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Dark Energy Vacuum Fluctuations, the Effective Phantom Phase, and Holography ; We aim at the construction of dark energy models without exotic matter but with a phantomlike equation of state an effective phantom phase. The first model we consider is decaying vacuum cosmology where the fluctuations of the vacuum are taken into account. In this case, the phantom cosmology with an effective, observational omega being less than 1 emerges even for the case of a real dark energy with a physical equation of state parameter omega larger than 1. The second proposal is a generalized holographic model, which is produced by the presence of an infrared cutoff. It also leads to an effective phantom phase, which is not a transient one as in the first model. However, we show that quantum effects are able to prevent its evolution towards a Big Rip singularity.

Thesis Orientifolds, Anomalies and the Standard Model ; In this thesis, we study aspects of Dbrane realizations of the Standard Model. Specifically, we study orientifold models with rotation and translation elements that break supersymmetry, provide the general consistency conditions and derive the massless spectrum for these type of orientifolds. These models contain in general anomalous U1 gauge fields. The GreenSchwarz mechanism cancels the anomaly and provides a mass term for the anomalous gauge fields. We calculate the bare mass for supersymmetric and nonsupersymmetric vacua and we show that higher dimensional anomalies can affect the masses of the anomalous U1s. Phenomenological aspects are also discussed. We evaluate the contribution of the extra U1 fields to the anomalous moments and it is shown that this imposes constraints on the magnitude of the string scale.

More about spontaneous Lorentzviolation and infrared modification of gravity ; We consider a model with Lorentzviolating vector field condensates, in which dispersion laws of all perturbations, including tensor modes, undergo nontrivial modification in the infrared. The model is free of ghosts and tachyons at high 3momenta. At low 3momenta there are ghosts, and at even lower 3momenta there exist tachyons. Still, with appropriate choice of parameters, the model is phenomenologically acceptable. Beyond a certain large distance scale and even larger time scale, the gravity of a static source changes from that of General Relativity to that of van DamVeltmanZakharov limit of the FierzPauli theory. Yet the late time cosmological evolution is always determined by the standard Friedmann equation, modulo small correction to the cosmological Planck mass'', so the modification of gravity cannot by itself explain the accelerated expansion of the Universe. We argue that the latter property is generic in a wide class of models with condensates.

Rcharged AdS5 black holes and large N unitary matrix models ; Using the AdSCFT, we establish a correspondence between the intricate thermal phases of Rcharged AdS5 blackholes and the Rcharge sector of the N4 gauge theory, in the large N limit. Integrating out all fields in the gauge theory except the thermal Polyakov line, leads to an effective unitary matrix model. In the canonical ensemble, a logarithmic term is generated in the nonzero charge sector of the matrix model. This term is important to discuss various supergravity properties like i the nonexistence of thermal AdS as a solution, ii the existence of a point of cusp catastrophe in the phase diagram and iii the matching of saddle points and the critical exponents of supergravity and those of the effective matrix model.

An Effective Dual AbelianHiggs Model from SU2 YangMills theory via Connection Decomposition ; It has long argued that confinement in nonAbelian gauge theories, such as QCD, can be account for by analogy with typed II superconductivity. In this paper, we show that it is possible to arrive at an effective dual AbelianHiggs model, the dual and relativistic version of GinzburgLandau model for superconductor, from SU2 YangMills theory based on the FaddeevNiemi connection decomposition and the orderdisorder assumptions for the gauge field. The implication of these assumptions is discussed and role of the resulted scalar field is analyzed associated with the electricmagnetic duality and theory vacuum. It is shown that the mass generation of the gauge vector field can arise from quantum fluctuation of the coset basis variable partial mathbfn, and the mass of the electric field is approximately equal to that of the scalar particle. A generalized dual London equation with topologically quantized singular vortices is derived for the static electric field from the our dual model.

Presentations of WessZuminoWitten Fusion Rings ; The fusion rings of WessZuminoWitten models are reexamined. Attention is drawn to the difference between fusion rings over Z which are often of greater importance in applications and fusion algebras over C. Complete proofs are given characterising the fusion algebras over C of the SUr1 and Sp2r models in terms of the fusion potentials, and it is shown that the analagous potentials cannot describe the fusion algebras of the other models. This explains why no other representationtheoretic fusion potentials have been found. Instead, explicit generators are then constructed for general WZW fusion rings over Z. The JacobiTrudy identity and its Sp2r analogue are used to derive the known fusion potentials. This formalism is then extended to the WZW models over the spin groups of odd rank, and explicit presentations of the corresponding fusion rings are given. The analogues of the JacobiTrudy identity for the spinor representations for all ranks are derived for this purpose, and may be of independent interest.

Strings as MultiParticle States of Quantum SigmaModels ; We study the quantum Bethe ansatz equations in the O2n sigmamodel for hysical particles on a circle, with the interaction given by the Zamolodchikovs' Smatrix, in view of its application to quantization of the string on the S2n1 x Rt space. For a finite number of particles, the system looks like an inhomogeneous integrable O2n spin chain. Similarly to OSp2mn2m conformal sigmamodel considered by Mann and Polchinski, we reproduce in the limit of large density of particles the finite gap KazakovMarshakovMinahanZarembo solution for the classical string and its generalization to the S5 x Rt sector of the GreenSchwarzMetsaevTseytlin superstring. We also reproduce some quantum effects the BMN limit and the quantum homogeneous spin chain similar to the one describing the bosonic sector of the oneloop N4 super YangMills theory. We discuss the prospects of generalization of these Bethe equations to the full superstring sigmamodel.

Phantom energy from graded algebras ; We construct a model of phantom energy using the graded Lie algebra SU21. The negative kinetic energy of the phantom field emerges naturally from the graded Lie algebra, resulting in an equation of state with w1. The model also contains ordinary scalar fields and anticommuting Grassmann vector fields which can be taken as two component dark matter. A potential term is generated for both the phantom fields and the ordinary scalar fields via a postulated condensate of the Grassmann vector fields. Since the phantom energy and dark matter arise from the same Lagrangian the phantom energy and dark matter of this model are coupled via the Grassman vector fields. In the model presented here phantom energy and dark matter come from a gauge principle rather than being introduced in an ad hoc manner.

