the mose project ( modeling eso sites ) aims at proving the feasibility of the forecast of all the most relevant classical atmospherical parameters for astronomical applications ( wind speed intensity and direction , temperature , relative humidity ) and the optical turbulence ot ( profiles ) with the integrated astro - climatic parameters derived from the i.e. the seeing ( ) , the isoplanatic angle ( ) , the wavefront coherence time ( ) above the two eso sites of cerro paranal ( site of the very large telescope - vlt ) and cerro armazones ( site selected for the european extremely large telescope - e - elt ) .the final outcome of the study is to investigate the opportunity to implement an automatic system for the forecast of these parameters at the vlt observatory at cerro paranal and at the e - elt observatory at cerro armazones .  the optical turbulence ( ot ) forecast is a crucial cornerstone for the feasibility of the elts : it is indeed fundamental to support all kind of ao facilities in an astronomical observatory and to perform the flexible - scheduling of scientific programs and instrumentation through the service mode .most of the scientific programs , associated to the most challenging scientific goals , require , indeed , frequently excellent optical turbulence conditions to be carried out . the traditional queue system , that is based on the quality of the scientific program but that does not take into account the ot conditions , leads necessarily to a paradox : the higher is the scientific challenge of a scientific program , the lower is the probability to complete the program itself . from thiswe derive that the service mode , that takes into account the status of the ot beside to the quality of the scientific program , is mandatory to optimize the exploitation of the elts . however , to implement a service mode we need to forecast the ot to know its status at different delayed times t with respect to the time at which the prediction is performed .the optimization of the _ use _ of a ground - based facility has therefore serious implications on the final scientific impact of the facility itself .we note , moreover , that the cost of a night of observation is of the order of hundreds of kdollars .the implementation of an ot forecast system leads therefore to a not negligible rationalization of costs versus scientific feedbacks .we remind also that , for evident statistical reasons , the advantage of the service mode can be fully achieved only if most of the available observing time is scheduled in this mode .for all these reasons elts plan to have , in their baseline configuration , permanent instruments located at different focal stations .it has been estimated that , at the e - elt , the typical time required to switch the beam from an instrument to another is of the order of 10 - 20 minutes .this is therefore the final minimal time - scale in terms of ot prediction that we can take as a reference .all these premises lead to the conclusion that our ability in forecasting the ot is fundamental for the success and the feasibility of the elts .the peculiar feature of the numerical approach , and more precisely of the mesoscale atmospheric models , is the possibility to describe a 3d map of the ( i.e. volumetric distribution of the optical turbulence in the troposphere ) in a region around a telescope of the order of a few tens of kilometers at a time t placed in the future .this is the unique method that aims at address directly the solution of the navier - stokes equation of the hydrodynamical flow above the earth .it is therefore intrinsically the most appropriate to detect directly a rapid change of the atmospheric status .the typologies of models that can be used to study thermodynamic evolution of the earth s atmosphere are : the general circulation models ( gcm ) , the non - hydrostatic meso - scale models , the models for large eddy simulations ( les ) and the models for direct numerical simulations ( dns ) .these models differ in their resolution and , as a consequence , also in the extent of the typical domain of the atmosphere that they can reconstruct .we deduce that each of these typologies of model is dedicated to resolve phenomena of different nature and that the numerical approach as well as the physics described inside each of these models is done following a completely different logic .the ot can not be resolved by the gcms because the spatio - temporal fluctuation of the ot is much smaller ( order of centimeter / meter ) than the typical resolution of the gcm (  km ) . with the dnsthe ot can be completely resolved but we can not forecast it because we definitely miss the link with initialization data i.e. with the evolution of the atmospheric flow at large spatial scales .the meso - scale models represent the right trade - off that permits to reconstruct the ot maintaining the link with the external spatio - temporal evolution of the atmospheric flow .the ot is completely parameterized in the meso - scale models . with the les the otis partially resolved and partially parameterized . in principleit is possible in perspective to use the les to improve the resolution of the simulations if initialized with outputs coming from meso - scale models .it has been observed that , when the horizontal resolution increases and reaches values of smaller than 10 km , the hydrostatic models show a tendency in distorting the spectrum of the gravity waves , particularly in proximity of mountain regions .for this reason , non - hydrostatic models are more suitable to reconstruct the atmospheric flow on such conditions .this is the first paper of a series aiming at collecting the main results we obtained in the context of mose . in section [ for_par ]we present the parameters that we intend to reconstruct with such a model and the importance they cover in the context of the astronomical observations and in the observational scheduling . in section [ model ]we describe the novelties of mose with respect to the status of art and we briefly describe the model we use for this study : meso - nh plus the astro - meso - nh package . in section [ config ]we describe the model configuration used for the mose project . in section [ obs_data ]we describe the whole set of measurements we used for the model validation . in section [ vert_atm ]we present the model validation in reconstructing the vertical stratification of the atmospherical parameters . in section [ conc ]we present the conclusions of the study .in the context of the mose project we focused our attention on the following parameters that are strictly related to the optimization of the ao systems and operational and observational programs scheduling activities : all the astroclimatic parameters ( , , ) and the atmospheric parameters from which the ot mainly depends on .+  + * - surface temperature : * the knowledge of the temperature near the ground is extremely important to thermalize the dome and reduce / eliminate the dome seeing , the most important contribution of the seeing experienced on ground - based images . the seeing inside the dome can be very hardly modeled being that the turbulence develops inside a confined environment and the kolmogorov theory is rarely respected under these conditions .it has been proved that the dome - seeing is mainly determined by ( t-t) and ( t-t) where t is the primary mirror temperature , t is the temperature inside the dome and t is the temperature outside the dome , near the ground . once t is forecasted , it is possible to tune t and t so as to minimize the temperature gradients and eventually eliminate the dome seeing .the temperature gradient near the ground is moreover extremely critical to well reconstruct the optical turbulence near the ground .it is fundamental for us to know how good or bad is the model performance in reconstructing this parameter to discriminate the potential discrepancies of the model .+  + * - surface wind speed : * the intensity of the wind speed near the ground can strongly affect the ao performances because of vibrations induced by all critical structures such as primary and secondary mirrors ( particularly critical are the adaptive secondaries ) .vibrations produced by wind speed bursts are among the most annoying source of noise for these elements and the accuracy of the ao correction is directly proportional to the noise introduced by such a kind of vibrations. an efficient forecast of the wind speed intensity can usefully optimize the use of the most sophisticated ao techniques and even decide when it is better to avoid ao observations if conditions do not permit to achieve required conditions . besides , the wind speed shear near the ground is one of the main cause for ot triggering together with the temperature gradient .the interest in studying the ability of the model in reconstructing this parameter is therefore similar to what already said for the surface temperature. +  + * - surface wind direction : * the wind direction is one of the atmospheric parameters that are more frequently and easily correlated to the local seeing characteristics . the prediction of the wind direction can therefore give a direct information on the probability to have bad or good seeing .it becomes very important when the wind speed is strong because , under this condition , the effects of the wind speed on the adaptive secondary ( vibrations ) are strongly dependent on the wind direction .