 to @xmath247 , there will exist with probability bounded from below a value @xmath6 at which the interface jumps from the left to the right of @xmath241 without hitting it . at this @xmath6 , there exist necessarily four arms of alternating colors originating at the site @xmath16 that has been flipped . the different possibilities are depicted in figure [ flip ] . + .,height=412 ] + for each given site @xmath16 on the grid @xmath248 , let us evaluate the probability that this occurs . when @xmath16 is not close to the boundary of the triangle , i.e. if it is at distance at least @xmath249 , then we see that four arms of alternating colors must originate from @xmath16 all the way to distance @xmath249 from @xmath16 . the probability is then bounded by @xmath250 ( recall that @xmath236 is fixed and that @xmath251 ) . + when @xmath16 is at distance @xmath252 from the boundary , then one must have four arms of alternating colors up to distance @xmath253 , and then two arms that cross a semi - annulus ( in a half - plane ) from radius @xmath253 to @xmath249 . combining this with quasi - multiplicativity and the known bounds ( 2 arms in a half - plane , 5 arms in the plane that give an upper - bound for the four - arm probability ) leads to a bound of the type @xmath254 + for any @xmath173 , there are at most a constant times @xmath135 points on our grid that are at distance exactly @xmath253 from the boundary of the triangle . hence , when we sum over all possible sites @xmath16 in the triangle , we get that the probability that between @xmath6 and @xmath255 a site @xmath16 is flipped in such a way that the curve jumps from the left to the right of the small disc is bounded by @xmath256 times @xmath257 ( for some constants @xmath258 that do not depend on @xmath145 ) . + it finally follows that for some positive constant @xmath239 , @xmath259 but if we apply russo s formula in a similar way to evaluate @xmath260 together with the fact that the four - arm probabilities are uniformly controlled for @xmath55 , we get that for some positive @xmath261 , @xmath262 hence , there exists a positive constant @xmath263 such that @xmath264 for all sufficiently large @xmath145 . in other words , @xmath265 for all sufficiently large @xmath145 , and this contradicts our assumption . * finally to conclude the proof of the proposition , let us suppose that we are not in the last scenario described in its statement i.e. that it is not true that for some @xmath266 , @xmath267 for all large @xmath145 . then it means that a subsequence of @xmath268 falls into one of the two cases that we have just studied . hence , the limiting probability measure is either the law of sle(6 ) or the dirac mass on the union of the two boundary segments . in this section , we are going to assume that we are in the intermediate regime where the discrete percolation parameter @xmath6 used at scale n satisfies @xmath269\ ] ] for some fixed @xmath270 . the previous alternative tells us that these are the `` non - trivial '' cases in the large - scale limit . we are going to exhibit asymmetry properties that enable to detect the difference with a critical interface . we will first derive a result in the discrete setting , and then a result in the continuous setting for the scaling limit . on the discrete level , it is possible to explore the interface dynamically : each time one discovers a new hexagon , one tosses a coin to decide if it is black or white , so that with probability @xmath6 ( resp . @xmath271 ) , one makes a 60 degree turn to the right ( resp . to the left ) . of course , one often bumps into an already discovered hexagon , and in this case , the turn is already determined by a previous tossing . hence , the percolation interface is the image under some map of a sequence of coin tosses . let us call @xmath272 and @xmath273 the number of black ( resp . white ) cells neighboring the path @xmath17 . [ das ] suppose that @xmath274 $ ] . then for any fixed @xmath153 , @xmath275 on the other hand , for critical percolation , @xmath276 * proof . * define @xmath277 . clearly the difference between the number of black neighbors discovered by @xmath17 and the number of white discovered neighbors evolves like a biased simple random walk with drift @xmath278 ( at each step the probability to add one is @xmath279 ) stopped after a certain random number of steps @xmath280 that is roughly of the order @xmath22 ( see proposition [ proplength ] ) . hence , we see that this difference will be of the order @xmath281 ( with high probability ) i.e. more precisely that for all @xmath159 , @xmath282 in the off - critical case where @xmath283 , we see that the drift term dominates because of proposition [ proplength ] so that the first statement follows readily . similarly , when @xmath284 , the result follows directly from proposition [ proplength ] . hence , the discrete interface in the off - critical regime where @xmath285 will have ( on a microscopical scale ) anomalously more `` black neighbors '' than `` white neighbors '' . moreover , the proof shows that one can detect a good approximation of the actual value of @xmath0 by looking at this difference because @xmath286 will be close to @xmath287 . but this result is not sufficient to deduce asymmetry of scaling limits . indeed , if we had for instance taken @xmath288 for some @xmath289 , then an analogous discrete asymmetry result would hold i.e. for some small @xmath159 @xmath290 but we have proved in the previous section that in this case , the interface still converges to sle(6 ) as @xmath18 ( and we know that sle(6 ) is symmetric ) . the goal of this section is to prove the following result : suppose that @xmath61 is the limit ( in law ) of a sequence of @xmath200 s where @xmath291 $ ] ( and @xmath195 ) . then the law of @xmath61 is singular with respect to that of sle(6 ) . * let us fix a very small positive @xmath292 . define the rectangle @xmath293\times [ 0 , 1/4]$ ] for a small fixed @xmath294 . define the segments @xmath295 \times \{1/8\}$ ] and @xmath296\times \{1/4\}$ ] , and the smaller triangle @xmath297 ( see figure [ subsets ] ) . for each small equilateral triangle @xmath298 of size @xmath198 ( i.e. that one can obtain by translating @xmath299 ) , we define analogously the sets @xmath236 , @xmath300 , @xmath301 and @xmath302 . we say that the triangle @xmath298 is _ good _ for @xmath61 , if at the first hitting time @xmath303 of @xmath304 , @xmath305 , and if @xmath61 does exit @xmath236 through @xmath301 after its first hitting time of @xmath300 . , we consider the subsets @xmath306 , @xmath307 , @xmath308 and @xmath309 . in any small equilateral triangle @xmath298 of size @xmath198 , we define similarly the corresponding sets @xmath236 , @xmath300 , @xmath301 and @xmath302.,width=453 ] let us define the connected component @xmath310 of @xmath311 $ ] that has the top boundaries of @xmath302 on its boundary . we consider the following three marked points on the boundary of @xmath310 : suppose that we go along the boundary of @xmath310 clockwise starting from the bottom right corner of @xmath302 ( that we call @xmath312 ) . then @xmath313 is the right - most point on @xmath314 and @xmath315 is the left - most point on @xmath314 ( see figure [ pivotal ] ) . we call @xmath316 ( resp . @xmath317 ) the part of the boundary of @xmath310 between @xmath312 and @xmath313 ( resp . between @xmath315 and @xmath312 ) . is very good.,width=340 ] when @xmath298 is a good triangle , we define @xmath318 to be the probability given by cardy s formula of the existence in @xmath310 of a crossing from @xmath316 to the part @xmath319 of the boundary between @xmath320 and @xmath315 . if after @xmath321 , @xmath61 does hit @xmath316 before @xmath317 , we then say that @xmath298 is _ very good _ for @xmath61 . if @xmath61 was an sle(6 ) , then @xmath318 would just be the conditional probability given @xmath322)$ ] that @xmath298 is very good for @xmath61 . but here , the law of @xmath61 is the limit of the law of near - critical percolation interfaces @xmath139 defined under @xmath213 , where @xmath323 and @xmath195 . by skorokhod s representation theorem , we can couple on the same probability space samples of all @xmath219 s and @xmath61 in such a way that @xmath324 almost surely just as in the proof of convergence of critical percolation interfaces to sle(6 ) ( as in @xcite for instance ) . for @xmath219 , we can also check if a triangle @xmath298 is good and very good . in fact , for each fixed triangle , the probability that its status for @xmath61 is not identical to its status for @xmath219 goes to zero as @xmath206 . indeed , if we suppose for instance that @xmath298 is good for @xmath61 but not for @xmath219 , then it means that a three - arm event occurs for @xmath61 and a priori bounds do exclude this . if we define the stopping time @xmath325 associated to the triangle @xmath298 and the path @xmath219 , this means that when @xmath298 is good , then @xmath326 $ ] converges almost surely to @xmath327 $ ] . so , the domains @xmath328 ( with obvious notation ) converge in carathodory topology towards @xmath310 almost surely . we now couple each realization of @xmath219 with a realization @xmath329 of critical percolation on the same lattice , in such a way that the realization used to define @xmath219 dominates @xmath329 ( _ i.e. _ its set of black sites is larger ) . then ( see e.g. @xcite ) , it follows that the probability @xmath330 that there exists a crossing from @xmath331 to @xmath332 in @xmath328 for @xmath329 ( with natural notation ) converges almost surely to @xmath318 . suppose now that the triangle @xmath298 is good for @xmath219 and consider the configurations as depicted on figure [ pivotal ] : we restrict ourselves to the case where there exist sites in a smaller rhombus of size comparable to @xmath333 from which four arms of alternating colors originate . for each such site @xmath16 , and conditionally on @xmath326 $ ] , the probability that this four - arm configuration exists for percolation of parameter @xmath334 $ ] in the domain not yet explored by @xmath219 is bounded from below by a constant @xmath239 times @xmath335 , uniformly over @xmath6 , @xmath145 and the choice of @xmath6 ( this follows from the uniform estimates for four arms , the separation lemmas and russo - seymour - welsh ) . the probability that this site is flipped from white to black when one increases @xmath6 from @xmath2 to @xmath247 , and that at this value @xmath6 the configuration is as described above , is therefore larger than @xmath336 finally , note that this event can happen for only one site ( when @xmath6 increases , since the crossing event is increasing , there can exist only one value of @xmath6 and therefore one site @xmath16 such that the state of @xmath16 is flipped exactly at @xmath6 and @xmath16 at that moment is pivotal ) . hence , we can sum over all sites @xmath16 in the small rhombus , and deduce that the conditional probability given @xmath337 $ ] that @xmath298 is very good is bounded from below by @xmath338 ( we have used the quasi - multiplicativity to estimate the ratio on the second line ) for all small @xmath198 and uniformly with respect to @xmath145 and to the good configurations @xmath326 $ ] . letting @xmath206 , we conclude that for any good triangle @xmath298 , the conditional probability given @xmath339 $ ] that @xmath298 is very good for @xmath61 is at least @xmath340 we now want to estimate the number of good triangles @xmath298 . we divide the triangle @xmath51 into @xmath341 small deterministic triangles . using the same method as when studying the dimension of @xmath61 ( and the arm - separation ideas that allow to estimate the probability that a triangle is good i.e. to say that the probability for a triangle @xmath298 to be good is comparable to the probability to be hit ) , we see that with probability going to @xmath9 as @xmath342 , the number of good triangles is at least @xmath343 . we now count how many triangles are very good among the first @xmath344 good ones , and we subtract the sum of the @xmath345 for these good triangles . if @xmath61 was an sle(6 ) , the obtained quantity @xmath346 would satisfy @xmath347 and @xmath348 . but , in our case , we see that @xmath349 and @xmath350 . if the sequence @xmath351 has been chosen to converge sufficiently fast to zero , we see that almost surely ( using borel - cantelli ) , for all sufficiently large @xmath176 , @xmath352 whereas if @xmath61 had been an sle(6 ) , we would almost surely have had @xmath353 for infinitely many @xmath176 s . we thus found an event that holds with probability one for @xmath61 , but with probability zero for sle(6 ) . seemingly , the fact that the laws of near - critical interfaces are singular with respect to the law of sle(6 ) surprises some theoretical physicists who work on this topic . recall that one important aspect of the sle approach to critical systems was precisely to show that critical conformally invariant models in the same `` universality class '' give rise to exactly the same curves in the scaling limit . for near - critical models that are not strictly conformally invariant such as near - critical percolation here , this strong `` universality '' can fail to be true . suppose that a random curve @xmath61 is the scaling limit of a near - critical percolation interface . the tightness arguments , together with the estimates for existence of multiple arms indicate that the curve @xmath61 is almost surely a loewner chain , and that it can be defined via its random driving function @xmath354 . it is of course a natural question to ask what this driving function could be ( recall that in the case of sle(6 ) , @xmath355 is a standard brownian motion ) . note that after each ( fixed or stopping ) time , we expect the curve @xmath61 to turn `` more right '' as what a sle(6 ) would do in the same situation . this leads naturally to the conjecture that ( if one extends properly the probability space ) one can couple @xmath354 with a standard brownian motion @xmath356 in such a way that @xmath357 is an increasing continuous process adapted to the filtration generated by the processes @xmath358 and @xmath359 . one may think that this contradicts the fact that the law of @xmath360 is singular with respect to that of @xmath292 ( since the curves are generated by the driving functions , this is equivalent to say that the law of @xmath61 is singular with respect to that of sle(6 ) ) because the law of brownian motion with drift is known to be absolutely continuous with respect to that of brownian motion . but this last fact is only valid under some regularity properties for the drift , and in the present case , one can expect this drift to be quite complicated ( its derivative measure might be supported on a set of exceptional times i.e. a fractal - type set ) . we have seen that important properties ( such as the dimension of the curve ) are shared by the critical interfaces and the near - critical interfaces in the scaling limit , so that the technology based on conformal invariance of the critical model still provides the correct description of the near - critical interfaces in terms of exponents ( this was used in @xcite to describe the `` percolation front '' ) . in fact , the near - critical percolation technology allows to prove the following result ( this is a direct consequence of the quasi - multiplicativity property and the fact that arm probabilities are comparable uniformly to the arm probabilities at @xmath4 ) : for any @xmath145 , there exists a constant @xmath361 , such that for any @xmath362 in @xmath51 , and for any sufficiently small @xmath72 , the ratio between the probability that @xmath61 visits the @xmath72-neighborhood of these @xmath145 points and the probability of the same event for sle(6 ) stays in @xmath363 for all small @xmath72 and uniformly over the choices of @xmath364 . loosely speaking , the `` finite - dimensional marginals '' of the law of @xmath61 are uniformly comparable to those of sle(6 ) ( even when the @xmath365 s are very close to each other ) . note that this is the type of functions that is computable via the conformal field theory technology . but this result does not contradict the fact that the law of @xmath61 is singular with respect to that of sle(6 ) . note for instance that the constant @xmath361 does depend on the number of considered points . our proof used the fact that we did not zoom on the behavior of the curve at just one point , but that we detected the asymmetry by looking at the mean of the behavior of the curve near to more and more points . laboratoire de mathmatiques , bt . 425 , universit paris - sud 11 , 91405 orsay cedex , france dpartement de mathmatiques et applications , cole normale suprieure , 45 rue dulm , 75230 paris cedex 05 , france

we study the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice . when one lets the percolation parameter @xmath0 vary with the size @xmath1 of the box that one is considering , three possibilities arise in the large - scale limit . it is known that when @xmath0 does not converge to @xmath2 fast enough , then the scaling limits are degenerate , whereas if @xmath3 goes to zero quickly , the scaling limits are sle(6 ) as when @xmath4 . we study some properties of the ( non - void ) intermediate regime where the large scale behavior is neither sle(6 ) nor degenerate . we prove that in this case , the law of any scaling limit is singular with respect to that of sle(6 ) , even if it is still supported on the set of curves with hausdorff dimension equal to @xmath5 .

nevertheless , it is commonly misdiagnosed , which leads to a poor prognosis and more aggressive treatments . subungual squamous cell carcinoma ( sscc ) is a rare entity with an extremely varied clinical presentation . the lack of awareness among physicians , its indolent natural history , and the higher prevalence of other benign conditions on the ungual apparatus are responsible for delay in its diagnosis . we have reported here four cases of sscc with a previous mistaken diagnosis of a benign process unsuccessfully treated for years . figure 1 shows the different clinical presentation of cases herein reported . the first patient presented with involvement of two digits . radiological studies did not reveal alterations , except for an incidental osteochondroma in the fourth patient . histological examination revealed sscc in all cases , but immunostaining for human papillomavirus ( hpv ) was only positive in the first patient , who presented with deeper tissue involvement [ figure 2 ] . all surgical procedures resulted in free - margin tumoral excisions , without recurrences or nodal involvement during follow - up between 5 and 30 months . clinical and histological data of the four study patients a ) keratotic and verrucous lesion below the nail plate mimicking a viral wart ( case 1 ) , ( b ) crusted subungual lesion ( case 2 ) , ( c ) erythematous and eroded lesion covered by crusts and keratotic material ( case 3 ) , ( d ) prominent onycholysis and fleshy nodular lesion ( case 4 ) ( a ) positive immunostaining for hpv in case 1 ( arrows)hpv immunostaining , 200 ) , ( b ) moderately differentiated subungual squamous cell carcinoma in the second patient . ( h and e , 100 ) , ( c and d ) well - differentiated squamous cell carcinoma in third and fourth patients . lobular aggregations of slightly atypical keratinocytes and incipient horn pearl formation ( arrows)(h and e , 100 ) tumors located in subungual tissues include squamous cell carcinoma ( scc ) , bowen 's disease , melanoma , basal cell carcinoma , and keratoacanthoma among others . usually , sscc affects a single digit , the thumb and the great toe being the most frequently involved . multiple fingers involvement has also been described . the incidence is higher in men between the fifth and seventh decades of life . the proposed aetiologies of the disease include chronic infection , chemical or physical microtrauma , genetic disorders such as congenital ectodermal dysplasia , radiation , tar , arsenic or exposure to minerals , sun exposure , immunosuppression , and previous hpv infection . hpv involvement has gained importance , as hpv dna was recovered from 60% to 90% of cases of sscc and > 60% were related to hpv 16 . genital - digital transmission has been suggested as a plausible pathogenetic factor in sscc , as hpv 16 is the most frequent serotype found in genital warts . however , there are probably other factors implicated in malignancy , as viral warts in hands are very common and the development of sscc remains rare . in the cases herein reported , all potential causative factors of sscc were excluded with the clinical history data and the physical examination . the clinical features may be variable and include chronic pain and swelling , onycholysis , or nail plate dyschromia . the most frequent presentation consists of wart - like appearance involving the nail bed and periungual areas in association with nail dystrophy . viral warts , onychomycosis , or chronic paronychia remain the most commonly mistaken entities . besides , the tumor masked by the nail plate , lack of awareness , and overlying secondary infections lead to misdiagnosis for an average of 4 - 40 years . therefore , exploratory nail plate removal and subsequent biopsy are advised in all patients with chronic nail conditions that fail to respond to conventional treatment . in patients with recurrent nail infections or chronic ulcerations , tissue culture is also needed . imaging studies may be done to assess possible bone involvement . as a result of delayed diagnosis , most patients with sscc present with invasive disease , with bony involvement ranging from 16% to 66% . sscc is considered a low - grade malignancy and less aggressive than scc arising elsewhere . the tendency to recurrence is higher on the nail unit than in other anatomic areas . this fact can probably be due to residual hpv in surrounding areas or , more frequently , due to incomplete tumor removal . wide local excision and simple excision have also been proven effective , the former being preferred because of the lower recurrence rate . amputation of the distal phalanx is usually the recommended treatment for patients with bone infiltration . radiation therapy has also been reported to be effective . in conclusion , a high index of suspicion for sscc is required . therefore , an early biopsy in chronic persistent or recurrent nail lesions , and subsequent early sscc diagnosis may prevent more aggressive treatments and assures a favourable prognosis . human papillomavirus infection probably has an important role in the development of subungual squamous cell carcinoma.subungual squamous cell carcinoma has a high recurrence rate . human papillomavirus infection probably has an important role in the development of subungual squamous cell carcinoma .

subungual tumors are rare in general . of all tumors , subungual squamous cell carcinoma ( sscc ) is the most frequent one . protean clinical presentations and the lack of awareness of the disease are responsible for an incorrect or delayed diagnosis and subsequent delayed treatment . we have reported here four patients with sscc who were previously wrongly diagnosed with a benign process and treated unsuccessfully for years . we would like to highlight the need of a biopsy in chronic or recurrent nail lesions that fail to respond to a previous conservative treatment in order to rule out sscc .

NBA player Bobby Brown is under fire in China after he posted a photo of his initials and uniform number name graffitied on the stones of the country’s ancient Great Wall, Chinese media reports. “Had a blast at the Great Wall of China today,” the 32-year-old point guard for the Houston Rockets wrote on his Weibo microblog on Monday afternoon, adding four photos, including one with his initials and uniform number, “BB #6”, on bricks at the wall, news portal sina.com reports. His post soon provoked outrage on China’s social media, as many Internet users criticised Brown for defacing China’s most famous cultural heritage. “Are you proud of your carving? This is a part of world heritage, not the toilet of your home,” one Weibo user commented before Brown’s post was removed. Travel taboos: how not to be an obnoxious tourist - wherever you're from Brown, who was in Beijing for the 2016 NBA Global Game China between the Houston Rockets and New Orleans Pelicans, later apologised on his microblog, and asked for forgiveness from fans and Chinese Internet users. “I respect the Chinese culture, I made an honest mistake … hope you forgive me,” he wrote in a post the next morning, which was later also removed. The rudeness of Chinese tourists has come under the spotlight in recent years in the wake of a series of incidents involving them. Chinese tourists leave their mark at attractions around Shanghai Disneyland In one such case, a teenager from Nanjing carved his name on the wall of a 3,500-year-old Egyptian temple in 2013, which later triggered nationwide introspection on poor behaviour by Chinese tourists abroad, which many said damaged the image of mainland tourists. ||||| Rockets' Bobby Brown slammed for writing on Great Wall of China Bobby Brown of the Rockets asked for forgiveness from Chinese citizens after drawing heavy criticism in China for inscribing his name and number on the country's Great Wall. Brown and the Rockets made the sightseeing stop during a trip to China with the New Orleans Pelicans for the NBA's Global Game China and he couldn't resist the urge to leave a little graffiti behind on the 2,221-year-old wall. His work came to light when he posted images on his Weibo microblog (kind of like China's Twitter), writing, "Had a blast at the Great Wall of China today." Chinese netizens became furious. "Are you proud of your carving? This is a part of world heritage, not the toilet of your home," one Weibo user commented before Brown's post was deleted, according to sina.com and SCMP.com. Brown, 32, later apologized. "We were out enjoying the Great Wall," he said in an interview before the team returned to Houston. "I had never been, it was my first time. I wrote my name on the wall in chalk. I saw different writings – I didn't mean any harm by it. I made a mistake. I could have just put my hand over it and erased it. It will never happen again. I've been playing in China for three years now and I have the utmost respect for the Chinese culture, and the way of living here. I pretty much adapted, coming from the states, here for three years. My teammates, the fans in Shenzhen and the fans all over were great to me, and I just want to sincerely apologize for that." The Houston Rockets' Bobby Brown captured his autograph on the Great Wall of China in this post on social media. The Houston Rockets' Bobby Brown captured his autograph on the Great Wall of China in this post on social media. Photo: Weibo The Houston Rockets' Bobby Brown apologized for writing on the Great Wall of China. The Houston Rockets' Bobby Brown apologized for writing on the Great Wall of China. Photo: Weibo Houston Rockets players pose for a picture at the Great Wall of China. Houston Rockets players pose for a picture at the Great Wall of China. Photo: Instagram The Rockets' Ryan Anderson was as dazzled on this week's second visit to the Great Wall of China as he was on his first trip with the Pelicans. The Rockets' Ryan Anderson was as dazzled on this week's second visit to the Great Wall of China as he was on his first trip with the Pelicans. window._taboola = window._taboola || []; _taboola.push({ mode: 'thumbnails-c', container: 'taboola-interstitial-gallery-thumbnails-5', placement: 'Interstitial Gallery Thumbnails 5', target_type: 'mix' }); _taboola.push({flush: true}); Bobby Brown of the Houston Rockets, left tries to throw past Tim Frazier of the New Orleans Pelicans, center and Dante Cunningham of the New Orleans Pelicans during a preseasons NBA game in Beijing, China, Wednesday, Oct. 12, 2016. (AP Photo/Ng Han Guan) less Bobby Brown of the Houston Rockets, left tries to throw past Tim Frazier of the New Orleans Pelicans, center and Dante Cunningham of the New Orleans Pelicans during a preseasons NBA game in Beijing, China, ... more Photo: Ng Han Guan, Associated Press Bobby Brown of the Houston Rockets, center tries to get past Alonzo Gee of the New Orleans Pelicans, left and Langston Galloway of the New Orleans Pelicans at right during a preseasons NBA game in Beijing, China, Wednesday, Oct. 12, 2016. (AP Photo/Ng Han Guan) less Bobby Brown of the Houston Rockets, center tries to get past Alonzo Gee of the New Orleans Pelicans, left and Langston Galloway of the New Orleans Pelicans at right during a preseasons NBA game in Beijing, ... more Photo: Ng Han Guan, Associated Press Houston Rockets' Bobby Brown poses during an NBA basketball media day Friday, Sept. 23, 2016, in Houston. (AP Photo/David J. Phillip) Houston Rockets' Bobby Brown poses during an NBA basketball media day Friday, Sept. 23, 2016, in Houston. (AP Photo/David J. Phillip) Photo: David J. Phillip, Associated Press window._taboola = window._taboola || []; _taboola.push({ mode: 'thumbnails-c', container: 'taboola-interstitial-gallery-thumbnails-9', placement: 'Interstitial Gallery Thumbnails 9', target_type: 'mix' }); _taboola.push({flush: true}); Photo: Weibo Image 1 of / 9 Caption Close Rockets' Bobby Brown slammed for writing on Great Wall of China 1 / 9 Back to Gallery Writing on the Great Wall is, of course, prohibited. "No matter who you are, you should not scratch graffiti on the Great Wall. As a world cultural relic, the Great Wall needs protection from both Chinese people and foreign tourists," a manager with the Mutianyu Great Wall Travel Service Co., Ltd., told Beijing Youth Daily. If tourists feel they must leave a message, there are designated "graffiti zones." The 32-year-old shooting guard has played parts of two seasons in the NBA, but hasn't played in the league since a stint with the Los Angeles Clippers in 2010, and he's fighting to make the Rockets' regular season roster. Brown has been playing overseas for the past five seasons, including three seasons in China. NBA teams have been going to China for decades, with the Washington Bullets becoming the first U.S. pro sports team to visit the country in 1979, shortly after diplomatic relations were normalized. Wes Unseld, then the team's star center, looked back in 2009, telling The Post's J. Freedom du Lac: "They just told us not to do anything stupid - which as members of a professional team we were apt to do sometimes. I learned some Chinese, too: hello, goodbye, I'm sorry - things like that." All these years later, missteps can still happen. At least Brown got off the bus and took in the Wall. "I was a history major in college and wanted to see everything I could," Unseld recalled. "We took a bus to the Great Wall, and a couple of my teammates didn't get off the bus. I don't know if they were tired or what, but I was embarrassed."

– It's not quite as bad as peeing on the Alamo, but Bobby Brown of the Houston Rockets is still getting a hard time from commenters in China after leaving graffiti on the country's Great Wall. Brown, who played in China for three seasons, not only tagged the wall in chalk, he posted a photo of it on his Weibo microblog Monday, reports the South China Morning Post. "Are you proud of your carving? This is a part of world heritage, not the toilet of your home," one outraged user commented. The Rockets were in China with the New Orleans Pelicans for the NBA's Global Games. Brown, 32, issued an apology, saying he has the "utmost respect" for Chinese culture, the Houston Chronicle reports. "I wrote my name on the wall in chalk. I saw different writings—I didn't mean any harm by it," he said. "I made a mistake. I could have just put my hand over it and erased it. It will never happen again." The state-run Beijing Youth Daily says "the Great Wall needs protection from both Chinese people and foreign tourists," and tourists who want to leave messages should use areas set up for that purpose. (This botched repair job did a lot more damage to the ancient wall.)

CHILDREN have been left screaming in terror after a fighter jet plunged from the sky, bursting into flames during a military airshow. Families watched on in horror as the jet ditched towards earth, sending a huge plume of flames and smoke into the air while performing stunts for the crowd. Pongsiri Thammaroekrit 5 The fighter jet went up in flames after crashing during an aerial show in Thailand The pilot, 34-year-old Group Captain Dilokrit Pattavee was killed in the crash, which happened in the southern city of Hat Yai during Thailand’s annual Children’s Day celebrations. It is understood that theRoyal Thai Air Force pilot was performing stunts in a Swedish-made JAS 39 Gripen jet when it crashed on Saturday morning. Defence ministry spokesman Major General Kongcheep Tantravanich told AFP: “One pilot was killed in the accident this morning.” Pongsiri Thammaroekrit 5 Hundreds of spectators screamed as a plume of smoke rose into the air Pongsiri Thammaroekrit 5 The jet, a Swedish-made 39C Gripen, was performing stunts for the Children’s Day SWNS:South West News Service 5 Group Captain Dilokrit Pattavee was killed in the crash during the Children’s Day air show Hundreds of people had gathered to see the aerial show on Saturday. In a video of the crash, the crowds can be heard screaming when flames are sent shooting into the air. Fire crews rushed to the site with flights diverted to the nearby Krabi airport. Stunned onlooker Penwipha Thuanthong said: ”It was scary. The poor pilot. I didn’t know if it was part of the show when he was flying towards the ground. “But he didn’t change direction then suddenly is killed. It was a tragedy. My children didn’t know what had happened and I had to explain to them. “He had been only married for a short time, life is just not fair.” RELATED STORIES MS804 MYSTERY Plane crash investigators in France examine theory that EgyptAir jet crashed after smartphone overheated ROAD DEATH TRAGEDY Teenager, 19, dies after Jaguar X-Type crashes into lamppost DEADLY MISTAKE Russian plane crash co-pilot ‘pulled the wrong lever' causing the overloaded plane to crash, killing 92 DOOMED FLIGHT Brit backpacker, 29, is killed and three others injured as tourist plane crashes on a remote Australian beach TEEN FIGHTS FOR LIFE 13-year-old lad in critical condition after suffering head injury in moped crash The Prime Minister has since expressed his condolences to the pilot, who was married three years ago, and his family. Authorities are now investigating just what happened with a separate committee reportedly set up to lead the inquiry. Pongsiri Thammaroekrit 5 The Prime Minister has now expressed his condolences for the family of the pilot killed in the crash No one else was injured in the crash. A Royal Thai Air Force spokesman said: “The Air Chief Marshal would like to express his deepest sorrow at the events that occurred. “The aircraft accident investigation unit and associated authorities in the area will investigate further to find out why this happened.” Thailand’s national Children’s Day is celebrated annually on the second Saturday of January. We pay for your stories! Do you have a story for The Sun Online news team? Email us at [email protected] or call 0207 782 4368

– A Thai air force pilot died when his fighter jet crashed at an air show Saturday during the country's Children's Day, the AP reports. Amateur video footage shows the JAS 39 Gripen jet maneuvering over the Hat Yai air base in southern Thailand when it suddenly lost altitude and crashed in a ball of fire away from spectators. The Ministry of Defense was investigating the cause of the crash. Deputy government spokesman Werachon Sukondhapatipakerachon said Prime Minister Prayuth Chan-ocha expressed condolences to the pilot's family. Children's Day is usually observed with public outings at military bases. The Sun says hundreds of spectators were in attendance.

A beetle and a fungus are killing off the trees that have become synonymous with the city, making way for trees that give more shade and use less water They are the sultry, swaying backdrop to countless films, posters and music videos, an effective way to announce: this is Los Angeles. Palm trees greet you outside the LAX airport, they line Hollywood Boulevard, stand guard over the Pacific and crisscross neighbourhoods poor and rich, a botanical army of stems and fronds which symbolise the world’s entertainment capital. Apparently not for much longer. LA’s palm trees are dying. And most won’t be replaced. A beetle known as the South American palm weevil and a fungus called Fusarium are killing palm trees across southern California. Others are dying of old age. “It’ll change the overall aesthetic because palm trees are so distinctive. It’s the look and feel of Los Angeles,” said Carol Bornstein, director of the nature gardens at the Natural History Museum of Los Angeles. A city tally in 1990 estimated the number of palms on city streets at 75,000, a number which has not been updated but is destined to plunge in coming decades, the Los Angeles Times reported this week, citing officials. No one knows how many will die, or how fast. For palm lovers, the even worse news is that they won’t be replaced, perhaps not even mourned. Authorities will instead plant other species that give more shade and consume less water – important factors for an overheating city. By the middle of the century, LA is expected to be three to five degrees fahrenheit warmer and to have triple the number of extreme heat days. “Palms are decorative and iconic, but Los Angeles is facing more and more heatwaves, so it’s important that we plant trees that provide adequate shade to protect people and cool the city down,” said Elizabeth Skrzat, programme director for City Plants, the city’s tree planting arm. History may record this as the moment La La Land put utility ahead of adornment. The city will continue to plant trees in certain designated areas, including Hollywood, and developers and homeowners will probably continue to plant palms. “I seriously doubt that palms will disappear entirely,” said Skrzat. Facebook Twitter Pinterest Becky Saava, a Ugandan tourist, on the Hollywood Walk of Fame. Photograph: Rory Carroll for the Guardian Even so, the looming die-off dismayed Becky Saava, 40, a tourist from Uganda who stood beneath giant palms on the Hollywood Walk of Fame. “They should sustain them – find out what fungus is killing them and fix it, leave the city the way it is now. Palm trees are part of it. They make the place so beautiful.” Across the street, Marcel Hidouche, a tour bus operator standing beneath another palm, said LA would rue their dwindling. “They’re relaxing. I feel like I’m on vacation, like I’m on an island and not in a big city. We come for the sunlight, not the shade.” The town of Fillmore, 50 miles north of Hollywood, has special reason to lament. In 2012 it cut down 26 queen palms to make its downtown resemble a more generic, anytown USA to lure film and TV productions. Only one species of palm – Washingtonia filifera, the California fan palm – is native to the state. All other species, from the exuberant, feather-topped Canary Island date palm to the more austere, svelte Mexican fan palm, are imports. Franciscan missionaries in the 18th century were believed to be the first to plant palms ornamentally in LA, a trend that took off in the early 20th century, when palms started adorning boulevards, parks and gardens. “It wasn’t the best choice of plants for a Mediterranean[-style] city. Especially one that has expanded so dramatically,” said Bornstein. David Fink, policy director of Climate Resolve, a not-for-profit organisation that promotes climate solutions for southern California, said the city’s love affair with palms was not necessarily a mistake but that it was time to move on. “The iconic association of palm trees with Los Angeles is a positive, but we’re now in a period where we have a better understanding of what’s needed. It makes sense that we replace the palms with trees that have wide expanses of shade and help cool things down.” Heat, he added, killed more people than other weather events combined. Facebook Twitter Pinterest Marcel Hidouche, a tour bus operator, on Hollywood Boulevard. Photograph: Rory Carroll for the Guardian Climate change has made California hotter and drier, a boon to bugs that destroy vegetation, said Andy Lipkis, the president of TreePeople, an LA-based advocacy group. Palms afforded LA little protection from heat, drought and flooding, plus they served as a habitat for the Norway rat, but their die-off signalled a wider crisis, he said. “It’s a wake-up call. Millions of trees are dying in southern California. One price tag for removing the dead trees over the next 30 years is $37bn. Trees have a much harder time growing and thriving in cities today because the climate is much harsher.” For all the advantages of other species, however, Lipkis said part of him would miss the palms. “Something that drives me crazy is people think of trees as decoration rather than life support. But I must admit there is something that they convey that goes along with the image,” he said in a phone interview. “I’m parked in a canyon right now watching four palms sway in the breeze. They don’t belong here, but there’s something a little bit good for the soul in the look.” ||||| Like so many things in Southern California, the palm tree was an import from somewhere else that over time became inextricably symbolic of its adopted home. But the trees, so identified with the sun-splashed excitement of Los Angeles, are facing a decidedly darker fate. They are dying of fatal fungus and under threat of invasive insects in parks and along streets. And for the most part, the city has chosen to replace them not with new palms but with native trees that are more drought-tolerant and shadier, said Leon Borodinsky, a tree surgeon for the department of Recreation and Parks. City officials say they don’t know how many palm trees have been lost. In 1990, a city tally put the number of palms on L.A.’s streets at 75,000. That number has declined, officials said, but they are not sure by how much. "Over the next 50 years, you will see a great loss in palms. It's already begun," added Jared Farmer, the author of Trees in Paradise. The decline in palm trees is part of a larger trend in L.A.’s treescape. In the next five years, the city will lose enough trees to disease and pests that it will take 30 to 50 years to replenish them, Borodinsky said. The loss of the palms is particularly noticeable because of their prominence in the city’s streetscape. In the 19th and early 20th centuries, Los Angeles decorated itself with a diversity of palms to enchant newcomers, Farmer said. The city imported its palm trees from all over the world, since only one species, the California fan palm, is native to the state. Palm trees dominate frontyards on Figueroa Street in this photo from 1890. (California Historical Society) Palm trees flourished in Los Angeles alongside the automobile and expansive freeways. "They came to represent the modern auto-based, decentralized metropolis that is L.A.," Farmer said. Hollywood sealed the deal as movies turned the palm tree into an internationally recognized symbol of Los Angeles. "Hollywood creates this connection between palm trees, celebrities, glamour, sex and extravagant riches," Farmer said.

– Invasive insects, fungus, and old age are killing off Los Angeles' iconic palm trees—and despite their fame. the city isn't planning on replacing many of them. As the city's estimated 75,000 palm trees die off, the city plans to replace them with species that consume less water and will help the city's people deal with the warming climate, the Guardian reports. "Palms are decorative and iconic, but Los Angeles is facing more and more heatwaves, so it’s important that we plant trees that provide adequate shade to protect people and cool the city down," says Elizabeth Skrzat of the city's tree-planting department. "Over the next 50 years, you will see a great loss in palms. It's already begun," Jared Farmer, author of Trees in Paradise, tells the Los Angeles Times. He says in the late early 20th century, the city imported palm species from all over the world, and they soon became the symbol of the expanding city. "Hollywood creates this connection between palm trees, celebrities, glamour, sex, and extravagant riches," he says. Environmentalists say the Los Angeles die-off is part of a wider crisis that is causing millions of trees to die across southern California as the state becomes hotter and drier, conditions in which bugs that destroy vegetation thrive.

results of the recent experiments @xcite on polarized electron - proton scattering , and their apparent disagreement @xcite with the electromagnetic form factors ( em ffs ) extracted from rosenbluth cross section measurements , indicate that much remains to be learned about nucleon em interactions . while a definitive understanding of the nucleon em ffs is still lacking , several theoretical models @xcite are able to describe their momentum - transfer dependence consistently with the jlab experiments @xcite . since the ultimate goal is to reach a coherent understanding of all aspects of the nucleon em interactions , important insights can be gained by describing as many different photon - nucleon reactions as possible in a unified theoretical approach . the dressed k - matrix model ( dkm ) @xcite has been developed for a description of real compton scattering in a wide energy region both below and above the pion production threshold . the central element of this model is a nonperturbative nucleon dressing based on the iterative use of dispersion relation , thus adding analyticity constraints to the properties of relativistic covariance , unitarity , crossing symmetry and gauge invariance of the usual k - matrix approaches . the parameters of the model are not entirely free : the convergence requirement of the dressing procedure imposes constraints on the allowed range of these parameters while introducing an interdependence among them . the thus constrained parameters were then completely fixed by a fit to compton cross sections and pion - nucleon ( @xmath0 ) phase shifts at intermediate energies @xcite . with all the parameters fully fixed , low - energy observables such as the nucleon polarizabilities @xcite , pion - nucleon scattering lengths and @xmath1-term @xcite were then calculated and shown to agree with experiment . the main reason for this success is that important analyticity ( causality ) constraints are implemented in dkm by the dressing of the @xmath2 , @xmath3 and @xmath4 vertices and of the nucleon and @xmath5 propagators with meson loops up to infinite order . the extent to which analyticity is fulfilled can be quantified by comparing the low - energy amplitudes with corresponding sum rules , both evaluated within the same model . within dkm , such a comparison was made for the baldin - lapidus and gerasimov - drell - hearn sum rules vs. the nucleon polarizabilities @xcite , and for the adler - weisberger and goldberger - miyazawa - oehme sum rules vs. the near - threshold @xmath0 amplitude @xcite . we generally found good agreement between the low - energy and sum - rule evaluations . in this report we extend the dressing procedure to the case of virtual space - like photons . the resulting dressed photon - nucleon ( @xmath2 ) vertex has six invariant functions depending on two invariant variables : the four - momenta squared of the photon and of one of the nucleons , the other nucleon being on - shell . by putting both nucleons on the mass shell we calculate the momentum - transfer dependence of the ratio of the proton em ffs . we find good agreement of our calculation with the jlab polarization - transfer measurements @xcite . the crucial point of this result is that the momentum - transfer dependence of the ratio of the ffs is calculated here with the the _ same _ parameters as used in refs . @xcite to describe the compton and @xmath0 amplitudes at low and intermediate energies . this shows that the dynamics of dkm captures features which are important in a wide kinematical range relevant to the photon - nucleon interactions . the most general lorentz - covariant structure of the @xmath2 vertex with an incoming off - shell photon ( four - momentum @xmath6 ) and an incoming off - shell nucleon ( four - momentum @xmath7 ) can be written as @xcite ^(p , q)= _ r= ( ^ f_1^r(p^2,q^2 ) + i f_2^r(p^2,q^2 ) + f_3^r(p^2,q^2 ) ) _ r(p / ) , where @xmath8 are the nucleon positive- and negative - energy projection operators , and the six invariant functions @xmath9 ( @xmath10 , @xmath11 ) are called half - off - shell ffs . the outgoing nucleon is on the mass shell , i. e. its four - momentum @xmath12 obeys @xmath13 . we consider protons interacting with real or virtual space - like photons , i. e. @xmath14 . the usual dirac and pauli ffs , denoted as @xmath15 and @xmath16 , respectively , are obtained by putting both the incoming and outgoing nucleons on the mass shell in : f_d , p(q^2 ) = _ p^2 m^2 f_1,2^+(p^2,q^2 ) . when the two nucleons are on - shell , @xmath17 do not enter the vertex since @xmath18 ; in addition , space - time reflection invariance requires @xcite that f_3^+(m^2,q^2)=0 . @xmath19 are related to the sachs ( electric and magnetic ) ffs @xmath20 by g_e(q^2)=f_d(q^2 ) + q^2 f_p(q^2 ) , g_m(q^2)=f_d(q^2 ) + f_p(q^2 ) . the @xmath2 vertex is calculated by dressing a bare vertex with an infinite number of meson loops including pions and vector isoscalar mesons . the @xmath3 and @xmath4 vertices and the nucleon and @xmath5 propagators , which enter in the loop integrals for the @xmath2 vertex , are also dressed nonperturbatively with pions , @xmath21 and @xmath22 mesons . the detailed description of the dressing technique for the @xmath2 vertex ( with real photons ) can be found in ref . @xcite , and for the @xmath3 , @xmath4 vertices and the propagators in ref . . this dressing is part of dkm @xcite where it amounts to restoring the principal - value parts of loop contributions to the compton and @xmath0 amplitudes . in the present work we have generalized the dressing procedure of ref . @xcite from real to virtual space - like photons in . thus we have calculated the six invariant functions @xmath9 for @xmath23 and @xmath14 , from which the momentum - transfer dependence of the em ffs has been obtained according to eqs . ( [ eq : diracpauli ] ) and ( [ eq : sachs ] ) . for brevity , in this report we will focus only on the important new features related to the off - shellness of the photon . we write the bare vertex as ^ + i _ b + h_b(q^2 ) . the renormalization consists in choosing the bare constant @xmath24 so that the dressed vertex with all particles on - shell reproduces the physical anomalous magnetic moment of the proton , i. e. @xmath25 , and adjusting @xmath26 so that the calculated function @xmath27 obeys . the ward - takahashi identity ( wti ) is a consequence of gauge invariance of the theory @xcite . it relates the @xmath2 vertex to the propagator @xmath28 of the off - shell proton : @xmath29 . thus the wti dictates that the half - off - shell ffs in must obey the following relations : f_1^+ ( p^2,q^2 ) & = & ( - 2 ( p^2 ) ( p^2 ) . + q^2 ) , + f_1 ^ -(p^2,q^2 ) & = & ( p^2 ) + q^2 , where the self - energy functions @xmath30 and @xmath31 enter into the dressed nucleon propagator @xmath32^{-1}}$ ] which was calculated together with the dressed @xmath5 propagator and @xmath3 and @xmath4 vertices @xcite . the renormalization conditions @xmath33 and @xmath34 can be explicitly written as ( m^2)(m-(m^2))=0 , 2 m ( m-(m^2 ) ) _ p^2=m^2- ( m^2)(2m_p^2=m^2 -1 ) = 1 . on expanding in powers of @xmath35 around @xmath36 and using eqs . ( [ eq : diracpauli ] ) , ( [ eq : pt_inv_f3pl ] ) , ( [ eq : ren_pole ] ) and ( [ eq : ren_res ] ) , we obtain the wti for the dirac ff of the proton : f_d(q^2 ) = 1 + q^2 ( 2 f_3^+(p^2,q^2 ) p^2 _ p^2=m^2 - ) , yielding the familiar constraint @xmath37 for an on - shell vertex with a real photon . note that we do not impose eqs . ( [ eq : wti_f1pl_off ] ) and ( [ eq : wti_f1mi_off ] ) by hand " at any stage of the dressing ; nevertheless , the resulting vertex does obey these constraints of the wti due to gauge invariance of the model . the ratio of the calculated proton em ffs is shown in as function of the photon momentum - squared , @xmath38 , together with the recent jlab measurements @xcite . we found that , in order to obtain accurate agreement with experiment over the wide range of momenta - transferred @xmath39 , the coupling of the vector isoscalar particle to the nucleon has to be different from the @xmath40 coupling given in ref . @xcite : while the part of the vertex proportional to @xmath41 is comparable to that of the @xmath40 vertex ( instead of @xmath42 as in @xcite , now we use @xmath43 ) , the part proportional to @xmath44 has to be quite large ( we need @xmath45 instead of @xmath46 ) . the other coupling constants are the _ same _ as in @xcite , i. e. as fixed in the description of the @xmath0 and compton scattering processes . it is important that even without the contribution of the vector isoscalar particle , we find the slope of the ratio of the ffs to be negative at @xmath47 , although in that case it is too steep . including the vector particle in the dressing makes the slope less steep . a negative slope of the ratio implies that the electric mean - square radius of the proton is larger that the magnetic mean - square radius normalized to the total magnetic moment , i. e. if . |_q^2=0 < 0 , then taking into account that @xmath48 , @xmath49 , and using the usual definitions of the mean - square radii . = -6 |_q^2=0 , we find > . note that the traditional one - photon exchange analyses of the rosenbluth cross sections would yield @xmath50 ( see , e. g. , ref . @xcite ) , which would imply equal electric and ( normalized ) magnetic radii , in sharp contrast to . we would also like to point out that the relation in is consistent with the well - known fact that the electric polarizability of the proton , @xmath51 , is larger than its magnetic polarizability , @xmath52 , _ _ m. thus one might speculate that the proton behaves as a larger " and hence more deformable " object in the presence of an electric field than in the presence of a magnetic field . since the mean - square radii are extracted from the momentum - transfer dependence of the ffs while the polarizabilities from compton scattering , the dressing procedure of dkm could provide a theoretical framework for understanding this ( possibly fortuitous ) similarity between eqs . ( [ eq : meanrads ] ) and ( [ eq : polaris ] ) . even though the ratio of the calculated ffs agrees with experiment very well as shown in , the model fails in describing @xmath53 and @xmath54 separately . this is demonstrated in for the electric ff . a possible remedy could be to use an appropriate ff in the bare @xmath2 vertex , which would introduce additional cut - off parameters . we have not done so in the present calculation since our aim is to keep the same model parameters as fixed in describing compton and @xmath0 scattering . in this way we impose a stringent dynamical constraint on the model . the dependence of the calculated @xmath2 vertex on the momentum - squared @xmath35 of the off - shell proton is illustrated in , where we show the @xmath35-dependence of the ratio of generalized ( half - off - shell ) sachs ffs which we define as g_e^gen(p^2,q^2)=f_1^+(p^2,q^2 ) + q^2 f_2^+(p^2,q^2 ) , g_m^gen(p^2,q^2)=f_1^+(p^2,q^2 ) + f_2^+(p^2,q^2 ) . the usual sachs ffs eqs . ( [ eq : sachs ] ) are obtained from eqs . ( [ eq : sachs_gen ] ) by taking the limit @xmath55 in accordance with . although the half - off - shell ffs are not measurable by themselves @xcite , they can be an important part of various models for physical processes . for example , a two - photon exchange contribution to electron - proton scattering contains @xmath2 vertices with an off - shell nucleon leg . so far the dependence of these vertices on the nucleon off - shell momentum has not been taken into account in the existing approaches @xcite . our calculation shown in suggests that this dependence may be significant . it should be borne in mind , however , that in view of the representation - dependence of the green s functions @xcite , the calculation of such off - shell vertices should be consistent with the model for the physical processes to which they are applied . in this report we extended the nonperturbative dressing procedure of the dressed k - matrix model ( dkm ) to calculate a @xmath2 vertex with an off - shell nucleon and an off - shell photon . the principal motivation for this work is to study the nucleon electromagnetic interactions in a dynamical approach which describes in a unified manner two distinct types of reactions : those where essential contributions come from an off - shell nucleon ( as in compton scattering ) and those where one probes the dependence on the momentum transferred by an off - shell photon ( as in form factors extracted from electron - proton scattering experiments ) . having previously applied dkm to compton and @xmath0 scattering , in this report we focused on the momentum - transfer dependence . we developed the dressing procedure to calculate the ratio of the proton electromagnetic form factors and found good agreement of our results with the recent jlab measurements . the main limitation of the present version of dkm is the difficulty in describing the momentum - transfer dependence of the individual form factors as accurately as their ratio . to resolve this problem , additional dynamical contents with attendant new parameters might be required in the model . rather than pursuing this direction in detail , we studied here to what extent one can describe the dependence of the nucleon em interactions on both the nucleon and photon variables using the _ same _ dynamical approach with a few predetermined parameters . our approach is based on essential symmetry constraints , including relativistic and gauge invariance , unitarity , crossing and causality , which are required in order to correlate in one model the very different kinematical regions explored in compton and @xmath0 scattering and in the proton form factors . we thank shmuel nussinov , ralf gothe , pawel mazur and peter blunden for useful discussions . this work was supported in part by the us national science foundation s grant no . one of the authors ( fm ) appreciates the support and hospitality of the nuclear theory group at bonn university . 99 m. k. jones _ et al . _ , ; o. gayou _ et al . _ , ; e. j. brash , a. kozlov , sh . li , and g. m. huber , . j. arrington , . m. r. frank , b. k. jennings , and g. a. miller , ; g. a. miller and m. r. frank , ; g. a. miller , . g. holzwarth , ; g. holzwarth , hep - ph/0201138 . e. l. lomon , . m. m. kaskulov and p. grabmayr , . s. dubnicka and a. z. dubnickova , hep - ph/0401081 . r. bijker and f. iachello , . s. kondratyuk and o. scholten , . s. kondratyuk and o. scholten , . s. kondratyuk , . s. kondratyuk and o. scholten , . s. kondratyuk , k. kubodera , f. myhrer , and o. scholten , . a. bincer , . j. d. bjorken and s. d. drell , _ relativistic quantum mechanics _ ( mcgraw - hill , 1964 ) . j. c. ward , ; y. takahashi , nuovo cimento , ser . 10 , * 6 * , 370 ( 1957 ) . j. arrington , hep - ph/0408261 . . fearing and s. scherer , . p. blunden , w. melnitchouk , and j. a. tjon , ; p. a. m. guichon and m. vanderhaegen , ; y. c. chen , a. afanasiev , s. j. brodsky , c. e. carlson , and m. vanderhaegen , ; m. p. rekalo and e. tomasi - gustafsson , nucl - th/0307066 . j. s. r. chisholm , ; r. haag , .

the dressed k - matrix model , developed previously for low- and intermediate - energy compton scattering , is generalized to calculate the photon - nucleon vertex with a virtual photon and an off - shell nucleon . using this model , the ratio of the proton electromagnetic form factors is computed . the calculated ratio is in excellent agreement with the ratio measured in polarized electron - proton scattering . # 1 # 1/ # 1 # 1 # 1#1 # 1eq . ( [ eq:#1 ] ) # 1[eq:#1 ] # 1fig . [ fig:#1 ] # 1[fig:#1 ] # 1table [ tab:#1 ] # 1[tab:#1 ] # 1section [ sec:#1 ] # 1[sec:#1 ] # 1#2#3*#1 * , # 3 ( # 2 ) # 1#2#3nucl . phys . # 1#2#3nucl . phys . a # 1#2#3nucl . phys . b # 1#2#3phys . lett . # 1#2#3phys . lett . b # 1#2#3phys . rev . # 1#2#3phys . rev . c # 1#2#3phys . rev . d # 1#2#3phys . rev . lett . # 1#2#3few - body sys . # 1#2#3ann . of phys . # 1#2#3z . phys . # 1#2#3z . phys .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Higher Education Tax Benefit Compliance Improvement Act''. SEC. 2. WAIVER OF PENALTIES FOR CERTAIN FAILURES RELATING TO INFORMATION RETURNS FOR HIGHER EDUCATION TUITION AND RELATED EXPENSES. (a) In General.--Section 6724 of the Internal Revenue Code of 1986 is amended by adding at the end the following new subsection: ``(f) Special Rules for Returns Related to Higher Education Tuition and Related Expenses.--Section 6721 shall not apply to any failure by an eligible educational institution (as defined in section 25A) to provide the TIN of an individual described in section 6050S(b)(2)(A) on any information return described in subsection (d)(1)(B)(xii) if the person required to file the return certifies under penalty of perjury that such person has complied with standards promulgated by the Secretary for obtaining the individual's TIN, unless it is shown that such certification is materially untrue.''. (b) Effective Date.--The amendment made by this section shall apply to returns filed after the date of the enactment of this Act. SEC. 3. PAYEE STATEMENT REQUIRED TO CLAIM CERTAIN EDUCATION TAX BENEFITS. (a) American Opportunity Credit, Hope Scholarship Credit, and Lifetime Learning Credit.-- (1) In general.--Subsection (g) of section 25A of the Internal Revenue Code of 1986 is amended by adding at the end the following new paragraph: ``(8) Payee statement requirement.--No credit shall be allowed under this section for any qualified tuition and related expenses paid by the taxpayer unless-- ``(A) the taxpayer has received a statement provided under section 6050S(d) which contains the TIN of the individual for whom a payment of qualified tuition and related expenses was made, or ``(B) in any case in which-- ``(i) the qualified tuition and related expenses are for a course for which academic credit is not offered by the eligible educational institution, or ``(ii) the eligible educational institution does not provide the taxpayer with a statement described in subparagraph (A) with respect to such qualified tuition and related expenses, the taxpayer maintains a record, in such form and manner as prescribed by the Secretary, showing the date and amount of the expenses.''. (2) Conforming amendment.--Paragraph (3) of section 25A(g) of such Code is amended by adding at the end the following flush sentence: ``For purposes of paragraph (8), a statement described in paragraph (8)(A) which is received by such individual shall be treated as received by such other taxpayer.''. (b) Deduction for Qualified Tuition and Related Expenses.-- (1) In general.--Subsection (d) of section 222 of the Internal Revenue Code of 1986 is amended by redesignating paragraph (6) as paragraph (7) and by inserting after paragraph (5) the following new paragraph: ``(6) Payee statement requirement.--No deduction shall be allowed under this section for any qualified tuition and related expenses paid by the taxpayer unless-- ``(A) the taxpayer has received a statement provided under section 6050S(d) which contains the TIN of the individual to whom a payment of qualified tuition and related expenses was made, or ``(B) in any case in which-- ``(i) the qualified tuition and related expenses are for a course for which academic credit is not offered by the eligible educational institution, or ``(ii) the eligible educational institution does not provide the taxpayer with a statement described in subparagraph (A) with respect to such qualified tuition and related expenses, the taxpayer maintains a record, in such form and manner as prescribed by the Secretary, showing the date and amount of the expenses.''. (2) Conforming amendment.--Paragraph (3) of section 222(c) of such Code is amended by adding at the end the following sentence: ``For purposes of paragraph (6), a statement described in paragraph (6)(A) which is received by such individual shall be treated as received by such other taxpayer.''. (c) Effective Date.--The amendments made by this section shall apply to taxable years beginning after the date of the enactment of this Act.

Higher Education Tax Benefit Compliance Improvement Act This bill amends the Internal Revenue Code to: (1) exempt an institution of higher education from tax penalties for failure to provide the tax identification number (TIN) of a person who claims a tax credit for tuition and related expenses if such institution certifies that it has complied with standards for obtaining the TIN, and (2) disallow the American Opportunity tax credit and the tax deduction for tuition and related expenses unless the taxpayer receives a payee statement containing the TIN of the individual claiming the credit or the deduction.

SECTION 1. SHORT TITLE. This Act may be cited as the ``Veterans' Educational Assistance Restoration Act of 2001''. SEC. 2. ELIGIBILITY FOR MONTGOMERY GI BILL BENEFITS OF CERTAIN ADDITIONAL VIETNAM ERA VETERANS. (a) Active Duty Program.--Section 3011(a)(1) of title 38, United States Code, is amended-- (1) by striking ``or'' at the end of subparagraph (A); (2) by adding ``or'' at the end of subparagraph (B); and (3) by adding at the end the following new subparagraph: ``(C) as of December 31, 1989, is eligible for educational assistance benefits under chapter 34 of this title and-- ``(i) was not on active duty on October 19, 1984; ``(ii) reenlists or reenters on a period of active duty after the date specified in clause (i); and ``(iii) after July 2, 1985, either-- ``(I) serves at least three years of continuous active duty in the Armed Forces; or ``(II) is discharged or released from active duty (aa) for a service- connected disability, for a medical condition which preexisted such service on active duty and which the Secretary determines is not service connected, for hardship, or for a physical or mental condition that was not characterized as a disability, as described in subparagraph (A)(ii)(I) of this paragraph, (bb) for the convenience of the Government, if the individual completed not less than 30 months of continuous active duty after that date, or (cc) involuntarily for the convenience of the Government as a result of a reduction in force, as determined by the Secretary of the military department concerned in accordance with regulations prescribed by the Secretary of Defense or by the Secretary of Transportation with respect to the Coast Guard when it is not operating as a service in the Navy;''. (b) Selected Reserve Program.--Section 3012(a)(1) of that title is amended-- (1) by striking ``or'' at the end of subparagraph (A); (2) by adding ``or'' at the end of subparagraph (B); and (3) by adding at the end the following new subparagraph: ``(C) as of December 31, 1989, is eligible for educational assistance under chapter 34 of this title and-- ``(i) was not on active duty on October 19, 1984; ``(ii) reenlists or reenters on a period of active duty after the date specified in clause (i); and ``(iii) after July 2, 1985-- ``(I) serves at least two years of continuous active duty in the Armed Forces, subject to subsection (b) of this section, characterized by the Secretary concerned as honorable service; and ``(II) subject to subsection (b) of this section and beginning within one year after completion of such two years of service, serves at least four continuous years in the Selected Reserve during which the individual participates satisfactorily in training as prescribed by the Secretary concerned;''. (c) Time for Use of Entitlement.--Section 3031 of that title is amended-- (1) in subsection (a)-- (A) by striking ``and'' at the end of paragraph (1); (B) by striking the period at the end of paragraph (2) and inserting ``; and''; and (C) by adding at the end the following new paragraph: ``(3) in the case of an individual who becomes entitled to such assistance under section 3011(a)(1)(C) or 3012(a)(1)(C) of this title, on the date of the enactment of this paragraph.''; and (2) in subsection (e)(1), by striking ``section 3011(a)(1)(B) or 3012(a)(1)(B)'' and inserting ``section 3011(a)(1)(B), 3011(a)(1)(C), 3012(a)(1)(B), or 3012(a)(1)(C)''.

Veterans' Educational Assistance Restoration Act of 2001 - Makes eligible for educational assistance benefits under the Montgomery GI Bill an individual who: (1) was not on active duty on October 19, 1984; (2) reenlists or reenters into active duty after such date; and (3) after July 2, 1985, either serves at least three years of continuous active duty or is discharged or released for a service-connected disability, preexisting medical condition, hardship, or a physical or mental condition for the convenience of the Government, as long as such individual completed not less than 30 months of continuous active duty on that date; or (4) is involuntarily released at the convenience of the Government due to a reduction in force. Makes eligible for such assistance a member of the Selected Reserve who: (1) was not on active duty on October 19, 1984, (2) reenlists or reenters active duty after such date; and (3) after July 2, 1985, serves at least two years of continuous active duty and at least four continuous years in the Selected Reserve during which the individual participates satisfactorily in required training.