Quantum properties of a nonAbelian gauge invariant action with a mass parameter ; We continue the study of a local, gauge invariant YangMills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator Fmunu D21 Fmunu. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent BRST symmetry. Although our action contains extra anticommuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless YangMills theories. The full theory is renormalized explicitly at two loops in the MSbar scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.

Higher Spin Gravitational Couplings and the YangMills Detour Complex ; Gravitational interactions of higher spin fields are generically plagued by inconsistencies. We present a simple framework that couples higher spins to a broad class of gravitational backgrounds including Ricci flat and Einstein consistently at the classical level. The model is the simplest example of a YangMills detour complex, which recently has been applied in the mathematical setting of conformal geometry. An analysis of asymptotic scattering states about the trivial field theory vacuum in the simplest version of the theory yields a rich spectrum marred by negative norm excitations. The result is a theory of a physical massless graviton, scalar field, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector of the model do have positive norms, but their evolution is no longer unitary and their amplitudes grow with time. The model is of considerable interest for braneworld scenarios and ghost condensation models, and invariant theory.

The Skyrmion strikes back baryons and a new large Nc limit ; In the large Nc limit of QCD, baryons can be modeled as solitons, for instance, as Skyrmions. This modeling has been justified by Witten's demonstration that all properties of baryons and mesons scale with Nc12 in the same way as the analogous mesonbased soliton model scales with a generic mesonmeson coupling constant g. An alternative large Nc limit the orientifold large Nc limit has recently been proposed in which quarks transform in the twoindex antisymmetric representation of SUNc. By carrying out the analog of Witten's analysis for the new orientifold large Nc limit, we show that baryons and solitons can also be identified in the orientifold large Nc limit. However, in the orientifold large Nc limit, the interaction amplitudes and matrix elements scale with Nc1 in the same way as soliton models scale with the generic meson coupling constant g rather than as Nc12 as in the traditional large Nc limit.

Inflation without Inflatons ; We propose a model for early universe cosmology without the need for fundamental scalar fields. Cosmic acceleration and phenomenologically viable reheating of the universe results from a series of energy transitions, where during each transition vacuum energy is converted to thermal radiation. We show that this cascading universe' can lead to successful generation of adiabatic density fluctuations and an observable gravity wave spectrum in some cases, where in the simplest case it reproduces a spectrum similar to slowroll models of inflation. We also find the model provides a reasonable reheating temperature after inflation ends. This type of model may also be relevant for addressing the smallness of the vacuum energy today.

A Microscopic Model for the Black hole Black string Phase Transition ; Computations in general relativity have revealed an interesting phase diagram for the black hole black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by boosting' plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the nearextremal domain where a microscopic model can be conjectured. When the compactification radius is very large or very small then we get the microscopic models of 41 dimensional nearextremal holes and 31 dimensional nearextremal holes respectively the latter is a uniform black string in 41 dimensions. We propose a simple model that interpolates between these limits and reproduces most of the features of the phase diagram. These results should help us understand how fractionation' of branes works in general situations.

Baxter Qoperator for graded SL21 spin chain ; We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N1 superYangMills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the quantum space in all sites corresponding to infinitedimensional representations of the SL21 group. We extend the method of the Baxter Qoperator to spin chains with supergroup symmetry and apply it to determine the eigenspectrum of the model. Our analysis relies on a factorization property of the Roperators acting on the tensor product of two generic infinitedimensional SL21 representations. It allows us to factorize an arbitrary transfer matrix into a product of three elementary' transfer matrices which we identify as Baxter Qoperators. We establish functional relations between transfer matrices and use them to derive the TQrelations for the Qoperators. The proposed construction can be generalized to integrable models based on supergroups of higher rank and, in distinction to the Bethe Ansatz, it is not sensitive to the existence of the pseudovacuum state in the quantum space of the model.

Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries ; We study the collective field formulation of a restricted form of the multispecies Calogero model, in which the threebody interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality transformations, which interchange, among other things, particles and antiparticles, and thus generalize the wellknown strongweak coupling duality symmetry of the ordinary Calogero model. We identify all these dualities, which form an Abelian group, and study their consequences. We also study the ground state and small fluctuations around it in detail, starting with the twospecies model, and then generalizing to an arbitrary number of species.

BiHermitian Supersymmetric Quantum Mechanics ; BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for 2,2 world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.

NonFactorisable Z2 times Z2 Heterotic Orbifold Models and Yukawa Couplings ; We classify compactification lattices for supersymmetric Z2 times Z2 orbifolds. These lattices include factorisable as well as nonfactorisable sixtori. Different models lead to different numbers of fixed pointstori. A lower bound on the number of fixed tori per twisted sector is given by four, whereas an upper bound consists of 16 fixed tori per twisted sector. Thus, these models have a variety of generation numbers. For example, in the standard embedding, the smallest number of net generations among these classes of models is equal to six, while the largest number is 48. Conditions for allowed Wilson lines and Yukawa couplings are derived.

Integrability in Theories with Local U1 Gauge Symmetry ; Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U1 generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U1 gauge symmetry are investigated.

Mutually Generics and Perfect Free Subsets ; We discuss ways of adjoining perfect sets of mutually generic random reals. In particular, we show that if V sub W are models of ZFC and W contains a dominating real over V, then Wr, where r is random over W, contains a perfect tree of mutually random reals over V. This result improves an earlier result by Bartoszynski and Judah and sheds new light on an old Theorem of Mycielski's. We also investigate the existence of perfect free subsets for projective functions f omegaomegan to omegaomega. In particular, we prove that every projective function has a perfect free subset in the Cohen real model, while in the Sacks real model the following holds every Delta12 function f omegaomega to omegaomega has a perfect free subset and there is a Delta12function f omegaomega2 to omegaomega without perfect free subsets. This is connected with recent results of Mildenberger. Finally, we show that the existence of a superperfect tree of Cohen reals over a model V of ZFC implies the existence of a dominating real over V, thus answering a question addressed by Spinas.