+  + * - vertical profiles on 20 km : potential temperature , wind speed intensity and direction and relative humidity : * such a stratification can be obtained , in principle , by gcms .however , it has been proved that gcms are not reliable in the low part of the atmosphere particularly in proximity of mountain regions because of their too low horizontal resolution and a too smooth orography .moreover , it is also worth reminding that a meso - scale model can produce a continuous temporal evolution of the vertical stratification of these parameters with a temporal sampling that can be freely selected ( in our study we use a temporal sampling of 2 min ) while information provided by gcm is sampled only at synoptic hours ( 00:00 , 06:00 , 12:00 and 18:00 ut ) .the meso - scale model technique appears therefore as particularly interesting for systematic calculations of the temporal evolution of the wavefront coherence time at astronomical observatories . besides , the wind speed intensity shear ( together with the potential temperature gradient ) are the fundamental cause of the ot triggering .it is therefore important to assure us how the model reconstructs the vertical stratification of these parameters to be able to discriminate the potential causes of model discrepancies or failures .the potential temperature of an air parcel is defined as the temperature which the parcel of air would have if it were expanded or compressed adiabatically from its existing pressure and temperature to a standard pressure p ( generally taken as 1000 mb ) :  where r is the gas constant r = 287 j , c is the specific heat capacity at constant pressure c = 1004 j , p is the pressure and t is the absolute temperature .it is preferable to study the stratification of instead of that of the absolute temperature t because is strictly related to the thermodynamic stability of the atmosphere that is one of the principal source triggering the optical turbulence . in the astronomical contextwe count already some studies aiming at characterizing the sites for their thermodynamic stability .+  +  +  + * - profiles : * the profiles tell us how the turbulence is spatially distributed in the whole atmosphere , where are located the main turbulent layers during a night .this is a fundamental information for the ao tomography .the algorithm used for the parameterization is the one described in .we refer the reader to the same paper for the detailed description of the theory connecting the dynamic turbulence with the optical turbulence and the algorithms used in the meso - nh model . in the context of the mose project we also tested a modified / new algorithm ( new parameterization ) in order to test which of the two ones provides better model performances . in a forthcoming paperthe algorithm will be presented as well as the results obtained .+  + * - integrated astro - climatic parameters : * in the context of the mose project it has been established to investigate the three most important integrated astro - climatic parameters : the seeing ( ) , the isoplanatic angle ( ) and the wavefront coherence time ( ) : ^{-3/5}\ ] ] ^{-3/5}\ ] ] ^{-3/5}\ ] ]  the knowledge of the values of these parameters is critical to manage and optimize the ao systems . the seeing is the main discriminant permitting us to identify the temporal windows in which the ao systems can be mostly effective , tell us how fast is the turbulence , tells us how much turbulence is present in the free atmosphere particularly in the high part of the atmosphere and it can be very useful to discriminate between ao observations to be done in narrow or wide field .which are the mose scientific goals with respect to the status of art ? in 1999 it has been proved for the first time that a meso - scale model could reconstruct reliable profiles . from a qualitative point of view, it has been proved that the shape of the profile could match the observed one , and from a quantitative point of view the observed and simulated integrated values of the turbulence present in the atmosphere were well correlated . in 2001 a calibration method for the model has been proposed and the whole technique has been validated on a statistic of 10 nights comparing simulations with measurements taken from different instruments ( balloons and generalized scidar ) . it has been proved that the dispersion of the seeing simulated and observed  25 was comparable to the dispersion obtained using different instruments  30 . in a successive timethe same technique has been applied in an autonomous way on a whole solar year at san pedro mrtir carrying out a complete statistical analysis of all the astro - climatic parameters permitting us to achieve the first complete and homogeneous analysis of the seasonal variation investigation of the ot ever done so far . in 2011 the model / technique has been validated using a richer statistical sample of gs measurements performed on 43 nights uniformly distributed along one year at mt . graham . at the same timeit has been also proved that this technique can be efficient in discriminating sites characterized by substantial different turbulence features .the meso - nh model has been applied to the internal antarctic plateau achieving two major conclusions : * ( 1 ) * it has been proved that such a model is able to discriminate between the sites on the top of the summit of a plateau characterized by a very thin surface layer ( dome c , dome a and south pole ) ; * ( 2 ) * thanks to the numerical technique ( meso - nh model ) , the first estimates of the ot vertical stratification ever done in the free atmosphere at dome a have been provided .+ we finally remind that , the heart of the ot parameterization used in our study has been implemented by the colleagues of mauna kea on the wrf mesoscale model for applications to the mauna kea observatory in an operational configuration . an extended review on alternative methods for the ot forecasts can be found in .we limit here to cases of an ot parameterized in a non - hydrostatical mesoscale model .the mose project aims at overcoming two major limitations that are typically encountered in studies focused on the optical turbulence forecast with atmospheric models : * ( 1 ) * the difficulty in having independent samples of measurements for the model calibration and model validation to estimate if and how the correlation between measurements and predictions on the validation sample changes with the increasing of the number of nights and to estimate if and how the statistical richness of the calibration sample affects the calibration itself ; * ( 2 ) * the difficulty in having a large number of simultaneous measurements done with different and independent instruments for the ot estimates ( in particular vertical profilers ) .this project is performed with the non - hydrostatic mesoscale atmospherical model meso - nh joined with the astro - meso - nh package for the calculation of the optical turbulence to perform the ot forecasts .an extended data - set of observations ( meteorological parameters and optical turbulence ) have been considered in the project .we took advantage of measurements obtained in the context of the site selection for the tmt ( american study ) at cerro armazones and on measurements taken routinely during the last decade and/or in a dedicated site testing campaign ( par2007 ) at cerro paranal ( details in section [ obs_data ] ) .all the numerical simulations of the nights presented in this study have been performed with the non - hydrostatical mesoscale numerical weather model meso - nh ] .the model has been developed by the centre national des recherches mtorologiques ( cnrm ) and laboratoire dareologie ( la ) de luniversit paul sabatier ( toulouse ) .the meso - nh model can simulate the temporal evolution of three - dimensional meteorological parameters over a selected finite area of the globe .the system of hydrodynamic equations is based upon an anelastic formulation allowing for an effective filtering of acoustic waves .it uses the gal - chen and sommerville coordinates system on the vertical and the c - grid in the formulation of arakawa and messinger for the spatial digitalization .it employs an explicit three - time - level leap - frog temporal scheme with a time filter .it employs a one - dimensional 1.5 turbulence closure scheme . for this studywe use a 1d mixing length proposed by bougeault and lacarrre .the surface exchanges are computed using isba ( interaction soil biosphere atmosphere ) module .  the optical turbulence and derived parameters are not an intrinsic part of the meso - nh model but it has been developed by our team in an independent package .the package ( called astro - meso - nh ) , includes the algorithms for the 2 parameterization and all the other integrated astro - climatic parameters ( seeing , isoplanatic angle , wavefront coherence time , scintillation rate , spatial coherence outer scale , .. ) .the first version of the code has been presented in . since thenthe code have been improved along the years in terms of flexibility providing a set of further outputs and permitting us to carry out different scientific studies mainly addressing the reliability of this technique .both the meso - nh code as well as the astro - meso - nh code for the optical turbulence are parallelized with open - mpi-1.4.3 .the model can therefore be run on local workstations as well as on the high performance computing facilities ( hpcf ) cluster of the ecmwf , in parallel mode so as to gain in computing time .