binary black holes have been the subject of numerous studies in the past two decades , both from the analytical and numerical point of view . these studies are motivated by the fact that the coalescence of two black holes is expected to be one of the strongest sources of gravitational waves detectable by the interferometric detectors ligo , geo600 , tama300 and virgo , currently coming on - line @xcite . from the analytical point of view , the most recent works are based on the post - newtonian formalism ( see e.g. ref . @xcite for a review ) or on the effective one - body approach developed by buonanno and damour @xcite . in these works , the black holes are treated as point mass particles , which is a very good approximation when the black holes are far apart . for closer configurations , one may turn instead to some numerical approach . the numerical studies can be divided in two classes : ( i ) the initial value problem for two black holes ( see ref . @xcite for a review ) and ( ii ) the time evolution of the initial data ( see ref . @xcite for a review and refs . @xcite for recent results ) . one of the major problems in this respect is to get physically relevant initial data . indeed , initial data representing two black holes have been obtained long ago by misner @xcite and lindquist @xcite , as well as brill and lindquist @xcite ( a modern discussion of these solutions can be found in ref . @xcite or appendices a and b of ref . . however these solutions correspond to two momentarily _ static _ black holes and are therefore far from representing some stage in the evolution of an isolated binary black hole in our universe . based on the seminal work of bowen and york @xcite , kulkarni , shepley and york @xcite have described a procedure to get initial data representing binary black hole with arbitrary positions , masses , spins and momenta . this procedure , known as _ conformal imaging _ , has been used by cook and other authors @xcite to numerically construct 3-dimensional spacelike hypersurfaces representing these initial data . these solutions constitute some generalization to the non - static regime of the misner - lindquist solution @xcite , the spacelike hypersurface having the same topology : two isometric asymptotically - flat sheets connected by two einstein - rosen bridges . also based on the bowen and york s work @xcite , another approach , the so - called _ puncture method _ , has been undertaken by brandt and brgmann @xcite and used recently by baumgarte @xcite . the resulting solutions also have arbitrary positions , masses , spins and momenta but their topology is different from that of the conformal - imaging approach : the spacelike hypersurface has now _ three _ asymptotically - flat sheets , which are not isometric . these three sheets are connected among themselves by two einstein - rosen bridges ; one of the sheets contains two throats and is supposed to represent our universe . these solutions hence constitute some generalization to the non - static case of the brill - lindquist solution @xcite . both the conformal - imaging and the puncture approaches assume that the metric of the spacelike hypersurface is conformally flat . a third approach to the problem relaxes this assumption ; it has been developed recently by matzner , maroronetti and collaborators @xcite . these authors use a linear combination of two boosted kerr - schild metrics as the conformal 3-metric in york s treatment of initial conditions @xcite . the main drawback of the three approaches described above is that they contain freely specifiable parameters , related to the values of positions , momenta and spins of the black holes , and it is difficult to figure out which parameters correspond to a physical configuration . in particular , it is not obvious at all how to select , among all these configurations , those that correspond to binary black holes on closed circular orbits . of course , the circular orbits are approximate representations of the exact orbital motion , which is inspiralling due to the loss of energy and angular momentum via gravitational radiation . however in the regime where the radiation reaction time scale is much longer than the orbital time scale , i.e. before the last stable orbit , we expect that the binary system can be approximated by a sequence of tighter and tighter circular orbits . note that the gravitational radiation reaction makes initially elliptic orbits become circular @xcite . it is thus legitimate to search for such orbits . this problem has been addressed by cook @xcite and pfeiffer et al . @xcite within the conformal - imaging approach and by baumgarte @xcite within the puncture approach ( see e.g. @xcite for a review of these computations ) . although they differ in the topology of the spacelike hypersurface ( two - sheeted for @xcite against three - sheeted for @xcite ) , both sets of studies rely on the _ effective - potential method _ proposed by cook @xcite . this method amounts to defining the binding energy by a somewhat ad - hoc formula , and to define the angular velocity of a circular orbit by minimizing the binding energy with respect to the angular momentum at fixed total energy and separation . this method can be criticized on the following ground : the only well defined global quantities on an asymptotically flat spacelike hypersurface are the adm total mass @xmath0 and adm total linear momentum . the latter can be chosen to be zero without any loss of generality . with some restrictions on the asymptotic gauge , the total angular momentum @xmath1 can also be defined @xcite . defining the binding energy would require the notion of individual mass for each hole , let say @xmath2 and @xmath3 , in order to set @xmath4 . however there does not exist any unique definition of the individual masses @xmath2 and @xmath3 for a binary black hole . in refs . @xcite the authors define @xmath2 and @xmath3 via the formula which relates the mass of a kerr black hole to its horizon area and its angular momentum . however such a formula is strictly demonstrated only for a isolated rotating black hole ( kerr spacetime ) . in particular , it does not take into account any tidal effect . our approach for finding circular orbits of binary black holes is very different : instead of considering 3-dimensional spacelike hypersurfaces , we adopt from the very beginning a 4-dimensional point of view , i.e. we consider a full spacetime containing two moving black holes . of course , in order to make the problem tractable , we introduce some approximations , the most significant being the assumption of strictly circular orbits , which amounts to endowing our spacetime with a killing vector field ( helical symmetry ) . an interesting pay - off is that the orbital angular velocity @xmath5 can be unambiguously defined as the rotation rate of the killing field with respect to some asymptotically inertial observers . this definition does not suffer from the ambiguity of the 3-dimensional approaches and is made possible only because we have re - introduced _ time _ in the problem . the presentation of this new approach is organized as follows . we set up the problem in sec . [ s : formulation ] , starting from the explicit construction of the spacetime manifold , introducing a metric , as well as a corresponding isometry on it , and finally imposing the helical symmetry . the einstein equations are then considered in sec . [ s : einstein ] , first in their general form and then after the assumption of a conformally flat 3-metric . global quantities such as the adm mass and the total angular momentum are discussed in this section , as well as the virial prescription for the orbital velocity . section [ s : asymptotic ] deals with the asymptotic behavior of the shift vector and the extrinsic curvature tensor and discusses the connection between helical symmetry and asymptotic flatness . finally sec . [ s : conclu ] contains the concluding remarks . we consider the spacetime to be a differentiable manifold @xmath6 with the topology of the real line @xmath7 times the misner - lindquist manifold @xcite . more precisely , for any couple of positive numbers @xmath8 and any couple of real numbers @xmath9 such that @xmath10 , let us consider the subset of @xmath11 obtained by removing the interior of balls of radius @xmath12 and @xmath13 and center @xmath14 and @xmath15 : : = \ { ( x , y , z ) , ( x - x_1)^2 + y^2 + z^2 a_1 ^ 2 ( x - x_2)^2 + y^2 + z^2 a_2 ^ 2 } . let us call @xmath16 and @xmath17 the 2-spheres defining the `` inner '' boundaries of @xmath18 : s_1 : = \ { ( x , y , z ) ^3 , ( x - x_1)^2 + y^2 + z^2 = a_1 ^ 2 } , s_2 : = \ { ( x , y , z ) ^3 , ( x - x_2)^2 + y^2 + z^2 = a_2 ^ 2 } . let us consider two copies @xmath19 and @xmath20 of @xmath18 and define @xmath21 and @xmath22 . the spacetime manifold @xmath6 is be then defined as the union @xmath23 with both @xmath16 and @xmath17 of each copy identified ( see fig . [ f : manifold ] ) . the reader is referred to sect . iv of ref . @xcite or sect . ii of ref . @xcite for a precise construction of the manifold structure in the vicinity of @xmath16 and @xmath17 . the part @xmath24 of @xmath6 will be designed hereafter as the _ upper space _ and the part @xmath25 as the _ lower space_. the boundaries @xmath26 and @xmath27 between @xmath24 and @xmath25 are called respectively _ throat 1 _ and _ throat 2_. hereafter we label by @xmath28 the points of @xmath24 considered as a part of @xmath29 ( @xmath19 being a part of @xmath30 ) , and by @xmath31 the points of @xmath25 considered as a part of @xmath29 . the corresponding two charts will be called the _ canonical coordinate systems_. these two charts cover @xmath6 minus the two throats . the whole manifold @xmath6 can be covered entirely by a single coordinate system : cccl c_1 : & m & & ^4 + & p & & \ { ll ( t , x_i , y_i , z_i ) & if p _ i + i_1(t , x_ii , y_ii , z_ii ) & if p _ ii . , where @xmath32 denotes the inversion through the 2-sphere @xmath16 : _ 1(t , x , y , z ) = ( t , a_1 ^ 2 ( x - x_1 ) ( x - x_1)^2 + y^2 + z^2 + x_1 , a_1 ^ 2 y ( x - x_1)^2 + y^2 + z^2 , a_1 ^ 2 z ( x - x_1)^2 + y^2 + z^2 ) . in a similar way , one can introduce the coordinate system @xmath33 associated with throat 2 . in the coordinate system @xmath34 or @xmath33 , the throats are not located at constant coordinate values . therefore , it is more convenient to introduce instead the polar coordinate system @xmath35 centered on throat 1 , as follows : @xmath36 and @xmath37 the throat 1 corresponds to @xmath38 . the polar coordinate system @xmath39 centered on throat 2 is introduced similarly . note that any of the two coordinate systems @xmath35 and @xmath39 covers the whole spacetime manifold @xmath6 . for the @xmath35 system , @xmath40 corresponds to @xmath41 and @xmath42 to @xmath43 . similarly , for @xmath39 system , @xmath40 corresponds to @xmath44 and @xmath42 to @xmath45 ( see fig . [ f : manicoord ] ) . from the very construction of @xmath6 , we have at our disposal the canonical mapping ( see fig . [ f : manifold ] ) [ e : def_i ] lccc i : & m_i & & m_ii + & ( t , x_i , y_i , z_i ) & & ( t = t , x_ii = x_i , y_ii = y_i , z_ii = z_i ) note that in terms of the @xmath35 coordinate system , this map can be written as an inversion through the sphere @xmath46 ( see fig . [ f : manicoord ] ) : [ e : i(r1 ) ] i(t , r_1,_1,_1 ) = ( t , a_1 ^ 2r_1 , _ 1 , _ 1 ) . in terms of the @xmath39 coordinate system , it looks like an inversion as well : [ e : i(r2 ) ] i(t , r_2,_2,_2 ) = ( t , a_2 ^ 2r_2 , _ 2 , _ 2 ) . let @xmath47 be a coordinate system on @xmath24 [ for instance @xmath48 , @xmath49 or @xmath50 and @xmath51 be a coordinate system on @xmath25 [ for instance @xmath52 , @xmath53 or @xmath54 . the map @xmath55 is fully characterized by its components @xmath56 with respect to the coordinates @xmath47 and @xmath51 : the image @xmath57 of a point @xmath58 with coordinates @xmath59 has the coordinates y^= i^(x^0,x^1,x^2,x^3 ) . let us now examine the action of the map @xmath55 on various fields on @xmath6 . if @xmath60 is a scalar field on @xmath25 , @xmath55 induces a scalar field on @xmath24 through [ e : def_i_fonct ] i _ * f : = f i , i.e. i_*f[p ] = f[i(p ) ] , for any point @xmath61 of @xmath24 . also @xmath55 maps any vector field @xmath62 on @xmath24 to a vector field @xmath63 on @xmath25 through [ e : def_i_vect ] i_*(f ) : = ( i _ * f ) , for any scalar field @xmath60 on @xmath25 . if vectors are represented by their components with respect to the coordinate bases @xmath64 and @xmath65 , one has i_*(f ) = ( i_*)^ and , according to definitions ( [ e : def_i_vect ] ) and ( [ e : def_i_fonct ] ) , i_*(f ) = v^ f ( i^(x^ ) ) = v^ . hence the matrix of the mapping @xmath66 between vectors on @xmath24 and vectors on @xmath25 is given by the jacobian matrix of @xmath55 : [ e : i_vect_jacob ] ( i_*)^= i^x^ v^ , where @xmath61 denotes any point of @xmath24 . the action of @xmath55 on vectors can be used to define the action of @xmath55 on 1-forms as follows : @xmath55 maps any 1-form @xmath67 on @xmath25 to a 1-form @xmath68 on @xmath24 through [ e : def_i_form ] i _ * ( ) : = ( i _ * ) , for any vector field @xmath62 on @xmath24 . if 1-forms are represented by their components with respect to the coordinate bases @xmath69 and @xmath70 , one has [ e : i_form_1 ] i _ * ( ) = ( i_*)_dx^ ( ) = ( i_*)_v^and , according to definition ( [ e : def_i_form ] ) , [ e : i_form_2 ] i _ * ( ) = _ dy^(i _ * ) = _ ( i_*)^ = _ v^ , where the third equality arises from eq . ( [ e : i_vect_jacob ] ) . comparing eqs . ( [ e : i_form_1 ] ) and ( [ e : i_form_2 ] ) leads to ( i_*)_= i^x^ _ at any point @xmath61 in @xmath24 . similarly , the action of @xmath55 on bilinear forms can be defined as follows : @xmath55 associates any bilinear form @xmath71 on @xmath25 to a bilinear form @xmath72 on @xmath24 according to [ e : def_i_bilin_comp ] i _ * ( , ) : = ( i_*,i _ * ) . one can show easily that in terms of the components with respect to the coordinate bases @xmath73 and @xmath74 , [ e : i_bilin_comp ] ( i _ * ) _ [ p ] = i^x^ i^x^ t_[i(p ) ] at any point @xmath61 in @xmath24 . we endow @xmath6 with a lorentzian metric @xmath75 with the following properties : \(1 ) @xmath75 is asymptotically flat at the ends of @xmath24 and @xmath25 : @xmath76 where @xmath77 is a flat metric . \(2 ) the canonical mapping @xmath55 is an isometry of @xmath75 : [ e : isometrie ] i _ * = . \(3 ) the @xmath78 sections of @xmath6 are maximal spacelike hypersurfaces with respect to @xmath75 . the assumption ( 1 ) is introduced because we consider only isolated systems . its connection with the quasi - stationarity hypothesis will be discussed in secs . [ s : hel_killing ] and [ s : non_flat ] . the assumption ( 2 ) is motivated by the fact that the schwarzschild and kerr spacetimes possess such an isometry . this can be readily seen when using isotropic ( quasi - isotropic for kerr ) coordinates instead of the standard schwarzschild ( boyer - lindquist ) ones . by virtue of eq . ( [ e : i_bilin_comp ] ) , the isometry condition ( [ e : isometrie ] ) can be expressed in terms of the components of @xmath75 at any point @xmath61 in @xmath24 : [ e : isometrie_g_cov ] i^x^ i^x^ g_[i(p ) ] = g_[p ] . it is also useful to write the isometry condition on the contravariant components of the metric tensor ; by means of a generalization of eq . ( [ e : i_vect_jacob ] ) , one gets : [ e : isometrie_g_contra ] g^ [ i(p ) ] = i^x^ i^x^ g^ [ p ] . the assumption ( 3 ) is motivated by the well - known good properties of maximal slicing @xcite , among which there is the singularity avoidance . in this article we use the standard 3 + 1 formalism of general relativity @xcite , foliating the spacetime by a family of spacelike hypersurfaces . from the very construction of @xmath6 , a natural foliation is by the @xmath79 hypersurfaces @xmath80 , where @xmath81 is the same coordinate as that introduced above . by virtue of assumption ( 3 ) , this constitutes a maximal slicing of spacetime . let us denote by @xmath82 the future directed unit normal to @xmath80 . being normal to @xmath80 , @xmath82 should be collinear to the gradient of @xmath81 : [ e : def_lapse ] = - n t , where @xmath83 is the _ lapse function _ , which can be seen as a normalization factor such to ensure that @xmath84 . let us now examine the behavior of @xmath82 under the isometry @xmath55 . by the definition ( [ e : def_i ] ) , @xmath55 preserves the hypersurface @xmath80 . according to the definition ( [ e : def_i_bilin_comp ] ) , the square of the norm of @xmath85 is ( i_*,i _ * ) = ( i _ * ) ( , ) . but thanks to the isometry condition @xmath86 , the last term in this equation is simply @xmath87 . hence i_*i _ * = - 1 , i.e. @xmath55 preserves the norm of @xmath82 . similarly , for any vector @xmath62 tangent to @xmath80 , @xmath55 preserves the scalar product @xmath88 , so that @xmath89 . but since @xmath80 is globally invariant under @xmath55 , @xmath63 represents any vector tangent to @xmath80 , so that @xmath85 is in fact normal to @xmath80 . having the same norm than @xmath82 , we conclude that [ e : i_n ] i _ * = . since @xmath81 , considered as a scalar field on @xmath6 , is preserved by @xmath55 , so is its gradient and the relation ( [ e : def_lapse ] ) , combined with ( [ e : i_n ] ) results then in the following transformation law for the lapse function : [ e : i_lapse ] i _ * n = n . in order to understand the significance of the @xmath90 sign in eqs . ( [ e : i_n ] ) and ( [ e : i_lapse ] ) , let us consider the case of a single static black hole , i.e. the ( extended ) schwarzschild spacetime . two kinds of maximal slicing of this spacetime are depicted in a kruskal diagram in fig . [ f : kruskal ] , starting from the same initial hypersurface @xmath91 . the first one corresponds to a symmetric lapse [ sign @xmath92 in eqs . ( [ e : i_lapse ] ) and ( [ e : i_n ] ) ] . the throat is located at @xmath93 ; the slicing penetrates under the event horizon ( @xmath94 ) , and accumulates on the spacelike hypersurface @xmath95 @xcite . the second slicing corresponds to an antisymmetric lapse [ sign @xmath96 in eqs . ( [ e : i_lapse ] ) and ( [ e : i_n ] ) ] . in fact , it corresponds to the standard schwarzschild solution in isotropic coordinates : [ e : ds2_schwarz ] ds^2 = - n^2 dt^2 + ( 1 + m2r ) ^4 , with [ e : n_schwarz ] n = 1 - m/2r 1 + m/2r . this lapse function is clearly antisymmetric under the transformation @xmath97 across the throat located at @xmath98 . the negative value of the lapse for @xmath99 is easily understandable when looking to fig . [ f : kruskal ] : while @xmath81 is running upward on the right part of the diagram ( corresponding to @xmath24 ) , it is running downward on the left part ( corresponding to @xmath25 ) . since in the kruskal diagram the future direction is everywhere upward , the lapse should be negative in @xmath25 . let us now consider a coordinate system @xmath100 on each @xmath80 . for instance , it can be chosen in one of the three coordinate atlas introduced so far : @xmath101 , @xmath102 and @xmath103 . @xmath104 constitutes then a coordinate system on @xmath6 . the _ shift vector _ @xmath105 associated with the coordinates @xmath104 is defined by the following orthogonal split of the coordinate basis vector @xmath106 : [ e : def_beta ] t = n + = 0 . since the transformation @xmath55 is purely spatial @xmath106 is preserved by it . by virtue of eqs . ( [ e : i_n ] ) and ( [ e : i_lapse ] ) , the product @xmath107 is also invariant with respect to @xmath55 . consequently [ e : i_beta ] i _ * = . the 3-metric induced by @xmath75 on the hypersurfaces @xmath80 is = + . from eqs . ( [ e : isometrie ] ) and ( [ e : i_n ] ) , we obtain immediately that @xmath55 is also an isometry for the 3-metric @xmath108 : [ e : i_gamma ] i _ * = . the components of the metric tensor can be expressed in terms of the lapse function and the components of the shift vector and the 3-metric , according to the classical formula [ e : metric_3p1 ] g _ dx^dx^= -(n^2 - _ i ^i ) dt^2 + 2_i dt dx^i + _ ij dx^i dx^j . the extrinsic curvature tensor @xmath109 of the hypersurface @xmath80 is given by the lie derivative of the 3-metric along the flow defined by the normal to @xmath80 : [ e : def_extr_curv ] = -12 _ . by the symmetry properties ( [ e : i_n ] ) and ( [ e : i_gamma ] ) , we obtain that [ e : i_k ] i _ * = . in what follows , we consider only polar coordinate systems centered on one of the two throats , i.e. either the system @xmath35 introduced in sec . [ s : construct ] or @xmath39 . for the sake of clarity we will drop the indices @xmath110 or @xmath111 on @xmath112 , @xmath113 and @xmath114 . it should be understood that the formulas will be valid for either coordinate system . the jacobian matrix of @xmath55 with respect to @xmath115 is easily deduced from eq . ( [ e : i(r1 ) ] ) or ( [ e : i(r2 ) ] ) : = ( 1 , -a^2r^2 , 1 , 1 ) , where @xmath116 denotes either @xmath12 or @xmath13 . from the isometry condition ( [ e : isometrie_g_contra ] ) expressed on @xmath117 , we get , since @xmath118 : [ e : isom_expl_n ] n[i(p)]^2 = n[p]^2 , for any point point @xmath61 in @xmath24 , i.e. we recover the already established relation ( [ e : i_lapse ] ) . from the isometry condition ( [ e : isometrie_g_contra ] ) expressed on @xmath119 we get @xmath120 & = & - { a^2\over r^2 } \beta^r[p ] \label{e : i_beta_r } \\ \beta^\theta[i(p ) ] & = & \beta^\theta[p ] \label{e : i_beta_t } \\ \beta^\varphi[i(p ) ] & = & \beta^\varphi[p ] \ , \label{e : i_beta_p}\end{aligned}\ ] ] where we have used @xmath121 and eq . ( [ e : isom_expl_n ] ) to go from @xmath119 to @xmath122 . again note that we recover the isometry condition ( [ e : i_beta ] ) . finally the isometry condition ( [ e : isometrie_g_cov ] ) expressed on @xmath123 results in @xmath124 & = & { a^4\over r^4 } \gamma_{rr}[i(p ) ] \label{e : iso_grr}\\ \gamma_{r\theta}[p ] & = & - { a^2\over r^2 } \gamma_{r\theta}[i(p ) ] \label{e : iso_grt}\\ \gamma_{r\varphi}[p ] & = & - { a^2\over r^2 } \gamma_{r\varphi}[i(p ) ] \label{e : iso_grp } \\ \gamma_{\theta\theta}[p ] & = & \gamma_{\theta\theta}[i(p ) ] \label{e : iso_gtt}\\ \gamma_{\theta\varphi}[p ] & = & \gamma_{\theta\varphi}[i(p ) ] \label{e : iso_gtp}\\ \gamma_{\varphi\varphi}[p ] & = & \gamma_{\varphi\varphi}[i(p ) ] \label{e : iso_gpp } \ .\end{aligned}\ ] ] comparing eqs . ( [ e : isometrie ] ) and ( [ e : i_k ] ) , we see that the isometries properties of the components @xmath125 of @xmath109 are the same as those above for @xmath126 , except possibly for an opposite sign . as discussed above , the behavior of the foliation with respect to the isometry @xmath55 involves a @xmath92 or @xmath96 sign in the transformation rules of the unit normal [ eq . ( [ e : i_n ] ) ] , lapse function [ eq . ( [ e : i_lapse ] ) ] and extrinsic curvature [ eq . ( [ e : i_k ] ) ] . in this article , we choose the sign to be the minus one . this is motivated by the fact that the maximal slicing with the @xmath92 sign of the schwarzschild spacetime ( left part of fig . [ f : kruskal ] ) does not respect the stationarity of the problem , i.e. the killing vector @xmath106 of schwarzschild geometry does not carry a slice of that foliation into another slice @xcite ( see also sec . iv of ref . @xcite ) . on the contrary , the slicing with the @xmath96 sign ( right part of fig . [ f : kruskal ] ) respects the stationarity of the problem . it seems to us more appealing to use a slicing which in the case of a single black hole , makes the problem time - independent . we regard the artificial time dependence resulting from the @xmath92 sign as an unnecessary complication . beside simplicity , another advantage of the @xmath96 sign choice is to allow us to test the numerical code by comparison with the standard form of the schwarzschild or kerr metric in the special case of a single black hole . thus , from now on , we set [ e : i_n_minus ] i _ * = - , [ e : i_lapse_minus ] i _ * n = - n , and [ e : i_k_minus ] i _ * = - . ( [ e : i_lapse_minus ] ) can be explicited for any point @xmath61 in @xmath24 : [ e : i_lapse_minus_expl ] n[i(p ) ] = - n[p ] , which amounts to choosing the @xmath96 sign when taking the square root of eq . ( [ e : isom_expl_n ] ) . an immediate consequence of eq . ( [ e : i_lapse_minus_expl ] ) is that the lapse function vanishes on the two throats : [ e : lapse_zero_throat ] n|_s_1 = 0 n|_s_2 = 0 . indeed from the very definition of @xmath55 [ eq . ( [ e : def_i ] ) ] and the construction of @xmath6 by identifications of the two copies of @xmath127 or @xmath128 , every point @xmath61 in @xmath127 or @xmath128 is a fixed point for @xmath55 . hence eq . ( [ e : i_lapse_minus_expl ] ) results in @xmath129 = - n[p]$ ] on @xmath127 and @xmath128 . similarly , eq . ( [ e : i_beta_r ] ) implies that the @xmath112 component of the shift vector vanishes on the throats : [ e : shift_r_zero_throat ] . ^r_1 | _ s_1 = 0 . ^r_2 | _ s_2 = 0 . taking the first derivatives of eqs . ( [ e : i_beta_r])-([e : i_beta_p ] ) , we get the additional following relations on the throats , as a consequence of the isometry of the shift vector : @xmath130 where we have dropped the indices 1 or 2 on @xmath112 , @xmath113 , @xmath114 and @xmath131 . note that relations ( [ e : dbr / dt_s ] ) and ( [ e : dbr / dp_s ] ) could have been obtained also as consequences of eq . ( [ e : shift_r_zero_throat ] ) since the throats are located at a constant value of the coordinate @xmath112 . equations ( [ e : iso_grr])-([e : iso_gpp ] ) and their first derivatives give the following values for the 3-metric on the throats : @xmath132 as a direct consequence of the isometry hypothesis , the throats @xmath16 and @xmath17 are minimal 2-surfaces of the spatial hypersurface @xmath80 . moreover , as shown by cook & york @xcite , the fact that @xmath109 is antisymmetric with respect to the isometry @xmath55 [ eq . ( [ e : i_k_minus ] ) ] implies that @xmath16 and @xmath17 are apparent horizons . as discussed in sect . [ s : intro ] , we consider binary black holes in the quasi - steady stage , i.e. prior to any orbital instability , so that the notion of closed circular orbits is meaningful . following detweiler @xcite , we translate these assumptions in terms of the spacetime geometry by demanding that there exists a killing vector field @xmath133 such that , near spacelike infinity , [ e : helical ] + _ 0 , where @xmath134 and @xmath135 are respectively the time coordinate and the azimuthal coordinate associated with an asymptotically inertial observer , and @xmath5 is a constant , representing the orbital angular velocity with respect to the asymptotically inertial observer . let us call @xmath133 the _ helical killing vector_. we refer the reader to @xcite for a detailed description of this concept . the helical symmetry amounts to neglecting outgoing gravitational radiation in the dynamics of spacetime . for non - axisymmetric systems as binaries are it is well known that imposing @xmath133 as an exact killing vector leads to a spacetime which is not asymptotically flat @xcite . in sec . [ s : non_flat ] , we will exhibit explicitly how the deviation from asymptotical flatness arises . however , from a physical point of view , the exact helical symmetry is too strong an assumption because it assumes that the binary system is rotating on a fixed orbit since the past time infinity . doing so , it has filled the entire space with gravitational waves , such that their total energy is a diverging quantity , whence the impossibility of asymptotic flatness . a weaker assumption , which is compatible with asymptotic flatness and sounds physically more reasonable , is the following one . due to the reaction to gravitational radiation the binary system is in fact spiraling . therefore in the past time infinity , it was infinitely separated . as a consequence , the amount of emitted gravitational waves was very weak . the integral of their energy density is now a converging quantity , which allows for asymptotic flatness . the quasi - stationarity hypothesis should then be understood as imposing a helical killing vector on a part of spacetime _ limited in time_. it is natural to demand that the isometry associated with the killing vector @xmath133 preserves , not only @xmath136 as a whole , but also the sub - structure of @xmath6 defined by @xmath24 , @xmath25 and the two throats . this amounts to demanding that for any of the coordinates system @xmath104 introduced above , where @xmath81 is the coordinate used explicitly in the construction of @xmath6 , [ e : l = d / dt ] = t . the above equality means that @xmath81 is an ignorable coordinate . it does not mean that the problem is stationary in the usual sense of this word , for @xmath133 is not timelike at spatial infinity : by virtue of relation ( [ e : helical ] ) , @xmath137 when @xmath138 . the above geometrical assumptions are intended to correspond to a physical system of two black holes in a quasi - steady state . we have not specified yet the rotation state ( spin ) of each black hole . in this article , we consider _ synchronized _ ( or _ corotating _ ) black holes . this rotation state can be translated geometrically by demanding that the two throats be _ killing horizons _ @xcite associated with the helical symmetry . this means that each null - geodesic generator of @xmath127 and @xmath128 must be parallel to @xmath133 . in particular , this implies that the killing vector @xmath133 is a null vector on the throats : [ e : rigidity ] . _ s_1 = 0 . | _ s_2 = 0 . as a guideline , note that this condition is verified by the helical killing vector @xmath139 of the kerr spacetime , where @xmath140 , @xmath141 and @xmath142 are respectively the killing vector associated with stationarity , the killing vector associated with axisymmetry and the rotation angular velocity of the black hole . this classical result is known as the _ rigidity theorem _ in the black hole literature @xcite . in a recent work , friedman et al . @xcite note that corotation ( in the above sense ) is the only possible rotation state consistent with the helical symmetry in the full einstein theory . however , a weaker definition of quasi - equilibrium ( not assuming that @xmath133 is an exact killing vector , as we do here ) allows for more general rotation states , as shown very recently by cook @xcite . combining eqs . ( [ e : l = d / dt ] ) and ( [ e : def_beta ] ) shows that @xmath133 is related to the lapse function , unit normal and shift vector through [ e : l_3p1 ] = n + , so that the scalar square of @xmath133 is = - n^2 + . thanks to the vanishing of the lapse on the throats , the rigidity condition ( [ e : rigidity ] ) is then equivalent to @xmath143 on @xmath127 and @xmath128 . but @xmath105 being a vector parallel to @xmath80 , @xmath144 ; the positive definiteness of the 3-metric @xmath108 implies then [ e : shift_zero_troat ] . s_1 = 0 . | _ s_2 = 0 . hence , not only the @xmath112-component of @xmath105 is zero [ eq . ( [ e : shift_r_zero_throat ] ) ] , but the total vector @xmath105 vanishes on the throats . the vacuum einstein equations can be written @xcite as the hamiltonian constraint equation : [ e : ham_contr ] r - k_ij k^ij = 0 , the momentum constraint equation : [ e : mom_contr ] d_j k^ij = 0 , and the `` dynamical '' equations : [ e : dk_ij / dt ] k_ijt - _ k_ij = - d_i d_j n + n ( r_ij - 2 k_ik k^k _ j ) , where @xmath145 denotes the ricci tensor of the 3-metric @xmath108 , @xmath146 the ricci curvature scalar , and @xmath147 the covariant derivative associated with @xmath108 . note that we have used the vanishing of the trace of @xmath109 , as a consequence of the maximal slicing ( assumption ( 3 ) in sec . [ s : metric_prop ] ) . besides , the geometrical relation ( [ e : def_extr_curv ] ) involving the extrinsic curvature results in the following equation : [ e : dg_ij / dt ] _ ijt - _ _ ij = - 2 n k_ij . following york @xcite , shibata & nakamura @xcite , and baumgarte & shapiro @xcite , we introduce the `` conformal metric '' _ ij : = ^-1/3 _ ij , where @xmath148 is the determinant of the 3-metric components @xmath126 . @xmath149 is a tensor density of weight @xmath150 . york @xcite has shown that it carries the dynamics of the gravitational field . one can introduce on @xmath80 a covariant derivative @xmath151 such that * @xmath152 ; * if @xmath126 is conformally flat ( @xmath153 ) , then @xmath154 , where @xmath155 is the covariant derivative associated with the flat metric @xmath156 . we refer to refs . @xcite for details in the case of cartesian coordinates and to ref . @xcite for any coordinate system . note that the property ( i ) is not sufficient to fully characterize @xmath151 since the covariant derivative @xmath147 fulfills it as well , reflecting the fact that @xmath157 is a metric density and not a metric tensor : there exists at least two distinct covariant derivatives `` associated '' with it . let us denote by @xmath158 the ricci tensor associated with the covariant derivative @xmath151 and by @xmath159 the corresponding scalar density : @xmath160 , where @xmath161 is the inverse conformal metric ^ij : = ^1/3 ^ij . let us also introduce the following tensor densities [ e : aij ] a_ij : = ^-1/3 k_ij a^ij : = ^1/3 k^ij , and denote by @xmath162 the operator @xmath163 . the hamiltonian constraint equation ( [ e : ham_contr ] ) can then be written as an equation for the determinant @xmath148 : [ e : ham_contr_gam ] d_i d^i + 112 d_i d^i = 32 ( r - ^1/3 a_ij a^ij ) . the momentum constraint equation ( [ e : mom_contr ] ) becomes [ e : mom_contr_a ] d_j a^ij + 12 a^ij d_j= 0 . the dynamical einstein equations ( [ e : dk_ij / dt ] ) can be decomposed into their trace part [ e : lap_tilde_n ] d_i d^i n + 16 d_i d^i n = ^13 n a_ij a^ij and their traceless part @xmath164 \tilde \gamma^{ij } \nonumber \\ & & + \tilde \gamma^{1/3 } \left ( 2 n \tilde \gamma_{kl } \tilde a^{ik } \tilde a^{jl } + \beta^k \tilde d_k \tilde a^{ij } - \tilde a^{kj } \tilde d_k \beta^i - \tilde a^{ik } \tilde d_k \beta^j + { 2\over 3 } \tilde d_k \beta^k \tilde a^{ij } \right ) = 0 \label{e : evol_aij } \ .\end{aligned}\ ] ] note that in eqs . ( [ e : lap_tilde_n ] ) and ( [ e : evol_aij ] ) , we have used the helical symmetry to set to zero the time derivatives and that we have explicited the lie derivatives along @xmath105 . similarly , the evolution equation ( [ e : dg_ij / dt ] ) for @xmath126 can be split into its trace part [ e : div_tilde_beta ] d_i ^i = - 12 ^i d_i and its traceless part [ e : a_ij = tilde_shift ] 2 n a^ij = d^i^j + d^j ^i - 2 3 d_k ^k ^ij . inserting this relation into the momentum constraint ( [ e : mom_contr_a ] ) results in the following equation for the shift vector : [ e : mom_constr_tilde_beta ] d_j d^j ^i + 13 d^i d_j ^j + ^ij r_jk ^k + a^ij ( n d_j-2 d_j n ) = 0 . we recognize here the _ minimal distortion _ equation of smarr & york @xcite , i.e. we recover the fact that the shift vector of coordinates co - moving with respect to a killing vector field is necessarily a minimal distortion shift . as a first step in this research project , we introduce the approximation of a conformally flat 3-metric : [ e : conf_flat ] = ^4 , @xmath165 being some scalar field , and @xmath166 the canonical flat 3-metric associated with the canonical coordinates @xmath167 and @xmath168 ( see sec . [ s : construct ] ) . such an approximation has been used in all previous studies of binary black hole initial data based on the conformal imaging approach @xcite or on the puncture approach @xcite . it has been relaxed in the recently developed kerr - schild approach @xcite . strictly speaking , the assumption ( [ e : conf_flat ] ) is exact only for a single non - rotating ( schwarzschild ) black hole . however , as discussed by mathews et al . @xcite , such an approximation is quite good even for a maximally rotating kerr black hole . as an immediate consequence of eq . ( [ e : conf_flat ] ) , we have = ^12 f , where @xmath60 is the determinant of the metric components @xmath156 . the conformal `` metric '' takes then the simple form _ ij = f^-1/3 f_ij ^ij = f^1/3 f^ij . by property ( ii ) of the covariant derivative @xmath151 ( see sect . [ s : gen_form ] above ) , another consequence of eq . ( [ e : conf_flat ] ) is that [ e : tilde_d = bar_d ] d_i = |d_i , where @xmath169 is the covariant derivative associated with the flat metric @xmath166 . note that , from the definition of @xmath162 , one has d^i = f^1/3 |d^i , where @xmath170 . it follows immediately from eq . ( [ e : tilde_d = bar_d ] ) that the ricci tensor @xmath158 is identically zero . the relations ( [ e : aij ] ) can be rewritten a_ij= f^-1/3 a_ij a^ij= f^1/3 a^ij , where we have introduced the tensor fields : [ e : hat_aij ] a_ij : = ^-4 k_ij a^ij : = ^4 k^ij . taking into account the above relations , the hamiltonian constraint equation ( [ e : ham_contr_gam ] ) becomes an elliptic equation for @xmath165 : [ e : eq_psi ] = - ^5 8 a_ij a^ij , where @xmath171 is the laplacian operator with respect to the flat metric @xmath166 . the momentum constraint equation , under the form ( [ e : mom_constr_tilde_beta ] ) , becomes [ e : eq_beta ] ^i + 13 |d^i |d_j ^j = 2 a^ij ( |d_j n - 6 n |d_j ) , whereas the trace part of the dynamical einstein equations , eq . ( [ e : lap_tilde_n ] ) , becomes [ e : eq_lapse ] n = n ^4 a_ij a^ij - 2 |d_j |d^j n . the traceless dynamical einstein equations ( [ e : evol_aij ] ) reduces to @xmath172 f^{ij } \nonumber \\ & & + { \psi^4\over 4 } \left [ 2 n f_{kl } \hat a^{ik } \hat a^{jl } + \beta^k \bar d_k(\hat a^{ij } ) - \hat a^{kj } \bar d_k \beta^i - \hat a^{ik } \bar d_k \beta^j + { 2\over 3 } \bar d_k \beta^k \ , \hat a^{ij } \right ] = 0 \ . \label{e : eq_dyn}\end{aligned}\ ] ] the trace part of the evolution equation for @xmath126 , eq . ( [ e : div_tilde_beta ] ) , becomes [ e : div_bar_beta ] |d_i ^i = - 6 ^i |d_i , whereas its traceless part ( [ e : a_ij = tilde_shift ] ) results in a relation between the extrinsic curvature tensor and the shift vector : [ e : hat_aij_shift ] a^ij = 12n ( l)^ij , where @xmath173 denotes the ( flat ) conformal killing operator @xcite applied to the vector @xmath105 : [ e : conformal_killing ] ( l)^ij : = |d^i ^j + |d^j ^i - 23 |d_k ^k f^ij . our approach is the following one : using eq . ( [ e : hat_aij_shift ] ) to evaluate @xmath174 , consider eqs . ( [ e : eq_psi ] ) , ( [ e : eq_beta ] ) and ( [ e : eq_lapse ] ) as coupled elliptic equations to be solved for respectively @xmath165 , @xmath105 and @xmath83 . the remaining five einstein equations , eqs . ( [ e : eq_dyn ] ) , are not used to get the solution . moreover , they are not satisfied by the solution @xmath175 , except in special circumstances ( e.g. spherical symmetry ) . this reflects the fact that the conformally flat form ( [ e : conf_flat ] ) constitutes only an approximation to the exact einstein equations . an interesting application of eqs . ( [ e : eq_dyn ] ) is then to evaluate its left - hand side in order to gauge the error resulting from the conformally flat approximation . besides , note that eq . ( [ e : div_bar_beta ] ) is not used in the above scheme . we will discuss this point in sec . [ s : regul ] . the system of eqs . ( [ e : eq_psi])-([e : eq_lapse ] ) , resulting from the assumption of conformal flatness and maximal slicing , has been already proposed by isenberg & nester @xcite , as well as wilson & mathews @xcite , as an interesting approximation to the full einstein equations . it has been used by many authors to compute binary neutron stars on circular orbits . the equations ( [ e : eq_psi ] ) , ( [ e : eq_beta ] ) and ( [ e : eq_lapse ] ) we are facing being elliptic , it is very important to discuss the boundary conditions to set on their solutions . thanks to the isometry @xmath55 , the computational domain is chosen to be half the full spacetime , i.e. only @xmath24 . its boundaries are then the spatial infinity and the two throats @xmath127 and @xmath128 . at spatial infinity , the metric should be asymptotically flat ( hypothesis ( 1 ) of sec . [ s : metric_prop ] ) . this implies that [ e : psi_infinity ] 1 r_1 r_2 and [ e : lapse_infinity ] n 1 r_1 r_2 . combining eqs . ( [ e : helical ] ) , ( [ e : l_3p1 ] ) and ( [ e : lapse_infinity ] ) , we get the asymptotic behavior of the shift vector : [ e : shift_infinity ] r_1 r_2 . the boundary conditions on the throats have been derived in sec . [ s : spacetime_metric ] . in particular , eqs . ( [ e : isom_grr_der ] ) , ( [ e : isom_gtt_der ] ) and ( [ e : isom_gpp_der ] ) are equivalent to the the following condition on the conformal factor @xmath165 : [ e : bound_psi ] . ( r_1 + 2 r_1 ) | _ s_1 = 0 . ( r_2 + 2 r_2 ) | _ s_2 = 0 . all the remaining equations listed in eqs . ( [ e : isom_grr_der])-([e : isom_gpp_der ] ) are automatically satisfied by the conformally flat form ( [ e : conf_flat ] ) . the boundary equation on the lapse have already been given [ eq . ( [ e : lapse_zero_throat ] ) ] : [ e : lapse_zero_throat_2 ] n|_s_1 = 0 n|_s_2 = 0 . as well as that on the shift vector , resulting from the rigid rotation hypothesis [ eq . ( [ e : shift_zero_troat ] ) ] : [ e : shift_zero_troat_2 ] . | _ s_1 = 0 . | _ s_2 = 0 . a direct consequence of eqs . ( [ e : lapse_zero_throat_2 ] ) and ( [ e : hat_aij_shift ] ) is that the shift vector on the throats should satisfy not only ( [ e : shift_zero_troat_2 ] ) but also [ e : lbeta_zero_throat ] . ( l)^ij | _ s_1 = 0 . ( l)^ij | _ s_2 = 0 , in order for the extrinsic curvature to be regular on the throat . note that in the case of a single rotating black hole , such a condition is equivalent to @xmath176 and @xmath177 . the first condition follows from e.g. eq . ( 10.25 ) of ref . @xcite and the last one from the rigidity theorem ( @xmath178 is constant and zero on the horizon ) . in the present case , the properties ( [ e : shift_r_zero_throat ] ) and ( [ e : dbr / dt_s])-([e : dbp / dr_s ] ) , which follow from the isometry @xmath55 , in conjunction with the property ( [ e : shift_zero_troat_2 ] ) , which follows from the rigidity assumption , on the throat , implied by eq . ( [ e : shift_zero_troat_2 ] ) , results in the vanishing of all the partial derivatives of the components @xmath122 with respect to @xmath113 and @xmath114 . ] imply that [ e : div_bar_beta_throat ] . |d_i ^i | _ s = . ^r r | _ s and @xmath179 therefore the condition ( [ e : lbeta_zero_throat ] ) is equivalent to [ e : dbrdr_throat ] . ^r_1 ^r_2 r_2 | _ s_2 = 0 . now the trace of the relation between the extrinsic curvature and the derivative of the 3-metric , eq . ( [ e : div_bar_beta ] ) , gives , when inserting eq . ( [ e : shift_zero_troat_2 ] ) in its right - hand side , . |d_k ^k | _ s_1 = 0 . |d_k ^k | _ s_2 = 0 . from eq . ( [ e : div_bar_beta_throat ] ) , it follows that eq . ( [ e : dbrdr_throat ] ) is satisfied as well . this establishes the regularity property ( [ e : lbeta_zero_throat ] ) . the above argument relies on the fact that eq . ( [ e : div_bar_beta ] ) , relating the trace of the extrinsic curvature tensor ( here zero ) to the divergence of the shift vector , is satisfied . however , as discussed in sec . [ s : scheme ] , we solve only eqs . ( [ e : eq_psi])-([e : eq_lapse ] ) to get the metric fields @xmath165 , @xmath83 and @xmath105 . this means that there is a priori no guarantee that eq . ( [ e : div_bar_beta ] ) is satisfied by the solution of ( [ e : eq_psi])-([e : eq_lapse ] ) ( see sec . iv.c of ref . @xcite for a discussion of this point ) . it has been argued recently by cook @xcite that if one reformulates the problem by assuming that the helical vector @xmath133 is not an exact killing vector , but only an approximate one as it is in reality then the only freely specifiable part of the extrinsic curvature , as initial data , is ( [ e : hat_aij_shift ] ) , not ( [ e : div_bar_beta ] ) . this means that the relation ( [ e : div_bar_beta ] ) between the extrinsic curvature and the shift is not as robust as the relation ( [ e : hat_aij_shift ] ) . another problem is that , when solving the system ( [ e : eq_psi])-([e : eq_lapse ] ) subject to the boundary conditions ( [ e : bound_psi])-([e : shift_zero_troat_2 ] ) , there is no guarantee not only that the solution for the shift vector obeys to eq . ( [ e : div_bar_beta ] ) but also that it obeys to the isometry conditions ( [ e : dbt / dr_s ] ) and ( [ e : dbp / dr_s ] ) [ the other isometry conditions , namely ( [ e : shift_r_zero_throat ] ) , ( [ e : dbr / dt_s ] ) and ( [ e : dbr / dp_s ] ) , are satisfied by virtue of the boundary condition ( [ e : shift_zero_troat_2 ] ) ] . in the companion article @xcite , we present a method to enforce the regularity condition ( [ e : dbrdr_throat ] ) as well as the isometry condition conditions ( [ e : dbt / dr_s ] ) and ( [ e : dbp / dr_s ] ) . this amounts to add , at each step of the iteration , a corrective term @xmath180 to the solution @xmath181 of the momentum constraint ( [ e : eq_beta ] ) , so that the shift vector = _ constr + _ cor is well behaved , i.e. satisfies ( i ) the rigidity boundary conditions ( [ e : shift_zero_troat_2 ] ) , ( ii ) the condition ( [ e : dbrdr_throat ] ) which ensures the regularity of the extrinsic curvature on the throats , and ( iii ) the isometry condition ( [ e : i_beta ] ) . if at the end of the iteration , @xmath180 has converged to zero , then we get a regular solution of the einstein equations in the conformal flatness approximation . on the contrary , if @xmath180 stays at some finite value , we get a solution which violates the momentum constraint equation . the numerical solutions we have computed @xcite belong to this category . however they have ( cf . iv.b of @xcite ) |_cor| < 10 ^ -3 || , which shows that the momentum constraint is only very slightly violated . taking into account the other approximations performed , e.g. conformal flatness , we find this to be very satisfactory . the total mass - energy content in a @xmath80 hypersurface is given by the arnowitt - deser - misner ( adm ) mass @xmath0 , which is expressed by means of the surface integral at spatial infinity [ e : m_adm_def ] m = 116 _ f^ik f^jl ( |d_j _ kl - |d_k _ jl ) ds_i ( see e.g. eq . ( 20.9 ) of ref . @xcite ) . in the case of the conformally flat 3-metric @xmath153 , this integral can be written [ e : m_adm_1 ] m = - 12 _ |d^i ds_i . by means of the green - ostrogradski formula , this expression can be converted into the volume integral of @xmath182 plus surface integrals on the throats ; using the hamiltonian constraint ( [ e : eq_psi ] ) to express @xmath182 , as well as the boundary condition ( [ e : bound_psi ] ) on the throats , one gets m = 116 ^5 a_ij a^ij d^3 x + a_1 4 _ r_1=a_1 _ 1 d_1 d_1 + a_2 4 _ r_2=a_2 _ 2 d_2 d_2 . the total angular momentum in a @xmath80 hypersurface is defined by the following surface integral at spatial infinity @xcite [ e : j_def ] j = 18 _ ( k^i _ j - k^k _ k f^i _ j ) m^j ds_i , where @xmath183 [ see eqs . ( [ e : helical ] ) and ( [ e : shift_infinity ] ) ] is the rotational killing vector of the flat metric @xmath166 ( to which @xmath108 is asymptotic ) . note that in the present case @xmath184 ( maximal slicing ) . note also that @xmath1 defined by eq . ( [ e : j_def ] ) coincides with the @xmath185-component of the vector @xmath186 defined by eq . ( 12 ) of bowen & york @xcite . as discussed by york @xcite , contrary to the definition ( [ e : m_adm_def ] ) of the adm mass , the definition ( [ e : j_def ] ) of @xmath1 requires some asymptotic gauge - fixing conditions stronger than the mere asymptotic flatness ( [ e : asymp_flat1])-([e : asymp_flat2 ] ) , because of the supertranslations ambiguity . some natural gauge - fixing conditions are provided by the asymptotic quasi - isotropic gauge proposed by york @xcite . such conditions are fulfilled by the conformally flat metric ( [ e : conf_flat ] ) . using the fact that @xmath187 at spatial infinity , we can replace @xmath188 by @xmath189 in eq . ( [ e : j_def ] ) and express @xmath1 by means of the green - ostrogradski formula as a volume integral plus surface integrals on the throats . the volume integral vanishes identically , as one can see by considering the following identity : |d_i ( ^6 a^ij f_jk m^k ) = |d_i ( ^6 a^ij ) f_jk m^k + 12 ^6 a^ij [ |d_i ( f_jk m^k ) + |d_j ( f_ik m^k ) ] . the first term on the r.h.s . vanishes by virtue of the momentum constraint ( [ e : mom_contr_a ] ) , which can be written as [ e : mom_contr_pa ] |d_i(^6 a^ij ) = 0 , whereas the second term vanishes for @xmath190 is a killing vector of the flat metric @xmath166 . thus the formula for @xmath1 reduces to integrals on the throats : [ e : j_throat ] j = - 1 8 _ r_1=a_1 ^6 a^ij f_jk m^k d|s_i - 1 8 _ r_2=a_2 ^6 a^ij f_jk m^k d|s_i , where @xmath191 denotes the surface element with respect to the flat metric @xmath166 and oriented toward the `` interior '' of the throats . the orbital angular velocity @xmath5 does not appear in the partial differential equations listed in sec . [ s : conf_flat_eq ] . it shows up only in the boundary condition ( [ e : shift_infinity ] ) for the shift vector . this contrasts with the binary neutron star case , where @xmath5 enters in the equation governing the equilibrium of the fluid ( see e.g. @xcite ) . at this point , it appears that , solving eqs . ( [ e : eq_psi])-([e : eq_lapse ] ) , with the boundary conditions ( [ e : psi_infinity])-([e : shift_infinity ] ) and ( [ e : bound_psi])-([e : shift_zero_troat_2 ] ) , one can get a solution @xmath192 for any given value of @xmath5 . for instance , if we set @xmath193 in the boundary condition ( [ e : shift_infinity ] ) , we get @xmath194 as a solution of ( [ e : eq_beta ] ) and the misner - lindquist solution for @xmath165 @xcite . of course , such a solution is not admissible on physical grounds , and we need an extra condition to fix @xmath5 . as a boundary condition at spatial infinity , we have demanded only that @xmath75 tends to the minkowski metric of flat spacetime [ conditions ( [ e : asymp_flat1])-([e : asymp_flat2 ] ) or ( [ e : lapse_infinity])-([e : shift_infinity ] ) ] . we could go a little further and demand instead that @xmath75 tends to the schwarzschild metric corresponding to the adm mass @xmath0 . this implies the following behavior for the conformal factor @xmath165 and the lapse @xmath83 [ cf . ( [ e : ds2_schwarz ] ) and ( [ e : n_schwarz ] ) ] : [ e : psi_schwarz ] ~1 + m 2 r r , [ e : lapse_schwarz ] n ~1 - m r r , where @xmath112 denotes either the coordinate @xmath195 or @xmath196 . from the very definition of @xmath0 , the behavior ( [ e : psi_schwarz ] ) is guaranteed by eq . ( [ e : m_adm_1 ] ) . however , the solution of ( [ e : eq_lapse ] ) is such that @xmath197 , with a priori @xmath198 . the behavior ( [ e : lapse_schwarz ] ) is thus a extra condition imposed on the system ( [ e : eq_psi])-([e : eq_lapse ] ) . this is the condition which will enable us to fix @xmath5 . let us show that for stationary spacetimes , i.e. in the case where @xmath133 is timelike at infinity , the extra condition ( [ e : lapse_schwarz ] ) follows from the remaining einstein equations ( [ e : eq_dyn ] ) , i.e. the equations that we have not used in the system ( [ e : eq_psi])-([e : eq_lapse ] ) . indeed , the quadratic terms of the type @xmath199 or @xmath200 which appear in eq . ( [ e : eq_dyn ] ) all decay at least as @xmath201 when @xmath202 . now , for stationary spacetimes , it can be seen that the lie derivative along @xmath105 of @xmath203 which appear in eq . ( [ e : eq_dyn ] ) , decays also at least as @xmath201 [ eq . ( [ e : lb_kangu ] ) below ] . then eq . ( [ e : eq_dyn ] ) implies that @xmath204 decays at least as @xmath201 , which means that the @xmath205 ( monopolar ) part of @xmath206 vanishes , i.e. [ e : viriel ] ^2 n ~1 + r^2 r . this is possible only if @xmath207 and @xmath83 have opposite monopolar @xmath205 terms , which implies the property ( [ e : lapse_schwarz ] ) . note that , for stationary spacetimes , the monopolar term of the lapse @xmath83 is the komar mass associated with the timelike killing vector . the condition ( [ e : lapse_schwarz ] ) is then intimately linked to the virial theorem : as already shown by two of us @xcite , a relativistic generalization of the classical virial theorem can be obtained provided that the komar mass coincides with the adm mass [ property ( [ e : lapse_schwarz ] ) ] . this last property has been shown to hold for asymptotically flat stationary spacetimes by beig @xcite . in order to exhibit more clearly the link with the virial theorem , let us combine eqs . ( [ e : eq_psi ] ) and ( [ e : eq_lapse ] ) to derive an equation for @xmath206 ( see e.g. eq . ( 51 ) of ref . @xcite ) : [ e : psi2_n ] ( ^2 n ) = n ^6 + 2 |d_i |d^i(n ) , where we have re - introduced a non - vanishing stress - energy tensor @xmath208 via @xmath209 for the benefit of the discussion when considering the newtonian limit . the condition ( [ e : viriel ] ) is equivalent to the vanishing of the monopolar term of @xmath206 , i.e. from eq . ( [ e : psi2_n ] ) and assuming a spacelike slice @xmath80 diffeomorphic to @xmath30 , [ e : grv3 ] _ _ t \ { n ^6 + 2 |d_i to the relativistic virial theorem given by eq . ( 29 ) of ref . @xcite , once the latter is specialized to a conformally flat 3-metric . the newtonian limit of eq . ( [ e : grv3 ] ) is nothing but the classical virial theorem : [ e : viriel_newt ] 2 t + 3 p + w = 0 , where @xmath210 is the total kinetic energy of the system , @xmath61 the volume integral of the pressure and @xmath211 the gravitational potential energy . note that the value of @xmath5 for two newtonian particles of individual mass @xmath212 in circular orbit ( radius @xmath213 ) can be obtained from eq . ( [ e : viriel_newt ] ) ( @xmath214 , @xmath215 , @xmath216 ) ; this results of course in the keplerian value @xmath217 . let us remark that detweiler @xcite has proposed to determine the orbital velocity @xmath5 of binary black holes in circular orbits by means of a variational principle . although he does not state it precisely , his variational principle also use the `` virial '' assumption ( [ e : lapse_schwarz ] ) [ cf . the not so well justified sentence `` in the gauge described in chapter 19 of misner et al . ( 1973 ) the flux integral at infinity is @xmath218 '' below his eq . ( 17 ) ] . a formula relating the adm mass @xmath0 , the total angular momentum @xmath1 , the angular velocity @xmath5 and some integrals on the throats can be obtained as follows . the key point is to notice that the einstein equations ( [ e : ham_contr ] ) , ( [ e : mom_contr ] ) , the trace of ( [ e : dk_ij / dt ] ) and ( [ e : dg_ij / dt ] ) imply , when @xmath106 is a killing vector [ eq . ( [ e : l = d / dt ] ) ] , the following remarkable identity @xcite : [ e : detw ] d^i(d_i n - k_ij ^j ) = 0 . note that this equation is fully general and does not assume that the 3-metric @xmath108 is conformally flat . the vanishing of the divergence ( [ e : detw ] ) enables one to use the green - ostrogradski formula to get an identity involving only surface integrals : _ ( d_i n - k_ij^j ) ds^i = - _ a=1 ^ 2 _ s_a ( d_i n - k_ij^j ) ds^i , where by convention @xmath219 is oriented towards the `` interior '' of the throats . from eq . ( [ e : lapse_schwarz ] ) , the flux integral of @xmath220 on the left hand side is equal to @xmath221 . using eqs . ( [ e : j_def ] ) and ( [ e : shift_infinity ] ) , the flux integral of @xmath222 is equal to @xmath223 . the second term on the right hand side vanishes because @xmath194 on the throats [ rigidity condition , eq . ( [ e : shift_zero_troat_2 ] ) ] , so that one is left with m - 2 j = -14 _ s_1 d_i n ds^i -14 _ s_2 d_i n ds^i . this formula generalizes to the binary black hole case the classical formula that smarr @xcite derived for a single rotating black hole ( the surface integral on the right hand side being then the black hole surface gravity multiplied by the horizon area ) . the asymptotic behavior ( near spatial infinity ) of the conformal factor @xmath165 and the lapse function @xmath83 are given by eqs . ( [ e : psi_schwarz ] ) and ( [ e : lapse_schwarz ] ) . the aim of this section is to get the asymptotic behavior of the shift vector @xmath105 and the extrinsic curvature tensor @xmath109 ( or equivalently @xmath224 ) . in doing so , we will gain some insight about the assumption of asymptotic flatness and the leftover einstein equations ( [ e : eq_dyn ] ) . to simplify the analysis , we restrict it to a system of identical black holes . we introduce a cartesian coordinate system @xmath225 such that @xmath226 is the direction along the two hole centers ( i.e. the centers of the spheres @xmath16 and @xmath17 ) , @xmath227 at the middle between the two , and @xmath185 is the direction perpendicular to the orbital plane . moreover , let us introduce coordinate systems centered on each hole , according to \ { lcl x_1 & = & x + d / 2 + y_1 & = & y + z_1 & = & z . \ { lcl x_2 & = & - x + d / 2 + y_2 & = & - y + z_2 & = & z . , where @xmath228 denotes the coordinate distance between the centers of the two spheres @xmath16 and @xmath17 . these two coordinate systems are represented in fig . [ f : coord_cart ] let us split eq . ( [ e : eq_beta ] ) for the shift vector in two parts , assuming that its right - hand side can be split in a part @xmath229 centered on hole 1 and another part centered @xmath230 on hole 2 . we therefore write [ e : decomp_betai ] ^i = m^i + _ 1^i + _ 2^i , where @xmath231 is the rotational killing vector @xmath232 of the flat metric @xmath166 already introduced in sec.[s : global ] , and @xmath233 and @xmath234 are the asymptotically vanishing solutions of [ e : eq_beta_a ] ^i_a + 13 |d^i |d_j ^j_a = s^i_a , a = 1 , 2 . let us solve eq . ( [ e : eq_beta_a ] ) for @xmath235 by means of the following decomposition @xcite : [ e : shift_shibata ] ^i_1 = 78 w^i_1 -18 ( _ 1 x^i_1 + w^j_1 x^i_1 x^j_1 ) , where @xmath236 denotes the cartesian coordinate system @xmath237 centered on hole 1 , and components with respect to that coordinate system are understood in eq . ( [ e : shift_shibata ] ) . @xmath238 and @xmath239 are solutions of the poisson equations @xmath240 provided that the source @xmath241 decays at least as @xmath242 as @xmath243 ( is the same radial coordinate as that introduced in sec . [ s : construct ] ] ) , the leading behavior of the solution to eq . ( [ e : poisson_w ] ) is given by the harmonic function [ e : w_monop ] ( w_1^x_1 , w_1^y_1 , w_1^z_1 ) = ( 0 , r_1 , 0 ) + o(r_1 ^ -2 ) , where @xmath244 is a constant . note that we have neglected the monopolar part of @xmath245 and @xmath246 with respect to that of @xmath247 . this amounts to considering that @xmath229 corresponds mainly to a motion along the @xmath248 direction , in accordance with the orbital motion . to understand this , let us note that taking the laplacian of expression ( [ e : w_monop ] ) results in the following form for @xmath241 : [ e : s_1_alpha ] ( s_1^x_1 , s_1^y_1 , s_1^z_1 ) = ( 0 , -4 ( x_1,y_1,z_1 ) , 0 ) , where @xmath249 denotes the dirac distribution . the newtonian limit for @xmath241 is s_1^i = 16 v^i , where @xmath250 and @xmath251 denotes the matter density and velocity respectively . this newtonian limit holds because in presence of matter the right - hand side of the shift equation ( [ e : eq_beta ] ) should contain the term @xmath252 times the momentum density of matter ( see e.g. eq . ( 52 ) of ref . @xcite ) . for two point mass particles of individual mass @xmath212 in circular orbit with angular velocity @xmath5 , this results in ( s_1^x_1 , s_1^y_1 , s_1^z_1 ) = ( 0 , -8 md ( x_1,y_1,z_1 ) , 0 ) . identification with ( [ e : s_1_alpha ] ) leads to the newtonian value of the coefficient @xmath244 : [ e : alpha_newt ] _ newt = 2 m d . regarding the poisson equation ( [ e : poisson_chi ] ) for @xmath239 , we notice that its source has a vanishing effective mass , at least if its leading order is as ( [ e : s_1_alpha ] ) ; consequently , the solution @xmath239 has no monopolar term in @xmath253 and decays as @xmath254 . this means that its gradient which enters in expression ( [ e : shift_shibata ] ) for the shift vector decays as @xmath255 . now , in this section , we are interested in the behavior of the shift vector up to the order @xmath256 only . therefore , we discard the solution for @xmath239 , writing [ e : chi_no_monop ] _ 1 = o(r_1 ^ -2 ) . inserting ( [ e : w_monop ] ) and ( [ e : chi_no_monop ] ) into ( [ e : shift_shibata ] ) yields [ e : sol_beta1_lin ] ( _ 1^x_1 , _ 1^y_1 , _ 1^z_1 ) = ( x_1 y_1 8 r_1 ^ 3 , 8 r_1 , z_1 y_1 8 r_1 ^ 3 ) + o(r_1 ^ -2 ) . let us remark that this solution is nothing but one of the three ( harmonic ) eigenvectors of the operator @xmath257 [ cf . ( [ e : conformal_killing ] ) ] which decay as @xmath258 . this can be seen by comparing with the list of these harmonic vectors provided by murchadha @xcite : the solution ( [ e : sol_beta1_lin ] ) above is the item ( 19.2 ) of murchadha s list . moreover , this author has shown that this harmonic vector is generated from linear momentum in the @xmath248 direction , in full accordance with the analysis performed above [ cf . ( [ e : s_1_alpha ] ) ] . at this stage , our solution ( [ e : sol_beta1_lin ] ) describes only the linear momentum of hole 1 . since we are considering corotating black holes , they must have individual angular momentum ( spin ) , in addition to their linear momentum , although neither the notion of individual spin nor individual linear momentum can be defined rigorously for a binary system in general relativity ( only the total angular momentum can be defined , as in sec . [ s : global ] ) . to take the rotation of the black holes into account , let us add a pure spin part to @xmath233 , of the type [ e : sol_beta1_spin ] ( _ 1,spin^x_1 , _ 1,spin^y_1 , _ 1,spin^z_1 ) = ( 2 s y_1 r_1 ^ 3 , -2 s x_1r_1 ^ 3 , 0 ) , where the constant @xmath259 is some parameter which measures the amount of spin , the latter being supposed to be aligned along the @xmath260 axis . note that ( [ e : sol_beta1_spin ] ) is a harmonic vector of the operator @xmath261 which decays as @xmath254 . it is nothing but the asymptotic part of the axisymmetric shift vector generated by a single rotating object [ see e.g. eq . ( 4.13 ) of ref . @xcite , where @xmath262 . adding ( [ e : sol_beta1_lin ] ) to ( [ e : sol_beta1_spin ] ) , we get the following final expression for the shift vector `` mostly generated '' by hole 1 : @xmath263 by symmetry , we get exactly the same expression for the components of the shift vector @xmath264 with respect to the coordinates @xmath265 . let us now express the components of both @xmath266 and @xmath264 with respect to the coordinates @xmath225 centered on the system . taking into account the orientations of @xmath237 and @xmath265 with respect to @xmath225 ( see fig . [ f : coord_cart ] ) , we obtain : @xmath267 and @xmath268 by adding together these two expressions [ cf . ( [ e : decomp_betai ] ) ] and performing an expansion to the order @xmath256 , we get the following asymptotic form of the total shift vector @xmath105 : @xmath269 note that , apart from the @xmath5 part , the total shift decays as @xmath256 , contrary to @xmath266 and @xmath264 , which decay as @xmath258 . from the above expression , @xmath105 can be linearly decomposed into three parts : [ e : decomp_beta ] = _ kin + _ angu + _ quad , with @xmath270 @xmath271 and @xmath272 @xmath273 is a pure kinematical term , which reflects that we use co - rotating coordinates . @xmath274 is , as we will see below , the part of the shift which carries the total angular - momentum of the system . as for @xmath275 introduced above [ eq . [ e : sol_beta1_spin ] ) ] , it has the familiar shape of a pure spin axisymmetric shift vector . @xmath276 is one of the nine harmonic vectors of the operator @xmath261 which decay as @xmath256 . it has the number ( 22.7 ) in murchadha s list @xcite . by the way , @xmath274 has the number ( 22.1 ) in the same list . as shown by murchadha @xcite [ cf . ( 29 ) ] , @xmath276 arises from the fact that the @xmath277 component of the quadrupole moment @xmath278 of the system is time varying with respect to some asymptotic inertial frame . this is the only such component . indeed , if we consider a newtonian system of two identical point mass particles on a circular orbit of diameter @xmath228 in the @xmath279 plane , the time derivative of its quadrupole moment with respect to the inertial frame is given by @xmath280 it is clear on this expression that at time @xmath281 , when the axes of the rotating frame coincide with those of the inertial frame ( our assumption in this discussion ) , the only non - vanishing component is @xmath282 . combining eqs . ( [ e : alpha_newt ] ) and ( [ e : dot_qxy ] ) , we see that the coefficient in front of the three components ( [ e : beta_quad_x])-([e : beta_quad_z ] ) of @xmath276 is @xmath283 . this justifies the label _ quad _ ( for quadrupole moment ) given to that part of the shift vector . the asymptotic behavior of the extrinsic curvature tensor is deduced from that of the shift vector via eqs . ( [ e : hat_aij ] ) and ( [ e : hat_aij_shift ] ) , which allows us to write ( taking into account that both @xmath165 and @xmath83 are equal to 1 at spatial infinity ) k^ij ~12 ( l)^ij r . since @xmath284 for @xmath273 is a killing vector of the flat metric @xmath166 , the decomposition ( [ e : decomp_beta ] ) of the shift vector leads to the following decomposition of the extrinsic curvature tensor : [ e : decomp_k ] = _ angu + _ quad , where @xmath285 and @xmath286 . inserting the formulas ( [ e : beta_angu_x])-([e : beta_angu_z ] ) in the explicit form ( [ e : conformal_killing ] ) of the operator @xmath287 results in the following components of @xmath288 : @xmath289 a similar computation for @xmath290 yields @xmath291 note that both @xmath292 and @xmath293 decay as @xmath294 . if we plug the formulas ( [ e : k_quad_xx])-([e : k_quad_zz ] ) into the surface integral ( [ e : j_def ] ) which gives the angular momentum , we get , after some straightforward calculations j(_quad ) = 0 . this means that all the angular momentum of the system is carried by @xmath292 . indeed , inserting the formulas ( [ e : k_angu_xx])-([e : k_angu_zz ] ) into eq . ( [ e : j_def ] ) gives j = j(_angu ) = d 4 + 2 s . for a non - relativistic point mass system , @xmath244 is given by eq . ( [ e : alpha_newt ] ) so that we get j(_angu)_newt = m d^2 2 + 2 s . the first term on the right - hand side is nothing but the orbital angular momentum of the system and the second terms is the sum of the spins @xmath259 of the two particles . hence @xmath295 is equal to the total angular momentum of the system . let us consider the five einstein equations that we have not taken into account for the solution of the problem , i.e. eqs . ( [ e : eq_dyn ] ) . thanks to the asymptotic behavior ( [ e : psi_schwarz ] ) , ( [ e : lapse_schwarz ] ) and ( [ e : viriel ] ) of @xmath83 and @xmath165 , all the terms involving products of gradients of @xmath83 or @xmath165 , as well as the ones involving second derivatives of @xmath206 , decay at least as @xmath201 . the quadratic term @xmath296 decays as @xmath297 for @xmath298 decays as @xmath294 , as seen above . the only remaining term in eq . ( [ e : eq_dyn ] ) is the lie derivative of @xmath203 along @xmath105 . asymptotically , one has _ a^ij = _ k^ij + o(r^-4 ) . it can be seen easily that only the lie derivative along @xmath273 matters : _ k^ij = _ _ kin k^ij + o(r^-6 ) . let us introduce the splitting ( [ e : decomp_k ] ) of @xmath298 into this expression . after some computations , we find that [ e : lb_kangu ] _ k^ij_angu = o(r^-4 ) , whereas @xmath299 which means that @xmath300 decays only as @xmath294 . we face here the incompatibility of helical symmetry and asymptotic flatness for systems that have a time - varying quadrupole moment ( recall that @xmath276 and hence @xmath301 is due to @xmath302 ) . indeed @xmath300 is the only term in the einstein equations ( [ e : eq_dyn ] ) which decays as slower as @xmath294 . it therefore can not be compensated by another term . this means that the five einstein equations ( [ e : eq_dyn ] ) are violated . note that this problem does not arise from the assumption of conformal flatness of the 3-metric @xmath108 . relaxing this condition would have resulted in asymptotic behaviors of @xmath105 and @xmath109 which would have been the same as that obtained here . note also that for a system such as an isolated rotating axisymmetric star ( or more generally for any stationary system ) , @xmath303 and @xmath304 , so that the problem of asymptotic flatness in eq . ( [ e : eq_dyn ] ) does not arise . we have presented an approach to the problem of binary black holes in circular orbit which is similar to that previously used in the literature to treat binary neutron stars , namely an approach based on the existence of a helical killing vector field along with the simplifying assumption of a conformally flat 3-metric . the differences between the two approaches lie in the boundary conditions on the throats in the black hole case . we have chosen a spacetime manifold with spatial sections of the misner - lindquist type , i.e. composed of two isometric asymptotically flat sheets . moreover , we have chosen the black holes to be corotating , which has the simple geometrical interpretation of the throats being killing horizons . by enforcing the isometry conditions on the shift vector , as well as the equation relating the trace of the extrinsic curvature to the divergence of the shift , possibly at the price of slightly modifying the momentum constraint , all the quantities which enter in the equations remain regular . notably the extrinsic curvature tensor remains finite on the throats , although the lapse vanishes there . we have proposed to compute the orbital angular velocity of the system by requiring that the conformal factor @xmath165 and the lapse function @xmath83 have the same monopolar @xmath205 term in their asymptotic expansions . this requirement reduces to the classical virial theorem at the newtonian limit . contrary to previous numerical approaches the conformal imaging one @xcite and the puncture one @xcite our method amounts to solving five , and not four ( the four constraints ) , of the einstein equations . this reflects the fact that we have re - introduced the time dimension in the problem . the formulation presented here has been implemented by means of a numerical code based on a multi - domain spectral method and we present the first results in the companion paper @xcite . these results can be used as initial data for computing the black hole coalescence within the 3 + 1 formalism @xcite . let us stress that the work presented in this article constitutes a first attempt to tackle the problem of binary black hole in circular orbits . in order to fully specify the problem and search for a unique solution , we had to make a number of concrete choices which have some degree of arbitrariness , such as the two - sheeted topology , the isometry across the throats and the resulting boundary conditions , or the rigid rotation of the black holes . these hypotheses could be changed to different ones , as for instance considering irrotational black holes instead of corotating ones . this shall be investigated in future works . e. seidel , in _ black holes and gravitational waves new eyes in the 21st century , proc . of the 9th yukawa international seminar , kyoto 1999 _ , edited by t. nakamura and h. kodama , prog . . suppl . * 136 * , 87 ( 1999 ) .

we present a new approach to the problem of binary black holes in the pre - coalescence stage , i.e. when the notion of orbit has still some meaning . contrary to previous numerical treatments which are based on the initial value formulation of general relativity on a ( 3-dimensional ) spacelike hypersurface , our approach deals with the full ( 4-dimensional ) spacetime . this permits a rigorous definition of the orbital angular velocity . neglecting the gravitational radiation reaction , we assume that the black holes move on closed circular orbits , which amounts to endowing the spacetime with a helical killing vector . we discuss the choice of the spacetime manifold , the desired properties of the spacetime metric , as well as the choice of the rotation state for the black holes . as a simplifying assumption , the space 3-metric is approximated by a conformally flat one . the problem is then reduced to solving five of the ten einstein equations , which are derived here , as well as the boundary conditions on the black hole surfaces and at spatial infinity . we exhibit the remaining five einstein equations and propose to use them to evaluate the error induced by the conformal flatness approximation . the orbital angular velocity of the system is computed through a requirement which reduces to the classical virial theorem at the newtonian limit . # 1 # 1 we dedicate this work to the memory of our friend and collaborator jean - alain marck .

over the past decade , several probe ablative therapies have emerged for the treatment of patients with small , localized renal tumors . cryoablation and radiofrequency ablation ( rfa ) have been studied in the greatest detail with promising intermediate oncological outcomes . various treatment approaches for the 2 modalities , namely laparoscopic and percutaneous , are currently practiced . the decision to choose one approach over another is related to surgeon preference , tumor location and accessibility ( anterior vs posterior ) , proximity to other abdominal organs , and patient habitus and comorbidities . during laparoscopic ablative surgery , the thermal probe is routinely placed through a separate skin incision to access the renal tumor . although no case reports of tract - site recurrences have been noted after probe - ablative nephron - sparing surgery , a theoretical risk of tract contamination exists . case reports of tract recurrence for renal cell carcinoma after laparoscopic nephrectomy have been reported , with greater risk noted in morcellated specimens and cases where extraction was done without a plastic bag . to reduce the number of skin incisions and eliminate tract exposure to the needle probe , we describe the use of bone wax ( tyco / syneture , mansfield , ma , usa ) to provide an airtight seal of a 5-mm laparoscopic port . the technique used for laparoscopic renal ablation ( cryo - therapy and rfa ) has previously been described . the main steps can be summarized as establishment of transperitoneal or retroperitoneal access , laparoscopic dissection for tumor exposure , laparoscopic ultrasonography followed by tru - cut needle biopsy of the renal mass . thereafter , bone wax was used to completely occlude the external opening of one of the established 5-mm laparoscopic ports ( ethicon endo - surgery , somerville , nj ) , which would provide optimal tumor access ( figure 1 ) . placement of either the cryoprobe or the rita starburst ( rita medical systems , fremont , ca ) ablation probe through the 5-mm port was successful in all patients while pneumoperitoneal pressure was maintained . additional bone wax was applied along the shaft of the probe to ensure an airtight seal once the thermal - needle was appropriately positioned into the center of the tumor ( figure 2 ) . following the treatment cycles , the 5-mm port and the probe were removed together from the abdominal wall , thus eliminating any contact with the skin tract . a new 5-mm port was repositioned into the surgical space by using the same skin tract . floseal ( baxter international , deerfield , il ) and argon beam coagulation were then used to ensure hemostasis before case completion . ( a ) application of bone wax ( 40 mm 15 mm ) to the outer surface of a standard 5-mm laparoscopic port . ( b ) the waxy , malleable material provides an ideal sealant and port - site reducer to allow an airtight entry of the renal ablative probe . note the additional bone wax application around the port - entry site to ensure airtight closure thus maintaining pneumoperitoneal pressure . we have used the bone wax sealant to aid with thermal probe positioning during laparoscopic ablative procedures . all treatments were successfully performed through previously established 5-mm laparoscopic ports while maintaining pneumoperitoneal pressure . a separate skin puncture was not required , and the ablation probe was never in contact with subcutaneous tissues of the abdominal wall . minimally invasive tissue ablative procedures are evolving into an appropriate treatment option for managing small and exophytic renal tumors in select patients . the laparoscopic approach to these modalities often requires the placement of the thermal probe through a separate skin incision to maintain pneumoperitoneal pressure . although rare , removal of the probe through the skin tract after lesion treatment may increase the potential for tumor cell transfer and port - site contamination . our described technique using bone wax has proved useful in utilizing an established 5-mm laparoscopic port and avoiding direct contact of the ablation probe with subcutaneous tissues . bone wax is a sterile mixture of beeswax , paraffin , and isopropyl palmitate , a wax - softening agent . this inexpensive material is often used to achieve local hemostasis of bone by acting as a mechanical barrier , particularly in orthopedic and sternotomy procedures . , it can easily be molded into the external canal of a laparoscopic port and can provide sufficient coaptation around the ablation need to ensure an airtight seal despite pneumoperitoneal pressures of 14 mm hg to 20 mm hg . despite its merits , this technique has several limitations . in obese patients , where the abdominal wall may be very thick , the additional 5 cm to 7 cm that may be gained by having the probe placed directly through the skin rather than through the laparoscopic port may be important in certain individuals . furthermore , tumors with larger diameters , irregular shapes , and patients with multiple tumors may require placement of several probes to deliver appropriate therapy . as such , the placement of additional 5-mm ports simply for probe insertion would be inappropriate . in these laparoscopic cases , where direct , percutaneous insertion is used , we recommend probe activation in the peritoneal cavity before extraction to eradicate potential tumor cells . use of bone wax is a simple , inexpensive technique to avoid separate skin incisions while minimizing tract - site contact with ablation probes .

purpose : we describe the use of a hemostatic wax sealant during laparoscopic renal ablative procedures to allow airtight transabdominal access of the treatment probe through a standard 5-mm port.methods:following tru - cut biopsy of the renal mass , bone wax was used to occlude the external opening of an established 5-mm laparoscopic port . the cryotherapy or radiofrequency treatment probe was then passed through the waxy material and inserted appropriately into the renal lesion while pneumoperitoneal pressure was maintained.results:in all cases , the bone wax provided a sufficient airtight seal to allow use of the 5-mm port during ablative therapy of renal masses.conclusions:use of bone wax during laparoscopic renal ablative surgery allows the use of an established 5-mm port , thus obviating a separate skin incision and reducing the tract - site exposure to the needle probe .

Letter from North Korean official to A.Q. Khan This is the letter purportedly written by Jon Byong Ho, a longtime confidante of the father and son who have ruled North Korea since 1948. Jon is an inside player who rarely travels and his signed documents have been seen by few officials outside North Korea, making it impossible to authenticate the letter with complete certainty. ||||| The founder of Pakistan’s nuclear bomb program asserts that the government of North Korea bribed top military officials in Islamabad to obtain access to sensitive nuclear technology in the late 1990s. Abdul Qadeer Khan has made available documents that he says support his claim that he personally transferred more than $3 million in payments by North Korea to senior officers in the Pakistani military, which he says subsequently approved his sharing of technical know-how and equipment with North Korean scientists. Khan also has released what he says is a copy of a North Korean official’s 1998 letter to him, written in English, that spells out details of the clandestine deal. Some Western intelligence officials and other experts have said that they think the letter is authentic and that it offers confirmation of a transaction they have long suspected but could never prove. Pakistani officials, including those named as recipients of the cash, have called the letter a fake. Khan, whom some in his country have hailed as a national hero, is at odds with many Pakistani officials, who have said he acted alone in selling nuclear secrets. Nevertheless, if the letter is genuine, it would reveal a remarkable instance of corruption related to nuclear weapons. U.S. officials have worried for decades about the potential involvement of elements of Pakistan’s military in illicit nuclear proliferation, partly because terrorist groups in the region and governments of other countries are eager to acquire an atomic bomb or the capacity to build one. A.Q. Khan in an undated photo. (AP) Because the transactions in this episode would be directly known only to the participants, the assertions by Khan and the details in the letter could not be independently verified by The Washington Post. A previously undisclosed U.S. investigation of the corruption at the heart of the allegations — conducted before the letter became available — ended inconclusively six years ago, in part because the Pakistani government has barred official Western contact with Khan, U.S. officials said. By all accounts, Pakistan’s confirmed shipments of centrifuges and sophisticated drawings helped North Korea develop the capacity to undertake a uranium-based route to making the bomb, in addition to its existing plutonium weapons. Late last year, North Korea let a group of U.S. experts see a uranium-enrichment facility and said it was operational. The letter Khan released, which U.S. officials said they had not seen previously, is dated July 15, 1998, and marked “Secret.” “The 3 millions dollars have already been paid” to one Pakistani military official and “half a million dollars” and some jewelry had been given to a second official, says the letter, which carries the apparent signature of North Korean Workers’ Party Secretary Jon Byong Ho. The text also says: “Please give the agreed documents, components, etc. to . . . [a North Korean Embassy official in Pakistan] to be flown back when our plane returns after delivery of missile components.” The North Korean government did not respond to requests for comment about the letter. Jehangir Karamat, a former Pakistani military chief named as the recipient of the $3 million payment, said the letter is untrue. In an e-mail from Lahore, Karamat said that Khan, as part of his defense against allegations of personal responsibility for illicit nuclear proliferation, had tried “to shift blame on others.” Karamat said the letter’s allegations were “malicious with no truth in them whatsoever.” The other official named in the letter, retired Lt. Gen. Zulfiqar Khan, called it “a fabrication.” The Pakistani Embassy in Washington declined to comment officially. But a senior Pakistani official, who spoke on the condition of anonymity “to avoid offending” Khan’s supporters, said the letter “is clearly a fabrication. It is not on any official letterhead and bears no seal. . . . The reference to alleged payment and gifts to senior Pakistani military officers is ludicrous.” There is, however, a Pakistani-Western divide on the letter, which was provided to The Post by former British journalist Simon Henderson, who The Post verified had obtained it from Khan. A U.S. intelligence official who tracks nuclear proliferation issues said it contains accurate details of sensitive matters known only to a handful of people in Pakistan, North Korea and the United States. A senior U.S. official said separately that government experts concluded after examining a copy of the letter that the signature appears authentic and that the substance is “consistent with our knowledge” now of the same events. Both officials spoke on the condition of anonymity because of the diplomatic sensitivity of the allegation. Olli Heinonen, a 27-year vet­eran of the International Atomic Energy Agency who led its investigation of Khan before moving to Harvard’s Kennedy School last year, said the letter is similar to other North Korean notes that he had seen or received. They typically lacked a letterhead, he said; moreover, he said he has previously heard similar accounts — originating from senior Pakistanis — of clandestine payments by North Korea to Pakistani military officials and government advisers. The substance of the letter, Heinonen said, “makes a lot of sense,” given what is now known about the North Korean program. Jon, now 84, the North Korean official whose signature appears on the letter, has long been a powerful member of North Korea’s national defense commission, in charge of military procurement. In August, the U.S. Treasury Department imposed financial sanctions on his department for its ballistic missile work. According to Khan, in the 1990s, Jon met then-Pakistani President Farooq Leghari, toured the country’s nuclear laboratory and arranged for dozens of North Korean technicians to work there. Khan detailed the payments Jon allegedly arranged in written statements that Henderson, a senior fellow at the Washington Institute for Near East Policy, shared with The Post. Henderson said he acquired the letter and the statements from Khan in the years after his 2004 arrest by Pakistani authorities. Henderson, who has written extensively about Khan, said he provided the letter to The Post because he lacked the resources to authenticate it himself. He said the letter and the statements constitute new evidence that Khan’s proliferation involved more-senior Pakistani officials than Khan himself. Khan has been freed from home detention but remains under round-the-clock surveillance in a suburb of Islamabad, where the government has recently threatened him with new sanctions for illicit communications. Some of Khan’s past statements have been called into question. Pakistani officials have publicly accused Khan — who is still highly regarded by many in his country — of exaggerating the extent of official approval he received for his nuclear-related exports to North Korea, Libya and Iran. In 2006, then-Pakistani President Pervez Musharraf accused Khan of profiting directly from nuclear-related commerce. Although Khan “was not the only one who profited from the sale of Pakistan’s nuclear weapons technology and components . . . by Pakistani standards, his standard of living was lavish,” and the disclosure of his private bank account in Dubai, the United Arab Emirates — with millions of dollars in it — was highly suspicious, said Mark Fitzpatrick, an acting deputy assistant secretary of state for nonproliferation during the George W. Bush administration. Khan says the bank account was used by associates and a charity he founded, and the Pakistani government never asked him to return any money. He said that in 2007 — six years after his formal retirement and complaints of financial hardship — Musharraf arranged for a lump-sum payment equivalent to $50,000 and a monthly pension of roughly $2,500, which Khan says “belied all those accusations and claims.” Although U.S. officials disagreed for years about North Korea’s uranium-enrichment capability, the dispute was settled in November when the Pyongyang government invited Siegfried Hecker — a metallurgist who formerly directed a U.S. nuclear weapons laboratory — to see a newly renovated building at Yongbyon that housed more than 1,000 enrichment centrifuges. Hecker said in an interview that although the government did not disclose their origins, their size, shape and stated efficiency were close to a centrifuge model, known as the P2, that Khan obtained illicitly from Europe. Khan has said that he helped give North Korea four such devices. “The combination of the Pakistani design, the Pakistani training and the major [Pakistani] procurement network they had access to” allowed North Korea to “put the pieces together to make it work,” Hecker said. According to Khan’s written account, the swap of North Korean cash for sensitive Pakistani technology arose during a squabble in 1996 over delays in Pakistan’s payment to North Korea for some medium-range missiles. U.S. officials said they had heard of this dispute. In the letter, Jon first thanks Khan for his assistance to North Korea’s then-representative to Islamabad, Gen. Kang Tae Yun, in the aftermath of a bizarre shooting incident in which an assailant supposedly gunning for Kang accidentally killed his wife. But the heart of the letter concerns two key transactions: the provision of a kickback to speed the overdue Pakistani missile-related payments and additional payments for the nuclear-related materials. Khan, in his written statements — including an 11-page narrative he prepared for Pakistani investigators while under house arrest in 2004 that was obtained by The Post — said the idea for the kickback came from a Pakistani military officer. Khan said Kang responded by delivering a half-million dollars in cash in a suitcase to a top Pakistani general, who declined it. Khan said Karamat, a more senior officer at the time, then said: “I should arrange with Gen. Kang to pay this money to him for some secret [Pakistani] army funds. He would then sanction the payment of their outstanding charges.” “I talked to Gen. Kang, and he gave me the $0.5 million in cash, which I personally delivered” to Karamat, Khan wrote. He says this payment only whetted the army’s appetite, however: Karamat, who had just become chief of the army staff, “said to me that he needed more money for the same secret funds and that I should talk to Gen. Kang.” Kang then started bargaining, saying that his superiors “were willing to provide another $2.5 million, provided we helped them with the enrichment technology,” Khan wrote. Once the details of that assistance were worked out, Khan wrote, “I personally gave the remaining $2.5 million to Gen. Karamat in cash at the Army House to make up the whole amount.” Khan said he transferred all the funds on two occasions in a small canvas bag and three cartons, in one case at the chief of army staff’s official residence. On the top of one carton was some fruit, and below it was $500,000 in cash, Khan wrote in a narrative for Henderson. Inside the bag was $500,000, and each of the other two cartons held $1 million, Khan wrote. If the account is correct, the ultimate destination of the funds in any event remains unclear. Pakistani officials said in interviews that they found no trace of the money in Karamat’s accounts after an investigation. But the military is known to have used secret accounts for various purposes, including clandestine operations against neighboring India in the disputed Kashmir region. Karamat said that such a delivery would have been impossible and that he “was not in the loop to delay, withhold or sanction payments” to North Korea. He called the letter “quite mind-boggling.” The letter also states that Zulfiqar Khan, Karamat’s colleague, received “half a million dollars and 3 diamond and ruby sets” to pave the way for nuclear-weapons-related transfers. Zulfiqar Khan, who later became the head of Pakistan’s national water and power company, was among those who had witnessed the country’s nuclear weapons test six weeks before the letter was written. Asked to respond, he said in an e-mail that he considered the entire episode “a fabrication and figment of imagination,” and he noted that he had not been accused of “any sort of dishonesty or irregularity” during 37 years as a military officer. He denied having any connection to North Korean contracts. The senior Pakistani official said that Karamat and Zulfiqar Khan were “amongst the first to initiate accountability” for Abdul Qadeer Khan and his colleagues, and that implicating them in illegal proliferation “can only be deemed as the vengeful reaction of a discredited individual.” In the letter, Jon requests that “the agreed documents, components” be placed aboard a North Korean plane. He goes on to congratulate Khan on Pakistan’s successful nuclear test that year and wish him “good health, long life and success in your important work.” The Pakistani intelligence service interrogated Karamat in 2004 about Khan’s allegations, according to a Pakistani government official, but made no public statement about what it learned. Musharraf, who oversaw that probe, appointed Karamat as ambassador to Washington 10 months later, prompting further scrutiny by the U.S. intelligence community of reports that Karamat had arranged the sale of nuclear gear for cash. Those inquiries, several U.S. officials said, ended inconclusively at the time because of Karamat’s denial and Washington’s inability to question Khan. Staff writer Joby Warrick in Islamabad contributed to this report. ||||| The founder of Pakistan's nuclear weapons program claims that in the late 1990s North Korean officials paid kickbacks to senior Pakistani military figures in exchange for critical weapons technology. Abdul Qadeer Khan has given a United States-based expert documents that appear to show North Korea's government paid more than $3.5 million to two Pakistani military officials as part of the deal, the expert told The Associated Press Wednesday. To back up his claim, Khan released what he said was a copy of a North Korean official's 1998 letter to him, written in English, that purports to describe the secret deal. Khan gave the documents to Simon Henderson of the Washington Institute for Near East Policy, an authority on Pakistan's weapons program. He did so because he has been accused by his government of running a covert nuclear smuggling operation without official knowledge or consent. "He gave it to me because he regarded it as showing that the story, the perception that he had been a rogue operator was false," Henderson said. The letter, along with a statement by Khan describing the deal, suggests that at least some top-level Pakistani military officials knew early on about some of Khan's extensive sale of nuclear weapons technology to other countries, including North Korea, Iran and Libya. If that's true, it could deepen the distrust between the United States and Pakistan, which are struggling to set aside their differences and cooperate in the battle against militant extremists in Afghanistan and Pakistan. The significance of the revelation is in dispute. Henderson said the documents prove Khan's claims that his nuclear arms smuggling network had high-level support from the Pakistani government, but others say the letter bolsters the government's claims it didn't know what Khan was up to. The Washington Post said it obtained the documents and first reported on them on its website Wednesday after a lengthy effort to authenticate them. The letter Khan released is dated July 15, 1998, and marked "Secret." It carries the apparent signature of North Korean Workers Party Secretary Jon Byong Ho. The text says, "Please give the agreed documents, components, etc. to a ... (North Korean Embassy official in Pakistan) to be flown back when our plane returns after delivery of missile components." The letter never mentions the word "nuclear." But Khan's written description of the events surrounding the letter makes it clear that the Workers Party official was referring to components and plans for Pakistani centrifuges used to enrich uranium. Highly enriched uranium can be used either to make fuel for nuclear reactors or to form the explosive core of a nuclear weapon. Jehangir Karamat, a former Pakistani military chief named as the recipient of the $3 million, said the letter was untrue. In an email to the Post from Lahore, Karamat said Khan, as part of his defense against allegations of personal responsibility for illicit nuclear proliferation, had tried "to shift blame on others." The other official, retired Lt. Gen. Zulfiqar Khan, called the letter "a fabrication." The Post said the assertions by Khan and the details in the letter could not be independently verified. But the newspaper quoted one senior U.S. official who said the signature appeared genuine and the contents were "consistent with our knowledge" of the events described. Another intelligence official said the letter contained information known only to a handful of people. Khan has long denied claims that he was working behind his government's back in his covert nuclear technology sales to foreign governments. "This is a piece of dramatic evidence that Khan did not act as a single rogue agent, but instead was operating at the instruction of others," Henderson said. "I think the main point of this is that Pakistan used this technology to trade for diplomatic advantage." David Albright, an authority on nuclear proliferation with the Institute for Science and International Security in Washington, disagreed, saying the letter and Khan's narrative are evidence he acted alone. "It shows that Khan was a rogue agent and that he colluded to provide centrifuge components to North Korea without Pakistani official approval," Albright said. He said that in Khan's narrative, which has not been released, the scientist claimed he had assured the military that North Korea would not use the centrifuges for its nuclear weapons program, since it already had more advanced technology for that purpose. Albright said the claim was false, but Pakistani military officials could have found it plausible.

– Pakistani military officials took more than $3.5 million in kickbacks from North Korea in exchange for essential nuclear weapons technology, according to Abdul Qadir Khan, the founder of Pakistan's nuclear weapons program. Khan has given documents detailing the transaction, which would have taken place in the late 1990s, to Simon Henderson at the Washington Institute for Near East Policy, Henderson tells the AP. "He gave it to me because he regarded it as showing that the story, the perception that he had been a rogue operator was false," Henderson explains. Khan has also released what he says is a letter sent from North Korea to him in 1998, which describes the deal in English. Western intelligence officials tell the Washington Post they're convinced the letter is real, and that it "makes a lot of sense" given what they already knew. Pakistani officials, however, say it's "clearly a fabrication." You can see the letter here.

recently , the cesarean delivery rate has been reported to be steadily increased in the united states [ 13 ] . approximately , one - third of births in the united states are now via cesarean delivery . the increase has been observed to be among women of all ages and race / ethnicities , in every state , and across all gestational ages . many theories have been proffered to explain this trend , including a decrease in vaginal births after cesarean delivery ( vbac ) , decreased vaginal births of breech presentation , and increased prevalence of high risk pregnancies such as advanced maternal age and some subjective indications during labor such as nonreassuring fetal status and arrest of dilation [ 1 , 2 ] . although cesarean delivery rates that are too low are associated with increased adverse events , cesarean delivery rates higher than the risk - adjusted expected rate for an institution have not been shown to improve maternal or neonatal outcomes , but they do add cost and unnecessary intervention . therefore , the examination of cesarean delivery rate concerning perinatal outcomes is very important for obstetricians . to date , however , there have not been sufficient observations concerning the cesarean delivery rate in japanese populations . in this study , we examined which specific factors contributed to the increase in cesarean delivery rate at our hospital over a 10-year period . the protocol for this study was approved by the ethics committee of the japanese red cross katsushika maternity hospital . our hospital is one of the major perinatal centers in tokyo , japan ( about 1,9002,000 deliveries per year ) . from january 2002 to december 2012 , data on the japanese singleton deliveries at 22-week gestation managed at the japanese red cross katsushika maternity hospital were collected . demographic information and the characteristics of labor were extracted from patient charts to examine the potential factors associated with the increasing cesarean delivery rate . in this study , the factors were selected according to previous studies [ 13 , 5 , 6 ] : nulliparity , advanced maternal age ( 35 years ) , pregnancy - induced hypertension ( pih ) , preterm delivery , low birth weight ( lbw : neonatal birth weight < 2,500 g ) and macrosomia ( neonatal birth weight 4,000 g ) , history of previous cesarean deliveries , and breech presentation . pih was defined as blood pressure 140/90 mmhg measured on two or more occasions at least six hours apart with the patient at rest . in our institute , the umbilical cord ph was measured at all deliveries . in addition , we do not perform cesarean sections for maternal request . in this study , to examine the effect of the increasing cesarean delivery rate on the obstetric outcome , the incidences of intrauterine fetal demise ( iufd ) , umbilical artery ph ( uaph ) < 7.1 , and severe perineal laceration ( perineal laceration either third- or fourth - degree laceration ) were calculated for each year . logistic regression modeling was used to estimate cesarean delivery rate over time and for each factor . linear regression was performed to estimate the trend over time for each factor , cesarean delivery rate for each factor , and obstetric outcomes . statistical analyses were carried out using the statistical software sas version 8.02 ( sas institute , cary , nc , usa ) , and differences with p < 0.05 were considered significant . from january 2002 to december 2012 , a total of 20,514 japanese singleton deliveries at 22-week gestation were managed at the japanese red cross katsushika maternity red cross hospital ; 4,086 ( 19.9% ) of those births were delivered by cesarean section . as shown in figure 1 , the cesarean delivery rate at our institution increased significantly during the study period ( 17.3% in 2002 versus 23.4% in 2012 , p < 0.01 ) . maternal demographic and obstetric - fetal characteristics among the deliveries , which are potential factors associated with the increasing cesarean delivery rate , during the study period are presented in table 1 . there was a significant increase in the prevalence of advanced maternal age ( 35 years ) during the study period ( 26.6% in 2002 versus 33.0% in 2012 , p < 0.01 ) . figure 2 shows the changes in cesarean delivery rate for each factor during the study period . as shown in figure 2 , the cesarean delivery rates with these factors were significantly higher than the average cesarean delivery rate among all deliveries . during the study period , the cesarean delivery rates in the cases of nulliparity , preterm delivery , lbw , previous cesarean deliveries , and breech presentation were increased significantly ( nulliparous women : 18.0% in 2002 versus 23.4% in 2012 , p < 0.01 ; preterm delivery : 39.5% in 2002 versus 57.5% in 2012 , p < 0.01 ; lbw : 35.8% in 2002 versus 57.5% in 2012 , p < 0.01 , previous cesarean deliveries : 66.7% in 2002 versus 90.0% in 2012 , p < 0.01 ; breech presentation : 76.2% in 2002 versus 94.5% in 2012 , p < 0.01 ) . table 2 shows the changes in the incidence of iufd , low uaph , and severe perineal laceration during the study period . during the study period , the incidence of iufd and low uaph were significantly decreased ( iufd : 0.8% in 2002 versus 0.3% in 2012 , p = 0.03 ; low uaph : 3.3% in 2002 versus 1.6% in 2012 , p < 0.01 ) . a negative correlation was found between the cesarean delivery rate and the incidence of low uaph for each year ( r = 0.92 , p < 0.01 ) . the major findings of the current study are as follows : ( 1 ) the cesarean delivery rate at our institute increased between 2002 and 2012 , ( 2 ) one of possible reasons for the increasing cesarean delivery rate is an increase in the prevalence of advanced maternal age ( 35 years ) , ( 3 ) other possible reasons for the increasing cesarean delivery rate are the increase in cesarean delivery rates in the cases of nulliparity , preterm delivery , lbw , previous cesarean deliveries , and breech presentation , and ( 4 ) the incidence of low uaph seemed to be improved associated with the increased cesarean delivery rate . this may be the first report examining the recent changes in cesarean delivery rate in japan . we found the trends in careful correspondences for various high - risk deliveries leading to the increased cesarean delivery rate at our institute in japan . these trends seem to be the same as those previously reported in the usa [ 13 , 5 , 6 ] and japan [ 79 ] . for example , in a recent observation at other perinatal centers in japan , cesarean delivery rate was about 50% in primiparous women aged 40 years . in our institute , there has been a significant increase in the primary elective cesarean delivery rate of singleton breech pregnancies due to medical counseling and maternal request between 2000 and 2005 . this phenomenon is associated with the acog recommendation in 2001 , which recommended cesarean delivery for the term singleton breech . an increased cesarean delivery rate in cases with precious cesarean deliveries seemed to be also an important factor contributing to the current results [ 13 , 5 ] . in our institute , intrapartum asphyxia has been observed to be independently associated with cases of trial of labor after cesarean delivery ( tolac ) in singleton deliveries beyond 37-week gestation . the asphyxia seemed to be associated with failed vacuum - extraction and/or forceps delivery during tolac . therefore , our previous findings may be encouraging for the counseling of patients regarding a possible attempt at tolac . from our impressions , these trends in delivery modes of cases with previous cesarean deliveries and those with breech presentation have been expanded to all areas of japan . unfortunately , there are some limitations in this study with the lack of taking into consideration confounders such as education / social economic status / immigrant status / antenatal cares access , all variables known to affect mode of delivery [ 13 , 5 , 6 ] . in addition , we believe that defensive medicine and litigation as an explicit incentive for performing cesarean section are unlikely to play a large role . in this study , the increased cesarean delivery rate seemed to contribute to the improvement of neonatal outcomes such as the decreased low uaph . therefore , it appears that on a global level , the birth process is becoming more medicalised and it may need the increasing in cesarean delivery rate in japan . on the other hand , the increasing in cesarean delivery rate in the past has contributed to the reduction in adverse events ; however , the impact of the increasing in cesarean delivery rate on the maternal and/or neonatal outcomes further from now can not be predicted . therefore , in the future , we have to pay attention be the changes in cesarean delivery rate and perinatal outcomes at our institute in japan . in conclusion the incident of low uaph seemed to be improved associated with the increased cesarean delivery rate .

objective . we examined which specific factors contributed to the increase in cesarean delivery rate at our hospital over a 10-year period . methods . from january 2002 to december 2012 , data on the japanese singleton deliveries at 22-week gestation managed at japanese red cross katsushika maternity hospital were collected . potential factors associated with the increasing cesarean delivery rate were selected according to previous studies . in this study , the incidences of intrauterine fetal demise , umbilical artery ph < 7.1 , and severe perineal laceration were calculated for each year . results . the cesarean delivery rate at our institution increased significantly during the study period ( 17.3% in 2002 versus 23.4% in 2012 , p < 0.01 ) . during the study period , the cesarean delivery rates in the cases of nulliparity , preterm delivery , low birth weight ( < 2,500 g ) , previous cesarean deliveries and breech presentation were increased significantly . the incidence of intrauterine fetal demise and low umbilical artery ph was significantly decreased , and a negative correlation was found between the cesarean delivery rate and the incidence of low umbilical artery ph for each year ( r = 0.92 , p < 0.01 ) . conclusion . at our institute , the neonatal outcomes seemed to be improved associated with the increased cesarean delivery rate between 2002 and 2012 .

the @xmath0 relation for tp - agb stars , first discovered by paczyski ( 1970a ) , has since then been employed in many studies involving this evolutionary phase . it is a basic ingredient in synthetic calculations of tp - agb evolution , and an important tool for the interpretation of observational data for agb stars . what the @xmath0 relation means in the classical sense is simply that the quiescent luminosity of a tp - agb star in the full - amplitude regime is mainly controlled by its core mass , without any dependence on the mass of its outer envelope . various theoretical analyses have been performed in the past to explain the existence of the @xmath0 relation from first principles , using either homology relations ( refsdal & weigert 1970 ; havazelet & barkat 1979 ; kippenhahn 1981 ) , or the equations of stellar structure under specific physical conditions ( see eggleton 1967 ; paczyski 1970b ; tuchman et al . 1983 ; jeffery 1988 ) . a transparent discussion of the validity of the @xmath0 relation was presented by tuchman et al . ( 1983 ) , to whom the reader should refer . there it is shown that an @xmath0 relation _ necessarily _ holds when the star consists of : * a _ degenerate core _ of mass @xmath1 surrounded by * a narrow _ radiative burning shell _ ( or double shell ) source providing most of the luminosity ( @xmath2 ) , beyond which there must exist * a _ thin _ ( with a mass @xmath3 ) and _ inert _ ( the luminosity is constant ) _ transition region in radiative equilibrium _ , extending up to the base of the convective envelope . then , because of the extreme steepness of the structural gradients across the radiative inert zone , it follows that the thermal evolution of the core is decoupled from that of the envelope . the relationship between the core mass and the luminosity , defined on the ground of this physical picture , is of linear nature , as confirmed by numerical results ( e.g. paczyski 1970a ; iben 1977 ; wood & zarro 1981 ; boothroyd & sackmann 1988a ) . hereinafter , such linear relation will be referred to as _ the classical @xmath0 relation_. however , such a simple @xmath0 relation does not hold for all agb stars . blcker & schnberner ( 1991 ) have shown that the @xmath0 relation can indeed break down in the most massive agb stars ( @xmath4 depending on the metallicity ) experiencing envelope burning ( or hot - bottom burning ) . in this context , substantial efforts have been made in order to accurately include this effect in synthetic tp - agb calculations ( marigo et al.1998 ; marigo 1998 ; wagenhuber & groenewegen 1998 ) . it must be emphasized that @xmath0 relations in synthetic calculations are always technically motivated relations intended to fit results of full stellar evolution calculations . by no means they are just the classical , physically motivated linear relations mentioned above . in the following , such relations will be referred to as _ technical @xmath0 relations_. very recently , herwig et al . ( 1998 , hereinafter hsb98 ) have claimed that the classical @xmath0 relation may also be violated in low - mass agb stars , as a consequence of efficient third dredge - up . more specifically , they present evolutionary sequences with a dredge - up efficiency close to @xmath5 or even higher is defined as the ratio between the dredged - up mass and the core mass increase during each inter - pulse period . ] , i.e. characterized by an almost constant or slightly decreasing core mass @xmath1 . despite of this fact , these sequences are found to evolve at increasing luminosity . this behavior is in apparent contradiction with the trend expected from the classical @xmath0 relation , predicting lower luminosities at lower core masses . in the present study we address the question whether these results present a _ further _ deviation from the classical @xmath0 relation , as claimed by hsb98 , or if they can be explained , at least partly , by the already known ( and understood ) deviations . a violation of the classical @xmath0 relation implies that , for some reason , the configuration defined in tuchman et al . ( 1983 ) is altered . for instance , the occurrence of hot - bottom burning ( or envelope burning ) in the most massive tp - agb stars causes the inert radiative buffer to disappear , due to the deep penetration of the convective envelope into the h - burning shell . another example refers to the first inter - pulse periods , when the luminosity of a tp - agb star is found to be lower than predicted by the classical @xmath0 relation for the same @xmath1 . in these initial stages the condition @xmath6 is not actually fulfilled , as the gravitational contraction of the core and the he - burning shell provide non - negligible contributions to the surface luminosity . in the context of the recent results by hsb98 , the first natural question is : does the third dredge - up in low mass tp - agb stars lead to a real violation of the classical @xmath0 relation ? in other words , is any of the conditions listed above not fulfilled ? the answer is : no . in fact , the degenerate core and the h - burning shell still exist in the quiescent regime after the dredge - up has occurred , as does the radiative inert buffer , since hsb98 are only considering stars which do not experience hot - bottom burning . the second question is : if the basic conditions for the existence of the classical @xmath0 relation are still fulfilled , what causes the deviation from the linear @xmath0 relation ? in order to answer the latter question , let us consider the previously known deviations from the classical @xmath0 relation . the first effect to consider is the initial luminosity evolution of tp - agb stars . in complete calculations of agb stars the first thermal pulses still take place during a phase of fast core contraction , at luminosities lower than given by the classical , linear @xmath0 relation . during a few thermal pulses , the luminosity gradually approaches this relation , up to the so - called _ full - amplitude regime_. during these first pulses unique relations between @xmath7 and @xmath8 are not expected to exist . the sequences of models shown by hsb98 in their figs . 2 and 3 refer to a relatively small number of pulse cycles , most of which have not yet attained the full - amplitude regime . more specifically , the two evolutionary sequences they computed with overshooting , for @xmath9 ( labelled @xmath10 in hsb98 ) and @xmath11 ( @xmath12 ) models , present only 14 and 12 thermal pulses , respectively . in each of these sequences , at least 6 of the pulse cycles are clearly in the sub - luminous phase which characterizes the first pulses . this can be seen in fig . [ fig_lmc ] . hsb98 compare their sequences with the @xmath0 relation from blcker ( 1993 ) . the latter is shown as a dotted line in fig . [ fig_lmc ] . this relation clearly predicts too faint luminosities if compared to the most luminous points in the sequences of models with no or little dredge - up , @xmath13 and @xmath14 . this inappropriateness of the blcker @xmath0 relation to describe the present hsb98 models probably derive from the different input physics used in both sets of models . we therefore prefer to define another linear @xmath0 relation , more appropriate to describe the asymptotic behaviour of the hsb98 models without dredge - up . this is shown as the solid line in fig . [ fig_lmc ] . this has been chosen to be the one which reasonably fits the 16 last inter - pulse periods ( out of 19 ) in the @xmath13 sequence , and the last 3 or 4 ( out of 23 ) in the @xmath14 one . both evolutionary sequences asymptotically approach this linear relation . in all the hsb98 evolutionary tracks , the first thermal pulses have luminosities which are lower than predicted by this asymptotic linear @xmath0 relation we adopt ( solid line ) . in the sequences with efficient dredge - up , only the very last quiescent models are more luminous than predicted by this relation for the same core masses . specifically , only the last 3 inter - pulse periods of the @xmath10 track , and the last 5 of the @xmath12 one are above the @xmath0 relation . the remaining points are all steadily increasing in luminosity , which is just the behavior expected for the first thermal pulses . the luminosity increase in the initial phase of the tp - agb evolution is partly due to the release of gravitational energy by the contracting core , and clearly constitutes a violation of the assumptions for the validity of the classical @xmath0 relation . however , this effect is well known and already taken into account in the technical @xmath0 relations in synthetic models ( e.g. groenewegen & de jong 1993 ; marigo et al . 1996 , 1998 , 1999 ; marigo 1998 ; wagenhuber & groenewegen 1998 ) . we note , however , that the behavior of @xmath15 for the two sequences with efficient dredge - up clearly deviates from those of the sub - luminous pulses without dredge - up , such that the presence of an additional effect resulting from the dredge - up is likely . another important point is related to the change of the surface chemical composition produced by the third dredge - up , and thus to the composition dependence of the @xmath0 relation . indeed , the fact that changes in the chemical composition of the envelope may affect but do not violate the classical @xmath16 relation had already been pointed out long ago from theoretical arguments ( e.g. refsdal & weigert 1970 ; kippenhahn 1981 ; tuchman et al . 1983 ) . as clearly derived from tuchman et al . ( 1983 ; see their equations ( 1.17 ) and ( 1.29 ) ) the @xmath0 relation contains a non - negligible dependence on the composition of the envelope , essentially expressed by three parameters : * a factor ( @xmath17 ) from the electron scattering opacity , * a factor ( @xmath18 ) from the mean molecular weight ( @xmath19 for a fully ionized gas ) , * a factor ( @xmath20 ) from the hydrogen burning rate . since then , various @xmath0 relations , both classical linear and technical ones which include a composition dependence , have been presented by different authors ( e.g. lattanzio 1986 ; boothroyd & sackmann 1988a ; wagenhuber & groenewegen 1998 ; tuchman & truran 1998 ) . from these studies it turns out that at any given core mass , the quiescent luminosity of a tp - agb star increases with increasing metallicity @xmath21 , helium content @xmath22 , ( both leading to a higher mean molecular weight @xmath23 ) , and cno abundances @xmath24 . for instance , based on calculations of full agb models , boothroyd & sackmann ( 1988a ) carefully analyzed the composition dependence , deriving a proportionality factor @xmath25 in their fitting formula of the @xmath0 relation . they found that at given core mass , stars of solar composition ( @xmath26 ) are @xmath27 more luminous than metal poor stars ( @xmath28 ) . it follows that the occurrence of recurrent dredge - up episodes in tp - agb stars is expected to alter ( not to break ) even the classical @xmath0 relation , as a consequence of the increase of the mean molecular weight in the envelope . of course , this effect has already been included in several synthetic calculations ( e.g. groenewegen & de jong 1993 ; marigo et al . 1996 , 1998 ; marigo 1998 ) , where @xmath0 relations with a metallicity dependence have been adopted . marigo ( 1998 ) has already pointed out that a deviation from the @xmath0 relation , corresponding to constant metallicity , can be caused by changes in the envelope composition . we have estimated , from the data presented in herwig et al . ( 1997 ; hereinafter hbse97 ) , herwig ( 1998 ) and hsb98 , the total change in the envelope composition due to the dredge - up events . for the @xmath29 @xmath10 track , the mean molecular weight @xmath23 is estimated to increase from 0.6314 to 0.6394 during the tp - agb evolution , whereas for the @xmath30 @xmath12 one , it increases from 0.6304 to 0.6376 . this implies that in both cases @xmath23 increases by 1.3 % in total . assuming @xmath31 ( following boothroyd & sackmann 1988a ) , this change in the envelope chemical composition would imply a change of 4% in the luminosity predicted by the linear @xmath0 relation for constant metallicity . this already accounts for one - third of the luminosity increase above the @xmath16 relation drawn in fig . [ fig_lmc ] . hsb98 claim that their evolutionary sequences do not present hot - bottom burning , since their core masses are `` lower than those associated to hot - bottom burning '' ( hbb ) . the highest core mass in their tracks is @xmath32 , whereas they consider hbb to be present only at higher core masses . however , the knowledge of the core mass is not enough to diagnose the possible occurrence of hbb . several authors ( boothroyd & sackmann 1992 ; vassiliadis & wood 1993 ; dantona & mazzitelli 1996 ; marigo 1998 ) find that the presence of hbb , and its associated `` over - luminosity '' , are sensitive to other stellar parameters as well , as e.g. the envelope mass , metallicity , mixing - length parameter , and to the details of the convection theory . the latter results have been obtained by means of stellar models that adopt canonical convection theories . it would be interesting to quantify whether the diffusive overshooting scheme applied by hsb98 to all convective boundaries , may also produce conditions favorable to hbb , i.e. higher temperatures at the bottom of the convective envelope at lower core masses . if this were the case the over - luminosity of the tracks may be partially ascribed to the occurrence of ( a possibly mild ) hbb . in this respect , however , no conclusion can be drawn without additional information about the hbs98 tracks . as remarked above , most of the luminosity behavior of the hsb98 tracks can be understood by means of already known effects taking place during the tp - agb evolution . hbs98 , however , explicitly mention a violation of the classical @xmath0 relation caused by dredge - up , and provide an explanation for the unusual behavior of their tracks based on the stellar core radius . the authors find that the core radii , @xmath33 , of their tp - agb models follow quite different paths in the @xmath34 plane , depending on whether the models experience dredge - up or not . then , considering the apparent lack of a unique @xmath35 relationship and using the homology relation @xmath36 , hsb98 conclude that the luminosity is not a function of @xmath1 alone , but also of @xmath33 . as a consequence , the @xmath0 relation should rather be seen as a @xmath37 relation . moreover , hsb98 claim that the over - luminosity above the @xmath0 relation of their evolutionary sequences with @xmath38 can be explained assuming @xmath39 a fact we can not confirm . in fig . [ fig_lmc2 ] , we plot the luminosity evolution of the hsb98 @xmath30 sequences , as derived both from their @xmath8 and @xmath1 values ( from their figs . 2 and 3 ; filled symbols ) . we then use the @xmath1 and @xmath33 values in order to obtain the equivalent luminosity from eq . ( [ eq_lmc2 ] ) above . this procedure however requires that we fix a value to the constant in this equation . the first point of the @xmath12 sequence is used for this purpose , so that we obtain the relation @xmath40 ( where all quantities are in solar units ) . the open symbols in fig . [ fig_lmc2 ] then show the luminosities as obtained from this latter relation . in this way , we have obtained the equivalent of fig . 4 in hsb98 . we find that the luminosities as derived from eq . ( [ eq_lmc2 ] ) are far from reproducing those given by the complete evolutionary sequences , although the general behaviour is similar . in contrast , hsb98 obtain quite a good match between the two sets of curves . examining their fig . 4 , and comparing it with fig . [ fig_lmc2 ] , we conclude that hbs98 adopt two different scales in their plot ( i.e. for the true luminosity and for the luminosity as obtained from eq . ( [ eq_lmc2 ] ) ) , which are not related by a single multiplicative constant . thus , their explanation of the luminosity evolution in terms of eq . ( [ eq_lmc2 ] ) is misleading , since obviously , the `` constant '' they adopt varies from model to model along the evolutionary sequences . the possible dependence of the luminosity on core radius deserves the following remarks . this dependence would reflect the release of gravitational energy by the contracting core . during the tp - agb evolution , the core contracts more rapidly during the first thermal pulses , until an almost constant and very low contraction rate is established in the full - amplitude regime ( herwig 1998 ) . another concurring effect comes from the decrease of the ratio @xmath41 between the gas and the total pressure at increasing luminosities . the homology relation actually predicts @xmath42 , where the exponents @xmath43 and @xmath44 are given in equation 3 of hsb98 . since @xmath45 , the radius dependence in eq . ( [ eq_lmc2 ] ) vanishes as we increase @xmath8 and hence @xmath46 . for both reasons , an @xmath0 relation independent of @xmath33 should hold after a certain time . unfortunately , the calculations by hsb98 have been stopped at the most important point , i.e. where the evolution of the core radius as a function of the core mass for the models with efficient dredge - up joins the standard @xmath34 relation described by the models without dredge - up after the initial pulses ( see their figure 3 ) . if , from this point on , both relations follow the same path , then the entire effect presented by hsb98 is indeed related to peculiar behaviour of the first pulses , before the settling of the full - amplitude regime . in this case , there would be no real violation of the @xmath0 relation . otherwise , if there is a different dependence of the core radius upon the core mass , the @xmath0 relation might be at least partly modified . if this were the case , it would be quite important to single out the physical effect produced by the convective dredge - up , which occurs at a thermal pulse , on the core radius during the subsequent quiescent evolution . in other words , why should the evolution of the core radius turn out different between models with and without dredge - up ? this point is not clear in the hsb98 analysis . to this respect , an interesting point is discussed by tuchman et al . ( 1983 ) , in their analytical demonstration of the @xmath0 relation from first principles . in brief , the authors shows that core radius of an agb star is larger than the radius of an ideal zero - temperature white dwarf ( for which a unique linear @xmath34 relation exists ) by a multiplicative factor , @xmath47 , which depends both on the core mass @xmath1 and on the temperature @xmath48 at the top of the h - burning shell ( i.e. bottom of the overlying inert radiative buffer ; see their equations 1.18 and 1.19 ) . this factor @xmath47 , being typically @xmath49 for relevant burning shells , decreases with @xmath1 and increases with @xmath48 . hence , in order to get a greater shrinkage of the core in the agb models with efficient dredge - up , while the core mass is kept constant , a lower temperature @xmath48 should be attained during the quiescent regime . this , in fact , would result in a smaller @xmath47 , and hence in a smaller @xmath33 . the final result would be a certain excess of luminosity with respect to the reference @xmath0 relation . unfortunately , no information about @xmath48 is given in hsb98 , but it would be worth investigating this point with the aid of full agb calculations . here we present the results of synthetic calculations carried out with different technical @xmath0 relations including a composition dependence and the first subluminous pulses ( see figs . [ lmcgrid ] and [ lmcd ] ) . the models are meant to be useful experiments , giving a first hint of how the quiescent luminosity of a tp - agb star may behave when dredge - up events strongly alter the envelope composition . calculations are carried out over a limited number of inter - pulse periods for a 3 @xmath50 tp - agb star with original solar composition ( i.e. @xmath51 , @xmath52 ) . the chemical composition of the envelope at the first thermal pulse is characterised by ( @xmath53 ) . the third dredge - up is assumed to occur once the full amplitude regime is attained , i.e. after the first subluminous pulses when the linear @xmath0 relation is approached . we adopt various values of the dredge - up parameter ( @xmath54 ) and two prescriptions for the composition of the dredged - up material . they are ( in mass fraction ) : * @xmath55he@xmath56 , @xmath57c@xmath58 , @xmath59o@xmath60 + ( according to boothroyd & sackmann 1988b ; bs88 ) * @xmath55he@xmath61 , @xmath57c@xmath62 , @xmath59o@xmath61 + ( according to hbse97 ) here we are not concerned to give a detailed description of dredge - up and its properties . for instance , we assume that dredge - up events take place at each thermal pulse in the full amplitude regime , whereas we expect that a significant increase of the envelope metallicity could , at a certain stage , even inhibit further occurrence of the process by decreasing the temperature at the base of the convective envelope during the post - flash luminosity maximum ( see e.g. boothroyd & sackmann 1988c ) . since most available @xmath0 formulae were obtained for relatively small ranges of metallicity , usually not super - solar , they may not give realistic results if the envelope metallicity increases to very high values . however , in this respect , the recent analysis developed by tuchman & truran ( 1998 ) is relevant . they have quantitatively investigated the composition influence upon the @xmath16 relation , in order to better estimate the luminosity of classical novae , objects in which shell hydrogen burning is known to occur in extremely metal - rich material ( e.g. @xmath63 ) . at such high values of the metallicity , the corresponding @xmath64 relation is shifted to significantly higher luminosities than predicted for solar composition . figure [ lmcgrid ] shows the locus traced by the @xmath65 tp - agb model experiencing dredge - up , adopting an efficiency @xmath66 and the hbse97 prescription for the chemical composition of the inter - shell . a grid of classical @xmath0 relations ( from boothroyd & sackmann 1988a ) is also plotted for increasing values of the mean molecular weight , ranging from @xmath67 to @xmath68 in steps of about @xmath69 . the envelope composition of the last calculated model ( @xmath70 pulse ) is characterised by ( @xmath71 ) . for a core mass @xmath72 the quiescent luminosity is @xmath73 , corresponding to an over - luminosity of about @xmath74 with respect to the case in which the chemical composition were unchanged and equal to that of the first thermal pulse . other examples are presented in fig . all models show that the deviations from the @xmath0 relation at constant metallicity are greater for increasing @xmath75 and/or for higher abundances of carbon and oxygen in the inter - shell . we can also note that models with @xmath76 also evolve to luminosities above the reference @xmath0 relation , despite the effective decrease of the core mass . finally , we remark that our synthetic results shown in fig . [ lmcd ] reproduce the behavior of the luminosity as found by hsb98 . for instance , the cases with @xmath77 and @xmath66 clearly resemble the sequences b@xmath78 and b@xmath79 in their fig . 2 , respectively . however , it must be specified that in our calculations with extremely efficient dredge - up ( @xmath80 ) , a considerable over - luminosity above the @xmath0 relation shows up after a much larger number of dredge - up episodes ( @xmath81 ) if compared to the results by hsb98 ( @xmath82 ) . this difference can be partly ascribed to the fact that in our case the onset of third dredge - up occurs only when the full - amplitude regime is attained , whereas in hsb98 dredge - up takes place from the first thermal pulses on , when other effects ( in addition to the chemical composition , see sects . [ sec_initpulses ] and [ other ] ) are likely to play a role . in this paper we claim that the results from hsb98 may partially be understood by means of the already known deviations from the classical linear @xmath0 relation . an important effect certainly present in their evolutionary calculations is the increase in luminosity associated with the initial core contraction that occurs during the first thermal pulse cycles of any tp - agb star . this phase of rapid luminosity evolution represents a substantial fraction of the tracks presented by hsb98 . in order to determine if dredge - up really leads to a violation of the classical @xmath0 relation , which is expected to hold for the later evolution of agb stars , the hsb98 evolutionary sequences should be extended in order to include a much larger number of thermal pulses . 1 . the small or negative changes in the core mass from pulse to pulse , which cause the tracks to evolve almost vertically in the @xmath0 diagram , instead of along a line of increasing core mass and luminosity . the changes in the surface chemical composition which make their quiescent luminosity deviate from that predicted by an @xmath0 relation obtained for a constant value of metallicity . none of these effects , however , implies a violation of the classical @xmath0 relation . the structural conditions for the existence of a @xmath0 relation are expected to hold only after the tracks enter in the full - amplitude regime , as remarked above . in this regard , we remark that the evolutionary tracks should be compared with the @xmath0 relation obtained from the current chemical composition of the envelope , and not with those obtained from tracks of constant metallicity . also , the possible presence of hot - bottom burning should be completely ruled out before we can tell about deviations from the @xmath0 relation . it would be of particular interest , for instance , to investigate the evolution of low - mass stars ( @xmath83 ) computed with a similar algorithm for convection as in hsb98 . it turns out that the correct interpretation of hsb98 results requires the analysis of additional quantities along their evolutionary tracks , other than the core mass , luminosity , and core radius . these quantities are : the fraction of the stellar luminosity provided by the release of gravitational energy ( necessary to identify if the full - amplitude regime has been reached ) , the surface chemical composition of the models ( necessary to better quantify the deviation from the initial @xmath0 relation due to composition changes ) ; the luminosity provided by nuclear burning in the convective envelope ( necessary to rule out the presence of hot - bottom burning ) ; and the temperature @xmath48 at the top of the h - burning shell ( useful to investigate its effect on the factor @xmath47 , defined in sect . [ other ] , and hence on the core radius @xmath33 ) . unfortunately , this information is not provided by hsb98 . we stress once more that synthetic tp - agb models have already been adopting _ technical non - linear _ @xmath0 relations , i.e.including significant deviations from linearity due to the sub - luminous first thermal pulses and changes in the surface chemical composition produced by dredge - up ( e.g. groenewegen & de jong 1993 ; marigo et al . 1996 ; marigo 1998 ) . moreover , the real breakdown of the @xmath0 relation caused by hot - bottom burning in the most massive agb stars have been accurately taken into account ( marigo et al.1998 ; marigo 1998 ; wagenhuber & groenewegen 1998 ) in these models . finally , we recall that the @xmath0 relation applies only to the quiescent inter - pulse periods , but not to the luminosity variations driven by thermal pulses . even the effect of the post - flash low - luminosity dip is usually included in synthetic tp - agb calculations . therefore , synthetic agb evolution calculations already include all known effects affecting the @xmath15-relation and do not rely on the assumption that the classical , linear @xmath0 relation is valid . a corresponding comment in hsb98 turns out to be inappropriate . as such , any _ new _ effect , as possibly indicated by the hsb98 calculations can easily be incorporated after sufficient data from full calculations are available . we thank f. herwig for providing additional information about his results , and p. wood for useful discussions . our referee , y. tuchman , is acknowledged for important comments about this paper . the work by l. girardi is funded by the alexander von humboldt - stiftung . blcker t. , 1993 , a&a 43 , 305 blcker t. , schnberner d. , 1991 , a&a 244 , l43 boothroyd a.i . , sackmann i .- j . , 1988a , apj 328 , 641 boothroyd a.i . , sackmann i .- , 1988b , apj 328 , 653 boothroyd a.i . , sackmann i .- j . , 1988c , apj 328 , 679 boothroyd a.i . , sackmann i .- j . , 1992 , apj 393 , l21 dantona f. , mazzitelli i. , 1996 , apj 470 , 1093 eggleton p.p . , 1967 , mnras 135 , 243 groenewegen m.a.t . , de jong t. , 1993 , a&a 267 , 410 havazelet d. , barkat z. , 1979 , apj 233 , 589 herwig f. , 1998 , phd thesis , christian - albrechts - universitt zu kiel herwig f. , blcker t. , schnberner d. , el eid m. , 1997 , a&a 324 , l81 ( hbse97 ) herwig f. , schnberner d. , blcker t , 1998 , a&a 340 , l43 ( hsb98 ) iben i. , 1977 , apj 217 , 788 jeffery c.s . , 1988 , mnras 235 , 1287 kippenhahn r. , 1981 , a&a 102 , 293 lattanzio j.c . , 1986 , apj 311 , 708 marigo p. , 1998 , a&a 340 , 463 marigo p. , bressan a. , chiosi c. , 1996 , a&a 313 , 545 marigo p. , bressan a. , chiosi c. , 1998 , a&a 331 , 564 marigo p. , girardi l. , bressan a. , 1999 , a&a 344 , 123 paczyski b. , 1970a , acta astr . 20 , 47 paczyski b. , 1970b , acta astr . 20 , 195 refsdal s. , weigert a. , 1970 , a&a 6 , 426 tuchman y. , glasner a. , barkat z. , 1983 , apj 268 , 356 tuchman y. , truran j.w . , 1998 , apj 503 , 381 vassiliadis e. , wood p.r . , 1993 , apj 413 , 641 wagenhuber j. , groenewegen m.a.t . , 1998 , a&a 340 , 183 wood p.r . , zarro d.m . , 1981 , apj 247 , 247

the core mass - luminosity ( @xmath0 ) relation of thermally pulsing asymptotic giant branch ( tp - agb ) stars is a key ingredient in synthetic calculations of their evolution . recently , herwig et al . ( 1998 ) have presented full calculations of tp - agb models with strong dredge - up occurring already during early thermal pulses . the resulting luminosity evolution differs appreciably from the simple linear @xmath0 relation . in this paper , we show that at least part of the luminosity evolution can be understood as being the result of two well - known effects : the gradual approach to the asymptotic behaviour that characterises the first thermal pulses , and the chemical composition changes of the envelope . both effects are already implemented in the @xmath0 relations used in synthetic models . consequently , these models are able to reproduce the behaviour of full calculations . whether additional effects , not yet taken into account , are present , can be decided only through additional calculations and data . we also comment on the validity of a linear @xmath0 relation and its possible violation , as mentioned by herwig et al .