Randomness and semigenericity ; Let L contain only the equality symbol and let L be an arbitrary finite symmetric relational language containing L . Suppose probabilities are defined on finite L structures with ''edge probability'' n alpha. By Talpha, the almost sure theory of random Lstructures we mean the collection of Lsentences which have limit probability 1. Talpha denotes the theory of the generic structures for Kalpha, the collection of finite graphs G with deltaalphaGG alpha. edges of G hereditarily nonnegative. THEOREM Talpha, the almost sure theory of random Lstructures is the same as the theory Talpha of the Kalphageneric model. This theory is complete, stable, and nearly model complete. Moreover, it has the finite model property and has only infinite models so is not finitely axiomatizable.

Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models ; Motivated by an exact mapping between anisotropic half integer spin quantum Heisenberg models and asymmetric diffusions on the lattice, we consider an anisotropic simple exclusion process with N particles in a rectangle of bbZ2. Every particle at row h tries to jump to an arbitrary empty site at row hpm 1 with rate qpm 1, where qin 0,1 is a measure of the drift driving the particles towards the bottom of the rectangle. We prove that the spectral gap of the generator is uniformly positive in N and in the size of the rectangle. The proof is inspired by a recent interesting technique envisaged by E. Carlen, M.C. Carvalho and M. Loss to analyze the Kac model for the non linear Boltzmann equation. We then apply the result to prove precise upper and lower bounds on the energy gap for the spinS, rm Sin frac12bbN, XXZ chain and for the 111 interface of the spinS XXZ Heisenberg model, thus generalizing previous results valid only for spin frac12.

Biological sequence analysis ; This talk will review a little over a decade's research on applying certain stochastic models to biological sequence analysis. The models themselves have a longer history, going back over 30 years, although many novel variants have arisen since that time. The function of the models in biological sequence analysis is to summarize the information concerning what is known as a motif or a domain in bioinformatics, and to provide a tool for discovering instances of that motif or domain in a separate sequence segment. We will introduce the motif models in stages, beginning from very simple, nonstochastic versions, progressively becoming more complex, until we reach modern profile HMMs for motifs. A second example will come from gene finding using sequence data from one or two species, where generalized HMMs or generalized pair HMMs have proved to be very effective.

Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps ; In this book we study the concepts of Fuzzy Cognitive Maps FCMs and their Neutrosophic analogue, the Neutrosophic Cognitive Maps NCMs.Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and farreaching consequences as a mathematical tool for modeling complex systems. Neutrosophic Cognitive Maps are generalizations of FCMs, and their unique feature is the ability to handle indeterminacy in relations between two concepts thereby bringing greater sensitivity into the results. Some of the varied applications of FCMs and NCMs which has been explained by us, in this book, include modeling of supervisory systems; design of hybrid models for complex systems; mobile robots and in intimate technology such as office plants; analysis of business performance assessment; formalism debate and legal rules; creating metabolic and regulatory network models; traffic and transportation problems; medical diagnostics; simulation of strategic planning process in intelligent systems; specific language impairment; webmining inference application; child labor problem; industrial relations between employer and employee, maximizing production and profit; decision support in intelligent intrusion detection system; hyperknowledge representation in strategy formation; female infanticide; depression in terminally ill patients and finally, in the theory of community mobilization and women empowerment.

Generalized Urn Models of Evolutionary Processes ; Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are Under what conditions does a population exhibit growth On the event of growth, at what rate does the population increase What is the longterm behavior of the distribution of genotypes To address these questions, we associate a mean limit ordinary differential equation ODE with the urn model. Previously, it has been shown that on the event of population growth, the limiting distribution of genotypes is a connected internally chain recurrent set for the mean limit ODE. To determine when growth and convergence occurs with positive probability, we prove two results. First, if the mean limit ODE has an attainable'' attractor at which growth is expected, then growth and convergence toward this attractor occurs with positive probability. Second, the population distribution almost surely does not converge to sets where growth is not expected

A model for separatrix splitting near multiple resonances ; We propose a model for local dynamics of a perturbed convex realanalytic Liouvilleintegrable Hamiltonian system near a resonance of multiplicity 1m, mgeq 0. Physically, the model represents a toroidal pendulum, coupled with a Liouvilleintegrable system of n nonlinear rotators via a small analytic potential. The global bifurcation problem is setup for the ndimensional isotropic manifold, corresponding to a specific homoclinic orbit of the toroidal pendulum. The splitting of this manifold can be described by a scalar function on an ntorus, whose kth Fourier coefficient satisfies the estimate Oe rhokcdotomega ksigma, kinZnsetminus0, where omegainRn is a Diophantine rotation vector of the system of rotators; rhoin0,piover2 and sigma0 are the analyticity parameters built into the model. The estimate, under suitable assumptions would generalize to a general multiple resonance normal form of a convex analytic Liouville integrable Hamiltonian system, perturbed by Oeps, in which case omegajsimomeps, j1,...,n.

MDL Convergence Speed for Bernoulli Sequences ; The Minimum Description Length principle for online sequence estimationprediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure a this quantity is finitely bounded, implying convergence with probability one, and b it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound comparable to the one for Bayes mixtures for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.

On the Strong Coupling Limit of the FaddeevHopf Model ; The variational calculus for the FaddeevHopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure YangMills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map S3 S2 is given, and a conjecture of Ward concerning the stability of this map in the full FaddeevHopf model is proved.

Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models ; We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of ndimentional Hermitian matrices as n tends to infinity. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of the model consists of two or more intervals, then in the global regime the variance of statistics is a quasiperiodic function of n generically in the potential, determining the model. We show next that the exponent of the Laplace transform of the probability law is not in general 12variance, as it should be if the Central Limit Theorem would be valid, and we find the asymptotic form of the Laplace transform of the probability law in certain cases.