Abstract: we present the overview of the mose project ( modeling eso sites ) aiming at proving the feasibility of the forecast of the classical atmospherical parameters ( wind speed intensity and direction , temperature , relative humidity ) and the optical turbulence ot ( profiles and the most relevant integrated astro - climatic parameters derived from the : the seeing , the isoplanatic angle , the wavefront coherence time ) above the two eso ground - based sites of cerro paranal and cerro armazones . the final outcome of the study is to investigate the opportunity to implement an automatic system for the forecast of these parameters at these sites . in this paper we present results related to the meso - nh model ability in reconstructing the vertical stratification of the atmospherical parameters along the 20 km above the ground . the very satisfactory performances shown by the model in reconstructing most of these parameters ( and in particular the wind speed ) put this tool of investigation as the most suitable to be used in astronomical observatories to support ao facilities and to calculate the temporal evolution of the wind speed and the wavefront coherence time at whatever temporal sampling . the further great advantage of this solution is that such estimates can be available in advance ( order of some hours ) with respect to the time of interest .   [ firstpage ]  turbulence - atmospheric effects - methods : numerical - method : data analysis - balloons - site testing


the inflationary models describe the dynamics of the first instants of the universe .each model introduces a characteristic signature of non - gaussianity into the anisotropy distribution of the cosmic microwave background ( cmb ) radiation .the level of non - gaussianity is described by the so - called _bardeen s potential _( ( * ? ? ?* bardeen ( 1980 ) ) ) : + g_{nl}[\phi_l^3(\textbf{x})]\ ] ] where is the gravitational potential field of the universe and is its gaussian part .the constants and , which parametrize the non - gaussian part , can be measured from the amplitude of the bispectrum and trispectrum of the field , i.e. the harmonic counterpart of the 3-point and 4-point correlation function of the field , respectively .  although there exist several optimal bispectrum estimators that allow to evaluate with high confidence ( see for instance ( * ? ? ?* komatsu ( 2005 ) ) or ( * ? ? ?* planck coll .( 2013 ) ) ) , the lack of an optimal trispectrum estimator has prevented the evaluation of strong constraints on so far .spherical needlets ( ( * ? ? ?* narcowich ( 2006 ) ) , ( * ? ? ?* baldi ( 2009 ) ) ) are a wavelet system on the sphere defined by setting : where , are a set of cubature points and weights on the sphere , is a constant related to the width of the needlet and is a weight function satisfying the three following conditions : a ) compact support , if , 0 otherwise ; b ) partition of unity , for all , ; c ) smoothness , , i.e. , is times continuously differentiable , for some or .the spherical needlet coefficients are provided by the analytical formula :   as a consequence of the partition of unity property , the following well - known reconstruction formula holds :    as argued earlier in ( * ? ? ?* baldi ( 2009 ) ) , spherical needlets enjoy an excellent localization property in real domain ( fig .[ fig : needlet_shape ] ) : more explicitly , spherical needlets are then quasi - exponentially localized around any cubature point .moreover , as extensively argued in the literature , the needlet coefficients evaluated on isotropic random fields are asymptotically uncorrelated , under mild regularity conditions .it is then possible to derive analytically their statistical properties , and to understand the role and expressions for correction terms under realistic experimental conditions ( noise and masks , see donzelli et al . for the bispectrum case ) +the sample trispectrum estimator is usually written using the spherical harmonics coefficients as : where is the gaunt integral defined for instance in ( * ? ? ?* marinucci peccati ( 2011 ) ) .this estimator is clearly unfeasible under realistic experimental conditions , due to the presence of missing data and anisotropic noise . as a consequence of the previous discussion , it is possible to exploit the needlet coefficients to derive an alternative , computationally feasible and statistically sound estimators of the trispectrum .more precisely , exploiting wick theorem on higher order moments of gaussian variables we propose the following needlet trispectrum : \\   \end{split}\ ] ]  heuristically , the needlet trispectrum is constructed combining quadruples of coefficients , evaluated at the scales of interest , and subtracting linear and quadratic components in order to cancel bias and minimize the variance .further details , and a software which exploits the needlet trispectrum to evaluate on cmb maps , will be provided in the forthcoming paper ( * ? ? ? * troja  ( 2014 ) ) .

Abstract: we propose a computationally feasible estimator for the needlet trispectrum , which develops earlier work on the bispectrum by ( * ? ? ? * donzelli ( 2012 ) ) . our proposal seems to enjoy a number of useful properties , in particular a ) the construction exploits the localization properties of the needlet system , and hence it automatically handles masked regions ; b ) the procedure incorporates a quadratic correction term to correct for the presence of instrumental noise and sky - cuts ; c ) it is possible to provide analytic results on its statistical properties , which can serve as a guidance for simulations . the needlet trispectrum we present here provides the natural building blocks for the efficient estimation of nonlinearity parameters on cmb data , and in particular for the third order constants and .


a major goal of proteomics is to determine structures of proteins rapidly .it is impractical to obtain very high resolution structures on a genome wide scale .furthermore , for processing biological functions it is important to characterize the dynamics and thermodynamics of a network of proteins . from a computational perspective, it is currently impossible to realize these goals using all - atom molecular dynamics simulations . thus , there is an urgent need to develop coarse - grained , yet reliable , models for protein structures .construction of such models requires the determination of interaction potentials between amino acid residues .the wealth of structural data on a number of proteins in the protein data bank ( pdb ) has been a source for obtaining interaction potentials .the idea of using the frequencies of amino acid pairing to determine potential interaction parameters was first proposed by tanaka and scheraga . with the exception of a few studies ,most of the `` knowledge - based '' potentials have been obtained solely in terms of residue - residue contacts .sippl and others have introduced an explicit distance dependence in the database - derived mean force potentials using the boltzmann formula .this method , known as the `` boltzmann device '' , assumes that the known protein structures from the pdb correspond to classical equilibrium states .the side chain - side chain ( sc - sc ) potentials can be related to distance - dependent probability densities by the relation \label{eq : boltzmann}\ ] ] where is the probability density for a side chain of type to be separated by a distance from a side chain of type , and the choice of the reference probability density is very important .sippl suggests that can be the distance between two atoms or some other structural parameter such as dihedral angles .other statistical potentials developed subsequently using this approach have interpreted as the distance - dependent probability density .  in recent years, a number of studies have evaluated the goodness of statistical potentials based on pairwise additive interactions between residues .these studies have concluded that pairwise additive potentials , dependent only on the radial distance between residues , are inadequate for structure prediction .one of the major drawbacks of using contact potentials or potentials that only depend on the radial distance is that the relative orientation between the amino acids , which plays a role in the packing of the protein interior , is not taken into account . to account for the dense interior of the folded states of proteins it is crucial to optimize the relative orientation of the participating side chains .it is the purpose of this paper to examine the relevance of interaction potentials between amino acids that include the orientational dependence .  by analyzing the angular distribution of side chains around amino acids , bahar andjernigan showed that some residue pairs have specific coordination states with much higher probabilities than those expected from random distributions .another indication that the relative residue - residue orientations are important is the recent success of the united - residue force field ( unres ) developed by scheraga and coworkers .the sc - sc interactions of the unres potentials are parameterized as van der waals potentials with a pair - specific angular dependence included in the well depth .the unres potentials employ a generalized gay - berne potential that assumes that the interacting sites are ellipsoids of revolution placed at the center of mass of the side chains .although the relative side chain orientations are described in a simplified manner , the success of the unres potentials demonstrates the importance of including orientational dependence in the side chain interaction potential .this idea is also supported by recent studies of protein side chain packing which found that current potentials can accommodate more than one rotamer for 95% of side chain positions .these studies suggest that interaction potentials that can discriminate between a large number of competing rotamer states are required .the main goals of this paper are ( a ) to extract statistical information about the relative residue - residue orientations and distances in proteins using the available high resolution pdb structures and ( b ) to investigate the utility of the orientational information in enhancing the ability of distance dependent potentials to identify native protein folds .these goals can contribute to a better understanding of the specific residue packing of native protein structures .motivated by the above mentioned results of jernigan et al . and scheraga et al . , we approached the first goal by defining local reference frames ( lrfs ) that permit a more precise , quantitative description of the relative orientation of a given pair of side chains .the new lrfs are related more closely to the three - dimensional configuration of the individual side chains , rather than to their relative position with respect to the backbone or to the neighboring residues .we could extract thus novel radial and angular dependent inter - residue statistical potentials that reflect the specific distributions of distances and relative sc - sc orientations as observed in native structures of real proteins . in order to address our second goal we tested the efficacy of the new potentials by using a large database of incorrect models of real proteins , known as decoys .these decoys are computer - generated models of protein structures , specifically designed for being used in evaluating the capacity of various potential functions to distinguish the native - like conformations from non - native ones .  