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(a) In General.--Section 527(j)(5) of the Internal Revenue Code of 1986 (relating to coordination with other requirements) is amended by striking ``or'' at the end of subparagraph (D), by redesignating subparagraphs (C), (D), and (E) as subparagraphs (D), (E), and (F), respectively, and by inserting after subparagraph (B) the following new subparagraph: ``(C) to any organization which is an exempt State or local political organization,''. (b) Exempt State or Local Political Organization.--Subsection (e) of section 527 of the Internal Revenue Code of 1986 (relating to other definitions) is amended by adding at the end the following new paragraph: ``(5) Exempt state or local political organization.-- ``(A) In general.--The term `exempt State or local political organization' means a political organization which-- ``(i) does not engage in any exempt function other than solely for the purposes of influencing or attempting to influence the selection, nomination, election, or appointment of any individual to any State or local public office or office in a State or local political organization, ``(ii) is subject to State requirements to report (and it so reports)-- ``(I) information regarding each separate expenditure from and contribution to, such organization, and ``(II) information regarding the person who makes such contribution or receives such expenditure, which would otherwise be required to be reported under this section, and ``(iii) with respect to which the reports referred to in clause (ii) are made public by the agency with which such reports are filed and are publicly available for inspection in a manner similar to that required by section 6104(d)(1). ``(B) Certain failures disregarded.--An organization shall not be treated as failing to meet the requirements of subparagraph (A)(ii) solely by reason of 1 or more of the following: ``(i) The minimum amount of any expenditure or contribution required to be reported under State law is not more than $300 greater than the minimum amount required to be reported under subsection (j). ``(ii) The State law does not require the organization to identify 1 or more of the following: ``(I) The employer of any person who makes contributions to the organization. ``(II) The occupation of any person who makes contributions to the organization. ``(III) The employer of any person who receives expenditures from the organization. ``(IV) The occupation of any person who receives expenditures from the organization. ``(V) The purpose of any expenditure of the organization. ``(iii) The organization makes de minimis errors in complying with State law requirements as long as the organization corrects the errors within a reasonable period after being notified of such errors. ``(C) Participation of federal candidate or office holder.--The term `exempt State or local political organization' shall not include any organization otherwise described in subparagraph (A) if a candidate for nomination or election to Federal public office or an individual who holds such office-- ``(i) controls or materially participates in the direction of the organization, ``(ii) solicits contributions to the organization, or ``(iii) directs, in whole or in part, disbursements by the organization.''. (c) Annual Return Requirements.-- (1) Income tax returns required only for political organization taxable income.--Paragraph (6) of section 6012(a) of the Internal Revenue Code of 1986 (relating to persons required to make returns of income) is amended by striking ``or which has'' and all that follows through ``section)''. (2) Information returns.--Subsection (g) of section 6033 of such Code (relating to returns required by political organizations) is amended-- (A) by striking ``political organization required to file a return under section 6012(a)(6)'' and inserting ``political organization (with the meaning of section 527, other than a political committee of a State or local candidate) which has gross receipts of $25,000 or more for the taxable year'', and (B) by adding at the end the following new sentence: ``In the case of an exempt State or local political organization (as defined in section 527(e)(5)), the preceding sentence shall be applied by substituting `$100,000' for `$25,000'.''. (3) Authorization to modify information returns.--The Secretary shall review for possible modification the annual return required under section 6033(g) of the Internal Revenue Code of 1986. (d) Effective Date.--The amendments made by this section shall take effect as if included in the amendments made by Public Law 106-230. SEC. 3. NOTIFICATION OF INTERACTION OF REPORTING REQUIREMENTS. (a) In General.--The Secretary of the Treasury, in consultation with the Federal Election Commission, shall publicize-- (1) the effect of the amendments made by this Act, and (2) the interaction of requirements to file a notification or report under section 527 of the Internal Revenue Code of 1986 and reports under the Federal Election Campaign Act of 1971. (b) Information.--Information provided under subsection (a) shall be included in any appropriate form, instruction, notice, or other guidance issued to the public by the Secretary of the Treasury or the Federal Election Commission regarding reporting requirements of political organizations (as defined in section 527 of the Internal Revenue Code of 1986) or reporting requirements under the Federal Election Campaign Act of 1971. SEC. 4. WAIVER OF PENALTIES. (a) Waiver of Filing Penalties.--Section 527 of the Internal Revenue Code of 1986 is amended by adding at the end the following: ``(k) Authority To Waive.--The Secretary may waive all or any portion of the-- ``(1) tax assessed on an organization by reason of the failure of the organization to give notice under subsection (i), or ``(2) penalty imposed under subsection (j) for a failure to file a report, on a showing that such failure was due to reasonable cause and not due to willful neglect.''. (b) Effective Date.--The amendment made by subsection (a) shall apply to any tax assessed or penalty imposed after June 30, 2000. SEC. 5. TECHNICAL CORRECTIONS TO SECTION 527 ORGANIZATION DISCLOSURE PROVISIONS. (a) Unsegregated Funds Not To Avoid Tax.--Paragraph (4) of section 527(i) of the Internal Revenue Code of 1986 (relating to failure to notify) is amended by adding at the end the following new sentence: ``For purposes of the preceding sentence, the term `exempt function income' means any amount described in a subparagraph of subsection (c)(3), whether or not segregated for use for an exempt function.''. (b) Procedures for Assessment and Collection of Penalty.--Paragraph (1) of section 527(j) of the Internal Revenue Code of 1986 (relating to required disclosure of expenditures and contributions) is amended by adding at the end the following new sentence: ``For purposes of subtitle F, the penalty imposed by this paragraph shall be assessed and collected in the same manner as penalties imposed by section 6652(c).''. (c) Duplicate Written Filings Not Required.-- (1) Subparagraph (A) of section 527(i)(1) of the Internal Revenue Code of 1986 is amended by striking ``, electronically and in writing,'' and inserting ``electronically''. (2) Subsection (i) of section 527 of such Code is amended by adding at the end the following new paragraph: ``(7) Electronic filing.--The Secretary shall develop procedures for submission in electronic form of notices required to be filed under this subsection and reports required to be filed under subsection (j).''. (d) Application of Fraud Penalty.--Section 7207 of the Internal Revenue Code of 1986 (relating to fraudulent returns, statements, and other documents) is amended by striking ``pursuant to subsection (b) of section 6047 or pursuant to subsection (d) of section 6104'' and inserting ``pursuant to section 6047(b), section 6104(d), or subsection (i) or (j) of section 527''. (e) Contents of Report.--Section 527(j)(3) of the Internal Revenue Code of 1986 (relating to contents of report) is amended-- (1) by inserting ``, date, and purpose'' after ``The amount'' in subparagraph (A), and (2) by inserting ``and date'' after ``the amount'' in subparagraph (B). (f) Contents of Notice.--Section 527(i)(3) of the Internal Revenue Code of 1986 (relating to contents of notice) is amended by striking ``and'' at the end of subparagraph (D), by redesignating subparagraph (E) as subparagraph (F), and by inserting after subparagraph (D) the following new subparagraph: ``(E) whether the organization intends to claim an exemption from the requirements of subsection (j) or section 6033, and''. (g) Timing of Notices.--Section 527(i)(2) of the Internal Revenue Code of 1986 (relating to time to give notice) is amended by inserting ``or, in the case of any material change in the information required under paragraph (3), not later than 30 days after such material change'' after ``established''. (h) Effective Dates.-- (1) Subsections (a) and (b).--The amendments made by subsections (a) and (b) shall apply to failures occurring on or after the date of the enactment of this Act. (2) Subsection (c).--The amendments made by subsection (c) shall take effect as if included in the amendments made by Public Law 106-230. (3) Subsections (d), (e), and (f).--The amendments made by subsections (d), (e), and (f) shall apply to reports or notices filed on or after the date of the enactment of this Act. (4) Subsection (g).--The amendments made by subsection (g) shall apply to material changes on or after the date of the enactment of this Act.

Amends the Internal Revenue Code to exempt State and local committees of candidates and of political parties from specified notification requirements. Exempts certain "exempt State or local political organizations" from specified reporting requirements. Defines "exempt State and local political organizations."Modifies characteristics of political organizations obligated to complete an informational return, such that specified political organizations with $25,000 or more in annual gross receipts must file, as well as "exempt state and local political organizations" with annual gross receipts of $100,000 or more. Directs the Secretary of the Treasury to review the components of such returns. Authorizes the Secretary to waive certain penalties for notification and reporting violations.Obligates political organizations to inform the Secretary whether they plan to seek exemptions from financial or informational returns.

to report the optical coherence tomography ( oct ) findings in a patient with unilateral macular coloboma . the oct revealed the crater - like depression in the macula , demonstrating atrophic neurosensory retina , and an absence of retinal pigment epithelium and choroid in the lesion . fa showed hypofluorescence corresponding to the size of the lesion in both early and late frames without leakage of dye at any stage . a 12-year - old boy was referred to our clinic for the evaluation of a macular lesion in the left eye . the best - corrected visual acuities were 20/20 in the right eye and 20/40 with -0.5 + 0.25 180 in the left eye . the fundus examination of the left eye showed a sharply - demarcated , oval - shaped , excavated lesion involving the temporal half of the foveal center with large choroidal vessels and bared sclera at the base ( fig . the lesion was approximately four disc diameters ( dd ) in width and two dd in height , and the retinal vessels were undisturbed at the margin . on red - free retinal nerve fiber layer photography , fluorescein angiography ( fa ) showed hypofluorescence corresponding to the size of the lesion in both early and late frames without leakage of dye at any stage ( fig . the immunologic tests including toxoplasmosis , rubella , syphilis , cytomegalovirus , herpes virus and human immunodeficiency virus were all negative . ca ) showed a crater - like depression accompanying atrophic neurosensory retina , and an absence of retinal pigment epithelium ( rpe ) and choroid in the lesion . increased backscattering due to bare sclera and choroidal vessels ocular coloboma , defined as an absence of ocular tissue resulting from a failure of a part of the fetal fissure to close , is classified as atypical when it involves areas of the eye that do not originate from the embryonic cleft.1,2 macular coloboma , classified as an atypical coloboma , can be present unilaterally or bilaterally . although macular coloboma has a characteristic appearance and location , it must be differentiated from post - inflammatory scarring resulting from ocular toxoplasmosis or macular dystrophies.3,4 sharma et al . evaluated a case of macular coloboma and provided histological evidence that these areas lacked choriocapillaries and rpe.5 the oct performs cross - sectional imaging of biological tissue , similar to a histological section , at a resolution of 10 to 20 m , and thus can be beneficial for the diagnosis of macular coloboma without histologic section . in our study , we reported an oct finding in a case of macular coloboma where we found an abnormal thinning of neurosensory retina , and an absence of rpe and choroidal tissue , leaving bared sclera in the lesion on the oct . currently , a new generation of ultra - high resolution oct technology has been introduced , using a femtosecond laser as the light source for imaging and achieving an axial image resolution of ~3 m . so , further study , using more advanced technology of oct , would be helpful for definitely differentiating macular coloboma from other causes of macular pathology such as macular dystrophies and macular degeneration secondary to inflammation .

purposeto report the optical coherence tomography ( oct ) findings in a patient with unilateral macular coloboma.methodsa 12-year - old male was presented with macular coloboma in the left eye . the optical coherence tomography was performed with fluorescein angiography ( fa).resultsthe oct revealed the crater - like depression in the macula , demonstrating atrophic neurosensory retina , and an absence of retinal pigment epithelium and choroid in the lesion . fa showed hypofluorescence corresponding to the size of the lesion in both early and late frames without leakage of dye at any stage.conclusionsthe oct can be beneficial to confirm the diagnosis of macular coloboma .

strong correlation between particles is one of the most important key issues in condensed matter physics . the recently developed ultracold fermi gases offer unique opportunities to study this important topic in a controlled manner , by maximally using highly tunable physical parameters . indeed , the crossover from the bardeen - cooper - schrieffer ( bcs ) type superfluid to the bose - einstein condensation ( bec ) of tightly bound molecules@xcite has been realized in @xmath2k@xcite and @xmath3li fermi gases@xcite , using a tunable pairing interaction associated with a feshbach resonance@xcite . this bcs - bec crossover demonstrates the usefulness of an ultracold fermi gas as a quantum simulator for strongly correlated fermion systems . in particular , this system is expected to be useful for the study of high-@xmath1 cuprates@xcite . the recent momentum - resolved photoemission - type spectroscopy developed by jila group@xcite is a powerful technique to probe microscopic properties of a cold fermi gas in the crossover region@xcite . this experiment is an analogue of the angle - resolved photoemission spectroscopy ( arpes ) in condensed matter physics@xcite . in the photoemission - type experiment developed by jila group@xcite , atoms are transferred to the third empty atomic state by rf - pulse . using this , one can directly measure the single - particle spectral weight ( sw ) , as well as the occupied density of states ( dos ) . as a remarkable experimental result , the pseudogap has been observed in @xmath2k fermi gas@xcite . the back - bending curve of single - particle dispersion has been observed as a characteristic signature of pseudogap phenomenon@xcite . the pseudogap has been considered as a crucial key issue in the underdoped regime of high-@xmath1 cuprates@xcite . so far , various mechanisms have been proposed to explain this phenomenon , such as preformed cooper pairs@xcite , antiferromagnetic spin fluctuations@xcite , localization of cooper pairs@xcite , and hidden order@xcite . however , the complete understanding has not been obtained yet , because of the complexity of high-@xmath1 cuprates . in contrast , the origin of the pseudogap observed in a @xmath2k fermi gas@xcite is well understood . namely , preformed pairs associated with strong pairing fluctuations are responsible for this phenomenon@xcite . thus , cold fermi gases are very suitable for the study of preformed pair scenario proposed in high-@xmath1 cuprates . recently , the pseudogap phenomenon above @xmath1 has been theoretically addressed in the literature of cold fermi gas@xcite . it has been shown that a gap like structure emerges in the single - particle excitation spectra in the pseudogap regime@xcite . it has been also pointed out the existence of two pseudogap temperatures @xmath4 and @xmath5@xcite : while a dip structure appears in dos below @xmath6 , a double - peak structure and back - bending dispersion are seen in sw below @xmath7 . in this paper , we investigate single - particle excitations and effects of strong pairing fluctuations in the bcs - bec crossover regime of a superfluid fermi gas . extending our previous paper for the pseudogap phenomenon above @xmath1@xcite to the superfluid phase below @xmath1 , we calculate dos within a @xmath0-matrix theory . we clarify how the pseudogap above @xmath1 evolves into the superfluid gap below @xmath1 . while the evolution is continuous in the weak - coupling bcs regime , the superfluid gap is shown to appear after the pseudogap disappears below @xmath1 in the crossover region . we also identify the region where pairing fluctuations dominate over single - particle properties in the phase diagram with respect to the temperature and interaction strength . recently , strong - coupling effects on sw has been discussed below @xmath1@xcite . in this paper , we also treat this quantity to examine how the pseudogap in dos is related to sw affected by pairing fluctuations . this paper is organized as follows . in sec . [ section2 ] , we explain our formulation based on a @xmath0-matrix theory . in sec . [ section3 ] , we present our numerical results for the superfluid dos , as well as sw , to discuss strong - coupling effects on these quantities . in sec . [ section4 ] , we present the phase diagram of a superfluid fermi gas to clarify the region where pairing fluctuations are crucial for single - particle excitations . throughout this paper , we set @xmath8 , and the system volume @xmath9 is taken to be unity . we consider a three - dimensional fermi gas , consisting of two atomic hyperfine states described by pseudospin @xmath10 . we assume that the two hyperfine states are equally populated , and ignore effects of a harmonic trap , for simplicity . we also assume a broad feshbach resonance as the origin of tunable pairing interaction . in this case , it is known that the detailed feshbach mechanism is not crucial for the study of interesting bcs - bec crossover physics , so that we can safely use the ordinary single - channel bcs model , given by @xmath11 here , @xmath12 is the creation operator of a fermi atom with pseudospin @xmath10 and the kinetic energy @xmath13 measured from the chemical potential @xmath14 ( where @xmath15 is an atomic mass ) . @xmath16 is a tunable pairing interaction associated with a feshbach resonance . in cold atom physics , this pairing interaction is conveniently measured in terms of the @xmath17-wave scattering length @xmath18 , which is related to @xmath19 as@xcite , @xmath20 where @xmath21 is a high - energy cutoff . in this scale , the weak - coupling bcs regime and the strong - coupling bec regime are , respectively , given by @xmath22 and @xmath23 , where @xmath24 is the fermi momentum . the region @xmath25 is called the crossover region . to consider fluctuations in the cooper channel below @xmath1 , it is convenient to rewrite eq . ( [ ham0 ] ) into the form consisting of the mean - field part and fluctuation contribution . introducing the nambu field , @xmath26 we have@xcite @xmath27\psi_{\bm p}-u\sum_{{\bm q}}\rho_+({\bm q})\rho_-(-{\bm q } ) . \label{ham}\ ] ] here , @xmath28 ( @xmath29 ) are pauli matrices acting on particle - hole space . @xmath30/2 $ ] are the generalized density operators , where @xmath31 . in eq . ( [ ham ] ) , the first term is the mean - field hamiltonian , where the superfluid order parameter @xmath32 is taken to be real and proportional to the @xmath33-component . in this choice , @xmath34 and @xmath35 physically describe the amplitude and phase fluctuations of the order parameter , respectively@xcite . namely , the last term in eq . ( [ ham ] ) describes effects of pairing fluctuations . in this paper , we take into account the last term in eq . ( [ ham ] ) within the @xmath0-matrix approximation@xcite . for this purpose , we introduce the @xmath36-matrix single - particle thermal green s function , given by @xmath37 here , @xmath38 is the mean - field green s function , where @xmath39 is the fermion matsubara frequency . the @xmath36-matrix self - energy @xmath40 describes fluctuation corrections . within the @xmath0-matrix theory , it is diagrammatically given by fig . [ fig1]@xcite . summing up the diagrams in fig . [ fig1 ] , we obtain @xmath41 where @xmath42 is the inverse temperature . @xmath43 is the boson matsubara frequency , and @xmath44/2 $ ] . the particle - particle scattering matrix @xmath45 is given by @xmath46^{-1}. \label{gamma}\end{aligned}\ ] ] here , @xmath47 is the lowest - order of the following correlation function : @xmath48 evaluating eq . ( [ corr ] ) within the zeroth order with respect to the last term in eq . ( [ ham ] ) , we have @xmath49 . \label{polari}\ ] ] executing the @xmath39-summation in eq . ( [ polari ] ) , we obtain in the @xmath0-matrix approximation employed in this paper . ( a ) self - energy correction . ( b ) particle - particle scattering matrix @xmath50 . the solid and dashed lines represent the mean - field green s function @xmath51 and pairing interaction @xmath52 , respectively . the bubble diagrams represent the zeroth order correlation functions @xmath47 ( where @xmath53 ) , describing pairing fluctuations below @xmath1 . the solid circles are pauli matrices @xmath54.,width=377 ] @xmath55 , \label{explicitpi1}\end{aligned}\ ] ] @xmath56\nonumber\\ & & \qquad\times\left[\tanh\left({\beta \over 2}e_{\bm p+\bm q/2}\right)+s\tanh\left({\beta \over 2}e_{\bm p-\bm q/2}\right)\right ] , \label{explicitpi2}\end{aligned}\ ] ] where @xmath57 is the bogoliubov single - particle excitation spectrum . the other components are given by @xmath58 , and @xmath59 . ( a ) and fermi chemical potential @xmath14 ( b ) in the bcs - bec crossover normalized by the fermi temperature @xmath60 . we use these results in calculating dos in sec . the upper and lower insets show @xmath1 and @xmath61 , respectively . ( @xmath1 is also shown in panel ( b ) as the dashed line . ) the first - order behavior seen in the crossover region ( @xmath62 ) is an artifact of the @xmath0-matrix approximation we are using in this paper . , width=340 ] dos is obtained from the analytic continued green s function , as @xmath63 where sw @xmath64 has the form @xmath65 the analytic continued self - energy @xmath66 involved in @xmath67 is given by @xmath68,\\ \sigma_{\bm p}(i\omega_n\to \omega_+)|_{12}&= & { 1 \over \pi } \sum_{{\bm q},s=\pm 1 } \int_{-\infty}^\infty dz { n_b(z)+f(se_{{\bm p}+{\bm q } } ) \over z - se_{{\bm p}+{\bm q}}+\omega_+}s{\delta \over e_{{\bm p}+{\bm q}}}{\rm im}\left[\gamma_{\bm q}^{++}(z_+)\right ] , \label{ana1}\end{aligned}\ ] ] where @xmath69 , and @xmath70 \label{hf}\ ] ] is the hartree self - energy . the other components are given by @xmath71 , and @xmath72 . ( [ ana0 ] ) and ( [ ana1 ] ) , we have carried out the matsubara frequency summation by using the spectral representation of @xmath73 , given by @xmath74 \over i\nu_n - z } , \\ \displaystyle \gamma_{\bm q}^{++}(i\nu_n ) = -{1 \over \pi } \int_{-\infty}^\infty dz { { \rm i m } \left[\gamma_{\bm q}^{++}(i\nu_n\to z_+ ) \right ] \over i\nu_n - z } . \end{array } \label{eq1}\end{aligned}\ ] ] we actually calculate eq . ( [ dosg ] ) after determining the superfluid order parameter @xmath75 and fermi chemical potential @xmath14 below @xmath1 . in the present @xmath0-matrix theory , they are obtained by solving the gap equation , @xmath76 together with the equation for the number of fermi atoms , @xmath77 this framework is a natural extension of the gaussian fluctuation theory developed by nozires and schmitt - rink ( nsr)@xcite , where the self - energy correction @xmath40 is taken into account up to the first order . this @xmath0-matrix theory can properly describe the bcs - bec crossover behaviors of @xmath1 and @xmath14@xcite . ( see the insets in fig . [ fig2 ] . ) in addition , this theory is consistent with the goldstone s theorem , in the sense that the particle - particle scattering matrix @xmath78 in eq . ( [ gamma ] ) has a pole at @xmath79 . indeed , the condition that eq . ( [ gamma ] ) has a pole at @xmath79 gives @xmath80 \right ] \left [ 1-u[\pi_{{\bm q}=0}^{++}(0)-\pi_{{\bm q}=0}^{+-}(0 ) ] \right]=0 . \label{check1}\ ] ] one finds from eqs . ( [ explicitpi1 ] ) and ( [ explicitpi2 ] ) that the factor @xmath81 $ ] vanishes identically when the gap equation ( [ gapeq ] ) is satisfied . we also note that , as in the nsr theory@xcite , the present @xmath0-matrix theory also shows the first - order phase transition in the bcs - bec crossover region ( see fig . [ fig2 ] . ) , which is , however , an artifact of the theory . to overcome this problem , one needs to include many - body scattering effect between molecules in a consistent manner@xcite . although this is an important problem in the bcs - bec crossover physics , in this paper , we leave it as a future problem and simply use @xmath75 and @xmath14 in fig . [ fig2 ] to examine strong - coupling effects on single - particle excitations below @xmath1 . at @xmath1 . lower panels : dos at @xmath82 . in this figure , the left and right panels show the results in the bcs side ( @xmath83 ) and in the bec side ( @xmath84 ) , respectively . at @xmath82 , small but finite intensity at @xmath85 seen in panel ( b1 ) is due to a small imaginary part ( @xmath86 ) introduced to the energy in numerical calculations . ] figure [ fig3 ] shows dos at @xmath1 ( upper panels ) , as well as at @xmath82 ( lower panels ) , in the bcs - bec crossover . in the upper panels , the pseudogap structure can be seen around @xmath87@xcite . this structure becomes more remarkable with increasing the interaction strength , reflecting the enhancement of pairing fluctuations . on the other hand , since thermal fluctuations are absent at @xmath82 , the well - known superfluid excitation gap associated with the superfluid order parameter @xmath75 appears in the lower panels in fig . the goal of this section is to show how the pseudogap at @xmath1 evolves into the superfluid gap below @xmath1 . in considering this problem , we first note the following two key issues which can be seen in fig . the first one is that the size difference between the pseudogap @xmath88 at @xmath1 and the superfluid gap @xmath89 at @xmath82 evaluated from fig . [ fig3 ] strongly depends on the interaction strength . as shown in fig . [ fig4](a ) , while @xmath88 is smaller than @xmath89 in the weak - coupling bcs regime , the former becomes larger than the latter in the bcs - bec crossover region . this implies that , while the pseudogap in the bcs regime may smoothly change into the superfluid gap below @xmath1 , the large pseudogap at @xmath1 in the crossover region needs to shrink below @xmath1 , in addition to the opening of the superfluid gap . at @xmath1 and superfluid gap size @xmath89 at @xmath82 evaluated from fig . [ fig3 ] . for comparison , we also show the energy gap @xmath90 in the bcs - leggett crossover theory@xcite ( which equals @xmath75 when @xmath91 , and equals @xmath92 when @xmath93 ) . the panel ( b ) shows the behaviors of these quantities in the strong - coupling bec regime , where one finds @xmath94 when @xmath95 . the inset shows how to determine @xmath88 and @xmath89 from fig . since the pseudogap actually does not have a clear energy gap , we conveniently define the gap size as the half of the dip size at @xmath96/2 $ ] , as shown in the inset , where @xmath97 and @xmath98 are the bottom energy and lower peak position , respectively . , width=377 ] the second key issue in fig . [ fig3 ] is that , although the pseudogap structure in dos looks similar to the superfluid gap , the former does not have the coherence peaks at the gap edges . however , even in the superfluid phase below @xmath1 , the coherence peaks are known to disappear by strong - coupling effects . in the present case , these strong - coupling effects involve pairing fluctuations excited thermally and the formation of tightly bound molecules . while the former effects are expected only at finite temperatures , the latter may exist down to @xmath82 in the bec regime . the latter effect can be easily confirmed by using the superfluid dos within the mean - field theory , given by @xmath99\left[\sqrt{\sqrt{\omega^2-\delta^2}+\mu}\left(\frac{\omega}{\sqrt{\omega^2-\delta^2}}+1\right)\right.\\ \ \left.+\theta(\mu^2+\delta^2-\omega^2)\sqrt{-\sqrt{\omega^2-\delta^2}+\mu}\left(\frac{\omega}{\sqrt{\omega^2-\delta^2}}-1\right)\right]\quad ( \mu>0),\\ \displaystyle \frac{m^{3/2}}{2\sqrt{2}\pi^2}\left[\theta(\omega-\sqrt{\mu^2+\delta^2})-\theta(-\omega-\sqrt{\mu^2+\delta^2})\right]\\ \ \times\left[\frac{\omega}{\sqrt{\omega^2-\delta^2}}+1\right]\sqrt{\sqrt{\omega^2-\delta^2}-|\mu|}\quad(\mu<0 ) . \end{cases } \label{bcsdos}\ ] ] in the bcs regime where @xmath91 , the singularity in @xmath100 in the upper equation gives the diverging coherence peaks at @xmath101 . in contrast , the singularity at @xmath102 in the lower equation is less important in the bec regime when @xmath93 , because dos is finite only when @xmath103 . since the negative @xmath14 in the bec regime is a strong - coupling effect associated with the formation of tightly bound molecules@xcite , the suppression of the coherence peaks in the bec regime at @xmath82 may be also regarded as a strong - coupling effect . from the above discussion , we find that the coherence peaks in dos may be used to determine the region where strong - coupling effects are less important and one can discuss superfluid properties to some extent within the _ weak - coupling mean - field _ bcs theory . and intensity of spectral weight @xmath64 in the weak - coupling bcs regime ( @xmath104 ) . , width=377 ] for @xmath105 ( unitarity limit).,width=377 ] for @xmath106 ( bec regime).,width=377 ] we now consider the superfluid dos @xmath107 below @xmath1 . figures [ fig5]-[fig7 ] show the temperature dependence of calculated @xmath107 in the bcs - bec crossover . in the weak - coupling bcs regime ( fig . [ fig5 ] ) , the pseudogap at @xmath1 is found to smoothly change into the superfluid gap below @xmath1 . one can see the growth of the coherence peaks in panels ( a2 ) and ( a3 ) , and the bcs - type superfluid dos having a clear gap structure with sharp coherence peaks is eventually realized far below @xmath1 ( panel ( a4 ) ) . we note that a similar continuous evolution from the pseudogap to the superconducting gap has been observed in the underdoped regime of high-@xmath108 cuprates@xcite . figure [ fig5 ] also shows the intensity of sw in the right panels . as discussed in our previous paper@xcite , the pseudogap phenomenon in sw is not remarkable in the bcs regime . indeed , a peak line corresponding to the free particle dispersion @xmath109 is only seen in panel ( b1 ) , although the pseudogap can be clearly seen in panel ( a1 ) . the expected superfluid gap simply opens at @xmath87 below @xmath1 , as shown in panels ( b2)-(b4 ) . comparing these results with the mean - field expression , @xmath110\delta(\omega - e_{\bm p } ) + { 1 \over 2 } \left [ 1-{\varepsilon_{\bm p}-\mu \over e_{\bm p } } \right]\delta(\omega+e_{\bm p } ) , \label{bcsspe}\ ] ] we find that the overall behavior of sw in the bcs regime is essentially the same as that in the mean - field theory . we obtain quite different results in the unitarity limit shown in fig . [ fig6 ] . in this case , panel ( a2 ) clearly shows that the superfluid gap structure is still absent around @xmath87 even at @xmath111 . this is because , although the superfluid order parameter @xmath75 itself is finite , the superfluid gap structure in dos is smeared out by strong pairing fluctuations at this temperature . however , panel ( a2 ) also shows that pseudogap structure becomes obscure , indicating the suppression of pairing fluctuations ( although they are still strong enough to smear out the superfluid gap in dos ) . this suppression of pseudogap below @xmath1 can be also seen in sw . in fig . [ fig6](b1 ) , we can see the typical pseudogap structure of sw , namely , the double - peak structure consisting of a positive energy ( particle ) and negative energy ( hole ) branches . at @xmath111 ( panel ( b2 ) ) , this double - peak structure becomes obscure due to the appearance of finite spectral intensity around @xmath87 . however , the superfluid gap still does not open at @xmath87 at this temperature , being consistent with panel ( a2 ) . at lower temperatures , when the pseudogap in dos almost disappears , fig . [ fig6](a3 ) shows that a dip structure appears around @xmath87 . correspondingly , sw also has a gap structure at @xmath87 , as shown in panel ( b3 ) . these superfluid gap structures develop at lower temperatures , and they eventually reduce to the bcs - type dos and sw far below @xmath1 , as shown in panels ( a4 ) and ( b4 ) , respectively@xcite . the above results indicate that , in the crossover region , the superfluid gap appears in dos after the pseudogap almost disappears . this is quite different from the continuous evolution from the pseudogap to the superfluid gas in the weak - coupling bcs regime . since strong pairing fluctuations , which is essential for the pseudogap phenomenon , must be suppressed to obtain the superfluid gap in dos and sw , the evolution from the pseudogap to superfluid gap is a competing phenomenon in the crossover region . in the strong - coupling bec regime , since tightly bound molecules have been already formed far above @xmath1 , dos has a clear gap structure even at @xmath1 , as shown in fig . [ fig7](a1 ) . because of this clear gap structure , although the shrinkage of this gap can be seen in panel ( a2 ) ( which is considered to correspond to the suppression of the pseudogap discussed in fig . [ fig6 ] ) , one can not precisely determine the temperature where the superfluid gap structure at @xmath87 starts to appear in fig . [ fig7 ] . in this regard , we note that the chemical potential @xmath14 is negative in the case of fig . thus , as will be discussed in sec . iv , one should regard the system in this regime as a molecular bose gas , rather than a fermi gas . figures [ fig7](b3 ) and [ fig7](b4 ) show the appearance of a sharp negative energy branch in sw far below @xmath1 . this means that the overall spectral structure becomes close to the mean - field superfluid result given by eq . ( [ bcsspe ] ) far below @xmath1 ( although the chemical potential @xmath14 remarkably deviates from the fermi energy @xmath112 . ) for the appearance of this negative energy ( hole ) branch , we briefly note that it is absent in the bec limit where the molecular formation occurs within the simple two - body physics . on the other hand , sw has both a positive energy ( particle ) and negative ( hole ) branches in the bcs regime , reflecting that cooper pairs are many - body bound states assisted by fermi surface . thus , the sharp hole branch in panels ( b3 ) and ( b4 ) indicates that the many - body effect still contributes to pair formation to some extent even in the bec regime at @xmath113 . in the strong - coupling bec limit , the green s function in eq . ( [ green ] ) reduces to@xcite @xmath114 ( we summarize the derivation of eq . ( [ gbeclim ] ) in the appendix . ) here , @xmath115 is the superfluid order parameter in the bec limit , and @xmath116 is the pseudogap parameter@xcite , where @xmath117 and @xmath118 represent the molecular condensate density and molecular non - condensate density , respectively . equation ( [ gbeclim ] ) shows that the single - particle excitation gap @xmath90 is given by @xmath119 where @xmath120 $ ] is the total fermion density , and we have used the expression @xmath121 in the bec limit@xcite . equation ( [ limitbec ] ) means that the excitation gap in dos becomes @xmath0-independent deep inside the bec regime . indeed , fig . [ fig4](b ) shows that @xmath122 when @xmath123 . in the extreme bec limit ( @xmath124 ) , eq . ( [ limitbec ] ) reduces to the half of the binding energy of a two - body bound state @xmath125 , as expected . before ending this section , we note that , although the overall structure of dos is very close to the bcs - type dos at @xmath82 ( see the lower panels in fig . [ fig3 ] . ) , the gap size @xmath89 in dos at @xmath82 is smaller than the magnitude of superfluid order parameter evaluated in the bcs - leggett crossover theory@xcite ( which consists of the mean - field gap equation and mean - field number equation ) , as shown in fig . [ fig4](a ) . this is because the self - energy correction @xmath126 in eq . ( [ green ] ) still affects single - particle excitations even at @xmath82 , although pairing fluctuations are suppressed far below @xmath1 . indeed , in the present @xmath0-matrix theory , the superfluid gap in dos is affected by the off - diagonal self - energy @xmath127 at @xmath128 even far below @xmath1 . in addition , the present strong - coupling theory involves effects of an effective molecular interaction within the born approximation , namely , the effective molecular scattering length equals @xmath129@xcite in the bec regime . this effective boson - boson interaction leads to the quantum depletion @xmath130 ( which describes the number of non - condensate fermions at @xmath82 ) , which decreases the condensate fraction @xmath131/2 $ ] , as well as the magnitude of superfluid order parameter in the bec regime given by eq . ( [ condbec ] ) . these effects are completely ignored in the bcs - leggett crossover theory@xcite , so that the superfluid gap size @xmath89 in dos becomes smaller than @xmath75 evaluated in the mean - field - type crossover theory . however , since these strong - coupling effects are eventually suppressed deep inside the bec regime , the difference between the two theories becomes small in the bec limit , as shown in fig [ fig4](b ) . is the temperature below which the superfluid gap appears in dos@xcite . @xmath132 in the bec regime ( @xmath93 ) gives a characteristic temperature below which thermal dissociation of bound molecules is suppressed . thus , the right side of this line may be regarded as the region of tightly bound molecular bose gas , rather than a fermi gas . @xmath4 is the pseudogap temperature obtained in ref . @xcite , where the pseudogap structure starts to appear in dos above @xmath1 . in addition to these characteristic temperatures , we also introduce @xmath133 as the temperature at which the bcs - type coherence peaks appear in dos . below @xmath133 , the system becomes close to the simple weak - coupling bcs state , at least with respect to single - particle excitations . ( b ) phase diagram of a cold fermi gas . pg : pseudogap phase . nf : normal fermi gas . nb : normal state molecular bose gas@xcite . sf : superfluid fermi gas with a superfluid gap in dos . mbec : bec of molecular bosons . we emphasize that only @xmath1 is the phase transition temperature , and the others are all crossover temperatures without being accompanied by any phase transition . , width=377 ] figure [ fig8 ] shows the phase diagram of a cold fermi gas in the bcs - bec crossover . in panel ( a ) , we introduce three characteristic temperatures , @xmath134 , @xmath4 , and @xmath132 , in order to conveniently identity the region where pairing fluctuations dominate over single - particle properties . @xmath134 is the temperature where the superfluid gap appears in dos below @xmath1@xcite . the region above @xmath134 is considered to be dominated by strong pairing fluctuations even in the superfluid state . @xmath4 is the so - called pseudogap temperature discussed in our previous paper@xcite , where the pseudogap starts to emerge in dos above @xmath1 . in addition , we also take into account the fact that physical properties in the strong - coupling bec regime are close to those of a molecular bose gas , rather than a fermi gas . noting that the molecular binding energy @xmath135 in this regime is deeply related to the fermi chemical potential as @xmath136 when @xmath93 , one may expect that the thermal dissociation of molecules is suppressed in the bec regime when @xmath137 ( @xmath93 ) . thus , it is convenient to regard the right side of the @xmath132-line in fig . [ fig8](a ) as the molecular bose gas regime@xcite . we briefly note that @xmath138 , @xmath4 , and @xmath132 , are all crossover temperatures without being accompanied by any phase transition . using these three characteristic temperatures in fig . [ fig8](a ) , we find that the region `` pg '' in fig . [ fig8](b ) , which is surrounded by @xmath4 , @xmath134 , and @xmath132 , is the one where the pseudogap structure in dos is remarkable . thus , we conveniently call this region the _ pseudogap region _ ( although , strictly speaking , the region below @xmath1 is the superfluid state ) . in this pseudogap regime , strong pairing fluctuations induce a gap - like structure in dos in both the normal and superfluid phases . below @xmath134 ( `` sf '' in fig . [ fig8](b ) ) , instead of the disappearance of the pseudogap , the superfluid gap starts to develop in dos , so that single - particle properties are dominated by superfluid gap . as one further decreases the temperature below @xmath134 , one eventually obtains the weak - coupling bcs - type dos characterized by a clear excitation gap and coherence peaks , as discussed in sec . iii . to conveniently include this , we also introduce the characteristic temperature @xmath133 at which the coherence peaks appear in dos@xcite in fig . [ fig8](a ) . below @xmath133 , single - particle properties are close to those in the weak - coupling mean - field bcs state . in the molecular bose gas regime ( `` nb '' and `` mbec '' in fig . [ fig8](b ) ) , a large single - particle excitation gap already exists above @xmath1 , reflecting a large molecular binding energy ( @xmath139@xcite ) . this large binding energy suppresses single - particle excitations accompanied by pair breaking in the superfluid phase below @xmath1 , so that excitations are dominated by collective bogoliubov modes , as in the case of bose superfluid . in this sense , we call the superfluid region in the molecular bose gas regime the bec of molecular bosons ( `` mbec '' in fig [ fig8](b ) ) . to summarize , we have investigated single - particle excitations and strong - coupling effects in the bcs - bec crossover regime of a superfluid fermi gas . extending our previous work above @xmath1 to the superfluid phase below @xmath1 , we have numerically calculated the superfluid dos , as well as sw , within the @xmath0-matrix theory . we have systematically examined how the pseudogap at @xmath1 evolves into the superfluid gap , as one decreases the temperature below @xmath1 . while the evolution is continuous in the weak - coupling bcs regime , the superfluid gap was shown to appear in dos after the pseudogap is suppressed below @xmath1 in the crossover regime . using these results , we have identified the pseudogap region where strong pairing fluctuations dominate over single - particle properties in the phase diagram of a cold fermi gas . since the observation of single - particle excitations has recently become possible in cold fermi gases by photoemission - type experiment , measurements of single - particle excitation spectrum affected by strong pairing fluctuations discussed in this paper would be an interesting problem to understand the strong - coupling superfluid properties in the bcs - bec crossover . in this paper , we have assumed a uniform fermi gas , for simplicity . in a trapped system , it is an interesting problem how the spatial inhomogeneity affects the evolution from the pseudogap to the superfluid gap below @xmath1 . since a real fermi gas is always trapped in a harmonic potential , this is also an important issue in comparing experimental data with theoretical calculations . we will discuss this problem in a future paper . we thank y. yanase , s. watabe , d. inotani and t. kashimura for fruitful discussions . this work was supported by the japan society for the promotion of science , and global coe program `` high - level global cooperation for leading - edge platform on access spaces ( c12 ) '' . in this appendix , we present the outline of the derivation of eq . ( [ gbeclim ] ) . for more details , we refer to refs . @xcite . in the bec limit , the particle - particle scattering matrix in eq . ( [ gamma ] ) reduces to@xcite @xmath140 where @xmath141 is the bogoliubov excitation spectrum of a molecular bec , and @xmath142 is the bose chemical potential . the number equation in the bec limit reduces to @xmath143 , where @xmath117 and @xmath144 are the molecular condensate and non - condensate density , respectively , given by @xmath145 using eq . ( [ gammapmbec ] ) , we approximate the self - energy in eq . ( [ self - energy ] ) to @xmath146 where we have approximately set @xmath79 in @xmath147 . using eq . ( [ selfebec2 ] ) , one obtains the diagonal component of the green s function as @xmath148 ^ 2 \over \displaystyle i\omega_n+\xi_p-{8\pi{\tilde n}_{\rm b } \over m^2a_{\rm s } } g_{\bm p}^0(i\omega_n)|_{11 } } } . \label{gbec}\end{aligned}\ ] ] expanding the denominator in eq . ( [ gbec ] ) up to @xmath149 , we obtain eq . 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we investigate single - particle excitations and strong - coupling effects in the bcs - bec crossover regime of a superfluid fermi gas . including phase and amplitude fluctuations of the superfluid order parameter within a @xmath0-matrix theory , we calculate the superfluid density of states ( dos ) , as well as single - particle spectral weight , over the entire bcs - bec crossover region below the superfluid transition temperature @xmath1 . we clarify how the pseudogap in the normal state evolves into the superfluid gap , as one passes through @xmath1 . while the pseudogap in dos continuously evolves into the superfluid gap in the weak - coupling bcs regime , the superfluid gap in the crossover region is shown to appear in dos after the pseudogap disappears below @xmath1 . in the phase diagram with respect to the temperature and interaction strength , we determine the region where strong pairing fluctuations dominate over single - particle properties of the system . our results would be useful for the study of strong - coupling phenomena in the bcs - bec crossover regime of a superfluid fermi gas .

SECTION 1. SHORT TITLE; TABLE OF CONTENTS. (a) Short Title.--This Act may be cited as the ``Cabin Fee Act of 2011''. (b) Table of Contents.--The table of contents of this Act is as follows: Sec. 1. Short title; table of contents. Sec. 2. Definitions. Sec. 3. Cabin user fees. Sec. 4. Cabin transfer fees. Sec. 5. Right of appeal and judicial review. Sec. 6. Consistency with other law and rights. Sec. 7. Regulations. SEC. 2. DEFINITIONS. In this Act: (1) Authorization; authorize.--The terms ``authorization'' and ``authorize'' mean the issuance of a special use permit for the use and occupancy of National Forest System land by a cabin owner under the Recreation Residence Program. (2) Cabin.--The term ``cabin'' means a privately built and owned recreation residence and related improvements on National Forest System land that-- (A) is authorized for private use and occupancy; and (B) may be sold or transferred between private parties. (3) Cabin owner.--The term ``cabin owner'' means-- (A) a person authorized by the Secretary to use and to occupy a cabin; and (B) a trust, heir, or assign of a person described in subparagraph (A). (4) Cabin transfer fee.--The term ``cabin transfer fee'' means a fee that is paid to the United States on the transfer of a cabin between private parties for money or other consideration that results in the issuance of a new permit. (5) Cabin user fee.--The term ``cabin user fee'' means an annual fee paid to the United States by a cabin owner in accordance with an authorization for the use and occupancy of a cabin. (6) Current appraisal cycle.--The term ``current appraisal cycle'' means the completion of Forest Service review and acceptance of-- (A) initial typical lot appraisals; or (B) second appraisals, if ordered by cabin owners and approved by the Forest Service. (7) Current cabin user fee.--The term ``current cabin user fee'' means the most recent cabin user fee, as adjusted under section 3(c). (8) Lot.--The term ``lot'' means a parcel of National Forest System land on which a person is authorized to build, use, occupy, and maintain a cabin. (9) National forest system land.--The term ``National Forest System land'' means National Forest System land derived from the public domain. (10) Recreation residence program.--The term ``Recreation Residence Program'' means the Recreation Residence Program established under the last paragraph under the heading ``Forest service'' in the Act of March 4, 1915 (16 U.S.C. 497). (11) Secretary.--The term ``Secretary'' means the Secretary of Agriculture, acting through the Chief of the Forest Service. (12) Typical lot.--The term ``typical lot'' means a cabin lot, or group of cabin lots, in a tract that is selected for use in an appraisal as being representative of, and that has similar value characteristics as, other lots or groups of lots within the tract. SEC. 3. CABIN USER FEES. (a) Payment of Cabin User Fees.--Cabin owners shall pay an annual cabin user fee established by the Secretary in accordance with this section. (b) Initial Cabin User Fees.-- (1) Establishment.--The Secretary shall establish initial cabin user fees in accordance with this subsection. (2) Assignment to value tiers.--On completion of the current appraisal cycle, as required by paragraph (4), the Secretary shall assign each permitted lot on National Forest System land to 1 of 9 tiers based on the following considerations: (A) Before assigning the lots to tiers, all appraised lot values shall be adjusted, or normalized, for price changes occurring after the appraisal, in accordance with the National Association of Homebuilders/Wells Fargo Housing Opportunity Index. (B) Second appraisal values that are not rejected by the Forest Service shall supersede initial lot appraisal values for the normalization and ranking process under subparagraph (A). (C) The tiers shall be established, on a national basis, according to relative lot value, with lots having the lowest adjusted appraised value assigned to tier 1 and lots having the highest adjusted appraised value assigned to tier 9. (D) The number of lots (by percentage) assigned to each tier is contained in the table set forth in paragraph (3). (E) Data from incomplete appraisals may not be used to establish the fee tiers under this subsection. (F) Until assigned to a tier under this subsection, the Secretary shall assess an interim fee for permitted cabin lots (including lots with incomplete appraisals), which shall be an amount equal to the lesser of-- (i) $4,500; or (ii) the amount of the current cabin user fee, increased by 25 percent. (3) Amount of initial cabin user fees.--The initial cabin user fees, based on the assignments under paragraph (2), are as follows: ------------------------------------------------------------------------ Approximate Percent of Fee Tier Permits Nationally Fee Amount ------------------------------------------------------------------------ Tier 1 8 percent $500 ------------------------------------------------------------------------ Tier 2 12 percent $1,000 ------------------------------------------------------------------------ Tier 3 12 percent $1,500 ------------------------------------------------------------------------ Tier 4 14 percent $2,000 ------------------------------------------------------------------------ Tier 5 14 percent $2,500 ------------------------------------------------------------------------ Tier 6 14 percent $3,000 ------------------------------------------------------------------------ Tier 7 11 percent $3,500 ------------------------------------------------------------------------ Tier 8 8 percent $4,000 ------------------------------------------------------------------------ Tier 9 7 percent $4,500. ------------------------------------------------------------------------ (4) Deadline for completion of current appraisal cycle.-- Not later than 3 years after the date of enactment of this Act, the Secretary shall complete the current appraisal cycle. (5) Effective date.--The initial cabin user fees required by this subsection shall take effect beginning with the first calendar year beginning after the completion of the current appraisal cycle. (c) Annual Adjustments of Cabin User Fee.-- (1) In general.--Subject to paragraph (2), the Secretary shall use changes in the Implicit Price Deflator for the Gross Domestic Product published by the Bureau of Economic Analysis of the Department of Commerce, applied on a 5-year rolling average, to assess an annual adjustment to cabin user fees. (2) Limitations.--Notwithstanding paragraph (1), cabin user fees established under this section shall be increased by not more than 25 percent in an annual adjustment under paragraph (a). (d) Effect of Destruction, Substantial Damage, or Loss of Access.-- (1) In general.--The Secretary shall reduce the cabin user fee to $100 per year for a cabin if-- (A) the cabin is destroyed or suffers substantial damage in an amount that is greater than 50 percent of replacement cost of the cabin; or (B) access to the cabin is significantly impaired, whether by catastrophic events, natural causes, or governmental actions, which results in the cabin being rendered unsafe or unable to be occupied. (2) Term of reduced fee.--The reduced fee under paragraph (1) shall be in effect until the later of-- (A) the last day of the year in which the destruction or impairment occurs; or (B) the date on which the cabin may be lawfully reoccupied and normal access has been restored. SEC. 4. CABIN TRANSFER FEES. (a) Payment of Cabin Transfer Fees.--In conjunction with the transfer of ownership of any cabin and the issuance of a new permit, the cabin owner transferring the cabin shall file with the Secretary a sworn statement declaring the amount of money or other value received, if any, for the transfer of the cabin. (b) Amount.--As a condition of the issuance by the Secretary of a new authorization for the use and occupancy of the cabin, the cabin owner transferring the cabin shall pay to the Secretary a cabin transfer fee in an amount determined as follows: ---------------------------------------------------------------------------------------------------------------- Consideration Received by Transfer Transfer Fee Amount ---------------------------------------------------------------------------------------------------------------- $0 to $250,000 $1,000 ---------------------------------------------------------------------------------------------------------------- $250,000.01 to $500,000.00 $1,000 plus 5 percent of consideration in excess of $250,000 up to $500,000 ---------------------------------------------------------------------------------------------------------------- $500,000.01 and above $1,000 plus 5 percent of consideration in excess of $250,000 up to $500,000 plus 10 percent of consideration in excess of $500,000. ---------------------------------------------------------------------------------------------------------------- (c) Index.--The Secretary shall use changes in the Implicit Price Deflator for the Gross Domestic Product published by the Bureau of Economic Analysis of the Department of Commerce, applied on a 5-year rolling average, to determine and apply an annual adjustment to the cabin transfer fee threshold amounts set forth in the table contained in subsection (b). SEC. 5. RIGHT OF APPEAL AND JUDICIAL REVIEW. (a) Right of Appeal.-- (1) In general.--Notwithstanding any action of a cabin owner to exercise rights in accordance with section 6, the Secretary shall by regulation grant to the cabin owner the right to an administrative appeal of the determination of a new cabin user fee, fee tier, cabin transfer fee, or whether or not to reduce a cabin user fee under section 3(d). (2) Applicable law.--An appeal under paragraph (1) shall be pursuant to the appeal process provided under subpart C of part 251 of title 36, Code of Federal Regulations (or a successor regulation). (b) Judicial Review.-- (1) In general.--A cabin owner that contests a final decision of the Secretary under this Act may bring a civil action in United States district court. (2) Venue.--The venue for an action brought before the United States district court under this subsection shall be in the Federal judicial district in which the cabin is located or the permit holder resides. (3) Effect on mediation.--Nothing in this Act precludes a person from seeking mediation for an action under this Act. SEC. 6. EFFECT. (a) In General.--Nothing in this Act limits or restricts any right, title, or interest of the United States in or to any land or resource. (b) Special Rule for Alaska.--In determining a cabin user fee in the State of Alaska, the Secretary shall not establish or impose a cabin user fee or a condition affecting a cabin user fee that is inconsistent with 1303(d) of the Alaska National Interest Lands Conservation Act (16 U.S.C. 3193(d)). SEC. 7. REGULATIONS. Not later than December 31, 2012, the Secretary shall issue regulations to carry out this Act.

Cabin Fee Act of 2011 - Directs the Secretary of Agriculture (USDA) to set an annual fee for, and requires the payment of such fee to the United States by, an authorized owner of a privately built and owned recreational cabin located on National Forest System land. Reduces such fee to $100 annually if access to a cabin is significantly impaired, either by natural causes or governmental actions, such that the cabin is rendered unsafe or unable to be occupied. Requires payment of a transfer fee to the United States upon the transfer of a cabin between private parties for consideration.

dwarf galaxies are the most numerous constituents in the universe and outnumber giant galaxies . in the prevailing hierarchical structure formation scenario ( e.g. , white & rees 1978 ; white & frenk 1991 ) , they play key roles as building blocks from which larger structures such as giant galaxies are formed . although most dwarf galaxies contain old stellar populations ( grebel 2000 ; grebel & gallagher 2004 ) , a general trend occurs in the evolution of galaxies in that more massive galaxies are formed at higher redshifts which is known as the `` downsizing '' effect ( cowie et al . 1996 ; smail et al . it is therefore important to investigate how they evolved over the age of the universe . extensive and epoch - making observations of local group dwarf galaxies using the hubble space telescope ( hst ) markedly improved our knowledge of their evolutionary process . these observations have revealed their intriguing star - formation histories , which has been succinctly summarized as `` no two local group dwarfs have the same star - formation history '' ( mateo 1998 ) . however , the achilles heel of hst is its small field of view . in the fornax dwarf spheroidal galaxy , coleman et al . ( 2004 , 2005 ) found `` lobed '' substructures , which are suggested to represent a disrupted merging companion dwarf galaxy located at @xmath7 core radii from the center and outside the tidal radius . evidence for the existence of substructures is also suggested by both photometric and dynamical analyses for ursa minor ( kleyna et al . 1998 ; wilkinson et al . 2004 ) , draco ( wilkinson et al . 2004 ) , and sextans ( kleyna et al . 2004 ; walker et al . 2006 ) . extended halo structures are also found in several close companion dwarf spheroidals of the milky way ( ursa minor , palma et al . 2003 ; carina , majewski et al . 2005 ; sculptor , westfall et al . 2006 ) , and their origin is often related to the tidal influence of the milky way . regarding stellar populations , da costa et al . ( 1996 ) first pointed out that leo ii , and i and sculptor show a significant radial gradient in hb morphology . since then many dwarf spheroidal galaxies have been reported to show radial gradients of stellar populations in the sense of a central concentration of young and metal - rich populations versus more extended metal - poor and old populations ( martnez - delgado , gallart & aparicio 1999 ; saviane , held & bertelli 2000 ; harbeck et al . 2001 ; tolstoy et al . 2004 ) . however , some exceptions exist , such as leo i ( held et al . 2000 ) and carina ( smecker - hane et al . 1994 ; harbeck et al 2001 ) , although a mild radial gradient was reported for carina ( koch et al . all these results demonstrate that even small dwarf galaxies , often described as simple systems , contain such complex structures inside . hence , it is important to explore the whole galaxy from this perspective . a combination of good image quality , depth , and a wide field of view is required for such purposes . one of the best facilities for conducting such observations is suprime - cam on the 8.2-m subaru telescope . we therefore carried out a wide - field imaging survey for the local group dwarf spheroidal galaxy leo ii . leo ii is one of the milky way companion dwarf spheroidal galaxies located about 233 kpc from us ( bellazzini et al . 2005 ) . in contrast to the close companion dwarf spheroidal galaxies such as sextans , ursa minor , and draco , leo ii resides in a relatively remote place from the milky way . the stellar content of leo ii was studied extensively by mighell & rich ( 1996 ) using wfpc2 on hst . they estimated the metallicity of leo ii to be @xmath8}=-1.60\pm0.25 $ ] based on the @xmath0 color - magnitude diagram , which is consistent with a recent spectroscopic measurement by bosler et al . ( 2004 ) who derived a median metallicity of @xmath8}=-1.57 $ ] based on the spectra obtained with keck lris . they also noted that leo ii started forming stars about 14@xmath91 gyr ago and formed most of its stellar population during the succeeding 7@xmath91 gyr , with a typical star having formed about 9@xmath91 gyr ago . a more recent study ( koch et al . 2007 ) showed that the mean metallicity of leo ii is -1.74 based on the measurement of the calcium triplet for 52 red giants . these investigators also estimated individual ages , and derived a wide age range ( 2 - 15 gyr , the same spread as found by bosler et al . 2004 ) and an essentially flat age - metallicity relation . dolphin ( 2002 ) reanalyzed the hst data and derived the star - formation history of leo ii . he claimed that the mean metallicity ( @xmath8}=-1.13 $ ] ) is higher than the estimates of mighell & rich ( 1996 ) and bosler et al . ( 2004 ) , owing to a young mean age of the stars in leo ii ( 9.4 gyr ) . however , the data are limited to the central small area ( 4.44 arcmin@xmath2 ) within the core radius of the galaxy ( @xmath10 , mateo 1998 ) . recently , bellazzini et al . ( 2005 ) published new @xmath0 photometry data obtained with the 3.5-m tng covering a relatively wide area of leo ii ( @xmath11 arcmin@xmath2 ) . they analyzed the spatial variation of the stellar content such as red clump stars and blue hb stars and the magnitude of the agb bump , which indicates that the main population of leo ii is @xmath12 8 gyr . however , their data are shallow ( @xmath13 ) and their analysis inevitably limited to features brighter than the hb level . our data obtained with suprime - cam on the 8.2-m subaru telescope constitute an excellent data set that gives a crucial clue for understanding the properties of the stellar content of leo ii . in section [ sec : obs ] , we present the details of our observation and data analysis and show our results in section [ sec : radprof ] through [ sec : age ] . on the basis of these results , we discuss the formation and evolution of leo ii in section [ sec : evol ] and give a summary in section [ sec : summary ] . here we adopt the distance modulus of leo ii to be @xmath14 and the reddening to be @xmath15 ( mateo 1998 ) . the observation was carried out in april 2001 using the subaru prime focus camera ( suprime - cam ; miyazaki et al . 2002 ) on the 8.2-m subaru telescope at mauna kea , hawaii . suprime - cam is a wide - field imager consisting of 10 2k@xmath44k ccds . it covers a sky area of @xmath16 arcmin@xmath2 with 0.2 arcsec per pixel sampling . because of the wide - field coverage and good image quality of the subaru telescope , suprime - cam is the most powerful instrument for investigating stellar contents of nearby galaxies . we used @xmath17 and @xmath18 filters and total exposure times are 3000 sec and 2400 sec in the @xmath17 and @xmath18 bands , respectively . several short exposures were also obtained to measure the luminosities of bright stars , which are saturated in long exposure frames . the sky condition was good and the typical stellar size ( fwhm ) was about 0.7 arcsec in both @xmath17 and @xmath18 bands . the details of the observation are given in tab . [ tab : obs ] . the data were reduced using the standard data analysis software for suprime - cam ( yagi et al . the reduction procedure is summarized as follows . the bias was subtracted from individual frames and bad pixels were masked . each frame was divided by the flat frame , which was created from object frames ( mostly blank fields ) taken in the same observing run . note that leo ii frames were excluded when creating the flat frames . the optical distortion caused by the prime focus corrector was corrected using an analytical expression of the optical distortion ( see miyazaki et al . 2002 ) , and the sky background was subtracted from each frame . then the two - dimensional position and the relative brightness of each frame were estimated using common stars found in adjacent ccd chips and different dither positions . finally we obtained a coadded image . the fwhms of stars in the resultant coadded images are 0.80 arcsec and 0.78 arcsec in the @xmath17 and @xmath18 bands , respectively . we used the central area ( 8000@xmath48000 pixels , [email protected] arcmin@xmath2 ) for the following analysis to guarantee a homogeneous signal - to - noise ratio over the wide field of view . as shown in fig . [ fig : leo2 ] , the survey area is wide enough and far beyond the tidal radius of leo ii ( 8.7 arcmin ; mateo 1998 ) . we applied daophot psf photometry software ( stetson 1987 , 1994 ) for the coadded images . the psf model was made from about 100 stars and we repeated iterations of the psf photometry three times to not miss faint stars . non - stellar objects such as galaxies and cosmic rays were excluded using shape and @xmath19 parameters calculated by daophot . combining bright stellar objects ( @xmath20 ) detected in short exposure frames and faint stellar objects ( @xmath21 ) detected in long exposure frames , 82252 objects were cataloged as stellar objects . zero - point magnitudes in both @xmath17 and @xmath18 bands were calibrated using bright stars ( @xmath20 ) listed in lee ( 1995 ) . we used short exposures for comparison since the bright stars listed in lee ( 1995 ) were saturated in long exposure frames . the zero - point magnitudes are accurate to 0.03 mag and 0.01 mag in the @xmath17 and @xmath18 bands , respectively . long exposure frames were calibrated using common stars ( typically 20 - 22 mag stars ) on both long and short exposure frames . long exposure frames are accurate to 0.01 mag ( relative to short exposures ) in both bands . the magnitude error and the detection completeness were estimated in the standard manner . we divided the 8000@xmath48000 pixel image into 80 @xmath4 80 grids consisting of 100@xmath4100 pixels . in each grid , an artificial star was added at random position using the addstar task in the daophot package , and the same psf photometry procedure was applied to the image . this process was repeated for 10 times per every 0.5 magnitude interval for the magnitude ranges of 23.5 mag @xmath22 26.0 mag and 22.5 mag @xmath23 25.0 mag , respectively . the magnitude error and the detection completeness were calculated from the result of the psf photometry for these artificial stars . the result for the @xmath17 band is shown in fig . [ fig : complete ] as a function of magnitude and the distance from the galaxy center . the detection completeness is @xmath24 for @xmath25 at any position in the galaxy , but it degrades to 0.6 at the galaxy center for @xmath26 . the 90% and 50% completeness limits at the galaxy center are 24.5 and 25.9 in @xmath17 band , respectively , and those for @xmath18 band are 22.7 and 24.7 , respectively . the magnitude is accurate to 0.02 mag for @xmath25 in most parts of the galaxy , but the degradation is severe at the galaxy center . for @xmath27 and @xmath28 , the detection is almost complete and the magnitude is accurate even at the crowded galaxy center . fig . [ fig : cmd ] shows the color - magnitude diagram of stellar objects found in the central @xmath29 arcmin@xmath2 area of the leo ii field . it is clearly seen that our data cover a wide magnitude range of stars in leo ii from the tip of the rgb ( @xmath30 ) to the turn - off point ( @xmath31 ) . remarkable features are the well - defined hb at @xmath32 and the narrow rgb . the red hb is characterized by a concentration of stars at the red side of the rr lyr instability strip ( @xmath33 ) that is well distinguished from the rgb . the hb extends to the blue side and forms another concentration at @xmath34 . it is obvious that the asymptotic giant branch ( agb ) merges into the rgb at @xmath35 and the rgb bumps detected by bellazzini et al . ( 2005 ) are clearly seen by eye at @xmath36 and @xmath37 . one might notice that @xmath520 stars with the same color as the red hb , but much brighter than the red hb , occur . they may possibly be helium - burning , high - mass stars ( mighell & rich , 1996 ; bellazzini et al . 2005 ) , although demers & irwin ( 1993 ) first argued that they are a photometric blend of hb and rgb stars . the other noteworthy feature in the color - magnitude diagram is the apparent bifurcation of the blue hb stars . the feature is also seen in bellazzini et al . ( 2005 ; fig.2 ) , and according to their identification , most of the brighter blue hb stars are variable stars cataloged by siegel & majewski ( 2000 ) . we examined the spatial distribution of these stars and found no particular maldistribution ( concentrated or uniform distribution ) . we note that the contamination from galactic stars is not severe compared to other milky way satellite galaxies ( e.g. , sextans , draco , and ursa minor ; see harbeck et al . 2001 ) since leo ii is located at a relatively high galactic latitude ( @xmath38 ) . the contamination becomes severe for @xmath39 . the typical photometric errors , which were calculated on the basis of the artificial star test ( thus including the effect of the crowding ) , are plotted as blue ( near center ) and red ( outskirts ) error bars in fig . [ fig : cmfea ] ( a ) . we first investigated the radial profiles of bright and faint rgb stars and blue and red hb stars . the blue and red hb stars are easily discerned as seen in fig . [ fig : cmd ] . we defined the blue hb stars as @xmath40 stars and the red hb stars as @xmath41 and @xmath42 + 22.08 $ ] . see fig . [ fig : cmfea ] for these criteria in detail . to identify rgb stars , we determined the mean rgb sequence which was fitted as , @xmath43 fig . [ fig : cmfea ] ( a ) shows how well the mean rgb sequence traces the data . the stars that deviate less than @xmath90.075 mag ( corresponding to 2.3@xmath44 ) in @xmath45 color from the mean rgb sequence are classified as rgb stars . the criteria enclose most of the rgb stars and separate red hb stars fairly well . we set the faint limit of the rgb at @xmath46 to avoid contamination from foreground stars and unresolved background galaxies , as well as to be free from the completeness correction . the rgb stars were subdivided into bright and faint rgb stars at the hb level ( @xmath47 , mighell & rich 1996 ) . we compared the mean rgb sequence with those of galactic globular clusters m 15 , ngc 6397 , m 2 , and ngc 1851 taken from da costa & armandroff ( 1990 ) in fig . [ fig : cmfea ] ( b ) . these clusters have metallicities [ fe / h ] of -2.17 , -1.91 , -1.58 , and -1.29 , respectively ( da costa & armandroff 1990 ) . the mean rgb sequence of leo ii lies in between ngc 6397 and m 2 , suggesting that the mean metallicity of leo ii would be between -1.91 and -1.58 if an old stellar population as galactic globular clusters is assumed . this value is consistent with those derived spectroscopically by bosler et al . ( 2004 ) and koch et al . the mean rgb sequence we obtained is slightly bluer than that derived by mighell & rich ( 1996 ) . their mean rgb sequence is just on the m 2 rgb sequence . a likely cause of this could be the difference in the size of the survey field and will be discussed further in sect . [ sec : rgb ] . we counted the number of stars in each stellar component ( i.e. , bright and faint rgb , blue and red hb ) in an annular area of @xmath48 and divided this by the area of the annulus to derive the number density . the characteristic radius @xmath49 for an annulus is defined as , @xmath50 in fig . [ fig : radprof ] the radial profiles for each stellar component are plotted as a function of the characteristic radius . the numbers are listed in tab . [ tab : radprof ] . we fitted the radial profile for each stellar component with the king profile and listed the best - fit parameters in tab . [ tab : king ] . the core and tidal radii calculated for all rgb stars are 2.76 arcmin and 8.63 arcmin , respectively , and are consistent with those derived by irwin & hatzidimitriou ( 1995 ) . bright rgb stars are slightly more concentrated than faint rgb stars in terms of the core radius . this is also confirmed by a cumulative number fraction plot shown in the inset of fig . [ fig : radprof ] . we calculated the ks probabilities that two different stellar components had the same spatial distribution . the probabilities are less than 1% except for the pair of bright rgb and red hb stars ( 76.3% ) . the king profile fitting for bright rgb stars is achieved for @xmath51 arcmin , as suggested by the best - fit tidal radius of 9.22 arcmin , and the number density of bright rgb stars shows the shallower slope for @xmath52 arcmin and a probable drop at @xmath53 arcmin . a similar trend is also seen for faint rgb stars , and the change in the slope occurs at @xmath54 arcmin ( c.f . , the best - fit tidal radius of 8.51 arcmin ) , although the number density may reach the field level at @xmath55 arcmin . the field contamination is estimated in the following way . ratnatunga & bahcall ( 1985 ) calculated the number of field stars with different colors toward the direction of leo ii . the number of field stars with @xmath56 and @xmath57 is estimated to be 0.14 arcmin@xmath58 based on their table . considering that the color of @xmath59 corresponds to a k0v star and hence , @xmath60 , and that most field stars are redder than @xmath61 , we expect 0.14 arcmin@xmath58 field stars in the color range of @xmath62 . we therefore estimated that 0.0165 arcmin@xmath58 field stars are in our bright rgb selection criteria ( @xmath57 and @xmath63 ) . we also estimated the number of field stars using the sdss dr5 archive data ( adelman - mccarthy et al . the bright rgb selection criteria were determined on the basis of the ( g , i ) color - magnitude diagram of leo ii and the number of stars within the criteria in the nearby field of leo ii ( 1 degree from leo ii ) was determined . the estimated field contamination is 0.0226 arcmin@xmath58 , which is consistent with that determined above . we therefore conclude that the number of field contaminations for the bright rgb stars is @xmath64 arcmin@xmath58 and that stars located at @xmath53 arcmin are likely to be dominated by the field population . adopting this field contamination number , we suggest that the shallower slope of the radial profile found for @xmath65 arcmin is real . the field contamination for faint rgb stars is expected to be smaller than @xmath64 arcmin@xmath58 because of the smaller magnitude coverage of the selection criteria , but contamination from background compact galaxies that are misclassified as stars may occur . the sdss data are too shallow to be used for estimating the field contamination . if stars found for @xmath53 arcmin consist of such a mixture of field contamination and the background compact galaxies as implied from the analysis for the bright rgb stars , the shallower slope found for @xmath66 arcmin is also suggested to be real . to further investigate the details of the extra - tidal structure , we made a smoothed surface brightness map for the entire survey field as follows . stars regarded as rgb or hb stars were listed and gaussians of 1 arcmin kernel multiplied by the luminosity of each star was placed at the position of each star . they were then coadded to obtain a smoothed surface brightness map . this operation makes hidden faint structures clearer . [ fig : densmap ] is the resuling smoothed surface brightness map . the isosurface - brightness contour of the bright part of the galaxy is almost circular , but it becomes more complicated at a lower surface brightness . the most remarkable feature of fig . [ fig : densmap ] is the diffuse knotty structure prominent in the eastern part of the galaxy ( @xmath67 = -11 , @xmath68 1 ) . the knot is more than five times more luminous than the position located at the same distance from the center at the opposite side of the galaxy , although the mean surface brightness is quite faint ( @xmath5 31 mag / arcsec@xmath58 ) . the knot contains four bright rgb stars in @xmath69 arcmin@xmath2 area and the expected field contamination number is 0.4 , indicating that the knot is 99.92% significant above the field population on the basis of poisson statistics . the extent of this knot is about 4 arcmin ( 270 pc in physical size ) with a width of 2.5 arcmin ( 170 pc ) , and it is small compared to the main body of leo ii . the magnitude of this knot was estimated to be @xmath70 by summing up luminosities of 15 stars found in the knot region that are brighter than @xmath46 . the value is close to the magnitude of the least luminous globular cluster . the knot must be more luminous because we neglected a contribution from underlying faint stars , and could be more luminous if it is indeed extended farther to the east ( out of our survey field ) , or if the main part of it is already merged with the main body of leo ii . it is possible that the substructure is a small globular cluster that is being disrupted and merging into the main body of leo ii . the other possibility is that the knot is composed of stars stripped from the main body of leo ii . the origin of the substructure is discussed further in sect . [ sec : evol ] . in brief , the hb morphology indicates a distribution in the color of hb stars . it is often parameterized as @xmath71 , where @xmath72 and @xmath73 are the numbers of blue and red hb stars , respectively , and @xmath17 is the number of stars lying on the rr lyr instability strip . intensive investigation on the hb morphology of globular clusters has shown that it depends primarily on metallicity in that less metal - rich systems show a bluer hb morphology , but it is also influenced by the _ second parameter _ , which is most likely to be age ( lee , demarque & zinn , 1994 ) . the hb morphology is thus a key measure in studying the properties of stellar populations and the variation in the hb morphology within a galaxy is often investigated ( e.g. , harbeck et al . 2001 ; tolstoy et al . 2004 ) . using our data , we can examine the detailed variation of the hb morphology over a wide radius from the center to far beyond the tidal radius of leo ii . [ fig : hbmorph ] shows the hb morphology index @xmath71 plotted as a function of the radius . the index is less than zero at any radius , indicating that red hb stars are more numerous than blue hb stars everywhere in leo ii . this value agrees with those obtained in other studies ( -0.68 , demers & irwin 1993 ; @xmath74 , mighell & rich 1996 ) . the index is small at the center of the galaxy and becomes larger as the radius increases for @xmath75 arcmin , reaching its maximum at @xmath76 arcmin . the trend is consistent with the findings of da costa et al . they showed that the hb morphology index is approximately constant out to @xmath77 arcmin but the fraction of blue hb stars increases beyond @xmath77 arcmin . this means that red hb stars are more concentrated to the center than blue hb stars for @xmath78 arcmin . the inset of fig . [ fig : hbmorph ] , which presents the cumulative number fraction of blue and red hb stars as a function of the radius , clearly shows this and confirms the result of bellazzini et al . ( 2005 ; see their fig . they suggest that age is the main driver of the population gradient . koch et al . ( 2007 ) support this suggestion although they did not detect any considerable metallicity or age gradient in leo ii . the trend of a centrally - concentrated red hb distribution is also observed in many dwarf spheroidal galaxies in the local group ( majewski et al . 1999 ; harbeck et al . 2001 ; tolstoy et al . 2004 ) . our results support the idea that the radial gradient of the hb morphology is common to dwarf spheroidal galaxies . for the outer part of the galaxy ( @xmath79 arcmin ) , the hb morphology index looks almost constant at @xmath80 , and the value is larger than that at the inner part ( @xmath81 arcmin ) . this means that blue hb stars are more numerous , implying that the stellar population in the outer region is less metal - rich and/or older than those in the inner part . we investigated the color distribution of the rgb stars . in an analogy to the hb morphology index , we used the rgb color index for the analysis , defined as @xmath82 , where @xmath72 and @xmath73 are the numbers of stars that deviate less than 0.075 mag bluer and redder from the mean rgb sequence , respectively ( see also fig . [ fig : cmfea ] ) . the mean rgb sequence is defined as eq . [ eq : rgbseq ] , and those stars @xmath83 were used . since the agb merges to the rgb from the blue side to to the bright part of the rgb , it is possible that the rgb color index may not have been determined correctly due to the contamination of agb stars , especially when the number fraction of agb stars to rgb stars is large . to estimate the influence of agb stars in the determination of the index , we derived the rgb color index using whole rgb stars ( @xmath83 ) and faint rgb stars ( @xmath84 ) . we plotted the results as open triangles ( whole rgb ) and filled squares ( faint rgb ) in fig . [ fig : rgbmorph ] . the color index derived from whole rgb stars at a fixed radius is slightly larger ( i.e. , bluer color ) than that derived from faint rgb stars , indicating an influence , albeit small , of agb stars . therefore , the rgb color index is more accurately derived by using faint rgb stars ( @xmath84 ) . the color index is distributed around zero at any radius except for the center where red rgb stars seem to be numerous . this fact gives a reasonable explanation for the color difference of the mean rgb sequence between this study and the redder mean rgb color of mighell & rich ( 1996 ) . since their survey was limited to a small area ( 4.44 arcmin@xmath2 ) at the galaxy center , they inevitably sampled red rgb stars , which are numerous at the center , and hence obtained a redder mean rgb color . this also suggests that the stellar population varies within a galaxy . the inset of fig . [ fig : rgbmorph ] shows the cumulative number fraction of both blue and red rgb stars . the radial distribution is quite similar between the blue and red rgb stars , in contrast to the same figure for blue and red hb stars ( fig . [ fig : hbmorph ] ) . however , the coincidence of the rgb color indices of the two stellar groups does not always mean that the stellar populations of two groups are identical . for example , the color index can not distinguish between broad and narrow color distributions around the mean rgb sequence ; thus , examining the color distributions around this sequence is of key importance , as shown in fig . [ fig : frgbchist ] . here we divided the stars into four groups according to radius , @xmath85 , @xmath86 , @xmath87 and @xmath88 , and made a color histogram for each group . the figure shows that the color distribution is generally broad , but varies as the radius changes . it appears that the color distribution for @xmath89 is very broad , suggesting that the stellar population at the galaxy center is not simple and is a mixture of several stellar populations of different ages and metal abundance . this is consistent with the results of mighell & rich ( 1996 ) , who noted the wide age spread ( @xmath90gyr ) for the stellar population at the center . the color distribution becomes more concentrated to @xmath91 for @xmath92 arcmin . this would imply that the stellar population for @xmath92 arcmin is more homogeneous compared to that for @xmath93 arcmin .. mighell & rich ( 1996 ) derived the age distribution of the stellar population in the center of the galaxy on the basis of the magnitude distribution of subgiant branch ( sgb ) stars . [ fig : cmfea ] ( c ) focuses on the color - magnitude diagram around the bottom of the rgb and the turn - off point . the green lines represent padova isochrones for ages 5 , 10 , and 15 gyr and metallicity z=0.0004 ( girardi et al . as shown in the figure , the isochrones are almost parallel to the @xmath45 axis ( i.e. , constant @xmath17 magnitude ) at the sgb ( @xmath94 ) , indicating that the magnitude at a fixed @xmath45 color can be translated to age . the difference in metallicity also affects the shape of the isochrone , but small differences in metallicity ( e.g. z=0.001 , shown as magenta lines in fig . [ fig : cmfea ] ( c ) ) do not change the shape significantly . since it is unlikely that metal rich population ( @xmath95 ) dominates the stellar population in leo ii as suggested by the shape of mean rgb sequence , we can estimate the age distribution using the magnitude distribution of sgb stars . we examined the magnitude distribution of stars with @xmath96 and @xmath97 , which we call sgb . the region in the color - magnitude diagram is shown as a cyan box in fig . [ fig : cmfea ] ( a ) and ( c ) . a difficulty , however , occurs in applying this method to our data ; the error in color becomes larger than the width of the selection criteria , @xmath97 , for @xmath98 . this increases the uncertainty in the number estimation of sgb stars fainter than @xmath99 . nevertheless , we were able to obtain a clue as to the age distribution in the following way . the key lies in the brighter sgb stars ( @xmath25 ) , which indicate the presence of a younger stellar population . we can estimate what fraction of the total stellar population the young population accounts for by comparing the number ratio of bright sgb stars to faint rgb stars with a theoretical calculation . we therefore investigated the number ratio of sgb stars to faint rgb stars as a function of the radius . to derive the number of sgb stars , the incompleteness of the detection and contaminations from unresolved background galaxies and the foreground stars must be properly corrected . we estimated the incompleteness for every 0.5 mag grid in the @xmath17 and @xmath18 bands and for 1 arcmin in radius using real images as explained in sect . [ sec : obs ] . [ fig : comp_mag ] shows the completeness as a function of magnitude in the @xmath17 and @xmath18 bands at different radii ( @xmath100 = 0 , 2.5 , 5.0 , 10.0 arcmin ) . with this incompleteness table in hand , the incompleteness at a given @xmath17 magnitude , color ( i.e. , @xmath18 magnitude , once @xmath17 magnitude is given ) , and radius is estimated by a linear interpolation . the numbers of sgb stars are corrected for incompleteness calculated above . to estimate the number of contaminations , we regarded stars found at @xmath101 as contaminations , and the magnitude distribution of ( incompleteness - corrected ) contaminations with @xmath97 were fitted to the 4th order polynomials as , @xmath102 . to derive the number of sgb stars in a given annulus , the contamination number function @xmath103 multiplied by the area of the annulus wa subtracted from the incompleteness - corrected number . the number ratios of sgb stars to faint rgb stars are plotted in fig . [ fig : sgfrgbratio ] as a function of the radius . in the figure , the number ratios are plotted separately for bright sgb stars ( @xmath104 , filled squares ) and intermediate sgb stars ( @xmath105 , open triangles ) . note that @xmath104 and @xmath105 populations roughly correspond to @xmath106 gyr and @xmath107 gyr populations , respectively . we noted that the number ratios for both bright and intermediate sgb stars increase toward the center of the galaxy . the slope is steeper for intermediate sgb stars . the number ratio can be calculated theoretically for a stellar population of fixed age and metallicity using padova isochrones and the initial mass function . we adopted salpeter s form for the initial mass function . the calculation shows that the number ratios for bright sgb stars ( @xmath104 ) range @xmath108 for z=0.0004 population stars . if a stellar population is dominated by a z=0.0004 population , the number ratio should be close to the value . the number for a z=0.001 population ranges @xmath109 . although the calculated values are different according to the adopted metallicity , the number ratios at any radius are well below all the calculated values . this indicates that a population younger than 4 gyr is not a dominant population , although it certainly resides in the galaxy center . the existence of a stellar population as young as 2 gyr reported by bosler et al . ( 2004 ) and koch et al . ( 2007 ) also supports our finding . the increase in the number ratio at the galaxy center suggests that ( 1 ) the fraction of the young population is higher at the center than at the periphery , ( 2 ) the metallicity of the young population is higher at the center than at the periphery , or ( 3 ) a combination of ( 1 ) and ( 2 ) . for intermediate sgb stars ( @xmath105 ) , the calculated number ratios range @xmath110 and @xmath111 for z=0.0004 and z=0.001 populations , respectively . the number ratio is @xmath112 at the center and @xmath113 within 3 arcmin from the center , indicating that an intermediate age population ( @xmath114 gyr ) is dominant at the galaxy center . this is consistent with the finding by mighell & rich ( 1996 ) and dolphin ( 2002 ) that a considerable stellar population younger than 8 gyr occurs at the center of leo ii . however , the number ratios of both bright and intermediate sgb stars become small as the radius increases , indicating that the stellar population at the outskirts of the galaxy is deficient in young population , i.e. , most of the stars are older than 8 gyr . the stellar population in the outskirts of the galaxy ( @xmath115 ) was shown to consist of mostly older stars ( @xmath6 8 gyr ) . if metal abundance is nearly homogeneous , such an old population must form a narrow color distribution at the rgb , which is confirmed by a concentrated distribution in @xmath45 color of faint rgb stars as shown in fig . [ fig : frgbchist ] . a comparison of padova isochrones with the color distribution of rgb stars in the outskirts suggests low - metal - abundance populations ( between z=0.0004 and z=0.001 ) in the outskirts if ages of @xmath116 gyr are assumed . the larger hb morphology index ( fig . [ fig : hbmorph ] ) also supports an old population with low metal abundance . we conclude that the dominant population in the outskirts of the galaxy is an old population with low metal abundance . the stellar population at the center of the galaxy , however , shows a variety of age . it is necessary to include stars younger than 10 gyr , but a young population with low metal abundance , for example , @xmath117 10 gyr and z=0.0004 population , is excluded since the isochrone would not trace the rgb distribution . therefore , a higher metal abundance ( z @xmath12 0.001 , possibly z @xmath12 0.004 for very young population ) is suggested . from the foregoing results , leo ii is suggested to have evolved as follows . leo ii first started to form stars over the whole galaxy about 15 gyr ago with a modest ( probably low ) star - formation rate . star formation lasted for some time and the interstellar gas gained metals . then about 8 gyr ago , star formation began to cease from the outskirts and the star - forming region gradually became more concentrated to the center . the star - forming activity had dropped to @xmath5 0 by @xmath5 4 gyr ago , except for the center where a small population younger than 4 gyr occurs . hensler et al . ( 2004 ) demonstrated the one - dimensional chemodynamical evolution of dwarf elliptical galaxies , and showed the interesting feature that the star - forming region shrinks as a galaxy evolves because of gas exhaustion in the galaxy . their simulation seems to outline the evolution of leo ii fairly well , although it requires a refinement to fully explain our results . since a population gradient within a galaxy is also observed for several local group dwarf spheroidal galaxies ( e.g. , harbeck et al . 2001 ) , a more refined chemodynamical model will be necessary to explain the population gradient in the future to clarify the evolution of dwarf spheroidal galaxies . the origin of the knotty substructure found at the extended halo of leo ii could be ( 1 ) a small globular cluster , which is disrupted and merged with the main body of leo ii , ( 2 ) stars stripped from the main body of leo ii , or ( 3 ) a foreground artifact . the properties of stellar populations such as hb morphology are almost the same between outside the tidal radius and at the outskirts of the main body , indicating that the knot would be dominated by old stars with low metal abundance . to further investigate the stellar population of the knot , we made a hess diagram from which field contaminations were statistically subtracted . in fig . [ fig : hess ] , although the field subtraction is not perfect , two significant concentrations of stars are observed around the red clump ( @xmath118 , @xmath119 ) and the turn - off point ( @xmath120 , @xmath121 ) like that seen in fig . [ fig : cmd ] . this suggests that the knot is likely to consist of a similar stellar population as that residing in the outskirts of leo ii and the probability of ( 3 ) is low . however , based on this figure , it is still difficult to determine whether possibility ( 1 ) or ( 2 ) is more likely . if the second scenario is true , the tidal influence of the galaxy would be the most efficient mechanism to strip stars from the main body of leo ii . indeed , many dwarf spheroidal galaxies such as draco and ursa minor are now known to host extra - tidal halo structures although they are closer to the galaxy and hence more influenced by the galactic tidal force . however , the present - day remote location of leo ii from the galaxy raises the question of whether the tidal force of the galaxy is enough to strip stars from the main body of leo ii . in addition , the fact that we do not detect any obvious extra - tidal structure at the opposite side of leo ii is unfavorable for this scenario . therefore , it is unlikely that tidally stripped stars are the origin of the knotty substructure . if the knot is indeed a result of the tidal stripping , it should be aligned to the direction parallel to the motion of leo ii . therefore , measuring the proper motion of leo ii would provide a clue to answering this problem , although it would still be quite challenging . the fact that no globular clusters are found to associate with less luminous dwarf spheroidals such as leo ii does not support the first scenario for the origin of the knot . but it is possible that leo ii formed together with a small number of globular clusters and we may be watching the disruption process of the last one that happened to survive until the recent past . it is interesting that kleyna et al . ( 2003 ) demonstrated the survival of a substructure for a hubble time in a cored dark - matter halo . they suggested that the substructures found in ursa minor are the remnants of a disrupted stellar cluster and that ursa minor possesses a cored dark - matter halo . following their idea , we suggest that leo ii may be another example of a galaxy with a cored dark - matter halo . recent numerical simulations suggest that dark halos of dwarf spheroidals are larger than previously thought , and hence , extra - tidal stars are gravitationally bound to the galaxies and are a part of the extended stellar halos ( hayashi et al . 2003 ; mashchenko et al . the extended halo structure found in this study might be a structure bound to leo ii according to the predictions of the simulations . we carried out a wide - field imaging survey of the local group dwarf spheroidal galaxy leo ii in the @xmath17 and @xmath18 bands using suprime - cam on the 8.2-m subaru telescope . the survey covered an area of @xmath1 arcmin@xmath2 , far beyond the tidal radius of the leo ii ( 8.63 arcmin ) . a total of 82252 stars was detected down to the limiting magnitude of @xmath3 , which is roughly 1 mag deeper than the turn - off point of the main sequence stars of leo ii . our main conclusions are summarized below . * the radial number density profile of bright rgb stars is shown to continue beyond the tidal radius ( @xmath122 arcmin ) . a change in the slope occurs near the tidal radius and the slope becomes shallower for @xmath52 arcmin . a hint of a drop is seen in number density at @xmath53 arcmin . a similar two - component profile is also observed for faint rgb stars . * a smoothed surface brightness map of leo ii suggests the existence of a small substructure beyond the tidal radius , which is as large as globular clusters in luminosity ( @xmath123 ) . it could possibly be a disrupted globular cluster of leo ii that had survived until the recent past . another possibility is that it is composed of stars stripped from the main body of leo ii , although this is unlikely . * the hb morphology index shows a radial gradient in the sense that red hb stars are more concentrated than blue hb stars . such a trend is also observed in several local group dwarf spheroidal galaxies . the hb morphology index implies that the stellar population in the outer part ( @xmath79 arcmin ) is more metal - poor and/or older than that in the inner part . * the rgb color index is almost constant at any radius except for the center , where a redder mean rgb sequence than ours was observed by mighell & rich ( 1996 ) . the color distribution of rgb stars around the mean rgb sequence shows a broader distribution at the center ( @xmath124 arcmin ) than the outskirts . this suggests a more homogeneous stellar population at the outskirts of the galaxy and a variety of stellar populations at the galaxy center . * the age distribution was estimated using brighter ( @xmath125 ) sgb stars . the presence of a younger stellar population than 4 gyr is suggested for the center , although it is not a dominant population . the contribution of an intermediate - age ( @xmath114 gyr ) stellar population seems to be considerable at the galaxy center , but the contribution of such a population is small at the outskirts . * the evolution of leo ii is suggested to be as follows . ( 1 ) leo ii first began forming stars throughout the whole galaxy with a constant ( inefficient ) star - formation rate . ( 2 ) the star formation then began to cease in the outskirts and the star - forming region gradually shrank toward the center . ( 3 ) the star - forming activity had dropped to @xmath5 0 by @xmath5 4 gyr ago except at the center , where a small population younger than 4 gyr is found . we thank the observatory staff of the subaru telescope for their excellent support . we are grateful to the anonymous referee for many valuable comments and suggestions which improve this paper very much .

we carried out a wide - field @xmath0 imaging survey of the local group dwarf spheroidal galaxy leo ii using the subaru prime focus camera on the 8.2-m subaru telescope . the survey covered an area of @xmath1 arcmin@xmath2 , far beyond the tidal radius of leo ii ( 8.63 arcmin ) , down to the limiting magnitude of @xmath3 , which is roughly 1 mag deeper than the turn - off point of the main sequence stars of leo ii . radial number density profiles of bright and faint red giant branch ( rgb ) stars were found to change their slopes at around the tidal radius , and extend beyond the tidal radius with shallower slopes . a smoothed surface brightness map of leo ii suggests the existence of a small substructure ( [email protected] arcmin@xmath2 , 270@xmath4170 pc@xmath2 in physical size ) of globular cluster luminosity beyond the tidal radius . we investigated the properties of the stellar population by means of the color - magnitude diagram . the horizontal branch ( hb ) morphology index shows a radial gradient in which red hb stars are more concentrated than blue hb stars , which is common to many local group dwarf spheroidal galaxies . the color distribution of rgb stars around the mean rgb sequence shows a larger dispersion at the center than in the outskirts , indicating a mixture of stellar populations at the center and a more homogeneous population in the outskirts . based on the age estimation using subgiant branch ( sgb ) stars , we found that although the major star formation took place @xmath5 8 gyr ago , a considerable stellar population younger than 8 gyr is found at the center ; such a younger population is insignificant in the outskirts . the following star - formation history is suggested for leo ii . star - forming activity occurred more than @xmath6 8 gyr ago throughout the galaxy at a modest star - formation rate . the star - forming region gradually shrank from the outside toward the center and star - forming activity finally dropped to @xmath5 0 by @xmath5 4 gyr ago , except for the center , where a small population younger than 4 gyr is present .