Model averaging and dimension selection for the singular value decomposition ; Many multivariate data analysis techniques for an mtimes n matrix m Y are related to the model m Y m M m E, where m Y is an mtimes n matrix of full rank and m M is an unobserved mean matrix of rank K mwedge n. Typically the rank of m M is estimated in a heuristic way and then the leastsquares estimate of m M is obtained via the singular value decomposition of m Y, yielding an estimate that can have a very high variance. In this paper we suggest a modelbased alternative to the above approach by providing prior distributions and posterior estimation for the rank of m M and the components of its singular value decomposition. In addition to providing more accurate inference, such an approach has the advantage of being extendable to more general dataanalysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.

Equivariant homotopy theory for prospectra ; We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The Ghomotopy theory is pieced together from the GUhomotopy theories for suitable quotient groups GU of G; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In the model category of equivariant spectra Postnikov towers are studied from a general perspective. We introduce proGspectra and construct various model structures on them. A key property of the model structures is that prospectra are weakly equivalent to their Postnikov towers. We discuss two versions of a model structure with underlying weak equivalences. One of the versions only makes sense for prospectra. In the end we use the theory to study homotopy fixed points of proGspectra.

Nagata's conjecture and countably compactifications in generic extensions ; Nagata conjectured that every Mspace is homeomorphic to a closed subspace of the product of a countably compact space and a metric space. This conjecture was refuted by Burke and van Douwen, and A. Kato, independently. However, we can show that there is a c.c.c. poset P of size 2omega such that in VP Nagata's conjecture holds for each first countable regular space from the ground model i.e. if a first countable regular space Xin V is an Mspace in VP then it is homeomorphic to a closed subspace of the product of a countably compact space and a metric space in VP. In fact, we show that every first countable regular space from the ground model has a first countable countably compact extension in VP, and then apply some results of Morita. As a corollary, we obtain that every first countable regular space from the ground model has a maximal first countable extension in model VP.

Model selection in HighDimensions A Quadraticrisk based approach ; In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a nonnegative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a quicktocompute approximation for the risk function. Its derivation is analogous to the Akaike Information Criterion AIC, but unlike AIC, the quadratic risk is a global comparison tool. The method does not require resampling, a great advantage when point estimators are expensive to compute. The method is illustrated using the problem of selecting the number of components in a mixture model, where it is shown that, by using an appropriate kernel, the method is computationally straightforward in arbitrarily high data dimensions. In this same context it is shown that the method has some clear advantages over AIC and BIC.

Stability of Kink Defects in a Deformed O3 Linear Sigma Model ; We identify the kinks of a deformed O3 linear Sigma model as the solutions of a set of firstorder systems of equations; the above model is a generalization of the MSTB model with a threecomponent scalar field. Taking into account certain kink energy sum rules we show that the variety of kinks has the structure of a moduli space that can be compactified in a fairly natural way. The generic kinks, however, are unstable and Morse Theory provides the framework for the analysis of kink stability.

An approach to exact solutions of the timedependent supersymmetric twolevel threephoton JaynesCummings model ; By utilizing the property of the supersymmetric structure in the twolevel multiphoton JaynesCummings model, an invariant is constructed in terms of the supersymmetric generators by working in the subHilbertspace corresponding to a particular eigenvalue of the conserved supersymmetric generators. We obtain the exact solutions of the timedependent Schrodinger equation which describes the timedependent supersymmetric twolevel threephoton JaynesCummings model TLTJCM by using the invariantrelated unitary transformation formulation. The case under the adiabatic approximation is also discussed. Keywords Supersymmetric JaynesCummings model; exact solutions; invariant theory; geometric phase factor; adiabatic approximation

Notes on Dilaton Quantum Cosmology ; In these notes we address the canonical quantization of the cosmological models which appear as solutions of the low energy effective action of closed bosonic string theory dilaton models. The analysis is restricted to the quantization of the minisuperspace models given by homogeneous and isotropic cosmological solutions. We study the different conceptual and technical problems arising in the Hamiltonian formulation of these models as a consequence of the presence of the so called Hamiltonian constraint. In particular we address the problem of time in quantum cosmology, the characterization of the symmetry under clock reversls arising from the existence of a Hamiltonian constraint, and the problem of inposing boundary conditions on the space of solutions of the WheelerDeWitt equation.

On the stability of normal states for a generalized GinzburgLandau model ; We formulate a spectral problem related to the onset of superconductivity for a generalized GinzburgLandau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the proximity effect' for a superconducting sample surrounded by a normal material. In the regime when the GinzburgLandau parameter of the superconducting material is large, we estimate the critical applied magnetic field for which the normal state will lose its stability, a result that has some roots in the physical literature. In some asymptotic situations, we recover results related to the standard' GinzburgLandau model, where we mention in particular the twoterm expansion for the upper critical field obtained by HelfferPan.

Anderson Localization for radial treelike random quantum graphs ; We prove that certain random models associated with radial, treelike, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model RLM and the random Kirchhoff model RKM. In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables iid. For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.

Stable localized pulses and zigzag stripes in a twodimensional diffractivediffusive GinzburgLandau equation ; We introduce a model of a twodimensional 2D optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporaldomain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubicquintic GinzburgLandau equation with an anisotropy of a novel type the equation is diffractive in one direction, and diffusive in the other. By means of systematic simulations, we demonstrate that the model gives rise to emphstable fully localized 2D pulses, which are spatiotemporal light bullets'', existing due to the simultaneous balances between diffraction, dispersion, and Kerr nonlinearity, and between linear and quintic losses and cubic gain. A stability region of the 2D pulses is identified in the system's parameter space. Besides that, we also find that the model generates 1D patterns in the form of simple localized stripes, which may be stable, or may exhibit an instability transforming them into oblique stripes with zigzags. The straight and oblique stripes may stably coexist with the 2D pulse, but not with each other.

Polychromatic solitons in a quadratic medium ; We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with slightly different carrier frequencies which is a direct analog of wavelengthdivision multiplexed WDM models, well known in media with cubic nonlinearity. The model takes a closed form with three different secondharmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons PCSs, with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple usual soliton taken at the same values of control parameters, which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple alloptical XOR logic gate.