before presenting our methods and the results that we obtained ,a few clarifications are necessary .first , a complete set of potentials for coarse - grained protein folding simulations should take into account interactions between side chains , interactions between side chains and peptide groups , and energetics dependent on torsional angles that define the backbone structure .we only investigate the specific features of sc - sc interactions , as has been done before in studies of statistical potentials that are only contact or distance dependent .secondly , we constructed our own corresponding set of distance - dependent potentials rather than employing potentials constructed by other authors . in this manner we minimized the possibility that a better parameter fitting , specific computational implementation , or other technical aspects could affect our results .finally , as in similar studies we do not directly address the issue of the dependence of the results on the training database size or sampling problems .instead , we used a standard , reproducible approach , by employing the set of non - homologous proteins that was used by scheraga et al . for similar purposes .the relative residue - residue orientations are thought to be directly related to the nature of the forces that shape the specific three - dimensional structures of proteins .however , a quantitative approach to the statistical extraction of these orientational information from high resolution structures is still needed .the necessity of including orientation dependent interactions is established in section [ sec : oops ] by computing correlation functions that probe orientational order in the pdb structures .it is shown that , for a given native state topology , the orientational packing of side chains may be decomposed into a linear combination of simple cluster geometries . however , the use of simple orientational order parameters is _ not sufficient _ for discriminating between basic protein architectures such as -helix or -sheet . as such, we are motivated to use more detailed quantitative descriptions of relative residue orientations . in order to achieve this goal , in section[ sec : lrfs ] we introduce definitions of amino acid dependent local reference frames ( lrfs ) that permit a standard description of the relative sc - sc orientations .a method for extracting the radial and angular dependent pair distribution functions is presented in section [ sec : pot ] , emphasizing the limits imposed on the statistical analysis by the accuracy of the available experimental database of protein structures .the specificity of sc - sc contacts suggests that the relative residue orientations should play a significant role in determining packing in proteins .this idea , supported by the study of bahar and jernigan , builds up on the more general theme of how side chains pack in the native states of proteins .the observation that the interior of protein structures is densely packed raises the question if one can use a simple crystal lattice description ( e.g. , , etc . ) for the side chain packing .while there are many qualitative descriptions of residue packing , they are mainly based on the notion that hydrophobic interactions are responsible for globular shapes and that specific polar interactions and hydrogen bonding are important stabilizing factors .because these studies do not address quantitatively the issue of relative side chain orientations , we used orientational order parameters ( oops ) to asses their importance .the orientational order parameters ( oops ) were introduced to analyze the internal structure of liquids and glasses and have been used as reaction coordinates for studying the structure of a nucleating system .the oops are defined in terms of `` bonds '' that connect a central particle to its neighbors . for each `` bond '', one can compute the corresponding values of the spherical harmonic functions that can be used as _ local order _parameters where is the position vector of the central particle and and are the polar and azimuthal angles of vector with respect to any reference frame ( see , e.g. ) . to make the values representative for describing the orientational order of an entire system of particles , the _ global _ orientational parameters are defined as where is the total number of bonds in the system .  both and on the choice of local reference frame in which the values are calculated .second- and third - order rotationally invariant combinations can be constructed using and where the term is the wigner-3j symbol . in liquids ,the ratio is not sensitive to the exact definition of neighboring bonds of a particle .the orientational order parameters and , together with the reduced order parameter have specific values for a number of simple cluster geometries such as face - centered - cubic ( fcc ) , hexagonal close - packed ( hcp ) , body - centered - cubic ( bcc ) , simple cubic ( sc ) and icosahedral ( icos ) .if only the spherical term ( ) dominates , then it is clear that orientational potentials are not expected to be important .the emergence of non - zero values of and not only signify that side chain orientations are important in dense packing but may also point to the nature of orientational ordering .all the low - order values ( ) of the parameters , and are sensitive to the structural details that are specific to the simple cluster geometries mentioned above . however , for practical reasons , monitoring the values of , , and suffices to discriminate between the different cluster geometries .the values of these four oops ( fig . [ fig : qlms]a ) serve as a reference to which the values computed using pdb structures can be compared .   * ( a ) * the values of the , , and orientational order parameters for simple cluster geometries .their specific differences permit a quantitative analysis of the internal order in atomic and molecular systems . *( b ) * the values of the , , and orientational order parameters estimated for three different sets of proteins with -helical and -strand architectures ( columns ) .the three rows correspond to averages calculated for all the types of side chains ( top ) , for the five most hydrophobic side chains only ( middle ) , and for the five most hydrophilic residues ( bottom ) .the values of and were multiplied by 10 . ]  due to scale differences between and , the values of and were multiplied by 10 .we calculated the , , and parameters ( shown in fig .[ fig : qlms]b ) for three sets of 50 proteins from the same family with -helical and -strand architectures listed in table [ tab : table1 ] . for each set , we have specifically selected homologue structures to maximize the possibility of finding oops that have different , characteristic values for different protein architectures ..[tab : table1 ] the three sets of protein structures used to investigate if a simple packing description is appropriate for protein residues .highly homologue sequences corresponding to alpha and beta architectures were specifically selected . [ cols="^,^,^,^,^,^ " , ]   the type of protein architecture and the number of residues are also factors that could influence the relative performance of the and potentials . a useful quantitative parameter that is directly related to the type of protein architecture is the contact order ( co ) of a protein structure .the co definition employed here is where is the total number of contacts and is the sequence separation , in residues , between contacting residues and .two residues are considered to be in contact when and any of the heavy atoms of residue is within 3.75  of any of the heavy atoms of residue  .when the co is small the protein structure presents mostly local contacts ( i.e. ) , and when co is larger , the contacts are nonlocal . as shown in fig .[ fig : zer - fit]a we observed an inverse proportionality between the co values calculated for all the native states of the decoys analyzed in this paper and the fraction of local contacts for various protein architectures . based on this observation, we investigated the relative performance of the and potentials as a function of co values ( fig .[ fig : zer - fit]b ) and sequence length ( fig .[ fig : zer - fit]c ) . in figs .[ fig : zer - fit]b and [ fig : zer - fit]c is shown the dependence of the difference for the energy z - scores on contact order values ( co ) and sequence length of the native state ( n ) .negative values correspond to better performing scores for the distance- and orientation - dependent potentials ( ) .the lines represent linear fits .while the trends are not very strong , it is observed that , for the energy z - scores the novel statistical potentials perform better then the potentials for longer proteins , presenting large contact orders , such as the -sheet structures from the `` ig_structal '' and `` ig_structal_hires '' sets .it is observed that the inclusion of the information on relative sc - sc orientations makes the current version of the statistical potentials more useful than for relatively large , globular proteins ( residues ) , with a significant content of -sheet structure and nonlocal contacts . at the same time, it is also observed that even for relatively short ( residues ) and -helical proteins ( low co values ) , both the and -scores can be improved when using potentials but for a smaller number of cases .these results suggest that details about side chain - backbone interactions should be included in statistical potentials for short or -helical proteins with a high content of local contacts .our results demonstrate that it is possible to improve the performance of energy based scoring functions by using statistical information extracted from the relative residue - residue orientations. calculations of orientational order parameters for investigating the residue packing in proteins showed that architecture dependent packing is best described by a linear combination of simple cluster geometries ( fcc , icos , hcp and bcc ) .this result reinforces the need for extracting orientation dependent potentials using pdb structures .we have defined a novel local reference system for each residue for quantitatively describing the relative three - dimensional orientations in a manner that is independent of the neighboring amino acids .arguments based on experimental resolution of protein structures were used to derive the optimal bin size employed for collecting statistical data with both angular and distance dependence .the orientational information has both common and complementary significance as compared to the information that can be extracted from the relative residue - residue distances alone .the tests that we performed on a standard data base