It was the Miracle in Iceland. With a heavy dose of crazy. In 1972, at the height of the Cold War — and some eight years before the United States men’s hockey team stunned the Soviet Union national team at the 1980 Olympics — American chess prodigy Bobby Fischer squared off against Russian legend Boris Spassky at the World Chess Championship in Reykjavik, Iceland, in arguably the most hotly anticipated and widely covered chess championship of all time. The Russians had dominated the world championships for 24 years. The mercurial Fischer was considered perhaps the most talented chess player in the U.S. history, but few gave him a prayer against the seemingly unbeatable and unflappable Spassky. Think “Rocky III” at the chess table —i f Rocky were an increasingly paranoid loner who made outrageous demands, loathed the media, was convinced his phones were bugged, routinely showed up late or not at all for important matches and was virtually incapable of having any kind of normal relationship with friends or family. Oh, and the whole world was watching. Edward Zwick’s “Pawn Sacrifice” is an enthralling piece of mainstream entertainment that captures the essence of Fischer’s mad genius, perfectly re-creates the tenor of the times AND works as a legit sports movie about the great game of chess, which, let’s face it, doesn’t quite lend itself to the sporting-drama arc as readily as football or hockey or, um, cricket. In an extended flashback sequence set in the Brooklyn of the 1950s, young Bobby Fischer (an excellent Aiden Lovekamp) is a chess-obsessed kid living with his single mother (Lily Rabe), a social activist with ties to the Communist Party. Mom is always chain-smoking and hosting meetings in the living room where everyone is talking about revolution, while Bobby keeps a lookout for the feds who frequently stop by to snap photos of the house. As Bobby tears up the local chess scene, defeating top-ranked local players three times his age, he attracts the attention of an attorney and manager (Michael Stuhlbarg) who’s well-connected in the ways of the chess world, and a priest and grandmaster (Peter Sarsgaard) who trains Bobby and is the closest thing Bobby has to a friend and father figure. Zwick adheres to the standard sports biopic conventions — montages of the protagonist in action, news footage, scenes featuring the man who will becomes the protagonist’s ultimate rival — as we follow the now grown-up Bobby (Tobey Maguire), who devotes every breathing moment to two pursuits: becoming the greatest chess player in history, and fending off the growing list of enemies, real and (mostly) imagined, who are out to get him. Whether you’re well-versed in the ways of the Sicilian Defense, Najdorf Variation, or you can’t tell a rook from a knight, “Pawn Sacrifice” does a stellar job of exploring the complexities of chess and the rich history of the game without getting bogged down in too much inside baseball. We get graphics reminiscent of “A Beautiful Mind” to give us a glimpse into the critical thinking of Fischer. Sarsgaard’s character acts as a commentator of sorts during the matches, cheering Bobby’s brilliant moves and throwing his hands up in frustration when the great one pulls an inexplicable stunt. Tobey Maguire’s a talented actor, but I’ve never found him particularly likable, even when he was playing Peter Parker. Here, though, Maguire gives the performance of his career — an authentic representation of Fischer’s genius, his somewhat charming eccentricities and his sad, inevitable decline into a full-fledged paranoid who became his own worst enemy and famously faded into a shell of himself. As Boris Spassky, Liev Schreiber deserves best supporting actor consideration. Schreiber’s performance is in Russian, save a very few lines in English. (Fun, odd fact: Schreiber has spoken Russian in four previous movies.) With the help of a script that gives Spassky a few key moments to shine on his own, Schreiber takes what could have been a standard-issue villainous Russian role and creates a character nearly as fascinating and complex as Fischer. It’s a mesmerizing turn. Fine acting abounds in this film. Stuhlbarg (“A Serious Man”) is a standout as Bobby’s manager, who is fiercely devoted to Fischer for what he claims are purely patriotic reasons. Sarsgaard gives his usual fine performance (though I could have done without the affectation of the priest constantly sucking on hard candy). Robin Weigert is heartbreakingly effective as Bobby’s mostly absentee mother. Lily Rabe does strong work as Bobby’s sister, who tries and tries to connect with Bobby, even after she knows he’s lost to his own narcissism and paranoia. We see footage of the real-life Bobby Fischer at the conclusion of “Pawn Sacrifice,” and if anything he seems even more bizarre than Maguire’s interpretation. It’s a reminder one should check out “Bobby Fischer Against the World,” the great documentary about the chess master. As a stand-alone work of fiction, however, “Pawn Sacrifice” is one of the best movies of the year. Bleecker Street Media presents a film directed by Edward Zwick and written by Steven Knight. Running time: 116 minutes. Rated PG-13 (for brief strong language, some sexual content and historical smoking). Opens Friday at local theaters. ||||| When it comes to kids vs. grown-ups, 9-year-olds typically have the upper hand only in burping contests and drawing pictures for Mom to hang on the refrigerator. So when chess grandmaster Larry Kaufman faced off against elementary school student Awonder Liang, things looked pretty good — until Kaufman inadvertently exposed his king on move 31. Liang seized his opportunity and soon walked away as the youngest player to beat a grandmaster. Less than a year later, the then-fourth-grader was a U.S. chess master himself. It’s been a long time — dating back to the 1970s glory days of Bobby Fischer — since the U.S. has been a power in the global chess world. Fischer’s heroics (and tantrums) were larger than life; indeed, he’s the subject of the new film Pawn Sacrifice starring Tobey Maguire. But don’t think America’s movie-worthy chess days are in the past. In a weird throwback in an era of video games, a chess renaissance is on in this country, with three American players in the world’s top 10. The question now: Will this 12-year-old from Wisconsin climb into those ranks someday? Certainly, he’s already pulled off a number of “youngest ever” feats, including youngest-ever U.S. chess player to achieve a technical level of play called an “IM norm” and youngest-ever U.S. chess player to become a master. With a 2361 FIDE rating, Liang is No. 1, top of the pile, for his age in the U.S. To lapse into chess-speak for a moment, he says his endgame is to win a world championship. And if he does, it won’t be with a coach, oddly enough. While most top players had coaches in their youth, Liang mainly teaches himself using only a computer. Fischer, of course, was also a child prodigy, one who became infamous for throwing fits on his way to stardom (later in life, he would become a nightmarish anti-American and anti-Semitic figure who died seven years ago in Iceland). It’s a jarring contrast with Liang, who carries his accomplishments lightly. In conversation, he speaks in terse adages, like Gary Cooper trapped in the game of kings. (For instance: “I was nervous, but I knew I would try my best”; “I plan to keep going and see how far I can get into chess.”) The round-faced child of Chinese immigrants, who wears his hair high and tight, might be a little fidgety at the board, but that’s about it. When he was 5, Liang asked his father to teach him the rules of chess after his older brother came home with a medal from a local tournament. He preps for a match the simple way: rest, eat, look over what his opponent might do and spot patterns. A few years ago, Liang regularly played Dennis Doren, a Wisconsinite with a good-but-not-great rating, who’d learned about Liang in the local paper after he won the under-8 world championship. It wasn’t even close: The 61-year-old says Liang crushed him nine out of 10 games. “I tried to teach him some stuff that I knew,” Doren says — but what took Doren a day to learn would take Liang just an hour. Liang’s favorite players not only include Fischer (of course) but also current world champion Magnus Carlsen and former world champion Garry Kasparov, who has taught a couple of Liang’s training sessions. Each year, Kasparov holds a chess boot camp for the country’s nerdiest chess players; in Liang’s first year, he was the youngest player invited. Liang also has a striking memory of games, Doren says. Once he was studying an opening with the then-9-year-old, who not only recognized it from one of Kasparov’s games but also remembered who won when Kasparov played it. But the pint-size pawn pusher faces plenty of obstacles, starting with an opponent that won’t face him across the board. “Chess is expensive,” says international master Greg Shahade. Coaching, tournament entry fees, hotels, plane tickets and other expenses add up — one trip to a top championship can cost $5,000. The Liang family’s resources are limited, which, in the worst-case scenario, could stalemate Awonder’s burgeoning career. Once, Doren set up an Indiegogo campaign to fund Liang’s trip to the World Youth Chess Championship and raised more than $3,000 (the campaign’s goal), but the process was time-consuming and complicated. Liang’s age, oddly enough, is another potential issue. Doren sometimes suspects that would-be backers who might support the kid’s championship dreams think he’s too young — meaning, basically, that he might still decide to spend his life doing something besides castling and en passant captures. (Will Liang, Awonder’s father, says he doesn’t necessarily agree, but grants that the point is arguable.) Some other countries, like Armenia, where chess is mandatory in school, provide government funding for promising players; the U.S. hasn’t been anywhere near as organized. But Liang hasn’t been boxed in yet. The Samford Fellowship, a U.S. grant for promising chess talent under 25 years old, pays out $42,000 for up to two years; it could be in Liang’s future if he can establish himself. Chess prodigies are getting younger and younger. International master Ken Regan says this is because today’s “prodigies are growing up in the Internet world” with more access to games via computer than ever before. Plus, because Liang hasn’t received much formal training, his game has some flaws. Awonder’s openings, his father admits, could use some work. But he’s got plenty of time to learn; he’s just starting seventh grade. ||||| As unlikely as it now seems, 1972 found the world in the grips of a chess obsession. This was largely due to the accomplishments of Bobby Fischer, a spookily gifted player from Brooklyn whose ascent in the game brought him to the frontlines of global politics, thanks to a World Championship match in Reykjavik, Iceland that pitted him against the Soviet star Boris Spassky. With the reputations of both sides of the conflict at stake, the match became a high-stakes event for those on both sides of the Cold War. It’s enough to make a man crack under the pressure, if he wasn’t cracked already. Pawn Sacrifice re-stages that match-up — and the political and media circus around it — after leading up to the event with a depiction of Fischer’s formative years. Its best moment connecting the two comes early. The opening scene shows Fischer (played as an adult by Tobey Maguire) alone in his hotel room on the eve of a game with Spassky. In the grips of paranoia, he’s afraid of being spied on, maybe by his opponents, or his own government, or forces that exist only in his head. From there, the film cuts to Fischer as seen through the lens of a camera held by an unseen watcher, first as an adult, then as a child, where his mother’s left-wing politics made being under surveillance a real possibility. As the saying goes: Just because you’re paranoid… From there, Pawn Sacrifice takes a pretty straight path from Brooklyn to Reykjavik. Fischer wows everyone he encounters, first as a self-taught, chess-obsessed child, then as a teenage prodigy, doing little else along the way except picking up admirers. Eventually, these include lawyer Paul Marshall (Michael Stuhlbarg), who does triple duty, also working as Fischer’s agent and his unofficial contact with the State Department, which views Fischer as a useful PR tool, despite his professed lack of interest in politics or most anything but chess—at least initially. “For him, Vietnam and The Beatles never happened,” Marshall explains. But in time, Fischer gets dragged into a world beyond chessmen and boards. Directed by Edward Zwick, a veteran of unsubtle-but-effective dramas such as Glory and Love & Other Drugs, Pawn Sacrifice, doesn’t offer much in the way of surprises or insight. It’s shot handsomely and builds in intensity as the mental illness that would later make Fischer first a recluse, then an international pariah—thanks to his tendency to spout off anti-American and anti-Semitic theories—takes hold. But it never fully captures how Fischer became Fischer or gets beneath the surface of its political themes. There’s much to recommend it anyway, though, thanks to some sharp lines from screenwriter Steven Knight (Eastern Promises, Locke) and first-rate performances from a cast that includes Peter Sarsgaard (as Fischer’s sympathetic fellow grandmaster, and Catholic priest, William Lombardy) and Liev Schreiber, as Spassky. Playing Spassky as a stone-faced rock star, Schreiber gets some of the film’s sharpest moments, particularly when, like Fischer, he starts to get obsessive about eliminating any distractions during the match. It’s as if Fischer’s madness is catching, even among those seemingly too cool to let anything worry them. But it’s largely Maguire’s movie, and he’s captivating whether quietly playing games in his head or talking himself up to the press while throwing out barbs to his opponents. He gives Fischer a crazed charisma of the sort that, Maguire’s work keeps suggesting, could, and almost certainly will, tip into madness. **** Accusations of insanity and perversity get thrown around in The New Girlfriend, as well, but they never quite stick to the accused. The latest from the reliably compelling French director Francois Ozon, the film adapts a 1985 short story by British mystery writer Ruth Rendell, and part of what makes the film work so well is the way Ozon plays it as a thriller, creating an atmosphere of dread that suggests something horrific just over the horizon—then never letting it arrive. There are secrets and lies at the heart of the film, but they’re not that kind of secrets and lies. Some of them are of the sort characters won’t even admit to themselves. Claire (Anaïs Demoustier) and Laura (Isild Le Besco) have been friends since childhood, even though Laura has always stayed a step ahead of her friend, turning boys’ heads before Claire, marrying first, having a child before her, and, as the film opens, even beating her to the grave by dying young. Claire has kept her jealousy unspoken, but, an early montage, she wears it on her face, Laura’s death leaves her with a sense of responsibility to her widower David (Romain Duris) and their young child, and with a sense of unresolved guilt — and some other unresolved feelings, too. She’s thrown, however, when she visits David’s home to find a strange woman caring for their child, only to discover that the woman is David wearing Laura’s clothes. It’s a habit Laura knew about, he tells her, one that he’d lost the desire for during their marriage, but had returned after her death, all quite, by his reckoning, “naturally.” At first repelled, Claire soon becomes a friend to David—renamed “Virginia” when in drag—arranging shopping expeditions and helping with fashion and grooming. Soon, Claire finds herself lying to her husband as she spends the weekend with Virginia, neither of them sure what they’re doing or where it will go. In films like Swimming Pool and Under the Sand, Ozon has leaned hard on Hitchcock for inspiration. He does the same here, via a Bernard Herrmann-inspired score by Philippe Rombi and elegant, unsettling camerawork. The film’s not really a thriller, but it’s still the right approach, capturing the way Claire’s time with David/Virginia unsettles her. Despite Virginia’s transformation—and Duris is terrific playing someone just getting comfortable wearing a new skin—it’s as much Claire’s story, and Ozon keeps emphasizing how much Laura’s loss has left her adrift and unsure who she is. The echoes of Vertigo fit in well, too. Though it winds its way to a much different destination (and features far more crossdressing), The New Girlfriend is, like Vertigo, very much a film about loss and what we do to fill the spaces vacated by those who leave us. Pawn Sacrifice opens in New York and L.A. on September 16. It expands to select theaters on September 18. The New Girlfriend opens in New York and L.A. on September 18, then expands in subsequent weeks. ||||| Viewers unfamiliar with the American chess champion Bobby Fischer might be forgiven for assuming, based on the casting of Tobey Maguire as a 30-ish Fischer in Pawn Sacrifice, that his genius was of the quiet, withdrawn variety. But while this movie version of Fischer does indeed suffer from mental health issues that make it difficult for him to form functional human relationships, one of the film’s strongest, most potentially surprising pleasures is the sight of Maguire playing both with and against his usual type. While this Fischer is a chess prodigy who spends a lot of time in his own head, easily distracted by bursts of life’s background noises, he also has a mouthy pro-athlete bravado that seems consistent with his Brooklyn upbringing. That attitude gives Maguire the opportunity to play a little meaner and wilder, reminiscent of his underrated work in Spider-Man 3 and The Good German (as a far less villainous character than he plays in either of those). His braggadocio recalls an overgrown child, with his casual dismissals of other chess players and antsy, loosey-goosey body language linking to his childhood impatience with waiting for his opponents’ moves. Maguire’s overgrown-boy look creates continuity between the younger versions of Fischer the movie shows before spending most of its time with the adult version in the ’60s and ’70s, leading up to a series of 1972 matches with Russian chess master Boris Spassky (Liev Schreiber, in a performance of relatively few lines and even fewer in English). Fischer’s mental problems and frequent encounters with Russians make him a perfect victim of Cold War paranoia, and he’s often convinced that he’s being followed and bugged. He may not be right (and his ranting against the commies and “the Jews” seems especially disturbed when other characters point out that he is, in fact, Jewish), but the methods aren’t unthinkable—and his trusty lawyer Paul Marshall (Michael Stuhlbarg) really is in contact with people in Washington, who see Fischer’s chess matches with the Russians as the rare winnable conflict with communists. It’s interesting material, especially when Fischer is sequestered with Marshall and his sort-of coach, Father Bill Lombardy (Peter Sarsgaard). The movie falters, though, when it tries to jazz up its historical context, with director Edward Zwick working overtime to express Fischer’s interior and exterior worlds cinematically. From a very early scene where he cuts to various sources of noise in Fischer’s childhood bedroom before dramatically racking focus on his trusty, soothing chess set, Zwick wields his visuals with enthusiastic bluntness, like a teacher convinced he’s bringing history to life by dressing up in a crazy costume. He cuts to archival footage, shots made to look like archival footage, cheesy quasi-surveillance shots, and plenty of slow-mo portents; little of it has the intended zing. The film’s most expressive visual moments are less showy: A static shot of his lawyer and coach in a hotel lobby, with Fischer pacing in and out of the frame as he complains about its shabbiness, conveys plenty about the trio’s relationship. Later, Zwick and editor Steven Rosenblum make a succinct (and funny) cut from the very beginning of a Fischer match to a shot of his opponent in a car, heading home, obviously defeated. Many of the chess matches are kept partially or entirely off screen; Pawn Sacrifice is largely about prep work, about Fischer’s endless psyche-up in the face of decreasing mental stability. When he gets nervous or agitated, he makes more demands and changes the terms of his deal; when he manages to actually begin a game, it feels like a major victory. When the time does come for the dramatization of the chess matches between Fischer and Spassky, the movie struggles to wring much drama past the first few games—understandable, really, for a 24-game series. Pawn Sacrifice also comes with a long, unwieldy postscript that covers the last 35 years or so of Fischer’s life, avoiding some biopic pitfalls by simply screeching to a halt and explaining the rest on screen. It’s a fitfully entertaining and well-acted movie that doesn’t quite come together—though maybe the frustrating lack of resolve is appropriate for Fischer’s arc-resistant life.

– In Pawn Sacrifice, Tobey Maguire plays troubled American chess prodigy Bobby Fischer, who will eventually battle Russian chess master Boris Spassky at the 1972 World Chess Championship. But can any actor really get inside Fischer's head? Here's what critics are saying: Richard Roeper sums up the film as "Rocky III at the chess table—if Rocky were an increasingly paranoid loner." Overall, it's "enthralling," "captures the essence of Fischer's mad genius, perfectly recreates the tenor of the times AND works as a legit sports movie about the great game of chess," he writes at the Chicago Sun-Times. Plus, "Maguire gives the performance of his career," and "Liev Schreiber deserves best supporting actor consideration" for his turn as Spassky. The film "doesn't offer much in the way of surprises or insight," and "never fully captures how Fischer became Fischer," but "there's much to recommend it anyway," writes Keith Phipps at Uproxx. "It's shot handsomely and builds in intensity." There are also "some sharp lines from screenwriter Steven Knight and first-rate performances." Schreiber is good, but Maguire steals the show. Jesse Hassenger at AV Club says "it's a fitfully entertaining and well-acted movie" but "doesn’t quite come together." Though "one of the film's strongest, most potentially surprising pleasures is the sight of Maguire playing both with and against his usual type," Hassenger says the film "struggles to wring much drama" out of a 24-game chess series. The lengthy postscript also seems a bit off. Joe Neumaier admits the movie isn't perfect. "The overall intelligence and strategy of the story is occasionally disturbed by moments of obvious movie bluster or emotional trickery. But that's easy to forgive," he writes at the New York Daily News. "The challenge of Pawn Sacrifice was to capture the colorful Cold War '70s, the inner strategies of one man's paranoid mind, and make chess cinematic. Check, and mate." This is Maguire's "best performance since Wonder Boys." (Is this 12-year-old the next Bobby Fischer?)

with the rapid experimental progress the ultracold atomic gases have offered a popular platform to investigate the strongly correlated one dimensional many - body systems @xcite for their high controllability and tunability . one dimensional quantum gases can be realized with strong anisotropic magnetic trap or two dimensional optical lattice @xcite and be described theoretically by an effective one dimensional ( 1d ) model olshanii , olshanii2,petrov , dunjko . in addition the effective 1d interaction can be tuned from the strongly attractive to the strongly repulsive interacting regime via the magnetic feshbach resonance or confinement induced resonance . not only the strongly interacting tonks - girardeau ( tg ) gases @xcite but also two counter - intuitive examples , i.e. , the repulsively bound atom pairs @xcite and the super tonks - girardeau ( stg ) gas - like phase of the attractive atomic gas haller , astrakharchik , batchelor , have been realized by a sudden quench of interaction from the strong repulsion to the strong attraction or vice versa , both of which are hard to realize in the traditional condensed matter physics and have no analog in solid state systems . it has been displayed that they are stable excited states and the stability could be understood from the quench dynamics of the 1d integrable quantum gas @xcite . so far , the stg gas has attracted intensive theoretical studies from various aspects @xcite . the experimental realization of stg gases and repulsively bound atom pairs open the door to stable highly excited quantum many - body phases . this also offers us a method to search for exotic quantum phases in 1d many - body systems . it has been predicted that such stable excited states can be prepared in optical lattice via sudden quantum quench @xcite and the effective super tonks - girardeau gases can be realized via strongly attractive one - dimensional fermi gases @xcite . theoretically the strongly interacting bose gases can not be well described in the mean - field theory due to the large quantum fluctuation in 1d system and one has to resort to non - perturbation methods . many methods such as bethe ansatz dunjko , fuchs , hao , guan , bosonization method @xcite , exact diagonalization @xcite , bose - fermi mapping method ( bfm ) @xcite and multi - configuration hartree theory @xcite were used to investigate the 1d quantum gases . it was shown that with the increase in repulsion strength the ground state density distribution of 1d bose gases continuously evolves from a gaussian - like distribution to a multi - peak structure while the momentum distribution remains the single peak structure of bosonic atoms @xcite . by a sudden quench of interaction from strong repulsion to strong attraction a tg gas shall transfer into a stg gas @xcite . because the quantum gas is very weakly coupled with the environment its energy dissipation is ignorable and this highly excited state shall be stable . by decreasing the attractive interaction of stg gas we can investigate the properties of the lowest scattering state for the bose gas with the change of attractive interaction from strongly to weakly interacting regime . in this work , by numerically solving the bethe ansatz equation we obtain exact wave function of the lowest scattering state of 1d bose gas trapped in a hard wall potential in the above interacting regime . we will focus on the density distribution , reduced one body density matrix ( robdm ) and two body correlation in the full attractive interaction regime . the present paper is organized as follows . section ii is devoted to the description of our model and bethe ansatz method . section iii will give the density profiles , robdm and two body correlation in the full attractive interacting regime . a summary is given in the last section . we consider @xmath0 interacting bose atoms of mass @xmath1 confined in a hard wall box of length @xmath2 , which is described by the hamiltonian @xmath3here the natural unit is used @xmath4 and @xmath5 is an interaction constant dependent on the effective 1d interaction strength @xmath6 , which can be tuned continuously from the strong attraction to the strong repulsion by feshbach resonance or confinement induced resonance . this model can be solved exactly by the bethe ansatz method @xcite . the many - particle wave function shall be formulated as the following general form @xmath7with @xmath8 , \label{wavefunction}\end{aligned}\]]where @xmath9 and @xmath10 are one of the permutations of @xmath11 , respectively , @xmath12 is the abbreviation of the coefficient @xmath13 to be determined self - consistently , and the summation @xmath14 ( @xmath15 ) is done for all of them . here @xmath16 indicate that the particles move toward the right or the left , @xmath17 is the step function and the parameters @xmath18 are known as quasi - momenta . in the following evaluation the length @xmath2 will be taken to be unity unless otherwise specified . for bosons the wave function should follow the symmetry of exchange , so the present problem is simplified into the solution of @xmath19 in the region of @xmath20 with the open boundary condition @xmath21for simplicity we shall ignore the subscript in @xmath22 . the wave function in other region @xmath23 can be obtained by the exchange symmetry of bose wave function . with some algebraic calculation , the wave function has the following explicit form @xmath24 \exp \left ( ik_{p_{n}}l\right ) \sin \left ( k_{p_{1}}x_{1}\right ) \\ & & \times \prod_{1<j < n}\sin \left ( k_{p_{j}}x_{j}-\sum_{l < j}\omega _ { p_{l}p_{j}}\right ) \sin \left ( k_{p_{n}}\left ( l - x_{n}\right ) \right)\end{aligned}\]]with @xmath25and @xmath26here @xmath27 denote sign factors associated with even(odd ) permutations of @xmath28 . the quasi - momenta are determined by numerically solving the bethe ansatz equations and the total wave function is given by eq.(wf ) through @xmath29 under the restriction of exchange symmetry . under the open boundary condition , we can obtain bethe - ansatz equations @xmath30whose logarithmic forms are formulated as @xmath31here @xmath32 is a set of integers to determine the eigenstates and for the ground state @xmath33 @xmath34 . the energy of the system is @xmath35 . for different interaction @xmath36.,width=302,height=226 ] for the repulsive interaction ( @xmath37 ) the solutions of eq . ( [ bae ] ) @xmath38 are real , while for the attractive interaction ( @xmath39 ) its solutions might be either real or complex . the real solutions correspond to scattering states , which can be obtained by solving eq . ( [ bae ] ) . we determine the quantum number @xmath40 in the limit of strong interaction ( @xmath41 ) or the limit of zero interaction ( @xmath42 ) . in the former situation the exact wave function can be constructed by means of the bose - fermi mapping method from the wave function of @xmath0 free fermions girardeaustg , i.e. , the eigenfunction of single particle in the hard wall trap @xmath43 with @xmath44 being integers . for the ground state @xmath45 and the excited states are obtained when some @xmath44 are replaced by the integers greater than @xmath0 . in the ground state of noninteracting limit all bose atoms shall condense into the ground state of single particle , which gives the exact many body function as @xmath46 . the wave function of excited states in noninteracting limit , however , takes the form of @xmath47 , where @xmath28 is an operator preserving the exchange symmetry of the many body wave function . by comparing these exact wave function with those obtained from eq . ( [ bae ] ) , the quantum number @xmath40 can be obtained . it is convenient to use the strong interacting limit here . as @xmath36 approximates to @xmath48 all terms in the summation of eq . ( [ bae ] ) vanish such that the quasimomenta @xmath49 . comparing the above exact solution we have @xmath33 ( @xmath45 ) for the ground state and the excited states correspond to @xmath50 . after deciding the quantum number it is easy to obtain the solution in the limit of @xmath51 . as @xmath36 approximate @xmath52 we have @xmath53 and as @xmath36 approximate @xmath54 we have @xmath55 . the complex solutions correspond to bound states , which can be obtained by assuming the solutions of complex form @xmath56 and solving the set of equations of @xmath57 and @xmath58 . for example , the complex solutions of bethe ansatz equations for the system of @xmath59 are assumed as @xmath60 and the bethe ansatz equations take the formulation of @xmath61 & = & ( -1)^{n}\frac{2\lambda -c}{2\lambda + c},\end{aligned}\]]where the integer @xmath62 is quantum number and for the ground state @xmath63 . as an example , we display the full energy spectrum for @xmath59 in fig . the scattering states are denoted by solid lines and the bound states are denoted by dashed lines . it is shown that the ground state for repulsive case is scattering state and that for attractive case is bound state . the excited state of attractive bose gas in the scattering state has been realized experimentally in ref . @xcite . by tuning the 1d interaction constant the bose atoms evolve from the weakly interacting thomas - fermi regime to the strongly repulsive tg regime in which the tg gas was realized , and then by quenching the interaction from the strong repulsion to the strong attraction the scattering states of attractive bose gas , i.e. , the stg gas , was realized . starting from a stable stg gas , we can further investigate the crossover behavior of the stg gas when one decreases the attractive interaction very slowly to the very weak limit . through an adiabatically slow change of the attractive interaction , the lowest scattering state of attractive 1d bose gas in the whole attractive regime could be reached . and @xmath64 ( from below to above).,width=340 ] in fig . 2 we display the quasimomentum distribution and the corresponding energy ( longitudinal axis ) for the lowest scattering state of the attractive bose gases with @xmath65 in the full attractive interacting regime . according to eq . ( [ bae ] ) in the limit of stg ( @xmath66 ) the solutions of bethe ansatz equation are equal to those of tg gas ( @xmath67 ) , i.e. , @xmath68 @xmath69 . we find that with the decrease of attractive interaction strength , @xmath70 tend to distribute with larger and larger space between them although the lowest quasimomentum @xmath71 increase first and then decrease . in the limit of noninteracting limit @xmath72 we have @xmath73 @xmath74 and the space between two neighbor @xmath70 has evolved from @xmath75 ( @xmath76 ) to @xmath77 ( @xmath78 ) . the energy of the lowest scattering state increases with the decrease of attractive interaction . in terms of the lowest scattering state wave function @xmath79 the important quantity in one dimensional interacting many - body system , the robdm , can be formulated as @xmath80 the diagonal part of robdm gives the expectation values of density distribution @xmath81 , and the off - diagonal part gives information of coherent properties of the gas . the fourier transformation of @xmath82 gives the momentum distribution @xmath83 for @xmath84 ( from the left above to the right below ) . , width=302,height=302 ] .,width=302,height=226 ] fig . 3 shows the robdm for the lowest scattering state of attractive bose gas with @xmath85 . it deserves to notice that for all attractively interacting strengthes there exists a strong enhancement of the diagonal contribution @xmath86 along the line @xmath87 . in the limit of strong attraction , the system displays the same behavior as tg gases that @xmath88 reduces rapidly as @xmath89 increases . for weaker attraction the off - diagonal part of robdm shall increase gradually and we have approximately @xmath90 when the attraction is weak enough . the density distributions of the lowest scattering state for different attractive interacting strength are displayed in fig . 4 . in the strongly attractive limit , it is shown that the density profile of the stg gas of @xmath0 atoms exhibits the fermi - like shell structure of @xmath0-peak similar to the density profile of the tg gas . this is due to the fact that the stg state in the limit of @xmath91 and the tg state in the limit of @xmath92 are actually identical . as the attraction decreases , the density distribution deviates the fermi - like distribution and the shell structure oscillates more and more dramatically . in the limit of @xmath36 approaching @xmath93 there appear @xmath94 peaks in the density profile . the atoms tend to populate at the center of the trap with the most probability and the density distribution displays an obvious peak in the center and oscillates in the region away from the center . in the limit of the strong attraction atoms populate in the @xmath0 lowest eigenstates of single particle so the density profiles show the structure of @xmath0-peak . as the decrease of attraction atoms populate at higher eigenstates and the peak number shall increase . as @xmath72 , atoms distribute at the @xmath0 lowest odd states of single particle such that the density profile exhibits @xmath94 peaks . . , width=302,height=226 ] the momentum distributions for the lowest scattering state are shown in fig . 5 . for strong attractive interaction , the atoms accumulate in the central regime close to zero momentum and the population distributions decrease rapidly for large momentum , which reflects the statistics of bosonic atoms . with the decrease of attraction the atoms distribute more extensively in higher momentum region and in the strong but finite attractive interaction ( e.g. @xmath95 ) the atoms distribute widely in the momentum space without an obvious zero - momentum peak . for even weaker attractive interaction , the probability of atoms locating at the zero momentum increases and the momentum distribution develops a prominent peak at zero point @xmath96 . away from the central peak , the momentum distribution starts to display shell structure , which however exhibits distinct feature from the momentum distribution of fermi gas . it is because the lowest scattering state is an excited state that the bose atoms populate in higher momentum region . ( from the left above to the right below).,width=302,height=302 ] it is also interesting to study the two body correlation function defined as @xmath97 which denotes the probability that one measurement will find an atom at the point @xmath98 and the other one at the point @xmath99 . in fig . 6 we display the two body correlation of lowest scattering state for the bose gas with @xmath100 . it turns out that two atoms with strong attractive interaction would try to avoid each other and try to keep away from each other in certain distance , while as the decrease in attraction the probability of finding two atoms in the adjacent region increase and arrive at the maximum as @xmath101 . in conclusion we have investigated the lowest scattering state of bose gas in the full attractive interacting regime with bethe ansatz method . by solving the bethe ansatz equations numerically the exact wave functions of the lowest scattering state were determined . based on the wave function we obtain the robdm , density profile , momentum distribution and two - body correlation . it is shown that in the stg limit the robdm of the lowest scattering state exhibit the same behavior as tg gas . with the decrease of attractive interaction the density distribution evolves from a @xmath0-peak shell structure to a @xmath102-peak one and bose atoms are located at the center of the trap with the most probability . the momentum distribution manifests the nature of bose statistics in the stg limit with an obvious zero - momentum peak . when the attraction keeps on deviating the stg limit the momentum distribution spreads more widely although the most probable position at which the atoms populate is still near the region of zero momentum . the change of the two body correlation function with the decrease in the attractive interaction is also discussed . this work was supported by nsf of china under grants no . 11004007 , no . 10821403 , no . 10974234 , and no . 11074153 , programs of chinese academy of sciences , 973 grant no . 2010cb922904 , no . 2010cb923103 and national program for basic research of most . y. hao was also supported by the fundamental research funds for the central universities no . 06108019 . s. chen , x. w. guan , x. yin , l. guan and m. t. batchelor , phys . a * 81 * , 031608(r ) ( 2010 ) ; l. guan and s. chen , phys . rev . lett . * 105 * , 175301 ( 2010 ) ; x. yin , x. w. guan , m. t. batchelor , and s. chen phys . rev . a * 83 * , 013602 ( 2011 ) .

we investigate the lowest scattering state of one - dimensional bose gas with attractive interactions trapped in a hard wall trap . by solving the bethe ansatz equation numerically we determine the full energy spectrum and the exact wave function for different attractive interaction parameters . the resultant density distribution , momentum distribution , reduced one body density matrix and two body correlation show that the decreased attractive interaction induces rich density profiles and specific correlation properties in the weakly attractive bose gas .

Photos: Photos: From the campaign trail From the campaign trail – Republican presidential candidate Mitt Romney and his running mate, Rep. Paul Ryan, order food at a Wendy's restuarant in Richmond Heights, Ohio, on Tuesday. Hide Caption 1 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney boards his campaign plane in Bedford, Massachusetts. The Romney camp has decided to continue campaigning on Election Day. Hide Caption 2 of 177 Photos: Photos: From the campaign trail From the campaign trail – President Barack Obama gets emotional at his final campaign rally in Des Moines, Iowa, on Monday, November 5, on the eve of the U.S. presidential election. Obama's speech included references to his 2008 campaign and his victory in the Iowa caucuses, which helped catapult his political career. 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Hide Caption 75 of 177 Photos: Photos: From the campaign trail From the campaign trail – Barack Obama and Jon Stewart speak during a break in the live taping of Comedy Central's "The Daily Show with Jon Stewart" on Thursday. Hide Caption 76 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters of Mitt Romney attend a campaign rally in Chesapeake, Virginia, on Wednesday, October 17. Hide Caption 77 of 177 Photos: Photos: From the campaign trail From the campaign trail – Mitt Romney is seen backstage through a campaign flag as he waits to take the stage at a rally in Chesapeake, Virginia, on Wednesday. Hide Caption 78 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters of Obama listen to him speak during a rally at Cornell College in Mt. Vernon, Iowa, on Wednesday. Hide Caption 79 of 177 Photos: Photos: From the campaign trail From the campaign trail – President Barack Obama arrives at Rickenbacker International Airport in Columbus, Ohio, for a campaign rally Wednesday. Hide Caption 80 of 177 Photos: Photos: From the campaign trail From the campaign trail – A group of men watch the presidential debate on television screens at an electronics store in Miami on Tuesday, October 16. Hide Caption 81 of 177 Photos: Photos: From the campaign trail From the campaign trail – Republican presidential candidate Mitt Romney talks with aides aboard his campaign plane en route to Ronkonkoma, New York, on Tuesday. Hide Caption 82 of 177 Photos: Photos: From the campaign trail From the campaign trail – A worker cleans a sign for the Commission on Presidential Debates before the second presidential debate in Hempstead, New York, on Tuesday. Hide Caption 83 of 177 Photos: Photos: From the campaign trail From the campaign trail – Members of the production crew ready final preparations for the second presidential debate between President Barack Obama and Republican nominee Mitt Romney on Tuesday. Hide Caption 84 of 177 Photos: Photos: From the campaign trail From the campaign trail – First lady Michelle Obama greets supporters during a campaign rally at Ohio Wesleyan University in Delaware, Ohio, on Monday, October 15. Hide Caption 85 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters of President Barack Obama cheer during the campaign rally at Ohio Wesleyan on Monday. Hide Caption 86 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama jokes about a telephone with campaign volunteers Alexa Kissinger, left, and Suzanne Stern as he makes calls from a campaign office in Williamsburg, Virginia, on Sunday, October 14. Hide Caption 87 of 177 Photos: Photos: From the campaign trail From the campaign trail – Dolls depicting Obama and Mitt Romney are on display at a gift shop at Baltimore/Washington International Thurgood Marshall Airport in Maryland on Sunday. Hide Caption 88 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney holds up a baby as he works the rope line after delivering remarks at a rally in Lebanon, Ohio, on Saturday, October 13. Hide Caption 89 of 177 Photos: Photos: From the campaign trail From the campaign trail – A supporter holds an American flag in front of the Ohio logo on his shirt as he stands with a crowd at Shawnee State University to hear Romney speak on Saturday. Hide Caption 90 of 177 Photos: Photos: From the campaign trail From the campaign trail – Mario Orosa, left, and Ron Cathey, right, chat with Obama during dinner at Smith Commons restaurant in Washington on Friday, October 12. Obama had dinner with contest winners who contributed to his re-election campaign. Hide Caption 91 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney, right, and GOP vice-presidential candidate Paul Ryan greet supporters as they arrive at a rally in Lancaster, Ohio, on Friday. Hide Caption 92 of 177 Photos: Photos: From the campaign trail From the campaign trail – Students walk past a political mural near Centre College in downtown Danville, Kentucky, where Vice President Joe Biden and Republican vice-presidential nominee Rep. Paul Ryan faced off Thursday, October 11. Hide Caption 93 of 177 Photos: Photos: From the campaign trail From the campaign trail – Ryan greets his son Sam after the debate in Danville, Kentucky, on Thursday. Hide Caption 94 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney, left, speaks with the Rev. Billy Graham during a visit to the Graham cabin in Montreat, North Carolina, on Thursday. Hide Caption 95 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama greets supporters at a campaign rally at the University of Miami on Thursday. Hide Caption 96 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney and New Jersey Gov. Chris Christie talk with supporters at Buns Bakery and Restaurant in Delaware, Ohio, on Wednesday, October 10. Romney is campaigning in Ohio with less than a month to go before the general election. Hide Caption 97 of 177 Photos: Photos: From the campaign trail From the campaign trail – Christie, left, and Romney walk up to the stage at Ariel Corporation in Mount Vernon, Ohio, on Wednesday. Hide Caption 98 of 177 Photos: Photos: From the campaign trail From the campaign trail – Centre College students Ben Boone, left, a stand-in for U.S. Vice President Joe Biden, and Tommy Munoz, a stand-in for Republican Vice Presidential candidate Paul Ryan, wave during a rehearsal for the vice presidential debate in Danville, Kentucky, on Wednesday. Hide Caption 99 of 177 Photos: Photos: From the campaign trail From the campaign trail – Members of the media watch as President Barack Obama arrives aboard Marine One on the South Lawn of the White House on Tuesday, October 9, in Washington. The president was returning from a two-day campaign trip to California and Ohio. Hide Caption 100 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama addresses supporters during a campaign event at The Ohio State University on Tuesday. Hide Caption 101 of 177 Photos: Photos: From the campaign trail From the campaign trail – Two Obama supporters, one holding a Big Bird book and the other clutching a picture of the president, listen while he speaks at a rally at Ohio State on Tuesday. Hide Caption 102 of 177 Photos: Photos: From the campaign trail From the campaign trail – Republican presidential candidate Mitt Romney departs a Wendy's restaurant with his dinner order in Cuyahoga Falls, Ohio, on Tuesday. Hide Caption 103 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters cheer as Romney delivers remarks on the James Koch Farm in Van Meter, Iowa, on Tuesday. Hide Caption 104 of 177 Photos: Photos: From the campaign trail From the campaign trail – Allan Banojakedjian, left, and Jesus Romero fill out their voter registration forms at the Miami-Dade Elections Department on the final day of registration for the upcoming presidential election. Hide Caption 105 of 177 Photos: Photos: From the campaign trail From the campaign trail – Rain doesn't keep Romney from campaigning in Newport News, Virginia, on Monday, October 8. Hide Caption 106 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama holds a campaign event Monday at the Bill Graham Civic Auditorium in San Francisco. Hide Caption 107 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama takes the stage at a campaign concert at the Nokia Theatre in Los Angeles on Sunday, October 7. The president has been on a three-day trip to California and Ohio. Hide Caption 108 of 177 Photos: Photos: From the campaign trail From the campaign trail – Air Force One leaves a shadow as it passes over the Forum on approach to Los Angeles International Airport on Sunday. Hide Caption 109 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama leaves the White House on Sunday to board Air Force One. Hide Caption 110 of 177 Photos: Photos: From the campaign trail From the campaign trail – Republican presidential candidate Mitt Romney and his wife, Ann, greet workers at the Tin Fish restaurant following a rally Sunday in Port St. Lucie, Florida. Hide Caption 111 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney casts a shadow on a banner as he speaks during a campaign event in Apopka, Florida, on Saturday, October 6. Hide Caption 112 of 177 Photos: Photos: From the campaign trail From the campaign trail – A supporter holds a photograph of Romney in Apopka on Saturday. Hide Caption 113 of 177 Photos: Photos: From the campaign trail From the campaign trail – Jon Bon Jovi performs at an Obama for America event at the House of Blues in Las Vegas on Saturday. It was the last day people in Nevada could register to vote in the upcoming presidential election. Hide Caption 114 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney speaks during a campaign event in St. Petersburg, Florida, on Friday, October 5. Hide Caption 115 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney supporters listen during Friday's campaign event in St. Petersburg. Hide Caption 116 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama smiles as he speaks during a campaign rally in Fairfax, Virginia on Friday. Hide Caption 117 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama is assisted with putting on a raincoat onstage during a campaign rally at Cleveland State University on Friday. Hide Caption 118 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney speaks in Fishersville, Virginia, as Secret Service members keep guard on Thursday, October 4. A day after the first presidential debate in Denver, Romney headed to Virginia to continue campaigning. Hide Caption 119 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney supporters bow their heads in prayer during Thursday's event at the Augusta Expoland in Fishersville, Viriginia. Hide Caption 120 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama addresses the crowd at the University of Wisconsin in Madison on Thursday. Hide Caption 121 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney greets police officers before boarding his campaign plane in Denver on Thursday. Hide Caption 122 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama speaks at a campaign rally in Denver on Thursday. He accused his Republican challenger of dishonesty over tax policy and other issues brought up in Wednesday night's presidential debate. Hide Caption 123 of 177 Photos: Photos: From the campaign trail From the campaign trail – Audience members cheer as Obama makes his way onto the stage at Sloan's Lake Park in Denver on Thursday. Hide Caption 124 of 177 Photos: Photos: From the campaign trail From the campaign trail – Reporters watch the final minutes of the debate between Romney and Obama in Denver on Wednesday, October 3. The first of four debates for the 2012 election -- three presidential and one vice-presidential -- was moderated by Jim Lehrer of PBS. Hide Caption 125 of 177 Photos: Photos: From the campaign trail From the campaign trail – A member of the U.S. Secret Service keeps watch from the top of a building as Obama takes part in a debate walk-through at the University of Denver on Wednesday. Hide Caption 126 of 177 Photos: Photos: From the campaign trail From the campaign trail – A seat is assigned to first lady Michelle Obama prior to Wednesday's debate. Hide Caption 127 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama stands at the podium as he speaks during the debate on Wednesday. Hide Caption 128 of 177 Photos: Photos: From the campaign trail From the campaign trail – Michelle and Barack Obama, left, join Mitt Romney and his family at the conclusion of the first presidential debate. Hide Caption 129 of 177 Photos: Photos: From the campaign trail From the campaign trail – University of Denver student Sam Garry sits at the moderator's desk before a presidential debate dress rehearsal at the University of Denver on Tuesday, October 2. Hide Caption 130 of 177 Photos: Photos: From the campaign trail From the campaign trail – Volunteers sit in for on-air television reporters on Tuesday in preparation for the first presidential debate in the Ritchie Center at the University of Denver. Hide Caption 131 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney greets a father and his daughter after having lunch Tuesday at a restaurant in Denver. Hide Caption 132 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama stares at the Hoover Dam in Nevada during a visit Tuesday. Hide Caption 133 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney boards his campaign plane in Bedford, Massachusetts, on Monday, October 1. The Republican candidate was heading to Denver for the first presidential debate on Wednesday. Hide Caption 134 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama hugs Chasstiry Vazquez after she indroduced him at a campaign event at Desert Pines High School in Las Vegas on Sunday, September 30. Hide Caption 135 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama supporters cheer during Sunday's event in Las Vegas. Hide Caption 136 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney leaves his campaign headquarters in Boston on Sunday. Hide Caption 137 of 177 Photos: Photos: From the campaign trail From the campaign trail – A boy reaches out to shake hands with Obama on Sunday in Las Vegas. The president was in Nevada ahead of Wednesday's presidential debate in Denver. Hide Caption 138 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney arrives at the Church of Jesus Christ of Latter-day Saints in Belmont to attend Sunday services. Hide Caption 139 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama talks on the phone with Prime Minister Benjamin Netanyahu of Israel in the Oval Office on Friday, September 28. Hide Caption 140 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney speaks during a rally at Valley Forge Military Academy and College in Pennsylvania on Friday. Hide Caption 141 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney talks to journalists aboard his campaign plane about his phone call with Netanyahu on Friday. Hide Caption 142 of 177 Photos: Photos: From the campaign trail From the campaign trail – Cadets listen to Romney speak at a campaign rally Friday at the Valley Forge Military Academy and College in Wayne, Pennsylvania. Hide Caption 143 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney addresses Friday's rally at the Valley Forge Military Academy and College. Hide Caption 144 of 177 Photos: Photos: From the campaign trail From the campaign trail – Vice President Joe Biden hugs U.S. Rep. Debbie Wasserman Schultz, chairwoman of the Democratic National Committee, as he arrives for a campaign event Friday in Boca Raton, Florida. Hide Caption 145 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney speaks at a Veterans for Romney campaign event in Springfield, Virginia, on Thursday, September 27. Hide Caption 146 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama supporters cheer at a campaign rally Thursday in Virginia Beach, Virginia. Hide Caption 147 of 177 Photos: Photos: From the campaign trail From the campaign trail – Veterans at the American Legion Post 176 pray before Romney speaks Thursday in Springfield. Hide Caption 148 of 177 Photos: Photos: From the campaign trail From the campaign trail – People listen to Obama speak at the Farm Bureau Live arena in Virginia Beach on Thursday. Hide Caption 149 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama delivers remarks Thursday in Virginia Beach. Hide Caption 150 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters cheer as Romney speaks at SeaGate Convention Centre in Toledo, Ohio, on Wednesday, September 26. Hide Caption 151 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney speaks during a roundtable discussion on manufacturing at American Spring Wire in Bedford Heights, Ohio, on Wednesday. Hide Caption 152 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters wait to see Obama on Wednesday at Toledo Express Airport in Bowling Green, Ohio. Air For One aborted an initial landing attempt in Ohio due to weather conditions. Hide Caption 153 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama addresses supporters at Bowling Green State University on Wednesday. Hide Caption 154 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney delivers remarks during a campaign rally Wednesday at Westerville South High School in Westerville, Ohio. Hide Caption 155 of 177 Photos: Photos: From the campaign trail From the campaign trail – Former President Bill Clinton introduces Obama during the Clinton Global Initiative annual meeting in New York on Tuesday, September 25. Hide Caption 156 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters cheer during a Republican campaign rally Tuesday with Romney and his running mate, Paul Ryan, at Dayton International Airport in Vandalia, Ohio. Hide Caption 157 of 177 Photos: Photos: From the campaign trail From the campaign trail – Ryan speaks Tuesday in Vandalia as Sen. Rand Paul, from left, Sen. Rob Portman and Romney listen. Hide Caption 158 of 177 Photos: Photos: From the campaign trail From the campaign trail – Former Florida Gov. Jeb Bush hugs a waitress as they wait for Ryan's arrival during a campaign stop at a restaurant in Miami's Little Havana neighborhood on Saturday, September 22. Hide Caption 159 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters cheer as they listen to Romney speak during a Juntos Con Romney Rally at the Darwin Fuchs Pavilion on Wednesday, September 19, in Miami. Hide Caption 160 of 177 Photos: Photos: From the campaign trail From the campaign trail – Romney shakes hands with supporters during the Juntos Con Romney Rally in Miami on Wednesday. Hide Caption 161 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama and David Letterman speak during a break in the taping of the "Late Show with David Letterman" on Tuesday, September 18, at the Ed Sullivan Theater in New York. Hide Caption 162 of 177 Photos: Photos: From the campaign trail From the campaign trail – A crew member opens the door to Air Force One after the jet arrived at John F. Kennedy Airport in New York on Tuesday. Hide Caption 163 of 177 Photos: Photos: From the campaign trail From the campaign trail – From left to right: Romney, his wife Ann, and son Tagg watch one of Tagg's sons play soccer in Belmont, Massachusetts, on Saturday, September 15. Hide Caption 164 of 177 Photos: Photos: From the campaign trail From the campaign trail – Ryan arrives onstage to address the Family Research Council Action Values Voter Summit on Friday, September 14. Hide Caption 165 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters wait for Romney to speak at a campaign rally at Lake Erie College in Painesville, Ohio, on Friday, September 14. Hide Caption 166 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama arrives at Andrews Air Force Base in Maryland on Thursday, September 13. Obama returned to Washington after a two-day campaign trip with events in Nevada and Colorado. Hide Caption 167 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters cheer as Romney speaks at a campaign rally in Fairfax, Virginia, on Thursday. Hide Caption 168 of 177 Photos: Photos: From the campaign trail From the campaign trail – An Obama supporter attends a rally in Las Vegas on Wednesday, September 12. Obama focused on economic policies during his two days of campaigning in Nevada and Colorado. Hide Caption 169 of 177 Photos: Photos: From the campaign trail From the campaign trail – Former President Bill Clinton speaks in support of Obama during a campaign stop in Miami on Tuesday, September 11. Hide Caption 170 of 177 Photos: Photos: From the campaign trail From the campaign trail – Obama is lifted up by Scott Van Duzer, owner of Big Apple Pizza and Pasta Italian Restaurant, during a visit to the restaurant in Fort Pierce, Florida, on Sunday, September 9. Obama was on a two-day bus tour across the state. Hide Caption 171 of 177 Photos: Photos: From the campaign trail From the campaign trail – President Obama greets supporters during a campaign stop at the Palm Beach County Convention Center in West Palm Beach, Florida, on Sunday. Hide Caption 172 of 177 Photos: Photos: From the campaign trail From the campaign trail – Mitt Romney walks through the garage area during a rain delay before the start of the NASCAR Sprint Cup Series Federated Auto Parts 400 at Richmond International Raceway on Saturday, September 8, in Richmond, Virginia. Hide Caption 173 of 177 Photos: Photos: From the campaign trail From the campaign trail – Ann Romney, wife of Republican presidential candidate Mitt Romney, waves to the crowd before speaking at a rally in Leesburg, Virginia, on Friday, September 7. Hide Caption 174 of 177 Photos: Photos: From the campaign trail From the campaign trail – Supporters try to stay dry in between rain showers while waiting for President Obama to speak at the University of Iowa on Friday. It was Obama's first day of campaigning after accepting the presidential nomination at the Democratic National Convention in Charlotte, North Carolina. Hide Caption 175 of 177 Photos: Photos: From the campaign trail From the campaign trail – A girl listens to President Obama speak at the University of Iowa on Friday. Hide Caption 176 of 177 ||||| Votes piled up and states were declared red or blue tonight, but as it had long been predicted, the race for the White House has come down to Ohio, encouraging President Obama's supporters and narrowing Mitt Romney's chance of victory. The president won swing states like Pennsylvania, Wisconsin and New Hampshire, states where Romney and Obama spent considerable time and money campaigning. Still outstanding are the large battleground states of Florida and Virginia. With much of the vote counted in both states Romney and Obama were separated by only one point in each state. And Obama clung to a slim lead in Ohio with more than 60 percent of the vote counted. Romney would have to win all three states to capture the White House. Obama must win one of those states to get a second term. The president began a hard-hitting campaign in Ohio long before Romney even became the nominee. His early efforts there and in Wisconsin created what he hoped would be a fire wall against Republican chances, retaining many of the independent white men who turned to Romney in other parts of the country. For the latest election results, click HERE. As expected Obama won his home state of Illinois and also won Romney's home state of Massachusetts. Early on Romney picked up much of the deep South and Oklahoma, while Obama picked up the New England states. Obama also won New Jersey, the state most affected by last week's superstorm Sandy, in which some affected voters cast paper ballots or voted via email. Obama also picked up 20 electoral votes in Pennsylvania, a state Democrats had long believed they would win, but for which Romney made a last ditch attempt to secure, visiting regularly in the final weeks of the campaign. For the latest election results, click HERE. The candidates were vying to reach the goal of 270 electoral votes needed to win the presidency. Bracing for a long night, Obama today warned that if the race is close, a clear winner in the presidential election may not be determined until Wednesday morning. "One way or another we're going to have a winner," he told ABC News' Washington, D.C., affiliate WJLA. "If it's close, it may spill into the morning, but I'm pretty confident that we'll end up having a president-elect come Wednesday." In the final hours of the campaign today, both men did what they felt was necessary to ensure victory. For the president that meant a traditional game of basketball, a game he has played before every major election that he has won. The president, who voted early last month, remained in his home state of Illinois today joining old friends and confidants on a basketball court in Chicago following a morning on television satellite interviews to voters in swing states. Among those on the court were Education Secretary Arne Duncan, Obama's former body man Reggie Love and former Chicago Bulls star Scottie Pippen. Obama's team won by about 20 points. Obama skipped playing the pre-election game before just one race, the 2008 New Hampshire primary which he subsequently lost. Since then, the game has become a campaign superstition. The Romney campaign kept stumping until the last minute, holding rallies in Ohio and Pennsylvania. Tune in to ABCNews.com for livestreaming coverage of Election 2012. Our Election Day show kicks off at noon, and the Election Night event begins at 7 p.m. Upon arriving in Pittsburgh this afternoon, Romney got off his plane to find an unexpected crowd of people packed into a garage across from the tarmac to greet him. Romney, visibly moved by the size of the crowd, walked to the fence that separated him from his supporters and stood for several moments with his hand to his heart as the crowd cheered. "That's when you know you're going to win," Romney told reporters. Keeping up that enthusiasm, Romney told reporters that he so far only drafted a victory speech, not a concession. He said if he won, he would likely buy a new puppy for the White House. "If, assuming I win, one of the benefits would be to get another Weimereiner," he said of the potential breed. Both campaigns toned down the rhetoric now that voting has begun. In Green Tree, Pa., Romney thanked volunteers and told them that in getting out the vote today they "don't need to be disparaging of the other guy. The president has run a strong campaign, I believe he is a good man and wish him well, and his family well... but it is time for a new direction. It is a time for a better tomorrow." Obama visited his campaign workers and after thanking them said, "Congratulations to Gov. Romney on a spirited campaign....I know his supporters are just as engaged." The costliest election in United States history is also one of the closest as voters formed long lines to finally pick their president after a long and divisive campaign. After spending nearly $1 billion apiece, Romney and the president are today in much the same place they were months ago at the campaign's outset. The president leads his Republican challenger by so small a margin it is statistically insignificant in most places. The tightness of the race was expressed at midnight, when the first town to open and close its polls, the tiny hamlet of Dixville Notch, N.H., evenly split its vote five to five. Mitt and Ann Romney cast their ballots this morning about 9 a.m. in Bedford, Mass., where the candidate remarked that he's feeling "very good" about his chances today. Asked who he voted for, Romney responded, "I think you know." Romney traveled today to Ohio and Pennsylvania for last-minute campaign stops. Ohio has emerged as a key to a Romney victory. Asked about his chances in Ohio, Romney said,"I feel great about Ohio." The Romneys, accompanied by their son Tagg, were greeted by chants of "Romney! Romney!" and a sign that read "Mitt and Ann enjoy your new White House." Romney also scheduled interviews with radio stations in Ohio and Virginia. The fate of the election will rest on the outcomes in a few hard-fought swing states ? Florida, Virginia, New Hampshire, Wisconsin, Pennsylvania and most crucially Ohio. Victory or defeat may very well come down to Ohio, a battleground whose 18 electoral votes may be as critical this year as Florida was in 2000. Both candidates know it, and have spent more time there than anywhere else. Ohio, or possibly Wisconsin, where Romney has trailed for months, create "a very narrow path to electoral college victory," said Matthew Dowd and Republican strategist and ABC News consultant. He said the first key state where polls will close is Virginia and a defeat or victory there for Romney could be crucial to the rest of his night. Obama Plays Basketball as Romney Works Ohio Crowd "I think Virginia is going to tell us a lot. It's going to tell us if this night ends early for Mitt Romney or if we're in for a long night," Dowd said. Which way will the electoral college electors go? Play with our electoral Game Changers map HERE. There are also a few critical demographic groups to watch, including Latinos, young people and women. Both campaigns have battled for the women's vote, but Donna Brazille, a Democratic strategist and ABC News consultant, said Obama has an advantage with women. "One thing to remember is that in the last six elections, Democrats are six and zero. We've won the women's vote in every election. That's what makes Democrats competitive," said Brazille. The final weeks of the campaign proved more exciting than any over the course of the past year and a half. After leading for months, Obama found himself trailing Romney for the first time following a lackluster performance in the first debate in Denver, Co., last month. But Romney's momentum appeared to have been blunted last week by superstorm Sandy, whose devastation knocked election coverage off the front page and seemed to tilt the race back in Obama's favor. ABCNews' Emily Friedman contributed to this report

– Mitt Romney and President Obama are taking two very different approaches on how they'll spend their last few hours as candidates, reports CNN. Obama will follow presidential candidate tradition and hunker down in his hometown of Chicago to await an outcome, as well as his personal tradition of playing a little basketball. He'll also do a couple of satellite interviews. The Republican nominee, meanwhile, is breaking with tradition in a sprint to the end, with last-minute rallies planned in Cleveland and Pittsburgh, and radio interviews in Virginia and Ohio, reports ABC News. Romney voted this morning in Belmont, Mass., with wife Ann and son Tagg.

over the past two decades , considerable biomedical successes have been achieved in the science of prevention of mother - to - child transmission of hiv ( pmtct ) in sub - saharan africa . effective interventions that can significantly reduce in utero , intra - partum and postnatal hiv transmission are now available [ 13 ] . despite the increasing availability of antiretroviral drugs for pmtct and the international mobilization for the implementation of these services , the escalation of pmtct interventions in many countries in africa has proved elusive and paediatric hiv remains an uncontrolled epidemic . in 2009 , only 35% of the 125 million pregnant women in low - and middle - income countries received an hiv test . in 2010 , united nations agencies prioritized the reduction of mother - to - child transmission of hiv , and called for its effective elimination by 2015 . in order to reach this ambitious target , strategies for increasing hiv testing among pregnant women , which is the entry point to subsequent pmtct interventions , are urgently needed . one such strategy consists of hiv screening in labour wards as recommended by the world health organization ( who ) , and is viewed as the last opportunity to identify pregnant women living with hiv and to initiate an antiretroviral prophylaxis aimed at pmtct . the experience of hiv screening in labour wards is rarely reported and its acceptance varies between 67 and 98% [ 812 ] . in west africa , the region of the world where hiv testing coverage is the lowest ( 21% ) , there has been no report to date on the use of this strategy . the objectives of the study are to describe missed opportunities for effective pmtct interventions and to assess the feasibility and acceptability of hiv screening in a labour ward in a west - african setting . a cross - sectional survey was conducted between may and august 2010 in the labour ward of the gynaecology obstetrics unit of the tokoin teaching hospital in lom , togo . it was not logistically possible to include all pregnant women admitted for labour in this unit during the study period . all pregnant women admitted for delivery on randomly selected days and periods of time were systematically included in the study ( monday from 8 am to 2 pm , wednesday from 2 pm to 8 pm , saturday from 8 pm to sunday 8 am ) . standardized forms were used to collect socio - demographic characteristics ( age , level of education , marital status , and number of previous pregnancies ) and pregnancy history ( number of antenatal visits , knowledge of hiv status , pmtct prophylaxis received ) , as well as mode of delivery , birth outcome , and anthropometric data of the newborn . this information was collected from maternal health records , the delivery registry and direct interviews with the women , which were conducted before or after delivery according to the time of delivery . on admission to the labour room the recommended national algorithm used for hiv diagnosis was : determine hiv-1/2 ( abbott diagnostics ) and first response hiv card test 1 - 2.0 ( pmc medical ) . a woman was considered as living with hiv when both tests were positive . in case of no concordance of the two tests , the blood sample was sent to the national reference laboratory for an elisa test . missed opportunity for hiv testing , defined as the proportion of women who did not know their hiv status before delivery . missed opportunity for an effective pmtct intervention defined as the proportion of women living with hiv who did not initiate any pmtct intervention before delivery . acceptance of hiv testing in a labour room . missed opportunity for hiv testing , defined as the proportion of women who did not know their hiv status before delivery . missed opportunity for an effective pmtct intervention defined as the proportion of women living with hiv who did not initiate any pmtct intervention before delivery . the distribution of continuous variables were compared using the wilcoxon rank - sum test , and comparisons between categorical variables were performed using the chi - square test or fisher 's exact test when appropriate . we estimated the prevalence of hiv infection with its 95% confidence interval ( 95% ci ) . all statistical analyses were performed with stata , version 9.0 ( statacorp , college station , texas , usa ) . the study 's protocol was approved by the national ethic committee of the ministry of health of togo in may 2010 . between may and august 2010 , 1530 pregnant women were admitted for delivery at the tokoin teaching hospital , and among them 508 ( 33.2% ) were enrolled in this study . there was no significant statistical difference between the women included and those not included in the study ( table 1 ) . median age was 27 years [ inter - quartile range ( iqr ) , 23 to 31 years ] , 87.8% were married or co - habiting with a partner . overall , 502 women ( 98.8% ) had attended at least one antenatal consultation before delivery : 106 ( 21.1% ) at the tokoin teaching hospital and 396 ( 78.9% ) at health facilities in the periphery of lom . may to august 2010 , lom , togo iqr : interquartile range . only for live birth ( n=1420 ) . a total of 502 ( 98.8% ) attended at least one antenatal visit and among them 359 ( 71.5% ) had information on their hiv status reported in their individual maternal health chart . figure 1 shows the proportion of women diagnosed for hiv infection during antenatal visits and in the labour ward . acceptance of hiv testing in the labour ward was 91.9% ( n=467 ) ; 90.8% ( 326/359 ) among those tested previously according to their antenatal record , and 94.6% ( 141/149 ) among those tested the first time in labour ward ( p=0.15 ) . acceptance of hiv testing in the labour ward was 91.0% ( 323/355 ) among women who declared knowing their hiv status and 94.1% ( 144/153 ) among those who did not ( p=0.234 ) . in univariate and multivariate analysis , none of studied variables were associated with the acceptance of hiv testing in the labour ward . overall , 467 women ( 91.9% ) accepted hiv testing in the labour ward and among them , 41 were living with hiv ( 8.8% , 95% ci : 6.4 to 11.2% ) . of these 41 women living with hiv , 27 ( 65.9% ) knew their hiv positive status already reported in the antenatal record and 14 ( 34.1% ) were newly diagnosed during labour ward screening . prevalence of hiv infection was 8.3% ( 27/326 ) among women for whom the hiv testing result was reported in their antenatal record , and 9.9% ( 14/141 ) among those who were tested for the first time ( p=0.56 ) . concordance of hiv testing between antenatal consultation and the labour ward is reported in table 2 . in addition to the 27 cases of hiv infection identified during pregnancy and confirmed during labour , 14 new cases were identified by testing in the labour ward . concordance of hiv testing between antenatal consultation and delivery ward , n ( % ) . may to august 2010 , lom , togo based on hiv testing information reported in the maternal health chart . overall , 41.5% ( n=17 ) of the 41 women living with hiv had not initiated any pmtct intervention antenatally . in multivariate analysis , the missed opportunities for antenatal pmtct interventions were associated with gravidity 2 ( adjusted odds ratio [ aor ] , 2.07 ; 95% ci : 1.29 to 3.33 ) , not being married ( aor , 1.82 ; 95% ci : 1.00 to 3.23 ) , and having made antenatal visits at health facilities in the periphery of lom ( aor , 3.57 ; 95% ci : 1.96 to 6.67 ) . among the 27 pregnant women who knew their status hiv antenatally , two had initiated antiretroviral therapy for their own health , 22 received zidovudine and a single - dose of nevirapine and three did not initiate any antiretroviral intervention before their admission to the labour ward . among the 14 women living with hiv diagnosed in labour room , all of them received an antiretroviral prophylaxis during labour . in this study carried out in the obstetrical ward at the tokoin teaching hospital , which is the biggest referral health centre for delivery in togo , we found that 92% of pregnant women agreed to be tested for hiv in the labour room . hiv prevalence in the labour room in this referral centre was 8.8% and the 14 newly diagnosed women ( 34% of the total ) initiated antiretroviral prophylaxis . in 2004 , hiv testing in labour rooms was recommended by the us centers diseases for control and prevention and in 2010 , who recommended that in the countries where hiv epidemic is considered generalized ( prevalence > 1% in pregnant women ) there should be hiv retesting in all hiv - negative or hiv status unknown women at the time of delivery . the rationale to focus on hiv testing in the labour ward in a country such as togo , which has an hiv testing coverage in pregnant women estimated at 18% , is the fact that this strategy is the last opportunity to introduce an antiretroviral prophylaxis for pmtct in order to reduce the many missed opportunities for intervention . the acceptance of hiv testing in the labour room was relatively higher than the percentage reported in a study in zambia where 67% of 217 women accepted to undergo hiv testing . elsewhere , the acceptance rate was 98% in a university hospital located in rural india and 85% in a us trial . overall , these studies , including ours , show that hiv testing is highly feasible and acceptable even in busy delivery wards . the key factor that may influence the acceptance of hiv testing in labour wards is the type of hiv test used . oral fluid - based rapid hiv tests seem more convenient and do not elicit patients fear of blood draw ( as reported in india ) . indeed , in the us study , low acceptance of hiv testing during the night shift was reported because of limited staff availability . in our study , 29% of pregnant women , despite having had antenatal care visits did not know their hiv status before entering the labour ward . therefore , as already supported by international guidelines , it is of the utmost importance to place standing orders in all labour rooms in sub - sahara africa to inform every woman that she will be tested unless she states otherwise . during this study firstly , the duration of pre - test counselling was short , on average 3 minutes , which was close to the duration of the individual pre - test counselling in african settings . secondly , the understanding of the message about hiv testing during labour was a concern , but we were unable to document it in this study . finally , the team discussed case by case whether they would postpone hiv testing until after delivery in order to ensure that patients were not coerced into hiv testing during labour . the prevalence of hiv among pregnant women admitted for delivery was estimated at 8.8% , more than twice the hiv prevalence reported in pregnant women in togo in 2009 ( 3.9% ) and very close to the hiv prevalence reported in lom , the capital of togo ( 6.3% ) the site selected for this study which is the reference centre located at the teaching hospital could explain the higher prevalence figure observed . among the 41 women identified as living with hiv in the labour ward , 17 ( 34% ) did not know their hiv status before being admitted to the labour ward and the testing procedure allowed the immediate initiation of arv prophylaxis to all of them . in rural india in 2007 , 11 out of 15 women living with hiv ( 73% ) learnt of their hiv status in the delivery room . in the absence of arv intervention in breastfeeding populations between 30 and 40% of pregnant women living with hiv transmit hiv to their infant . according to the study reported in malawi , which included hiv - exposed infants whose mothers did not receive antiretroviral prophylaxis , the rate of hiv transmission was 15.5% at eight weeks of life in children who received zidovudine + single - dose nevirapine , a 50% reduction compared to no intervention . first , it was conducted in a single labour ward and specifically in a referral centre . therefore , our sample is not representative of all pregnant women in togo , limiting the generalization of the findings to the rest of the country . second , the choice to propose an antiretroviral prophylaxis to newly diagnosed pregnant women living with hiv was part of the project intervention and an anonymous cord blood - surveillance strategy was not used to measure pmtct coverage as done previously in the pearl survey . despite these limitations , this is to our knowledge the first study conducted in the largest delivery ward in togo and the first one evaluating the feasibility and acceptance of hiv testing during labour in west africa . since only 1.2% women refused hiv testing , the hiv prevalence estimate is very close to the true prevalence in pregnant women attending this hospital . in conclusion , hiv testing in the labour room is highly feasible and acceptable and can significantly reduce missed opportunities for effective pmtct interventions . the implementation of this strategy should be put in place in all maternity hospitals and the dedicated staff should be trained for this procedure as well . however , involuntary testing is a potential challenge to implementing provider initiating testing strategy in the labour ward . this salvage intervention for pmtct will increase the pmtct coverage which remains low in sub - saharan africa and will help to will reinforce the linkage for early infant diagnosis . in the context of virtual elimination of mtct by 2015 , all the authors contributed to the writing of the manuscript and all the authors agree with the manuscript 's results and conclusions . pmtct , prevention of mother - to - child transmission of hiv ; mtct , mother - to - child transmission of hiv . this study was performed thanks to funding from the institut de sant publique epidmiologie dveloppement ( isped ) of the bordeaux segalen university in bordeaux ( france ) and the french national aids research agency ( anrs ) through the pac - ci research program in abidjan ( cote d'ivoire ) .

backgroundhiv screening in a labour ward is the last opportunity to initiate an antiretroviral prophylaxis among pregnant women living with hiv to prevent mother - to - child hiv transmission . little is known about the feasibility and acceptability of hiv screening during labour in west africa.findingsa cross - sectional survey was conducted in the labour ward at the tokoin teaching hospital in lom ( togo ) between may and august 2010 . pregnant women admitted for labour were randomly selected to enter the study and were interviewed on the knowledge of their hiv status . clinical and biological data were collected from the individual maternal health chart . hiv testing or re - testing was systematically proposed to all pregnant women . among 1530 pregnant women admitted for labour , 508 ( 32.2% ) were included in the study . information on hiv screening was available in the charts of 359 women ( 71% ) . overall , 467 women accepted hiv testing in the labour ward ( 92% ) . the hiv prevalence was 8.8% ( 95% confidence interval : 6.4 to 11.7% ) . among the 41 women diagnosed as living with hiv during labour , 34% had not been tested for hiv during pregnancy and were missed opportunities . antiretroviral prophylaxis had been initiated antenatally for 24 women living with hiv and 17 in the labour room.conclusionsthis study is the first to show in west africa that hiv testing in a labour room is feasible and well accepted by pregnant women . hiv screening in labour rooms needs to be routinely implemented to reduce missed opportunities for intervention aimed at hiv care and prevention , especially pmtct .

if @xmath0 is a complex square matrix of size @xmath9 , the _ numerical range _ of @xmath4 is the compact subset of the complex plane defined by @xmath10 where @xmath11 is the usual scalar product in @xmath12 and @xmath13 . it is quite obvious that @xmath14 , where @xmath15 ( the _ spectrum _ of @xmath4 ) is the collection of all eigenvalues of @xmath4 , and that @xmath16 for any unitary matrix @xmath17 . moreover , a celebrated result due to toeplitz @xcite and hausdorff @xcite asserts that @xmath18 is always a convex subset of the complex plane . in particular , @xmath18 contains the convex hull of @xmath15 , and it is easy to verify that @xmath19 if the matrix @xmath4 is normal , namely @xmath20 . the interested reader is referred to chapter 1 of @xcite for a detailed discussion of the various properties of the numerical range , including complete proofs . let @xmath21 be the unit sphere in @xmath12 , considered as a real manifold of dimension @xmath22 . by definition , the numerical range @xmath18 is the image of the _ numerical map _ @xmath23 defined by @xmath24 the algebraic and geometric properties of the map @xmath25 have been extensively studied , see @xcite . in particular , the set of all critical values of @xmath25 , which we denote by @xmath26 , has received a lot of attention , because this is an interesting object which contains a lot of information on the matrix @xmath4 . for instance , it is known that @xmath27 and @xmath28 . in addition , there exists a real algebraic curve @xmath29 with the property that @xmath30 , where @xmath31 denotes the set of all line segments joining pairs of points of @xmath32 at which @xmath32 has the same tangent line @xcite . under generic assumptions on @xmath4 , the bitangent set @xmath31 is empty , and the critical set @xmath33 is therefore the union of a finite number of closed curves , one of which is the boundary of the numerical range @xmath18 . this distinguished curve is smooth , and encloses all the other ones in its interior . we refer to section [ s : geom ] below for more details on the geometry of the singular set , and to section [ s : examples ] for a few concrete examples . our purpose in this paper is to introduce another mathematical quantity which is naturally related to the numerical map @xmath25 . given @xmath0 , the _ numerical measure _ of @xmath4 is the probability measure @xmath1 on @xmath34 defined by the formula @xmath35 for all continuous functions @xmath36 . here @xmath37 denotes the euclidian measure on the unit sphere @xmath38 , normalized as a probability measure . in words , the numerical measure is thus the image under the numerical map of the normalized euclidean measure on the unit sphere . equivalently , if @xmath39 is a random variable that is uniformly distributed on @xmath38 , the numerical measure @xmath1 is just the distribution of the random variable @xmath40 . this probabilistic intepretation will be useful later , especially in section [ s : stat ] . our first goal is to establish a few general properties of the numerical measure @xmath1 . it is clear by construction that @xmath1 is invariant under unitary conjugations of @xmath4 , namely @xmath41 for all @xmath42 . this is precisely the reason why we used the euclidean measure on @xmath38 in the definition . it is also easy to verify that the support of @xmath1 is exactly the numerical range @xmath18 , see section [ s : general ] below . less obvious , perhaps , is the fact that @xmath1 is absolutely continuous with respect to the lebesgue measure @xmath43 on @xmath18 , so that we can define the _ numerical density _ @xmath5 as the radon - nikodym derivative of @xmath1 with respect to @xmath43 ( in the particular situation where @xmath18 reduces to a line segment @xmath44 , we understand @xmath43 as the one - dimensional lebesgue measure on @xmath44 , see section [ s : general ] . ) we also prove that the numerical density @xmath5 is strictly positive in the interior of @xmath4 , a property that can be interpreted as a strong version of hausdorff s theorem @xcite . finally , we shall see that the singular support of @xmath1 is contained in the critical set @xmath33 , which means that the numerical density @xmath5 is smooth outside @xmath33 . in fact , we conjecture that @xmath45 for all @xmath46 , but this has not been proved yet . after these general properties have been established , our next goal is to give a more precise description of the numerical density @xmath5 . for this purpose , it is convenient to distinguish between various cases : * 1 . * ( _ the scalar case _ ) if @xmath18 is reduced to a single point @xmath47 , then @xmath48 ( where @xmath49 denotes the identity matrix ) and @xmath50 . in this trivial situation , there is of course no need to introduce a numerical density . ( _ the hermitian case _ ) assume that @xmath51 and that @xmath52 is a line segment . then we can find @xmath53 , @xmath54 $ ] , and a hermitian matrix @xmath55 such that @xmath56 . if @xmath57 are the eigenvalues of @xmath55 , we shall see in section [ s : normal ] that the numerical measure @xmath58 is absolutely continuous with respect to lebesgue s measure on @xmath59 , and that the corresponding density @xmath60 is exactly the normalized _ @xmath6-spline _ of degree @xmath61 with knots @xmath62 @xcite . in particular , @xmath60 is polynomial of degree @xmath61 on each interval @xmath63 $ ] , vanishes identically outside @xmath64 $ ] , and is continuous at each point @xmath65 together with its derivatives up to order @xmath66 , where @xmath67 is the multiplicity of @xmath65 as an eigenvalue of @xmath55 ( if @xmath68 , then @xmath60 is discontinuous at @xmath65 . ) this gives an explicit representation of the numerical measure @xmath58 , and the measure @xmath1 is the image of @xmath58 under the affine isometry @xmath69 . ( _ the normal case _ ) suppose now that @xmath70 and that @xmath0 is a normal matrix whose spectrum @xmath15 is not contained in a line segment . then @xmath71 is a convex polygon with nonempty interior , and it turns out that the numerical density @xmath5 is the _ bivariate b - spline _ of degree @xmath72 whose knots are the eigenvalues of @xmath4 . here we refer to the work of w. dahmen @xcite for the definition and the main properties of multivariate @xmath6-splines . in this particular case , the critical set @xmath33 is thus the collection of all line segments joining pairs of eigenvalues of @xmath4 , and the density @xmath5 is polynomial of degree @xmath72 in each connected component of @xmath73 . in the generic situation where no straight line contains more than two eigenvalues of @xmath4 , one can show that @xmath5 is continuous together with its derivatives up to order @xmath74 ( and is discontinuous on @xmath75 if @xmath76 . ) ( _ the nonnormal case _ ) finally , we consider the most interesting situation where the matrix @xmath77 is not normal . in that case , there is no explicit formula for the numerical density , but the problem can be reduced in some sense to the hermitian case by the following simple observation . for any @xmath78 , let @xmath79 be the hermitian matrix defined by @xmath80 where @xmath81 and @xmath82 . then @xmath83 for all @xmath84 . now , if the random variable @xmath39 is uniformly distributed on @xmath38 , the distribution of @xmath85 is by definition the numerical measure @xmath86 , whereas the distribution of @xmath87 is easily identified as the two - dimensional _ radon transform _ of the numerical measure @xmath1 , evaluated at @xmath88 $ ] . we thus have @xmath89 where @xmath90 denotes the two - dimensional radon transformation . since the numerical density of @xmath79 is known to be the @xmath6-spline based on the eigenvalues @xmath91 of @xmath79 , we can reconstruct the numerical measure @xmath1 by inverting the radon transformation in , using the the well - known _ backprojection _ method which plays an important role in tomography @xcite . this provides a useful representation formula for the numerical density , as well as an efficient algorithm for numerical calculations , see section [ s : radon ] for more details . it is worth mentioning here that the critical set @xmath33 can be conveniently characterized using the family of hermitian matrices @xmath79 associated with @xmath4 . indeed , if we define the eigenvalues @xmath92 in such a way that they depend analytically on @xmath93 , one can shown that the algebraic curve @xmath32 which generates @xmath33 is given by @xmath94\bigr\}~,\ ] ] see @xcite and section [ s : geom ] below . in the generic case where @xmath95 for all @xmath96 $ ] , the bitangent set @xmath31 is empty and @xmath97 . as was already mentioned , the numerical density @xmath5 is smooth ( in fact , real - analytic ) on each connected component of @xmath98 . the regularity across @xmath33 is more difficult to study , but we shall show in section [ ss : regular ] that @xmath5 is everywhere of class @xmath99 if @xmath70 and @xmath0 satisfies some generic hypotheses , which exclude in particular the case of normal matrices . in addition , for an arbitrary matrix of size @xmath8 , we shall prove that all derivatives of @xmath5 of order @xmath61 vanish identically in some distinguished regions , which have the following geometric characterization . for any @xmath100 , let @xmath101 be the number of straight lines containing @xmath102 which are tangent to the curve @xmath32 , see below for a precise definition where possible multiplicities are taken into account . it is easy to verify that @xmath101 is constant in each connected component of @xmath73 , and that @xmath103 @xcite . the distinguished regions where @xmath5 is polynomial of degree @xmath72 ( if @xmath70 ) or @xmath104 ( if @xmath105 ) are exactly those connected components of @xmath73 on which @xmath101 _ takes its maximal value _ this remarkable property of the numerical density , which is one of our main results , will be established in section [ ss : poly ] . the geometric condition @xmath106 is always satisfied in the complement of the numerical range , where @xmath5 vanishes identically , but for many matrices of size @xmath70 is it also met in some regions inside @xmath18 . for instance , in the three - dimensional example represented in fig.[fig1 ] , it is easy to verify that @xmath107 if @xmath102 is outside @xmath18 or inside the cuspidal triangle , and @xmath108 in the intermediate region where the numerical density is not constant . [ cols="^,^ " , ] * example 4 . * as a final example , we consider the case of a normal matrix @xmath109 whose eigenvalues @xmath110 are not colinear . then the numerical range is the triangle with vertices @xmath111 and the numerical density is a multiple of the characteristic function of @xmath18 . in that situation @xmath112 , where @xmath32 is the set of all vertices and @xmath31 the set of all edges of the triangle . in this section , we study the numerical measure from a statistical point of view , and we establish various convergence results which show that the measure @xmath1 of a large matrix @xmath0 is concentrated in a neighborhood of the barycenter of the spectrum @xmath15 . [ prop : stat ] for any @xmath113 , the first moment of the probability measure @xmath1 is the normalized trace of @xmath4 : @xmath114 and the variance of @xmath1 is given by @xmath115 * proof . * let @xmath116 denote the entries of @xmath4 . applying definition with @xmath117 , we have to compute the average of @xmath118 over the unit sphere . by symmetry , the average of @xmath119 is equal to zero if @xmath120 and to @xmath121 if @xmath122 . thus @xmath123 to compute the second moment , we take @xmath124 and proceed in exactly the same way . by symmetry , the average of @xmath125 is zero unless @xmath126 and @xmath127 , or @xmath128 and @xmath129 . moreover , it is easy to verify that the average of @xmath130 is equal to @xmath131 if @xmath132 and to @xmath133 if @xmath134 , where @xmath135 thus @xmath136 this gives the desired result , since @xmath137 . ' '' '' now we consider a sequence of matrices @xmath138 such that @xmath139 for each @xmath140 . as is well known , we have @xmath141 where @xmath142 . as a consequence , if we suppose that @xmath143 as @xmath144 , it follows from that the variance of @xmath145 converges to zero as @xmath144 . this gives : [ c : weakconv ] assume that @xmath139 and that @xmath146 as @xmath144 . then the measure @xmath147 converges weakly to zero as @xmath144 . we recall that the _ numerical radius _ of a matrix @xmath0 is defined by @xmath148 and satisfies @xmath149 @xcite . thus , a sequence of matrices @xmath150 is uniformly bounded ( in the operator norm ) if and only if the numerical ranges @xmath151 are all contained in a bounded region of the complex plane . under this assumption , proposition [ prop : stat ] shows that the variance of @xmath145 is @xmath152 as @xmath144 , so that the numerical measure is asymptotically concentrated in a disk of radius @xmath153 around the mean @xmath154 . in the introduction , we have observed that the numerical measure @xmath145 is the distribution of the random variable @xmath155 when the vector @xmath156 is uniformly distributed on the unit sphere @xmath38 . with this interpretation , corollary [ c : weakconv ] is reminiscent of the weak law of large numbers in probability theory . under slightly stronger assumptions , it is also possible to obtain a pointwise convergence result in the spirit of the strong law of large numbers . without loss of generality , we assume from now on that @xmath157 for all @xmath140 , so that the measure @xmath145 is centered at the origin . [ prop : sconv ] assume that @xmath150 satisfies @xmath157 for all @xmath140 and @xmath158 if for each @xmath140 the random variable @xmath156 is uniformy distributed on the unit sphere @xmath38 , then @xmath159 converges almost surely to zero as @xmath144 . * proof . * it is clearly sufficient to prove the result for hermitian matrices @xmath160 , because the general case then follows by considering the real and imaginary parts of @xmath159 . we thus assume that @xmath161 for all @xmath140 , and we denote by @xmath162 the eigenvalues of @xmath160 . for each @xmath140 , let @xmath163 be independent and identically distributed complex random variables with density function @xmath164 , @xmath53 . in particular , we have @xmath165 for each @xmath166 . since the euclidean measure on @xmath38 is the projection on the unit sphere of the standard gaussian measure in @xmath12 , we obtain a uniformly distributed random variable on @xmath38 by setting @xmath167 , where @xmath168 and @xmath169 is a unitary matrix such that @xmath170 . thus @xmath171 where @xmath172 by the strong law of large numbers , the denominator @xmath173 converges almost surely to @xmath174 as @xmath144 , hence it remains to show that the numerator @xmath175 converges almost surely to zero . but this follows from classical theorems on the limiting behavior of weighted sums of independent random variables , see @xcite . since for each @xmath140 the random variables @xmath176 ( @xmath177 ) are independent , have zero mean and finite second order moment , and since by the coefficients @xmath178 satisfy @xmath179 the results of ( * ? ? ? * section 3 ) imply that @xmath180 converges almost surely to zero as @xmath144 . ' '' '' the results established so far show that for a sequence of traceless matrices @xmath150 the numerical measure @xmath145 tends to concentrate on the origin as @xmath144 . under stronger assumptions , we now prove that the rescaled measure @xmath181 converges to a gaussian distribution , as in the classical central limit theorem . we first consider the hermitian case , which is somewhat simpler . [ p : clh ] let @xmath182 be a sequence of hermitian matrices such that @xmath150 and @xmath157 . we assume that @xmath183{}\ , 0~ , \qquad \hbox{and}\quad \frac{1}{n}\,{\mathop{\mathrm{tr}}}(a_n^2 ) \,\xrightarrow[n\to\infty]{}\ , \sigma^2 > 0~.\ ] ] then the rescaled numerical measure @xmath181 converges weakly to the normal distribution @xmath184 as @xmath144 . * proof . * we use the same notations as in the proof of proposition [ prop : sconv ] . for each @xmath140 , the numerical measure @xmath145 is the distribution of the random variable @xmath185 where @xmath162 denote the eigenvalues of @xmath160 and @xmath163 are independent complex random variables with density function @xmath164 . since @xmath173 converges almost surely to @xmath174 as @xmath144 , we have to show that @xmath186 converges in law to @xmath184 . to do that , we use the lindeberg - feller theorem for triangular arrays of random variables ( * ? ? ? * section 2.4.b ) . let @xmath187 so that @xmath188 . for each fixed @xmath140 , the random variables @xmath189 are independent and satisfy @xmath190 for @xmath191 . moreover , @xmath192{}\ , \sigma^2 > 0~.\ ] ] finally , for any @xmath193 , we have @xmath194 where @xmath195 . thus , using the first assumption in , we obtain by a direct calculation @xmath196{}\ , 0~.\ ] ] invoking the lindeberg - feller theorem , we conclude that @xmath197 converges in law to @xmath184 , which is the desired result . ' '' '' * remark . * since the numerical density of a hermitian matrix is a @xmath6-spline , proposition [ p : clh ] shows under very general assumptions that @xmath6-splines of degree @xmath8 satisfy a central limit theorem in the limit @xmath144 . in the particular case of uniform @xmath6-splines , this result was obtained by unser _ et.al . _ in @xcite . before considering more general matrices , we would like to mention an alternative proof of proposition [ p : clh ] which has its own interest . the starting point is a very nice formula for the moments of the numerical measure of a hermitian matrix @xmath198 . fix @xmath166 and let @xmath199 denote the eigenvalues of @xmath4 . using or with @xmath200 , we find @xmath201 where @xmath202 is the @xmath203-dimensional simplex defined in and @xmath204 . to evaluate the right - hand side , we apply the multinomial formula @xmath205 where the sum runs over all multi - indices @xmath206 of order @xmath207 . here we use the standard notations @xmath208 and @xmath209 . now , it is not difficult to verify that @xmath210 for any @xmath206 with @xmath211 . we thus obtain the following identity @xmath212 which shows that the @xmath213-th moment of the numerical measure @xmath1 is the complete symmetric homogeneous polynomial of degree @xmath213 in the variables @xmath214 , divided by the combinatorial factor @xmath215 which is just the number of terms in the sum . using the newton identities , the right - hand side of can be decomposed into as a sum of products of elementary symmetric polynomials of the form @xmath216 , see ( * ? ? ? ( 2.14 ) ) . if we assume that @xmath217 , then @xmath218 and the number of nonzero terms in the sum is considerably reduced . using these remarks , it is not difficult to show that , under the assumptions of proposition [ prop : sconv ] , the @xmath213-th moment of the rescaled numerical measure @xmath181 satisfies @xmath219{}~ \begin{cases } 0 & \hbox{if } k \hbox { is odd}~ , \\ 2^{-k/2}\sigma^k\frac{k!}{(k/2 ) ! } & \hbox{if } k \hbox { is even}~. \end{cases}\ ] ] since the moments in the right - hand side are those of the normal law , we conclude that @xmath181 converges weakly to @xmath184 as @xmath144 . we now consider general matrices @xmath220 , and obtain a central limit theorem by applying proposition [ p : clh ] to the radon transform of @xmath160 . [ th : limgen ] let @xmath182 be a sequence of matrices satisfying @xmath221 , @xmath157 , and @xmath222 as @xmath144 . we assume that @xmath223{}\ , a > 0~ , \qquad \frac{1}{n}\,{\mathop{\mathrm{tr}}}(a_n^2 ) \,\xrightarrow[n\to\infty]{}\ , b\in[0,a)~.\ ] ] then the rescaled numerical measure @xmath181 converges weakly to the gaussian measure @xmath224 as @xmath225 , where @xmath226 * proof . * for each @xmath227 , the hermitian matrices @xmath228 satisfy the assumptions of proposition [ p : clh ] , with @xmath229 let us denote by @xmath230 and @xmath231 the numerical measures of @xmath232 and @xmath233 , respectively . since @xmath231 is the radon transform of @xmath230 , the two - dimensional fourier transform @xmath234 for @xmath235 is precisely the one - dimensional fourier transform of @xmath231 evaluated at @xmath236 @xcite . thus , applying proposition [ p : clh ] , we find @xmath237{}\ , \frac{1}{\sigma(\theta)\sqrt{2\pi } } \int_{{\mathbb r}}e^{-ixr } e^{-x^2/(2\sigma(\theta)^2)}{\,\mathrm{d}}x \,=\ , e^{-\sigma(\theta)^2r^2/2}~,\ ] ] for any @xmath238 , @xmath227 . this shows that @xmath230 converges weakly as @xmath144 to the measure @xmath239 on @xmath34 defined by @xmath240 inverting the fourier transform , this gives @xmath241 with @xmath242 as in . ' '' '' * remarks . * if we assume for simplicity that @xmath243 is uniformly bounded , we can suppose ( up to extracting a subsequence ) that @xmath244 converges as @xmath144 to some @xmath245 . however , we have to assume in that @xmath246 in order to get a universal gaussian limit . + * 2 . * similarly , the first assumption in implies that @xmath247 converges , after extracting a subsequence , to some @xmath248 with @xmath249 . multiplying @xmath160 by a unit complex number , we can assume that @xmath250 , but in the borderline case where @xmath251 the limiting measure @xmath252 should be replaced @xmath253 . * example . * let us consider the jordan block of size @xmath8 : @xmath254 since @xmath255 and @xmath256 , the assumptions of theorem [ th : limgen ] are satisfied with @xmath257 and @xmath258 . thus the numerical measure of @xmath259 converges weakly to the normal distribution @xmath260 as @xmath144 . in this example , the measure @xmath145 has in fact a radially symmetric density for all @xmath140 , see section [ ss : rad ] . as a conclusion , we briefly mention a natural extension of our work , which is left for future investigation . recall that a homogeneous polynomial @xmath261 $ ] of total degree @xmath8 is _ hyperbolic _ in the direction @xmath262 if , on the one hand , it has partial degree @xmath8 with respect to the first variable @xmath263 , and on the other hand the @xmath8 roots of the univariate polynomial @xmath264 are real for every vector @xmath265 . hyperbolic polynomials arise as principal symbols of hyperbolic differential operators of order @xmath8 in @xmath266 space variables , see @xcite . as an example , if @xmath267 are hermitian matrices , the polynomial @xmath268 is hyperbolic . in the particular case where @xmath269 , it has been conjectured in @xcite , and proved in @xcite , that all monic hyperbolic polynomials are of the form . this is no longer true if @xmath270 . it might be argued that a large part of our work is not really about matrices , but rather concerns hyperbolic polynomials in @xmath7 variables . indeed , if @xmath0 and @xmath271 , @xmath272 are as in , the eigenvalues @xmath273 of the hermitian matrix @xmath79 are the solutions of the equation @xmath274 where @xmath275 is the hyperbolic polynomial associated with @xmath276 . as was shown in section [ s : radon ] , the numerical measure @xmath1 is entirely determined by the eigenvalues @xmath92 , hence by the polynomial @xmath277 . this in turn suggests a natural way to associate to any hyperbolic polynomial @xmath278 of degree @xmath8 in @xmath279 variables a probability measure @xmath280 on @xmath281 , which coincides with the numerical measure @xmath1 when @xmath269 and @xmath282 . given a unit vector @xmath283 , let @xmath284 be the roots of the polynomial equation @xmath285 , and let @xmath286(s)$ ] be the normalized @xmath6-spline with knots @xmath287 . the `` numerical measure '' of @xmath278 is then the unique probability measure @xmath280 on @xmath281 whose radon transform satisfies @xmath288 where , by definition , @xmath289 for any interval @xmath290 . in this generalized setting , the counterpart of normal matrices is the case where the polynomial @xmath278 split into linear factors @xmath291 when @xmath292 and the vectors @xmath293 span the affine space @xmath281 , the density of @xmath280 with respect to the lebesgue measure is the multivariate @xmath6-spline in @xmath266 variables , whose nodes are the @xmath293 s . it is piecewise polynomial of degree @xmath294 . in the generic situation where any @xmath295-uplet of vectors @xmath293 is an affine basis , it is of class @xmath296 , see @xcite . again the density is @xmath297-concave in this case . as in the two - dimensional case , the measure @xmath280 can be expressed in terms of @xmath298 using the back - projection method . the example above suggests that , as the space dimension increases , the measure @xmath280 becomes more singular . then , the inversion formula has to be understood in the sense of distributions . in the three - dimensional case @xmath299 , we arrive at the simple expression @xmath300 where @xmath301 denotes the euclidean measure on the unit sphere @xmath302 . as an example , in the particular situation where @xmath303 , which corresponds to the differential operator @xmath304 of the wave equation , we obtain @xmath305 . this shows that , when @xmath270 , the support of @xmath280 does not need to be convex . because the wave equation satisfies the huyghens principle , this example suggests that the link between polynomial regions of the density and lacunas of differential operators persists in higher dimensions . l. grding . linear hyperbolic partial differential equations with constant coefficients . _ acta math . _ , * 85 * ( 1951 ) , pp 162 . an inequality for hyperbolic polynomials . _ j. math . _ , * 8 * ( 1959 ) , pp 957965 .

we introduce and carefully study a natural probability measure over the numerical range of a complex matrix @xmath0 . this _ numerical measure _ @xmath1 can be defined as the law of the random variable @xmath2 when the vector @xmath3 is uniformly distributed on the unit sphere . if the matrix @xmath4 is normal , we show that @xmath1 has a piecewise polynomial density @xmath5 , which can be identified with a multivariate @xmath6-spline . in the general ( nonnormal ) case , we relate the radon transform of @xmath1 to the spectrum of a family of hermitian matrices , and we deduce an explicit representation formula for the numerical density which is appropriate for theoretical and computational purposes . as an application , we show that the density @xmath5 is polynomial in some regions of the complex plane which can be characterized geometrically , and we recover some known results about lacunas of symmetric hyperbolic systems in @xmath7 dimensions . finally , we prove under general assumptions that the numerical measure of a matrix @xmath0 concentrates to a dirac mass as the size @xmath8 goes to infinity .