Emergence of a complex and stable network in a model ecosystem with extinction and mutation ; We propose a minimal model of the dynamics of diversity replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the conventional replicator equation and the generalized LotkaVolterra equation. We reach several significant conclusions as follows 1 a complex ecosystem can emerge when mutants with respect to speciesspecific interaction are introduced; 2 such an ecosystem possesses strong resistance to invasion; 3 a typical fixation process of mutants is realized through the rapid growth of a group of mutualistic mutants with higher fitness than majority species; 4 a hierarchical taxonomic structure like familygenusspecies emerges; and 5 the relative abundance of species exhibits a typical pattern widely observed in nature. Several implications of these results are discussed in connection with the relationship of the present model to the generalized LotkaVolterra equation.

Simulated Dynamical Weakening and Abelian Avalanches in MeanField Driven Threshold Models ; Meanfield coupled lattice maps are used to approximate the physics of driven threshold systems with long range interactions. However, they are incapable of modeling specific features of the dynamic instability responsible for generating avalanches. Here we present a method of simulating specific frictional weakening effects in a mean field slider block model. This provides a means of exploring dynamical effects previously inaccessible to discrete time simulations. This formulation also results in Abelian avalanches, where rupture propagation is independent of the failure sequence. The resulting event size distribution is shown to be generated by the boundary crossings of a stochastic process. This is applied to typical models to explain some commonly observed features.

Exchange operator formalism for Nbody spin models with nearneighbors interactions ; We present a detailed analysis of the spin models with nearneighbors interactions constructed in our previous paper Phys. Lett. B 605 2005 214 by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finitedimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.

Algebraic nonlinear collective motion ; Finitedimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl3, R and contains the angular momentum algebra so3 is determined. The subset of divergencefree sl3, R vector fields is proven to be indexed by a real number Lambda. The Lambda0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positive Lambda, the droplets have a neck that becomes more pronounced as Lambda increases; for negative Lambda, the droplets contain a spherical bubble of radius Lambda13. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm3 which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm3 Lie algebra. These representations model fissioning isotopes Lambda0 and bubble and twofluid nuclei Lambda0.

A number projected model with generalized pairing interaction ; A meanfield model with a generalized pairing interaction that accounts for neutronproton pairing is presented. Both the BCS as well as numberprojected solutions of the model are presented. For the latter case the LipkinNogami projection technique was extended to encompass the case of nonseparable protonneutron systems. The influence of the projection on various pairing phases is discussed. In particular, it is shown that numberprojection allows for mixing of different pairing phases but, simultanously, acts destructively on the protonneutron correlations. The basic implications of protonneutron pairing correlations on nuclear masses are discussed. It is shown that these correlations may provide a natural microscopic explanation of the Wigner energy lacking in meanfield models. A possible phase transition from isovector to isoscalar pairing condensate at high angular momenta is also discussed. In particular predictions for the dynamical moments of inertia for the superdeformed band in 88Ru are given.

The two pion decay of the Roper resonance ; We evaluate the two pion decay of the Roper resonance in a model where explicit rescattering of the two final pions is accounted for by the use of unitarized chiral perturbation theory. Our model does not include an explicit epsilon or sigma scalarisoscalar meson decay mode, instead it generates it dynamically by means of the pion rescattering. The two ways, explicit or dynamically generated, of introducing this decay channel have very different amplitudes. Nevertheless, through interference with the other terms of the model we are able to reproduce the same phenomenology as models with explicit consideration of the epsilon meson.

Application of the generalized twocenter cluster model to 10Be ; A generalized twocenter cluster model GTCM, including various partitions of the valence nucleons around two alphacores, is proposed for studies on the exotic cluster structures of Be isotopes. This model is applied to the 10Be alpha alpha n n system and the adiabatic energy surfaces for alphaalpha distances are calculated. It is found that this model naturally describes the formation of the molecular orbitals as well as that of asymptotic cluster states dependeing on their relative distance. In the negativeparity state, a new type of the alpha 6He cluster structure is also predicted.

ProtonNeutron Coupling in the Gamow Shell Model the Lithium Chain ; The shell model in the complex kplane the socalled Gamow Shell Model has recently been formulated and applied to structure of weakly bound, neutronrich nuclei. The completeness relations of Newton and Berggren, which apply to the neutron case, are strictly valid for finiterange potentials. However, for longrange potentials, such as the Coulomb potential for protons, for which the arguments based on the MittagLeffler theory do not hold, the completeness still needs to be demonstrated. This has been done in this paper, both analytically and numerically. The generalized Berggren relations are then used in the first Gamow Shell Model study of nuclei having both valence neutrons and protons, namely the lithium chain. The singleparticle basis used is that of the HartreeFockinspired potential generated by a finiterange residual interaction. The effect of isospin mixing in excited unbound states is discussed.

Beyond the relativistic meanfield approximation configuration mixing of angular momentum projected wave functions ; We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic meanfield models. A model is developed which uses the generator coordinate method to perform configuration mixing calculations of angular momentum projected wave functions, calculated in a relativistic pointcoupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the constrained relativistic meanfield BCS equations in an axially deformed oscillator basis. A number of illustrative calculations are performed for the nuclei 194Hg and 32Mg, in comparison with results obtained in nonrelativistic models based on Skyrme and Gogny effective interactions.

Beyond the relativistic meanfield approximation II configuration mixing of meanfield wave functions projected on angular momentum and particle number ; The framework of relativistic selfconsistent meanfield models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angularmomentum and particlenumber projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic meanfield LipkinNogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic pointcoupling contact nucleonnucleon effective interaction in the particlehole channel, and a densityindependent deltainteraction in the pairing channel. Illustrative calculations are performed for 24Mg, 32S and 36Ar, and compared with results obtained employing the model developed in the first part of this work, i.e. without particlenumber projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions.

Aftershocks in CoherentNoise Models ; The decay pattern of aftershocks in the socalled 'coherentnoise' models M. E. J. Newman and K. Sneppen, Phys. Rev. E54, 6226 1996 is studied in detail. Analytical and numerical results show that the probability to find a large event at time t after an initial major event decreases as ttau for small t, with the exponent tau ranging from 0 to values well above 1. This is in contrast to Sneppen und Newman, who stated that the exponent is about 1, independent of the microscopic details of the simulation. Numerical simulations of an extended model C. Wilke, T. Martinetz, Phys. Rev. E56, 7128 1997 show that the powerlaw is only a generic feature of the original dynamics and does not necessarily appear in a more general context. Finally, the implications of the results to the modeling of earthquakes are discussed.