of artificially generated decoy structures suggest that this complementarity can be very important for a large class of protein structures .the novel distance and orientation dependent statistical potentials were shown to present an enhanced ability to recognize native - like protein folds , especially for larger structures with high contact orders ( e.g. immunoglobulins ) .they should find use in constructing the next generation of coarse grained off - lattice protein simulations .these new potentials could also be instrumental in developing more efficient computational methods for structure prediction on much larger scales than it is currently possible , addressing one of the major goals of proteomics . to achieve thisit will be important to also include the relative orientations between side chains and the protein backbone .we thank ruxandra i. dima , alan van giessen and tom keyes for useful discussions . this work was supported by the national institutes of health r01 ns41356 - 01 ( jes and dt ) , the national science foundation che-9975494 ( jes ) , and che-0209340 ( dt ) .the authors are grateful to the center for scientific computing and visualization at boston university for computational resources .the data visualization was carried out using vmd and matlab ( the mathworks , inc . ,natick , ma ) .previous studies suggest that only protein structures that are determined with a resolution of 2 or better should be used in the computation of  from protein databases .a resolution of 2 for protein structures that are determined by x - ray crystallography corresponds to an accuracy of + /-0.2 in atomic positions .the 2  resolution is often good enough to accurately assign hydrogen bonds and to allow for a limited interpretation of solvent structure .the high resolution structural data are binned for the construction of either radial or orientation dependent pair distributions and .it is important , therefore , to identify the minimal radial and angular bin sizes that ensure a certain high level of confidence that the information has been analyzed correctly and that no important artifacts due to the limitations of the experimental methods have been overlooked . in building a statistical distribution , the data that is collected from protein structures consists of inter - atomic distances . we expect that such data has an accuracy of .  for the radial dependence of the data ,let the bin size be . in the process of assigning a certain pair distance to a certain bin, if that value is exactly at the bin boundary , we have a probability of correct assignment . on the other hand ,if the value is exactly in the middle of the bin , this probability is maximum ( if than ) .we estimate that the probability of correct radial assignment depends on the bin size and the accuracy as this estimate is based on the assumption that the probability of correct assignment to a certain bin of a certain pair distance value is directly proportional to the difference between that value and the nearest bin boundary , or that . using the above assumed conditions for the values of at the bin middle and on the boundary , we find that therefore , for the average probability of correct assignment we find that from this result we can infer that for , if we choose a radial bin size , the confidence of correct bin assignment is about 65.6% . in this workwe employ a radial bin width of .this bin width is at least twice larger than the values employed by other authors .however , it ensures that we have a confidence level of at least 83.3% that the radial bin assignment is correct ., is used instead of the linear dependence assumed above , with the same constraints ( and ) for the same value , the confidence level for a bin size  is estimated to be 87.3% , and only 71.5% for . ]similar considerations are used for studying the angular orientation pair distributions . consider the polar coordinate system and the division of the and values .we assume that we have bins in and bins in .the solid angle corresponding to one angular bin is .this solid angle is proportional to the ratio between the area element that insures a certain high value for the confidence level of correct assignment , and the square of the corresponding minimum pair distance ( radius ) at which we expect that confidence level .let us require a confidence level of 80% at a distance of 5 . at larger distancesthe confidence level will be higher , but it will decrease at closer ranges . since , and ,  and , we have . this reasoning leads us to employ the nearest even value of for the number of bins that divide the angular interval for .previous studies used a smaller value ( ) .  the use of a larger radial bin size ( 1.2 vs. 0.5 ) than previously suggested , is needed to ensure a high confidence level ( at least 83.3% ) of correct radial bin assignment . here, we employ twenty radial distance bins with  for distances starting at .when we collect statistical data on the relative 3-dimensional orientation of pairs of residues , we obtain a similarly high confidence level by using for and for .all the calculations presented in this section are based on the assumption that all protein structures analyzed have a resolution of 2 or better .if proteins of different structural resolution are analyzed , the optimal bin size can be estimated accordingly .these arguments assure that optimal radial and angular bin sizes ( i.e. values that are small enough to provide a good resolution , yet large enough to correspond to a high statistical confidence level ) are employed .

Abstract: we present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard boltzmann device . the importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with -helical and -sheet architecture . extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues . using the local reference frames and histograms of the radial and angular correlation functions for a standard set of non - homologue protein structures , we construct the anisotropic pair potentials . the performance of the orientation dependent potentials was studied using a large database of decoy proteins . the results demonstrate that the new distance and orientation dependent residue - residue potentials present a significantly improved ability to recognize native folds from a set of native and decoy protein structures .


* side - channel attacks * ( sca ) have been put forward mainly by paul kocher _et al . _ in 1996 in .this first description of a sca explained how the mere observation of the duration of computations could allow an attacker to retrieve the secret key .the attack was then improved and extended to other cryptosystems  .  in 1999kocher _ et al ._ described what they called `` '' .this new attack used the power consumption instead to the duration but yielded the same result : the retrieval of the secret key .the process of this latter attack is relatively simple : a large number of cryptographic operations are monitored and the cipher text stored together with the electric consumption. then guesses were made of some parts of the secret key , which were confirmed or or not by a statistical processing the data .other attacks against various cryptosystems were based on this method .countermeasures soon appeared to protect systems based on a strong algebraic structure . at heprotection of opposite symmetric cryptosystems often consisted in introducing some randomization either in the computing process or power consumption to prevent the statistical processing of the acquired data .however `` counter - countermeasures '' also appeared .some other protection schemes were designed .an interesting and apparently efficient countermeasure is the wddl  which duplicates each signal in the circuit so that whatever the value is , one of the lines will toggle .this countermeasure was enhanced by an improved routing of related signals , which reduces the differences between the power consumptions of a 1 and a 0.  * asynchronous circuits * , the history of which dates back to 1950 , are nowadays increasingly considered as a viable alternative to classical synchronous designs .indeed they feature some very useful properties such as flexibility , robustness , high speed and low power .this article brings another good reason to consider asynchronous designs : a greater resistance against _ side - channel attacks_.  some industrial applications of asynchronous asic and fpga begin to appear both in the academic world  and in the industry  .  at the same timesynchronous circuits are suffering from problems arising from the distribution of the clock signal through the ic and the excessive power consumption ( and thus dissipation ! ) .as an asynchronous circuit has no centralized clock , the problems associated with the clock distribution , clock skew and power consumption do not exist .in addition this circuits offers advantages like :  * average - time performance , * lower electromagnetic radiation , * better robustness towards variations of the power voltage , * better robustness towards fabrication process variations  , * better composability and modularity because of the simple handshake interfaces and the local timing  and * better scrambling of the _ side - channel _ information  .asynchronous circuits thus seem to be a viable alternative which would remove these limiting factors  .due to these advantages , there has been a resurgence of interest in asynchronous design , especially in the reprogrammable field .there have been several recent successful design projects such as aspro-216  , aes crypto - processor  , many of philips designs targeting low power  , projects focused on designing an asynchronous fpga from a synchronous one , like montage  and pga - stc  or targeting asynchronous application - specific fpgas , locally synchronous , like galsa  and stacc  or completely asynchronous like papa  , and other recent works  .pga - stc was developed to implement two - phase bundled - data systems such as micro pipelines , galsa for massively parallel computing architecture , stacc for reconfigurable computation and papa was mainly created and optimized for pipe - lined processes .* this article * describe the design of the plb of a new asynchronous fpga with security as the main requirement , even at the expense of performance . indeed in the particular case of cryptography performance is second to security even if it can not be ignored .the fpga must be able to implement various styles of asynchronous protocols and different representations of data so as to enable comparisons between these representations and protocols as for their ability to thwart the side - channel attacks .section [ asynchronous - representation ] describes the representation of data and the different asynchronous protocols used in the fpga .we also discuss their suitablity for trusted computing .section [ 4-phase - protocol ] shows the construction of the plb to implement the 4-phase protocol using both binary and ternary representations of data .section [ 2-phase - protocol ] shows the necessary additions to the plb to accommodate the 2-phase protocols .section [ programming - the - fpga ] shows how the fpga is programmed .finally section [ conclusion ] concludes the article .as opposed to synchronous data , whose validity is guaranteed by the timing of some global `` clock '' signal , the asynchronous computations are synchronized by the availability of data and , when necessary , by a request / acknowledge handshake signalling .  