Need proof that Chicago diners have bought into the hype surrounding Grant Achatz' new Chicago restaurant, Next? Check Craigslist. Fans of Achatz' brand of avant-garde cooking are literally paying thousands of dollars for the privilege of eating at his newest outpost. The restaurant operates on a ticket system -- secure a ticket and you're in for a meal. But demand drives up prices, and since the seats are limited, scalpers are having a field day. Recent Craigslist postings have the coveted tickets listed for as much as $3,000 . Achatz proved his cooking chops at Alinea, but he's going to have to put out some pretty impressive food to satisfy diners who ponied up that much dough. Read the full story at The Huffington Post. ||||| Just a day after tickets to Grant Achatz’s new restaurant, Next, went on sale, tickets have popped up on Craigslist starting at $575. That low, low price gets buyers two seats at a four-top table with two other strangers. But, hey, there are wine pairings. Really big spenders might be more interested in dining at the restaurant’s chef’s table, which features a 16-course meal for six people, including wine pairings. Face value on the tickets—including tip—is $165 per person. Craigslist price? $3,000. Most tickets are going for $800 to $1000 for two diners, and include the confirmation e-mail the original purchasers received. Of course, that’s not to say some sleazy ticket broker didn’t make up a fake e-mail address, buy tickets, and then sell them 30 times under a fake name—but, hey, that’s the risk buyers take, right? For its part, Next is kind of shirking responsibility. Co-owner Nick Kokonas told Eater, “We cannot help ticket re-sales any more than the Cubs.” True, but do Next’s confirmation e-mails have holograms on them? Maybe that’s something to look into on the menu’s next iteration—Bangkok 2312, anyone? Editor's note: Kokonas commented on this article (see below) and noted that, "Actually, the entirety of my comment to them was that we do not want scalping, that we require confirmation of BOTH parties – buyer beware -– and that we will not honor tickets that have not confirmed the sale with us. THEN I said that I wish I could stop it but we cannot legally do so any more than the Cubs. The tickets are required to be transferable by law for face value. We are not shirking responsibility -- we are trying hard to ensure that the tickets are real, which is all we can do. When we can send holograms by email, let me know." Fair enough, Nick. Thanks for commenting! ||||| Having trouble getting tickets to Grant Achatz's new Chicago restaurant, Next? You could try Craigslist, where there's a hot black market trade in tables going on. Of course, you'll end up paying a lot more than if you just went through the restaurant, but hey! Grant Achatz doesn't open a new restaurant every day. The official prices for Next vary depending on what time you make your reservation, but are around $85 per person for the current menu (plus wine, tax and gratuity). The resale prices, on the other hand, can be anywhere from a $500 mystery reservation to a $3,000 ticket for six to the "kitchen table," which features an expanded 16 course meal. The average ticket seems to hover around $1,000 for a table for two. ||||| Grant Achatz's Next Restaurant just opened and already tickets have popped up on Craigslist and eBay, selling from $500 to $3000. Co-owner Nick Kokonas told Eater Chicago that he was "surprised how quickly" tickets showed up. We're not. For those lucky enough to score reservations, certainly some of them must have had the intention to re-sell their tickets all along, especially with the potentially high profit margins. The crop of Craigslist tickets range in perceived value, as some include wine pairings, while the $3000 ticket advertises the much-coveted chef's table. Original ticket prices are as low (relatively speaking) as $85 per person. (This whole secondary market for Next tickets makes us wonder: does food taste better when you know you'll never be able to have it again?) The jury is out on whether this ticketing system will be a successful reservation concept, even for such a high-demand, rotating-concept restaurant (read more about the concept here, here, here and here). With tickets selling for such high prices, the process currently seems to favor those who are willing and able to spend top dollar to secure a seat. Kokonas tells the AV Club that they are not encouraging scalping and Next requires the confirmation of both parties of any ticket transfers. "I wish I could stop it but we cannot legally do so any more than the Cubs," he says. Clearly hearing it from those who sense their chances of enjoying the 3-month Escoffier run at Next dwindling, Achatz echoed this same messaging over Twitter on Friday: So, just think of Next as sort of a perpetual World Series! Games every night, new teams every three months.

– Want to eat at Next, the highly anticipated new restaurant from top Chicago chef Grant Achatz? Then expect to pay quite a bit for the experience. Unless you can snag your own ticket (which isn't cheap at $85 per person), a ticket bought on Craigslist or eBay will set you back $500 to $3,000, Slashfood notes. The difference in prices for the scalped tickets can be explained by what options they include, the Huffington Post reports: Some include wine pairings, while the most expensive are at the chef's table. Eater notes that the average ticket price seems to be around $1,000 for a two-person table. Co-owner Nick Kokonas tells the AV Club the restaurant doesn't encourage scalping and adds, "I wish I could stop it but we cannot legally do so any more than the Cubs."

takotsubo cardiomyopathy ( tcm ) has emerged as an important differential diagnosis in patients presenting with acute chest pain . tcm is associated with severe emotional or somatic stress and is characterized by extensive left ventricular dysfunction in the absence of coronary artery obstruction of sufficient magnitude to explain the extent of left ventricular involvement . thus , tcm is distinct from coronary artery disease ( cad ) and acute myocardial infarction ( ami ) . although patients with concomitant significant cad traditionally were excluded from the tcm cohorts , several groups , including our own , have provided substantial evidence for co - existing cad in some tcm patients. here , we take this association one step further and present a case in which the patient simultaneously suffered from ami and tcm , and in which we believe that a primary coronary event triggered tcm . an 88-year old woman presented to the emergency department with acute onset of chest pain . her copd was considered mild and had remained stable for many years . over the last year she had single - handedly been caring for her demented husband , a situation she described as increasingly stressful and anxious . electrocardiography ( ecg ) revealed atypical st elevation in precordial leads ( figure 1 ) . acute coronary angiography revealed a plaque rupture in the first diagonal branch ( figure 2a and 2b ) and percutaneous coronary intervention ( pci ) was performed . three days after the event , echocardiography was repeated and could not detect any akinesia ( video 1 ) . six months later , cardiac functions had further improved and was estimated to be entirely normal , without any trace of regional wall motion defects . thus , this patient adhered to the diagnostic criteria for tcm ( table 1 ) . ( a & b ) : evidence of plaque rupture in a small diagonal branch could be detected on the acute angiogram ( arrows ) . ventriculography ( c : diastole ; d : systole ) revealed typical left ventricular apical ballooning and an akinetic region that extended well beyond the vascular territory of the occluded vessel . although causality can not be conclusively inferred from this association , we believe that the somatic stress associated with ami may have caused tcm in this patient . thus , she can be considered to have been at increased risk of developing tcm . tcm is typically preceded by an acute somatic or emotional stressor and is believed to be caused by elevated levels of catecholamines . , among the somatic stressors known to be associated with tcm are intracranial events , severe infection , surgical trauma and respiratory disease . because a relationship has been described between tcm and many acute syndromes associated with increased somatic stress , it is intuitive to assume that ami , another acute condition associated with considerable somatic stress , could be associated with tcm . similar to other forms of severe somatic disease , ami is associated with increased levels of catecholamine . however , in ami , catecholamine is particularly high in the periinfarct zone . thus , if anything , ami would be expected to more frequently associate with tcm than other somatically stressful syndromes . we propose that tcm and ami may not be mutually exclusive conditions , and that they may be intertwined in ways we have yet to discover . if this is true , developing strategies for reversing takotsubo may improve the outcome in patients presenting with cardiogenic shock secondary to ami . recent evidence indicates that takotsubo is a cardiocirculatory syndrome that associates with low peripheral resistance and low blood pressure despite adequate tissue perfusion . in other words , patients with tcm display a different cardiocirculatory profile compared to patients with only ami . because standard acute heart failure therapy with vasopressors and/or inotropes may be directly harmful in tcm , clinicians would probably do well to withhold these therapies in hypotensive patients with tcm that do not display signs of tissue hypoperfusion . because optimal treatment of hypotensive patients may depend on whether or not ami is complicated by tcm if echocardiography had not been performed in this patient immediately on admission , we believe that this patient may have been diagnosed with only myocardial infarction and the diagnosis of tcm may have been overlooked . it may be prudent to perform echocardiography without delay in patients presenting with acute chest pain and elevated troponins .

takotsubo cardiomyopathy ( tcm ) is an acute cardiac syndrome characterized by extensive , but potentially reversible , left ventricular dysfunction in the absence of an explanatory coronary obstruction . thus , tcm is distinct from coronary artery disease ( cad ) and acute myocardial infarction ( ami ) . however , substantial evidence for co - existing cad in some tcm patients exist . herein , we take this association one step further and present a case in which the patient simultaneously suffered from ami and tcm , and in which we believe that a primary coronary event triggered tcm . an 88-year - old female presented with chest pain . echocardiography revealed apical akinesia with hypercontractile bases . an occluded diagonal branch with suspected acute plaque rupture was identified on the angiogram , but could not explain the extent of akinesia . cardiac function recovered completely . thus , this patient adhered to current diagnostic criteria for tcm . tcm is a well - known complication for other conditions associated with somatic stress . it is therefore intuitive to assume that ami , which also associates with somatic stress and elevated catecholamine , can cause tcm . our case illustrates that tcm and ami may occur simultaneously . although causality can not be conclusively inferred from this association , the somatic stress associated with ami may have caused tcm in this patient .

in view of the rapid development of the experimental realization of quantum information processing ( qip ) by using different physical systems , it is an urgent obligation to find a proper strategy for detection of entanglement . one of the most commonly used systems in the study of physical realizations of qip is an ensemble system and the best - known technology therein is nuclear magnetic resonance ( nmr ) @xcite . the ensemble system of nmr has been employed for implementation of even relatively complicated quantum algorithms @xcite . however , nmr has been facing difficulty with regard to the existence of entanglement @xcite . the complication actually arises because of somewhat confusing ensemble behavior of the nmr system . the confusion manifests itself when macroscopic quantities , such as results of nmr measurement involving an average over a large number of molecules , are used to detect microscopic properties , such as entanglement between pairs of nuclear spins inside each molecule . in fact , it has been shown that , for some particular case of nmr implementation of quantum nonlocal algorithms , the apparent nonlocal behavior of the highly mixed states in nmr is due to a large number of molecules involved in the ensemble system @xcite . hence , highly mixed states of nmr are separable and can not be used for immaculate implementation of quantum nonlocal algorithms for which entanglement is believed to play an essential prerequisite role @xcite . on the other hand , ensemble quantum computing ( qc ) pertains some inevitable advantages . it is particularly workable since spin manipulation is performed easily by applying corresponding pulses . in addition , ensemble qc , such as nmr , is supported by a long term research in the area of spectroscopy . thus , it would be unfair and also inefficient to totally ignore ensemble qc . we have been involved in realization of qip by means of electron nuclear double resonance spectroscopy ( endor ) @xcite . although this system should be taken as an ensemble system at the moment , it has been profoundly evaluated for more elaborated nonlocal qip through experimental studies @xcite . however , after applying entangling operations in an experiment , it might still be premature to claim that the state is properly entangled enough for implementation of nonlocal qip . at least some qualitative detection of general multipartite entanglement for a particular system of interest should be examined in advance . detection of a general multipartite entanglement is one of the most challenging problems for an experimental study in qip . there are several approaches in this context . one may first employ a full state tomography with which the complete density matrix would be obtained . then , direct application of an existing entanglement measure would be evaluated on the quantum state in order to extract information about the entanglement of the state . this is , however , a bit too general to be efficient . the density matrix of the quantum state includes far more information than necessary for an entanglement estimation only . furthermore , it is difficult to find a sufficient condition of entanglement for a given state in general if the dimension of the state is neither @xmath0 nor @xmath1 for which the peres - horodecki criterion @xcite would be applicable . detection of entanglement of a quantum state through violation of the bell inequalities also should not be taken to be perfect since there are entangled states that do not violate any known bell inequalities @xcite . still one may try the existing approaches that work for a state that is totally unknown in advance @xcite . however , this may not be the most proper choice for our system of interest since as long as we are working in an experiment , we have definitely some knowledge about the state , i.e. , through the prepared initial state or applied operations . if this is the case , it would be more appropriate to define an entanglement detector measure that is easily workable with less experimental effort by taking advantage of the available information on the state . we have studied the concept of entanglement witness ( ew ) @xcite with the motivation to introduce an entanglement detection applicable for a particular system of interest . the ew is an observable which has non - negative expectation values for all separable states . therefore , detection of a negative value indicates the entanglement of the state . in addition to the very fast development in the theory of ews for different classes of states @xcite , in experiments also detection of entanglement by the use of witness operators has attracted special attention @xcite . for physical systems in thermodynamical limits , witness operators are developed @xcite . in addition , ews are generated for detecting entanglement of mixed states that are close to a given pure state @xcite . ews are used for characterizing different classes of a multipartite quantum state @xcite . after determination of the ew for a particular expected state in an experiment , the important task is to decompose it into local operators that are easily measurable in the given physical system . this approach for detection of entanglement is operationally possible and , for most cases , is a simple method @xcite . in refs . @xcite detection of multipartite entanglement with few local measurements is studied . throughout the study on this issue , it has been more appreciated to operationally simplify the entanglement detection process by modifying the required observables for the particular working system and/or decreasing the number of local measurements . generally speaking , previously introduced methods for detection of entanglement by the use of ews require several projective measurements on the copies of a state in order to extract the outcome . however , it is somehow operationally difficult to prepare several copies of a quantum state to be measured for detection of entanglement . therefore , it is more advantageous if an ew works just with a single run experiment . also , the detection process would be better to be specially modified for the particular working system . for instance , if the physical system of interest is an ensemble system , then the available measurements are ensemble average measurements . we work with ensemble systems . therefore , ensemble average measurements should be employed here , in contrast with the projective measurements widely used in the previous works . therefore , in this work , we propose a proper single - experiment - detectable ( sed ) ew for the ensemble system qc . the most significant result of our work is that our schemes require only a single - run experiment to detect entanglement by using nondestructive ensemble average measurements , which allow us to measure several non - commuting operators simultaneously . a well known example of nondestructive measurement is the free induction decay measurement that is frequently used in nmr quantum computing . this paper is organized as follows . first in the following section we will briefly summarize the concept of the ew and will give a short review particularly for multipartite ews . then , in the third section we will introduce and prove a method with which the conventional ew can be transformed into a collection of separate but simultaneous measurements of individual local systems of the ensemble qc . the analysis of this section is based on the assumption that the density matrix is diagonal after application of the disentangling operations introduced there . in the subsequent section , a different sed ew , which works without any assumption on the density matrix , is introduced . as a drawback , however , we have to introduce an ancillary qubit . in sec . [ five ] we will extend discussions on our scheme , study the complexity of the corresponding quantum circuits for sed ew , and give some remarks on the behavior of this scheme under generally existing noise in the system . a density matrix @xmath2 is entangled if and only if there exists a hermitian operator @xmath3 , called an entanglement witness ( ew ) , such that @xmath4 where @xmath5 denotes the set of separable states @xcite . therefore , it is concluded that a state is entangled if some negative value is obtained in measurement of an ew . there are several methods to construct an ew @xcite . for the case in which a density matrix has a negative eigenvalue when partially transposed , the construction of the ew is very simple . the partially transposed projector onto the eigenvector corresponding to the negative eigenvalue of the partial transpose of the state is an ew @xcite . one important and notable point about ews appears when dealing with the multipartite case . ews can be used to detect different kinds of multipartite entanglement by defining the space @xmath5 in eq . ( [ define ] ) to be the set of states that does not have a special kind of entanglement to be detected @xcite . let us give an example . while all the entanglements for two qubits are actually equivalent to each other , for three qubits there are two classes of genuine pure tripartite entangled states @xcite . the entangled states from different classes can not be transformed into each other by local operations and classical communications ( locc ) . one class is the greenberger - horne - zeilinger ( ghz ) class that includes entangled states locc - equivalent to @xcite @xmath6 this classification can be extended to more general tripartite mixed states . we remind the reader that a tripartite ( and generally any multipartite ) state @xmath2 is separable if it can be written as a convex combination of fully separable states . however , a state @xmath2 may not be fully separable but biseparable , i.e. , it can be written as a convex combination of biseparable pure states . if a tripartite state @xmath2 is neither fully separable nor biseparable then it is entangled , in either the ghz class or the w class @xcite . corresponding to each class of entangled states , there are ews already known . needless to say , these entanglement witnesses are not sufficient to decide if the system possesses a genuine multipartite entanglement . for instance , for the ghz state , the ew is @xmath7 while for the w state , it is @xmath8 where @xmath9 is the identity operator @xcite . the ew that detects a genuine tripartite entanglement of a pure state @xmath10 , and of states close to @xmath10 , is given by @xcite @xmath11 where @xmath12 and @xmath13 denotes the set of biseparable states . then @xmath14 for all biseparable states @xmath15 and @xmath16 . the coefficient @xmath17 in eq . ( [ alpha ] ) is determined by using the schmidt decomposition @xcite . for an ensemble system , it is desirable to find an observable that can be performed by a small number of experiments to satisfy operational requirements . any ew that is defined for the state @xmath18 , which is the most expected state after the applied operations and is close to the experimentally realized state @xmath2 , should be decomposed into a linear combination of individual polarization operators , in order to make it locally measurable . in this paper , we introduce a new method with which an ew for multipartite states can be measured just with a single - run experiment . for starting up an experiment , the state is supposed to be initialized to a simple fiducial state , such as @xmath19 , for an @xmath20-qubit system . from now on we will drop the subscripts @xmath21 to simplify notation , unless otherwise stated . however , in an ensemble qc , the initial state is prepared in the form of a pseudopure state as follows @xmath22 where @xmath23 characterizes the fraction of the state @xmath18 . it is important to note here that the confusion regarding the concept of entanglement in an ensemble system is intrinsically apart from the concept of pseudopure state as an initial state . a pseudopure state is used for making the required input state for qc . improvement of experimental conditions above some definite threshold is required to realize an entangled state experimentally . in other words , the pseudopure state still can be used for realization of a genuine entangled state if the experimentally required conditions are all satisfied . here , we do not enter into the discussion of the very large required number of steps for making a pseudopure state as we suppose that , anyhow , we are given some prepared input state for which the status of entanglement should be studied . in order to produce a particular entangled state , the corresponding entangling operation @xmath24 is applied on a state @xmath18 to yield @xmath25 the corresponding pseudopure state is @xmath26 note that , even though the entangling operation @xmath24 is applied , @xmath27 may or may not be entangled , and our task is to detect entanglement of @xmath27 in order to examine whether @xmath27 is applicable for some quantum nonlocal algorithm , for example . the corresponding conventional ew , eq . ( [ ew ] ) , for @xmath28 is @xcite @xmath29 where @xmath30 is determined properly so that we do not get a negative value for separable states @xcite . the entanglement witness @xmath31 detects @xmath27 as entangled if @xmath32 where @xmath33 for instance , if a state @xmath34 is the experimentally achieved pseudopure state for the state @xmath35 eq . ( [ ghz ] ) , then @xmath36 is @xmath37 . this large value of @xmath23 is in accordance with the results of studies on entanglement of pseudopure states which are indeed mixed states @xcite . one may still work with entanglement for an ensemble system without being engaged in the concept of a pseudopure state @xcite . however , if the state should be used for a quantum computation it is a formidable task to prepare a pseudopure state that works exactly as a pure state under unitary operations for qc . generally speaking , the expectation value of the observable @xmath31 is given after several measurements on copies of state @xmath27 . if @xmath38 then @xmath27 is entangled . in this work , we introduce a strategy with which the ew can be detected in a single run - measurement . the most usual and convenient measurement in an ensemble qip is the spin magnetization @xmath39 of the @xmath40th spin . then , we find the proper @xmath20-partite ew , which we call @xmath41 , that satisfies the following equation @xmath42 and is detectable in a single run measurement as long as @xmath41 is written as @xmath43 the unitary operator @xmath44 should be appropriately defined in addition to the coefficients @xmath45 . it should be noted that eq . ( [ equality ] ) is state dependent . now we will show that there exists some unitary operator @xmath44 in addition to the set of coefficients @xmath45 such that eq . ( [ equality ] ) is satisfied . we also give an explicit example of the solution . the unitary operator @xmath44 includes the inverse entangling operation @xmath46 and @xmath47 that is introduced for eq . ( [ equality ] ) to be satisfied as in fig . [ figone ] . it is possible to use a unitary transformation @xmath44 and individual polarizations of output qubits to find the value of @xmath48 . it is assumed that @xmath49 is diagonal . see the text for details . ] suppose @xmath49 , the state after applying the inverse entangling operation @xmath46 , is a diagonal matrix with a possible classical correlation . although this assumption is often satisfied , it can be dropped for a general proof if an ancillary qubit is added to the quantum circuit . indeed , for this case the only required measurement would be on the spin magnetization of the ancillary qubit . this is discussed in the next section . in the present case , out task is to find some proper unitary transformation @xmath44 and coefficients @xmath50 such that eq . ( [ equality ] ) holds under the condition that @xmath51 is diagonal . we first prove by induction that eq . ( [ equality ] ) is satisfied for any @xmath20 and later give an explicit example of tripartite states . by setting @xmath52 and @xmath53 , we find for the left and right - hand sides ( lhs and rhs ) of eq . ( [ equality ] ) @xmath54.\end{aligned}\ ] ] consider the case where @xmath55 and let us denote the matrix @xmath56 by @xmath57 . by inspecting eqs . ( [ lhs ] ) and ( [ rhs ] ) , we immediately notice that there is a solution in which the @xmath58 element of @xmath59 is @xmath60 while all the other diagonal elements vanish . note that the off - diagonal elements are arbitrary thanks to the assumed diagonal form of @xmath49 . typically , we can take @xmath61 , @xmath62 , and @xmath63 then , @xmath64 as promised . therefore , the equality eq . ( [ equality ] ) is satisfied for the case @xmath55 . we will take advantage of this typical @xmath57 and the corresponding parameters in the following proof . now we use mathematical induction . suppose that @xmath65 transforms @xmath66 to @xmath67 . then , we show that with a class of parameters , the unitary transformation @xmath68 maps @xmath69 to @xmath70 . the unitary operator @xmath71 is a permutation operation that comprises transpositions : @xmath72 , @xmath73 , @xmath74 , @xmath75 . this set of transpositions may be written in terms of ket vectors in the binary system : @xmath76 , @xmath77 , @xmath74 , @xmath78 , or equivalently @xmath79th qubit . we also defined @xmath80 . this unitary transformation is easy to implement . by noting the equation @xmath81 we find that a single hadamard gate acting on the @xmath82th qubit and a single c@xmath83 gate with zero - conditional - control qubits @xmath84 and the target qubit @xmath85 do the job . now we give the details of the proof . suppose that for @xmath20 qubits we have the unitary operator @xmath65 and coefficients @xmath86 and @xmath87 that satisfy eq . ( [ equality ] ) so that @xmath88 here also the off - diagonal terms are not important . then , for @xmath85 qubits , we have the equation @xmath89i\otimes{v'}_n^\dagger\nonumber\\ & = & \frac{1}{2 } \left(\begin{array}{cc } a_n&0\\ 0&a_n \end{array}\right)\\ & { } & + a_{n+1}\ ; { \rm diag}(1_1,\ldots,1_{2^n},-1_{2^n+1},\ldots,-1_{2^{n+1}}).\notag\end{aligned}\ ] ] this should be transformed to the form : @xmath90 in order for eq . ( [ equality ] ) to be satisfied . to this end , we apply some unitary transformations to @xmath91 . first , we use the permutation @xmath71 . then we have @xmath92 it should be noted that the off - diagonal terms of eq . ( [ bn1 ] ) have been also transformed under the application of @xmath93 . under this transformation , the following permutations of the matrix elements , in decimal notation , take place . for @xmath94 @xmath95 and , for @xmath96 @xmath97 particularly , the off - diagonal elements of the @xmath0 diagonal blocks of @xmath98 are replaced with elements that are @xmath99 . now , the @xmath0 diagonal blocks in @xmath100 are @xmath101 , from the upper left to the lower right . then we set @xmath102 and apply @xmath103 to @xmath100 . all the diagonal blocks but the first one transform to @xmath104 since @xmath105 . then we obtain @xmath106 therefore , the unitary transformation @xmath107 and coefficients @xmath108 , @xmath109 , and @xmath102 satisfy the equality eq . ( [ equality ] ) for all @xmath110 under the imposed condition . the following example with @xmath111 will clarify the above proof . for @xmath112 , we have @xmath113 furthermore , by applying the permutation operator @xmath114 , we obtain @xmath115 this permutation is realized by two transpositions @xmath116 and @xmath117 with respect to the row labels ( numbered from 1 to 8) , and the same transpositions with respect to the column labels . with ket and bra labels , these are transpositions @xmath118 , @xmath119 , @xmath120 , and @xmath121 . therefore , the off - diagonal terms , that is the second term in the right - hand side of eq . ( [ foradd ] ) , are written as the matrix @xmath122 note that all the off - diagonal elements of the @xmath0 diagonal blocks of this matrix have disappeared . adding up the first and third terms of the right - hand side of eq . ( [ foradd ] ) and substituting @xmath123 , all the diagonal blocks are mapped to @xmath124 , except the first diagonal block that remains as @xmath125 . then we use the block - diagonal unitary transformation @xmath126 where @xmath127 is the hadamard operation . then this leads to @xmath128 thus we found that the unitary transformation @xmath129 satisfies @xmath130 . this shows that the equality eq . ( [ equality ] ) holds for @xmath111 . in this section we will show how to detect multipartite entanglement for a general case , without imposing the condition that the state density matrix be diagonal after the disentangling operation @xcite . for this idea , we use a single uninitialized ancillary qubit . consider a single ancillary qubit initially in a thermal equilibrium state : @xmath131}_{\rm in } = p{|0\rangle}{\langle 0|}+(1-p){|1\rangle}{\langle 1|}$ ] . for a general proof ( gen ) , consider an entangled state generated from @xmath132 by using some entangling unitary operation @xmath24 , i.e. , @xmath133 . then the ew is @xmath134 . for instance for the bipartite case , @xmath135 is non - negative for all positive partial transpose states when @xmath136 is set to the largest schmidt coefficient of @xmath137 @xcite . our interest is not specific to bipartite ews but applicable to general entanglement . in order to test @xmath135 in a single nmr experiment , we introduce the quantum circuit in fig . [ figancillawm ] . quantum circuit with a polarization measurement to implement the ew @xmath135 . ] recall the relation @xmath138 let us write @xmath139 . in the quantum circuit , the diagonal element before the polarization measurement is @xmath140\;\mbox{c$^n$not}^\dagger\}.\end{aligned}\ ] ] here @xmath141 picks up the diagonal elements from a matrix @xmath142 . after setting @xmath143 , it is rewritten as @xmath144\mbox{c$^n$not}^\dagger\nonumber\\ & { } & \hspace{-0.8cm}=\tilde p(0\ldots0)[p{|1\rangle}{\langle 1|}+(1-p){|0\rangle}{\langle 0|}]\otimes{|0\ldots0\rangle}{\langle 0\ldots0|}\notag\\ & { } & + [ p{|0\rangle}{\langle 0|}+(1-p){|1\rangle}{\langle 1|}]\otimes\sum_{k\not = 0}\tilde p(k){|k\rangle}{\langle k|}.\end{aligned}\ ] ] the diagonal part @xmath145}_{\rm out}$ ] of the reduced density operator of the ancillary qubit before the measurement is @xmath146\notag\\ & { } & + [ 1-\tilde p(0\ldots0)][p{|0\rangle}{\langle 0|}+(1-p){|1\rangle}{\langle 1|}]\nonumber\\ & { } & \hspace{-0.8cm}=[\tilde p(0\ldots0)(1-p)+p(1-\tilde p(0\ldots0))]{|0\rangle}{\langle 0|}\notag\\ & { } & + [ \tilde p(0\ldots0)p+(1-p)(1-\tilde p(0\ldots0))]{|1\rangle}{\langle 1|},\end{aligned}\ ] ] where use has been made of the identity @xmath147 . thus we have @xmath148}_{\rm out}z=(1 - 2p)[2\tilde p(0\ldots0)-1].\ ] ] this leads to @xmath149}_{\rm out}z.\ ] ] consequently , @xmath150}_{\rm out}z.\ ] ] thus , the value of @xmath151 can be found by using the initial polarization @xmath152}_{\rm in}z=2p-1 $ ] and the output polarization @xmath152}_{\rm out}z$ ] of the ancillary qubit . extending this method , it is easy to construct a quantum circuit of concatenated ews to discriminate different types of multipartite entanglement from each other . suppose we want to measure @xmath153 types of multipartite entanglement with a set of ews @xmath154 , where @xmath155 . then we can test all of @xmath156 using @xmath153 measurements as shown in fig . [ figancillawmconcat ] . for example , tripartite entanglement can be differently written in the form of the ghz state or the w state . for a general tripartite state @xmath2 this can be checked by applying disentangling operations for the ghz state ( @xmath157 ) and the w state ( @xmath158 ) . this is shown in fig . [ figancillawmconcat ] if substitutions are made as @xmath159 and @xmath160 and @xmath161 . the entanglement of the state @xmath27 would be detected by measurements of the ancillary qubit . in order to realize the quantum circuit fig . [ figancillawmconcat ] with a system such as nmr , one needs to make several free - induction ( nondecay ) measurements in a single run of a nmr experiment . in a conventional nmr experiment , however , generally one free - induction decay ( fid ) measurement is made at a particular point where the experiment is ceased . indeed , there have been experiments involving multiple fid measurements , such as the cory-48 @xcite pulse sequence . although it is not of particular interest to nmr researchers , in principle it is possible to take an instant free - induction measurement . one possible way is to apply a @xmath162 pulse and take signals of the precession for some microseconds duration ( that is , small enough to keep coherence ) , and then apply a @xmath163 pulse . thus , it is a realistic idea to have multiple free - induction measurements in a single run of an experiment . the number of two - qubit quantum gates to compose @xmath164 is @xmath165 . this is clear from the quantum circuit of @xmath164 in fig . [ figvp ] . let us write the number of basic gates to compose @xmath164 by @xmath166 . then @xmath167 , from which we obtain @xmath168 . here we used the fact that an in - place c@xmath169 gate ( @xmath142 is a @xmath170 unitary matrix ) is composed of @xmath171 two - qubit gates ( see , _ e.g. _ , ref . @xcite , p.184 ) . quantum circuit to compose @xmath164 . ] if we can use a highly selective pulse , the gate c@xmath172 may be performed in a single step , although this usually takes a long time of order @xmath173 . in addition to the circuit complexity to compose @xmath164 , the circuit complexity for the inverse of an entangling operation @xmath24 should be considered as well . usually , this circuit complexity is less than @xmath165 . for example , a quantum circuit to generate a ghz - like state from some pure initial state can be composed of several not gates , one hadamard gate , and @xmath174 controled - not ( cnot ) gates . consequently the total circuit complexity is usually @xmath165 . in case an ancillary qubit is employed , the dominant circuit complexity is due to the c@xmath175not gate . on the assumption that the internal circuit of disentangling operations @xmath176 ( here , @xmath177 may be ghz , w , etc . ) have circuit complexities on the order of @xmath178 , the total circuit complexity of the quantum circuit of fig . [ figancillawmconcat ] is @xmath179 . although the proposed methods enable a single experiment to detect entanglement without copies of states , the size of quantum circuits used in the measurement process is considerably larger than that for usual entangling operations . thus noise ( namely , probabilistic errors ) in quantum gates can skew the result of entanglement detection with a higher probability than conventional entanglement detection using multiple copies of a state , assuming that error during preparation of copies of a state is negligible . in a simple model @xcite , we assume that a quantum gate @xmath44 acting on the target block @xmath180 of qubits suffers from a noise such that a desired unitary transformation takes place with success probability @xmath181 ; otherwise , a reduced density operator acting on @xmath180 becomes a maximally mixed state with failure probability @xmath182 . the superoperator of this noise is @xmath183}/2^{\mathrm{len}(\mathbf{t})},\end{aligned}\ ] ] where @xmath184 is the number of qubits in @xmath180 ; @xmath185}/2^{\mathrm{len}(\mathbf{t})}$ ] is the maximally mixed state of @xmath180 and @xmath186 in the first term is the identity matrix acting on the rest of the qubits . although this noise model is rather simple , analytical calculation of the output of a quantum circuit of our interest under this noise is quite complicated and does not result in a tractable equation . instead , we present a result for a particular example of the quantum circuit shown in fig . [ figone ] in the case of a three - qubit input starting from the thermal state @xmath187^{\otimes 3}$ ] . we set the success probability as @xmath188 for single - qubit gates and @xmath189 for cnot gates . noise is assumed to exist in individual quantum gates including the entangling operation @xmath24 . we investigate the output @xmath190 in eq . ( [ equality ] ) under the above noise . we choose the conventional entanglement witness for the class of the ghz state given in eq . ( [ convewghz ] ) and decomposition into sed ew using the method that we have introduced in sec . 3 . numerical results of outputs of entanglement witnesses are plotted against @xmath191 and @xmath192 in fig . [ ewcomparison ] . as illustrated in the figure , positive values are returned in the range of @xmath191 in which the noise - free entanglement witness ( i.e. , the case of @xmath193 ) returns negative values . a sed ew is more fragile against noise than a conventional one in the sense that the range of @xmath192 in which negative values are returned is small . nevertheless , it is important that we never obtain a negative value for a separable state even under noise in this example . for a general case , a mathematical proof for returning non - negative values for all separable states is not easy because it is strongly dependent on the structure of the quantum circuit that has been used for the scheme introduced in this paper . one way to improve the robustness is to increase the value of @xmath181 . recently , a high gate fidelity was reported by using a classical numerical optimization in nmr quantum computing ( _ e.g. _ ref . @xcite ) and this technique may be applicable for this purpose . this technique can also reduce the number of pulses needed to implement a large quantum gate . thus it seems a possible way to make proposed entanglement detection methods practical in the future . we proposed two schemes to reconstruct an entanglement witness into nonlocal operations and local measurements so that a single experiment without copies of a state is sufficient . in one scheme , an ancillary qubit is not required but the quantum state must satisfy some condition , while an uninitialized ancillary qubit is required in the other scheme where no condition is imposed on the quantum state . computational complexities and noise behavior have been discussed . we would like to thank masato koashi for pointing out an error in the description of concatenated ews in the draft and kazuyuki takeda for discussions . r.r . is grateful to vlatko vedral for helpful discussions . is supported by the jsps . m.n . would like to thank mext for partial support ( grant no . 13135215 ) . is supported by crest of japan science and technology agency .

in this paper we provide an operational method to detect multipartite entanglement in ensemble - based quantum computing . this method is based on the concept of the entanglement witness . we decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements . individual single- qubit measurements are performed simultaneously ; hence complete detection of entanglement is performed in a single- run experiment . in this sense , our scheme is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state for detection of entanglement .

multiverse theory ( also known as meta universe theory ) is a group of models assuming that our physical reality encompasses more than one universe , i.e. there exists at least one more universe other than ours @xcite . several types of such multiverses are known in literature ( e.g. [ 1 - 3 ] and @xcite ) . some of these models suggest that our reality has infinitely many universes , while others postulate that we live in a multiverse with a finite number of universes . in cosmology , the idea of infinitely many universes has received a lot of attention in recent years @xcite . most multiverse theories imply that universes might not be uniquely identified through their macroscopic state at present or past , i.e. their macrostates could be quite similar during long and even infinite time intervals . the ultimate universe model ( also known as the mathematical multiverse ) @xcite satisfies this property and postulates that every possible state is in one - to - one correspondence with each universe from the multiverse horizon . one of the most common explanations of the big - bang is given by quantum fluctuation theory , which suggests that our universe began from a quantum fluctuation , and if so , it is natural to deduce that in our physical reality these fluctuations are taking place in all of our space and time dimensions ( see @xcite for instance ) . therefore , an infinite number of such fluctuations implies a vast multiverse of infinite number of universes . the multiverse type that we shall focus on is the quilted multiverse @xcite , whose space and time dimensions presumably contain infinite number of universes . this type of multiverse was first introduced in @xcite , and was defined as follows : physical reality contains infinitely many universes in infinite space and time dimensions , where every possible event @xmath0 will occur an infinite number of times . the quilted multiverse provides a theoretical probabilistic approach for the existence of events before the event horizon in our physical reality . within the quilted multiverse , the event horizon includes events that occur infinitely many times , duplicated in infinitely many universes . in terms of tegmark s hierarchy @xcite , the quilted multiverse we shall study corresponds to a level 1 multiverse . this type of multiverse postulates that every universe in the multiverse shares the same physical constants ( e.g. the planck constant @xmath1 and the speed of light @xmath2 ) , while other types of multiverses suggest that the physical constants and even physical laws are different within different universes ( e.g. string theory landscape @xcite ) . the main argument for this kind of multiverse with different physical constants is that for different universe we would have different spontaneous symmetry breaking and thus different physics . since there are already several arguments against this type of multiverse ( see @xcite for instance ) , we will focus in this paper on the quilted multiverse where parallel universes share the same physical constants and same physical laws . from definition 1 we deduce that there are universes within the quilted multiverse that are not only close at a given time now ( i.e. similar in a sense that will be defined below ) but have been very close for a substantially large time interval . we claim in this work that the quilted multiverse is not consistent with basic thermodynamic assumptions . in the following section we discuss a thermodynamic arrow of time defined by the stability of entropy increase . in section [ sec3 ] we examine some characteristics of the quilted multiverse . in section [ sec4 ] we present an inconsistency of the quilted multiverse and the proposed thermodynamic arrow of time . section [ sec5 ] discusses an upper bound to the number of parallel universes in the quilted multiverse , and section [ sec6 ] concludes the paper . [ arrow_of_time ] time seems to incessantly `` flow '' in one direction , raising the ancient question : why ? this intensively discussed question can be answered in several ways by introducing seemingly different time arrows : thermodynamic , cosmological , gravitational , radiative , particle physics ( weak ) , quantum and others @xcite . we employ in this paper the cosmological arrow of time , which points in the direction of the universe s expansion . this choice implies that parallel universes with the same macrostate will have the same time . our main argument , however , will rely on thermodynamic stability under small perturbations which allows to define another crucial arrow of time - _ the macroscopic behavior of a large system is stable against perturbations as far as its future is concerned , but very unstable as far as its past is concerned . the positive direction of time is thus determined according the system s stability under small perturbations . indeed , performing a slight microscopic change in the system s past will not change , in general , its macrostate at future times , i.e. the system will end up its time evolution with the same high entropy macrostate . however , when propagating backwards in time , such a slight change in the system s future will have far - reaching consequences on its past @xcite . this is the key observation we shall utilize next . the difference in terms of stability between future and past stems from the fact that any perturbation of a microstate will tend to make it more typical of its macrostate and thus small perturbations will not interfere with ( forward in time ) typical evolution . backwards in time , however , the microstate will propagate towards a smaller phase space volume which is untypical of the macrostate . this difference in lyapunov stability was rigorously quantified , e.g. in @xcite . in this paper we will formally treat a universe parallel to ours , having at present time a similar macrostate or even the same macrostate , yet with a slightly different microstate as a perturbation . then we will try to apply the above reasoning . in what follows we quantify some microscopic and macroscopic properties of the quilted multiverse . we expect the upper bound on the number of parallel universes in the quilted multiverse to be a function of some distance measure @xmath3 , which quantifies the differences between a pair of universes described by their microstates @xmath4 . when @xmath3 is small we naturally expect the upper bound on the number of parallel universes to decrease because then there are fewer pairs of universes that satisfy @xmath5 for some small @xmath6 . the upper bound will be denoted by @xmath7 the value of @xmath8 is the number of all the microstates that satisfy @xmath9 therefore , @xmath8 is simply the sum of all indicator functions of the condition @xmath10 for each pair of indices @xmath11 thus @xmath8 can be written explicitly as follows : @xmath12 where @xmath13 is the indicator function . suppose we have three universes , @xmath14 and @xmath15 , such that they have the same bound on the differences between their states , that is@xmath16 let us now assume that the space in each universe is separated into @xmath17 three - dimensional volumes ( e.g. cubes ) , each described by some macroscopic parameter . we shall assume for concreteness that this parameter is entropy , i.e. entropies @xmath18 @xmath19 are assigned to these volumes . then , for the @xmath20 universe , we have the following set of entropies : @xmath21 we now wish to find the variation of the entropies between the pair of universes @xmath22 and @xmath23 to obtain this goal , let us now present two different approaches:1 ) we simply calculate the covariance of the entropies , and then compare these measures . we compute the covariances @xmath24 and @xmath25 @xmath26 now , in the case that the absolute value of the covariance @xmath27 is less than @xmath28 i.e.@xmath29 we say that universe @xmath30 is closer to universe @xmath31 than to universe @xmath32 \2 ) we take into account the `` extreme variation '' between the entropy values of the universes . suppose that the maximum difference between universes @xmath22 is greater than the distance between universes @xmath33 i.e.,@xmath34}{\sup}\left ( \left\vert s_{k}^{j}-s_{k}^{j}\right\vert \right ) < \underset{k\in\lbrack1,n]}{\sup}\left ( \left\vert s_{k}^{i}-s_{k}^{m}\right\vert \right ) .\ ] ] then we say that universes @xmath35 are closer than universes @xmath23 before we claim that the quilted multiverse is inconsistent with the instability of entropy decrease discussed in sec . [ arrow_of_time ] , let us define some mathematical symbols which will be useful later on . first , suppose that we have an infinite number of universes , denoted by@xmath36 where each universe @xmath37 has the microstate @xmath38 , and @xmath39 is the cosmological time . further , let us define a distance measure @xmath3 , which quantifies the difference between each microstate of the @xmath40th universe , @xmath41 and another state of the @xmath42th universe , @xmath43 at some time @xmath44@xmath45 for @xmath46 . according to this definition and the definition of the quilted multiverse , for every @xmath47 there exist at least two universes such that@xmath48 where @xmath49 $ ] is some long time interval comparable with the age of the universe . now , from the definition of the quilted multiverse , we know that every possible event will occur an infinite number of times . therefore , this model suggests that there exists a set @xmath50 containing all the possible pairs @xmath51 such that@xmath52 where @xmath53 , while the latter is the set of all possible pairs from the infinite set of universes ( [ u111 ] ) . we now show that ( [ w111 ] ) is not consistent with thermodynamic arrow of time defined in sec . [ arrow_of_time ] . first , notice that if we have a thermodynamic system @xmath54 with the quantum state @xmath55 at the cosmological time @xmath56 , there exist more than one possible quantum state @xmath57 that will produce @xmath58 in time @xmath59 i.e. there is no one - to - one correspondence between the previous state of the universe and the present one . in fact , there is a very large number of possible states . therefore , the backwards evolution in time ( presumably dictated by the same dynamical rules ) of two very close universes at present will result in two very far universes at the past ( see fig . [ fig1 ] ) , thus negating ( [ w111 ] ) . there is only a negligibly small probability that two close universes at present , will evolve backwards in time to two close universes in the past . this can be stated mathematically as follows : if@xmath60 then , it is not true in general that @xmath61 for an arbitrary @xmath62 hence , the claim that many universes approximately share both our present and past ( see @xcite for instance ) , is not consistent with our notion of a thermodynamic arrow of time . this is an outcome of the following fundamental fact discussed in sec . [ arrow_of_time ] : the time direction in which entropy grows is stable against minor changes at a given @xmath56 , while the opposite direction is highly unstable . furthermore , the entropy corresponding to our universe at present time is most likely to be the minimal one ; it will grow in both directions of time , allowing @xmath3 to be small only for very short time intervals . it could have been interesting to apply the above considerations to other kinds of multiverses . however , when the values of physical constants , and moreover , physical laws themselves , become different from those we know , the distance between our universe and others might be very large at present and hence stability is not expected to play a major role . on the other side of the scale , there is the many worlds interpretation ( also known as the quantum multiverse ) , but for overcoming the conceptual difficulties appearing in it we refer the reader to other considerations appearing elsewhere @xcite . the number of possible universes can be represented by the boltzmann relation between entropy @xmath63 and the set @xmath64 of possible microstates corresponding to the same macrostate , @xmath65 where @xmath66 is the boltzmann constant . then , given the entropy of the i - th universe , @xmath67 @xmath68 is@xmath69 assuming that during its 13.8 billion years of history the universe has reached a very large entropy @xmath70 , we have a huge set of possible microstates @xmath71 let us examine a pair of universes having at @xmath56 close states , i.e. @xmath72 , where @xmath73 , @xmath74 and @xmath75 . we claim that at arbitrary time @xmath76 they will most likely have @xmath77 , and the probability that @xmath78 will be close to zero . this follows from the fact that @xmath79 is now the backward - in - time evolution of @xmath80 , @xmath81 which is a set with very large number of possibilities , so that the probability @xmath82 will be zero . another way to see this inconsistency is to consider the point of minimal entropy during the lifetime of our universe . when picking at random another hypothetical universe having at present the same macrostate as our universe , it is most likely to have its minimal entropy at some other time other than ours ( most likely after ours ) . hence , the histories of the two universes can not be the same , unless we focus at present only on the zero measure of macrostates having their minimal entropy at exactly the same time as ours . we shall try to approach the problem from a different perspective now , beginning with some qualitative considerations . one should note two extreme distance scales . when two universes are exponentially close at some point in time , they may evolve backwards to exponentially close initial states , thereby creating no inconsistency . on the other hand , if two universes are far apart right now , stability ( which corresponds to small perturbation ) again plays no role . between these two contingent cases , lie the problematic distances to which instability considerations can be applied . this may pose a constraint on the distribution of universes within a multiverse - there might be many universes which are very far from each other , and many universes which are extremely close , but we do not expect too many universes to be intermediately close when we demand consistency over time . let us examine now a @xmath83-dimensional phase space , with some distance measure @xmath84 . let us suppose for simplicity that the phase space is discrete and focus on some large yet finite part of it . we can therefore think about this sector as a hypercube with a fine grid . a universe @xmath30 within this sector is represented at any moment as a point @xmath85 on the grid , where @xmath86/@xmath87 encapsulates the three position / momentum vectors , respectively , of each particle in this universe . we now start to gradually fill the hypercube with more and more points . we start by locating the points far away from each other , and thus the universes are very different . at some stage of this process , we will have to put the points closer to each other , a distance @xmath88 apart . we thus unavoidably created at least two universes that are too close to each other . too close , in the sense that one can be thought of as a small perturbation to the other , and then upon backward evolution in time , they would reach inconsistent states . to resolve this inconsistency we must pose a condition on the possible distance between the universes , and eventually on their density . in the case that@xmath89 for some large value of @xmath90 we find a consistent multiverse that does not violate the thermodynamical stability . of course , this multiverse is different than the quilted multiverse , and hence we call it the modified quilted multiverse . as opposed to the ordinary quilted multiverse , it might coexist with thermodynamic laws . we now apply similar arguments to those appearing at the end of the previous section . as @xmath91 @xmath92 are very large sets , the upper bound on the number of consistent parallel universes tends asymptotically to zero as @xmath93 tends to infinity , i.e.@xmath94 as happens with any discrete probability distribution approaching the continuum limit . multiverse theory has various models that describe different structures of the physical reality . one of these models is the quilted multiverse , which postulates that every possible event is occurring infinitely many times in nature , thus there are infinitely many universes resembling ours . at first glance , this model seems to be self - consistent . however , we have shown that this model negates basic thermodynamic principles . the difference between microstates in two close universes can not be @xmath95 small at each point in time , or even along a finite , sufficiently large time interval . therefore , any possible type of multiverse would better not assume such a relation between two universes . moreover , every universe must have its unique past and future in the sense that there is no other universe with the same , or even very close , state over a substantial part of its life time . we therefore have to limit ourselves only to those universes whose macrostates at present time evolve backwards to the same point in time of minimal entropy such as ours . these obviously reside in an exponentially small fraction of phase space and may evolve in a consistent way . we wish to thank avshalom c. elitzur and daniel rohrlich for helpful comments . y.a . acknowledges support of the israel science foundation grant no . 1311/14 , of the icore excellence center `` circle of light '' and of dip , the german - israeli project cooperation . was supported by erc adg nlst . thanks the john templeton foundation ( project i d 43297 ) and from the israel science foundation ( grant no . 1190/13 ) . the opinions expressed in this publication are those of the authors and do not necessarily reflect the views of any of these supporting foundations .

theoretical achievements , as well as much controversy , surround multiverse theory . various types of multiverses , with an increasing amount of complexity , were suggested and thoroughly discussed by now . while these types are very different , they all share the same basic idea our physical reality consists of more than just one universe . each universe within a possibly huge multiverse might be slightly or even very different from the others . the quilted multiverse is one of these types , whose uniqueness arises from the postulate that every possible event will occur infinitely many times in infinitely many universes . in this paper we show that the quilted multiverse is not self - consistent due to the instability of entropy decrease under small perturbations . we therefore propose a modified version of the quilted multiverse which might overcome this shortcoming . it includes only those universes where the minimal entropy occurs at the same instant of ( cosmological ) time . only these universes whose initial conditions are fine - tuned within a small phase - space region would evolve consistently to form their close states at present . _ keywords : multiverse theory , quilted multiverse , arrow of time , stability ; _

SECTION 1. SHORT TITLE. This Act may be cited as the ``Medical Device Regulatory Improvement Act''. SEC. 2. CLARIFICATION OF LEAST BURDENSOME. (a) Premarket Approval.--Section 513(a)(3)(D) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 360c(a)(3)(D)) is amended-- (1) by redesignating clause (iii) as clause (iv); and (2) by inserting after clause (ii) the following: ``(iii) In carrying out clause (ii), the Secretary-- ``(I) shall not request information unrelated or irrelevant to a demonstration of reasonable assurance of device safety and effectiveness; ``(II) shall consider alternative approaches to evaluating device safety and effectiveness in order to reduce the time, effort, and cost of reaching proper resolution of the issue; ``(III) shall use all reasonable mechanisms to lessen review times and render regulatory decisions; ``(IV) shall determine whether pre-clinical data, such as well-designed bench and animal testing, can meet the statutory threshold for approval; and ``(V) if clinical data are needed, shall utilize, whenever practicable, alternatives to randomized, controlled clinical trials, such as the use of surrogate endpoints.''. (b) Substantial Equivalence Determination.--Section 513(i)(1)(D) of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 360c(i)(1)(D)) is amended-- (1) by striking ``(D) Whenever'' and inserting ``(D)(i) Whenever''; and (2) by adding at the end the following: ``(ii) In carrying out clause (i), the Secretary-- ``(I) shall focus on whether the device has the same intended use as the predicate device and is as safe and effective as a legally marketed device; ``(II) shall not request or accept information unrelated or irrelevant to the substantial equivalence evaluation; ``(III) shall review the labeling of the device to assess the intended use of the device, and shall not evaluate issues that do not present a major impact on the intended use as set forth in the labeling; ``(IV) shall consider alternative approaches to evaluating substantial equivalence in order to reduce the time, effort, and cost of reaching proper resolution of the issue; and ``(V) shall use all reasonable mechanisms to lessen review times and render regulatory decisions.''. SEC. 3. CONFLICTS OF INTEREST. Section 712 of the Federal Food, Drug, and Cosmetic Act (21 U.S.C. 379d-1) is amended to read as follows: ``SEC. 712. CONFLICTS OF INTEREST. ``Except as otherwise provided in this Act, each advisory committee under the Federal Advisory Committee Act that provides advice or recommendations to the Secretary regarding activities of the Food and Drug Administration is subject to the provisions in such Act and the members of each such committee are subject to the provisions regarding Federal employees and special Government employees, as applicable, in title I of the Ethics in Government Act of 1978 and section 208 of title 18, United States Code.''. SEC. 4. MANAGEMENT AND INNOVATION REVIEW. (a) In General.--Not later than 60 days after the date of enactment of this Act, the Secretary of Health and Human Services (referred to in this section as the ``Secretary'') shall enter into a contract with an eligible entity to carry out the activities described in subsection (c). (b) Eligible Entity.--To be eligible to enter into a contract with the Secretary under subsection (a), an entity shall-- (1) be an entity with experience in evaluating the management and operating structure of large organizations; and (2) submit to the Secretary an application at such time, in such manner, and containing such information as the Secretary may require. (c) Activities.--The entity with which the Secretary enters into the contract under subsection (a) shall, pursuant to such contract, conduct an extensive review of the management and regulatory processes at the Center for Devices and Radiological Health of the Food and Drug Administration to ensure any actions carried out by such Center take into consideration the potential impacts on innovation with respect to medical devices and other products regulated by such Center. (d) Report.--Not later than 1 year after the date that the Secretary enters into the contract with the eligible entity under subsection (a), such entity shall submit to Congress and the Secretary a report that describes the findings and recommendations of such entity based on the review conducted under subsection (c). (e) Funding.--To carry out this section, the Secretary shall use funds otherwise available for the operation of the Office of the Secretary.

Medical Device Regulatory Improvement Act - Amends the Federal Food, Drug, and Cosmetic Act to require the Secretary of Health and Human Services (HHS), in determining the least burdensome appropriate means of evaluating device effectiveness, to: (1) not request information unrelated or irrelevant to demonstration of reasonable assurance of device safety and effectiveness; (2) consider alternative approaches to evaluating device safety and effectiveness; (3) use all reasonable mechanisms to lessen review times and render regulatory decisions; (4) determine whether pre-clinical data can meet the statutory threshold for approval; and (5) utilize, whenever practicable, alternatives to randomized, controlled clinical trials if clinical data are needed. Requires the Secretary, in determining the least burdensome means of determining substantial equivalence, to: (1) focus on whether the device has the same intended use as the predicate device and is as safe and effective as a legally marketed device, (2) not request or accept information unrelated or irrelevant to the substantial equivalence evaluation, (3) review the labeling of the device to assess the intended use of the device and not evaluate issues that do not present a major impact on the intended use as set forth in the labeling, (4) consider alternative approaches to evaluating substantial equivalence, and (5) use all reasonable mechanisms to lessen review times and render regulatory decisions. Repeals conflict-of-interest provisions that are specific to the Food and Drug Administration (FDA) and provides for the continued applicability of conflict-of-interest provisions otherwise applicable to advisory committees, federal employees, and special government employees. Requires the Secretary to contract with an eligible entity for a review of the management and regulatory processes at the Center for Devices and Radiological Health.

Ray Price, one of country music's most beloved voices, died at home Monday afternoon at the age of 87, his family said through a spokesman. Price had been hospitalized in Texas recently, and had been fighting a battle against pancreatic cancer since late last year. On Thursday (Dec. 12), the singer entered hospice care, leaving a message to fans: "I am at peace. I love Jesus. I'm going to be just fine. Don't worry about me. I'll see you again one day." Country radio veteran Bill Mack, who has been acting as a spokesman for the family in recent days, relayed on Facebook that Price's wife Janie called him to confirm the singer had died. "Ray Price left for heaven at 4:43 PM Central Time," he writes. "He went in perfect peace." The AP is reporting that Billie Perryman, the wife of family friend Tom Perryman, also confirmed his death. Earlier, on Sunday, multiple news sources posted that Price had died, with many splashing the headline across home pages and social media. The story snowballed after Price's son, Cliff, wrote on Facebook that he had "heard" his father had passed. Later, he took the post down and said he had been "deceived by some cruel people." Price's musical career spanned some 65 years, and his recordings stand among the most versatile in the format's history -- ranging from honky-tonk to western swing to a more lush sound in the 1960s that brought him some of the biggest hits of his career. Watch: Ray Price Classics He was born January 12, 1926 in Perryville, Texas. Upon turning 18, Price enlisted in the Marines, where he stayed for two years. He began performing on Abilene radio station KRBC in 1948, and moved on to the Big D Jamboree in Dallas the next year. The singer would move to Nashville not too long after signing a contract with Columbia Records. His first five releases failed to dent the charts, but he would make his debut in 1952 with "Talk To Your Heart," which would climb all the way to No. 3 on Billboard's Hot Country Songs. Upon his move to Music City, Price lived with Hank Williams for a time between his marriages to Audrey and Billie Jean. Scoring a second hit with "Don't Let The Stars Get In Your Eyes," Price's star was on the rise. He formed his band, the Cherokee Cowboys, in 1953. The names of the future artists that would be included in the lineup reads like a Who's who, including Roger Miller, Willie Nelson, Darrell McCall, and Johnny Paycheck. It was at this point, that Price began to develop a signature sound – with the 4/4 shuffle being an integral trademark. Some of his biggest hits of the era included "City Lights," "Crazy Arms," and 1959's "Heartaches By The Number," a Harlan Howard-written gem that many consider to be the best country record of that era. Ray Price Had 'Crazy' Run on Billboard Charts As the 1960s dawned, Price continued to dominate the charts with singles such as "Pride," "Walk Me To The Door," and "Burning Memories." He also was the first artist to record "Make The World Go Away," earning a No. 2 hit with the song two years before Eddy Arnold recorded his version. Though the hits continued for Price, he was feeling somewhat restless musically. He hadn't had a number one hit since 1959, and artists such as Arnold were enjoying success with a more lush style -- known as "The Nashville Sound." So, Price began to tinker with his sound. The first major example of this was his recording of "Danny Boy" in 1967. Though some critics took aim at the heavy use of strings, the record hit the top ten -- and earned him his second biggest ranking on the Hot 100 at No. 60. The next few years saw him continue to refine that sound, with records such as "I'm Still Not Over You" and "She Wears My Ring" being among his biggest chart hits of the latter part of the decade. By 1970, the singer found the perfect record for his new style -- from a new singer / songwriter in town named Kris Kristofferson. Price's recording of "For The Good Times" became his first chart-topper in eleven years, and just missed the top ten on the pop charts, as well. The first half of the decade saw some of his most memorable -- and successful work. "I Won't Mention It Again," "The Lonesomest Lonesome," and "She's Got To Be A Saint" all performed well on the chart, with his final Billboard number one coming in 1973 with "You're The Best Thing That Ever Happened To Me." Price's stint with Columbia came to an end the next year, with his signing to Myrrh Records. The hits continued for Price, albeit at a slower rate. Two of his first singles for his new label home, "Like Old Times Again," and "Roses And Love Songs," were top-five hits in 1974-75, but his records were relegated to top-40 status more and more throughout the rest of the 70s, as he switched to ABC / Dot, and then to Fred Foster and Monument Records. Things changed swiftly as the 1980s dawned. He moved to Dimension Records, and returned to the top ten with "It Don't Hurt Me Half As Bad" and "Diamond In The Stars" in 1981. He teamed with former band member Willie Nelson for the gold-selling "San Antonio Rose" in 1980 -- earning a No. 3 hit with a cover of Bob Wills' "Faded Love." He switched labels once again, this time to Step One -- where he remained until the early 1990s. His last charted single came in 1989 with "Love Me Down To Size," which peaked at No.79. Though his hit making days on the charts were over by the 1990s, Price continued to record and tour. He was inducted into the Country Music Hall of Fame in 1996, and performed at venues across the United States and abroad. He teamed up with Nelson and Merle Haggard for the 2007 disc "Last Of The Breed." Released on Lost Highway, the album gave Price his final bow on the charts as it peaked at No. 7 on the Country Albums chart. All along, the singer remained a crowd favorite. He still recorded from time to time, appearing with Rascal Flatts on the 2011 Anna Wilson CD "Countrypolitan Duets," reprising "You're The Best Thing That Ever Happened To Me." Diagnosed with pancreatic cancer in late 2012, the singer valiantly fought the disease -- even recording a new album in the process. That disc, tentatively titled "Love Songs In Nashville," is expected be released in 2014. He even kept his sense of humor along the way. Price told the San Antonio Express-News concerning his illness. "The doctor said that every man will get cancer if he lives to be old enough. I don't know why I got it -- I ain't old!" Ray Price was one of country music's last living links to the days of Hank Williams and 78 RPM records. Whether it be a shuffle, a Bob Wills swing tune, or a sentimental love song with a string section, he did it all -- and did it all very well. He will be missed, but his music will endure. ||||| Country Music Hall of Fame member Ray Price , one of country's prime hitmakers from the 1950s through the 1970s, died Monday (Dec. 16) at his home in Mount Pleasant, Texas, following a battle with pancreatic cancer.Whether moaning honky-tonk blues or purring an intimate love song, Ray Price set dauntingly high standards. To appreciate his musical reach, one had only to listen to his first hit, "Talk to Your Heart" (1952), move on to the earnest shuffle of "City Lights" (1958) and then consider his sonorous, lavishly orchestrated "For the Good Times" (1970).Although Hank Williams , his friend and one-time roommate, was an early vocal influence, Price was marked just as deeply by the great crooners of his youth -- Bing Crosby, Frank Sinatra, Nat King Cole and Perry Como.Born Jan. 12, 1926, in Perryville, Texas, Noble Ray Price came of age in a world far less musically fragmented than it is now.Radio was still the exciting media then, and even small stations boasted an inspiring mixture of locally-grown and network-carried sounds -- everything from rural string bands to romantic pop warblers to symphony orchestras. Paving the way for Price in country music were the likes of Eddy Arnold Red Foley and Tennessee Ernie Ford , middle-of-the-road crooners who regularly commuted between hillbilly and mainstream minstrelsy.Price's musical apprenticeship was brief. After serving in the Marines from 1944 to 1946, he enrolled at North Texas Agricultural College, intending to become a veterinarian. However, he began performing around campus and eventually dropped out of school. In 1948, he made his radio debut in Abilene, Texas, where he began billing himself as the Cherokee Cowboy.The next year, he progressed to the Big D Jamboree in Dallas. After recording briefly for Dallas-based Bullet Records, Price signed to Columbia in 1951. While still in Texas, Price fell under the artistic sway of Hank Williams. In Nashville, the two became close friends and, for a while, roommates. After Williams died, Price temporarily hired his band, the Drifting Cowboys. Later editions of Price's stellar bands included Roger Miller Willie Nelson and Johnny Paycheck To the degree that Price mimicked Williams' style, he did it well. But he soon moved beyond it. The song that gave Price his own solid musical presence came in 1956. Sweeping in on a wave of fiddle and tears, "Crazy Arms" shot to No. 1 (Price's first of eight visits to the top) and stayed there for 20 weeks. The next year, "My Shoes Keep Walking Back to You" crossed over to the pop charts. He would have nine more pop crossovers, the loftiest being "For the Good Times," which went to No. 11 in 1971.Price notched his second-most durable hit in 1958 with "City Lights," a 13-week chart-topper. Although he routinely achieved Top 5 and Top 10 status throughout the 1960s, he did not reach No. 1 again during that decade. But as early as 1965, with "The Other Woman" and "Don't You Ever Get Tired of Hurting Me," Price showed he was already into his smooth ballad stage, a point he drove home in 1967 with a lush and dramatic version of "Danny Boy.""For the Good Times" re-energized Price's career. Besides its crossover success, it earned him a Grammy for best country vocal performance and set him up for three more No. 1 singles: "I Won't Mention It Again" (1971), "She's Got to Be a Saint" (1972) and "You're the Best Thing That Ever Happened to Me" (1973). His last of 109 charted country singles came in 1989 with "Love Me Down to Size."Price was elected to the Country Music Hall of Fame in 1996 at the age of 70. Still elegant and in superb voice, he greeted the millennial year of 2000 with the primarily pop album,, a duets album with Nelson, was released in 2003.In 2007, Price, Nelson and Merle Haggard released, a two-disc project for Lost Highway Records, and conducted a brief tour under the same name.During a November 2012 interview with thenewspaper, Price revealed he had be diagnosed with pancreatic cancer. At the time, he acknowledged he had been receiving chemotherapy for six months. The cancer was discovered while his gallbladder was being removed after a gall stone attack.He was hospitalized several times during the past year, including being admitted in October for treatment of sepsis, a complication of an infection when chemicals released into the bloodstream to fight the infection cause inflammation throughout the body.Price was dismissed from the hospital and spent Thanksgiving Day at home. He was readmitted to the intensive care unit of East Texas Medical Center in Tyler, Texas, on Dec. 2.Price's family announced on Thursday (Dec. 12) that Price had opted for home hospice care rather than seek further treatment.