A New Free Core Nutation Model with Variable Amplitude and Period ; Three most long and dense VLBI nutation series obtained at the Goddard Space Flight Center, Institute of Applied Astronomy, and U.S. Naval Observatory were used for investigation of the Free Core Nutation FCN contribution to the celestial pole offset. Some recent studies have showed that the FCN period orand phase does not remain constant, but varies in a rather wide range of about 410490 days for equivalent period. To implement this result in the practice, a new FCN model with variable amplitude and period phase is developed. Comparison of this model with observations shows better agreement than existing one. After correction of the differences between observed VLBI nutation series and the IAU2000A model, they decreased to a level about 100 microarcseconds.

A Generalized Preferential Attachment Model for Complex Systems ; Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry.

A geostrophiclike model for large Hartmann number flows ; A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi twodimensional, i.e. uniform in the direction of the magnetic field, except in thin socalled Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number Ha 1. This is analogous to the case of low Ekman number rotating flows, with Ekman layers replacing Hartmann layers. This has been at the origin of the homogeneous model for flows in a rotating frame of reference, with its rich structure geostrophic contours and shear layers of Stewartson, Munk and Stommel. In magnetohydrodynamics, the characteristic surfaces introduced by Kulikovskii play a role similar to the role of the geostrophic contours. However, a general theory for quasi twodimensional magnetohydrodynamics is lacking. In this paper, a model is proposed which provides a general framework for quasi twodimensional magnetohydrodynamic flows. Not only can this model account for otherwise disconnected past results, but it is also used to predict a new type of shear layer, of typical thickness Ha14.

A Generalized Preferential Attachment Model for Business Firms Growth Rates I. Empirical Evidence ; We introduce a model of proportional growth to explain the distribution Pg of business firm growth rates. The model predicts that Pg is Laplace in the central part and depicts an asymptotic powerlaw behavior in the tails with an exponent zeta3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and sizevariance relationships.

A Generalized Preferential Attachment Model for Business Firms Growth Rates II. Mathematical Treatment ; We present a preferential attachment growth model to obtain the distribution PK of number of units K in the classes which may represent business firms or other socioeconomic entities. We found that PK is described in its central part by a power law with an exponent phi2b1b which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution PK is exponential. Using analytical form of PK and assuming proportional growth for units, we derive Pg, the distribution of business firm growth rates. The model predicts that Pg has a Laplacian cusp in the central part and asymptotic powerlaw tails with an exponent zeta3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the sizevariance relationship of the firm growth rates.

General multistate models for agents with internal bias ; We present a model of interpersonal comparisons appearing as a generalization of a multistate model for elements with internal bias. Within this model agents suffering under dissatisfaction compare them with their neighbors. The internal bias are the preformed preferences, and the states are represented by the visual contacts that an agent makes to the baskets of herhis neighbors. The topology of the comparisons is a random network. We compare the behavior between altruistic and nonaltruistic agents and we find out that altruistic behavior alters the robustness of the network.

Identification and Measurement of Neighbor Dependent Nucleotide Substitution Processes ; The presence of neighbor dependencies generated a specific pattern of dinucleotide frequencies in all organisms. Especially, the CpGmethylationdeamination process is the predominant substitution process in vertebrates and needs to be incorporated into a more realistic model for nucleotide substitutions. Based on a general framework of nucleotide substitutions we develop a method that is able to identify the most relevant neighbor dependent substitution processes, measure their strength, and judge their importance to be included into the modeling. Starting from a model for neighbor independent nucleotide substitution we successively add neighbor dependent substitution processes in the order of their ability to increase the likelihood of the model describing given data. The analysis of neighbor dependent nucleotide substitutions in human, zebrafish and fruit fly is presented. A web server to perform the presented analysis is publicly available.

Locality and Causality in Hidden Variables Models of Quantum Theory ; Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which either i are nontrivial counterexamples to this conjecture or ii possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner's and similar hidden variables models can be extended to an important class of generalized observables. Finally a result of Fine on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.

Probability Models and Ultralogics ; In this paper, we show how nonstandard consequence operators, ultralogics, can generate the general informational content displayed by probability models. In particular, a probability model that predicts that a specific single event will occur and those models that predict that a specific distribution of events will occur.

Lindbladian Evolution with Selfadjoint Lindblad Operators as Averaged Random Unitary Evolution ; It is shown how any Lindbladian evolution with selfadjoint Lindblad operators, either Markovian or nonMarkovian, can be understood as an averaged random unitary evolution. Both mathematical and physical consequences are analyzed. First a simple and fast method to solve this kind of master equations is suggested and particularly illustrated with the phasedamped master equation for the multiphoton resonant JaynesCummings model in the rotatingwave approximation. A generalization to some intrinsic decoherence models present in the literature is included. Under the same philosophy a proposal to generalize the JaynesCummings model is suggested whose predictions are in accordance with experimental results in cavity QED and in ion traps. A comparison with stochastic dynamical collapse models is also included.

A model of quantum reduction with decoherence ; The problem of reduction wave packet reduction is reexamined under two simple conditions Reduction is a last step completing decoherence. It acts in commonplace circumstances and should be therefore compatible with the mathematical frame of quantum field theory and the standard model. These conditions lead to an essentially unique model for reduction. Consistency with renormalization and timereversal violation suggest however a primary action in the vicinity of Planck's length. The inclusion of quantum gravity and the uniqueness of spacetime point moreover to generalized quantum theory, first proposed by GellMann and Hartle, as a convenient framework for developing this model into a more complete theory.