a formal description of delay insensitive representation of data can be found in  . in the * * q**uasi-**d**elay * * i**nsensitive ( qdi ) protocols the request is carried by the data itself .this allows to obtain a reliable design , independent of the routing .the data are transmitted together with the availability information and thus a logic signal or , shorter a `` * * signal * * '' , must be represented by more than a single electrical signal or , shorter , a `` * * wire * * '' representation on a single wire per signal would be acceptable in some cases but we shall restrict ourselves in the following pages to standard cmos levels :  . ] . in this article ,a wire is able to take one of two values , which we denote * 0 * and * 1 * regardless of their actual electric implementation .  in order to avoid glitches, a sufficient condition is that _ given a signal represented by wires , the transmission of a new value of must consist in * exactly one * of the wires changing its electrical state_. this means that the number of wires is greater than or equal to the number of the states of . as silicon and routing is a precious resource , the number of wires representing a given signal will thus be equal to the number of possible values of this signal .the most frequently used kind of signal is the binary signal , which carries a \{*`1'*,*`0 ' * } information .such a signal is encoded with 2 wires .this representation is called `` * * dual - rail * * '' or `` 2 ''. however ternary signals , which carry a \{*`0'*,*`1'*,*`2 ' * } information , can also be thought of .such a signal is represented by 3 wires and one speaks of `` 3 '' representation .this representation is more compact than the _ 1-out - of-2 _ as for arithmetic : 6 wires in 2 represent 3 2 signals which can take 8 valid values , compared to two _ 1-out - of-3 _ signals , which can take 9 valid values .however due to the greater complexity of gates in 3 representation , the binary signals are most of the time preferred .an asynchronous design may need additional signals , which are specialized to synchronisation .these signal carry no _ data _ information and can thus be coded on a single wire .they will be referred to as _ acknowledge_signals .the inputs of the gates which receive such a signal will be denoted those driving these signals will be called .there are two main families of qdi asynchronous communication protocols , which differ by the nature of the signalling information : the protocols and the protocols .   under a protocol ,valid values of a signal are separated by a special value , denoted .the transmission of a value from an emitter to a receiver proceeds as follows :  [ cols=">,<,^,<",options="header " , ]   [ [ synchronization ] ] synchronization + + + + + + + + + + + + + + +  the synchronization is performed by a device called `` -decision - wait '' ( or , shorter : ) .[ 2phe-1x2 ] depicts the schematic of the .the works as follows :  1 .  in the initial state ,the following relations hold : , and , which imply and .( because , idem for ) ; 2 .assume toggles and thus becomes equal to , the c - elementtransmits the common value of its inputs to , 3 .as toggles , toggles too and becomes equal to .4 .  until , we have and : even if one of the inputs toggles , the c - elements will remain stable ; 5 .  when , and toggle and the system is back in the initial state .if one wants to combine the computation stage with the , it can not be done in 2 lut .it is not because of the complexity of the functions : each of and is a function of 2 feed - backs , 1 at most 3 , at least if one does not want to implement trivial , constant functions .however , the set of 2 luttogether would need 2 feed - backs , 1 4 , which is one more than the number of available wires .thus we must use a full plb .if we use the full plb , the memory element will provide the necessary c - elementand the lutbecome purely combinatorial .the inputs will be assigned following eq .[ edge-2x1-in - eq ] and depicted on fig .[ 2008-edge - all-2x1dw ] :   then the lutare programmed as by eq .[ edge-2x1-lut - eq ]    the protocolis difficult to implement in a fpga without special hardware added to the plb : it takes two plb to implement a single 2-input gate .however this protocol has advantages as for security because the instantaneous value of the wires is not significant in itself .for instance * ` 1'*is represented alternatively by the rising and the falling edge of a given wire . an attacker trying dpa , for instance , would have to exhibit the difference between the average consumption of both edges on wire 1 and the same average on wire 0.the fpga can be partially programmed : it is divided in square blocks which can be programmed separately from the other .the programming chain is a set of asynchronous fifo memories .an elementary stage of these fifo is depicted by fig .[ 2008-jmm - fifo - pg ] .  at reset time ,all c - elements are set to zero by a general reset wire .then the programming bits are fed to the fifo , separated by .the last stage of each fifo is particular : the _ acknowledge_signal is controlled by an external pin . during the programming of the block ,acknowledge_signal is held low . this way the programming bits are stacked in the fifo andthe fpga becomes functional .if a partial reconfiguration is wanted , the chosen blocks are cleared by allowing the _ acknowledge_signal of their last stage to acknowledge the value in the last stage .then the fifo is activated again until all bits have gone thought it . at this point ,acknowledge_signal is blocked again and the fifo is ready to receive a new set of configuration bits .  during the configuration of the fpga ,all outputs of plb are kept at 0 to avoid short - circuits .the plb are programmed first , while all switchboxes are left in an insulation mode .then the switchboxes are programmed to connect the newly reconfigured part to be connected to the still working part .it is the designer s responsibility to ensure that the new part can create no conflict with the existing part .we have presented the programmable logic block of an asynchronous fpga , which is oriented towards security rather than performance . in particularwe have chosen not to implement one of the advantages of an asynchronous design , which usually allows to compute in average time : the early evaluation .this choice is deliberate as early evaluation is a security risk  .the fpga can accommodate various sizes of data as well as various styles of asynchronous control , thus making it possible for the end user to design mixed styles of logic , depending on the applicative requirements .incidentally , this fpga is also a valuable prototype that allows to perform comparisons between styles of asynchronous protocols .a silicon is being manufactured and will be used for intensive testing .the different resistances of the various protocols against sca will be evaluated .in particular the strict link under the protocolbetween the value of a signal and the one of the wire will decide whether this protocol is suitable at all for a secure implementation .

Abstract: _ side - channel attacks _ are efficient attacks against cryptographic devices . they use only quantities observable from outside , such as the duration and the power consumption .   attacks against synchronous devices using electric observations are facilitated by the fact that all transitions occur simultaneously with some global clock signal .   asynchronous control remove this synchronization and therefore makes it more difficult for the attacker to insulate _ interesting intervals_. in addition the coding of data in an asynchronous circuit is inherently more difficult to attack .   this article describes the programmable logic block of an asynchronous fpga resistant against _ side - channel attacks_. additionally it can implement different styles of asynchronous control and of data representation .


the notion of entanglement , first noted by einstein , podolsky and rosen , is considered one of the main features of quantum mechanics , being subject of study in several areas recently .thus , it is of paramount importance both the understanding and the quantification of entanglement in composite quantum systems , being these one of the main challenges of modern quantum theory .  despite being a subjectwidely studied in systems of non - identical particles , or whose particles , though identical , are well separated from each other , being thus distinguishable , less attention was given to the case where this separation is very small , such that the overlap of their wave functions is no longer negligible . in this casewe have to take into account the indistinguishability of the particles , being the space of quantum states restricted to symmetric or antisymmetric subspaces of the hilbert space , depending on the bosonic or fermionic nature of the system .the study of entanglement for systems of indistinguishable particles has been , however , a subject of great controversy , leading to different approaches in its treatment . amongthe most mentioned we have : quantum correlations , entanglement of modes , entanglement of particles .the concept of quantum correlations is based on the notion that the correlations generated by mere ( anti-)symmetrization of the state due to indistinguishability of their particles do not constitute truly as entanglement .we will analyse , in this paper , the quantum correlations in systems of indistinguishable fermions .the entanglement in two - fermion sates with a four - dimensional single - particle space ( ) can be characterized by the schliemann concurrence . for pure states in arbitrary dimension, one can use the von neumann entropy of the reduced single - particle density matrix as a measure of entanglement .however , the problem of quantification or even detection of entanglement in the general case is still open .a useful concept is that of entanglement witness : a hermitian operator with non - negative expectation value for all separable states , but which can have a negative expectation value for an entangled state .we will focus on optimal entanglement witnesses ( oew ) , that can be used not only to _ witness _ the entanglement , but also to quantify it . in this paper, we will see how to determine such oews , and especially how to use them to quantify the quantum correlations in fermionic systems .we will also confront our measure of entanglement with the _ quantum discord _ . in order to do that, we will define a quantum discord for fermionic particles .previous studies of quantum discord in systems of indistinguishable particles , like in , employ the notion of correlation of modes , which are distinguishable .this paper is organized as follows . in sec.