– A link to the golden days of Hank Williams and 78rpm records is gone: Legendary country singer Ray Price died today at home in Texas at age 87, Billboard reports. He had battled pancreatic cancer since last year. "I am at peace. I love Jesus," he said in a message to fans this week. "I'm going to be just fine. Don't worry about me. I'll see you again one day." His career lasted some 65 years, including styles like honky-tonk, western swing, and the the lush "Nashville sound" of the 1960s and 70s. Born in 1926 in Texas, Price started off by singing at a radio station at age 18. Relocating to Nashville, he scored a No. 3 country hit with "Talk to Your Heart" in 1952, then moved to Music City and confirmed his stardom with "Don't Let The Stars Get In Your Eyes." He formed the Cherokee Boys—which included future stars like Roger Miller, Willie Nelson, and Darrell McCall—and created a signature sound with a 4/4 shuffle. In the 1960s he turned to a lush style with strings, releasing hits like "Danny Boy" and "I'm Still Not Over You." He was elected to the Country Music Hall of Fame in 1997 and kept recording in his later years, CMT notes, even after his cancer diagnosis last year. "Whether it be a shuffle, a Bob Wills swing tune, or a sentimental love song with a string section, he did it all—and did it all very well," reports Billboard. "He will be missed, but his music will endure."

tumours were initiated by intratracheal infection of mice with a lentiviral vector expressing cre - recombinase10 . cell lines were created by enzymatic and mechanical dissociation of individual lung tumours and metastases harvested from mice 8 - 14 months after tumour initiation . rna was extracted using trizol , analyzed for rna integrity , and prepared with affymetrix genechip wt sense target labelling and control reagents kits , followed by hybridization to affymetrix genechip mouse exon 1.0 st arrays . western blotting used standard methods and antibodies to nkx2 - 1 ( epitomics , inc ) , hmga2 ( biocheck , inc ) , and hsp90 ( bd transduction laboratories ) as a loading control . immunohistochemistry was performed on formalin - fixed , paraffin - embedded 4m sections using the abc vectastain kit ( vector laboratories ) with antibodies described above . nkx2 - 1 was stably knocked - down with a plko - based lentiviral vector ( openbiosystems / trc ) . mscv - puro retroviral vectors were used for stable expression of nkx2 - 1 and nkx2 - 1 * ( created with 4 silent mutations using quikchange lightning site - directed mutagenesis ( stratagene ) . hmga2 was stably knocked - down with an mscv - hygro retroviral vector . for intravenous transplantation 10 cells resuspended in 200l pbs tumours were initiated by intratracheal infection of mice with a lentiviral vector expressing cre - recombinase10 . cell lines were created by enzymatic and mechanical dissociation of individual lung tumours and metastases harvested from mice 8 - 14 months after tumour initiation . rna was extracted using trizol , analyzed for rna integrity , and prepared with affymetrix genechip wt sense target labelling and control reagents kits , followed by hybridization to affymetrix genechip mouse exon 1.0 st arrays . western blotting used standard methods and antibodies to nkx2 - 1 ( epitomics , inc ) , hmga2 ( biocheck , inc ) , and hsp90 ( bd transduction laboratories ) as a loading control . immunohistochemistry was performed on formalin - fixed , paraffin - embedded 4m sections using the abc vectastain kit ( vector laboratories ) with antibodies described above . nkx2 - 1 was stably knocked - down with a plko - based lentiviral vector ( openbiosystems / trc ) . mscv - puro retroviral vectors were used for stable expression of nkx2 - 1 and nkx2 - 1 * ( created with 4 silent mutations using quikchange lightning site - directed mutagenesis ( stratagene ) . for intravenous transplantation 10 cells resuspended in 200l pbs were injected into the lateral tail vein . for intrasplenic transplantation

despite the high prevalence and poor outcome of patients with metastatic lung cancer , the mechanisms of tumour progression and metastasis remain largely uncharacterized . we modelled human lung adenocarcinoma , which frequently harbours activating point mutations in kras1 and inactivation of the p53-pathway2 , using conditional alleles in mice35 . lentiviral - mediated somatic activation of oncogenic kras and deletion of p53 in the lung epithelial cells of kraslsl - g12d/+;p53flox / flox mice initiates lung adenocarcinoma development4 . although tumours are initiated synchronously by defined genetic alterations , only a subset become malignant , suggesting that disease progression requires additional alterations . identification of the lentiviral integration sites allowed us to distinguish metastatic from non - metastatic tumours and determine the gene expression alterations that distinguish these tumour types . cross - species analysis identified the nk-2 related homeobox transcription factor nkx2 - 1 ( ttf-1/titf1 ) as a candidate suppressor of malignant progression . in this mouse model , nkx2 - 1-negativity is pathognomonic of high - grade poorly differentiated tumours . gain - and loss - of - function experiments in cells derived from metastatic and non - metastatic tumours demonstrated that nkx2 - 1 controls tumour differentiation and limits metastatic potential in vivo . interrogation of nkx2 - 1 regulated genes , analysis of tumours at defined developmental stages , and functional complementation experiments indicate that nkx2 - 1 constrains tumours in part by repressing the embryonically - restricted chromatin regulator hmga2 . while focal amplification of nkx2 - 1 in a fraction of human lung adenocarcinomas has focused attention on its oncogenic function69 , our data specifically link nkx2 - 1 downregulation to loss of differentiation , enhanced tumour seeding ability , and increased metastatic proclivity . thus , the oncogenic and suppressive functions of nkx2 - 1 in the same tumour type substantiate its role as a dual function lineage factor .

graphene is attracting considerable attention due to its unusual electronic properties including : large mean free path , relativistic " dispersion of the low - lying electron states , and valley " degeneracy @xcite . these remarkable features made many researchers hope that some day graphene mesoscopic structures might revolutionise nanoscience . thus , a substantial amount of effort has been invested investigating graphene devices , such as quantum dots @xcite , bilayer structures @xcite , and nanoribbons @xcite . studying the physics of nanoribbons , a certain discrepancy between results of first - principle calculations @xcite , experiments @xcite , and single - electron approximations @xcite was stumbled upon : whereas the single - electron approximation predicts that , depending on its width , an armchair nanoribbon could be either semiconducting or metallic , both experiments and first - principle calculations suggest that it is always semiconducting : a nanoribbon of any width @xmath0 has gap at the fermi level ; the magnitude of the gap scales as @xmath1 . two different mechanisms were proposed to explain this disagreement . according to the first mechanism the gap is due to electron - electron interactions @xcite . at zero doping the interaction induces a charge gap . the physics here is similar to the mott transition in the hubbard model at half filling . if the coulomb coupling constant @xmath2 is large ( @xmath3 , where @xmath4 is the carbon - carbon hopping amplitude ) , the gap scales as @xmath2 . if @xmath2 is small , the gap vanishes faster than @xmath2 . since @xmath5 , such mechanism is consistent with the observed scaling @xmath6 for small @xmath0 only . for large @xmath0 the gap decays faster than @xmath1 . another way to explain the gap was outlined in @xcite , where first - principle computations have shown that the length of the carbon - carbon bonds at the hydrogen - passivated edge is shorter than the length of the bonds in the bulk . due to this , the hopping amplitude across the bonds dangling from the nanoribbon edge ( @xmath7 ) differs from @xmath4 : @xmath8 , @xmath9 ( see fig.[edge - h ] where the short bonds are shown in bold ) . because of @xmath10 , the nanoribbon s hamiltonian acquires an additional term . it couples states with the same momentum above and below the fermi energy ; such coupling opens a gap in the electronic spectrum . assuming that @xmath10 depends mainly on the chemical properties of the edge ( e.g. , nature of the passivating radical or absence thereof ) , one can demonstrate that the effective strength of this coupling is inversely proportional to @xmath0 . thus , the relation @xmath6 is recovered . in addition to these mechanisms , other instabilities can be present as well . which mechanism of gap generation dominates depends on a variety of factors , such as electrostatic screening by the gate electrode , mechanical forces applied to the nanoribbon , edge passivation , etc . in this paper we will study in detail the second mechanism described above . we will show that the armchair nanoribbon is unstable toward the deformations of the edge bonds . specifically , we prove the following : if the radical passivating the edge is carefully picked ( to ensure that it does not modify the hopping at the edges : @xmath11 ) , then the total energy of the nanoribbon would become a decreasing function of the edge bond deformation . in other words , spontaneous deformations of the dangling bonds are favourable for they decrease the total nanoribbon energy . such deformations make @xmath7 unequal to @xmath4 . to understand the physics behind this , it is convenient to describe such deformation using a real one - component ( ising - like ) order parameter @xmath10 . at the mean - field level we can state that the energy of the deformed bonds is increased by the amount @xmath12 , while the energy of the conducting electrons decreases by the amount @xmath13 . since @xmath14 , the total energy , @xmath15 , always has a minimum at not - zero @xmath16 . it is useful to extend the analogy between our system and the ising model further . notice that our chemical forces deforming the edge bonds are similar to the magnetic field " coupled to the order parameter ( the magnetisation " ) in the ising model . thus , it is natural to refer to these chemical forces as the edge field " . in practice , we have very limited control over the magnitude of the edge field " : it is very difficult to select the radical attached to the nanoribbon s edge to guarantee that @xmath17 . using the analogy between our nanoribbon and the ising model , we conclude that , since the field " is always switched on , our system is always away from the critical regime . yet even a system with a strong edge field " may be tuned to criticality by disordering the field " . this way , the disorder may be used as a tool to control spectral properties of nanoribbons . disorder can be introduced by passivating the edges by radicals of two different types , randomly distributed along the length of the nanoribbon . the hopping amplitude at the edge @xmath7 would become a function of the coordinate along the ribbon : @xmath18 where @xmath19 is independent of @xmath20 , while @xmath21 is the disordered part . in such system the electronic spectrum is very sensitive to the relative strengths of @xmath19 and @xmath22 : when the disorder is weak , the spectrum has ( pseudo)gap due to non - zero @xmath19 term ; when @xmath23 , the pseudogap closes , and the nanoribbon is in the disorder - dominated regime . the crossover between these two regimes can be observed with the help of transport measurements . in a nanoribbon whose length @xmath24 is thermodynamically large , the conductance vanishes exponentially in both regimes : when there is no disorder , the finite gap removes density of states from the fermi level ; when there is disorder , the wave functions are localized . thus , for very long nanoribbons the conductance is suppressed regardless of the disorder strength . the situation is different for a mesoscopic sample . note that the localization is a weaker phenomenon than the gap opening in the sense that the inverse of the localization length @xmath25 is the second order in the disorder strength : @xmath26 , while the inverse of the length scale @xmath27 charachterizing the gap size is linear in @xmath10 : @xmath28 . that is , a longer nanoribbon is required to observe a well - developed localization . therefore , it is possible to choose @xmath24 sufficiently short to have no localization features at any disorder , and yet long enough to observe the spectral gap when the disorder is low . thus , when the disorder is absent , the low - temperature conductance of the sample is exponentially suppressed due to the gap ; otherwise , the conductance is finite down to the lowest temperatures . therefore , the disorder effectively closes the gap . the paper is organized as follows . in sect . [ model ] we derive the model for a nanoribbon with deformed edges . the instability of the nanoribbon toward the deformation of the edge bonds is discussed in sect . [ instability ] . in sect . [ disorder ] we investigate the effect of disorder on the transport properties of the nanoribbon . [ conclusions ] presents the conclusions . in this section we will obtain the hamiltonian for a graphene nanoribbon with deformed edge bonds . our derivation relies on basic facts of the graphene physics which are discussed in ref . @xcite . for completeness , in this subsection we quickly rederive basic single - electron properties of a graphene sheet . this gives us an opportunity to introduce notation we will need below . it is common to describe a graphene sample in terms of a tight - binding model on a honeycomb lattice . such lattice can be split into two sublattices , denoted by @xmath29 and @xmath30 . the hamiltonian of a graphene sheet is given by : @xmath31 where @xmath32 runs over sublattice @xmath29 . the vectors @xmath33 ( @xmath34 ) connect the nearest neighbours . these are ( see fig . [ ribbon ] ) : @xmath35 the symbol @xmath36 denotes the carbon - carbon bond length , which is about 1.4 . the corresponding schrdinger equation can be written as : @xmath37 where @xmath38 ( @xmath39 ) denotes the wave function value at the site @xmath32 ( at the site @xmath40 ) of sublattice @xmath29 ( sublattice @xmath30 ) . the primitive vectors of the honeycomb lattice are : @xmath41 they connect nearest neighbours on the same sublattice . since the primitive cell contains two atoms , it is convenient to define a two - component ( spinor ) wave function : @xmath42 with this notation the action of @xmath43 on spinor @xmath44 can be expressed as : @xmath45.\end{aligned}\ ] ] for every @xmath46 there are two eigenstates : @xmath47 with the eigenvalues : @xmath48 the states with negative ( positive ) energy are filled ( empty ) at @xmath49 . the quantity @xmath50 vanishes at six points within the brillouin zone ( see fig . [ bz ] ) : @xmath51 and @xmath52 . these are the locations of the famous dirac cones of graphene . these six cones can be split into two equivalence classes : the locations of any two cones inside the same equivalence class differ by a reciprocal lattice vector . thus , we do not need all six of them . two inequivalent cones are sufficient : @xmath53 consider now the electron states of the armchair nanoribbon ( see fig . [ ribbon ] ) . such nanoribbon is defined by the condition @xmath54 . the width of the nanoribbon @xmath0 is a multiple of @xmath55 : @xmath56 where @xmath57 is an integer . the schrdinger equation for the edge sites differs from eqs . ( [ sch_a ] ) and ( [ sch_b ] ) . for sites on the upper edge ( @xmath58 ) we can write : @xmath59 note the absence of the summation over the lattice vectors in the right - hand side of these equations . this boundary condition is called free . it can be easily generalized for the lower edge . an armchair nanoribbon is invariant under a shift over @xmath60 along the @xmath20-axis . thus , a @xmath60 long nanoribbon segment can be thought of as a nanoribbon unit cell . there are @xmath61 graphene unit cells in a nanoribbon unit cell . the nanoribbon brillouin zone is : @xmath62 now we assume that all carbon - carbon bonds of our system have the same hopping amplitude @xmath4 ( that is , the deformation of the edge bonds is absent ) . the wave function @xmath63 satisfies the free boundary conditions eqs . ( [ sch_a_edge ] ) and ( [ sch_b_edge ] ) at @xmath64 and similar conditions at @xmath65 . it is not convenient , however , to work with such boundary conditions directly . fortunately , if we add an additional row of lattice sites at each edge and demand that the wave function vanishes at these auxiliary sites ( see fig . [ ribbon ] ) , then the wave function at the real edge sites satisfies the free boundary condition . in other words , our _ free _ boundary condition problem for a nanoribbon of width @xmath0 is equivalent to the _ zero _ boundary condition problem for a nanoribbon of width @xmath66 . thus , we want : @xmath67 the eigenfunction of the hamiltonian @xmath43 , eq . ( [ h ] ) , satisfying eq . ( [ bc ] ) can be written as follows : @xmath68 where @xmath69 are complex coefficients . note that this eigenfunction has a well - defined value of the momentum @xmath70 along the @xmath20-axis , but not of the momentum @xmath71 along the @xmath72-axis , since our system has no translational invariance in the @xmath72-direction . the values of @xmath71 and @xmath69 in eq . ( [ nanoribbon_wf ] ) must be chosen to satisfy eq . ( [ bc ] ) . since the spinor @xmath73 remains the same when the sign of @xmath71 changes , we derive : @xmath74 = 0 , \\ c_1 = - { \exp } \left ( { -i \sqrt{3 } k_y a_0 } \right ) c_2.\end{aligned}\ ] ] we then obtain the following quantization condition : @xmath75 where @xmath76 is an integer . thus , the nanoribbon spectrum @xmath77 consists of a set of one - dimensional branches labelled by an integer , @xmath76 . using the above results it is possible to construct explicitly the nanoribbon eigenfunction however , for our purposes it is more convenient to define an effective hamiltonian for a given branch . let us look for a nanoribbon hamiltonian eigenfunction in the form : @xmath78,\end{aligned}\ ] ] where the spinor @xmath79 is defined as : @xmath80 in this equation @xmath81 , and @xmath82 is an integer . substituting the expression for @xmath83 into the schrdinger equations ( [ sch_a ] ) and ( [ sch_b ] ) , we obtain : @xmath84.\end{aligned}\ ] ] in @xmath85-space this equation has the form @xmath86 , where the effective hamiltonian for branch @xmath76 is : @xmath87 . % % % % % % % % % % % % % % % % % % % % % % % % % % % % \label{h_eff_k}%%%%%%%%%%%%% % % % % % % % % % % % % % % % % % % % % % % % % % % % % \end{aligned}\ ] ] this hamiltonian possesses accidental symmetry : the nanoribbon remains unchanged under a shift by @xmath60 along the @xmath20-axis , yet the effective hamiltonian @xmath88 is invariant under a shift by @xmath89 . that is , the effective symmetry of the hamiltonian is higher than the geometric symmetry of the underlying system . this symmetry is destroyed when the edge bonds are deformed . however , since in this paper we are interested in the low - energy properties of the system , this peculiarity will play no role in what follows . within our labelling scheme the same branch may appear under different values of index @xmath76 . obviously , @xmath76 and @xmath90 correspond to the same branch . furthermore , if @xmath91 , @xmath92 , and @xmath93 , both @xmath76 and @xmath94 define the same branch . this means that there are @xmath61 independent branches : @xmath95 this is precisely the number of graphene unit cells in a nanoribbon unit cell . the hamiltonian of the nanoribbon is the direct sum of the @xmath96 s : @xmath97 the dispersion associated with a specific branch is given by eq . ( [ graphene_energy ] ) , where @xmath71 is fixed by eq . ( [ quantization ] ) . in other words , a branch samples the function @xmath50 along the line @xmath98 let us now find out under which circumstances the gapless branches appear . [ @xmath76 satisfies eq . ( [ band_index ] ) ] is gapless if the complex equation ( a system of two real equations ) @xmath99 has a root satisfying eq.([nanoribbon_bz ] ) . solving this system of trigonometric equations one can prove that a zero eigenvalue at @xmath100 appears when @xmath101 . the latter condition is fulfilled if the argument of the cosine is @xmath102 . this is possible provided that @xmath103 , where : @xmath104 and @xmath105 is an integer . in other words , the gapless branch is present only when @xmath106 is divisible by 3 . this agrees with the conclusions of ref . @xcite , where the single - electron calculations for a nanoribbon with no edge deformation was performed . the effective hamiltonian for the gapless branch is : @xmath107 , \\ \varepsilon_{k_x \pm } = \pm 2 t \left| \sin \left ( \frac{3}{4 } k_x a_0 \right ) \right|.\end{aligned}\ ] ] the gapless branch is characterized by @xmath108 . since @xmath109 is the location of the cone @xmath110 ( [ k ] ) ] , one can say that the gapless branch is found in the nanoribbon spectrum only when the quantization condition eq . ( [ quantization ] ) allows for existence of the branch passing through the cone @xmath110 . in this section we show that the electronic branch , which appears to be gapless according to the calculations reported above , is , in fact , unstable toward the spontaneous opening of the gap . we prove that the edge bond deformation is one possible instability leading to the gap generation . to establish such an instability we need to calculate the ground state energy of the nanoribbon with edge bonds deformed as shown on fig . [ edge - h ] . to achieve this aim we first determine how the edge deformation affects the hamiltonian of the gapless branch . we denote by @xmath111 the contribution to the hamiltonian due to edge deformation . the subscript ` l ' ( ` h ' ) corresponds to a bond deformation at the lower ( higher ) edge of the nanoribbon ( see fig . [ ribbon ] ) . the matrix element of @xmath112 between two states is equal to : @xmath113 the summation in this formula runs over the deformed bonds at the lower edge : @xmath114 . substituting in eq . ( [ matrix_element ] ) wave functions consistent with eq . ( [ bc ] ) , i.e. , @xmath115 \\ \nonumber = \psi { \rm e}^{- i k_x x } \sin \left ( \frac{4 \pi y}{3 \sqrt{3 } a_0 } + \frac{2 \pi } { 3 } \right),\end{aligned}\ ] ] we find : @xmath116.\end{aligned}\ ] ] therefore , for @xmath117 satisfying eq.([nanoribbon_bz ] ) , hamiltonian @xmath112 equals to : @xmath118 where @xmath119 in the denominator comes from the wave function normalization . it is trivial to demonstrate that @xmath120 . superficially , this identity appears to be incorrect : clearly , there should be a difference between the lower and higher edges at the level of the hamiltonian . however , we must remember that the expression eq . ( [ h_l ] ) is not the total hamiltonian @xmath112 ( which is indeed different from @xmath121 ) , but rather its projection on the subspace spanned by a specific branch . these projections can not discriminate between the lower and the higher edge . the total edge hamiltonian @xmath122 is equal to twice @xmath112 . thus , the hamiltonian for a nanoribbon with the deformed edge bonds is : @xmath123 whose dispersion is given by @xmath124 , where : @xmath125 which has a gap @xmath126 . since our formerly gapless branch now acquired the gap , it might be confusing to refer to such branch as ` gapless ' . instead , we will now call it ` @xmath105 branch ' , where @xmath105 is given by eq . ( [ n0 ] ) . heuristically , one can say that the gap appears because the boundary conditions at the edges have changed . indeed , we explained that the gapless branch exists because the quantization condition eq . ( [ quantization ] ) makes this branch pass through the dirac cone . when the edge structure is altered , the boundary conditions are altered as a result . the latter induces a modification of the quantization rule . thus , in @xmath85-space , the @xmath105 branch shifts slightly off the cone pinnacle s location and acquires a gap . to demonstrate the existence of an edge - induced instability we need to calculate the energy of the @xmath105 branch : @xmath127 it is easy to show that : @xmath128 where @xmath129 is the ground state energy calculated at @xmath130 . the next term is the most singular correction to @xmath131 due to @xmath132 . this correction is not analytic in @xmath132 . one also needs an expression for the nanoribbon lattice energy due to the bond deformation : @xmath133 where @xmath134 is the variation in the edge bond length , @xmath135 is the stiffness of the bond ( the energy @xmath136 is composed of the energy of two deformed bonds per unit cell of the nanoribbon ; the energy of a single deformed bond is @xmath137 . to proceed further we need to know how to relate the deformation of the bond @xmath134 and @xmath10 . such information may be extracted from the quantum chemical calculations @xcite . however , to demonstrate that our system is unstable it is enough to assume that at small @xmath134 we have @xmath138 . then one can write the following expression for @xmath139 : @xmath140 where @xmath141 is a phenomenological constant . finally , it is straightforward to check that the total nanoribbon energy @xmath142 has two minima at @xmath143 , where : @xmath144 \ne 0 . % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % \label{t*}%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % \end{aligned}\ ] ] this expression shows that the nanoribbon energy is smallest when the bonds at the edges are deformed and the @xmath105 branch has a gap . note that the calculations presented above rely on the mean - field approximation . the latter is applicable to our one - dimensional system since the order parameter ( the bond deformation ) is ising - like . thus , no goldstone mode is present , and we do not have to worry about critical fluctuations . above we demonstrated that an armchair nanoribbon of any width has a gap in its electronic spectrum . there are two caveats to our discussion , however . first , we proved that for our system at least one gap - opening instability exists . we did not prove , yet , that the discussed mechanism is the only possible path to generate the spectral gap . for example , the electron - electron interaction can induce a gap @xcite . ultimately , the strongest instability must be determined by comparing the energies associated with particular mechanisms . the energy @xmath145 characterizes the strength of the edge deformation instability . this energy scale quickly vanishes for wider nanoribbons ( @xmath57 is large ) or stiff " edge bonds ( @xmath141 is large ) . under these conditions other mechanisms might be important . second , due to special properties of the carbon atoms at the edge , it is likely that the edge bonds are deformed by chemical forces , which are more powerful than any intrinsic instability , including the one we have discussed . first - principle numerical simulations support this point : analysing fig . 3 of ref . @xcite , we note that the edge bonds are deformed even in nanoribbons where the unstable @xmath105 branch is absent ; moreover , the deformation magnitude is independent of the nanoribbon width . one can say that our order parameter @xmath132 is coupled to the fictitious field " , which takes the system away from criticality ( see table [ parallel ] ) . . analogy between the ising model and the nanoribbon of graphene . [ cols="^,^,^",options="header " , ] in such a situation @xmath146 ; however , the value of @xmath132 and corresponding spectral gap is determined not by eq . ( [ t * ] ) but rather by the strength of the external edge field " . thus , the nanoribbon s spectral properties are controlled by the chemical structure of the edges . if we find a way to vary the effects of the chemical edge structure , we may tune the electronic properties of the nanoribbon to our needs . this problem can be dealt with the help of three different approaches . first , one can try to hand - pick passivating radicals to guarantee preservation of the edge structure . second , one can treat different edges of the nanoribbon with different radicals , which deform the edge bonds in opposite direction . clearly , these two proposals require considerable experimental work . a third approach seems more promising : to close effectively the gap it is enough to disorder the edge field " . we will examine this idea in the next section . as we have seen in the previous section , edge bond deformations can open a gap in the electronic spectrum of an armchair nanoribbon . the magnitude of the gap is determined by the chemical properties of the passivating radical at the nanoribbon s edges . in this section we investigate how the chemical disorder at the edges affects the nanoribbon s spectrum . we will see that the disorder effectively weakens the edge field " . we consider a nanoribbon whose edges are treated by two different radicals , ` @xmath147 ' and ` @xmath148 ' , which distort the bonds in opposite directions : @xmath149 when these radicals randomly attach to the nanoribbon s edges , the edge field " becomes disordered . by adjusting the concentrations @xmath150 of the two radicals , it is possible to vary the relative strengths of @xmath151 and @xmath22 : @xmath152 these two quantities are defined by eq . ( [ t_edge ] ) . the effective hamiltonian for the @xmath105 branch in the presence of disorder is equal to : @xmath153.\end{aligned}\ ] ] the coordinate representation of @xmath154 may be obtained through a procedure similar to the derivation of @xmath112 in sect . [ model ] . below we will assume a gaussian distribution law for the random quantity @xmath22 with the correlation function : @xmath155 or , in fourier space : @xmath156 here : @xmath157 sets the scale for the disorder strength variation , the scale @xmath158 is the disorder correlation length . the function @xmath159 is a broadened @xmath160-function " . it is even and non - negative , vanishes quickly for @xmath161 . in addition , this function is normalised by the condition : @xmath162 its fourier transform @xmath163 satisfies : @xmath164 in the plane - wave basis , the hamiltonian @xmath122 can be written as : @xmath165 in eqs . ( [ deltah ] ) and ( [ tau ] ) , the length @xmath24 appears in the denominator due to wave function normalization . in these equations we defined the dimensionless random field @xmath166 to show explicitly how the disorder matrix elements scale with the nanoribbon length @xmath24 @xcite . as we see from eq . ( [ deltah ] ) , the disordered and homogeneous parts of the edge hamiltonian enter as two different terms . each term induces a specific modification of the nanoribbon s spectrum : _ the ordered part opens a gap , the disorder part localizes the wave functions . _ the localization , however , is a weaker phenomenon than the gap generation . intuitively , this sounds quite reasonable : the effects of disorder may average out " to zero , while the ordered term acts coherently " over the whole sample length . to make this statement rigorous we will apply perturbation theory in orders of @xmath122 . we will show that for a nanoribbon of a certain length the disorder may be treated with the help of perturbation theory , while the ordered term may not . to prove this we separately consider the two pieces of @xmath122 . perturbation theory is applicable when the level spacing @xmath167 is much larger than the matrix elements of @xmath122 . to establish applicability range of the perturbation theory in orders of @xmath151 , we have to compare @xmath168 with the gap @xmath169 . thus , perturbation theory works if : @xmath170 the length scale @xmath171 is analogous to the compton length @xmath172 of the dirac equation . when the disorder is absent ( @xmath173 ) , the gap has its biggest value , and @xmath171 is the shortest : @xmath174 thus , one can say that perturbation theory in @xmath151 works for any value of @xmath175 if @xmath176 the perturbation theory in @xmath22 is applicable when : @xmath177 this inequality may be transformed into : @xmath178 the scale @xmath179 is the localization length . ( our treatment of the disordered regime follows closely ref . @xcite . ) when @xmath180 ( or , equivalently , @xmath181 ) the disorder is the strongest . we can define the shortest possible localization length @xmath182 . it can be estimated as follows . if @xmath181 , @xmath183 has its largest possible value : @xmath184 therefore , if the sample length satisfies : @xmath185 the perturbation theory in the disorder strength is justified for any concentration @xmath175 . it is possible to prove that @xmath186 . indeed , this inequality is equivalent to : @xmath187 both factors on the left - hand side of this expression are much larger than unity . therefore , unless @xmath158 is very big , @xmath186 . loosely speaking , this inequality suggests that the disordered field is a much weaker perturbation than the ordered one . consider now a nanoribbon whose length @xmath24 satisfies : @xmath188 this means that even the strongest disorder ( @xmath189 ) can not create a well - developed localization in our nanoribbon ; on the other hand , when the sample is close to perfect order ( @xmath190 ) the spectral gap fully manifests itself . let us now study the electrical conductance of such nanoribbon . assume first that our system has no edge disorder : @xmath191 . then @xmath192 , and eq . ( [ pert_order ] ) is violated . therefore , the edge field " opens a gap in the spectrum . the dimensionless conductance @xmath2 of a sample with the gap is exponentially small at @xmath49 : @xmath193 when we slightly disorder our system by introducing a small concentration @xmath175 of radicals ` @xmath148 ' , the conductance increases since @xmath151 decreases [ see eq.([dt ] ) ] . thus , _ the disorder improves electrical conductance ! _ in the opposite limit of complete disorder , we have @xmath180 , and the localization length becomes @xmath189 . perturbation theory may now be applied since eq . ( [ pert_disorder ] ) holds true . instead of a disorder - induced localization , which is a non - perturbative phenomenon , in a sufficiently short nanoribbon the disorder creates weak corrections to the properties of @xmath194 . in such sample the conductance remains finite even at @xmath49 . thus , we reach the following counter - intuitive conclusion : _ a completely ordered nanoribbon shows insulating " behaviour , while a disordered one shows metallic " . _ [ we put quotes around insulating " and metallic " for metal and insulator are quantum phases , which can be unambiguously defined only in the thermodynamic limit @xmath195 ; however , the latter limit is incompatible with eq . ( [ meso ] ) . ] as the system moves from perfect order to total disorder , it passes through a crossover from insulating " to metallic " conductance . indeed , eq . ( [ g_order ] ) is applicable only when @xmath196 is much bigger than unity . if @xmath197 one can validate the perturbation theory not only in orders of @xmath22 , but also in orders of @xmath151 [ see eq.([pert_order ] ) ] . therefore , once @xmath24 exceeds @xmath171 , the exponential dependence of @xmath2 is replaced by a slower function , and @xmath2 remains of order unity down to the completely disordered regime . finally , let us comment on the conductance behaviour in a thermodynamically large sample , whose length satisfies : @xmath198 in this situation both terms of @xmath122 can not always be treated with the help of perturbation theory . consequently , the conductance is always exponentially suppressed : when there is perfect order , the conductance follows eq.([g_order ] ) ; in the opposite case ( complete disorder ) we have : @xmath199 the latter equation is a manifestation of wave function localization , which can only be observed in a sample whose length exceeds @xmath179 . comparing eqs . ( [ g_dis ] ) and ( [ g_order ] ) with the help of eq . ( [ hier ] ) , we note that , as well as in the case of a short nanoribbon , the conductance of a perfectly ordered sample is much smaller than the conductance of a totally disordered sample . the conductance @xmath2 of a long nanoribbon is a non - monotonous function of disorder ( see fig . [ conduct ] ) . such a behaviour is a consequence of the crossover from the gap - dominated to the disorder - dominated regime . when the concentration @xmath175 is small , the gap is the dominant parameter controlling the conductance . under such circumstances eq.([g_order ] ) is obeyed . the disorder acts mainly to reduce the gap . thus , if disorder is weak , then @xmath2 is an increasing function of @xmath175 . as @xmath175 keeps growing , @xmath171 increases , while @xmath179 decreases . the crossover occurs at : @xmath200 and the sample enters the disorder - dominated regime . the conductance is given by eq . ( [ g_dis ] ) . it is a decreasing function of @xmath175 when the latter is close to 1/2 . in this paper we studied the effects of edge bond deformations on the electronic properties of nanoribbons . we have seen that a nanoribbon of a certain width is unstable with respect to a spontaneous deformation of the edge bonds . while such deformation increases the energy of the affected bonds , it also reduces the electronic energy . as a result of a ` bond instability ' the electronic spectrum acquires a gap at the fermi level . we also pointed out that this instability is difficult to observe in a real system . the culprit is the chemical structure of the edges , which deforms the bonds to optimize the chemical energy at the edges . although it might be hard to remove this chemical modification of the edge bonds , it is quite possible to reduce its effect on the electronic spectrum by disordering the radicals passivating the edge bonds . we demonstrated that the disorder can vary the electrical conductance of a nanoribbon . in case of a short nanoribbon , the conductance would change from insulating " regime at low disorder to a metallic " regime at high disorder . when the nanoribbon s length is large , the conductance is a non - monotonous function of the disorder . thus , the disorder may be a useful tool which allows one to control the electric transport through nanoribbons . we gratefully acknowledge partial support from the national security agency ( nsa ) , laboratory physical science ( lps ) , army research office ( aro ) , national science foundation ( nsf ) grant no . eia-0130383 , jsps - rfbr 06 - 02 - 91200 , and core - to - core ( ctc ) program supported by japan society for promotion of science ( jsps ) . ss acknowledges support from the epsrc via no . ep / d072581/1 , ep / f005482/1 , and esf network - programme `` arrays of quantum dots and josephson junctions '' . avr is grateful for the support provided by the dynasty foundation and by the rfbr grant no . 06 - 02 - 16691 . e.g. , l.a . ponomarenko , f. schedin , m.i . katsnelson , r. yang , e.w . hill , k.s . novoselov , a.k . geim , science * 320 * , 356 ( 2008 ) ; t.g . pedersen , c. flindt , j. pedersen , n.a . mortensen , a.p . jauho , k. pedersen , , 136804 ( 2008 ) ; a. matulis , f.m . peeters , , 115423 ( 2008 ) ; f. kuemmeth , s. ilani , d.c . ralph , p.l . mceuen , nature * 452 * , 448 ( 2008 ) ; b.d . gerardot , d. brunner , p.a . dalgarno , p. ohberg , s. seidl , m. kroner , k. karrai , n.g . stoltz , p.m. petroff , r.j . warburton , nature * 451 * , 441 ( 2008 ) . e.g. , e.v . castro , n.m.r . peres , j.m.b . lopes dos santos , a.h . castro neto , f. guinea , , 026802 ( 2008 ) ; j.b . oostinga , h.b . heersche , x.l . liu , a.f . morpurgo , l.m.k . vandersypen , nat . mat . * 7 * , 151 ( 2008 ) ; k. kechedzhi , v.i . falko , e. mccann , b.l . altshuler , , 176806 ( 2007 ) ; t. ohta , a. bostwick , t. seyller , k. horn , e. rotenberg , science * 313 * , 5789 ( 2006 ) . e.g. , m. wimmer , i. adagideli , s. berber , d. tomanek , k. richter , , 177207 ( 2008 ) ; x.l . wang , l. zhang , s.w . lee , h.j . dai , science * 319 * , 1229 ( 2008 ) ; p. avouris , z.h . chen , v. perebeinos , nat . nanotechnology * 2 * , 605 ( 2007 ) ; l. yang , m.l . cohen , s.g . louie , nano letters * 7 * , 3112 ( 2007 ) ; j. guo , y. yoon , y. ouyang , nano letters * 7 * , 1935 ( 2007 ) .

we investigate the electronic band structure of an undoped graphene armchair nanoribbon . we demonstrate that such nanoribbon always has a gap in its electronic spectrum . indeed , even in the situations where simple single - electron calculations predict a metallic dispersion , the system is unstable with respect to the deformation of the carbon - carbon bonds dangling at the edges of the armchair nanoribbon . the edge bonds deformation couples electron and hole states with equal momentum . this coupling opens a gap at the fermi level . in a realistic sample , however , it is unlikely that this instability could be observed in its pure form . namely , since chemical properties of the dangling carbon atoms are different from chemical properties of the atoms inside the sample ( for example , the atoms at the edge have only two neighbours , besides additional non - carbon atoms might be attached to passivate unpaired covalent carbon bonds ) , it is very probable that the bonds at the edge are deformed due to chemical interactions . this chemically - induced modification of the nanoribbon s edges can be viewed as an effective field biasing our predicted instability in a particular direction . yet by disordering this field ( e.g. , through random substitution of the radicals attached to the edges ) we may tune the system back to the critical regime and vary the electronic properties of the system . for example , we show that electrical transport through a nanoribbon is strongly affected by such disorder .

This undated still frame taken from the first publicly released video of the giant cat, provided by the Center for Biological Diversity, shows the only known wild jaguar in the United States roaming in a mountain range just south of Tucson, Ariz. "El Jefe"—Spanish for "the boss"—has been living in the Santa Rita Mountains 25 miles south of downtown Tucson for over three years, according to the Center for Biological Diversity. (Center for Biological Diversity via AP) The only known wild jaguar in the United States is seen roaming around a creek and other parts of a mountain range in southern Arizona in the first publicly released video of the giant cat. "El Jefe"—Spanish for "the boss"—has been living in the Santa Rita Mountains about 25 miles south of downtown Tucson for over three years, according to the Center for Biological Diversity. El Jefe is about 7 years old and is one of only four or five jaguars that have been spotted in the U.S. in the last 20 years. He's the only documented wild jaguar in the country. "A lot of people have no idea that we have jaguars in the United States or that they belong here," said Randy Serraglio of the Tucson-based environmental group. "In bringing this video, we hope to inspire people to care about these animals and support protection for their homes." Conservationists say El Jefe's habitat is threatened by a proposed open-pit copper mine in the mountains. The proposed Rosemont Mine has been in the works for several years but is tied up in the permitting phase. The mine will sit on "a very small fraction of the jaguar's 50 miles-plus range," said Patrick Merrin, vice president of the Hudbay Rosemont project. The mine will span nearly 8 square miles in the Santa Rita mountains' more than 215 square miles, he said. An undated still frame taken from the first publicly released video of the giant cat, provided by the Center for Biological Diversity, the only known wild jaguar in the United States is seen roaming in a mountain range just south of Tucson "El Jefe"—Spanish for "the boss"—has been living in the Santa Rita Mountains 25 miles south of downtown Tucson for over three years, according to the Center for Biological Diversity. (Center for Biological Diversity via AP) "We will continue to work with the federal agencies to establish appropriate conservation and mitigation measures for the jaguar and other plants and animals," Merrin said in a statement. The videos of El Jefe were captured by Conservation CATalyst, an organization focused on conserving cats that the Center for Biological Diversity works with. Conservation CATalyst has about a dozen cameras in the areas where El Jefe lives and plans to add more, Serraglio said. "We're getting a good sense of where he likes to go and what areas he likes to use, and travel corridors and that sort of thing," he said. Jaguars roamed the Southwest, but they disappeared over the past 150 years because of habitat loss and predator control programs aimed at protecting livestock. A hunter shot and killed the last verified female jaguar in the U.S. in 1963 in northern Arizona. Conservationists don't know where El Jefe's mother may be, but they say he first popped up in the Whetstone Mountains in 2011 when he was about 3 years old. "She must be somewhere not too far away," Serraglio said. Explore further: Feds allege crime in death of wild jaguar in Ariz. ||||| For Immediate Release, February 3, 2016 Contact: Aletris Neils, Conservation CATalyst, (602) 717-2406 Randy Serraglio, Center for Biological Diversity, (520) 784-1504 Chris Bugbee, Conservation CATalyst, (305) 498-9112 New Video Shows America's Only Known Wild Jaguar Video of Arizona's Jaguar Is First Ever to Be Released to Public TUCSON, Ariz.— Conservation CATalyst and the Center for Biological Diversity released new video today of the only known wild jaguar currently in the United States. Captured on remote sensor cameras in the Santa Rita Mountains just outside Tucson, the dramatic footage provides a glimpse of the secretive life of one of nature’s most majestic and charismatic creatures. This is the first ever publicly released video of the jaguar, and it comes at a critical point in this cat’s conservation. The video is available for media to embed and use on our Facebook page or for download. The camera project is part of ongoing efforts to monitor mountain ranges in southeastern Arizona for endangered jaguar and ocelot. Chris Bugbee, a biologist with Conservation CATalyst, has been collecting data on the Santa Rita jaguar for the past three years (formerly through the University of Arizona). “Studying these elusive cats anywhere is extremely difficult, but following the only known individual in the U.S. is especially challenging,” said Bugbee. “We use our specially trained scat detection dog and spent three years tracking in rugged mountains, collecting data and refining camera sites; these videos represent the peak of our efforts.” “These glimpses into his behavior offer the keys to unlocking the mysteries of these cryptic cats” said Aletris Neils, executive director of Conservation CATalyst. “We are able to determine he is an adult male jaguar, currently in prime condition. Every new piece of information is important for conserving northern jaguars and we look forward to building upon on these data so that we can collectively make better decisions on how to manage these fascinating and endangered cats.” “Jaguars have always occurred in Arizona and yet we know so little about them in the northern portion of their range. Arizona should be poised to harbor and protect both jaguars and ocelots as they continue to disperse out from Sonora,” said Bugbee. “Just knowing that this amazing cat is right out there, just 25 miles from downtown Tucson, is a big thrill,” said Randy Serraglio, conservation advocate with the Center. “El Jefe has been living more or less in our backyard for more than three years now. It’s our job to make sure that his home is protected and he can get what he needs to survive.” El Jefe, as he has come to be known in Tucson, has been photographed repeatedly by remote sensor cameras in the Santa Ritas over the past few years. He is the only verified jaguar in the United States since Macho B was euthanized as a result of capture-related injuries in March 2009. “Jaguars are solitary cats that only tolerate each other for reproduction,” said Neils. But a huge conflict is brewing that threatens to destroy El Jefe’s home. A Canadian mining company is pushing to develop a massive open-pit copper mine right in the middle of the big cat’s territory. The mile-wide open pit and 800-foot-high piles of toxic mine waste would permanently destroy thousands of acres of occupied, federally protected jaguar habitat where this jaguar lives. “Clearly, the Santa Rita Mountains are a vital part of this cat’s home range,” said Bugbee. “This jaguar has been photographed in every month of the year in these mountains — there are more than 100 detections of him in the Santa Ritas since 2013 — how could anyone argue the importance of these mountains?” “The Rosemont Mine would destroy El Jefe’s home and severely hamstring recovery of jaguars in the United States,” said Serraglio. “At ground zero for the mine is the intersection of three major wildlife corridors that are essential for jaguars moving back into the U.S. to reclaim lost territory. The Santa Rita Mountains are critically important to jaguar recovery in this country, and they must be protected.” Conservation CATalyst and Center experts are available for interviews and field trips to the area. Background In October the rare cat was named “El Jefe,” which means “the boss” in Spanish, after a vote by Tucson school kids and others. The Tucson-based Center for Biological Diversity has been working for decades to save jaguars in the United States, with the hope that El Jefe will soon be joined by more jaguars that wander up from Mexico. In 2014 the Center secured more than 750,000 acres of federally protected critical habitat for U.S. jaguar recovery. Jaguars — the third-largest cats in the world after tigers and lions — once lived throughout the American Southwest, with historical reports on the South Rim of the Grand Canyon, the mountains of Southern California and as far east as Louisiana. Jaguars disappeared from their U.S. range over the past 150 years, primarily due to habitat loss and historic government predator control programs intended to protect the livestock industry. The last verified female jaguar in the country was shot by a hunter in 1963 in Arizona’s Mogollon Rim. This research builds upon a three-year project (2012- 2015) from the University of Arizona surveying jaguars and ocelots throughout southern Arizona and New Mexico. The Center for Biological Diversity is a national, nonprofit conservation organization with more than 990,000 members and online activists dedicated to the protection of endangered species and wild places. Conservation CATalyst is a Tucson-based nonprofit organization specializing in conducting scientific research on cats that are in conflict with people. ||||| There are about 15,000 jaguars living in the wild today. They are solitary creatures, preferring to live and hunt alone. But the one living and hunting in the United States takes the word “loner” to another level: The jaguar, nicknamed “El Jefe,” is the only known wild jaguar in the country. El Jefe, which means “the boss” in Spanish, made his public debut Wednesday in video footage released by the Seattle-based Conservation CATalyst and the Tucson, Arizona-based Center for Biological Diversity. The brief clip shows the big cat roaming the grassy forest floor of the Santa Rita Mountains, outside Tucson, navigating rocky creeks, and just doing jaguar-y things: Conservation CATalyst and the Center for Biological Diversity released new video today of the only known wild jaguar currently in the United States.Captured on remote sensor cameras in the Santa Rita Mountains just outside of Tucson, the dramatic footage provides a glimpse of the secretive life of one of nature’s most majestic and charismatic creatures. This is the first-ever publicly released video of the #jaguar, recently named 'El Jefe' by Tucson students, and it comes at a critical point in this cat’s conservation. Learn more here: http://www.biologicaldiversity.org/news/press_releases/2016/jaguar-02-03-2016.html Posted by Center for Biological Diversity on Wednesday, February 3, 2016 Since 2013, El Jefe has been photographed by motion-detecting cameras more than 100 times. But jaguars are notoriously elusive creatures. The 41-second video posted Wednesday is the product of three years of tracking. Chris Bugbee, a biologist at Conservation CATalyst, said in a statement that researchers regularly tinkered with camera locations and even used a dog specially trained to sniff out wildlife feces to track down El Jefe. Historically, jaguars are not uncommon in Arizona. Their range once extended north from Argentina to Central America and Mexico and up into south-central states and even California and Louisiana. But the big cats all but disappeared from the U.S. in the last century, mostly due to habitat loss and federal population-control programs intended to protect livestock. Will Rizzo described the bleak state of the jaguar in the U.S. in Smithsonian magazine in 2005: In 1963, a hunter in Arizona’s White Mountains shot a female, the last of her sex to be documented in the United States. Two years later, the last legally killed jaguar, a male, was taken by a deer hunter in the Patagonia Mountains, south of Tucson. In 1969, Arizona outlawed most jaguar hunting, but with no females known to be at large, there was little hope the population could rebound. During the next 25 years, only two jaguars were documented in the United States, both killed: a large male shot in 1971 near the Santa Cruz River by two teenage duck hunters, and another male cornered by hounds in the Dos Cabezas Mountains in 1986. The conservation centers say a proposed copper mine by a Canadian company in the middle of the Santa Rita Mountains threatens to cleave thousands of acres from the jaguar’s natural territory.

– America got a good look at the United States' only known wild jaguar in a 41-second video released Wednesday. "The dramatic footage provides a glimpse of the secretive life of one of nature’s most majestic and charismatic creatures," the Center for Biological Diversity states in a press release. El Jefe, as the jaguar is known, has made his home in Arizona's Santa Rita Mountains, and this is the first video of him ever released. “Just knowing that this amazing cat is right out there, just 25 miles from downtown Tucson, is a big thrill,” the center's Randy Serraglio says. The video is the result of three years of tracking using remote cameras, the Atlantic reports. "In bringing this video, we hope to inspire people to care about these animals and support protection for their homes," Serraglio tells Phys.org. Jaguars disappeared from the US due to a loss of habitat and the implementation of livestock protection programs over the past century. El Jefe has been the only jaguar verified to be living in the US wilderness since 2009. And only four or five of the big cats have been spotted in the US in the past two decades. “These glimpses into his behavior offer the keys to unlocking the mysteries of these cryptic cats,” one conservationist says. "Every new piece of information is important for conserving northern jaguars." It's not going to be easy. A Canadian company wants to build a copper mine with a "mile-wide open pit and 800-foot-high piles of toxic mine waste" right in the middle of the federally protected jaguar habitat where El Jefe lives, the Center says. "The Santa Rita Mountains are critically important to jaguar recovery in this country, and they must be protected," Serraglio says. (One captive jaguar was determined to be "too fat" to mate.)

Legal scholars were as startled as anyone by the scale of the damages awarded by a Florida jury on Friday to the retired professional wrestler known as Hulk Hogan in his suit against Gawker.com for posting a sex tape. But several experts on the First Amendment said on Saturday that the $115 million award was very likely to be reduced and that even if the verdict against Gawker survived scrutiny in higher courts, any wider effect on press freedoms was likely to be limited. The celebrity former wrestler and reality television star, whose real name is Terry G. Bollea, sued Gawker for invasion of privacy after the website posted in 2012 a black-and-white tape made in 2007 that showed Mr. Bollea having sex with the wife of a friend of his at the time, Todd Clem, a radio shock jock who had legally changed his name to Bubba the Love Sponge Clem. Mr. Bollea said the videotape was made and distributed without his permission. The jury’s award of damages was greater than Mr. Bollea asked for, an indication of how strongly the six jurors condemned Gawker for posting the intimate scenes. The court could still add punitive damages. ||||| A Florida jury today ordered Gawker Media to pay $115 million for publishing a sex tape showing Terry Bollea, also known as Hulk Hogan, having sex with his friend's wife. The stunning sum, which may have punitive damages added to it, is a life-threatening event for the New York-based network of news and gossip sites. Gawker Media was one of the first successful, large, digital-only news companies. The final sum is even more than the $100 million Bollea was seeking. Bollea also sued Gawker founder Nick Denton and former editor Albert Daulerio, and the jury found those two men personally liable as well. The sex tape was made about a decade ago, during a period in which the professional wrestler Hogan testified that he was going through a difficult phase with his then-wife. Todd Clem, a Florida radio personality who later legally changed his name to Bubba the Love Sponge, encouraged Hogan to sleep with his wife Heather. In 2012, Bollea sued Clem, saying he didn't know Clem had filmed him. Clem has made conflicting statements about whether Bollea knew about the taping. Clem settled the lawsuit, reportedly for $5,000. That left Gawker, Denton, and Daulerio as the targets of Bollea's wrath. He sued them for $100 million in damages, and the case went to trial in St. Petersburg, Florida, on March 7. The case raises issues about the limits of the First Amendment in the digital age. Gawker argued that it had a legitimate news reason to publish the tape, since Bollea had talked about his sex life—specifically about sleeping with Clem's wife—in numerous venues. Bollea's reputation took a huge hit last year, and he got fired from his job at World Wrestling Entertainment. That outcome wasn't fallout from the Gawker article, however. In a section of the sex tape that could be described as "pillow talk" (which wasn't published by Gawker), Bollea went on a racist diatribe. He repeatedly used the N-word and other racial insults, expressing disappointment that his daughter was in a relationship with a black man. The racial epithets were leaked by other news sites, including Radar Online and the National Enquirer. Other news sites posted stills from the tape, but only Gawker posted video. They showed one minute and 41 seconds of the tape, which included just nine seconds of sexual content. The company says it made about $11,000 from the post, countering assertions by Bollea attorneys that it was worth hundreds of thousands of dollars. "What's disturbing about Gawker isn't what they do in a vacuum," Bollea lawyer Kenneth Turkel said during closing arguments. "It's how proud they are of it." Denton was "playing God over Bollea’s right to privacy," he added. Bollea says he still feels humiliated over the tape's publication. Gawker editors said the publication of the tape, and accompanying essay, was a commentary about celebrity sex tapes. “He’s talked about his sex life, how big his penis is, and when he talks about his penis it’s to promote his daughter’s singing career," said Gawker's attorney Michael Sullivan. "He’s discussed his sexual encounters. Now he tells you this was the Hulk Hogan character." Gawker has a right to publish news stories, even ones with objectionable content, Sullivan told the jury. "If they can make a claim like this, the Internet as we know it will cease to exist," Sullivan said. As the case went to the jury, Gawker Media released a statement saying that they expect an appeals court will need to resolve the case. It reads in part: We're disappointed the jury was unable to see key evidence and hear testimony from the most important witness... Hulk Hogan's best friend Bubba the Love Sponge—who made the tape and offered up his wife in the first place—originally told his radio listeners that Hulk Hogan knew he was being taped. The jury was only able to hear a questionable version of events. Bubba should have been required to appear in court and explain what really happened. Gawker owns several other popular online news sites, including the gadget site Gizmodo, Lifehacker, Deadspin, Kotaku, Jezebel, and Jalopnik. The company employs about 250 people and has been majority-owned by Denton since it was founded. He recently took outside investment for the first time to be able to pay for this litigation and possible damages. ||||| It's hard to think of a case with details more spectacular: A videotape featuring wrestling star Hulk Hogan having sex in a canopy bed with the young wife of a good friend — a guy whose legal name is Bubba the Love Sponge Clem. Hogan, whose real name is Terry Bollea, sues the website that published portions of the tape, the New York-based gossip site Gawker.com. A Florida jury deliberates just six hours before ruling in Bollea's favor and awarding him a staggering $115 million in damages. Aside from offering jaw-dropping details, the case also raises crucial issues about privacy in the age of Internet phenomena such as revenge porn. "People are thinking a little bit more about the concept of what is newsworthy, because what's changed is the concept of who a public figure is," said Mary Anne Franks, a professor at the University of Miami School of Law and the legislative and tech policy director of the nonprofit Cyber Civil Rights Initiative, which advocates for privacy issues. "Society can be contemptuous toward a celebrity because they're a celebrity, and people think that a celebrity can deal with this," Franks said. "But nowadays you can be turned into a public figure because of a sex tape that is released of you." The verdict's legal scope is, for now, limited. Friday's decision emerged from a jury trial in a district court, which means it doesn't set precedent. "It might have influence on plaintiffs or attorneys based on the same claims against publishers," said Amy Gajda, a law professor at Tulane University and author of "The First Amendment Bubble: How Privacy and Paparazzi Threaten a Free Press." "But it wouldn't have precedence until it is decided on appeal. And at that point, it will have binding precedential value only within that particular jurisdiction of Florida." Still, the case might be cited by other courts deciding similar cases. "Any time there is an unusual fact pattern," she said, "courts will look to other states for a similar pattern." Which means that Bollea vs. Gawker Media may wield some influence as a reference point for other jurisdictions, but its results can't be held up as binding legal precedent. (Unless, of course, the case ended up at the U.S. Supreme Court.) But the Hulk Hogan verdict has emboldened privacy advocates, who say that 1st Amendment rights don't trump an individual's right to privacy — no matter how famous the person. Unlike other celebrity-versus-media legal battles, the issue here was privacy, not whether published material was defamatory or false. You should be able to control who sees you naked. It doesn't matter if you are promiscuous or not promiscuous. — Mary Anne Franks, University of Miami School of Law professor and the legislative and tech policy director of the Cyber Civil Rights Initiative Howard Weitzman, a Santa Monica-based attorney who represents celebrity clients such as pop star Justin Bieber — nude photos of him were recently leaked online — said that the Hogan case sends an important message. "I believe there is a growing dislike of reckless conduct in this age of digital distribution," he said in an email. "When someone's privacy is clearly violated, the 'victim' is entitled to some safeguards. In my opinion, such distributors have a duty to act in a decent and responsible manner rather than rushing to satiate perceived prurient interests." Gajda said that the legal notion of privacy extends back to 1890, when Samuel Warren and Louis Brandeis published a much-cited Harvard Law Review article, "The Right to Privacy," and that this includes matters of a sexual nature. "In my assessment of the cases and the law and society, nudity and issues involving sex have traditionally been protected from the time right to privacy began," she said. So while the media may be free to cover some famous person's sexcapade as "newsworthy," posting images or video of the act without permission can violate the celebrity's privacy. In the Internet age, it's a concept that is being put to the test as nude photos and old sex videos pop up online, distributed by vindictive ex-lovers or hackers who bust into iCloud (such as the hackers who posted revealing images of actress Jennifer Lawrence to the Web in 2014). After a photo or a video appears on the Internet, the Web's cut-and-paste powers of regeneration make it virtually impossible to take down — even if an individual is armed with a pile of injunctions. It's an issue that isn't just affecting celebrities, but private citizens too, who have to contend with the phenomenon of revenge porn. "The term we prefer is 'nonconsensual pornography,'" Franks said. "It's not about the motives of the person who posted it. It's sexually explicit material distributed without consent." Certainly, Hulk Hogan is an unusual poster boy for a privacy movement because the reality show star has openly discussed his physical endowments and his sexual exploits, among other unsavory bits. But Franks says his public persona is not the issue. "He doesn't seem like a victim in the traditional way, but we need to think about the principle here," she said. "You should be able to control who sees you naked. It doesn't matter if you are promiscuous or not promiscuous." Though celebrity sex tapes back in the days of Rob Lowe and Pamela Anderson may have been greeted with some public amusement, these days they are just as likely to raise public ire. When the images of Lawrence were published, some writers described it as a "sexual assault" and another example of the harassment of women. Lawrence called it a "sexual violation." All of this may explain why the jury in Florida was so willing to award Hogan such an extraordinary sum -- $15 million more in damages than he was seeking. Whether the amount or the verdict will stick on appeal remains to be seen. But at a moment in which questions of privacy are in the ether — from NSA surveillance to the FBI's battle with Apple over its iPhone source code — attitudes about what might appear to be a silly celebrity sex tape may be shifting. "In a way," said Gajda, "these cases call out for a Supreme Court resolution." Twitter: @cmonstah ALSO All 62 aboard Dubai airliner killed in crash in southern Russia Lucy Jones is leaving her job - to shake up more than just earthquakes

– Hulk Hogan on Friday won an eye-popping $115 million from Gawker Media for publishing a sex tape—more than he sought and what Ars Technica called a potentially "life-threatening event" for Gawker—but what are the real implications for celebrity privacy and for media freedom? The short answer, legally speaking, is not much, reports the New York Times—yet. A trial verdict in a lower court does not set precedent, but Gawker plans to appeal, and precedent could be set if the verdict is upheld in higher courts—which tend to give more weight to First Amendment than do lower courts, notes the Times. "I think the damages are crazy, but I just don’t see this as a terrible blow to the First Amendment," a media law expert says. "This was an unusual and extremely private matter," he continues, in that Hogan was filmed without his knowledge and the video published without his consent; the verdict "could be bad for the future of sex tapes, but I’m not sure it would be a threat to anything else." Still, notes the Los Angeles Times, the case could be a shot in the arm for privacy advocates, and what one First Amendment professor thinks could be "a slight tilting back toward privacy ... There are those who say that if privacy means anything, it means a sex tape, aired on the Internet for millions to gawk at." And though the Gawker case could be what the New York Times calls "an outlier," in that most traditional media wouldn't have published the tape in the first place, a law professor tells the LA Times: "You should be able to control who sees you naked."

the discovery that most elliptical galaxies and spiral bulges host a black hole at their centers , plus the tight relations observed between black - hole mass @xmath3 and galaxy luminosity @xmath9 or stellar velocity dispersion @xmath10 @xcite , suggest that the formation and growth of central black holes is deeply intertwined with that of their host galaxies . recent theoretical work ( e.g. , @xcite ) supports this view , and also predicts how the relations between the properties of black holes and their host galaxies have changed over time . direct observation of the evolution of the @xmath0 and @xmath1 relations over cosmological time would offer unique insight into galaxy and black - hole formation . there have been many attempts to measure the evolution of the @xmath3 relations ; we cite a partial list of these : * @xcite examine a sample of quasars at redshifts up to 3.3 . the luminosity @xmath9 and velocity dispersion @xmath10 of the host galaxy in such objects can not be measured reliably because the light from the galaxy is overwhelmed by the quasar flux ; instead , they use the width of the narrow [ o iii ] emission line as a surrogate for @xmath10 . they estimate the black - hole mass using the `` photoionization '' method , which is based on an empirically calibrated relation involving the continuum luminosity of the active galactic nucleus ( agn ) and the width of the h@xmath11 or other broad emission lines . the theoretical assumptions that underlie this relation are that the bulk velocities of the emitting clouds are determined by their orbital motion in the gravitational field of the black hole , and that the emitting region is photoionized by an ultraviolet continuum spectrum of fixed shape . they find an @xmath0 relation that is consistent with the local one , suggesting that this relation is independent of redshift . * using similar methods on a larger but lower - redshift quasar sample from the sloan digital sky survey , @xcite find that galaxies of a given dispersion at @xmath12 have black - hole masses that are larger by @xmath13 than at @xmath14 . * @xcite and @xcite measured the velocity dispersion of 14 seyfert i galaxies at redshift @xmath15 ; they used stellar absorption lines , which should provide a more direct measure of the dispersion than emission lines . they measured the black - hole mass using the photoionization method . they found that galaxies of a given dispersion at @xmath15 host black holes having @xmath16 . * @xcite measured the bulge luminosities of 11 quasar hosts in the redshift range @xmath17 using the hubble space telescope ( hst ) , and estimated their black - hole masses using the photoionization method . they conclude that the @xmath1 relation at @xmath18 is close to the relation at @xmath14 ; @xmath19 . this result is remarkable since black holes can only grow with time , while elliptical galaxies fade with time as their stars die : even if the black holes do not grow at all , passive stellar evolution models would predict @xmath20 between @xmath21 and @xmath22 at @xmath23 . if their result is correct , then either black holes must be ejected from the galaxy centers and replaced with smaller ones , or the galaxy luminosity must grow substantially through mergers . a common thread among all these investigations and others is that the high - redshift sample is selected by some measure of agn visibility . black - hole masses and galaxy properties are then derived and an @xmath0 or @xmath1 relation is fitted to the data . since the low - redshift relations are linear in @xmath24 , @xmath6 , and @xmath7 ( eqs . [ eqn : msig ] or [ eqn : ml_hr ] below ) , the high - redshift data are often analyzed by assuming that the slope of the relation is the same as at low redshift and estimating the offset in the intercept or zero - point , which may be expressed as @xmath20 at fixed @xmath9 or @xmath10 . any such offset is then interpreted as evidence that the ratio of @xmath3 to @xmath10 or @xmath9 has changed over time . of course , the offset can be ( and sometimes is ) equally well expressed as @xmath25 or @xmath26 at fixed black - hole mass . proof of evolution in the @xmath3 relations requires demonstrating that the high- and low - redshift galaxy samples were assembled with no selection effects that would bias the relation between the typical galaxy properties and black - hole masses being measured or , at least , that the selection effects in the high- and low - redshift samples were the same . this may be a more difficult task than has commonly been assumed . the local black - hole sample has mostly been drawn from `` normal '' galaxies with quiescent or low levels of nuclear activity . despite the proximity of these galaxies , detecting and weighing their central black holes requires exquisite spatial resolution , very high signal - to - noise observations , and elaborate modeling of the observations . investigating the properties of black holes in nearby galaxies remains a frontier problem ; to date , dynamically determined black - hole masses are available for only slightly more than three dozen galaxies . since there was little evidence of a black hole in most of these galaxies before hst observations were taken ( except sometimes for a modest rise in the velocity dispersion in spectra taken at ground - based resolution ) , and since black holes are found in almost all nearby galaxies that have been examined carefully with hst , the black holes in local quiescent galaxies are selected mainly on the basis of galaxy properties such as @xmath9 or @xmath10 . the techniques used to measure black - hole masses in quiescent galaxies at low redshift can not be used at high redshift , both because the radius of influence of the black hole can not be resolved beyond a few tens of mpc , and because the galaxies have substantially lower surface brightness , by the factor @xmath27 . black holes at high redshift are identified instead by their association with agn . the observer thus _ first _ locates a black hole that is accreting matter and weighs it by the properties of the agn emission lines ( a difficult task , but one that we shall not examine in detail here ) , and then _ secondly _ attempts the ( still difficult ) task of measuring the properties of the host galaxy . the existence and properties of the agn depend both on the properties of the black hole ( mass , spin , orientation ) and on the properties of the galaxy ( mass inflow rate , orientation , etc . ) . in short , selection is done at low redshift by galaxy properties , and at high redshift by a combination of black - hole and galaxy properties that depends on the method used . galaxy samples obtained with different selection techniques will generally satisfy different @xmath3 relations . this effect , analogous to the @xcite bias that is familiar in studies of galactic structure , arises because of the cosmic scatter in the @xmath3 relations there is not ( so far as we know ) an exact 11 relation between black - hole mass and any single measurable property of galaxies such as @xmath9 or @xmath10 . in this paper we argue that determinations of the redshift evolution of the @xmath3 relations may be strongly biased by selection effects unless the same sample selection techniques are used at all redshifts . correcting for the selection bias introduced by the use of different sample selection criteria at different redshifts is extremely difficult : to make accurate corrections it is necessary to know both how the selection depends on the galaxy and black - hole properties and the cosmic scatter in the @xmath3 relations . at present we have only crude upper limits to the latter quantity . we shall show that even if the cosmic scatter were known , the bias in the samples described above usually can only be corrected with additional information , such as how galaxy properties and black - hole mass determine the probability distribution of agn luminosity . the selection bias can be especially large at large @xmath3 , as the following argument shows . consider the @xmath1 relation . at high @xmath9 the number density of galaxies falls off rapidly , as illustrated by the steep cutoff in the @xcite luminosity function . cosmic scatter in the @xmath1 relation implies that there is a distribution of black - hole masses at a given @xmath9 . the rare high - mass black holes can arise from either the peak of this distribution in the rare galaxies with large @xmath9 , or from the high - mass tail of the distribution in the more numerous galaxies of modest @xmath9 . if the number density of galaxies is falling off rapidly with @xmath9 , the contribution from galaxies with modest @xmath9 may actually overwhelm the population of black holes of similar mass associated with galaxies of higher @xmath9 . this problem was first explicitly identified by @xcite in the context of the correlation between black - hole mass and dark - matter halo mass , and by @xcite in the context of the @xmath0 relation , but apparently has not been appreciated by most observers studying the evolution of the @xmath3 relations . in this paper we present a more general exposition of the biases incurred when studying evolution of the @xmath3 relations by comparing samples obtained by different selection criteria and at different redshifts . we start by considering the extraction of samples from hypothetical joint distributions of @xmath3 and @xmath9 or @xmath5 we then consider the selection bias that occurs if the high - redshift samples are selected by agn flux or luminosity . we discuss the prospects of correcting for selection bias , and argue that selection bias may place fundamental limits on the determination of the evolution of the @xmath3 relations . we conclude with a brief review of attempts to measure the evolution of the @xmath3 relations and how they may have been affected by selection bias . understanding object selection bias requires knowledge of the joint probability distribution of black - hole mass @xmath3 and a galaxy property @xmath28 which for the present discussion is either @xmath6 , where @xmath9 is the rest - frame @xmath29-band galaxy luminosity , or @xmath7 , where @xmath10 is the line - of - sight velocity dispersion in the main body of the galaxy ( the precise definition of @xmath9 or @xmath10 does not concern us , so long as it is defined consistently in all samples ) . the true form of the joint distribution unfortunately is unknown ; however , we can construct a hypothetical form of this distribution that accurately represents the present state of the observations , and in any case suffices to show how sample selection bias can occur . we write the probability of finding a galaxy in the interval @xmath30 and @xmath31 as @xmath32 where @xmath33 . from the definition of conditional probability this can be rewritten as @xmath34 where @xmath35 is the probability that a randomly chosen galaxy in a given volume lies in the interval @xmath31 and @xmath36 is the probability that the black - hole mass lies in the range @xmath30 given that the galaxy property is @xmath37 . the function @xmath38 is then given by either the volume - limited luminosity function more properly , the luminosity function of early - type galaxy components ( ellipticals and spiral bulges ) , since these are the components that correlate with black - hole mass or the velocity - dispersion distribution of early - type components . without loss of generality , we may write @xmath39 $ ] where @xmath40 and @xmath41 , so @xmath42 is the mean value of @xmath43 at a given value of the galaxy property @xmath37that is , @xmath42 is either the @xmath1 or @xmath0 relation . the limited observational data on black - hole masses in local galaxies is consistent with the hypothesis that @xmath44 is independent of @xmath45 adopting this hypothesis for simplicity we have @xmath46g(s ) . \label{eqn : joint}\ ] ] the intrinsic variance or `` cosmic scatter '' in black - hole mass at a given value of galaxy property @xmath37 is @xmath47 observational errors may make @xmath44 appear to be yet broader , but for this discussion , we assume that observational errors are negligible ; the selection effects that we are concerned with are solely due to the fact that there is an intrinsic and irreducible range of @xmath3 at any @xmath48 it should be stressed that although the functional form ( [ eqn : joint ] ) is consistent with the available data , it is far from unique . as a foil , we may consider the form @xmath49\phi_\bullet(\mu ) . \label{eqn : jointa}\ ] ] a physical model that motivates ( [ eqn : joint ] ) is one in which the galaxy property @xmath37 determines the black - hole mass @xmath43 with a cosmic scatter described by the function @xmath50 , while ( [ eqn : jointa ] ) is motivated by models in which the black - hole mass @xmath43 determines the galaxy property @xmath37 , with cosmic scatter described by the function @xmath51 . if @xmath52 , then @xmath53 is the number of black holes per unit volume with log mass in the range @xmath54 we do not know which of ( [ eqn : joint ] ) or ( [ eqn : jointa ] ) is correct ( possibly neither , or both ) ; our motivation for choosing the former is that it provides a simple representation of what local observations of black holes in inactive galaxies measure . of the three functions that contribute to @xmath55 , @xmath38 is probably the best determined . we discuss the galaxy - property functions in detail in @xcite , but summarize them briefly here . for the galaxy luminosity function we use the @xcite sloan digital sky survey ( sdss ) luminosity function , transformed to the @xmath29-band and redshift @xmath56 , augmented with the @xcite luminosity function of brightest cluster galaxies , which appear to be undercounted in the sdss . we note that the blanton et al . function refers to total rather than bulge luminosity in s0 and spiral galaxies ; however , this difference is less important at the bright end of the luminosity function , where the selection effects are strongest . for the velocity - dispersion function we use the @xcite sdss results , augmented at the high-@xmath10 end as prescribed by @xcite to account for an artificial high-@xmath10 cut - off in sheth et al . both functions are shown in figure [ fig : g ] . the function @xmath42 should be the least - squares fit of @xmath24 to @xmath6 or @xmath7 in a sample selected by galaxy properties . the @xmath0 relation @xmath42 is based on the galaxy sample from @xcite augmented by a few galaxies with more recent @xmath3 determinations ( see @xcite ) . in contrast to the treatment in @xcite , which treated @xmath3 and @xmath10 symmetrically , the appropriate treatment for our purposes is a least - squares fit of @xmath24 on @xmath7 , which gives : @xmath57 for @xmath58 ( which we will use throughout this paper ) . we discuss the @xmath1 relation in detail in @xcite ; in brief we use the @xcite relation between @xmath3 and galaxy _ mass _ , transformed back to luminosity by adopting the mass - to - light ratio @xmath59 based on the @xmath60 estimates given in @xcite . a least - squares fit of @xmath3 on @xmath61 for galaxies with @xmath62 gives : @xmath63 equations ( [ eqn : msig ] ) and ( [ eqn : ml_hr ] ) have the form @xmath64 where @xmath65 and @xmath66 are constants . @xcite show that the @xmath0 and @xmath1 relations make different predictions for @xmath3 in luminous or high - dispersion galaxies , which have lower @xmath10 values for a given luminosity than is implied by eliminating @xmath3 from equations ( [ eqn : msig ] ) and ( [ eqn : ml_hr ] ) . thus at least one of the @xmath0 or @xmath1 relations must curve away from the linear fit ( [ eqn : msrel ] ) in the most luminous galaxies . we are not concerned with this issue here , and simply show the different selection biases that can result from using @xmath10 or @xmath9 as the galaxy property that correlates with @xmath3 , _ assuming _ that the linear relation ( [ eqn : msrel ] ) holds at all masses . however , the reader should bear in mind that neither the @xmath1 or @xmath0 relation is well determined at high galaxy masses , where the potential selection bias is most important . the scatter function , @xmath67,$ ] is poorly known at best . for this analysis , we assume that at any galaxy @xmath9 or @xmath10 , @xmath68 is described by a normal distribution about @xmath42 , with cosmic scatter @xmath69 . thus @xmath70\,d\mu= { d\mu\over \sqrt{2 \pi{\sigma_\mu}^2 } } \exp\left [ - { [ \mu - f(s)]^2 \over 2{\sigma_\mu}^2}\right ] . \label{eqn : prob}\ ] ] again , we emphasize that @xmath69 does not embody any observational errors in the determination of @xmath71 it represents the intrinsic spread in @xmath3 at any galaxy property . @xcite conclude that only an upper limit to @xmath69 is presently known for either the @xmath0 or @xmath1 relation , both because of the small sample of reliable @xmath3 determinations , and because of uncertainties in the observational errors in @xmath3 , which must be accurately measured to isolate the contribution of @xmath69 to the total residuals . for the present analysis we will explore the sensitivity of the selection biases to @xmath69 on the assumption that @xmath72 for dispersion @xmath10 and @xmath73 for luminosity @xmath9 . apart from the poor knowledge of @xmath69 , there are at least two other major uncertainties in the function @xmath50 : ( i ) a more general treatment would allow for the possibility that it varies with @xmath37 ; ( ii ) there is little or no justification of the assumed normal form . as will be shown below , for the most massive black holes or galaxies , the selection bias may depend on the form that @xmath67 $ ] takes at several standard deviations away from the mean , yet an observational determination of the form of @xmath50 in this region would require a sample of well - determined black - hole masses several orders of magnitude larger than is presently available . thus at the highest black - hole masses , the selection bias is likely to depend sensitively on knowledge that is not presently at hand , so it is not possible to apply reliable corrections for this bias . with these caveats , in figure [ fig:2df ] we show estimates of @xmath55 as modeled by equation ( [ eqn : joint ] ) for each of the @xmath0 and @xmath1 relations , and two assumed values of @xmath74 projection of @xmath55 onto the @xmath43-axis produces the mass function of black holes , @xmath75g(s)\,ds.\end{aligned}\ ] ] the importance of cosmic scatter for converting the luminosity or dispersion function @xmath38 to a black - hole mass function has been discussed several times @xcite . what may be less appreciated , however , is that cosmic scatter implies that the most massive bhs are often hosted by modest galaxies that _ a priori _ would not be expected to harbor bhs of high mass . to illustrate this point , figure [ fig : bh_df ] shows @xmath76 for four different versions of @xmath77 the salient feature is that as the cosmic scatter @xmath69 increases , the contribution to the density of the most massive black holes from the wings of the scatter function @xmath50 overwhelms the `` native '' population of massive black holes harbored by the galaxies with the largest values of property @xmath37 . a second illustration of this point occurs in the top two panels in figure [ fig : bh_cuts ] , which show the probability distribution of @xmath9 and @xmath10 for @xmath78 : note that the solid curves , corresponding to @xmath79 for @xmath9 and 0.3 for @xmath10 , have a prominent shoulder to the right of the peak , the peak arising from low - luminosity or low - dispersion galaxies , and the shoulder from high luminosities and dispersions . the source of the selection bias can be seen more directly in figure [ fig:2df ] , which shows @xmath55 for each of the @xmath0 and @xmath1 relations , and two assumed values of @xmath69 . only for @xmath80 is there an exact relation between @xmath3 and @xmath10 or @xmath81 our model for @xmath55which may not be correct , but is consistent with the data implies that the density contours in figure [ fig:2df ] are symmetric about the mean relationship ridge - lines in the vertical direction ; in other words , the conditional probability of @xmath43 given @xmath37 is symmetric about @xmath82 . on the other hand , the conditional probability of @xmath37 given @xmath43 , @xmath83 is not symmetric about @xmath84 , as seen in figure [ fig : bh_cuts ] , which shows the distribution of @xmath37 at selected values of @xmath8 as @xmath3 and @xmath69 increase , the distribution of @xmath37 for a given @xmath3 moves further and further away from the value implied by the inverse of the @xmath3 relations , @xmath85 , where @xmath65 and @xmath66 are the coefficients given in equation ( [ eqn : msrel ] ) . for @xmath86 @xmath87 generally falls well out in the wings of the distribution of @xmath37 for both @xmath9 and @xmath88 particularly for the larger values of @xmath74 the galaxies with @xmath84 for the highest mass black holes are so far down in the step cutoffs of the @xmath9 and @xmath10 distribution functions that they are completely overwhelmed by the population of galaxies of modest mass that harbor high mass black holes as statistical outliers . the mean value of @xmath37 at a given @xmath3 is @xmath89\,ds\over \int g(s ) h\left[\mu - f(s)\right]\,ds}. \label{eqn : means}\ ] ] this is shown as the red lines in figure [ fig:2df ] . the mean of @xmath6 or @xmath7 at a given @xmath3 is offset from @xmath90 which is just the @xmath37 location of the @xmath3 relation ridgelines shown in the figure . in the presence of cosmic scatter , the mean @xmath37 of a sample of galaxies that host a black hole of given @xmath43 is different from the mean @xmath43 hosted by a sample of galaxies of given @xmath37 . this difference is the source of the selection bias . selection bias typically occurs because the galaxy samples used to probe the @xmath3 relations at cosmological distances are not selected by galaxy @xmath9 or @xmath10 , but by the visibility of their agns . for most of the discussion in this section we shall assume that agn luminosity does not depend directly on @xmath4 @xmath88 or any other galaxy property unrelated to @xmath8 this model is appropriate if , for example , the probability that the agn associated with a black hole of mass @xmath3 has luminosity @xmath91 is given by @xmath92 and @xmath93 and @xmath94 . the physical content of this assumption is that the luminosity history of an agn is determined by the black - hole mass and scales with the eddington luminosity , which is proportional to @xmath3 . we first consider the bias that occurs in a sample in which ( i ) all of the objects are in a narrow redshift range ; ( ii ) the survey contains all agns brighter than a given flux . in this case the probability that an agn in the relevant redshift range is accepted in the survey depends only on its luminosity @xmath91 , and by equation ( [ eq : probone ] ) this in turn depends only on its black - hole mass @xmath43 . thus the probability distribution of a galaxy property @xmath37 at a given value of @xmath43 is not biased by the selection , and is simply @xmath95 ( eq . [ eq : scond ] ) . some examples are shown in figure [ fig : bh_cuts ] , which plots the probability distribution of @xmath96 for several values of black - hole mass @xmath3 and cosmic scatter @xmath69 . here @xmath97 is the inverse of the @xmath1 or @xmath0 relation ( eq . [ eqn : joint ] ) . the mean values of the distributions @xmath98 are displaced to values lower than @xmath87 in most of the examples shown . as expected , the width and offset of the distributions are larger for larger values of @xmath69 . also as expected , the offsets are generally larger for more massive black holes . @xmath99 is shown as the red lines in figure [ fig:2df ] ; the offset of these lines from the relation @xmath82 demonstrates the selection bias . in this model , the selection bias can be corrected : an assumed form for the probability distribution @xmath55 such as ( [ eqn : joint ] ) with redshift - dependent parameters can be used to compute @xmath95 , which can then be fitted to the distribution of galaxy property @xmath37 in the sample at a given value of black - hole mass @xmath43 ( separate issues , discussed in [ sec : difficult ] , are whether this model for the selection effects is realistic and whether the assumed form of @xmath55 is correct ) . however , most papers in the literature have not taken this approach , so it is worthwhile to estimate the biases that might be introduced by using simpler statistics to estimate the evolution in the @xmath3 relations . figure [ fig : bh_bias ] shows the object selection bias @xmath100 as a function of @xmath3 and @xmath69 . in this example we have expressed the bias in terms of galaxy properties , since we have selected by @xmath71 however , it may also be represented as @xmath101 where @xmath66 is the slope given in equation ( [ eqn : msrel ] ) . note that the bias is not always a monotonic function of black - hole mass , nor does it always have the same sign . in this simple model , the bias at black - hole masses of @xmath102 is @xmath103 in the @xmath0 relation for @xmath104 , and @xmath105 in the @xmath1 relation for @xmath79and even larger at larger black - hole masses . the bias is smaller at lower @xmath9 or @xmath10 , but we caution that the near - zero bias in the @xmath1 relation at small @xmath3 is an artifact of our assumption that the luminosity function has the @xcite form at low luminosities ( see below ) , and this may not be true for the early - type galaxy components that are believed to host the black holes . figure [ fig : bh_bias ] also shows that a significant portion of the bias comes from galaxies with @xmath106 for the larger values of @xmath74 indeed for @xmath107 nearly half of the bias comes from such galaxies for all but the smallest @xmath69 shown . thus , not only is the bias sensitive to @xmath108 it also depends on the shape of the wings of the error distribution . if , as is likely , the wings are more extended than in our assumed log - normal distribution , the bias will be even larger . many of the features in these plots can be understood analytically . from the definition of @xmath98 ( equation [ eqn : means ] ) and equation ( [ eqn : msrel ] ) , we can write @xmath109\,dx\over \int h(x)g[b^{-1}(\mu - a - x)]\,dx}. \label{eq : meanss}\ ] ] if the cosmic scatter @xmath110 is not too large , we can evaluate this by expanding @xmath38 in a taylor series , @xmath111_{s=(\mu - a)/b}+\hbox{o}(\sigma_\mu^4 ) . \label{eq : meansss}\ ] ] this result shows that ( i ) the bias is proportional to @xmath112 if @xmath69 is not too large ; ( ii ) the bias in @xmath98 is positive if @xmath38 declines with @xmath37 and proportional to @xmath113this is why the bias is large and negative for the most luminous or high - dispersion galaxies ; ( iii ) the bias is near zero if @xmath38 is constant , which corresponds to a luminosity function @xmath114 when @xmath115 . the bias in the left panel of figure [ fig : bh_bias ] is small for low - luminosity galaxies because the assumed luminosity function is close to this form . a different statistical method , which more closely parallels the approach used in most observational papers , is simply to estimate the average value of the difference between @xmath43 and the prediction of the @xmath116 relation ( [ eqn : msrel ] ) for all the galaxies in the sample , @xmath117 let us assume that the survey flux limit at the given redshift corresponds to a luminosity @xmath118 with @xmath119 . then @xmath120 where @xmath121 , and @xmath122 the luminosity function ( number per unit volume ) of agns is @xmath123 , where @xmath124 which is just the inner integral of the denominator of ( [ eq : xxxx ] ) . to evaluate the inner integral in the numerator of equation ( [ eq : xxxx ] ) , note that the functional form of @xmath125 ( eq . [ eqn : prob ] ) implies that @xmath126 , so @xmath127 integrating the right side of the equation by parts , and noting that @xmath128 gives @xmath129 thus @xmath130 remarkably , the result depends only on the directly observable luminosity function @xmath131 for the type of agn targeted in the survey , and is independent of assumptions about the luminosity history @xmath132 or the distribution of host galaxy properties @xmath38 . also , in contrast to the analogous result ( [ eq : meansss ] ) , equation ( [ eq : biasone ] ) is not just the first term in a taylor series in @xmath112 but valid for all values of @xmath112 , no matter how large . to illustrate the application of this result , we adopt the quasar luminosity function from @xcite , @xmath133 with @xmath134 and @xmath135 , where @xmath136 is the `` break '' luminosity . the corresponding bias @xmath20 is shown as a function of the lower luminosity limit @xmath137 in figure [ fig : bh_biasst ] . note that the bias in figure [ fig : bh_biasst ] becomes smaller but does not vanish as the survey goes to fainter and fainter luminosity limits : asymptotically , @xmath138 which equals @xmath139 . as a second example , we examine the bias in a flux - limited sample of agn . we assume that the survey galaxies are distributed uniformly in euclidean space , that the probability distribution of agn luminosities is given by equation ( [ eq : probone ] ) , and that the survey contains all galaxies with flux @xmath140 exceeding some limiting flux @xmath141 . the bias is then given by @xmath142 where @xmath143 is the volume within which an agn of luminosity @xmath144 can be detected , @xmath145 is the solid angle covered by the survey , and @xmath146 is the number density of galaxies . we have @xmath147 where @xmath148 is defined by equation ( [ eq : defphi ] ) . to evaluate the inner integral in the numerator of equation ( [ eq : xxx ] ) we use equation ( [ eq : parts ] ) , which yields @xmath149 where the last line follows from an integration of the numerator by parts . the results of the previous subsections depend on the assumption that the probability distribution of agn luminosity is determined by the black - hole mass and not the galaxy properties ( eq . [ eq : probone ] ) . a foil to this is to assume that the luminosity is determined by the galaxy properties and not the black - hole mass . thus equation ( [ eq : probone ] ) is replaced by @xmath150 where @xmath151 is a constant . in this case @xmath152 in any flux - limited or luminosity - limited sample @xcite . given the example bias calculations shown in the previous section , it may be tempting to conclude that similar bias corrections may be estimated and applied after the fact to existing surveys to determine the @xmath0 or @xmath1 relations . we believe that in general such corrections are difficult or impossible to apply reliably to current surveys , for the following reasons . in the examples above , we assumed that at any galaxy property @xmath28 @xmath94 followed a normal distribution about the mean @xmath153 relation @xmath82 , with standard deviation characterized by a cosmic scatter @xmath74 we saw that the bias is very sensitive to @xmath69 ( in most examples @xmath154 ) yet this parameter is poorly known for either the @xmath0 or @xmath1 relations , in part because an accurate estimate of @xmath69 requires knowing the observational errors in the @xmath3 determinations . @xcite have studied this problem and conclude only that @xmath155 for the @xmath0 relation and @xmath156 for the @xmath1 relation . moreover , the @xcite analysis assumes , as we do , that @xmath69 is constant over the parameter range of the @xmath3 relations ; the sample of galaxies with well - determined @xmath3 is simply too small to explore the possibility that it is not . even if an accurate estimate of @xmath69 were available , the functional form of the distribution of @xmath157 is unknown . the assumption of a normal distribution is an obvious first step , yet the steep falloff of the @xmath9 or @xmath10 distribution at large values means that the selection bias for large black - hole masses is sensitive to the wings of this distribution , where @xmath158 . the assumed normal distribution is likely to _ under_estimate the selection bias since more realistic distributions have fatter tails . given that the local black - hole sample is so small that @xmath69 is poorly determined , the sample of galaxies with good @xmath3 determinations would have to be several orders of magnitudes larger before an accurate form for the scatter function could be determined . the @xmath3 relations are imperfectly known at @xmath159 and in particular the range of @xmath9 or @xmath10 that is used to determine them is rather limited . for example , in the sample of 31 local galaxies with measured black - hole masses used by @xcite to determine the @xmath0 relation , the interquartile ranges in @xmath9 and @xmath10 are only factors of 5.3 and 1.6 respectively . thus , the calculation of the selection biases for @xmath160 must contend with the fact that there are only a few black holes observed in this mass range in the local sample ( 4 in the @xcite sample ) . @xcite show that the @xmath161 relation must be curved ( in logarithmic coordinates ) in the sense that @xmath10 appears to increase only slowly ( if at all ) with @xmath9 for the most luminous galaxies . this implies that the present log - linear @xmath0 and @xmath1 relation can not be consistent at high galaxy luminosity . the joint @xmath153 distributions shown in figure [ fig:2df ] are thus based on extrapolated estimates at the highest @xmath3 values that are likely to change if more and better determinations of black - hole masses @xmath160 become available . the heart of our analysis of selection bias in [ sec : bhmass ] and [ sec : bhmasstwo ] is the assumption that the black hole determines the agn luminosity , or more precisely that the galaxy properties do not . this is clearly true if , for example , ( i ) black holes radiate either at the eddington luminosity @xmath162 or not at all , and ( ii ) the bolometric correction is independent of galaxy properties . this assumption is also true in more general circumstances , for example , ( i ) can be replaced by the weaker assumption that the probability that a black hole is radiating at some @xmath91 depends only on the ratio @xmath163 ( eq . [ eq : probone ] ) . this assumption may be approximately correct : for example , @xcite find that their simulations are well - fit by a model in which the probability distribution of agn luminosities depends only on @xmath164 where @xmath165 is the peak luminosity of the agn and @xmath166 . nevertheless , if galaxy properties do affect the agn luminosity most likely by determining the feeding rate of matter onto the black hole at luminosities @xmath167then the biases will be different from those presented in [ sec : bhmass ] and [ sec : bhmasstwo ] . in the limiting case that the agn luminosity is determined entirely by galaxy properties rather than black - hole mass , as might be plausible for low - luminosity agns , there is no selection bias in a flux- or luminosity - limited survey ( [ sec : prop ] ) . we have assumed that the joint probability distribution of black - hole mass @xmath43 and galaxy property @xmath37 can be modeled by equation ( [ eqn : joint ] ) . this corresponds to a physical model in which the galaxy property is the independent variable , and the black - hole mass is determined by the properties of the galaxy through the cosmic - scatter function @xmath168 and the @xmath3 relation @xmath42 . this assumption is convenient for modeling the local sample of galaxies with @xmath3 determinations , which was selected by galaxy properties , plus the ready knowledge of @xmath169 the volume distribution of @xmath48 the alternative model provided by equation ( [ eqn : jointa ] ) , in which the black - hole mass is the independent variable and the galaxy property is determined by the black hole through the function @xmath170 , is much more difficult to fit to the local observations as we have little direct knowledge of @xmath171 the black - hole mass function . however , our present understanding of black - hole and galaxy formation does not allow us to say which model , if either , is correct . most of our estimates of selection bias have been based on the assumption that surveys are complete to a given agn luminosity or flux , but this is an oversimplification . any survey that is based on measurements of the luminosity of the host galaxy requires that the host is bright enough and large enough to be separated from the agn . any survey that uses the velocity dispersion measured from stellar absorption lines requires that the absorption lines are strong enough , and that agn emission lines in the vicinity of the absorption lines are weak enough , to allow a reliable dispersion measurement . at the opposite extreme , surveys of low - luminosity agns require that the emission lines are strong enough to be detected against the continuum flux from the galaxy . in such studies the selection depends in a complex way on properties such as the ratio of agn to galaxy luminosity , and on galaxy properties other than @xmath9 or @xmath10 , such as the effective radius or central surface brightness . we have intended this paper mainly as a planning guide for future surveys to explore the evolution of the @xmath3 relation , rather than as a critique of existing surveys . the following brief comments on existing surveys are mostly intended to illustrate the application and impact of the estimates of selection bias that we have made in earlier sections . several authors have determined the @xmath0 relation for nearby agns , and compared this to the local relation for inactive galaxies . using seven seyfert 1 galaxies with black - hole masses measured by reverberation mapping , @xcite find @xmath172 . for 16 agns with reverberation - based black - hole masses @xcite find @xmath173 ( although onken et al . interpret their result in terms of calibrating the reverberation - mapping method rather than an offset in the @xmath0 relation ) . @xcite have compared the black - hole masses in dwarf seyfert 1 galaxies to an extrapolation of the @xmath0 relation to lower dispersions ; using black - hole masses based on the photoionization method calibrated by the standard `` isotropic '' formula , they find @xmath174 ( although they interpret their results with onken et al.s calibration and thus find @xmath175 ) . @xcite have measured the @xmath0 relation in 88 nearby agn using the photoionization method to determine @xmath3the sample is much larger than that of @xcite but the photoionization mass estimates are less direct than those from reverberation mapping . they find @xmath176 . similarly , @xcite have determined the @xmath1 relation from a sample of 29 quasars with @xmath177 ; they determine black - hole masses using the photoionization method and luminosities using hst photometry . they find @xmath178 , although they interpret their result in terms of recalibrating the photoionization method . a common feature of the @xcite , @xcite , @xcite , and @xcite samples is that their black - hole masses are relatively modest : generally @xmath179 and often more than an order of magnitude smaller . selection bias occurs at all @xmath2 depending on the local slopes of the @xmath9 and @xmath10 distributions , but these samples are safely removed from the very strong biases seen at large values of @xmath9 , @xmath10 , and @xmath3 , where the distribution functions are falling rapidly . although we have emphasized selection bias in the context of low- and high - redshift samples with similar black - hole masses , one selected by galaxy properties and one by black - hole mass , selection bias can also arise if the two samples are selected in the same way but are centered on different black - hole mass ranges . we further note that selection effects in these samples are difficult to model for example , ( i ) as @xcite point out , the agn variability timescale depends on luminosity , and if the timescale is too long , reverberation mapping is impractical ; ( ii ) to be able to measure the velocity dispersion requires some minimum ratio of the luminosity of the host galaxy to the luminosity of the agn . if we make the simplest possible assumption , that the samples of nearby galaxies are complete but flux - limited , then equation ( [ eq : fluxlim ] ) implies @xmath180 . @xcite , building on the initial work of @xcite , examine a sample of 14 seyfert 1 galaxies at @xmath181 , measuring the velocity dispersions from stellar absorption lines and the black - hole masses by the photoionization method . compared to the local sample of inactive galaxies with measured black - hole masses , they find @xmath16 ; note that this result is based on a calibration of the photoionization masses that _ assumes _ that the @xcite sample should have exactly the same @xmath0 relation as inactive galaxies , which need not be the case if selection bias is accounted for . @xcite argue that their offset @xmath20 is robust because the black - hole masses are measured by the same technique , with the same calibration , in the local and high - redshift samples , but the selection bias in the two samples is likely to be quite different ; the @xcite sample is more nearly flux - limited , while the @xcite sample is more nearly luminosity - limited , and the selection bias in these two cases is quite different ( eqs . [ eq : fluxlim ] and [ eq : biasone ] ) . a useful next step in assessing the bias would be to determine the luminosity function for agn selected by the criteria used by @xcite , for use in equation ( [ eq : biasone ] ) . it may also be significant that the typical @xmath182 in the @xcite sample is roughly an order of magnitude less massive than the typical @xmath183 in the @xcite sample . as is evident in figure [ fig : bh_bias ] , the bias is a strong function of @xmath2 and indeed the bias in the @xmath0 relation changes sign at @xmath184 . thus we would expect that selection bias might affect the results even if the @xcite sample were chosen in precisely the same way as the @xcite sample . figure [ fig : bh_bias ] predicts a bias of @xmath185 at @xmath183 for @xmath186 . this is only 40% of the offset claimed by @xcite . thus , it appears that selection bias can not explain all or even most of the @xcite @xmath187 ; however , given the uncertainties discussed in the previous section , the possibility that the correction may be as large as the claimed offset can not be ruled out . @xcite find @xmath19 compared to the local @xmath1 relation , using a sample of 11 quasars at @xmath23 ; the black - hole masses are determined with the photoionization method . if we assume that the velocity dispersion of the host galaxy does not change between @xmath188 and @xmath14 , and that the luminosity of the host fades by 12 magnitudes as predicted by passive stellar evolution , then this result corresponds to @xmath1890.8 as measured by the @xmath0 relation . however , the potential selection bias is rather large for this sample , partly because the cosmic scatter in the @xmath1 relation may be larger than in the @xmath0 relation . if the sample is luminosity limited , the model shown in the left panel of figure [ fig : bh_bias ] predicts @xmath190 for @xmath79 for the range of black - hole masses in the sample , and the flux - limited model predicts @xmath191 for @xmath79 ( note that our assumption of a euclidean metric is not valid at @xmath188 , and should be generalized to a realistic cosmological model ) . a further complication is that their method requires measuring the bulge luminosity in the presence of the bright agn , so imposes a selection on the ratio of agn to galaxy luminosity . without an accurate estimate of the selection bias for the @xcite sample , their measurement of @xmath192 does not provide clear evidence for rapid evolution in the ratio of black - hole mass to stellar mass in the galaxy . @xcite find that galaxies of a given dispersion at @xmath12 have black - hole masses that are larger by @xmath193 than at @xmath194 . in contrast to most other studies , they carefully consider the effects of selection bias using monte - carlo models and conclude that for @xmath104 selection bias increases @xmath24 by @xmath195 at low redshift and @xmath196 at @xmath12 , contributing a net offset of @xmath197 . they also argue that scatter in the relationship between the width of the [ o iii ] emission line and the true stellar dispersion contributes an additional offset of @xmath198 , so after correcting for these biases @xmath13 . their estimates of selection bias are similar to , but somewhat smaller than , the bias that we estimate for their sample from equations ( [ eq : biasone ] ) and ( [ eq : fluxlim ] ) , assuming that the low - redshift sample is flux - limited and the high - redshift sample is luminosity - limited ; we believe our estimates are more robust because they do not depend on an assumed form for the distribution @xmath132 of agn luminosities at a given black - hole mass . finally , we note that theoretical models of the evolution of the @xmath0 relation @xcite predict @xmath199 at @xmath200 . strong selection bias could reduce or eliminate the difference between this prediction and the positive values of @xmath20 found at high redshift in most of the above studies . we have described a selection bias that affects investigations into the cosmological evolution of the @xmath0 or @xmath1 relations . we summarize the main points as follows : * cosmic scatter in the @xmath0 or @xmath1 relations means that a galaxy of given @xmath9 or @xmath10 will host black holes with a range of @xmath3 values . * the steep decline in the luminosity function for the most luminous galaxies means that the rare occurrence of high - mass black holes in numerous `` modest '' galaxies overwhelms the frequent occurrence of black holes of similar mass in the rare galaxies with very high luminosity . a similar conclusion applies to dispersion instead of luminosity . * selection of a sample of black holes hosted by inactive galaxies at low redshift explores the distribution of black - hole masses @xmath3 that a galaxy will host , given its luminosity @xmath9 or dispersion @xmath5 selection of a sample by agn luminosity at high redshift explores the distribution of @xmath9 or @xmath10 at a given @xmath3 ( if , as is likely , the distribution of agn luminosity is determined mainly by the black - hole mass rather than the galaxy properties ) . confusing the two distributions may create a false signature of evolution . * the selection bias is substantial for the current estimates of the cosmic scatter in the @xmath1 or @xmath0 relations , particularly for galaxies containing the most massive black holes . neither the root - mean - square cosmic scatter nor the shape of the scatter function is known accurately and hence the bias can not be reliably corrected for , given our present and even foreseeable state of knowledge . * our rough estimates of selection bias as applied to a number of evolutionary studies show that the potential bias may be larger than many of the @xmath201 or @xmath202 values observed . with the notable exceptions of @xcite and @xcite , it appears that most studies of the evolution of the @xmath3 relations have not considered the effects of selection bias . in most cases , accounting properly for selection bias is likely to reduce the the evolution in the @xmath3 relations that has been observed in recent surveys . * the only way to avoid selection bias is to choose high- and low - redshift galaxy samples using precisely defined , objective criteria that are precisely the same for the two samples . to our knowledge , this has not yet been done . the work was initiated during a lorentz center workshop attended by the authors . we thank the staff of the lorentz center and dr . tim de zeeuw for hosting us . we thank drs . karl gebhardt , richard green , and nadia zakamska for useful conversations . barth , a. j. , greene , j. e. , & ho , l. c. 2005 , , 619 , l151 bernardi , m. , et al.2003 , , 125 , 1849 bernardi , m. , et al.2006 , , 131 , 2018 blanton , m. r. , et al . 2003 , , 592 , 819 boyle , b. j. , shanks , t. , croom , s. m. , smith , r. j. , miller , l. , loaring , n. , & heymans , c. 2000 , , 317 , 1014 dressler , a. 1989 , in iau symposium 134 , active galactic nuclei , ed . d. osterbrock and j. s. miller ( dordrecht : kluwer ) , 217 ferrarese , l. , & merritt , d. 2000 , , 539 , l9 fine , s. , et al . 2006 , , 373 , 613 gebhardt , k. , et al . 2000a , , 539 , l13 gebhardt , k. , et al . 2000b , , 543 , l5 gebhardt , k. , et al . 2003 , , 583 , 92 greene , j. e. , & ho , l. c. 2006 , , 641 , l21 hring , n. & rix , h. 2004 , , 604 , l89 hopkins , p. f. , hernquist , l. , cox , t. j. , di matteo , t. , robertson , b. , & springel , v. 2005 , , 163 , 1 kormendy , j. 1993 , in the nearest active galaxies , ed . j. beckman , l. colina and h. netzer ( madrid : consejo superior de investigaciones cientificas ) , 197 kormendy , j. , & richstone , d. 1995 , , 33 , 581 labita , m. , treves , a. , falomo , r. , & uslenghi , m. 2006 , , 373 , 551 lauer , t. r. , et al . 2007 , , 662 , 808 magorrian , j. , et al . 1998 , , 115 , 2285 malmquist , k. g. 1924 , medd . lund astron . obs . ser . ii , 32 , 64 novak , g. s. , faber , s. m. , & dekel , a. 2006 , , 637 , 96 onken , c. a. , ferrarese , l. , merritt , d. , peterson , b. m. , pogge , r. w. , vestergaard , m. , & wandel , a. 2004 , , 615 , 645 peng , c. y. , impey , c. d. , rix , h .- w . , kochanek , c. s. , keeton , c. r. , falco , e. e. , lehr , j. , & mcleod , b. a. 2006 , , 649 , 616 postman , m. , & lauer , t. r. 1995 , , 440 , 28 robertson , b. , hernquist , l. , cox , t. j. , di matteo , t. , hopkins , p. f. , martini , p. , & springel , v. 2006 , , 641 , 90 salviander , s. , shields , g. a. , gebhardt , k. , & bonning , e. w. 2006 , astro - ph/0612568 schechter , p. 1976 , , 203 , 297 sheth , r. k. , et al . 2003 , , 594 , 225 shields , g. a. , gebhardt , k. , salviander , s. , wills , b. j. , xie , b. , brotherton , m. s. , yuan , j. , & dietrich , m. 2003 , , 583 , 124 tremaine , s. et al . 2002 , , 574 , 740 treu , t. , malkan , m. a. , & blandford , r. d. 2004 , , 615 , l97 tundo , e. , bernardi , m. , hyde , j. b. , sheth , r. k. , & pizzella , a. 2006 , astro - ph/0609297 yu , q. , & lu , y. 2004 , , 602 , 603 yu , q. , & tremaine , s. 2002 , , 335 , 965 woo , j .- h . , treu , t. , malkan , m. a. , & blandford , r. d. 2006 , , 645 , 900 or velocity dispersion @xmath7 at selected values of @xmath3 ( @xmath203 is given in the upper right of each panel ) . these probability distributions are obtained by taking horizontal cuts through the joint distributions shown in figure [ fig:2df ] , and are appropriate when the sample selection is on black - hole mass . two distributions are shown with dashed and solid lines , corresponding respectively to @xmath204 for @xmath61 on the left or @xmath205 for @xmath7 on the right . the horizontal coordinate is the difference between either @xmath61 or @xmath7 and the nominal values @xmath97 determined from the @xmath1 or @xmath0 relations ( [ eqn : msig ] ) and ( [ eqn : ml_hr]).,title="fig : " ] or velocity dispersion @xmath7 at selected values of @xmath3 ( @xmath203 is given in the upper right of each panel ) . these probability distributions are obtained by taking horizontal cuts through the joint distributions shown in figure [ fig:2df ] , and are appropriate when the sample selection is on black - hole mass . two distributions are shown with dashed and solid lines , corresponding respectively to @xmath204 for @xmath61 on the left or @xmath205 for @xmath7 on the right . the horizontal coordinate is the difference between either @xmath61 or @xmath7 and the nominal values @xmath97 determined from the @xmath1 or @xmath0 relations ( [ eqn : msig ] ) and ( [ eqn : ml_hr]).,title="fig : " ]

programs to observe evolution in the @xmath0 or @xmath1 relations typically compare black - hole masses , @xmath2 in high - redshift galaxies selected by nuclear activity to @xmath3 in local galaxies selected by luminosity @xmath4 or stellar velocity dispersion @xmath5 because agn luminosity is likely to depend on @xmath3 , selection effects are different for high - redshift and local samples , potentially producing a false signal of evolution . this bias arises because cosmic scatter in the @xmath0 and @xmath1 relations means that the mean @xmath6 or @xmath7 among galaxies that host a black hole of given @xmath3 , may be substantially different than the @xmath6 or @xmath7 obtained from inverting the @xmath1 or @xmath0 relations for the same nominal @xmath8 the bias is particularly strong at high @xmath2 where the luminosity and dispersion functions of galaxies are falling rapidly . the most massive black holes occur more often as rare outliers in galaxies of modest mass than in the even rarer high - mass galaxies , which would otherwise be the sole location of such black holes in the absence of cosmic scatter . because of this bias , @xmath3 will typically appear to be too large in the distant sample for a given @xmath9 or @xmath5 for the largest black holes and the largest plausible cosmic scatter , the bias can reach a factor of 3 in @xmath3 for the @xmath0 relation and a factor of 9 for the @xmath1 relation . unfortunately , the actual cosmic scatter is not known well enough to correct for the bias . measuring evolution of the @xmath3 and galaxy property relations requires object selection to be precisely defined and exactly the same at all redshifts .

in the discrete formulation of two - dimensional quantum gravity , known as _ dynamical triangulations _ , the micro canonical , or fixed area , partition function is defined as the sum over all possible ways of gluing @xmath2 equilateral triangles together to form a piecewise linear manifold ( with an appropriate topology ) : @xmath3 in the case of matter coupled to gravity , the triangulations @xmath4 are weighted with the partition function @xmath5 for the corresponding matter fields . in eq . ( [ * 11 ] ) @xmath6 represents the class of triangulations ( of area @xmath2 ) included in the partition function . different classes correspond to different discretization of the manifolds . two commonly used classes are : _ combinatorial _ triangulations @xmath7 , and _ degenerate _ triangulations @xmath8 . in the former a vertex is not allowed to connected to itself , nor can any two vertices be connected by more than one link this excludes tadpole and self - energy diagrams in the dual graph . this restriction is eased for degenerate triangulations . clearly @xmath9 . in cases where the model eq . ( [ * 11 ] ) has been solved , it has been shown that @xmath10 and @xmath11 are in the same universality class @xcite . but how general is this universality , i.e. how much restriction can be imposed on the triangulations before the critical behavior of the model changes clearly including only one triangulation would produce different result . in the work presented here , we investigate this by considering a new class of triangulations @xmath12 , the class of _ minimal triangulations _ , in which only vertices with coordination number 5 , 6 , and 7 are allowed . this is as far as we can go in suppressing curvature fluctuations , while still retaining the fluid nature of the surfaces . we will demonstrate , by studying the critical behavior of pure gravity and an ising matter coupled to gravity , that this restriction does not change the critical behavior of the model . an additional motivation for studying this class of triangulations is that they more closely resemble conventional condensed matter systems . previously studied models of dynamical triangulations allow vertices with arbitrary high curvature , whereas a real system places a cut - off on the number of interaction for a single particle . that minimal dynamical triangulations are in the usual universality class of @xmath13 gravity , implies that the kpz - exponents might be realized in a real system ( yet to be discovered ) . we start by investigating this model in the absence of matter ( @xmath14 ) . to determine the critical behavior we study the fractal structure of the surfaces . more precisely we measure the string susceptibility exponent @xmath15 , which governs the critical behavior of the grand canonical partition function @xmath16 . in numerical simulations , @xmath15 is obtained from the size distribution of minimal neck baby universes @xmath17 @xcite ; @xmath18^{\gamma_s-2}.\ ] ] for pure gravity @xmath19 . we have measured the distribution @xmath17 for minimal triangulations , this is shown in fig . [ fig1 ] ( curve @xmath20 ) . for comparison we also show the corresponding distribution measured on combinatorial triangulations ( curve @xmath21 ) . in addition fig . [ fig1 ] includes a distribution measured on triangulations obtained from minimal triangulations via node decimation . we will discuss this later . although , for large baby universes , the slope of the distributions @xmath20 and @xmath21 is similar , fig . [ fig1 ] clearly shows much bigger finite size effects for minimal triangulations . this is easily understood , as the restrictions on minimal triangulations effectively smoothens the surfaces locally in fact there is a lower cut - off on the size of the baby universes . an estimate of @xmath15 for the minimal triangulations yields @xmath22 for @xmath23 and @xmath24 for @xmath25 , compared to @xmath26 for combinatorial triangulations and the exact value @xmath27 . the same result is also obtained by using a recently proposed real - space rg method for dynamical triangulations ; _ node decimation _ @xcite . applying node decimation we have blocked the minimal triangulations repeatedly , down to 250 nodes , using a blocking factor of 2 . note that under blocking , the minimal triangulations flow into the wider class of combinatorial triangulations . we then measure the distribution @xmath17 on the ensemble of blocked triangulations . this is shown in fig . clearly the distribution obtained from minimal triangulations via blocking is much closer to the distribution for combinatorial triangulations than the original this implies that the finite size effects are reduced in the blocking . this also implies that under blocking the model flows towards a non - trivial fixed point , corresponding to @xmath13 gravity . the reductions of finite size effects is also apparent in the value of @xmath15 , measured on the blocked triangulations . this is shown in table [ tab1 ] . under blocking the measured value of @xmath15 approaches the exact value . .measured values of @xmath15 for minimal dynamical triangulations ( without matter ) after applying varying levels of node decimation with a blocking factor of @xmath28 . [ cols="^,^,^,^,^ " , ] [ tab2 ] we have also investigated the critical behavior of an ising model coupled to minimal triangulations , for lattice sizes @xmath29 to 8000 . in this case @xmath30 where @xmath31 is an ising spin placed on vertex @xmath32 . the ising spins were updated using a swendsen - wang cluster algorithm and approximately @xmath33 sweeps performed per data - point . we must first determine the infinite volume critical coupling @xmath34 . this is done by locating the peaks in the specific heat @xmath35 and the derivate of binders cumulant @xmath36 ; both are expected to approach @xmath34 as @xmath37 the height of @xmath36 scales like @xmath38 . this procedure yields @xmath39 for the ising model coupled to minimal dynamical triangulations . using this estimate of @xmath34 , we then determine other critical exponents using finite size scaling . we have the magnetization ; @xmath40 , the magnetic susceptibility ; @xmath41 , and the specific heat ; @xmath42 . the exponents are shown in table 2 together with the kpz and onsager predictions . we indicate the finite size effects by imposing different lower cut - off s on the lattice size used . but the conclusion is clear the measured exponents agree very well with the kpz - exponents . in this paper , we have investigated the critical behavior of a so - called minimal dynamical triangulation model of @xmath13 gravity . in this model only vertices of coordination numbers 5 , 6 , and 7 are allowed this effectively suppresses the high curvature fluctuations . by studying the fractal structure of pure gravity , and the critical properties of an ising model coupled to gravity , we conclude that the critical behavior is not affected by this restriction to minimal triangulations the model is in the same universality class as with combinatorial or degenerate triangulations . this implies that large curvature fluctuations do not play an important role in determining the continuum structure of @xmath13 quantum gravity . this result agrees with recent studies of a matrix - model formulation of @xmath43-gravity , where similarly the @xmath43-term can be used suppress the curvature fluctuations locally . in @xcite it was shown that the @xmath43 operator is irrelevant in the continuum limit at large length scales the model always reduces to that of pure gravity .

we study numerically the dynamical triangulation formulation of two - dimensional quantum gravity using a restricted class of triangulation , so - called _ minimal triangulations _ , in which only vertices of coordination number 5 , 6 , and 7 are allowed @xcite . a real - space rg analysis shows that for pure gravity ( central charge @xmath0 ) this restriction does not affect the critical behavior of the model . furthermore , we show that the critical behavior of an ising model coupled to minimal dynamical triangulations ( @xmath1 ) is still governed by the kpz - exponents .