Optimal classicalcommunicationassisted local model of nqubit GreenbergerHorneZeilinger correlations ; We present a model, motivated by the criterion of reality put forward by Einstein, Podolsky, and Rosen and supplemented by classical communication, which correctly reproduces the quantummechanical predictions for measurements of all products of Pauli operators on an nqubit GHZ state or cat state''. The n2 bits employed by our model are shown to be optimal for the allowed set of measurements, demonstrating that the required communication overhead scales linearly with n. We formulate a connection between the generation of the local values utilized by our model and the stabilizer formalism, which leads us to conjecture that a generalization of this method will shed light on the content of the GottesmanKnill theorem.

Quantum Machine and SR Approach a Unified Model ; The GenevaBrussels approach to quantum mechanics QM and the semantic realism SR nonstandard interpretation of QM exhibit some common features and some deep conceptual differences. We discuss in this paper two elementary models provided in the two approaches as intuitive supports to general reasonings and as a proof of consistency of general assumptions, and show that Aerts' quantum machine can be embodied into a macroscopic version of the microscopic SR model, overcoming the seeming incompatibility between the two models. This result provides some hints for the construction of a unified perspective in which the two approaches can be properly placed.

Symmetry, model reduction, and quantum mechanics ; Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland 2005a,b is surveyed and clarified. The quantum Hilbert space is constructed from the parameters of the various experiments using group representation theory. It is shown under natural assumptions that a subset of the set of unit vectors of this space, the generalized coherent state vectors, can be put in correspondence with questions of the kind What is the value of the complete parameter together with a crisp answer to that question. Links are made to statistical models in general, to model reduction of overparametrized models and to the design of experiments. It turns out to be essential that the range of the statistical parameter is an invariant set under the relevant symmetry group.

Analysis and identification of quantum dynamics using Lie algebra homomorphisms and Cartan decompositions ; In this paper, we consider the problem of model equivalence for quantum systems. Two models are said to be inputoutput equivalent if they give the same output for every admissible input. In the case of quantum systems, the output is the expectation value of a given observable or, more in general, a probability distribution for the result of a quantum measurement. We link the inputoutput equivalence of two models to the existence of a homomorphism of the underlying Lie algebra. In several cases, a Cartan decomposition of the Lie algebra sun is useful to find such a homomorphism and to determine the classes of equivalent models. We consider in detail the important cases of two level systems with a Cartan structure and of spin networks. In the latter case, complete results are given generalizing previous results to the case of networks of spin particles with any value of the spin. In treating this problem, we prove some instrumental results on the subalgebras of sun which are of independent interest.

Classical spin models and the quantum stabilizer formalism ; We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of qstate spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and highlow temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded treewidth.

Particles and strings in a 21D integrable quantum model ; We give a review of some recent work on generalization of the Bethe ansatz in the case of 21dimensional models of quantum field theory. As such a model, we consider one associated with the tetrahedron equation, i.e. the 21dimensional generalization of the famous YangBaxter equation. We construct some eigenstates of the transfer matrix of that model. There arise, together with states composed of pointlike particles analogous to those in the usual 11dimensional Bethe ansatz, new stringlike states and stringparticle hybrids.

Novel integrable spinparticle models from gauge theories on a cylinder ; We find and solve a large class of integrable dynamical systems which includes CalogeroSutherland models and various novel generalizations thereof. In general they describe N interacting particles moving on a circle and coupled to an arbitrary number, m, of suN spin degrees of freedom with interactions which depend on arbitrary real parameters xj, j1,2,...,m. We derive these models from SUN YangMills gauge theory coupled to nondynamic matter and on spacetime which is a cylinder. This relation to gauge theories is used to prove integrability, to construct conservation laws, and solve these models.

Bianchi Type I Massive String Magnetized Barotropic Perfect Fluid Cosmological Model in General Relativity ; Bianchi type I massive string cosmological model with magnetic field of barotropic perfect fluid distribution through the techniques used by Latelier and Stachel, is investigated. To get the deterministic model of the universe, it is assumed that the universe is filled with barotropic perfect fluid distribution. The magnetic field is due to electric current produced along xaxis with infinite electrical conductivity. The behaviour of the model in presence and absence of magnetic field together with other physical aspects is further discussed.

Rotationallyinvariant slaveboson formalism and momentum dependence of the quasiparticle weight ; We generalize the rotationallyinvariant formulation of the slaveboson formalism to multiorbital models, with arbitrary interactions, crystal fields, and multiplet structure. This allows for the study of multiplet effects on the nature of lowenergy quasiparticles. Nondiagonal components of the matrix of quasiparticle weights can be calculated within this framework. When combined with cluster extensions of dynamical meanfield theory, this method allows us to address the effects of spatial correlations, such as the generation of the superexchange and the momentum dependence of the quasiparticle weight. We illustrate the method on a twoband Hubbard model, a Hubbard model made of two coupled layers, and a twodimensional singleband Hubbard model within a twosite cellular dynamical meanfield approximation.

A discriminating probe of gravity at cosmological scales ; The standard cosmological model is based on general relativity and includes dark matter and dark energy. An important prediction of this model is a fixed relationship between the gravitational potentials responsible for gravitational lensing and the matter overdensity. Alternative theories of gravity often make different predictions for this relationship. We propose a set of measurements which can test the lensingmatter relationship, thereby distinguishing between dark energymatter models and models in which gravity differs from general relativity. Planned optical, infrared and radio galaxy and lensing surveys will be able to measure EG, an observational quantity whose expectation value is equal to the ratio of the Laplacian of the Newtonian potentials to the peculiar velocity divergence, to percent accuracy. We show that this will easily separate alternatives such as LambdaCDM, DGP, TeVeS and fR gravity.

On the generalized FreedmanTownsend model ; Consistent interactions that can be added to a free, Abelian gauge theory comprising a finite collection of BF models and a finite set of twoform gauge fields with the Lagrangian action written in firstorder form as a sum of Abelian FreedmanTownsend models are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra. The interacting Lagrangian action contains a generalized version of nonAbelian FreedmanTownsend model. The consistency of interactions to all orders in the coupling constant unfolds certain equations, which are shown to have solutions.