[backgrounds ] we recall some known concepts and tools of the theory of entanglement , as the witnessed entanglement and the quantum correlations , which will be essential to the development of the ideas throughout the article . in sub - sec.[witnessed.entanglement ] , we recall the definition of optimal entanglement witness , and briefly discuss its use as an entanglement quantifier . in sub - sec.[quantum.correlations ]we recall the ideas associated with the concept of quantum correlations , as well as the schliemann concurrence . in sub - sec.[discord ] we revise the concept of quantum discord for distinguishable particles . in sec.[quantifying.quantum.correl ]we introduce our method for quantifying the quantum correlations in fermionic systems using witness operators , and define the fermionic generalized robustness .we also extend the notion of quantum discord to fermions , such that it takes into account the particles indistinguishability , and introduce the _ fermionic geometric discord_. in sec.[numerical.results ] we show numerical results , comparing the fermionic generalized robustness , the schliemann concurrence , and the fermionic geometric discord .we finish the illustration of the method with a beautiful _ quantum phase diagram _ yielded by the five - partite fermionic generalized robustness in the extended hubbard model .we conclude in sec.v .we will see , in this section , some familiar concepts from the theory of entanglement , namely , _ witnessed entanglement _ , quantum correlations and quantum discord .a reader already familiarized with such concepts might skip to the next section of the article .entanglement witnesses are hermitian operators ( observables - ) whose expectation values contain information about the entanglement of quantum states .the operator is an entanglement witness for a given entangled quantum state if the following conditions are satisfied : its expectation value is negative for the particular entangled quantum state ( ) , while it is non - negative on the set of separable states ( ) ( ) .we are particularly interested in optimal entanglement witnesses ._ _ is the oew for the state if where represents a compact subset of the set of entanglement witnesses .oews can be used to quantify entanglement .such quantification is related to the choice of the set , where different sets will determine different quantifiers .we can define these quantifiers by :   an example of a quantifier that can be calculated using oew is the generalized robustness of entanglement ( ) , which is defined as the minimum required mixture such that a separable state is obtained .precisely , it is the minimum value of such that be a separable state , where can be any state .we know that the generalized robustness can be calculated from eq.[oew ] , using , where is the identity operator ; in other words ,   the construction of entanglement witnesses is a hard problem . in an interesting method proposed by brando and vianna , the optimization of entanglement witnesses is cast as a _ robust semidefinite program _ ( rsdp ) . despite rsdpis computationally intractable , it is possible to perform a probabilistic relaxation turning it into a semidefinite program(sdp ) , which can be solved efficiently .the space state for indistinguishable fermions is antisymmetric under permutation of particles . in this case , it is convenient to use the _ second quantization _ formalism , in order to deal with the antisymmetric states in the _ fock space_. accordingly we introduce an algebra of operators which satisfy the following anti - commutation relations : where and are the fermionic creation and annihilation operators , respectively , so that their application on the vacuum state ( ) creates / annihilates a fermion in state `` i '' .the vacuum state is defined so that .an immediate and disturbing consequence of the antisymmetric structure of the state space can be seen even in the simplest example of a two - fermion system , which , if analysed in the usual way , will always be considered entangled .we must therefore rethink the way entanglement is calculated for systems of indistinguishable particles , as well as its physical interpretation .in the case which the identical particles are localized in _ distinct _ laboratories and _ independently _ prepared , it is natural to think that the entanglement calculated in the usual way should not have any relevant physical meaning ; or rather , `` no quantum prediction , referring to an atom located in our laboratory , is affected by the mere presence of similar atoms in remote parts of universe '' .we are interested in the case of identical particles that are sufficiently close together such that the overlap between their wave functions is no longer negligible , and therefore they are indistinguishable .fermionic systems of this kind can be described using slater determinants .consider , for example , a two - fermion state represented by a single slater determinant , namely , where and correspond to orthonormal wave functions ( _ spin - orbitals _ ) .it is easy to see , in this simple case , that the anti - symmetrization of coordinates introduces correlations between the fermions , namely , the well known _ exchange contributions _ from the hartree - fock theory . on the other hand ,a single slater determinant is solution of a one - particle schrdinger equation and , therefore , can have no quantum correlation between the particles . considering statesdescribed by more than one slater determinant introduces additional correlations beyond the exchange contribution. we will then interpret such additional correlations as the analog of quantum entanglement in systems of distinguishable particles , calling them as _ fermionic entanglement _ .a measure of fermionic entanglement was proposed in as the analogous of wootters concurrence .notwithstanding , such measure , called schliemann concurrence ( ) , is valid only for two - fermion states with a four - dimensional single - particle hilbert space ( ) , i.e. the antisymmetric space of lowest dimension where can exist quantum correlated states .  in order to define the schliemann concurrence , we have to introduce some operators .let be the operator of particle - hole transformation : being the single - particle hilbert space dimension .similarly , define as the anti - linear operator of complex - conjugation , satisfying the following relations : thus , given the operator , called operator of dualisation , and the dual states , we have that the schliemann concurrence for states is given by where are , in descending order of magnitude , the square roots of the singular values of the matrix .the total amount of correlations ( classical and quantum ) carried in a bipartite system is quantified by the mutual information : where is the shannon ( von neumann ) entropy for the classical ( quantum ) system . in the classical case , the mutual information has another interpretation : it measures the decrease of ignorance about the subsystem , when is known . in this case , an equivalent expression for the mutual information reads : where is the conditional entropy on given . in quantum systemsthis equivalence is not always true .the disagreement between these expressions is called _ quantum discord _ , and can be used to quantify quantum correlations : however , there is an ambiguity in due to the freedom of choice for the measurement operators , where for each set of measurements on b , the conditional entropy value may be different and consequently also the mutual information .the quantum discord is thus redefined by minimizing its value over all measurement operators .the mutual information is thus properly defined by : and it is known to quantify classical correlations .thus , the quantum discord measures the difference between the total and classical correlations on the system , therefore being a quantifier of quantum correlations .note however that quantum discord is not a measure of entanglement , and quantum separable states usually have non - zero discord .the quantum states with null discord are those which are a mere encoding of classical statistical distributions , and can be written in the form : where and are orthonormal basis .given the set ( ) of states with zero - discord , formed by the states above , it is clear that the minimal distance between a state and this set can be used to quantify the quantum discord : where is the schatten .a usual measure of quantum discord is based on the -norm , or hilbert - schmidt norm , proposed by daki _in this section we will present our method for quantifying fermionic entanglement using witness operators . after defining the set of separable states pertinent to our case ,i.e. the fermionic states without entanglement , we will introduce a method for determining oews .in particular , we will see which constraints to impose on the set of witnesses ( eq.[oew ] ) in order to obtain a quantifier analogous to the generalized robustness ( eq.[rob.generalized ] ) .we also will define a notion of quantum discord for fermions and confront it to entanglement .we know that states without entanglement are those that can be described by a single slater determinant , or a convex mixture of them .consider as the fock space of indistinguishable fermions sharing a -dimensional single - particle hilbert space .we have then the following definition of `` separable '' states : + _ * state with no fermionic entanglement ( separable ) : * _ a state has no fermionic entanglement if it can be decomposed as where , and is an orthonormal basis of fermionic creation operators for the space of a single fermion ( ) . of course, the states defined by eq.[separable.state.fock ] are not separable in the usual mathematical sense , meaning that they are product states or convex mixtures of it .but we will insist in referring to them as _ separable _ ,for they are just anti - symmetrization of the usual distinguishable separable states .entanglement , in the case of distinguishable particles , is defined in opposition to separability , i.e. , an entangled state is that one which is not separable .we want to keep this notion .it is interesting to note that , as in the case of distinguishable particles , the set of separable states is invariant under _ local operations _ , taking now into account that the local operations must be symmetric , due to the indistinguishability of the particles .let be a _ local symmetric operation _( lso ) , i.e. , an operation that respects the pauli exclusion principle and does not involve any interaction between particles . an lso can be written as : where is a linear operator acting on the hilbert space of a single particle .given a fermionic separable pure state ( i.e. a single slater determinant ) , where is the anti - symmetrization operator , is an orthonormal basis , and noting that = 0 $ ] , we see that and such result clearly extends to mixed states .summarizing , given a separable state , we have that , indicating that in order to have quantum entanglement , the particles must interact by means of some global operation .now we adapt brando and vianna s technique in order to obtain a new algorithm to determine oews for indistinguishable fermions in the fock space .the new method can be enunciated as follows ._ * determination of oew using rsdp : * _ a fermionic state is entangled if and only if the optimal value of the following rsdp is negative :  _ minimize subject to _  where is the dimension of the single particle hilbert space , is an orthonormal basis of fermionic creation operators , is the anti - symmetrization operator , and is an operator acting on the space of one fermion .the notation means that is a positive semidefinite operator .if is entangled , the operator that minimizes the problem corresponds to the oew of . + _ * proof : * _ it is known that a state is entangled if and only if there exists a witness operator such that and for every separable state . consider a general separable state as given by eq.