During one interview, agents watched Mr. Miller as he grew aroused while he looked through a book of images of children, two law enforcement officials said. At another point during questioning, when agents asked Mr. Miller about the possibility of Etan’s being buried in the basement, he asked back, “What if the body was moved?” Mr. Miller’s stepson, Jason C. Webley, has said he had never heard of any rape accusations against his stepfather. He also said he did not believe that his stepfather had anything to do with Etan’s disappearance. Mr. Miller’s lawyer, Michael Farkas, said his client “has absolutely no responsibility for the terrible tragedy that befell young Etan Patz, and he grieves for Etan’s fate as all New Yorkers have for decades.” In the intervening years, Agent MacDonald chipped away at the case off and on, even as he juggled it with more active cases, like a large gang investigation in Yonkers. He also played a critical role, three law enforcement officials said, in capturing the Boston gangster Whitey Bulger, who was found in Santa Monica, Calif., last year. Agent MacDonald met some resistance from Etan’s family. Stanley K. Patz, Etan’s father, would meet with the new investigator, but Julie Patz had had enough of new investigators over the years. There were a number of meetings between Mr. Patz and Agent MacDonald before she would participate. Etan’s sister, Shira, however, “shut down” under the agent’s direct interview style, the official familiar with the investigation said. The F.B.I. considers her potentially an important witness because they believe that if Etan ever offered any hint of inappropriate advances by Mr. Ramos or other adults in the days preceding his disappearance, Shira might know. With its suspicions of Mr. Miller rising, the F.B.I. brought in a cadaver-sniffing dog to examine the basement less than a month ago, and the dog’s response suggested the possibility that human remains might once have been buried there. The case is at a precarious juncture, as the digging ended its fourth day on Sunday, with investigators expected to begin again at 8 a.m. on Monday. “If they find remains, the case is solvable,” one law enforcement official said. “If none are found, I fear we’re at a dead end.” Mr. MacDonald was transferred to Maine last year and handed over the case to another agent, Jed Salter. But Agent MacDonald has returned for the dig. “He’s hopeful, but realistic as well,” an official said. ||||| New York (CNN) -- The search of a New York City basement for clues in the disappearance of 6-year-old Etan Patz more than three decades ago has ended with no "obvious" human remains found, NYPD Deputy Commissioner Paul Browne said Monday. An FBI evidence team, along with police, planned to do another check to be sure nothing was missed. A field test on what was considered a possible bloodstain found in the basement was negative, a source briefed on the investigation told CNN. The stain, some possible strands of hair and a piece of paper will be analyzed at an FBI laboratory in Quantico, Virginia, the source said. The boy's family was informed Sunday afternoon that the search had come up empty, according to a law enforcement source. Officials were wrapping up at the scene Monday, Browne said, less than 100 yards from Etan's home. They removed two Dumpsters that contained some concrete slabs taken from the basement, which was a carpenter's workshop at the time Etan vanished. The trash bins and their contents were taken to a location where they can be safeguarded, a source familiar with the investigation said. The basement is about a half-block from where the boy's family still lives. Etan went missing May 25, 1979, a block from his home in the New York neighborhood of SoHo. It was the first time he walked to a bus stop by himself. Days after Etan went missing, the carpenter who worked out of the basement poured a new concrete floor, and it wasn't dug up until now, according to a law enforcement source. About a month ago, a cadaver dog reacted to the floor in a way that suggested the possibility of human remains, a law enforcement source said. The carpenter, Othniel Miller, 75, has not been charged with a crime. He had no involvement in the disappearance, his lawyer said. "Mr. Miller has been cooperating with this investigation for over 30 years," attorney Michael Farkas said Friday. "He has continued to cooperate on multiple occasions. And I am going to assist him in cooperating to the fullest extent possible." Miller's daughter, Stephanie Miller, told CNN affiliate WCBS that her father had cooperated with federal agents, saying he "doesn't have anything to do with it." FBI agents, assisted by the NYPD, discovered the possible bloodstain over the weekend by spraying the chemical luminol, which can indicate the presence of blood but is not always conclusive, according to a source,who was also briefed on the investigation. Investigators recently relaunched their inquiry into the cold case, often described as a milestone effort that helped draw the plight of missing children into the national consciousness. Authorities said that both new and old information led them to Miller, a part-time handyman who met Etan the day before he disappeared and gave him a dollar. It was interest in Miller that prompted authorities to bring a cadaver dog about 10 days ago to the SoHo basement, where Etan apparently had encountered the carpenter, then 42, a source said. When agents interviewed Miller about his connection to the basement, the source said, Miller blurted out, "What if the body was moved?" Farkas, the attorney, said he would speak to authorities about that alleged remark. "I don't know that he asked that," Farkas said. Miller was picked up by the FBI on Thursday and was questioned and returned to his Brooklyn apartment, a source said. In 2010, Manhattan District Attorney Cyrus Vance Jr. said his office decided to take another look at the decades-old mystery. FBI leads were then culled from that case file, sources said. The investigation garnered national headlines as authorities splashed the child's image on the sides of milk cartons in the hopes of gathering more information. Etan was officially declared dead in 2001 as part of a civil lawsuit filed by his family against a drifter, Jose Antonio Ramos, a convicted child molester acquainted with the boy's babysitter. A judge found Ramos responsible for the death and ordered him to pay the family $2 million. He never paid the money. Though Ramos has been considered a key focus of the investigation for years, he has never been charged in the case. He is serving a 20-year sentence in a Pennsylvania prison for molesting a different boy and is set to be released this year. A source said investigators want to expand the pool of possible suspects beyond Ramos. Stan and Julie Patz, Etan's parents, wouldn't comment on the developments. A notice on the apartment building said, "To the hardworking and patient media people: The answer to all your questions at this time is 'no comment.' Please stop ringing our bell and calling for interviews." SoHo -- a Lower Manhattan neighborhood now known for its boutique shops, art galleries and loft apartments -- at the time was a grittier locale where abandoned storefronts dotted the streets. The boy's disappearance raised awareness of child abductions and led to new ways to search for missing children. President Ronald Reagan named May 25, the day Etan went missing, National Missing Children's Day. CNN's Susan Candiotti, Deb Feyerick, Ross Levitt, Adam Reiss, and Josh Levs contributed to this report.

– The case of Etan Patz was opened in 1979 and almost closed five years ago, but a fairly low-ranking FBI agent brought it back into the limelight—culminating in the recent search of a New York City basement, reveals the New York Times. Agent Thomas McDonald took on the hopeless-looking case following another agent's promotion; seeking "some measure of peace" for Patz's family, McDonald contacted old witnesses and developed a 50-page "Patzifesto" containing his findings. In the course of McDonald's work, doubts were raised about the previous top suspect, Jose Ramos, who tended to develop close relationships with the children he abused; no such link between Ramos and Patz was uncovered. New suspect Othniel Miller's name popped up as part of McDonald's search. When asked about a basement burial in one interview, he asked agents, "What if the body was moved?" Meanwhile, the basement search is due to resume today, following a sudden halt yesterday, amid rain. At that point, reporters spotted something being loaded into a van, CNN notes. Yesterday, investigators reportedly found what may be a blood stain on a cinder block.

the presence of large dust masses in high redshift quasars ( qsos ) has been revealed by mm and sub - mm observations of samples of @xmath9 qsos in the sloan digital sky survey ( sdss ) ( bertoldi et al . 2003 ; priddey et al . 2003 ; robson et al . 2004 ; beelen et al . 2006 ; wang et al . 2008 ) . the detection of dust thermal emission and the inferred far - ir ( fir ) luminosities of these objects suggest masses of warm ( @xmath10k ) dust of a few @xmath11m@xmath12 . observations of qsos and galaxies at high redshift are strongly affected by the presence of dust and our ability to interpret the observed properties of high redshift sources depends on a detailed understanding of the star formation history and the history of metal and dust pollution in their interstellar medium ( ism ) . dust properties , such as grains chemical composition and size distribution , are of primary importance in modeling the extinction curves in both the local universe ( cardelli , clayton & mathis 1989 ; pei 1992 ; weingartner & draine 2001 ) and at high redshifts ( maiolino et al . 2004 ; stratta et al . 2007 ; gallerani et al . 2010 ) . yet , the origin of dust at such early epochs is still unclear . among the stellar sources , the cool and dense atmosphere of asymptotic giant branch ( agb ) stars and the expanding ejecta of core collapse supernova ( sn ) offer the most viable sites of dust grains condensation . a sn origin has often been advocated as the only possible explanation for the large amount of dust observed in high redshift qsos since it is usually assumed that low and intermediate - mass stars ( @xmath13m@xmath12 ) must evolve on a timescale comparable to the age of universe at redshift @xmath14 ( about 1 gyr , morgan & edmunds 2003 ; marchenko 2006 ; dwek , galliano & jones 2007 ) before they reach the dust producing stages . this scenario has been tested through observations of the reddened quasar sdssj1048 + 46 at @xmath15 ( maiolino et al . 2004 ) and of the spectral energy distribution ( sed ) of the @xmath16 grb 050904 ( stratta et al . 2007 ) and the @xmath17 grb 071025 ( perley et al . 2010 ) . in these sources , the inferred dust extinction curve is different with respect to any of the extinction curves observed at low @xmath18 , and it shows a very good agreement with the extinction curve predicted for dust formed in sn ejecta . this is an indication that the properties of dust may evolve beyond @xmath19 . in a recent study , gallerani et al . ( 2010 ) find that the extinction curves of a sample of qsos with @xmath20 deviate from the small magellanic cloud ( smc ) extinction curve ( the one which better describe the @xmath21 quasar reddening ) , suggesting that production mechanisms and/or dust processing into the ism must be different at high redshift . on the theoretical side , the evolution of dust in the early universe is still poorly understood . some of the models developed so far are still consistent with the scenario where most of the dust in qso at @xmath22 is produced by sne . however these estimates either neglect dust destruction by interstellar shocks ( maiolino et al . 2006 ; li et al . 2008 ) or make extreme assumptions on sn dust condensation factors ( dwek , galliano & jones 2007 ) . in addition , it has been shown that only @xmath23$]% of the newly condensed dust survives the passage of the sn reverse shock and grains are reduced both in number and in size , depending on the surrounding ism density as well as on dust composition ( see bianchi & schneider 2007 ; nozawa et al . 2007 ; bianchi et al . 2009 ) . in a previous paper ( valiante et al . 2009 ; hereafter v09 ) we showed that agb stars can provide a non negligible contribution to dust formation at high @xmath18 , being able to produce dust already @xmath24 $ ] myr after the onset of the star formation , which is about the mean lifetime of a @xmath25m@xmath12 star ( see e.g. padovani & matteucci 1993 ; raiteri et al . 1996 ) . in particular , for a standard stellar initial mass function ( imf ) , the characteristic timescale at which agb stars dominate dust production ranges between 150 and 500 myr , depending on the assumed star formation history and on the stellar initial metallicity . hence , we concluded that these stellar dust sources must be taken into account when modeling dust evolution at high redshift . in v09 we applied a simple chemical evolution model with dust to the host galaxy of the @xmath26 sdss j1148 + 5251 qso ( hereafter j1148 ) using as an input to the model the star formation history obtained in a numerical simulation by li et al . ( 2007 ) ; this simulation predicts that a large stellar bulge is already formed at @xmath26 , in agreement with the local smbh - stellar mass relation , through a series of strong bursts triggered by galaxy mergers in the hierarchical evolution of the system . we found that the total mass of dust predicted at @xmath26 is within the range of values inferred by observations of sdss j1148 , with a substantial contribution ( 80% ) of agb - dust . we concluded that stellar sources can account for the huge dust mass observed at these early cosmic epochs , even when dust destruction by sn shocks is taken into account , at the price of having a total stellar mass of @xmath27 , which can hardly be reconciled with the dynamical mass of @xmath28 inferred from co observations within 2.5 kpc from the qso center ( walter et al . 2004 ) . the above critical point has been recently emphasized by michalowski et al . ( 2010 ) who showed that using stellar masses approximated as the difference between the dynamical and the h@xmath29 gas masses for @xmath30 qsos , stellar sources of dust are not efficient enough to account for the dust mass inferred in these systems . therefore , they suggest additional non - stellar dust formation mechanism ; in particular , significant dust grain growth in the interstellar medium of these qsos . indeed , dust grains formed in stellar outflows can serve as growth centers for accretion of icy mantels in dense molecular clouds ( mc , see e.g. draine 1990 ) . it is already well known that mc - grown dust is the dominant component in the milky way ( see e.g. zhukovska et al . 2008 ) . given the large masses of molecular gas detected in co for most of these systems , draine ( 2009 ) suggested that the bulk of their dust mass is the result of grain growth and that sn are required to produce the metals that compose the grains and the seed " grain surface area on which more material can grow in mcs . with the present work we investigate the nature of dust in high-@xmath18 qsos host galaxies focusing in particular on j1148 at @xmath31 . to this aim , we have improved the semi - analytic code galaxy merger tree and evolution ( gamete ) , developed by salvadori , schneider & ferrara ( 2007 , hereafter ssf07 ) to model the hierarchical assembly and merger history of a qso host galaxy at @xmath31 , together with its central super massive black hole including feedback from the active galactic nucleus ( agn ) in the form of a galactic - scale wind . the chemical evolution network has also been modified to describe the evolution of dust taking into account the specific stellar lifetimes , and the evolution of dust in the ism through destruction by interstellar shocks and dust - growth in mcs . this code , which we will refer to as gamete / qsodust , will enable us to overcome the main limitations of v09 analysis , namely : _ ( i ) _ we will be able to model different possible star formation histories for j1148 discussing their impact on the chemical properties of the qso host and , in particular , on the final dust mass , and _ ( ii ) _ we will be able to explore the relative importance of stellar sources of dust ( sn and agb ) and of grain growth in mcs . at the same time , the model can be constrained using the properties directly observed or inferred from observations of j1148 , such as the mass of the central black hole , the total mass of gas and stars , the mass in metals and dust . the paper is organized as follows : in section 2 we will introduce the main physical properties of the qso j1148 and its host galaxy discussing the observational uncertainties . in section 3 we will briefly summarize the basic features of the original gamete code and present the parameters adopted to simulate the hierarchical assembly of a qso host halo at @xmath26 . in section 4 we will discuss the new features of the code which allow to follow the formation and evolution of the central black hole and its effects on the parent host galaxy through agn - driven feedback . in section 5 we describe the chemical evolution network , including the evolution of dust in the ism . in section 6 we will present the results and in section 7 we will discuss their implications . finally , in section 8 we will draw the main conclusions of this work . in what follows we adopt a lambda cold dark matter ( @xmath32cdm ) cosmology with @xmath33 , @xmath34 , @xmath35 , and @xmath36 km / s / mpc . the age of the universe at a redshift @xmath26 is 900 myr . in this section we briefly summarize the physical properties of this extremely luminous qso and of its host galaxy which have been derived observationally . the full list of properties , and observational uncertainties , is provided at the end of this section . the mass of the dark matter halo where j1148 is hosted , @xmath37 , is usually estimated by requiring that the number density in halos with masses @xmath38 at @xmath22 matches the observed space density of qsos at the same redshift ( fan et al . depending on the cosmological model , this generally yields to @xmath39 m_{\odot}$ ] . the space density of observed qsos with average redshift @xmath40 and luminosity m@xmath41 is @xmath42 mpc@xmath43 ( fan et al . 2004 ) . for our adopted cosmological model , this would require a minimum halo mass of @xmath44 . to compare with previous analyses ( volonteri & rees 2006 ; valiante et al . 2009 ) in this work we generate monte carlo realizations of the merger histories adopting a value of @xmath45 . the implications of a different halo mass and redshift will be addressed in a forthcoming paper , where a larger sample of qsos will be investigated . j1148 is a very luminous qso with absolute ab magnitude of the continuum in the rest - frame at 1450 of @xmath46 ( fan et al . 2003 ) . assuming a power law @xmath47 with @xmath48 the corresponding b - band magnitude where the factor 0.12 comes from the zero point difference between the ab and the vega - based magnitude system for qso - like spectra . ] and luminosities are @xmath49 and @xmath50 where the effective wavelength of the b - band is @xmath51 . the energy requirement to power such luminosity suggests the presence of a black hole mass of at least several billion solar masses . a virial estimate of the black hole mass of @xmath52 was obtained by willott et al . ( 2003 ) using the mg@xmath53 @xmath542800 line - width and the scaling relations derived by mclure & jarvis ( 2002 ) . using the same scaling relations but also the virial estimator provided by vestergaard ( 2002 ) , barth et al . ( 2003 ) consistently found a bh mass in the range @xmath55 from both the widths of the c@xmath56 @xmath541549 and mg@xmath53 emission lines . beside the factor 2.5 - 3 estimated uncertainty in the adopted scaling relations , this method assumes that the dynamic of the line - emitting gas is dominated by gravitational forces . note , however , that for objects radiating close to the eddington limit , the effect of radiation pressure can not be neglected and may lead to a non negligible upward correction of the estimated bh masses ( marconi et al . 2008 ; lamastra et al . 2010 ) . high - resolution vla observations of j1148 have enabled to resolve co ( 3 - 2 ) line emission both spatially and in terms of velocity ( walter et al . the molecular gas is extended to a radius of @xmath57 kpc from the center and a total mass of @xmath58 has been derived , assuming a co intensity - to - gas mass conversion factor appropriate for ultra luminous infrared galaxies ( ulirgs , walter et al . 2004 ) . assuming that the gas is gravitationally bound and forms an inclined disk with inclination angle @xmath59 , walter et al . ( 2004 ) infer a dynamical mass of @xmath60 . the molecular disk inclination angle is the main source of uncertainty in the dynamical mass estimates ( wang et al . walter et al ( 2004 ) correct for an inclination of @xmath61 , on the basis of the broad co fwhm detected , obtaining @xmath62 with 50% uncertainty . the derivation of the stellar bulge mass is extremely uncertain . indeed this can be either estimated by extrapolating the local @xmath63 relation ( marconi & hunt 2003 ; haring & rix 2004 ) at high redshift , @xmath64 ( if a bh mass of @xmath65 is considered ) , or by subtracting from the observed dynamical mass the h@xmath29 gas mass , @xmath66 m@xmath67 . it is evident that these estimates are unconsistent , since they differ by almost two orders of magnitude . such a discrepancy persists , though alleviated , even if we assume that the stellar bulge mass of the host galaxy of j1148 was 10 times the scale length of the molecular gas emission . assuming a density profile of @xmath68 , the stellar mass would be @xmath69 ( walter et al . 2004 ) . further constraints on the evolution of the qso host galaxy come from observations of the gas phase metallicity and elemental abundances in both the broad and narrow line regions ( blrs , nlrs ) . blrs metallicity tracers are emission lines ratios , such as feii / mgii ( e.g. barth et al . 2003 ) , nv / civ ( e.g. pentericci et al . 2002 ) and ( siiv+oiv)/civ ( nagao et al . 2006 ; juarez et al . 2009 ) , together with other metal lines like cii ( e.g. maiolino et al . 2005 ) , and oi ( becker et al . the observed ratios are similar to those observed in low-@xmath18 qsos , indicating blrs metallicities which are several times solar , @xmath70 ( nagao et al . 2006 , juarez et al . 2009 ) and suggesting that the ism of the qso host was significantly enriched by heavy elements . however , the blrs are small nuclear regions , of less than a few pc , containing a total mass of @xmath71 ; thus , we consider such a high metallicity as an upper limit . conversely , nlrs have larger masses and a size which is roughly comparable to the size of the host galaxy and represent a good tracer of the chemical properties on galactic scales , since their metal content reflects the past star formation history of the galaxy ( matsuoka et al . 2009 and references therein ) . to date however , only measurements of the nlrs metallicity up to redshift 4 are available . focusing on the civ / heii and ciii / civ flux ratios , matsuoka et al . ( 2009 ) point out that even nlrs show no significant metallicity evolution with redshift , up to @xmath72 . for the highest redshift sample these authors find a nlr metallicity of about @xmath73 . we adopt this value as a lower limit for the ism metallicity of j1148 . the dust present in the host galaxy is probably characterized by multi - temperature components : hot ( @xmath74 k ) , warm ( @xmath75 k ) and cold ( @xmath76 k ) . the hot dust component , directly heated by the agn activity , has been observed for several @xmath77 qsos with spitzer ( charmandaris et al . 2004 ; jiang et al . 2010 ) and represents the least contribution to the total mass of dust . warm dust , associated to starburst regions , dominates the emission in the rest - frame far - ir . for j1148 , it has been observed in 4 bands : at 1.2 mm ( bertoldi et al . 2003 ) , 850@xmath78 m , 450@xmath78 m ( robson et al . 2004 ) , and 350@xmath78 m ( beelen et al . the cold dust , finally , may represent the largest component . its emission , however , would be hidden by the warmer component even if its mass were @xmath79 times larger ( dunne et al . 2000 ) . in the rest - frame far - ir the emission is optically thin , @xmath80 , and the dust mass can be estimated from the flux observed in a given band @xmath81 as , @xmath82 where @xmath83 is the opacity coefficient per unit dust mass , @xmath84 is the planck function for a dust temperature @xmath85 , and @xmath86 is the luminosity distance to the source . in the rayleigh - jeans part of the spectrum , dust radiates as a grey - body with @xmath87 . integrating over the spectrum one obtains the corresponding far - ir luminosity , @xmath88 although in principle with four photometric points it could be possible to simultaneously fit @xmath89 , @xmath90 , and @xmath85 , at the redshift of j1148 the observations do not fully sample the rayleigh - jeans part of the spectrum , preventing a determination of @xmath90 . therefore , the estimated mass of dust and fir luminosities for j1148 quoted in the literature have been derived under different assumptions for @xmath90 and @xmath91 . the resulting dust masses , fir luminosities and dust temperatures are listed in table [ table : dustmass ] and have been calculated through a @xmath92 fit using all the observed points in the range @xmath93 @xmath78 m - @xmath94 mm . taking into account the intrinsic error on the estimated fluxes , the typical error associated to a single fit is @xmath95 . as it can be inferred from the table , we have considered , in addition to dust absorption coefficients already adopted in previous works ( cases a - c ) , a fit to the weingartner & draine ( 2001 ) model for the smc in the relevant frequency range ( case d ) as well as the dust optical properties expected for sn dust following the model by bianchi & schneider ( 2007 , case e ) . the quasar host chemical evolution predicted by the additional models presented here , b4 and b5 , are shown in fig . [ fig : b4b5chemevo ] . even if the evolution at the highest redshifts is ( slightly ) different ( the predicted masses are slightly higher and the curves are progressively smoother ) , the final masses of gas , stars and metals are very similar to what predicted by model b3 ( right lower panel in fig . [ fig : chemevo ] ) . on the other hand , we find that model b4 is in agreement with the observed dust mass within the @xmath96 dispersion on the average evolution ( i.e. at least in one of the 50 merger histories the associated sfh is able to reproduce the observed properties of the quasar host ) , whereas model b5 , which is characterized by a sfh with less intense and more frequent bursts , is not able to reproduce the observed dust mass . models b3 , b4 and b5 for a single merger tree realization ( thin lines ) . the panels show the effects of different values of the parameter @xmath97 : 0.05 ( b3 , left panel ) , 0.1 ( b4 , central panel ) and 0.25 ( b5 , right panel ) . thick solid lines refer to the average over 50 merger tree realizations ( see text).,width=332 ] 1 . by averaging the results over a set of merger tree realizations the specific features of each single sfh , such as the number , intensity and redshift distribution of starbursts and the intensity and position of the burst triggered by the last major merger , are partly washed out . 2 . an increasing number of starbursts does not produce a larger final dust mass . the higher is the number of bursts ( over the whole host galaxy evolution ) , the smaller is their intensity , approaching a " quiescent like " sfh ( see model b5 ) ; the final dust mass is strongly limited by destruction ( see section [ sec : dustresults ] ) . baker j.g . , centrella j. , choi d. , koppitz m. , & van meter j. 2006 , phys . 96 , 111102 barth a.j . , martini p. , nelson c.h . , ho l.c . , 2003 , apj , 594 , l95 barlow m.j . , krause o. , swinyard b.m . , sibthorpe b. , besel m.a . , wesson r. , ivison r.j . , et al . , 2010 , a&a , 518 , l138 baugh c.m . , lacey c.g . , frenk c.s . , granato g.l . , silva l. , bressan a. , benson a.j . , cole s. , 2005 , mnras , 356 , 1191 bautista m.a . , dunn j.p . , arav n. , korista k.t . , moe m. , benn c. , 2010 , apj , 713 , 25 beelen a. , cox p. , benford d.j . , dowell c.d . , kovacs a. , bertoldi f. , omont a. , carilli c.l . 2006 , apj , 642 , 694 becker g.d . , sargent w.l.w . , rauch m. , simoncoe r.a . , 2006 , apj , 640 , 69 begelman m.c . , volonteri m. , rees m.j . , 2006 , mnras , 370 , 289 bertoldi f. , carilli c.l . , cox p. , fan x. , strauss m.a . , beelen a. , omont a. , zylka r. 2003 , a&a , 406 , l55 bianchi s. , schneider r. 2007 , mnras , 378 , 973 bianchi s. , schneider r. , valiante r. 2009 , aspc , 414 , 65 bondi h. , hoyle f. , 1944 , mnras , 104 , 273 booth c.m . , & schaye j. , 2009 , mnras , 398 , 53 bromm , v. & loeb a. 2003 , apj , 596 , 34 cardelli , j. a. , clayton g. c. , and mathis j. s. 1989 , apj , 345 , 245 campanelli m. , lousto . c. , marronetti p. , & zlochower , y. 2006 , phys . 96 , 111101 charmandaris , v. et al . 2004 , apjs , 154 , 142 ciotti l. , ostriker j.p . , proga d. , 2009 , apj , 699 , 89 ciotti l. , ostriker j.p . , proga d. , 2010 , apj , 717 , 708 cole s. , lacey c.g . , baugh c.m . , frenk c.s . , 2000 , mnras , 319 , 168 cox t.j . , jonsson p. , somerville r. s. , primack j. r. & dekel a. 2008 , mnras , 384 , 386 daddi e. , elbaz d. , walter f. , bournaud f. , salmi f. , carilli c. et al . 2010 , apjl , 714 , 118 dasyra k.m . 2006 , apj , 651 , 835 davies r.l . , sanchez f.m . , genzel r. , tacconi l.j . , hicks e.k.s . , friedrich s. , stenberg a. , 2007 , apj , 671 , 1388 debuhr j. , quataert e. , ma c.p . , hopkins f. , 2010 , mnras , 406 , l59 di matteo t. , springel v. , hernquist l. , 2005 , nat , 433 , 604 di matteo t. , colberg j. , springel v. , hernquist l. , 2008 , apj , 676 , 33 draine b.t . 1990 , in the evolution of the interstellar medium , ed . l. blitz . 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we present a semi - analytical model for the formation and evolution of a high redshift quasar ( qso ) . we reconstruct a set of hierarchical merger histories of a @xmath0 m@xmath1 dark matter halo and model the evolution of the corresponding galaxy and of its central super massive black hole . the code gamete / qsodust consistently follows : _ ( i ) _ the black hole assembly via both coalescence with other black holes and gas accretion ; _ ( ii ) _ the build up and star formation history of the quasar host galaxy , driven by binary mergers and mass accretion ; _ ( iii ) _ the evolution of gas , stars , metals in the interstellar medium ( ism ) , accounting for mass exchanges with the external medium ( infall and outflow processes ) ; _ ( iv ) _ dust formation in supernova ( sn ) ejecta and in the stellar atmosphere of asymptotic giant branch ( agb ) stars , dust destruction by interstellar shocks and grain growth in molecular clouds ; _ ( v ) _ the agn feedback which powers a galactic - scale wind , self - regulating the black hole growth and eventually halting star formation . + we use this model to study the case of sdss j1148 + 5251 observed at redshift 6.4 . we explore different star formation histories for the qso host galaxy and find that population iii stars give a negligible contribution to the final metal and dust masses due to rapid enrichment of the ism to metallicities @xmath2 z_{\odot}$ ] in progenitor galaxies at redshifts @xmath3 . if population ii / i stars form with a standard initial mass function ( imf ) and with a characteristic stellar mass of @xmath4 m@xmath1 , a final stellar mass of @xmath5\times 10^{11 } m_{\odot}$ ] is required to reproduce the observed dust mass and gas metallicity of j1148 . this is a factor 3 to 10 higher than the stellar mass inferred from observations and would shift the qso closer or onto the stellar bulge - black hole relation observed in the local universe ; alternatively , the observed chemical properties can be reconciled with the inferred stellar mass assuming that population ii / i stars form according to a top - heavy imf with @xmath6 m@xmath1 . we find that sne dominate the early dust enrichment and that , depending on the shape of the star formation history and on the stellar imf , agb stars contribute at redshift @xmath7 . yet , a dust mass of @xmath8 \times 10 ^ 8 $ ] m@xmath1 estimated for j1148 can not be reproduced considering only stellar sources and the final dust mass is dominated by grain growth in molecular clouds . this conclusion is independent of the stellar initial mass function and star formation history . [ firstpage ] galaxies : evolution , high - redshift , ism ; quasars : general ; stars : agb and post - agb , supernovae : general , ism : dust , extinction

i met henry kandrup as a graduate student at maryland in 1985 , having recently decided to switch from experiment to theory . my first interaction with postdocs at the time an intimidatingly higher form of life occurred when henry suggested that he and another postdoc , ping yip , and i take up the question of landau damping and stability of star clusters . while i was happy to work with henry and ping , most of the time i was struggling to understand cryptic conversations laced with mathematical jargon `` functions of compact support , '' `` consider the following inner product , '' and so on . since i was nt following too much of this , i decided it was better to go away and catch up by reading every paper that was even vaguely related to the topic . this turned out to be much easier than expected , and one night i came up with a simple way of combining henry s previous work on stability with conventional landau damping theory from plasma physics . coming in to the department late in the morning i showed the first set of notes to henry . he looked at them , did not say much which was unusual and went back home . next day , as i entered my office , i was stunned to find , slipped under the door , a complete preprint of a paper , all equations written in by hand in henry s beautiful copperplate . he had gone home , generalized my notes to the problem at hand , worked through the entire thing , come back late at night , and typed the preprint on an electric typewriter ( this was just before the advent of word processing ) , finishing as the sun came up . after this incident , i was _ really _ afraid of postdocs ! my early interactions with henry were very wide - ranging ; we discussed all sorts of topics , from classical statistical mechanics to quantum gravity , and on all of them he was very well - informed and entertainingly opinionated . the years went by quickly , henry moved on to other places and so did i. although we argued and collaborated now and then as of old , in my memory the early years have a certain luminescence . my favorite remembrance of henry is that after he had demolished somebody s hapless piece of research in one of our discussions , he would look up , smile in a disarming way , and say , `` true ? '' it usually was . one of the topics henry and i discussed at considerable length and depth was the nature of chaos in multi - particle systems and its role in controlling aspects of the dynamical behavior of statistical averages . while we did not always agree , these discussions certainly attuned my thinking about the problem . in this contribution , i present a discussion of how to think about chaos in a physical way , from the point of view of realistic experiments . the basis of the arguments applies to both classical and quantum systems and serves to bring together these two great dynamical traditions that are seemingly at such odds with each other . the work reported here is the result of several collaborations between subsets of the authors . while i do not know what henry s opinions would have been on this subject , however , i am sure he would not have been quiet ! in classical theory unlike in quantum mechanics the status of dynamical chaos is apparently clear : chaos exists observationally and is well - described theoretically by newton s equations . ( nevertheless , even here , a deeper look at the physical meaning of chaos is certainly helpful ; we return to this presently . ) it is in the context of quantum theory , however , that the notion of chaos appears so puzzling and mysterious . because of the kosloff - rice theorem @xcite and related results @xcite , it is clear that quantum evolution of the wave function or the density matrix is integrable ; hence , chaos can not exist in quantum mechanics in the canonical sense . this is the basic stumbling block to defining a quantum notion of nonintegrability . one may argue that real quantum systems are always coupled to an environment and hence their evolution `` for all practical purposes , '' ( fapp ) , in bell s famous phrase @xcite should be described by unitarity - breaking master equations rather than the unitary evolution assumed by the kosloff - rice theorem . perhaps this way out , although not fundamentally satisfying to the purist , is enough by itself , but it is easy to see what is wrong with the argument . fundamentally , any fully quantum dynamical description must arise from a hamiltonian describing the system , its environment , and their coupling . the master equation represents the evolution of the reduced density matrix for the system which arises from tracing over the environment variables in the full ( system plus environment ) density matrix . since the full evolution must satisfy kosloff - rice , the evolution of the reduced density matrix can not be nonintegrable . thus , the fundamental problem we are faced with is this : we are familiar with chaos in the real world , but our fundamental theory of dynamics which passes every experimental test beautifully seemingly does not have a natural place within it to tolerate even the existence of the concept . this should not come as a surprise ; after all , the trajectories of classical mechanics are apparently `` real '' and effortless to contemplate , but they too , have no natural place in quantum mechanics . now it is true that quantum mechanics is an intrinsically probabilistic theory , but that , in itself , is not the real issue . classical theory can be easily cast as fundamentally probabilistic as well , via the classical liouville equation describing the evolution of a classical probability in phase space . ( for an attempt at an even closer analogy , see ref . @xcite and the discussion in ref . @xcite . ) as discussed further below , the key point is rather that , unlike special relativity , where @xmath0 smoothly transitions between einstein and newton , the limit @xmath1 is singular . the symmetries underlying quantum and classical dynamics unitarity and symplecticity , respectively are fundamentally incompatible with the opposing theory s notion of a physical state : quantum - mechanically , a positive semidefinite density matrix ; classically , a positive phase - space distribution function . in the rest of this article , we will expose the singular nature of the @xmath1 limit and discuss a physical point of view applicable to both classical and quantum systems which will enable us to explain how trajectories and chaos appear in real experiments . at this point , it should be clear that the questions taken up in this contribution are not those usually considered under the research area called `` quantum chaos . '' there , one is primarily interested in the quantum behavior of a system with a classically chaotic hamiltonian , what might happen to the validity of certain approximations ( e.g. , semiclassical approaches to calculating the quantum propagator ) and whether classical trajectories and phase space structures can provide some insight into the nature of quantum wavefunctions . but one does not actually study quantum chaos . we distinguish between _ isolated _ evolution , where the system state evolves without any coupling to the external world , _ unconditioned open _ evolution , where the system evolves coupled to an external environment but where no information regarding the system is extracted from the environment , and _ conditioned open _ evolution where such information _ is _ extracted . in the third case , the evolution of the physical state is driven by the system evolution , the coupling to the external world , and by the fact that observational information regarding the state has been obtained . this last aspect system evolution _ conditioned _ on the measurement results via bayesian inference leads to an intrinsically nonlinear evolution for the system state , and distinguishes it from unconditioned evolution . while the concept of conditioned evolution of the system state is familiar to engineers and mathematicians , especially systems engineers and control theorists @xcite , it is not yet completely familiar territory to the majority of physicists . nevertheless , driven by the impressive progress in the experimental state - of - the - art in quantum and atomic optics and in nanoscience @xcite , these notions are now being employed as everyday tools at least in some fields . the conditioned evolution provides , in principle , the most realistic possible description of an experiment . to the extent that quantum and classical mechanics are eventually just methodological tools to explain and predict the results of experiments , this is the proper context in which to compare them and discuss the nature of predictions for real experiments . the explicit incorporation of information gained via measurement also provides a structure to address the quantum - classical transition more generally , and to frame the question of where chaos exists within this structure . the fact that quantum and classical mechanics are fundamentally incompatible in many ways , yet the macroscopic world is well - described by classical dynamics has puzzled physicists ever since the laying of the foundations of quantum theory . it is fair to say that not everyone is satisfied with the state of affairs including many seasoned practitioners of quantum mechanics . of course , the notion of measurement in quantum mechanics the denial of reality to system properties unless they are measured is such a revolutionary concept that it engenders much more unease @xcite , even today . the problem is that , were quantum mechanics the final theory , it could deny reality to the measurement results themselves unless they were observed by another system and so on , _ ad infinitum_. in order to `` solve '' the `` measurement problem , '' it originally appeared impossible to think of quantum mechanics as a fundamental theory without relying on the existence of a classical world - view within which to embed it @xcite . although we still can not dispel the unease invoked by the measurement problem , it is important to stress that the quantum - classical transition can be understood independently . this transition should not be confused with the measurement problem . a partial understanding of the classical limit arises from the idea familiar from nonequilibrium statistical mechanics that weak interactions of a system with an environment are universal @xcite . these interactions can effectively suppress certain nonclassical terms in the quantum evolution @xcite . however , at best they only allow for the emergence of a classical probabilistic evolution and it can be shown that the mere existence of such interactions is insufficient to yield classical evolution in all cases @xcite . finally , this picture alone can not explain the results of actual measurements where information can be continuously extracted from the environment and used to define operational notions of a trajectory . we now go in to these questions in more detail . suppose we are given an arbitrary system hamiltonian @xmath2 in terms of the dynamical variables @xmath3 and @xmath4 ; we will be more specific regarding the precise meaning of @xmath3 and @xmath4 as position and momentum later . the hamiltonian is the generator of time evolution for the physical system state , provided there is no coupling to an environment or measurement device . in the classical case , we specify the initial state by a positive phase space distribution function @xmath5 ; in the quantum case , by the ( position - representation ) positive semidefinite density matrix @xmath6 or , completely equivalently , by the corresponding wigner distribution function @xmath7 ( not positive ) . the wigner distribution @xcite is a `` half - fourier '' transform of @xmath6 , defined as @xmath8 where @xmath9 and @xmath10 . the evolution of an _ isolated _ system is then given by the classical and quantum liouville equations for the _ fine - grained _ distribution functions ( i.e. , the evolution is entropy - preserving ) : @xmath11 f_{cl}(x , p ) , \label{cle}\ ] ] @xmath12 f_w(x , p ) \nonumber\\ & & + \sum_{\lambda = 1}^\infty\frac{(\hbar/2i)^{2\lambda}}{(2\lambda + 1 ) ! } \partial_x^{2\lambda+1}v(x ) \partial_p^{2\lambda+1 } f_w(x , p ) , \label{qle } \end{aligned}\ ] ] where we have assumed for simplicity that the potential @xmath13 can be taylor - expanded ; this does not alter the nature of any of the following arguments . note that these evolutions are both linear in the respective distribution functions . the limiting form @xmath14 is allowed classically , and , on substitution in eqn . ( [ cle ] ) , yields the expected newton s equations . these may then be interpreted as equations for the particle position and momentum , although we must emphasize that this identification is only formal at this stage . quantum mechanically , this ultralocal limit is not permitted since @xmath7 must be square - integrable , therefore even formally no direct particle interpretation can exist . in both cases , if one allows for initially localized distributions but which nevertheless have some finite width , it is easy to see that if @xmath13 is nonlinear , quite generically the distribution will eventually spread over the allowed phase space and not remain localized . as alluded to in the introduction , the extension to open systems is conceptually trivial , but very difficult to implement in practice . to the original system hamiltonian , we now add pieces representing the environment and the system - environment coupling . if the environment is in principle unobservable , then a ( nonlocal in time ) linear master equation for the system s reduced density matrix is in theory derivable by tracing over the environmental variables . in practice , tractable equations are impossible to obtain without drastic simplifying assumptions such as weak coupling , timescale separations , and simple forms for the environmental and coupling hamiltonians . in any case , the important point to note is that the act of tracing over the environment does not change the linear nature of the equations . generally speaking , master equations describing open evolution of _ coarse - grained _ distributions augment the rhs of eqns . ( [ cle ] ) and ( [ qle ] ) with terms containing dissipation and diffusion kernels connected via generalized fluctuation - dissipation relations @xcite . while the classical diffusion term vanishes in the limit of zero temperature for the environment , this is not true quantum mechanically due to the presence of zero - point fluctuations . in contrast to classical theory , where measurement can be , in principle , a passive process , in quantum theory measurement creates an irreducible disturbance on the observed system ( quantum `` backaction '' ) . this being so , if our aim is that measurement yield dynamical information rather than strongly influence dynamics the desired measurement process must yield a limited amount of information in a finite time . hence , simple projective ( von neumann ) measurements are clearly not appropriate because they yield complete information instantaneously via state projection . nevertheless , this fundamental notion of measurement can be easily extended @xcite to devise schemes that extract information continuously @xcite . the basic idea is to have the system of interest interact weakly with another ( e.g. , atom interacting with an electromagnetic field ) and make projective measurements on the auxiliary system ( e.g. , photon counting ) . because of the weak interaction , the state of the auxiliary system gathers very little information regarding the system of interest , and therefore this system , in turn , is only perturbed slightly by the measurement backaction . only a small component of the information gathered by the projective measurement of the auxiliary system relates to the system of interest , and a continuous limit of the measurement process can be taken . in the continuous limit , the evolution of the system density matrix is fundamentally different from the equations discussed above for the case of open evolution . the master equation describing the evolution of the reduced density matrix conditioned on the results of the measurements contains a term that reflects the gain in information arising from the measurement record ( `` innovation '' in the language of control theory ) . this term , arising from applying a continuous analog of bayes theorem , is intrinsically nonlinear in the distribution function . the coupling to an external probe ( and the associated environment ) will also cause effects very similar to the open evolution considered earlier , and there can once again be dissipation and diffusion terms in the evolution equations . the primary differences between the classical and quantum treatments , aside from the kinematic constraints on the distribution functions , are the following : ( i ) the ( nonlocal in @xmath4 ) quantum evolution term in eqn . ( [ qle ] ) , and ( ii ) an irreducible diffusion contribution due to quantum backaction reflecting the _ active _ nature of quantum measurements . we now consider a simple model of position measurement to provide a measure of concreteness . in this model , we will assume that there are no environmental channels aside from those associated with the measurement . suppose we have a single quantum degree of freedom , position in this case , undergoing a weak , ideal continuous measurement @xcite . here `` ideal '' refers to no loss of information during the measurement , i.e. , a fine - grained evolution with no increase in entropy . then , we have two coupled equations , one for the measurement record @xmath15 , @xmath16 where @xmath17 is the infinitesimal change in the output of the measurement device in time @xmath18 , the parameter @xmath19 characterizes the rate at which the measurement extracts information about the observable , i.e. , the _ strength _ of the measurement @xcite , and @xmath20 is the wiener increment describing driving by gaussian white noise @xcite , the difference between the actually observed value and that expected . the other equation the nonlinear stochastic master equation ( sme ) specifies the resulting conditioned evolution of the system density matrix , given in the wigner representation , @xmath21\right . \nonumber\\ & & + \left.dt\sum_{\lambda = 1}^\infty \ ! \frac{\left ( \hbar/2i\right)^{2\lambda}}{(2\lambda + 1 ) ! } \partial_x^{2\lambda+1 } v(x , t ) \partial_p^{2\lambda+1 } \right ] f_w(x , p , t ) \nonumber \\ & & + dt\sqrt{8k}(x - \langle x \rangle)f_w(x , p , t)dw , \label{condq}\end{aligned}\ ] ] where @xmath22 is the diffusion coefficient arising from quantum backaction and the last ( nonlinear ) term represents the conditioning due to the measurement . in principle , there is also a ( generalized ) damping term @xcite , but if the measurement coupling is weak enough , it can be neglected . if we choose to average over all the measurement results , which is the same as ignoring them , then the conditioning term vanishes , but _ not _ the diffusion from the measurement backaction . thus the resulting linear evolution of the coarse - grained quantum distribution is not the same as the linear fine - grained evolution ( [ qle ] ) , but yields a conventional open - system master equation . moreover , for a given ( coarse - grained ) master equation , different underlying fine - grained sme s may exist , specifying different measurement possibilities . in contrast to the quantum case , the corresponding ( ideal ) classical conditioned master equation [ set @xmath23 in eqn . ( [ condq ] ) , holding @xmath19 fixed ] , @xmath24\right]f_{cl}(x , p , t ) \nonumber\\ & & + dt \sqrt{8k}(x - \langle x \rangle)f_{cl}(x , p , t)dw , \label{condc}\end{aligned}\ ] ] does not have the backaction term as these classical measurements are _ passive _ : averaging over all measurements simply gives back the liouville equation ( [ cle ] ) , and there is no difference between the fine - grained and coarse - grained evolutions in this special case . [ in general , classical diffusion terms from ordinary open evolution can also coexist , as in the _ a posteriori _ evolution specified by the kushner - stratonovich equation @xcite , of which eqn . ( [ condc ] ) is a special case . ] as a final point , we delay our discussion of how the classical trajectory limit is incorporated in eqn . ( [ condc ] ) , i.e. , the precise sense in which the `` the position of a particle is what a position - detector detects , '' to the next section . if quantum mechanics is really the fundamental theory of our world , then an effectively classical description of macroscopic systems must emerge from it the so - called quantum - classical transition ( qct ) . it turns out that this issue is inextricably connected with the question of the physical meaning of dynamical nonlinearity discussed above . having written down the relevant evolution equations , we now analyze two notions of the qct and how they emerge from the equations . quantum mechanics is intrinsically probabilistic , but classical theory as shown above by the existence of the delta - function limit for the classical distribution function is not . since newton s equations provide an excellent description of observed classical systems , including chaotic systems , it is crucial to establish how such a localized , or trajectory , description can arise quantum mechanically . we will call this the _ strong _ form of the qct . of course , in many situations , only a statistical description is possible even classically , and here we demand only the agreement of quantum and classical distributions and the associated dynamical averages . this defines the _ weak _ form of the qct . it is clear that if the strong form of the qct holds , then , via trivial coarse - graining , the weak form follows automatically . the reverse is not true , however : results from a coarse - grained analysis can not be applied to the fine - grained situation . moreover , the violation of the conditions necessary to establish the strong form of the qct need not prevent the existence of a weak qct . we now discuss and establish the conditions under which these transitions occur . since the strong form of the qct requires treating the localized limit , a cumulant expansion for the distribution function immediately suggests itself , whereas , for the more nonlocal issues relevant to the weak form of the qct , a semiclassical analysis turns out to be natural . it is easy to see that the strong form of the qct is impossible to obtain from either the isolated or open evolution equations for the density matrix or wigner function . as mentioned already , for a generic dynamical system , a localized initial distribution tends to distribute itself over phase space and then continue to evolve either in complicated ways ( isolated system ) or asymptote to an equilibrium state ( open system ) , whether classically or quantum mechanically . in the case of conditioned evolution , however , the distribution can be localized due to the information gained from the measurement , and evolve in a quite different manner . in order to quantify how this happens , let us first apply a cumulant expansion to the ( fine - grained ) conditioned classical evolution ( [ condc ] ) . this results in the following equations for the centroids ( @xmath25 , @xmath26 ) , @xmath27 where @xmath28 along with a hierarchy of coupled equations for the time - evolution of the higher cumulants . these equations are the continuous measurement , real - world , analog of the formal ultralocal newtonian limit of the distribution function in the classical liouville equation ( [ cle ] ) . whereas eqns . ( [ cumc ] ) always apply , our aim is to determine the conditions under which the cumulant expansion effectively truncates and brings their solution very close to that of newton s equations . this will be true provided the noise terms are small ( in an average sense ) and the force term is localized , i.e. , @xmath29 , the corrections being small . the required analysis involves higher cumulants and has been carried out elsewhere @xcite . it turns out that the distribution is localized provided @xmath30 and the motion of the centroid will effectively define a smooth classical trajectory the low - noise condition as long as @xmath31 where @xmath32 is the action scale of the system . note that this condition does not bound the measurement strength : classically we can always extract as much information as needed at least in principle to gain the trajectory limit . this , then , is the `` realistic '' derivation of newton s equations . we now turn to the quantum version of these results . in this case , the analogous cumulant expansion gives exactly the same equations for the centroids as above , while the equations for the higher cumulants are different . ( the evolution of classical and quantum averages is the same to gaussian order , with the first differences arising at the next order @xcite . ) we can again investigate whether a trajectory limit exists . localization holds in the weakly nonlinear case if the classical condition above is satisfied . in the case of strong nonlinearity , the inequality becomes @xcite @xmath33 because of the backaction , the low - noise condition is implemented in the quantum case by a double - sided inequality : @xmath34 where the action is measured in units of @xmath35 , @xmath36 being dimensionless . the left inequality is the same as the classical one discussed above , however the right inequality is essentially quantum mechanical . the measurement strength can not be made arbitrarily large as the backaction will result in too large a noise in the equations for the centroids . as the action @xmath36 is made larger , both inequalities are satisfied for an ever wider range of values of @xmath19 . for sufficiently large @xmath36 , the actual value of @xmath19 becomes irrelevant and the dynamics becomes effectively classical . to recapitulate , for continuously measured quantum systems , trajectories that emerge in the macroscopic limit follow newton s equations , and hence can be chaotic as shown elsewhere @xcite . thus , as speculated in a prescient paper by chirikov @xcite , measurement indeed provides the missing link between `` quantum '' and `` chaos , '' at least in the classical limit . finally , in experiments one usually considers the measurement record itself rather than the estimated state of the system as we have discussed so far . as measurement introduces a white noise , it is important to investigate the condition under which the record tracks the estimate faithfully . if @xmath37 is the time over which the continuous measurement is averaged to obtain the record ( this averaging being a necessary part of any finite - bandwidth experiment ) , and we allow ourselves a maximum of @xmath38 as the position noise , it is easy to see that the measurement strength needs to satisfy @xcite @xmath39 to demonstrate these results for a concrete example , we revisit the results of ref . @xcite for a driven , duffing oscillator , with system hamiltonian @xmath40 with @xmath41 , @xmath42 , @xmath43 , @xmath44 , @xmath45 . this hamiltonian has been used before in studies of quantum chaos @xcite and quantum decoherence @xcite and , in the parameter regime used , a substantial area of the accessible phase space is stochastic . and @xmath46 . ( b ) the position variance , @xmath47 , as a function of time . note the smallness of the scale on the y - axis!,width=321,height=283 ] numerical calculations at various values of @xmath35 confirm that as @xmath35 is reduced , both the steady - state variance , and the resulting noise ( for optimal measurement strengths ) are reduced , as expected . as the dynamical time scale of this problem is @xmath48 ( in units of the driving period ) , the continuous observation record was averaged over a period of @xmath49 . similarly , as the range of the motion covers distances of @xmath50 , we demand that the position be tracked to an accuracy of @xmath49 to define an effective `` trajectory . '' to satisfy this , we need to have @xmath51 or larger [ cf . ( [ kobs ] ) ] . in our example , we choose the energy to be @xmath52 , the corresponding typical action turns out to be @xmath50 , and the typical nonlinearity makes the rhs of eqn . [ klarge ] , @xmath53 . we see that a choice of @xmath54 and @xmath55 , satisfies all the constraints for a classical motion . in fig . [ fig00 ] we demonstrate that in this regime , localization is maintained along with low levels of trajectory noise . [ fig00](a ) shows a typical phase space trajectory , with the position variance during the evolution , @xmath56 , plotted in fig . [ fig00](b ) . we find that the width @xmath57 is always bounded by @xmath58 . furthermore , as is immediately evident from the smoothness of the trajectory in fig . [ fig00](a ) , the noise is also negligible on these scales . additionally , one can verify that the quantum trajectory evolution and that given by a classical trajectory with an equivalent noise are essentially identical and chaotic yielding a lyapunov exponent of @xmath59 . we return to discuss the lyapunov exponent later below . the weak form of the qct utilizes the _ coarse - grained _ distribution function ( averaging over all measurements ) , whereas the strong form refers to the _ fine - grained _ distribution for a single measurement realization . it is important to reiterate that nonexistence of the strong form of the qct does not influence the existence of the weak form of the qct : it does not matter if the distribution is too wide , as long as the classical and quantum distributions agree , and , even if the backaction noise is large , the coarse - grained distribution can remain smooth and the weak quantum - classical correspondence still exist . consequently , this correspondence has to be approached in a different manner . in fact , the weak version is just another way to state the conventional decoherence idea @xcite ; however , as discussed elsewhere @xcite , mere suppression of quantum interference does not guarantee the qct even in the weak form . we now focus on a semiclassical analysis of the weak qct for bounded , classically chaotic open systems @xcite . this analysis is best regarded as a _ regularization _ of the singular @xmath60 limit via the environmental interaction . this is distinct from the state _ localization _ characteristic of the strong form of the qct . given a small , but finite , value of @xmath35 , the aim is to establish the existence of a timescale beyond which the dynamics of open quantum and classical systems becomes statistically equivalent if the environmental interaction is sufficiently strong . it has been demonstrated @xcite that , for a bounded open system with a classically chaotic hamiltonian , the weak form of the qct is achieved by two parallel processes , both relying essentially on the existence of environmental diffusion . first , the semiclassical approximation for quantum dynamics , which breaks down for classically chaotic systems due to overwhelming nonlocal interference , is recovered as the environmental interaction filters these effects . second , environmental noise restricts the foliation of the unstable manifold , the set of points which approach a hyperbolic point in reverse time , allowing the semiclassical wavefunction to track this modified classical geometry . in this way , the noise prevents classical chaos from breaking the semiclassical approximation as @xmath1 , and thus regularizes this limit . note that this approach explicitly incorporates both the stretching and folding typical of hyperbolic regions as well as the role of the environment as a filter on a phase - space quantum distribution . we begin with a simple model of a quantum system weakly coupled to the environment so as to maintain complete positivity for the subsystem density matrix , @xmath61 , while subjecting it to a , time - local , unitarity - breaking interaction . these conditions mathematically constrain the master equation to be of the so - called lindblad form @xcite . if this environmental interaction couples to the position , as is often the case , the master equation takes the form : @xmath62 where @xmath63 , the classical liouville operator , and @xmath64 , the quantum correction , can be easily identified from eqn . ( [ qle ] ) . we note in passing that while the sum of @xmath63 and @xmath64 is clearly unitary , individually the operators are not unitary @xcite . in this simple master equation , we have neglected the dissipative environmental channel and kept the diffusive channel for two reasons : ( i ) the coupling to the environment is always assumed to be weak and the dissipative timescales are , hence , very long , longer than the dynamical timescales of interest , ( ii ) the weak form of the qct arises only from the diffusive channel , hence , dissipative effects are not of interest here . when @xmath65 , this equation reverts to the classical fokker - planck equation . it is important to keep in mind that the specific form of the diffusion coefficient depends strongly on the physical situation envisaged . thus , if the master equation describes a weakly coupled , high temperature environment , @xmath66 ( @xmath67 is the damping coefficient ) @xcite , whereas for a weak , continuous measurement of position , the diffusion due to quantum backaction is @xmath68 @xcite . the discussion below holds for all of these cases . once the qct occurs , the effects of @xmath69 in the evolution specified by eqn . ( [ wme ] ) are subdominant . therefore , to understand how environmental noise acts in this limit , it suffices to consider the behavior of the corresponding classical fokker - planck equation . to do this , it is convenient to examine the underlying langevin equations for noisy trajectories that unravel the evolution of the classical distribution function when @xmath65 . these are given by @xmath70 using weak - noise perturbation theory , one can perform an expansion about a hyperbolic fixed point and in this way obtain the spreading of the position and momentum due to the diffusion . as a trajectory evolves , it simultaneously smoothes over a transverse width in phase space of size @xmath71 where @xmath72 is the local lyapunov exponent @xcite . the smoothing implies a termination in the development of new phase space structures at some finite time @xmath73 , whose scaling behavior can be determined . ( caveat : this need not be true in a non - compact phase space . ) the average motion of a trajectory is identical to its deterministic motion , so that at time @xmath74 , if the initial length in phase space is @xmath75 ( @xmath76 has units of square - root of phase - space area ) , its current length will be approximately @xmath77 as its forward time evolution will be dominated by its component in the unstable direction . here @xmath78 is the time - averaged positive lyapunov exponent . if the region is bounded within a phase space area @xmath79 , the typical distance between neighboring folds of the trajectory is given by @xmath80 where @xmath81 still carries the units of the square root of phase space area . however , since phase structures can only be known to within the width specified above , the time at which any new structure will be smoothed over is defined by @xmath82 the above two equations can be used to determine @xmath83 , which only weakly depends on @xmath84 and the prefactor in eqn . ( [ dist ] ) . due to the smoothing , one does not see an ergodic phase space region , but one in which the large , short - time features that develop prior to @xmath73 are pronounced and the small , long - time features that develop later are smoothed over by the averaging process . therefore , to approximate noisy classical dynamics , a quantum system need not track all of the fine scale structures , but only the larger features that develop before the production of small scale structures terminates . to establish the conditions under which quantum dynamics can track this modified phase space geometry , a semiclassical analysis can be performed . in the wigner function formalism , the breakdown of the semiclassical approximation for chaotic systems can be associated with an appealing geometric picture @xcite based on a uniform approximation in phase space the berry construction . we now use this construction to understand how quantum interference in phase space is smoothed over by the diffusion associated with environmental coupling . a general mixed state is an incoherent superposition of pure state wigner functions , where an individual semiclassical pure state wigner function can be formed by substituting the van - vleck semiclassical wavefunction in eqn . ( [ wdef ] ) . if we allow @xmath85 to be perturbed by noise we can rewrite the classical action @xcite @xmath86 following berry @xcite , we now rewrite the action for the @xmath87th solution to the hamilton - jacobi equation as @xmath88 where @xmath89 is the @xmath87th branch of the momentum curve for a given @xmath85 . if we average over all noisy realizations , after separating the contributions from identical branches , the following suggestive expression for the noise averaged semiclassical wigner function obtains : @xmath90 + \nonumber\\ & & { 2i}\sum_{i < j}{\cal j}_{ij}\sin\bigg[\frac{1}{\hbar } \bigg\{\int_{q_{c}(0)}^{\bar{q}_{+}}dq'p_{i}(q',t)- \int_{q_{c}(0)}^{\bar{q}_{-}}dq'p_{j}(q',t)\nonumber\\ & & -\int_{0}^{t}dt'\left({\cal h}_i-{\cal h}_j\right ) + \phi_{i}-\phi_{j}\bigg\}\bigg]\bigg);\\ \label{semiwig } & & { \cal j}_{ij}\equiv { c_{i}(\bar{q}_{+},t)c_{j}(\bar{q}_{-},t)\over \sqrt{|j_{i}(\bar{q}_{+},t)||j_{j}(\bar{q}_{-},t)|}}\end{aligned}\ ] ] for jacobian determinant @xmath91 and transport coefficient @xmath92 ; @xmath93 and @xmath94 , where @xmath95 is the @xmath87th maslov index @xcite . the dominant contributions to the integrals can be analyzed in the stationary phase approximation @xcite . if @xmath96 , these would contribute phase coherences at values of @xmath97 that satisfy @xmath98 for the first term in the sum and @xmath99 for the second term , the former being the famous berry midpoint rule . for a chaotic system , berry argued that , due to the proliferation of momentum branches , @xmath89 , arising from the infinite number of foldings of a bounded chaotic curve as @xmath100 , a semiclassical approximation would eventually fail , since the interference fringes stemming from a given @xmath101 could not be distinguished after a certain time from those emanating from the many neighboring branches @xcite . while the precise value of this time has since been challenged numerically , the essential nature of this physical argument has remained valid @xcite . in the present case , however , the presence of noise acts as a dynamical gaussian filter , damping contributions for any solutions to the above equation which are greater than @xmath102 . in other words , noise dynamically filters the long `` de broglie '' wavelength contributions to the semiclassical integral , the very sort of contributions which generally invalidate such an approximation . if we rescale the above result and combine it with our understanding of how noise effects classical phase space structures , we can qualitatively estimate whether or not a semiclassical picture is a valid approximation to the dynamics . as already discussed , @xmath83 is the time when the formation of new classical structures ceases and @xmath103 is the associated scale over which classical structures are averaged . the key requirement is then that the semiclassical phase filters contributions of size @xmath104 in other words , for a given branch , the phases with associated wavelengths long enough to interfere with contributions from neighboring branches are strongly damped , and the intuitive semiclassical picture of classical phase - space distributions decorated by local interference fringes recovered . the weak form of the qct is completed when the inequality ( [ result ] ) is satisfied . substituting the scale of classical smoothing ( [ nscale ] ) in this inequality , we find @xmath105 [ note that the purely classical quantity @xmath83 is first independently determined by solving eqn . ( [ nscale ] ) and then compared to the right side of the above equation . ] while the left hand side of the inequality contains the mutually dependent @xmath83 and @xmath84 , the right hand side depends only on fixed properties of the system and @xmath35 . this condition , therefore , defines a threshold at which the semiclassical approximation becomes stable and that may be set in terms of either @xmath84 or @xmath83 . once the threshold is met , @xmath83 becomes the time beyond which the semiclassical description is valid . the semiclassical nature of this condition becomes more evident on defining @xmath106 which , given that @xmath107 is an areal scale in phase space for the diffusion averaged dynamics , has dimensions of action . a physical interpretation is more apparent on rewriting ( [ tstar ] ) as @xmath108 , which is readily identified as the usual condition for the validity of a semiclassical analysis . the weak form of the qct can also be demonstrated using the duffing example @xcite . the dynamical evolution of the bounded motion is dominated by the homoclinic tangle of a single hyperbolic fixed point . as a result , the long - time chaotic evolution can be completely characterized by the unstable manifold associated with that fixed point @xcite . the value of @xmath35 is now set to @xmath109 , significantly larger than when studying the strong form of the qct . the weak form of the qct for a driven duffing oscillator @xcite : sectional cuts of wigner functions ( dashed lines ) and classical distributions ( solid lines ) , after 149 drive periods , taken at @xmath110 for diffusion coefficient values ( a ) @xmath111 ; ( b ) @xmath112 ; ( c ) @xmath113 . other parameter values are stated in the text ; the height is specified in scaled units.,width=384 ] the evolution of the corresponding distributions was numerically calculated for both the classical and quantum master equations . [ fig : sliceplot ] shows sectional cuts at @xmath110 of the quantum and classical phase space distribution functions for three different values of the diffusion coefficient , @xmath114 , after time @xmath115 evolution periods . as already mentioned , @xmath83 varies slowly with @xmath84 , and in the three cases shown , @xmath83 ranges only from @xmath116 ( note that @xmath117 ) . it is easy to check that the inequality ( [ tstar ] ) is strongly violated for @xmath111 , mildly violated for @xmath112 , and approximately satisfied for @xmath113 . for @xmath111 , the classical and quantum sections show no similarities , as expected . the quantum wigner function also shows large negative regions , reflecting strong quantum interference . on increasing @xmath84 to @xmath118 the magnitude of quantum coherence decreases dramatically and the classical and quantum slices have the same average value , as well as specific agreement on some large scale features . the two disagree , as expected , on the small scale structures . this indicates that , while the quantum and classical distributions do not exactly match , the wigner function has now become sensitive to the larger features of the noise averaged classical distribution function , indicative of the transition to a semiclassical regime . at @xmath113 , there is near perfect agreement between classical and quantum distribution functions , save on the smallest scales . when @xmath84 is of order unity , the inequalities enforcing the strong qct at the level of individual trajectories @xcite are satisfied and the agreement is essentially exact . however , as indicated by fig . [ fig : sliceplot](c ) , detailed agreement for quantum and classical distribution functions can begin at much smaller values of the diffusion constant . phase space rendering of the wigner function at time @xmath119 periods of driving @xcite . the early time part of the unstable manifold associated with the noise - free dynamics is shown in blue . the value of @xmath112 is not sufficient to wipe out all the quantum interference which , as expected , is most prominent near turns in the manifold.,width=384 ] for more detailed evidence that , at @xmath112 , one is entering a semiclassical regime , in fig . [ fig : wigman ] we superimpose an image of the large scale features of the classical unstable manifold on top of the full quantum wigner distribution at @xmath112 after 149 drive periods [ case ( b ) of fig . 2 ] . the quantum phase space clearly exhibits local interference fringes around the large lobe - like structures associated with the short - time evolution of the unstable manifold . the appearance of local fringing about classical structures is direct evidence of a semiclassical evolution , where interference effects appear locally around the backbone of a classical evolution . this is in sharp contrast to the global diffraction pattern seen for @xmath96 , where the contributions from individual curves can not be distinguished , suppressing the appearance of any classical structure @xcite . at this point , our analysis of measured quantum dynamical systems may be said to have harmonized quantum and classical mechanics in the sense that the strong and weak forms of the qct have appeared naturally . while this is certainly pleasing , we wish to go further and ask whether the formalism can be tested by making predictions that are experimentally verifiable and depend uniquely on the nonlinear nature of the conditioned evolution . one very interesting idea is the real - time control of quantum systems using state - estimation as pioneered by belavkin @xcite or direct feedback of the measured classical current @xcite . although quantum feedback control applications @xcite have their own importance , we now return to the original burning question : is there chaos in quantum mechanics ? in a limiting case , the answer is clearly in the affirmative . we have already shown that quantum distributions , provided certain conditions are met , can evolve while staying localized and be only very weakly perturbed by noise . in the classical limiting case , we recover localized classical trajectories , and these can certainly be chaotic . but what if these conditions are not satisfied ? this is the question addressed and answered in ref . @xcite . by defining and computing the lyapunov exponent for an observed quantum system deep in the quantum regime , we were able to show that the system dynamics is chaotic . further , the lyapunov exponent is not the same as that of the classical dynamics that emerges in the classical limit . since the quantum system in the absence of measurement is not chaotic , this chaos must emerge as the strength of the measurement is increased , and we examined the nature of this emergence . to do this , we must first make certain that we can quantify the existence of chaos in a robust way . the rigorous quantifier of chaos in a dynamical system is the maximal lyapunov exponent @xcite . the exponent yields the ( asymptotic ) rate of exponential divergence of two trajectories which start from neighboring points in phase space , in the limit in which they evolve to infinity , and the neighboring points stay infinitesimally close . the maximal lyapunov exponent characterizes the sensitivity of the system evolution to changes in the initial condition : if the exponent is positive , then the system is exponentially sensitive to initial conditions , and is said to be chaotic . we now discuss how this notion can be applied to observation - conditioned evolution of quantum expectation values . a single quantum mechanical particle is in principle an infinite dimensional system . however , for the purpose of defining an observationally relevant lyapunov exponent , it is sufficient to use a single projected data stream : let us consider the expectation value of the position , @xmath120 . the important quantity is thus the divergence , @xmath121 , between a fiducial trajectory and a second trajectory infinitesimally close to it . it is important to keep in mind that the system is driven by noise . since we wish to examine the sensitivity of the system to changes in the initial conditions , and not to changes in the noise , we must hold the noise realization fixed when calculating the divergence . the lyapunov exponent is thus @xmath122 where the subscript @xmath36 denotes the noise realization . this definition is the obvious generalization of the conventional ode definition to dynamical averages , where the noise is treated as a drive on the system . indeed , under the conditions when ( noisy ) classical motion emerges , and thus when localization holds , it reduces to the conventional definition , and yields the correct classical lyapunov exponent . to combat slow convergence , we measure the lyapunov exponent by averaging over an ensemble of finite - time exponents @xmath123 instead of taking the asymptotic long - time limit for a single trajectory . a key result now follows : in unobserved , i.e. , isolated quantum dynamical systems , it is possible to prove , by employing unitarity and the schwarz inequality , that @xmath72 vanishes ; the finite - time exponent , @xmath124 , decays away as @xmath125 @xcite . from the kosloff - rice theorem we know , of course , that the lyapunov exponent must be zero , since the overall evolution is integrable , but this result gives us a quantitative statement regarding the decay of the exponent . it turns out that this particular result applies also to the evolution of averages in isolated classical systems and , in this sense , is more general than kosloff - rice . as we have emphasized earlier , once measurement is included , the evolution becomes nonlinear and the lyapunov exponent need not vanish classically or quantum mechanically . as a particular system of interest , we turn once again to the duffing oscillator , this time with @xmath126 , which is small enough so that the system makes a transition to classical dynamics when the measurement is sufficiently strong . as we increase the measurement strength , we can examine the transformation from essentially isolated quantum evolution all the way to the known chaos of the classical duffing oscillator . to examine the emergence of chaos , in ref . @xcite we solved for the evolution of the system for @xmath127 . when @xmath128 , the distribution is spread over the entire accessible region , and ehrenfest s theorem is not satisfied . conversely , for @xmath129 , the distribution is well - localized ( fig . [ fig0 ] ) , and ehrenfest s theorem holds throughout the evolution . since the backaction noise , characterized by the momentum diffusion coefficient , @xmath130 , remains small , at this value of @xmath19 the motion is that of the classical system , to a very good approximation . position distribution for the duffing oscillator with measurement strengths @xmath131 ( red ) and @xmath129 ( green ) , demonstrating measurement - induced localization ( @xmath129 ) as the measurement coupling is increased @xcite . the momentum distribution behaves similarly.,width=321,height=245 ] phase space stroboscopic maps @xcite for the observed duffing oscillator for 4 different measurement strengths , @xmath132 , 0.01 ( top ) , and 1 , 10 ( bottom ) . contour lines are superimposed to provide a measure of local point density at relative density levels of @xmath133 and @xmath134.,width=359,height=321 ] stroboscopic maps help reveal the global structural transformation in phase space in going from quantum to classical dynamics ( fig . [ fig1 ] ) . the maps consist of points through which the system passes at time intervals separated by the period of the driving force . for very small @xmath19 , @xmath135 and @xmath136 are largely confined to a region in the center of phase space . somewhat remarkably , at @xmath131 , although the system is largely delocalized , as shown in fig . [ fig0 ] , nontrivial structure appears , with considerable time being spent in certain outer regions . by @xmath137 the localized regions have formed into narrower and sharper swirling coherent structures . at @xmath129 the swirls disappear , and we retrieve the uniform chaotic sea of the classical map ( the small `` holes '' are periodic islands ) . the swirls in fact correspond to the unstable manifolds of the classical motion . classically , these manifolds are only visible at short times , as continual and repeated folding eventually washes out any structure in the midst of a uniform tangle . in the quantum regime , however , the weakness of the measurement , with its inability to crystallize the fine structure , has allowed them to survive : we emphasize that the maps result from long - time integration , and are therefore essentially time - invariant . to calculate the lyapunov exponent we implemented a numerical version of the classical linearization technique @xcite , suitably generalized to quantum trajectories . the method was tested on a classical noisy system with comparison against results obtained from solving the exact equations for the lyapunov exponents @xcite . the calculation is very numerically intensive , as it involves integrating the stochastic schrodinger equation equivalent to the sme ( [ condq ] ) over thousands of driving periods , and averaging over many noise realizations ; parallel supercomputers were invaluable for this task . the computations show that as @xmath74 is increased , for nonzero @xmath19 , the value obtained for @xmath124 falls as @xmath125 , following the behavior expected for @xmath138 , until a point at which an asymptotic regime takes over , stabilizing at a finite value of the lyapunov exponent as @xmath100 . this behavior is shown in fig . [ fig2 ] for three values of @xmath19 . the lyapunov exponent as a function of @xmath19 is shown in fig . the exponent increases over two orders of magnitude in an approximately power - law fashion as @xmath19 is varied from @xmath139 to @xmath140 , before settling to the classical value , @xmath141 . the results in figs . [ fig2 ] and [ fig3 ] show clearly that chaos emerges in the observed quantum dynamics well before the limit of classical motion is obtained . finite - time lyapunov exponents @xmath124 for measurement strengths @xmath142 , averaged over 32 trajectories for each value of @xmath19 ( linear scale in time , top , and logarithmic scale , bottom ; bands indicate the standard deviation over the 32 trajectories ) @xcite . the ( analytic ) @xmath125 fall - off at small @xmath19 values , prior to the asymptotic regime , is evident in the bottom panel . the unit of time is the driving period.,width=321,height=377 ] we also computed the lyapunov exponent for the quantum system when its action is sufficiently small that smooth classical dynamics can not emerge , even for strong measurement @xcite . taking a value of @xmath143 , we find that for @xmath144 , @xmath145 , for @xmath131 , @xmath146 and for @xmath147 , @xmath148 . thus the system is once again chaotic , and becomes more strongly chaotic the more strongly it is observed . from these striking results , it is clear that there exists a purely _ quantum _ regime in which an observed system , while behaving in a fashion quite distinct from its classical limit , nevertheless evolves chaotically with a finite lyapunov exponent , also distinct from the classical value . the emergence of chaos @xcite : the lyapunov exponent @xmath72 as a function of measurement strength @xmath19 . error - bars follow those of fig . 6 , taken at the final time.,width=321,height=245 ] it is worth pointing out that an analogous analysis can also be carried out for a continuously observed classical system . as mentioned previously , an _ unobserved _ probabilistic classical system also has provably zero lyapunov exponent : the average of @xmath3 for an ensemble of classical particles does not exhibit chaos , due to the linearity of the liouville equation @xcite . if we consider a noiseless observed chaotic classical system possible since classical measurements are by definition passive ( no backaction noise ) then even the weakest meaningful measurement will , over time , localize the probability density , generating an effective trajectory limit , and thus the classical lyapunov exponent , @xmath149 @xcite . noise can always be be injected into classical systems as an external drive , nevertheless , in the limit of weak noise , the system will once again possess the noiseless exponent @xmath149 : in a classical system the external noise is not connected to the strength of the measurement , so one can simultaneously have strong measurement and weak noise , which , as we have seen , is possible in the quantum theory only under specific conditions @xcite . as one way to understand the classical case , we can employ the quantum result as an intermediate step . consider the quantum lyapunov exponent at a fixed value of @xmath19 ( where @xmath150 ) as in fig . if the value of @xmath35 is now reduced , the dynamics of the system must tend to the classical limit as the quantum - classical correspondence inequalities of ref . @xcite are better satisfied . thus the lyapunov exponent in the classical limit of quantum theory which , to a very good approximation , is just classical dynamics driven by weak noise must tend to @xmath149 . if , however , the noise is not weak , an observed classical system , like a quantum system outside the classical regime , will also not be localized , and may well have an exponent different from @xmath149 . in addition , one may expect the non - localized quantum and classical evolutions to have quite different lyapunov exponents , especially when @xmath35 is large on the scale of the phase space , as quantum and classical evolutions generated by a given nonlinear hamiltonian are essentially different @xcite . the nature of the lyapunov exponent for non - localized classical systems , and its relationship to the exponent for quantum systems is a very interesting open question . to summarize , we have presented a simple analysis of continuously observed classical and quantum dynamical systems . this analysis is in fact required to deal with next - generation experiments and underlies the nascent field of real - time quantum feedback control . major results include an intuitive and quantitative understanding of the quantum - classical transition . it is pleasing that both the strong and weak forms of the qct can eventually be understood as a macroscopic limit of observed - system quantum mechanics , i.e. , whenever the observed system action @xmath151 . perhaps , most interestingly , we have obtained clear predictions for dynamical chaos in observed quantum systems that are far from the classical regime . we emphasize that the chaos identified here is not merely a formal result even deep in the quantum regime , the lyapunov exponent can be obtained from measurements on a real system as in near - future cavity qed and nanomechanics experiments @xcite . experimentally , one would use the known measurement record to integrate the sme ( [ condq ] ) ; this provides the time evolution of the mean value of the position . from this fiducial trajectory , given the knowledge of the system hamiltonian , the lyapunov exponent can be obtained by following the procedure described here . sh thanks the organizers of the 16th florida workshop in nonlinear astronomy and physics , dedicated to the memory of henry kandrup , for their kind invitation to lecture at the meeting . large - scale parallel computing support from los alamos national laboratory s institutional computing initiative is gratefully acknowledged . this research is supported by the department of energy , under contract w-7405-eng-36 . wigner , phys . rev . * 40 * , 749 ( 1932 ) ; v.i . tatarskii , usp . nauk * 139 * , 587 ( 1983 ) [ sov . uspekhi * 26 * , 311 ( 1983 ) ] ; m. hillery , r.f . oconnell , m.o . scully , and e.p . wigner , phys . rep . * 106 * , 121 ( 1984 ) . kadanoff and g. baym , _ quantum statistical mechanics _ ( addison - wesley , redwood city , 1989 ) ; r. zwanzig , _ nonequilibrium statistical mechanics _ ( oxford university press , new york , 2001 ) ; k. blum , _ density matrix theory and applications _ ( plenum press , new york , 1996 ) . l. diosi , phys . lett . * 129a * , 419 ( 1988 ) ; v.p . belavkin and p. staszewski , phys . lett . * 140a * , 359 ( 1989 ) ; y. salama and n. gisin , phys . lett . * 181a * , 269 ( 1993);c.m . caves and g.j . milburn , phys . a * 36 * , 5543 ( 1987 ) ; h.m . wiseman and g.j . milburn , phys . a * 47 * , 642(1993 ) ; h.j . carmichael , _ an open systems approach to quantum optics _ ( springer - verlag , berlin , 1993 ) ; g.j . milburn , quantum semiclass . opt . * 8 * , 269 ( 1996 ) ; t.a . brun , am . * 70 * , 719 ( 2002 ) ; p. warszawski and h.m . wiseman , j. opt . b * 5 * , 1 ( 2003 ) . t. bhattacharya , s. habib and k. jacobs , phys . 85 * , 4852 ( 2000 ) ; phys . a * 67 * , 042103 ( 2003 ) . see also , s. ghose , p. alsing , i. deutsch , t. bhattacharya , and s. habib , phys . a * 69 * , 052116 ( 2004 ) . belavkin , comm . phys . * 146 * , 611 ( 1992 ) ; v.p . belavkin , rep . phys . * 43 * , 405 ( 1999 ) ; a.c . doherty and k. jacobs , phys . a * 60 * , 2700 ( 1999 ) ; a.c . doherty , s. habib , k. jacobs , h. mabuchi , and s .- m . tan , phys . a * 62 * , 012105 ( 2000 ) . see , e.g. , h.m . wiseman , s. mancini , and j. wang , phys . a * 66 * , 013807 ( 2002 ) ; r. ruskov and a.n . korotkov , phys . b * 66 * , 041401(r ) ( 2002 ) ; a. hopkins , k. jacobs , s. habib , and k. schwab , phys . rev . b * 68 * , 235328 ( 2003 ) ; d.a . steck , k. jacobs , h. mabuchi , t. bhattacharya , and s. habib , phys . lett . * 92 * , 223004 ( 2004 ) .

the relationship between chaos and quantum mechanics has been somewhat uneasy even stormy , in the minds of some people . however , much of the confusion may stem from inappropriate comparisons using formal analyses . in contrast , our starting point here is that a complete dynamical description requires a full understanding of the evolution of _ measured systems _ , necessary to explain actual experimental results . this is of course true , both classically and quantum mechanically . because the evolution of the physical state is now conditioned on measurement results , the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions . due to this feature , the physically more complete treatment reveals the existence of dynamical regimes such as chaos that have no direct counterpart in the linear ( unobserved ) case . moreover , this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system , both at the level of trajectories as well as distribution functions . finally , we have the striking prediction that time - series from measured quantum systems can be chaotic far from the classical regime , with lyapunov exponents differing from their classical values . these predictions can be tested in next - generation experiments .

Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Video: Watch arrest of Kalamazoo shooting suspect | 3:29 Patrol car video released Monday by the Kalamazoo County Sheriff's Office shows the arrest of Jason Dalton, 45, following a shooting spree in and around Kalamazoo on Feb. 20 that left 6 dead and 2 wounded. Dalton says his Uber app controlled him. Kalamazoo County Sheriff's Department 1 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS 911 call: Kalamazoo shooting spree | 3:05 Kalamazoo County Sheriff's Office released 911 recordings connected with the Feb. 20 shooting spree on March 14, including this one from the Cracker Barrel scene. Robert Allen 2 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Parents: Abigail Kopf showing improvement, still critical | 0:28 Kalamazoo shooting victim Abigail Kopf is showing signs of improvement, but she's still in critical condition, her parent's said Thursday. WZZM 3 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Man details harrowing ride with Michigan suspect | 0:50 An Uber passenger says he called the police to report an erratic driver more than an hour before authorities allege the driver began shooting people at random, killing six and wounding two others before being arrested. (Feb. 22) AP 4 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Mom 'numb' after losing son, husband in Kalamazoo shooting | 1:28 Tyler Smith and his dad Richard were shot while they were at a car dealership, the second stop in a shooting rampage in Kalamazoo, Michigan. VPC 5 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Uber becomes focus of Kalamazoo killings | 1:44 The suspect in the Kalamazoo shooting spree was an Uber driver and allegedly took fares the night of the shootings. 6 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Kalamazoo shooting: What we know about the suspect | 0:49 Jason Dalton is accused of killing six people and injuring two others in a random shooting spree across Kalamazoo, Michigan. 7 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Kalamazoo shooting suspect faces arraignment | 2:37 Authorities say Jason Dalton had no criminal history prior to Saturday's shooting spree across Kalamazoo, Michigan. He is accused of killing six people and critically injuring two others. 8 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Prosecutor: Kalamazoo shooting suspect showed no emotion | 1:02 Jason Dalton was described as cooperative and non-combative following a deadly shooting spree that killed six people and left two others critically hurt in Kalamazoo, Michigan. VPC 9 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS 6 killed in Kalamazoo, Michigan shooting spree | 0:44 Jason Dalton is accused of killing six people and critically injuring two others, including a mother who was shot in front of her children. VPC 10 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS 'Random' shooting spree leaves 6 dead In Kalamazoo | 0:50 Police arrested 45-year-old Jason Dalton after a brief car chase. A weapon was found in his vehicle. Newslook 11 of 12 Skip in Skip x Embed x Share CLOSE KALAMAZOO DEADLY SHOOTINGS Neighbors: Kalamazoo suspect a good family man | 1:19 Gary and Sally Pardo, neighbors of Jason Dalton of Cooper Twp., who is suspected of killing six people in Kalamazoo on Saturday night, speak to the Detroit Free Press. Andraya Croft, Special to the Free Press 12 of 12 Last VideoNext Video Video: Watch arrest of Kalamazoo shooting suspect 911 call: Kalamazoo shooting spree Parents: Abigail Kopf showing improvement, still critical Man details harrowing ride with Michigan suspect Mom 'numb' after losing son, husband in Kalamazoo shooting Uber becomes focus of Kalamazoo killings Kalamazoo shooting: What we know about the suspect Kalamazoo shooting suspect faces arraignment Prosecutor: Kalamazoo shooting suspect showed no emotion 6 killed in Kalamazoo, Michigan shooting spree 'Random' shooting spree leaves 6 dead In Kalamazoo Neighbors: Kalamazoo suspect a good family man Tiana Carruthers is recovering after being shot Saturday near Kalamazoo. She was the first of eight people allegedly shot by Uber driver Jason Dalton. (Photo: Courtesy family photo) Tiana Carruthers was at a playground late Saturday afternoon at her Richland Township apartment complex with her young daughter, a niece and three other children when a man pulled up to the curb in a silver-colored SUV and motioned for her to come over. When Carruthers, 25, approached, the man — later identified as alleged Kalamazoo shooter and Uber driver Jason Dalton — mumbled, asked if she knew a woman by a certain name, then calmly pulled a gun out from his coat and shot her once near her shoulder, Carruthers' grandmother Phoenix Windwalker told the Free Press in an interview Tuesday morning. Carruthers turned, screamed for the children to run and blocked them from the gunman with her body, as she was shot at least two more times in the hip and leg area, before the gunman sped off, Windwalker said. Police said they recovered 10 spent shell casings at the scene. Carruthers was the first victim of the random shootings in the city and surrounding areas that took place over the next four hours, leaving six people dead and two wounded. Windwalker said her granddaughter is a hero. "The children were saved," Windwalker said. "Her 7-year-old daughter saw her get shot, along with her niece and the three other children. She saved the children by doing what she did, which was really courageous for her and I'm proud of her, but I feel so, so sorry for her. It's just not fair." Seven of the bullets pierced the siding in the nearest townhome. “Some hit the boards, four actually went through our bedroom wall closet,” said Tammy George, 45, who’s lived in the townhome about two years. “We had three kids in the room at the time. They thank God they were OK.” She said they didn’t know the building had been hit until an investigative team was on the scene with lasers. George, who was home when the shooting occurred, at first didn’t think the gunshots just outside were real. “When it happened there was several kids out there playing, and I thought it was fireworks,” she said. “The playground is constantly full.” On Tuesday, it was empty. Neighbors said that was unusual. George and Jamie Schippers, 38, who lives across the street, both said that they went outside and found Carruthers. She told them that the shooter had asked if she knew, or was, “Maisey.” They said the shooter then drove around the block, returned and opened fire, which differs from the grandmother’s account. “I was trying to keep her kind of calm, and she was doing really good,” Schippers said. “She wasn’t freaking out or anything at all.” George said Carruthers asked about her kids, and the kids said she’d told them to run. Orange markers could still be seen on the pavement Tuesday, marking the tire skids from the shooter's vehicle as it fled the scene. Police say they believe Dalton, a 45-year-old married father of two, might have fired at least 30 rounds across three crime scenes Saturday from a 9mm semiautomatic handgun. Six people were killed. Carruthers and a 14-year-old girl were severely injured in separate shootings. The victims ranged from 14 to 74 years old. Windwalker said her granddaughter was outside her apartment at the playground because she was getting ready to take her daughter to a gymnastics class in the area. "I don’t understand if the Uber driver was bringing a passenger there or picking up a passenger," Windwalker said. "They’ve never said one way or the other why he was there. We know that he called her over to the vehicle, he asked her if she knew such and such person and she said no, saw the gun and he shot her in the shoulder." Windwalker said she wasn't sure of the name Dalton said to her granddaughter before firing the gun at her. Fortunately, Carruthers is expected to make a full recovery, Windwalker said. She's had two surgeries and has rods in both of her legs now, according to her grandmother, who said doctors said it could be six or eight months before she'll be able to walk again. "They had to put a cadaver bone in her collarbone because the bone in her collarbone was shattered and they couldn’t repair it," Windwalker said. "Before she went into her second surgery, Tiana almost went into a depression, she wanted to see her daughter. She got to talk to her, see her, spend some time with her. And my great-granddaughter, she got to know her mother was OK and that she’s alive. That relieved her." Windwalker said she was floored and overcome with worry and grief when she heard her granddaughter was shot. "My daughter called me while I was on a conference call talking to some friends," Windwalker recalled. "She said Tiana’s been shot. Everyone was so worried, stressed out. She's got a long road ahead of her." Windwalker said she wasn't surprised when she heard the story behind her granddaughter's shooting. She said Carruthers has always been selfless and kind. "She’s a good person," Windwalker said. "And she is real protective of her daughter, who is her only child. ...And she would be very protective of any other person's child because children can't protect themselves when something like this happens." Keoki Kekahuna-Carruthers, Tiana Carruthers' uncle, said his niece has always been "a very smart young lady" and a good mother. "It's a shame this tragedy has happened to her," he said. "I'm a combat vet and I've never understood the random acts of violence on innocent people." Buy Photo (Photo: Jessica J. Trevino/Detroit Free Press) Dalton sat motionless Monday afternoon when arraigned on the charges connected to the shooting spree, which officials say occurred while he continued to take Uber fares. He was arraigned on six murder charges and 10 other felony counts. Dalton's family went public Monday, condemning the shootings and offering their condolences to the victims and their families in a statement provided to the Free Press. But Windwalker said Dalton needs to pay a heavy price for his alleged crimes. "I feel that he should get the death penalty," Windwalker said. "Death is not right, but he killed six innocent people and injured two people and almost killed five children. ...I believe in God and I believe if you do something wrong, you deserve to get punished. He does not deserve to have life. He needs to be put out of his misery. I can forgive him, but the way I feel when a person goes out and takes a person's life in cold blood ... It's an eye for an eye." Buy Photo (Photo: Robert Allen Detroit Free Press) Contact Katrease Stafford: [email protected] or 313-223-4759. Read or Share this story: http://on.freep.com/1XKV7HG ||||| Jason Dalton is seen on closed circuit television during his arraignment in Kalamazoo County, Michigan on February 22, 2016. REUTERS/Kalamazoo County Court/Handout via Reuters KALAMAZOO, Mich. The Michigan Uber driver charged with murdering six people switched vehicles after sideswiping a car at the start of the shooting spree, authorities said on Tuesday, adding they hoped his phone would help establish a motive for the killings. It was also disclosed that the suspect, Jason Dalton, who was reported to have obtained a community college degree in law enforcement two decades ago, visited a gun shop shortly before the shootings and bought a heavy-duty jacket that could conceal a small pistol. Dalton, 45, was denied bail on Monday after a court hearing in which a detective testified that he admitted to the five-hour shooting rampage over the weekend in Kalamazoo, Michigan, about 150 miles (240 km) west of Detroit. Hours before the first shooting occurred on Saturday evening, Dalton and a friend visited Southwick's, a gun shop he frequented in nearby Plainwell, a shop employee told Reuters. Dalton was a regular customer who usually spent time chatting with the staff, but he bought the jacket and left the store within 10 minutes, said the employee, who asked not to be identified. "He’s in here enough for me to know he talks to the guys about guns and different stuff,” she said. Searching for a motive behind the violence, investigators focused on a 9mm semi-automatic handgun and a cellphone seized from Dalton, as well as the fact that he picked up fares for the Uber car-hailing service between or after the shooting episodes, authorities said. At least one passenger who rode in Dalton's car that night, apparently after the rampage had begun, recounted that the Uber driver seemed oddly calm and even appeared to be fatigued to the point of almost falling asleep at the wheel. "He didn't say much and he didn't act abnormal. He was rather quiet," Marc Dunton, 39, told Reuters of the ride he shared with two friends, taking the front-passenger seat beside Dalton. Prosecutors say Dalton randomly shot at people at an apartment complex, a car dealership and a restaurant, killing six and badly wounding two others, including a 14-year-old girl left in critical condition. "Right after the first shooting at the apartments, he left the scene and sideswiped a car," said Paul Matyas of the Kalamazoo County Sheriff's Department. The accident prompted him to switch cars, from a silver Chevrolet Equinox to a Chevy HHR, both vehicles belonging to his family, Matyas said. Dunton said he was picked up in an HHR. Another Uber passenger, Matthew Mellen, told CNN he rode in Dalton's Equinox and that Dalton seemed normal until he received a call on his cellphone, at which point he began driving erratically, running stoplights and a stop sign and sideswiping another vehicle. Matyas said investigators were examining Dalton's Uber contacts and working to "track his phone calls, track his whereabouts" in the hours before his arrest early on Sunday. Detroit-based NBC affiliate WDIV-TV reported that Dalton graduated from Kalamazoo Valley Community College in 1992 with an associate's degree in law enforcement and criminal justice but did not enroll at the school's police academy. He had no criminal record, authorities said. (Additional reporting by Barbara Goldberg in New York and Jon Herskovitz in Austin, Texas; Editing by Tom Brown and Peter Cooney) ||||| Please enable Javascript to watch this video KALAMAZOO, Mich. — Amid the tragedy that struck Kalamazoo Saturday night, claiming the lives of six innocent people, a hero emerged. According to police, a mother who was walking with children used her body to shield them from gunfire. Her name is Tiana Carruthers. “You look at where bullets ended, looking where the victims were and looking where the suspect vehicle was, I truly believe her actions were very courageous and likely led to the saving of some children’s lives,” said Kalamazoo County Sheriff Richard Fuller. Police said she was walking home with children after enjoying the afternoon at the park. That’s when the gunman approached and engaged her in a brief conversation. “The suspect’s activities changed where at some point she decided to tell the children to run,” said Fuller. “Then she stayed behind the children and that’s when the suspect opened fire.” Police said the gunman shot her multiples times in front of her home in a housing complex. When detectives arrived on the scene, they immediately taped off her home and the adjacent parking lot. As for Carruthers, she was immediately rushed to the hospital. Fuller said she’s undergone surgery more than once since the shooting. “She’s in the hospital and the hospital is just trying to take care of their patient, which I greatly appreciate,” said Fuller. “They’re trying to keep her comfortable and on the road to recovery because her road is going to be a long road.” Fuller said that he and Kalamazoo Mayor Bobby Hopewell keep in constant contact with family. They both are asking everyone to respect the family's wish for privacy during this difficult time. The mother released a statement Tuesday afternoon saying in part “We appreciate every prayer and tender thought extended to us.” “They were thankful as well a they send condolences to everyone elses families,” said Fuller. “They have great, heavy hearts right now because they recognize that this is a community in pain.”

– As investigators try to piece together Saturday night's shooting rampage in Kalamazoo, Mich., the first person to be shot is emerging as a hero. Kalamazoo County Sheriff Richard Fuller says Tiana Carruthers, a 25-year-old mother, was with several children outside an apartment complex when alleged gunman Jason Dalton approached her, Fox17 reports. She told the kids to run inside and was shot three times when he opened fire. "You look at where bullets ended, looking where the victims were and looking where the suspect vehicle was, I truly believe her actions were very courageous and likely led to the saving of some children's lives," the sheriff says. Carruthers was hospitalized with gunshot wounds in the shoulder, hip, and leg. Dalton, an Uber driver, went on to kill six people and critically injure another, police say. Carruthers' grandmother, Phoenix Windwalker, tells the Detroit Free Press that Carruthers' actions were heroic. "The children were saved," Windwalker says. "Her 7-year-old daughter saw her get shot, along with her niece and the three other children. She saved the children by doing what she did, which was really courageous for her and I'm proud of her, but I feel so, so sorry for her. It's just not fair." She says her granddaughter has had two surgeries and has been told it could be as long as eight months before she can walk again. Police, who are still trying to uncover a motive for the shootings, say Dalton sideswiped a car after leaving the scene and switched to another vehicle, Reuters reports. (Uber has admitted receiving a complaint about Dalton before the shootings.)

Lil Wayne is recovering after being hospitalized for seizures. TMZ initially reported that Wayne was in critical condition. The 30-year-old rapper was rushed to Cedars Sinai Tuesday. He was released the next day but was taken to the hospital again after being found unconscious in his room, TMZ reported. According to TMZ, Wayne had been placed in an induced coma. The rapper Mack Maine tweeted, however, that Wayne is home "alive and well." Another rapper, Birdman, tweeted, "My son is in good spirit..feelin much betta...be home soon." UPDATE, 9:33: Lil Wayne tweets he is doing "good." I'm good everybody. Thx for the prayers and love. — Lil Wayne WEEZY F (@LilTunechi) March 16, 2013 UPDATE, 9:13:: HLN anchor Richelle Carey tweets that an official statement says Lil Wayne is recovering: BREAKING>OFFICIAL statement from Young Money publicist: "We can confirm Lil Wayne did have a seizure and that he is recovering." #Weezy — RICHELLE CAREY (@RichelleCarey) March 16, 2013 UPDATE, 9:08: A Billboard editor tweets that a "close source just let me know that Lil Wayne is 'recovering.'" UPDATE, 9:02: TMZ has removed from its report a claim that Lil Wayne is "being prepared for his last rites." See tweets below. Warning: graphic language. Wayne is alive and well! We watching the Syracuse game...thanks for the prayers and concern..he will update you all soon. #love — Mack Maine (@mackmaine) March 16, 2013 My son is in good spirit..feelin much betta...be home soon.YMCMB — BIRDMAN (@BIRDMAN5STAR) March 16, 2013 We will be releasing an official statement shortly but dont believe the nonsense about comas and tubes to breathe...that's false!! — Mack Maine (@mackmaine) March 16, 2013 @tmz it's certain shit you should not talk about or play with if u don't kno what u talking bout....don't deceive the fans or the people — Mack Maine (@mackmaine) March 16, 2013 @tmz and definitely don't try to kill a man before his time....so from the bottom of my soul and on behalf of my fam......FUCK YOU — Mack Maine (@mackmaine) March 16, 2013 The story is currently developing... Also on HuffPost: ||||| As reports circulate that rap superstar Lil Wayne, 30, clings to life after a suspected sizzurp binge, the hip-hop musician's drug of choice is under the glare of the public spotlight as never before. Here now is everything you need to know about the dangerous recreational narcotic. What is sizzurp? Sizzurp is an addictive concoction that gets the user high, made by combining prescription-strength cough syrup with sugary sodas like Mountain Dew or Coca-Cola, to which hard candies like Jolly Ranchers are added for more flavor. It's typically sipped out of Styrofoam cups. REPORT: Rep Says Lil Wayne 'Recovering' How does it get you high? Prescription cough syrup contains the active ingredients codeine and promethazine. Codeine is a part of a group of drugs called narcotic pain medicines. Usually prescribed for mild to moderately severe pain, the drug produces euphoric side effects. Promethazine is a sedative antihistamine that is frequently prescribed to treat motion sickness and insomnia and can enhance codeine's effects. Over-the-counter cough syrups like Robitussin can also be used to make sizzurp, but their effects are more hallucinatory than purely euphoric. Adding ingredients such as vodka and crushed painkillers can increase the impairment of motor skills and general lugubriousness associated with a sizzurp high. What's the downside of sizzurp? The drink is highly addictive and can lead to an overdose. Codeine and promethazine can be deadly when mixed with booze or consumed in high doses. Dextromethorphan, the active ingredient in most over-the-counter cough syrups, can cause increased heart rate, fever and liver damage when taken at sizzurp levels, which can reach 25 times the recommended dose. Rapper Pimp C died in 2008 of a cough-syrup overdose, according to the L.A. County Coroner's office. What are other street names for sizzurp? There are several alternate names for sizzurp. Most popular is "purple drank," so called for the purple hue the cough syrup gives it. It's also known as "lean," "syrup," "barre" and "purple jelly." PHOTOS: Lil Wayne Through the Years Who invented sizzurp? While the drink has been abused as far back as the 1960s, sizzurp as we know it has its origins in the hip-hop culture of the South. It's thought to have gained widespread popularity in Houston's underground rap scene in the 1990s with the music of DJ Screw -- progenitor of the "chopped and screwed" music style associated with sizzurp -- and Three 6 Mafia, who wrote an ode to the concoction, "Sippin' on Some Syrup," in 2000. From Texas, it spread to nearby states, including Lil' Wayne's home state of Louisiana, where the rap prodigy quickly adopted the drink. Wayne was shown drinking it extensively in the 2009 documentary The Carter, and subsequently protested the film's release partly because of that. How prevalent is sizzurp abuse among teenagers? Since it's cheap and easy to make, it's very popular among U.S. teens. A 2012 survey found 5.5 percent of 12th graders said they'd gotten high off cough medicine in one form or another. STORY: The Secrets of Cedars-Sinai, Hollywood's Glamour Hospital Has sizzurp been glamorized by Lil' Wayne's music? Yes. Lil' Wayne immortalized sizzurp on countless tracks, most famously in his 2008 single "Me and My Drank" ("Up in the studio me and my drank / Please let me be and let me do my thang / Thinkin about a certain somebody, that perfect somebody sexy purple body.") Other songs to feature sizzurp: "Throw Some D’s," "Phone Home," "Kush," "Watch My Shoes" and guest raps on tracks like Kanye West’s "Barry Bonds" and DJ Khaled’s "We Takin’ Over." What does sizzurp look like in action? ||||| Lil Wayne has been hospitalized, but according to his camp and his official Twitter account _ he's OK. FILE - In this Sept. 6, 2012 file photo, Lil Wayne accepts the award for best hip-hop video for "Hyfr"at the MTV Video Music Awards in Los Angeles. The multiplatinum rapper was hospitalized on Friday... (Associated Press) FILE - In this Feb. 1, 2013 file photo, recording artist Lil Wayne meets fans and celebrates his contemporary street wear apparel brand TRUKFIT at his hometown Macy's, in New Orleans. The multiplatinum... (Associated Press) FILE - In this Feb. 1, 2013 file photo, recording artist Lil Wayne meets fans and celebrates his contemporary street wear apparel brand TRUKFIT at his hometown Macy's, in New Orleans. The multiplatinum... (Associated Press) FILE - In this March 1, 2012 file photo, Lil Wayne performs at the Caesars Entertainment "Escape To Total Rewards" concert, in Los Angeles. The multiplatinum rapper was hospitalized on Friday night,... (Associated Press) The multiplatinum rapper was hospitalized in Los Angeles on Friday and reps confirmed he was "recovering." He apparently tweeted to his fans from his official account on Friday night: "I'm good everybody. Thx for the prayers and love." A person close to the superstar's camp who asked for anonymity because of the sensitivity of the matter confirmed to The Associated Press that Lil Wayne had a seizure. He has a history of seizures in recent years that have led to previous hospital visits. While there were some reports that Lil Wayne was fighting for his life, members of his Young Money camp denied it on Twitter. Before the tweet from Lil Wayne's account, rapper Mack Maine tweeted: "Wayne is alive and well! We watching the Syracuse game...thanks for the prayers and concern. he will update you all soon." Rapper Birdman, Lil Wayne's mentor, also downplayed reports that Lil Wayne was in grave condition, tweeting: My son is in good spirit..feelin much betta...be home soon." The 30-year-old New Orleans native, whose given name is Dwayne Michael Carter Jr., is one of the biggest stars of not only his genre but in all music. He's due to release his 10th album, "I Am Not a Human Being," on March 26. ___ Follow Nekesa Mumbi Moody at http://www.twitter.com/nekesamumbi

– Lil Wayne is in the hospital after two separate bouts of seizures, but just how serious it is remains in dispute. TMZ has him in critical condition in the ICU at Cedars Senai in Los Angeles, with his condition stabilizing but his very survival uncertain. A tweet last night from the rapper's official feed, however, reads, "I'm good everybody. Thx for the prayers and love." (TMZ is skeptical he sent it himself.) His official reps will confirm only that he is "recovering," reports AP. According to TMZ's account, Lil Wayne went to the hospital on Tuesday with seizures and was released the next day. A bodyguard found him unconscious about an hour later, and by the time he got back to the hospital, the 30-year-old rapper had to be restrained on a bed because he was shaking uncontrollably. The site says he had gone on a sizzurp binge, and the Hollywood Reporter has the details on the drink, which is a combination of prescription-strength cough syrup—for the codeine—and something like Mountain Dew and candy. Click for more.

SECTION 1. FINDINGS. Congress finds the following: (1) American society has long been known for being a ``melting pot'', boasting citizens from all countries and continents across the world. (2) After reaching America's shores, naturalized United States citizens and aliens lawfully admitted for permanent residence have taken advantage of educational and entrepreneurial opportunities thereby allowing these individuals to contribute to the economic and cultural riches that define our great Nation. (3) Many of these new Americans still have connections to their countries of origin--forming community, educational, religious, and other organizations in the United States that continue to tie them to their homelands. These new Americans send remittances that total more than $70,000,000,000 per year to help loved ones abroad sustain dreams and build new ones. (4) At a time when the events of September 11, 2001, have resulted in new and different security concerns for the United States, it is critical that every attempt be made to better understand those foreign countries that receive United States assistance. (5) Due to national security implications, the United States Government can no longer afford to conduct foreign policy without the benefit of engagement of foreign countries, including on a cultural, social, technical, and economic basis. (6) Naturalized United States citizens and aliens lawfully admitted for permanent residence should be encouraged to use the same skills that they have contributed to the development of the United States toward the development of their countries of origin in order to-- (A) take part in introducing or enhancing democratic values abroad; (B) capitalize on America's diversity to establish strong cross-border relationships that can create multilateral bonds for generations to come; (C) utilize multilingual and multicultural segments of American society to ease and reduce costs for project transitions in foreign countries; and (D) encourage long-term sustainable development in foreign countries in which such development has been difficult to obtain. (7) Currently, projects under many foreign assistance programs do not involve naturalized United States citizens or aliens lawfully admitted for permanent residence who are from the recipient country in leadership roles in the planning, design, and implementation of the projects, and consequently-- (A) project leaders often do not transfer critical skills to individuals in the recipient country, making it difficult for long term development to take place; and (B) increased costs relating to cultural adjustment often occur that might not occur if individuals originally from the recipient country were involved in the projects. (8) Because many United States Government departments and agencies face management constraints that make it necessary to bundle projects and activities for foreign countries under ``Mega'' contracts and grants, it has become increasingly difficult for smaller United States organizations and businesses owned or controlled by naturalized United States citizens, or aliens lawfully admitted for permanent residence, who are from such foreign countries to compete to carry out those projects and activities. (9) To encourage the transference of skills, knowledge, and democratic values that will lead to long-term sustainable development and require fewer transition costs, special preferences should be given to naturalized United States citizens, or aliens lawfully admitted for permanent residence, who are seeking United States foreign assistance funding for projects in their countries of origin. SEC. 2. REQUIREMENT TO PROVIDE DEVELOPMENT AND HUMANITARIAN ASSISTANCE FUNDS TO FOREIGN COUNTRIES THROUGH UNITED STATES ENTITIES OWNED OR CONTROLLED BY INDIVIDUALS FROM THOSE FOREIGN COUNTRIES. Notwithstanding any other provision of law, up to 10 percent of funds made available to each Federal department and agency for any fiscal year (beginning with fiscal year 2005) to carry out United States development assistance or humanitarian assistance programs shall be made available to foreign countries through the activities of United States organizations or businesses that are owned or controlled by naturalized United States citizens, or aliens lawfully admitted for permanent residence, who are from such foreign countries. SEC. 3. REPORT. Not later than January 1 of each year, the President shall prepare and transmit to the appropriate congressional committees a report that contains a description of the implementation of section 3 for the preceding fiscal year. Each such report shall specify the number and dollar value or amount (as the case may be) of prime contracts, subcontracts, grants, and cooperative agreements awarded to organizations and individuals described in such section during the preceding fiscal year. SEC. 4. DEFINITIONS. In this Act: (1) Appropriate congressional committees.--The term ``appropriate congressional committees'' means the Committee on International Relations of the House of Representatives and the Committee on Foreign Relations of the Senate. (2) United states development assistance or humanitarian assistance programs.--The term ``United States development assistance or humanitarian assistance programs'' means programs to provide development assistance or humanitarian assistance under major budget functional category 150 (relating to International Affairs), including programs under-- (A) chapter 1 of part I of the Foreign Assistance Act of 1961 (relating to development assistance); (B) chapter 10 of part I of that Act (relating to the Development Fund for Africa); (C) chapter 11 of part I of that Act (relating to assistance for the independent states of the former Soviet Union); (D) chapter 12 of part I of that Act (relating to assistance for the countries of the South Caucasus and Central Asia region); (E) chapter 4 of part II of that Act (relating to the Economic Support Fund); or (F) the Support for East European Democracy (SEED) Act of 1989.

Requires up to ten percent of funds made available to Federal departments and agencies for U.S. development or humanitarian assistance programs in any fiscal year to be made available to foreign countries through U.S. organizations or businesses that are owned or controlled by naturalized U.S. citizens or lawful permanent residents from those countries.

One of the last great liberal lions, former New York Governor Mario Cuomo died on New Year’s Day at 82, leaving behind a legacy both enormous and unfulfilled. Earlier Thursday, Cuomo’s son Andrew Cuomo was inaugurated to his second term as governor of New York. In his speech, Andrew Cuomo said his father was too ill to attend the inauguration ceremony, noting that the two spent New Year’s Eve together Wednesday. In a statement released Thursday, Governor Andrew Cuomo’s office confirmed that the former governor died of natural causes in his home. “Governor Cuomo presented 11 consecutive balanced budgets, reduced taxes, and implemented comprehensive governmental ethics and fiscal reforms,” the statement says, noting that “2014 marked 60 years of marriage to first lady Matilda Raffa Cuomo.” In addition to his wife and son Andrew, the former governor is survived by daughter Margaret, daughter Maria, daughter Madeline and son Christopher. “An Italian Catholic kid from Queens, born to immigrant parents, Mario paired his faith in God and faith in America to live a life of public service – and we are all better for it,” President Obama said in a statement released Thursday. Obama called Andrew Cuomo Thursday to extend his condolences, according to White House spokesman Eric Schultz. In the era of Ronald Reagan, Mario Cuomo was an unabashed liberal who famously called out the president’s sunny optimism during a 1984 Democratic National Convention keynote speech that catapulted the governor into a national leader and became a touchstone for a generation of progressives. While Reagan called America a “Shining City on a Hill,” Cuomo said “this nation is more ‘A Tale of Two Cities.’” “A shining city is perhaps all the president sees from the portico of the White House and the veranda of his ranch, where everyone seems to be doing well,” Cuomo said. But there exists, “another part to the shining the city … where students can’t afford the education they need, and middle-class parents watch the dreams they hold for their children evaporate.” Cuomo served three terms as governor of New York, but never ran for president, as many Democrats expected him to do. His indecision over whether to run for president even earned him a nickname: Hamlet on the Hudson. And in 1992, Cuomo came so close to a run that he had an airplane waiting on the runway, ready to fly him to New Hampshire to enter the race. He never boarded the plane. Another chance for national office came a few years later when President Bill Clinton offered to appoint Cuomo to the Supreme Court, but he turned that down as well. Cuomo’s decisions not to seek either office have haunted some liberals, but not Cuomo. He told The New York Times in 2011 that he always believed there was someone more qualified than he to sit in the Oval Office or on the Supreme Court. Cuomo was also a staunch defender of government’s ability to help people, often citing his own family’s rags-to-riches immigrant story. During the peak of “tough-on-crime politics,” Cuomo led the fight against the death penalty both in his home state and nationally. Cuomo was religious, but pro-choice at a time when abortion rights were not a litmus test for Democrats. He explained his relationship with religion and politics at a famous speech at Notre Dame University that, along with his convention speech, helped make him one of the greatest political orators of the 20th Century. A savvy deal-maker who was willing to make compromises to get things done, Cuomo often said, “You campaign in poetry, but govern in prose.” ||||| + READ ARTICLE Mario Cuomo, the former New York governor whose fiery, eloquent advocacy of liberal policies made him a key figurehead in the Democratic Party for years, died Thursday. He was 82, and his death was confirmed by the office of his son, current New York Gov. Andrew Cuomo. Cuomo died just hours after his son was inaugurated to a second term as governor. Andrew Cuomo said during his inauguration Thursday that his father was too ill to attend. Cuomo’s family said he died “from natural causes due to heart failure this evening at home with his loving family at his side.” President Barack Obama paid tribute to “a determined champion of progressive values, and an unflinching voice for tolerance, inclusiveness, fairness, dignity, and opportunity.” White House spokesman Eric Schultz said the President also phoned Andrew Cuomo to personally extend his condolences. “An Italian Catholic kid from Queens, born to immigrant parents, Mario paired his faith in God and faith in America to live a life of public service—and we are all better for it,” Obama said in a statement. “His own story taught him that as Americans, we are bound together as one people, and our country’s success rests on the success of all of us, not just a fortunate few.” Mario Cuomo served as governor from 1983 to 1994, during which he was twice considered a clear frontrunner for the Democratic presidential nomination. But both times, in 1988 and 1992, he declined to run. His keynote speech at the 1984 Democratic convention is remembered as a forceful defense of liberalism—and a searing attack on then-President Ronald Reagan. “Mr. President, you ought to know that this nation is more ‘a tale of two cities’ than it is just a ‘shining city on a hill,'” Cuomo said then. Cuomo often found his liberal policy ambitions in New York thwarted by a harsh economic climate, but his personification of the Democratic Party’s liberal wing at a time when conservatism was ascendant made him a political player far beyond the state’s borders. The 1984 convention speech was a high-water mark in his political career, and he very publicly flirted with White House runs in the years ahead. In a dramatic moment in December of 1991, Cuomo kept an airplane waiting on the tarmac while he mulled whether to fly to New Hampshire to hand in his application to be on the primary ballot on the day it was due. A budget clash with Republicans in the state legislature kept him from leaving, and he announced that he wouldn’t run. Had he decided to run in 1992 it’s possible Bill Clinton would have never become president. “We have lost a true progressive giant with Governor Mario Cuomo’s passing today,” former New York Gov. David Paterson wrote on Twitter. Former New York Gov. George Pataki called Cuomo “a proud son of immigrants, possessed of a soaring intellect [and] a great New Yorker.” —With reporting by Zeke Miller / Washington Read next: Vice President Biden, Gov. Cuomo and Mayor de Blasio Honor Life of Fallen Officer Sign up for THE BRIEF and more view example Listen to the most important stories of the day. ||||| But he was no longer the formidable figure in New York he had been. His popularity ratings had dropped. State legislators, who had never been fond of him, were emboldened to challenge him. He pinned the blame for this erosion of support on the way the news media had covered his response to all the talk about a presidential run. “You’ve done everything but call me a liar,” he told The Washington Post, speaking generally of the press. “You said that I was cute. You said that I misplayed the game. You said that I was really waiting for another scenario. Well, the net result of that is it costs me credibility, because you spent all those months saying I was conning people.” Recession, too, was looming and state revenues were declining. Still, in 1990, he won a third term. His Republican opponent, Pierre A. Rinfret, a financial consultant and economics adviser to presidents, had not been taken seriously even by his own party. It was a convincing but unsatisfying victory: Mr. Cuomo had done better against Mr. O’Rourke four years before. When he returned to Albany to deliver his ninth State of the State address, Mr. Cuomo suggested diminished ambitions for his next term. “This is a wonderful year for raw truth,” he said. “We don’t have any money.” But he had one more presidential flirtation left in him: in October 1991, while on a trip to Chicago, he said he was “looking at” a run. Many of his supporters had grown weary of such talk, some viewing it as a ruse to reinvigorate his sagging political image. And that December, with the planes waiting on the runway, he announced again that he would not be a candidate for president. ||||| Long before Bill de Blasio summoned the ghost of Charles Dickens, long before the phrase “income inequality” became part of the political lexicon, long before shimmering castles rose in the Midtown sky in celebration of a new gilded age, there was Mario Matthew Cuomo, son of immigrants, child of the New Deal, keeper of his party’s conscience. Cuomo became a political sensation through a medium thought to belong to another era: words. Beautiful, poetic, meaningful words, spoken in a strong, clear voice, with a cadence that turned even a clumsy phrase into a baroque masterpiece. He was reared in a household of Italian speakers; English, his greatest companion and most formidable ally, was his second language. It was hardly a wonder that embedded in all those beautiful words there was a palpable love of American possibilities. Where else, he might have asked, could an Italian-speaking kid from Queens become not just an orator but a philosopher whose texts will be read for as long as American political thought matters? Cuomo was a relative political unknown in 1984, when the Democratic Party’s presidential nominee, Walter Mondale, asked him to deliver the keynote address at the party’s national convention in San Francisco. Mondale had heard something about Cuomo’s use of the English language, heard something about a speech he gave in Albany on January 1, 1983, after taking the oath of office as governor of New York. On that first of 4,380 days he would spend in residence on Eagle Street, Mario Cuomo spoke of “the idea of the family, mutuality, the sharing of benefits and burdens for the good of all.” “There is an ideal essential to our success,” he said, “and no family that favored its strong children or that in the name of even-handedness failed to help its vulnerable ones would be worthy of the name.” There are people with us still who vividly remember that speech not only because of the words and not only because of the power of the man who spoke them, but also because nobody else in public life spoke like that. Not in 1983. The age belonged to Ronald Reagan, the onetime New Dealer who preached the gospel of self-reliance and regaled the nation with anecdotes about individuals who made themselves rich, or, if already rich, then even richer. The age belonged to Reagan’s ideological sidekick, Margaret Thatcher, who said there was no such thing as society. And here was this man from Queens, Mario Cuomo, all but saying that these powerful people were peddling lies. “It has become popular is some quarters,” he said, “to argue that the principal function of government is to make instruments of war and to clear obstacles away from the strong. It is said that the rest will happen automatically. The cream will rise to the top. … Survival of the fittest may be a good working description of the process of evolution, but a government of humans should elevate itself to a higher order, one which tries to fill the cruel gaps left by chance, and by a wisdom we don’t fully understand.” From his listening post in Washington, New York Times columnist James (Scotty) Reston announced that “the governor may be on to something.” Hoping that Reston was right, Mondale arranged for Mario Cuomo to face the nation on a July evening in the Moscone Center in San Francisco. Today, at a time when the president of the United States bears the name Barack Hussein Obama, it is quite impossible to appreciate the impact of a man named Mario Cuomo speaking on behalf of a presidential candidate to a national television audience numbering in the tens of millions. Covering that convention, I recall a man from the South—Texas, I seem to remember—reminding us Northerners that all those vowels in the governor’s name might not sit well with his America. He at least pronounced Cuomo’s last name correctly. There were many in that convention hall in San Francisco who seemed to believe the governor was related to the old crooner, Perry Como. He came to the podium, waved, and then excused himself from the usual preliminaries, “the stories and the poetry and the temptation to deal in nice but vague rhetoric.” Instead, he offered a polite but passionate assault on Ronald Reagan’s America, his shining city on a hill. “A shining city is perhaps all the president sees from the portico of the White House and the veranda of his ranch, where everyone seems to be doing well,” Cuomo said. “But there's another city; there's another part to the shining city; the part where some people can't pay their mortgages, and most young people can't afford one; where students can't afford the education they need, and middle-class parents watch the dreams they hold for their children evaporate. … There is despair, Mr. President, in the faces that you don't see, in the places that you don't visit in your shining city. In fact, Mr. President, this is a nation—Mr. President you ought to know that this nation is more a ‘Tale of Two Cities’ than it is just a ‘Shining City on a Hill.’" Mario Cuomo said these things in 1984, to a nation that was in thrall to Reagan and his narrative of an America reborn and resurgent. Cuomo continued with phrase upon devastating phrase, asking the president to consider those left behind, pleading with the American people to see the poor and the disenfranchised not as failures and losers, but fellow citizens of the same city, of one city and a single nation. To be in that hall on that night 30 years ago was to be in Chicago in 1896, when a former congressman named William Jennings Bryan called on his fellow Democrats to hear the voices of those left behind, to prevent their crucifixion on a cross of gold. He was nominated for president on the spot. The rules of politics had changed since Bryan’s time; Mario Cuomo could be no more than a surrogate for the party’s duly anointed candidate, Mondale. But the delegates left San Francisco knowing they had nominated the wrong man, a fine man no doubt, but a man who could not stir the soul. Mario Cuomo would never run for president, even though the party saw him as a savior after Mondale lost 49 states—all but Minnesota—that year. Cuomo chose not to run in 1988, and the Democratic consolation prize was Michael Dukakis. He chose not to run in 1992, when a plane was waiting to take him from Albany to New Hampshire to file late-minute paperwork for the state’s primary. Cuomo said he could not run for president because he had to figure out the state’s budget, a curious explanation he would reiterate in years to come, no matter how bizarre it seemed. For Democrats who had never forgotten the San Francisco speech, for hundreds of patronage holders and reporters in Albany, Cuomo’s announcement, made 90 minutes before a 5 o’clock filing deadline, was one of the great could-have-beens in modern political history. William Faulkner once said that for young white men in the South, it is always a few minutes before two o’clock on July 3, 1863 in Gettysburg, and General George Pickett and his men “are in position behind the rail fence … waiting for Longstreet to give the word.” For those who worked for or who covered Mario Cuomo a generation ago, there are times when it once again is 3:15 p.m. on Friday, December 20, 1991. A small plane is warming up, bound for Manchester, N.H., and Governor Cuomo’s office has just scheduled a press conference on the second floor of the state Capitol. Mario Cuomo’s hold on the imagination of his fellow Democrats was all about soaring rhetoric and political poetry. But it was the governor himself who noted that politicians campaign in poetry but govern in prose. And as a governor, Cuomo’s record was more prosaic than many Democrats and journalists from outside the state realized. He built more prisons than any other governor in the state’s history. He and his legislative colleagues couldn’t deliver a budget on time. He cut taxes but didn’t raise the state’s minimum wage until 1990, after he had been governor for seven years. By 1994, as he tried in vain to win a fourth term, he found himself talking about improvements made to Thruway rest stops during his watch. Hardly the stuff of poetry. His principled stand against capital punishment—which he shared with his predecessor, Hugh Carey—won him accolades from liberals tired of Democratic compromises and cave-ins. His nuanced defense of abortion rights, brilliantly argued in a speech at the University of Notre Dame in 1985, earned him the support of powerful activists who policed the party’s pro-choice orthodoxy. Combined with his wonderful speeches, those two positions earned Cuomo a reputation as the Democratic Party’s leading liberal spokesman at a time when liberalism was banished to the political wilderness. But it was, in many ways, an illusion. If Bill Clinton is credited with the political gymnastic known as triangulation, Mario Cuomo deserves recognition for embracing a form of political bifurcation even if party diehards insisted that he was the true liberal they had been yearning for since Adlai Stevenson led them to principled disaster twice in the 1950s. Cuomo disdained the term “liberal,” preferring to describe himself as a pragmatic progressive or a progressive pragmatist. The rhetorical sleight of hand was evident even in some of the speeches that sent liberal heart aflutter. “We believe in only the government we need, but we insist on all the government we need,” Cuomo said in his San Francisco speech. On other occasions, he noted that government required both a head and a heart, of the need to provide jobs as well as justice. Conservative. Liberal. Pragmatic progressive. Progressive pragmatist. This careful attention to linguistic detail could be exasperating for those looking for simple, straightforward answers. People like, well, reporters. Along with others who covered Cuomo far more closely, I knew that the right question phrased the wrong way would lead only to a Cuomo verbal assault and a non-answer. He’d attack the question. He’d question the attacker. I can hear his voice now: Governor, other Democrats are saying you should raise the minimum wage. Who? I can’t tell you that, governor. How can I answer the question if I don’t know who is saying these things? Why do you allow people to hide behind a veil of anonymity? Is this the way you always operate? The issue here is not the minimum wage but the people who are making statements without putting their names to those statements. That’s the real issue here. This imaginary conversation was pretty close to daily reality for Albany’s press corps, although visiting journalists from the Beltway generally were spared the full Mario treatment. That accounted for the disparate narratives: Mario the Poet versus Mario the Lawyer. In 1994, as he sought to become only the second New York governor to win a fourth four-year term (the first one was Nelson Rockefeller; Al Smith won four two-year terms), Cuomo published a collection of his speeches, reminding so many of his supporters why they adored him. The volume was called More Than Words. It is a suitable epitaph for a politician who used words to inspire, to probe, to critique, and to provoke. Yes, he will be remembered best as an orator, but there was something more about him, something more than the pretty pictures he painted with the English language. He was unafraid to challenge a comforting narrative with impertinent questions at a time when others preferred to simply go along and get along. Yes, that required more than words. That required ideas, that required courage, and that required intelligence. Mario Cuomo had all three. CORRECTION: The original version of this article stated incorrectly that Walter Mondale won Massachusetts in 1984, rather than Minnesota.

– The late Mario Cuomo is being called a "liberal icon" (Time), a "liberal beacon" (the New York Times), and even a "liberal lion" (MSNBC), but in his appreciation at Capital New York, Terry Golway points out that Cuomo himself wasn't a big fan of the l-word: "Cuomo disdained the term 'liberal,' preferring to describe himself as a pragmatic progressive or a progressive pragmatist." Golway writes that Cuomo's thinking shows up in lines like this one: “We believe in only the government we need, but we insist on all the government we need." Yes, the government had to provide jobs, Cuomo argued, but it also had to provide justice. It needed to be both compassionate and strong, to have both a "head and a heart," writes Golway. That was Cuomo: "Conservative. Liberal. Pragmatic progressive. Progressive pragmatist." Read his full post.

Senate Majority Leader Mitch McConnell of Ky., right, accompanied by Sen. John Barrasso, R-Wyo. leave a Senate Republican conference leadership election meeting on Capitol Hill in Washington, Wednesday,... (Associated Press) Senate Majority Leader Mitch McConnell of Ky., right, accompanied by Sen. John Barrasso, R-Wyo. leave a Senate Republican conference leadership election meeting on Capitol Hill in Washington, Wednesday, Nov. 16, 2016, after Senate Republicans re-elected McConnell to be majority leader in the upcoming... (Associated Press) WASHINGTON (AP) — The Latest on Donald Trump's transition to the presidency. (All times EST): 8:50 p.m. Donald Trump's transition team says the incoming president is planning to require officials to pledge that they won't lobby the government for five years after leaving the Trump administration. Transition spokesman Sean Spicer says Trump will require new government officials to terminate their role as either state or federal lobbyists before joining the administration. And he says government officials will agree to a five-year lobbying ban after leaving. Trump has vowed to "drain the swamp" when he begins his White House administration next year. Spicer says people leaving government "won't be able to use that service to enrich themselves." ___ 6:28 p.m. Kansas congressman Tim Huelskamp says someone "close to the transition" of President-elect Donald Trump has contacted him about becoming agriculture secretary. Huelskamp lost the GOP primary in his agriculture-heavy Kansas district this year after he was booted from the House Agriculture Committee amid fights with Republican leadership. He also opposed a five-year farm law enacted in 2014. The Kansas Farm Bureau, Kansas Livestock Association and National Association of Wheat Growers endorsed Huelskamp's challenger, Roger Marshall. Huelskamp said Wednesday that the USDA needs major reform, including stronger work requirements for food stamps. Some other possible candidates for agriculture secretary include Charles Conner of the National Council of Farmer Cooperatives, a former Bush USDA official; former Georgia Gov. Sonny Perdue; Texas Agriculture Commissioner Sid Miller; and Nebraska cattle rancher Charles Herbster. ___ 5:45 p.m. South Carolina's lieutenant governor says a member of Donald Trump's transition team has asked if he's interested in being attorney general. Henry McMaster also says he's been told that South Carolina Gov. Nikki Haley is being considered for secretary of state. McMaster tells The Associated Press he was contacted Wednesday. The former U.S. attorney and two-term state attorney general declined to specify who on the team called him. McMaster was an early backer of Trump. Haley endorsed and campaigned with Sen. Marco Rubio for South Carolina's first-in-the-South presidential primary. When Rubio dropped out, she backed Ted Cruz and continued to criticize Trump. ___ 5:15 p.m. President-elect Donald Trump and Vice President-elect Mike Pence have received their first looks at the President's Daily Brief — the highest level intelligence document prepared in the United States. Trump received his on Tuesday and Pence was briefed on Wednesday in Washington, according to an individual familiar with the briefings schedule. The individual, who was not authorized to discuss the briefings, spoke only on condition of anonymity. Intelligence officials briefed Trump and Pence after the GOP convention, but the President's Daily Brief has more detail, including information about U.S. covert operations. President Harry S. Truman started the practice because he first learned about the U.S. project to develop an atomic bomb only 12 days into his presidency. He pledged not to leave his successor in that position. ___ 3:08 p.m. Donald Trump is considering charter school advocate Eva Moskowitz to serve as education secretary, according to a senior Trump official. The official says Moskowitz, the founder of Success Academy Charter Schools, was at Trump Tower Wednesday meeting with the president-elect's team. Moskowitz is a former New York City councilwoman and a Democrat. She's clashed with Mayor Bill de Blasio over the expansion of some of her charter schools. De Blasio was also at Trump Tower Wednesday meeting with the president-election. The Trump official discussed Moskowitz on the condition of anonymity because the official was not authorized to publicly discuss the internal transition process. --By Julie Pace ___ 2:40 p.m. Vice President Joe Biden says he's not worried about the incoming administration's readiness to take over the White House. Biden told reporters after meeting with Vice President-elect Mike Pence on Wednesday that he's "confident on day one everything will be in good hands." Addressing reports of infighting within President-elect Donald Trump's transition team, Biden said that "no administration's ready on day one. We weren't really on day one." Biden and his wife Jill spent nearly two hours with their successors Wednesday afternoon, sitting down for lunch with the Vice President-elect and his wife, Karen, and giving them a tour of the vice presidential residence and grounds. Biden also said he's not worried about the new administration dismantling his legacy, despite the President-elect's very different policy agenda. Biden said that he hopes the Pences enjoy the home at Washington's Naval Observatory as much as he did. ___ 2:30 p.m. The top Republican in the Senate says "it's time for the election to be over." Majority Leader Mitch McConnell also declined to answer questions about President-elect Donald Trump's appointment of Steve Bannon as senior counselor, saying he wouldn't comment about White House staffing. Bannon's hiring has come under fire because of his Breitbart news site's derogatory comments about blacks, Muslims and women. McConnell told reporters on Wednesday that he would not go back and re-litigate what was said during a hotly contested presidential race. He said the focus is on working with Trump to repeal and replace the health care law, overhaul the tax system and deal with other issues. He also declined to comment on Trump's call for a ban on all executive-branch officials from lobbying for five years after leaving their government jobs. ___ 1:55 p.m. House Democrats have sent a letter to President-elect Donald Trump asking him to rescind the appointment of Breitbart News executive Steve Bannon as a senior White House adviser. The letter, which has signatures from 169 out of the 188 Democrats in the House, says the appointment of conservative flame-thrower Bannon undermines Trump's ability to unite the country. It points out stories from the website that are derogatory toward Jews and Muslims, among other groups. "Millions of Americans have expressed fear and concern about how they will be treated by the Trump Administration and your appointment of Mr. Bannon only exacerbates and validates their concerns," the letter reads. Rep. David N. Cicilline, D-R.I, organized the effort. "Bigotry, anti-Semitism, and xenophobia should have no place in our society," he said. ___ 1:10 p.m. New York City Mayor Bill de Blasio says he met with President-elect Donald Trump and "let him know that so many New Yorkers are fearful" of what his administration could bring. De Blasio spoke to reporters after his hour-long meeting at Trump Tower Wednesday, which he categorized as "respectful" and "candid" with a real "give-and-take." The mayor, a liberal Democrat, and Trump have previously clashed. He said concerns with Trump's support of aggressive policing tactics, his tax plans and any move to deport immigrants living in the United States illegally. De Blasio said that Trump "loves this city" and added that he urged the Republican president-elect to send a "sign of unity" to his hometown, which overwhelmingly voted for Democrat Hillary Clinton. ___ 11:50 a.m. A spokesman for President-elect Donald Trump says the transition team is "not going to rush" to put forward potential Cabinet selections. Jason Miller said Wednesday that Trump's team wants to feel confident their choices will be able to be confirmed by the Senate and can implement the president-elect's vision. Miller told reporters at Trump Tower in New York City that President Barack Obama did not have "his entire Cabinet formed within the first week" after his election in 2008. He said the transition team has a "very solid plan" and they're taking a "methodical approach" to filling Trump's Cabinet and White House. ___ 11:35 a.m. Over 300 U.S. businesses have signed a statement calling on President-elect Donald Trump to support the Paris Agreement on climate change — including General Mills, eBay, Intel, Unilever, and dozens of other Fortune 500 companies. Their statement reads "implementing the Paris Agreement will enable and encourage businesses and investors to turn the billions of dollars in existing low-carbon investments into the trillions of dollars the world needs to bring clean energy and prosperity to all." The statement is addressed to Trump, President Barack Obama and members of Congress. It calls on elected U.S. officials to maintain the country's policy and financial commitments to lower carbon emissions. Lara Birkes, chief sustainability officer of Hewlett Packard Enterprise, says "the Paris Agreement was a vital step forward, but its power is in our collective action." ___ 11:32 a.m. Czech President Milos Zeman has called U.S. President-elect Donald Trump's former wife, Ivana, to thank her for her "courage" and interest to become the new U.S. ambassador to Prague. In a Wednesday statement, Zeman said he's pleased with that because "the U.S. cannot send a better ambassador to Prague" than her. Zeman said he would be delighted to meet her at the Prague Castle, the seat of presidency and is looking forward to introduce her to his wife, also named Ivana. Ivana, Trump's first wife and the mother of his three oldest children, is of Czech origin. Zeman was among several European leaders, including Hungarian Prime Minister Viktor Orban, who endorsed Trump during the campaign. Zeman said he shared Trump's views of migration and the fight against the Islamic terrorism. Trump's presidential transition team provided no readout of the conversation between the Czech leader and his ex-wife. ___ 9:15 a.m. The White House Correspondents' Association says it is "unacceptable" that President-elect Donald Trump is traveling without a regular pool of journalists to inform the public of his whereabouts. Trump left his residence Tuesday night for a family dinner after his transition team had told journalists he would not be in public the rest of the day. A protective pool of journalists is supposed to join the president or president-elect's motorcade to record their whereabouts and be on hand in the event of breaking news. Trump spokeswoman Hope Hicks has said the team plans to respect the traditions of press access at the White House. WHCA President Jeff Mason says "the time to act on that promise is now." Mason says it is critical that journalists covering the president-elect "be allowed to do their job." __ 7:50 a.m. Ohio congressman Tim Ryan says Democrats should get back to economic basics of manufacturing, not veer to its liberal wing in the wake of Republican Donald Trump's election victory. Ryan is considering challenging Rep. Nancy Pelosi as House Democratic leader because he says the party risks sliding back into an ideological past rather than moving forward. He told MSNBC's "Morning Joe" on Wednesday that Democrats "have to grab that idea of making things in America again." "No one wants to hear about job retraining," he said. "They want jobs." ___ 6:30 a.m. President-elect Donald Trump is denying reports that efforts are underway to get security clearances for his adult children. In a post on his verified Twitter account @realDonaldTrump early Wednesday, the billionaire businessman who's to be inaugurated as the nation's 45th president on Jan. 20, said, "I am not trying to get top security clearances for my children." Trump, who has been immersed in transition planning at his office skyscraper in New York in recent days, added, "This was a typically false news story." There had been rampant speculation in recent days that such an effort was being attempted. Asked about it earlier this week, Kellyanne Conway, who was Trump's campaign manager, said in a broadcast interview she wasn't "intimately' familiar with the issue and indicated she couldn't confirm it. 4:20 a.m. Turkey's president has criticized protests in the United States against Donald Trump, saying the president-elect should be respected and given time to show how he will govern. Speaking to reporters on Wednesday before a visit to Pakistan, Recep Tayyip Erdogan said the protesters were "attacking" Trump because "the person they wanted wasn't elected president." Erdogan said: "Hold on a second. The election process just ended, show some respect! How will he govern, let's see that first." The Turkish leader added: This is important in terms of showing who respects democracy in the world." 3:30 a.m. President-elect Donald Trump hadn't been seen in public for days when he walked into New York's 21 Club to applause from fellow diners. The unannounced evening out with family was a contrast to the behind-the scenes machinations that suggested a struggling transition as names surfaced and sank for top administration positions. Not to worry, Trump suggested in a Tuesday night tweet: "Very organized process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are!" Before dinner at the midtown Manhattan restaurant— he broke with protocol and left his press contingent behind — Trump met with the head of his transition team, Vice President-elect Mike Pence, but another day passed without a Cabinet announcement. ||||| New York City mayor Bill de Blasio speaks to the press in front of Trump Tower after his meeting with president-elect Donald Trump, November 16, 2016 in New York City. President-elect Donald Trump met Wednesday with one of his harshest critics, New York City Mayor Bill De Blasio. "I let him know that so many New Yorkers were fearful and that more had to be done to show that this country can heal, that people be respected,’’ said De Blasio, speaking to reporters in front of Trump Tower after the hourlong meeting. Trump’s proposals to deport immigrants in particular “flew in the face of all that was great about New York City, the ultimate city of immigrants.’’ During the meeting, De Blasio, a liberal Democrat who supported Hillary Clinton in the presidential campaign, said he warned that New York City would refuse to cooperate with the deportations and with Trump’s calls to reinstate stop-and-frisk tactics to reduce crime. He also complained to Trump about rising anti-Semitism, aggravated by the presidential campaign, and about Trump’s proposal to dismantle Wall Street regulation by repealing the Dodd-Frank Act. Trump’s staff offered less detail about the meeting. "I think they both said it was a very productive meeting,’’ Trump advisor Kellyanne Conway told reporters. I was glad that the mayor came here, obviously mayor of the nation's largest city and a neighbor to the new president-elect, so it was good that that happened.’’ ||||| The sprawling, 10-person Democratic leadership team that Chuck Schumer assembled on Wednesday will allow him to hear from everyone from Bernie Sanders to Joe Manchin. And Democrats are going to need all the wisdom they can summon — from all quarters of the party — to survive what’s coming at them in 2018. Story Continued Below Still nursing their wounds after last week’s thrashing, Democrats already are grappling with how to defend 10 senators up for reelection in 2018 in states that Donald Trump carried, some resoundingly. Republicans are targeting a quintet of senators from conservative states where Trump walloped Hillary Clinton: Montana, Missouri, Indiana, North Dakota and West Virginia. The GOP could amass a filibuster-proof majority by running the table in those states and other battlegrounds. To prevent that, Schumer will need to mine his fellow leaders to accommodate vulnerable Democrats with profoundly different ideologies and political circumstances — from Wisconsin’s Tammy Baldwin, who also was tapped for a leadership spot, to West Virginia’s Manchin, who has gone out of his way to align himself with Trump voters this week. That means appealing to the white working class in some states — and stoking minority and liberal turnout in others. “People agree with us but didn’t believe in us,” said Sen. Brian Schatz of Hawaii, a liberal member of the caucus. “The left-right spectrum has been scrambled. And so, it’s no doubt we have a daunting map. But I think the way to run in this new environment is with authenticity, with passion, with connectivity.” The foreboding map, coupled with competing political imperatives for different vulnerable members, has party leaders looking to drive wedges between Trump and Republican leaders in the early going. But ultimately, if Democrats hope to avoid ceding even more power to Republicans in two years, they’ll have to seize back the issues — and voters — that Trump snatched away. “Those Trump voters are the same people who elected me to the Senate. You can say they’re different people, but they’re not different people,” said Sen. Heidi Heitkamp (D-N.D.). “I resist the characterizations that people make of good hardworking people. … I don’t give a lot of consideration to what the ‘party’ does.” “I’m proud of the fact that we’re a party of diversity and inclusivity, but that doesn’t mean we shouldn’t be talking to everyone. And I feel like we’ve neglected to do that,” said Sen. Claire McCaskill of Missouri, a moderate also up for reelection in 2018. Heitkamp and McCaskill said Manchin’s appointment signals that party brass aren’t abandoning the Democratic centrists that won them a hefty 55-seat majority in 2012. But for Manchin personally, the appointment could cut both ways. He hopes that being in the room with Democratic leaders who are guiding an increasingly liberal party will be a boon for his reelection prospects. On the other hand, Republicans could tag him as a leader of a party that’s not winning any popularity contests in West Virginia. “That could be a blessing and a curse from my standpoint,” Manchin said in an interview. “If they condemn me for that, then so be it. But I got a chance to speak for them and other working Americans. … We might not win [the argument], but you’re going to have your voice heard.” Manchin, McCaskill, Heitkamp and Sens. Joe Donnelly of Indiana and Jon Tester of Montana will have ample latitude over the next two years to break with their party and vote with Trump and congressional Republicans. Still, Senate Majority Leader Mitch McConnell (R-Ky.) needs eight Democratic defectors on legislation — and there aren’t enough moderates in the minority to consistently give it to him. That means centrists can vote against more liberal party leaders, even while the rest of the party holds the line to block conservative policy. A preview of that dynamic was on display this week as liberals attacked Trump for appointing Steve Bannon to his inner circle, but moderate senators refrained. That’s not to say the red-state Democrats will be with Trump on everything. Some said they intend to hold the president-elect accountable for his campaign promise to curb the influence of lobbyists. “Draining the swamp, I’m going to work with him on that stuff. It does bother me that it does look like he’s filling the swamp right now. But that’s OK. Let’s give him a chance to get started,” Tester said. “Pay close attention. Make sure that he delivers on the promises he’s made,” McCaskill added. Indeed, a host of vulnerable Democrats recognize that Trump has pilfered some populist issues from Democrats. They see an opportunity to either team with Trump on those issues — or reclaim them if he fails to follow through. “The kinds of things he was talking about are the things that I fight for every single day: Fair trade, currency manipulation, closing tax loopholes, taking jobs overseas. I’ve got 10 bills I’m happy to have him support,” said Sen. Debbie Stabenow of Michigan, a state where Trump narrowly leads but has not officially won. Stabenow, who is also up in 2018, was named to the No. 4 leadership post heading Senate Democrats’ messaging arm. Republicans are bullish about padding their majority in the midterms. While Democrats may take back seats in the House, winning back the Senate is almost impossible, given that they will be on offense in just two battlegrounds, Arizona and Nevada, and defending 25 seats. The political imbalance was made clear when Democrats announced their sprawling leadership team — but didn’t name a campaign chairman. Meanwhile, Sen. Cory Gardner of Colorado had already locked up the GOP’s campaign arm and was itching to get to work. “We have a number of seats that we will be competitive in. We know that the map presents opportunities that we didn’t have in 2016,” Gardner said. Indeed, Republicans have opportunities that the party wasn’t banking on just a few weeks ago. Trump won Wisconsin, Michigan, Pennsylvania, Florida and Ohio — states that have ranged from bright blue to purple over the past two decades. Suddenly, senators like Stabenow, Baldwin, Bob Casey of Pennsylvania, Sherrod Brown of Ohio and Bill Nelson of Florida are alluring targets for Republicans. It’s an added headache for Schumer as he charts the party’s legislative strategy. Longtime Democratic hands like Nelson don’t seem worried that the political landscape in their states has shifted. Democrats had myriad opportunities to put away GOP incumbents this year and knocked off only two, demonstrating that it’s still hard to oust a sitting senator. “Just be myself,” Nelson said when asked how he appeals to Trump voters. “Just be my bipartisan, consensus-building self.” ||||| Trump takes US presidency into uncharted waters with series of tweets attacking the New York Times, hours after ducking reporters to visit restaurant Donald Trump has renewed his fight with the American media, criticizing the New York Times, ducking reporters to visit a restaurant and turning to Twitter as a means of direct communication. The US president-elect even appeared to allude to his reality TV show The Apprentice as he denied reports that his transition process is in turmoil and plagued by infighting. Trump waged an unprecedented one-man war against the media during his election campaign, banning some organisations from his rallies and regularly inciting his supporters to boo and jeer reporters. He used Twitter, on which he has more than 15 million followers, to berate his critics and throw out often incendiary statements. Hillary Clinton: 'There have been times when I wanted never to leave the house again' Read more Not even his elevated status as president-elect appears to have changed his habits. Whereas Barack Obama gave his first press conference three days after his election in 2008, Trump is yet to do so, instead giving a primetime TV interview and unleashing a barrage of tweets, yet again taking the US presidency into uncharted waters. “Very organized process taking place as I decide on Cabinet and many other positions,” he posted on Twitter late on Tuesday. “I am the only one who knows who the finalists are!” His reference to “the finalists” seemed to deliberately evoke The Apprentice, in which contestants battled each other for a chance to work at his business and he told those who fell short: “You’re fired!” The Twitter storm resumed early on Wednesday morning when he denied media reports that his three adult children – Don Jr, Eric and Ivanka – would be receiving security clearances, raising potential conflicts of interest. “I am not trying to get ‘top level security clearance’ for my children. This was a typically false news story.” And then he singled out the New York Times, which during the campaign revealed how he may have avoided paying taxes for 18 years and which endorsed Hillary Clinton for president. This week the paper has reported on disarray in the transition and said that, while the presidents of Egypt and Israel got through to Trump quickly by phone, UK prime minister Theresa May had to wait 24 hours. Facebook Twitter Pinterest New York mayor Bill de Blasio talks to the press in front of Trump Tower after meetings with the president-elect on Wednesday. Photograph: Jewel Samad/AFP/Getty Images “The failing @nytimes story is so totally wrong on transition,” Trump tweeted. “It is going so smoothly. Also, I have spoken to many foreign leaders.” He added: “I have recieved [sic] and taken calls from many foreign leaders despite what the failing @nytimes said. Russia, U.K., China, Saudi Arabia, Japan, Australia, New Zealand, and more. I am always available to them. @nytimes is just upset that they looked like fools in their coverage of me.” His decision to mention Russia first will not have escaped critics of Trump’s apparent admiration for president Vladimir Putin. The New York Times pointed out that it had reported that Trump had taken calls from the leaders of Egypt, Israel, Russia and Britain, but said they had been “conducted haphazardly” and without the state department guidance that is typical for such conversations. Trump’s shoot-from-the-hip style was met with criticism. David Frum, a former speechwriter for George W Bush, tweeted: “It will never stop being insane that the president-elect of the United States foams at his critics on Twitter.” It is fine to publish a list of foreign leaders who called to congratulate him, Frum added: “But to toss names out there in a Twitter rage to answer a perceived media slight?! When does President Trump compromise an important secret?” Further concerns were raised about Trump’s handling of the media when he broke with protocol on Tuesday night, going out to dinner at a steakhouse after his transition team had told journalists he would not be out in public the rest of the day. Trump reportedly received a standing ovation and cheers on arriving at 21 Club in midtown Manhattan. The White House Correspondents’ Association said it was “unacceptable” that Trump was traveling without a regular pool of journalists to inform the public of his whereabouts. A protective pool of journalists is supposed to join the president or president-elect’s motorcade to record their whereabouts and be on hand in the event of breaking news. The Trump team has said it plans to respect the traditions of press access at the White House. Jeff Mason, president of the White House Correspondents Association, insisted: “The time to act on that promise is now. Pool reporters are in place in New York to cover the president-elect as he assembles his new administration. It is critical that they be allowed to do their jobs.” On Wednesday, Jason Miller, a spokesperson for Trump, admitted that there was room for improvement. “Last night probably was an example where there could have been a little bit better communication,” he told reporters. “But again, our goal going forward is to get you guys the best information in a timely fashion. “But I would also say – would also stand up for the president-elect and say that, for some in the media, unless they’re actually sitting at the table, seeing if he’s getting the chicken or the fish, that they will never be happy. And there always needs to be some kind of balance for respecting some degree of privacy. But to your initial point, we do think that there will be improved communication and our goal is to make sure that something like last night doesn’t happen again.” Asked when the billionaire businessman would do a press conference, Kellyanne Conway, his campaign manager, replied: “Shortly, I would say. Some time soon. But obviously he’s meeting with – talking to heads of state and possible members of his cabinet and senior team, filling out his senior leadership team. A lot of activity going on upstairs.” On a conference call with reporters Wednesday night, Miller and RNC strategist Sean Spicer announced that landing teams would be deployed in the coming days to start the transition process and noted that all of those joining landing teams would sign a pledge to not serve as a lobbyist at the federal and state level for the next five years. They also noted several of the meetings that the president-elect had held with potential cabinet members on Wednesday, including senator Jeff Sessions, general Mike Flynn, representative Tom Price, representativeMike Pompeo and charter school leader Eva Moskowitz. They added that Trump is expected to meet Thursday with governor Nikki Haley, governor Rick Scott and former secretary of state Henry Kissinger, among others. Former House speaker Newt Gingrich said the media would have to adapt to Trump’s “hands-on CEO” style. “It probably confuses the traditional political press because they apply traditional standards and you can’t do that with Trump,” he told Fox News. Gingrich added that he was “100%” sure he did not want a cabinet post as transition talks continued at Trump Tower, where the tycoon’s second wife, Marla Maples, was spotted on Tuesday afternoon. Trump transition team in disarray after top adviser 'purged' Read more The departure of former US representative Mike Rogers as a national security adviser followed the removal of New Jersey governor Chris Christie as head of Trump’s transition team in favour of Vice-President-elect Mike Pence, who did not sign a memorandum of understanding with Barack Obama’s White House until Tuesday night. The appointment of Steve Bannon, a media executive accused of far-right ties, and the role of Trump’s son-in-law Jared Kushner have fuelled discontent. On Wednesday Bernie Sanders, the leftwing Democrat who ran against Hillary Clinton in the 2016 Democratic primary, called the appointment of Bannon “totally unacceptable”. “In a democratic society we can disagree all we want over issues, but racism and bigotry cannot be part of any public policy,” Sanders aid. “The appointment of Mr Bannon by Mr Trump must be rescinded.” Former New York mayor Rudy Giuliani appears to be haggling for the prize job of secretary of state. But the transition team is reviewing Giuliani’s paid consulting work for foreign governments including Qatar, Saudi Arabia and Venezuela, the Associated Press reported. He is also under scrutiny over speeches he made on behalf of the Mujahideen-e Khalq, a fringe Iranian dissident group. The group, which operates in exile, was designated a foreign terrorist organization by the US state department in 1997 for its long and bloody history, including its involvement in the killing of Americans in Iran in the 1970s. Speaking fees paid by several MEK front groups to Giuliani and other politicians potentially broke laws on Americans receiving money from designated terrorist organisations. Another visitor to Trump Tower on Wednesday was current New York mayor Bill de Blasio, a Democrat. He said he wanted to give Trump a feel of concerns everyone is feeling about his presidency. “I talked to him about concerns of potential deportations, I gave him the perspective of the NYPD [New York police department],” De Blasio said, describing New York “the ultimate city of immigrants.” There are more than 900 Muslim members of the NYPD, the mayor said, and citizens rely on their willingness to protect the city. “I let him know that so many New Yorkers were fearful and that more had to be done to show that this country can heal, that people be respected.” De Blasio added: “Even though I have very real differences with the president-elect, he is a New Yorker, I do think he loves this city.” ||||| Tweet with a location You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more

– As they survey the shattered landscape of American politics, Democrats looking for the way forward have realized something: Donald Trump is closer to their party than to traditional Republicans on issues including infrastructure spending and paid maternity leave. The New York Times reports that after last week's defeat, Democrats face "a profound decision" on whether to work with Trump on issues where they have common ground—and try to win back working-class white voters in the process—or do all they can to block him in the hope of winning back the House in 2018. Congressional Republicans are already preparing initiatives that align with some Trump promises. In other coverage: The AP reports that a spokesman for Trump's transition team says officials joining the new administration will be required to quit any lobbying roles—and they will have to pledge that they won't return to lobbying the government for five years after leaving government. The Washington Post takes a look at the different associates and factions jostling for influence as Trump assembles his team. Art of the Deal ghostwriter Tony Schwartz says things are following a familiar pattern: "Trump sees himself as the straw that stirs the drink," he says. "He has almost no interest in the details of how things happen, but he has an intense interest in being the decision-maker." Politico looks ahead to the 2018 midterms and finds that the Senate map is a brutal one for Democrats. Winning back the chamber could be almost impossible for the party, and there is a real chance that the Republicans could end up with a filibuster-proof majority. The Guardian reports that the president-elect appears to be feuding with the media again—especially the New York Times. In tweets early Wednesday, Trump denied reports of chaos in the transition team and failure to speak to foreign leaders, saying he has taken calls from many of them and the Times is "just upset that they looked like fools in their coverage of me." The Los Angeles Times reports that Trump met with New York City Mayor Bill De Blasio on Wednesday. The mayor, one of Trump's fiercest critics, told reporters afterward that he let him know "more had to be done to show that this country can heal, that people be respected" and warned that the city would not cooperate with plans to deport immigrants.

SECTION 1. SHORT TITLE. This Act may be cited as the ``No Taxpayer Funding for Abortion Act''. SEC. 2. PROHIBITING TAXPAYER FUNDED ABORTIONS AND PROVIDING FOR CONSCIENCE PROTECTIONS. Title 1 of the United States Code is amended by adding at the end the following new chapter: ``CHAPTER 4--PROHIBITING TAXPAYER FUNDED ABORTIONS AND PROVIDING FOR CONSCIENCE PROTECTIONS ``SEC. 301. PROHIBITION ON FUNDING FOR ABORTIONS. ``No funds authorized or appropriated by federal law, and none of the funds in any trust fund to which funds are authorized or appropriated by federal law, shall be expended for any abortion. ``SEC. 302. PROHIBITION ON FUNDING FOR HEALTH BENEFITS PLANS THAT COVER ABORTION. ``None of the funds authorized or appropriated by federal law, and none of the funds in any trust fund to which funds are authorized or appropriated by federal law, shall be expended for health benefits coverage that includes coverage of abortion. ``SEC. 303. PROHIBITION ON TAX BENEFITS RELATING TO ABORTION. ``For taxable years beginning after the date of the enactment of this section-- ``(1) no credit shall be allowed under the internal revenue laws with respect to amounts paid or incurred for an abortion or with respect to amounts paid or incurred for a health benefits plan (including premium assistance) that includes coverage of abortion, ``(2) for purposes of determining any deduction for expenses paid for medical care of the taxpayer or the taxpayer's spouse or dependents, amounts paid or incurred for an abortion or for a health benefits plan that includes coverage of abortion shall not be taken into account, and ``(3) in the case of any tax-preferred trust or account the purpose of which is to pay medical expenses of the account beneficiary, any amount paid or distributed from such an account for an abortion shall be included in the gross income of such beneficiary. ``SEC. 304. LIMITATION ON FEDERAL FACILITIES AND EMPLOYEES. ``No health care service furnished-- ``(1) by or in a health care facility owned or operated by the Federal government; or ``(2) by any physician or other individual employed by the Federal government to provide health care services within the scope of the physician's or individual's employment, may include abortion. ``SEC. 305. CONSTRUCTION RELATING TO SEPARATE COVERAGE. ``Nothing in this chapter shall be construed as prohibiting any individual, entity, or State or locality from purchasing separate abortion coverage or health benefits coverage that includes abortion so long as such coverage is paid for entirely using only funds not authorized or appropriated by federal law and such coverage shall not be purchased using matching funds required for a federally subsidized program, including a State's or locality's contribution of Medicaid matching funds. ``SEC. 306. CONSTRUCTION RELATING TO THE USE OF NON-FEDERAL FUNDS FOR HEALTH COVERAGE. ``Nothing in this chapter shall be construed as restricting the ability of any nonfederal health benefits coverage provider from offering abortion coverage, or the ability of a State or locality to contract separately with such a provider for such coverage, so long as only funds not authorized or appropriated by federal law are used and such coverage shall not be purchased using matching funds required for a federally subsidized program, including a State's or locality's contribution of Medicaid matching funds. ``SEC. 307. NON-PREEMPTION OF OTHER FEDERAL LAWS. ``Nothing in this chapter shall repeal, amend, or have any effect on any other federal law to the extent such law imposes any limitation on the use of funds for abortion or for health benefits coverage that includes coverage of abortion, beyond the limitations set forth in this chapter. ``SEC. 308. CONSTRUCTION RELATED TO STATE OR LOCAL LAWS. ``Nothing in this chapter or any other federal law shall be construed to require any State or local government to provide or pay for any abortion or any health benefits coverage that includes coverage of any abortion. ``SEC. 309. TREATMENT OF ABORTIONS RELATED TO RAPE, INCEST, OR PRESERVING THE LIFE OF THE MOTHER. ``The limitations established in sections 301, 302, 303, and 304 shall not apply to an abortion-- ``(1) if the pregnancy is the result of an act of forcible rape, or incest with a minor; or ``(2) in the case where a woman suffers from a physical disorder, physical injury, or physical illness that would, as certified by a physician, place the woman in danger of death unless an abortion is performed, including a life-endangering physical condition caused by or arising from the pregnancy itself. ``SEC. 310. APPLICATION TO DISTRICT OF COLUMBIA. ``In this chapter: ``(1) Any reference to funds appropriated by Federal law shall be treated as including any amounts within the budget of the District of Columbia that have been approved by Act of Congress pursuant to section 446 of the District of Columbia Home Rule Act (or any applicable successor Federal law). ``(2) The term `Federal government' includes the government of the District of Columbia. ``SEC. 311. NO GOVERNMENT DISCRIMINATION AGAINST CERTAIN HEALTH CARE ENTITIES. ``(a) Nondiscrimination.--A Federal agency or program, and any State or local government that receives Federal financial assistance (either directly or indirectly), may not subject any individual or institutional health care entity to discrimination on the basis that the health care entity does not provide, pay for, provide coverage of, or refer for abortions. ``(b) Health Care Entity Defined.--For purposes of this section, the term `health care entity' includes an individual physician or other health care professional, a hospital, a provider-sponsored organization, a health maintenance organization, a health insurance plan, or any other kind of health care facility, organization, or plan. ``(c) Administration.--The Office for Civil Rights of the Department of Health and Human Services is designated to receive complaints of discrimination based on this subsection, and coordinate the investigation of such complaints. ``SEC. 312. HEALTH BENEFITS COVERAGE DEFINED. ``In this chapter the term `health benefits coverage' means the package of services covered by a managed care provider or organization pursuant to a contract or other arrangement.''.

No Taxpayer Funding for Abortion Act - Prohibits: (1) the expenditure of funds authorized or appropriated by federal law or funds in any trust fund to which funds are authorized or appropriated by federal law for any abortion or for health benefits coverage that includes coverage of abortion; (2) any tax benefits for amounts paid or incurred for an abortion or for a health benefits plan (including premium assistance) that includes coverage of abortion; and (3) the inclusion of abortion in any health care service furnished by a federal health care facility or by any physician or other individual employed by the federal government. Exempts from such prohibitions an abortion if the pregnancy is the result of rape or incest with a minor, or if the woman suffers from a physical disorder, injury, or illness that would, as certified by a physician, place the women in danger of death unless an abortion is performed, including a life-endangering physical condition caused by or arising from the pregnancy itself. Makes such prohibitions applicable to federal funding within the budget of the District of Columbia. Prohibits federal agencies or programs and states and local governments that receive federal financial assistance from discriminating against any individual or institutional health care entity on the basis that such entity does not provide, pay for, provide coverage of, or refer for abortions. Designates the Office for Civil Rights of the Department of Health and Human Services (HHS) to receive, and coordinate the investigation of, discrimination complaints.

according to mermin and wagner @xcite there is no ferromagnetic or antiferromagnetic order in the one- and two - dimensional isotropic heisenberg models with interactions of finite range at nonzero temperature . this statement is proven due to bogoliubov s inequality in the general case . here we construct excitations that cause a destruction of a long - range nematic or mixed ferromagnetic - nematic order . this is an extension of the results of belavin and polyakov @xcite . we model a planar magnet by a square atomic lattice with the same spin @xmath1 at each site . we describe this two - dimensional spin system by a generalized heisenberg hamiltonian , taking into account high powers of the exchange interaction @xmath2 , where @xmath3 is a vector of spin operators at site @xmath4 . by a mean field approximation we obtain a classical long - range equation from the quantum heisenberg one . an equation for a mean field ( the field of magnetization and multipole moments ) is a hamiltonian equation on a coadjoint orbit of lie group . at the same time , this is a generalization of the well - known landau - lifshitz equation for a magnetization field . in this context we obtain effective hamiltonians for the magnetic system in question . using khlerian structure of coadjoint orbits , we construct effective hamiltonians such that their minimums are proportional to topological charges of excitations . in addition , we produce these mean field configurations that give minimums to the hamiltonians . as mentioned above , we represent the spin system by a planar atomic lattice with the same spin @xmath1 at all sites . we assign three spin operators @xmath5 to each atom @xmath4 ; the operators obey the standard commutation relations @xmath6 = i\varepsilon_{abc } \hat{s}^c_n \delta_{nm},\ ] ] where @xmath7 @xmath8 @xmath9 run over the values @xmath10 , and @xmath11 is the kronecker symbol . we are interested in so called high spins @xmath12 . in this case , we can describe the system by the following _ bilinear - biquadratic hamiltonian _ @xmath13 here @xmath14 runs over the nearest - neighbour sites , @xmath4 runs over all sites of the lattice , constants @xmath15 and @xmath16 denote exchange integrals . in the case of spin @xmath17 , the above hamiltonian can include also the bicubic exchange , namely @xmath18 where @xmath19 denotes the corresponding exchange integral . one can easily write a generalized heisenberg hamiltonian for the system of an arbitrary spin @xmath1 or greater than @xmath1 . this hamiltonian contains all powers of the exchange interaction up to @xmath20 . it can be reduced to a bilinear form if one takes the @xmath0-dimensional space of irreducible representation of the group su(2 ) . the spin operators @xmath21 over this space generate a complete associative matrix algebra , which has a sufficient number of operators to reduce the corresponding hamiltonian to a bilinear form . for example , in the case of spin @xmath22 the appropriate space of representation is 3-dimensional , and we choose a canonical basis in the form : @xmath23 . the spin operators @xmath21 generate the algebra @xmath24 . in order to form a basis in the algebra we take the tensor operators of weight 2 @xmath25 in addition to the spin operators . the introduced operators are called _ quadrupole operators_. in the case of spin @xmath26 the appropriate space of representation is 4-dimensional , and @xmath27 of @xmath21 by the tensor operators of weights 2 and 3 , defining them by the following formulas : @xmath28 @xmath29 we call the tensor operators of weight 3 _ sextupole operators_. in what follows we denote all tensor operators over the chosen space of representation by @xmath30 . in terms of representation operators a generalized heisenberg hamiltonian gets a bilinear form . for the hamiltonians considered above we have : @xmath31 where @xmath32 is the overall number of sites in the lattice , the obtained bilinear hamiltonians are su(2)-invariant , because they are constructed from representation operators of the group su(2 ) . here a mean field is a field of expectation values for the operators @xmath33 calculated after spontaneous breaking of symmetry . the breaking of symmetry is performed by switching on an external magnetic field , which specifies an order in the system ; then the external field vanishes . such kind of averages is also called _ quasiaverages _ @xcite . we denote a mean field averaging by @xmath34 , and components of the mean field by @xmath35 . a mean field approximation of the bilinear - biquadratic hamiltonian has the form @xmath36 where @xmath37 is a number of the nearest - neighbour sites . evidently , a mean field hamiltonian remains @xmath38-invariant . then by an action of the group @xmath38 it can be reduced to a diagonal form . of course , this reduction is possible only in the case of thermodynamical equilibrium and an infinite lattice , when the mean field becomes constant and the dependance on site @xmath4 can be omitted . moreover , almost all components of the mean field vanish , except the components corresponding to diagonal operators of @xmath30 . for the bilinear - biquadratic hamiltonian a diagonal form is the following : @xmath39 the remaining components are suitable to serve as _ order parameters_. the component @xmath40 describes a normalized _ magnetization _ ( a ratio of the @xmath37-projection of magnetic moment to a saturation magnetization ) . the components @xmath41 and @xmath42 are normalized _ projections of quadrupole _ and _ sextupole moments _ , respectively . possible values of order parameters can be obtained from the _ self - consistent equations _ @xmath43 for all diagonal operators @xmath44 . here we use the density matrix with the one - site hamiltonian @xmath45 . note , that for the standard heisenberg hamiltonian , when only the spin operators are considered , a self - consistent equation turns into the well - known weiss equation . in the case of bilinear - biquadratic hamiltonian , an analysis of self - consistent equations gives the following . we adduce probable values of order parameters in the limit @xmath46 as @xmath47 : 1 ) @xmath48 ; 2 ) @xmath49 ; 3 ) @xmath50 ; 4 ) @xmath51 , @xmath52 . two of the solutions correspond to states with the ferromagnetic order , because they have a nonzero magnetization @xmath40 . the other two solutions correspond to states with the quadrupole order ( so called nematic states ) , which are states with zero magnetization . solutions 2 ) and 4 ) are unstable and called partly ordered . if @xmath16 becomes negative , only solution 1 ) remains . these results accord with the results of @xcite and with the phase diagram of ordered states in a one - dimensional spin system from @xcite . in what follows we consider an su(3)-invariant system with the bilinear - biquadratic hamiltonian . the su(3)-invariance is reached by assigning @xmath53 ; this is the boundary line between the ferromagnetic and the nematic regions ( see @xcite ) . it means the system can appear in the both states . in the case of hamiltonian @xmath54 , the maximal su(4)-invariance is reached as @xmath55 , that is located within the ferromagnetic region . now we apply the mean field averaging to the quantum heisenberg equation @xmath56.\ ] ] the averaging is performed with the assumption of zero correlations between fluctuations of @xmath30 at distinct sites : @xmath57 . then we take a large - scale limit and obtain the landau - lifshitz like equation @xmath58 where @xmath59 are structure constants of the lie algebra of @xmath30 with the commutation relations @xmath60=ic_{abc}\hat{p}^c_n \delta_{nm}$ ] . equation is an equation of motion for the mean field @xmath61 over the plain @xmath62 that replaces the lattice . in the case of standard heisenberg hamiltonian coincides with the landau - lifshitz equation for an isotropic magnet . therefore , in the general case we call a _ generalized landau - lifshitz equation _ for the vector field @xmath63 . the vector field has 8 components if one exploits the bilinear - biquadratic hamiltonian , and 15 components for the hamiltonian with the bicubic exchange . the generalized landau - lifshitz equation can be interpreted as a _ hamiltonian equation on a coadjoint orbit of lie group_. in the case of spin @xmath64 we deal with the group @xmath65 , in the case of an arbitrary spin @xmath1 the group is @xmath66 . note , that the matrices @xmath67 serve as a basis in the corresponding lie algebra @xmath68 , and components of the mean field @xmath63 serve as coordinates in the dual space to @xmath68 . we start with brief description of the groups su(3 ) and su(4 ) . for more material see , in particular , @xcite . the group su(3 ) has two types of orbits : the generic @xmath69 of dimension 6 , and the degenerate @xmath70 of dimension 4 . each orbit of su(3 ) is defined by two numbers @xmath71 and @xmath72 , which are values of the coordinates @xmath40 and @xmath41 at an initial point ( a point in the positive weyl chamber ) . simultaneously , these numbers are limiting values of the mean field components @xmath40 and @xmath41 at zero temperature . for a degenerate orbit one has to assign @xmath73 , or @xmath74 . evidently the degenerate orbits with @xmath73 are domains of mean field configurations that realize nematic states . ferromagnetic states are realized on all other orbits of su(3 ) . the group su(4 ) has four types of orbits : the generic @xmath75 of dimension @xmath76 , the degenerate @xmath77 of dimension 10 , the degenerate @xmath78 of dimension 8 , and the maximal degenerate @xmath79 of dimension 6 . each orbit is defined by numbers @xmath71 , @xmath72 , @xmath80 , which are limiting values of the mean field components @xmath40 , @xmath41 , @xmath42 . almost all orbits are domains of ferromagnetic mean field configurations . nematic states are realized on the degenerate orbits of dimension 8 as @xmath81 and @xmath72 is arbitrary . so it is probable to reveal a nematic state even in the ferromagnetic region of the phase diagram @xcite . as shown above , _ limiting values of diagonal components of a mean field _ serve as order parameters . simultaneously , they _ define a coadjoint orbit _ where the corresponding mean filed configuration lives . each orbit possesses a hamiltonian system with an equation of motion and a group - invariant hamiltonian . for a degenerate orbit of su(3 ) the equation is @xmath82 where @xmath83 denotes a dimensional constant . the values @xmath71 , @xmath72 of order parameters ( a magnetization and a projection of quadrupole moment ) define an orbit via the following equations , which we call constraints : @xmath84 here @xmath85 is a symmetric tensor . the corresponding su(3)-invariant hamiltonian is the following @xmath86 where the dimensional constant @xmath87 has a meaning of exchange integral . obviously , equations and coincide . it is easy to show , that coincides with the equation of motion on a maximal degenerate orbit . recall , that is obtained when correlations between fluctuations of @xmath30 are neglected . presumably , equations of motion on other orbits are derived from via the mean field averaging with more complicate correlation rules . a generic orbit of su(3 ) is determined by the following equations : @xmath88 the su(3)-invariant hamiltonian on this orbit has the form @xmath89where @xmath90 is a quadratic form in @xmath63 : @xmath91 . for more details see @xcite . the hamiltonian systems on coadjoint orbits of su(3 ) serve as _ classical effective models _ for the spin system of @xmath92 with biquadratic exchange . evidently , these models describe large - scale ( or slow ) fluctuations of the mean field . in this paper we suppose that the order parameters @xmath71 , @xmath72 are fixed numbers . but generally speaking , they depend on a temperature @xmath93 and the interaction constant @xmath15 . taking into account these dependencies , one can consider small - scale ( or quick ) fluctuations of the mean field . each coadjoint orbit of a semisimple lie group is a homogeneous space that admits a khlerian structure . thus one can introduce a complex parameterization of an orbit . for this purpose we use a _ generalized stereographic projection _ ( for more details see @xcite ) . in the case of group su(3 ) , the projection is represented by the following formulas : @xmath94 @xmath95 the coordinates @xmath96 ( bruhat coordinates according to @xcite ) parameterize a generic orbit of @xmath65 . in the case of a degenerate orbit , one has to assign @xmath73 and @xmath97 , or @xmath98 and @xmath99 . in terms of @xmath100 the effective hamiltonians and have the form @xmath101 where @xmath102 is a complex coordinate on the plane obtained from the atomic lattice after a large - scale limiting process ( see section [ s : mfa ] ) . the tensor @xmath103 is non - degenerate and positively defined , thus it can serve as a metrics on an orbit . its components @xmath104 come from for a degenerate orbit , and from for a generic one . in terms of the auxiliary vector fields @xmath105 and @xmath106 we have @xmath107 note , that in terms of @xmath100 the tensor @xmath103 does not depend on a particular orbit . being a khlerian manifold an orbit of su(3 ) possesses a khlerian potential . for this purpose we use a potential @xmath108 of the kirillov - kostant - suoriau form : @xmath109 a topological structure of the orbit is characterized by the second cohomology group @xmath110 of dimension 2 . that is why there exist two basis 2-forms , for example generated by the potentials @xmath111 , @xmath112 . each of them defines a topological charge @xmath113 on a degenerate orbit only one potential is governing , and only one topological charge exists . then the expressions for @xmath114 and @xmath115 differ only in a sign . evidently , @xmath116 is realized if the equality holds , that takes place if @xmath117 are holomorphic or antiholomorphic functions_. here we use an idea of belavin and polyakov @xcite . for a generic orbit we define a topological charge by @xmath118 . in order to extend inequality to generic orbits with the topological charge @xmath119 , we construct an effective hamiltonian by the following formula : @xmath120 in terms of @xmath100 it is reduced to the form with the metrics @xmath121 then we get @xmath122 and _ a minimum of @xmath123 is realized if the equality holds , that takes place if @xmath117 are holomorphic or antiholomorphic functions_. now we construct a particular class of topological excitations that give minimums to the effective hamiltonians @xmath124 , and @xmath123 defined by . we describe these excitations by holomorphic functions @xmath125 . each set @xmath126 @xmath127 , @xmath128 represents a mean field configuration of the system in question . first , we consider a degenerate orbit of @xmath65 with @xmath73 , @xmath129 , where a nematic state is realized . in order to satisfy the limiting conditions : @xmath130 , @xmath131 , the functions @xmath125 have to vanish as @xmath132 . let @xmath133 be a large - scale excitation in the magnet in question . the corresponding mean field configuration is obtained by substitution of into . a behavior of the components @xmath40 and @xmath41 is represented on the fig.1 . as @xmath132 the values of @xmath40 , @xmath41 tend to @xmath71 , @xmath72 . 1 . profiles of the mean field components @xmath40 , @xmath41 in the case of configuration . suppose @xmath134 . by shifting of the coordinate @xmath37 one can easily reduce to the configuration @xmath135 and calculate its topological charge : @xmath136 in the case of @xmath137 the topological charge equals 2 . it can be interpreted as follows . each pole of a mean field configuration represents a kind of belavin - plyakov soliton . each soliton gives a unit topological charge . thus , two distinct solitons have the topological charge 2 . no continuous deformation take a configuration of topological charge 2 to a configuration of topological charge 1 . if we allow noncontinuous deformation , then two solitons can meet at any point and join into one , at the same time an energy is released . from , it follows that the released energy equals @xmath138 per one pole . note , that the energy of configuration does not depend on parameters of solitons : @xmath139 , @xmath140 , @xmath141 , @xmath142 . it means that the excitation can grow ( when @xmath143 and @xmath144 grow ) preserving an energy . such growth immediately leads to destruction of an order in the system . one can construct a configuration with more than two solitons : @xmath145 here @xmath139 , @xmath141 , @xmath146 , and @xmath147 are fixed complex numbers . if all values @xmath146 and @xmath147 are distinct , a topological charge equals @xmath148 . when a pole of the function @xmath149 coincides with a pole of @xmath150 , the topological charge decreases by 1 . but a coincidence of two poles of the same function ( for example @xmath149 ) does not lead to a decrease of the topological charge . it is easy to see , that the minimal energy of configuration equals @xmath151 . now we consider a generic orbit , where a ferromagnetic state is realized . suppose @xmath152 and @xmath129 . in this case , we describe a mean field in the magnet by the effective hamiltonian @xmath123 , defined by . let @xmath153 be a large - scale excitation of the mean field . a calculation of topological charges gives : 1 ) @xmath154 , @xmath155 , if @xmath156 or @xmath157 , 2 ) @xmath158 , @xmath155 , if @xmath159 , 3 ) @xmath158 , @xmath160 , if @xmath161 or @xmath162 . each generalized heisenberg hamiltonian with high powers of the exchange interaction can be reduced to a bilinear form . by a mean field averaging we obtain a classical system from the original quantum one . an averaging of the heisenberg equation gives a landau - lifshitz like equation for a mean field . using lie group apparatus , we construct effective hamiltonians for the classical system with su(3 ) symmetry . one of them @xmath163 is an su(3)-analogue of the hamiltonian commonly used in theory of magnetism . in addition , we propose another one @xmath123 , which is biquadratic in the mean field . further , we construct examples of topological excitations that give minimums to the hamiltonians . such excitations can change their shapes and grow preserving an energy . this is a probable scenario for the destruction of an ordered state in a 2d magnet at nonzero temperature , that agrees with the mermin - wagner theorem . this work is partly supported by the grant of the international charitable fund for renaissance of kyiv - mohyla academy .

we construct a class of topological excitations of a mean field in a two - dimensional spin system represented by a quantum heisenberg model with high powers of exchange interaction . the quantum model is associated with a classical one ( the continuous classical analogue ) that is based on a landau - lifshitz like equation , and describes large - scale fluctuations of the mean field . on the other hand , the classical model is a hamiltonian system on a coadjoint orbit of the unitary group su(@xmath0 ) in the case of spin @xmath1 . we have found a class of mean field configurations that can be interpreted as topological excitations , because they have fixed topological charges . such excitations change their shapes and grow preserving an energy .