[separable.state.fock ] .the semi - positivity condition is equivalent to : for all note however that to satisfy eq.[awa ] , it is sufficient that the operator be positive semidefinite . thus follows directly that the operator satisfying the problem in eq.[rsdp ] corresponds to an optimal entanglement witness .+ the rsdp given above is solved by means of probabilistic relaxations it terms of sdps , as done in , where the set of infinite constraints is exchanged by a finite sample .thus the witness operator obtained is such that satisfy most of the constraints in eq.[rsdp ] . the small probability ( ) that a constraint be violated ( i.e. ) diminishes as the size of the sample of constraints increases .the constraint restricts the operator to the space of antisymmetric entanglement witnesses ( ) .the other constraint , , follows directly from the anti - symmetrization of eq.[rob.generalized ] , and implies that the oew corresponds to the anti - symmetrized version of the generalized robustness , namely ,  measures the minimum required mixture with a fermionic state such that all the entanglement of is washed out . in other words ,the generalized robustness is the minimum value of such that be a separable state ( eq.[separable.state.fock ] ) , where can be any fermionic state .   versus schliemann concurrence , for random fermionic states uniformly distributed according to the haar measure .( top ) the two entanglement measures are equal for pure states .the small dispersion seen in the top panel is due to numerical imprecision in the calculation of in the region of very low entanglement .( bottom ) in the case of mixed states , the is an upper bound to .the continuous line in the bottom panel corresponds to the straight line , and is just a guide to the eye.,title="fig : " ]  versus schliemann concurrence , for random fermionic states uniformly distributed according to the haar measure .( top ) the two entanglement measures are equal for pure states .the small dispersion seen in the top panel is due to numerical imprecision in the calculation of in the region of very low entanglement .( bottom ) in the case of mixed states , the is an upper bound to .the continuous line in the bottom panel corresponds to the straight line , and is just a guide to the eye.,title="fig : " ]   for the families of two - fermion states defined in eq.[family.states ] , on the space . ]_ * fermionic geometric discord : * _ abiding by the notion that mere anti - symmetrization does not generate any kind of quantum correlation , we are led to the following definition of fermionic states without quantum discord : where is the anti - symmetrization operator , and are the states in eq.[discord.distinguishable ] , which encode classical probability distributions .although these states do not have any kind of quantum correlations , they can not be treated like classical probability distributions , since they respect quantum rules : like the pauli exclusion principle .  our proposed measure forthe quantum discord in fermionic states will be a geometric measure like eq.[geom.discord.distinguishable ] . given a fermionic state , the fermionic geometric discord is given by , where is the set of zero - discord anti - symmetric states ( eq.[fermionic.states.no.discord ] ) .in this section we will illustrate our method .we start by investigating _bipartite entanglement _ in the space , which has the smallest dimension allowing for quantum correlations in fermionic systems . in this case, we can compare the fermionic generalized robustness ( - eq.[rob.generalized.fermionic ] ) with the schliemann concurrence ( - eq.[schiemann.concurrence.fermions ] ) .then we investigate the bipartite entanglement in a one - parameter family of states in the space , with going from 2 to 4 .we also compare our fermionic geometric discord ( - eq.[geom.fermionic.disc ] ) with the fermionic generalized robustness for another one - parameter family of states in the space .we finish with calculations of _ multipartite entanglement _ in the extended hubbard model ( ehm ) , where can characterize _ quantum phase transitions_.  in fig.1 , we plot the fermionic generalized robustness against the schliemann concurrence for states generated randomly in the space .it is remarkable that and are one and the same for pure states , and is an upper bound for in the case of mixed states .recall that , in the case of two distinguishable qubits , the wootters concurrence and the generalized robustness also keep this same relation .now we consider the following one - parameter family of states , in the space : where ( ) is a pure state with just a single slater determinant ; is the maximally entangled pure state of singlet type , i.e. the one with spin quantum numbers ; and is the anti - symmetrizer , which corresponds to the identity operator in the antisymmetric space . controls the entanglement of the state , is chosen such that the state is normalized , and . in fig.2 ,the fermionic generalized robustness is plotted against , for spaces of different dimensions .we see that behaves correctly , showing that the mixed state has much entanglement when the contribution of the singlet is large , and it has low , or none , entanglement when the contribution of either or is large .  , and fermionic geometric discord for the families of two - fermion states defined in eq.[family.states ] ( top ) and eq.[family.state.two ] ( bottom ) , on the space .,title="fig : " ] , and fermionic geometric discord for the families of two - fermion states defined in eq.[family.states ] ( top ) and eq.[family.state.two ] ( bottom ) , on the space .,title="fig : " ]    consider another one - parameter family of states , in the space : in fig.3, we confront the fermionic generalized robustness and the fermionic geometric discord , for the two families of states ( eq.26 , eq.27 ) defined above . in the two cases , we see that the discord is always an upper bound for the entanglement , and states without entanglement can have a non - null discord , which is particularly dramatic in the second family . in the first family of states ,the functional forms for the discord and entanglement are very similar , whereas they are very different in the second family .note , in the second family , the abrupt vanishing of entanglement ( a discontinuous derivative for ) , while the discord shows an asymptotic behavior .  to conclude , we illustrate the calculation of multipartite entanglement of fermions interacting according to the extended hubbard model , defined by the hamiltonian : where and define the on - site and nearest - neighbor coulomb interactions , controls hopping between sites , is the number of sites , and is the particle number operator on site with spin .fig.4 shows the five - partite fermionic generalized robustness of the ground state as a function of and , for the case of five fermions and five sites .the ground state is obtained by numerical diagonalization of the hamiltonian .one can see that the fermionic generalized robustness characterizes three distinct regions , corresponding exactly to the three distinct phases provided by the known phase diagram of the model , namely charge - density wave ( up ) , spin - density wave ( right ) and phase separation ( bottom ) .it is interesting to note that five fermions in five sites , with periodic boundary conditions , is the smallest size of the system which presents such phase transitions .the occurrence of these phase transitions is dependent on long range interactions .surprisingly , the second - neighbor interactions present in our five fermions model is already _ long range _enough for the onset of phase transitions .we performed a calculation with four fermions in four sites , and the resulting figure is a uninteresting flat surface for the entanglement .in summary , we presented a method to quantify quantum correlations in systems of fermionic indistinguishable particles .the method is based on the use of optimal entanglement witnesses , which can be calculated with arbitrary precision by means of sdps . in particular, we obtained the generalized robustness for fermionic systems ( ) , and numerically showed its relation to the schliemann concurrence .we also introduced the fermionic geometric discord ( ) , and observed that it is an upper bound for the fermionic entanglement .however , the physical meaning of quantum discord for fermionic systems needs to be better understood .it is comforting to know that the quantum discord for a single slater determinant , or for the fermionic maximally mixed state , is null , but the nature of quantum correlations conveyed by a convex mixture of slater determinants is still obscure to us , and will be investigated in future works .finally , we used the five - partite fermionic generalized robustness to characterize quantum phase transitions in the extended hubbard model , showing the utility of entanglement as a quantum order parameter .s. kais , `` entanglement , electron correlation , and density matrices '' , in _ reduced - density - matrix mechanics : with application to many - electron atoms and molecules , a special volume of advances in chemical physics , vol .134 _ , edited by david a. mazziotti . series editor stuart a. rice .2007 john wiley & sons , inc .

Abstract: we present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators . the method associates the problem of finding the optimal entanglement witness of a state with a class of problems known as semidefinite programs ( sdps ) , which can be solved efficiently with arbitrary accuracy . based on these optimal witnesses , we introduce a measure of quantum correlations which has an interpretation analogous to the generalized robustness of entanglement . we also extend the notion of quantum discord to the case of indistinguishable fermions , and propose a geometric quantifier , which is compared to our entanglement measure . our numerical results show a remarkable equivalence between the proposed generalized robustness and the schliemann concurrence , which are equal for pure states . for mixed states , the schliemann concurrence presents itself as an upper bound for the generalized robustness . the quantum discord is also found to be an upper bound for the entanglement .