Neutrino Masses in the LeeWick Standard Model ; Recently, an extension of the standard model based on ideas of Lee and Wick has been discussed. This theory is free of quadratic divergences and hence has a Higgs mass that is stable against radiative corrections. Here, we address the question of whether or not it is possible to couple very heavy particles, with masses much greater than the weak scale, to the LeeWick standard model degrees of freedom and still preserve the stability of the weak scale. We show that in the LWstandard model the familiar seesaw mechanism for generating neutrino masses preserves the solution to the hierarchy puzzle provided by the higher derivative terms. The very heavy right handed neutrinos do not destabilize the Higgs mass. We give an example of new heavy degrees of freedom that would destabilize the hierarchy, and discuss a general mechanism for coupling other heavy degrees of freedom to the Higgs doublet while preserving the hierarchy.

Higher Order Statistsics of Stokes Parameters in a Random Birefringent Medium ; We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of the rotation group. We show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the Mueller matrix and the Stokes vector throughout the propagation. It also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. We will also discuss how this model allows a generalization of the concepts of reduced Stokes parameters and degree of polarization to higher order statistics. We give some notes on how it can be extended to more general random media.

Inverse problems in imaging systems and the general Bayesian inversion frawework ; In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Bayesian estimation framework is presented which can handle, in a coherent way, all these problems. One of the main steps, in Bayesian inversion framework is the prior modeling of the unknowns. For this reason, a great number of such models and in particular the compound hidden Markov models are presented. Then, the main computational tools of the Bayesian estimation are briefly presented. Finally, some particular cases are studied in detail and new results are presented.

Heterogeneity and Increasing Returns May Drive SocioEconomic Transitions ; There are clear benefits associated with a particular consumer choice for many current markets. For example, as we consider here, some products might carry environmental or green' benefits. Some consumers might value these benefits while others do not. However, as evidenced by myriad failed attempts of environmental products to maintain even a niche market, such benefits do not necessarily outweigh the extra purchasing cost. The question we pose is, how can such an initially economicallydisadvantaged green product evolve to hold the greater share of the market We present a simple mathematical model for the dynamics of product competition in a heterogeneous consumer population. Our model preassigns a hierarchy to the products, which designates the consumer choice when prices are comparable, while prices are dynamically rescaled to reflect increasing returns to scale. Our approach allows us to model many scenarios of technology substitution and provides a method for generalizing market forces. With this model, we begin to forecast irreversible trends associated with consumer dynamics as well as policies that could be made to influence transitions

SineGordon solitons, auxiliary fields, and singular limit of a double pendulums chain ; We consider the continuum version of an elastic chain supporting topological and nontopological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the nontopological degrees of freedom are frozen, and the model reduces to the sineGordon equations and thus supports wellknown topological soliton solutions. We consider a singular perturbative expansion around this limit and study in particular how the nontopological field assume the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such phenomenon to arise in a quite large class of fieldtheoretical models.

Stability in generic mitochondrial models ; In this paper, we use a variety of mathematical techniques to explore existence, local stability, and global stability of equilibria in abstract models of mitochondrial metabolism. The class of models constructed is defined by the biological description of the system, with minimal mathematical assumptions. The key features are an electron transport chain coupled to a process of charge translocation across a membrane. In the absence of charge translocation these models have previously been shown to behave in a very simple manner with a single, globally stable equilibrium. We show that with charge translocation the conclusion about a unique equilibrium remains true, but local and global stability do not necessarily follow. In sufficiently low dimensions i.e. for short electron transport chains it is possible to make claims about local and global stability of the equilibrium. On the other hand, for longer chains, these general claims are no longer valid. Some particular conditions which ensure stability of the equilibrium for chains of arbitrary length are presented.

Why the Standard Model ; The Standard Model is based on the gauge invariance principle with gauge group U1xSU2xSU3 and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation spacetime has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F. The raison d'etre for F is to correct the Ktheoretic dimension from four to ten modulo eight. We classify the irreducible finite noncommutative geometries of Ktheoretic dimension six and show that the dimension per generation is a square of an integer k. Under an additional hypothesis of quaternion linearity, the geometry which reproduces the Standard Model is singled out and one gets k4with the correct quantum numbers for all fields. The spectral action applied to the product MxF delivers the full Standard Model,with neutrino mixing, coupled to gravity, and makes predictionsthe number of generations is still an input.

Epidemic Waves, Small Worlds and Targeted Vaccination ; The success of an infectious disease to invade a population is strongly controlled by the population's specific connectivity structure. Here a network model is presented as an aid in understanding the role of social behavior and heterogeneous connectivity in determining the spatiotemporal patterns of disease dynamics. We explore the controversial origins of longterm recurrent oscillations believed to be characteristic to diseases that have a period of temporary immunity after infection. In particular, we focus on sexually transmitted diseases such as syphilis, where this controversy is currently under review. Although temporary immunity plays a key role, it is found that in realistic smallworld networks, the social and sexual behavior of individuals also has great influence in generating longterm cycles. The model generates circular waves of infection with unusual spatial dynamics that depend on focal areas that act as pacemakers in the population. Eradication of the disease can be efficiently achieved by eliminating the pacemakers with a targeted vaccination scheme. A simple difference equation model is derived, that captures the infection dynamics of the network model and gives insights into their origins and their eradication through vaccination.

Exact models with nonminimal interaction between dark matter and either phantom or quintessence dark energy ; A method for deriving FriedmannRobertsonWalker FRW solutions developed in Int. J. Mod. Phys. Dbf 519967184, is generalized to account for models with nonminimal coupling between the dark energy and the dark matter. New quintessence and phantom flat FRW solutions are found. Their physical significance is discussed. Additionally, the aforementioned method is modified so that, coincidence free solutions can be readily derived. Besides, we review some aspects of the phantom barrier crossing. In this regard we present a model which is free from the coincidence problem and, at the same time, does the crossing of the phantom barrier omega1 at late time. Finally, we give additional comments on the non predictive properties of scalar field cosmological models with or without energy transfer.

Decomposition driven interface evolution for layers of binary mixtures I. Model derivation and stratified base states ; A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on modelH describing the coupled transport of the mass of one component convective CahnHilliard equation and momentum NavierStokesKorteweg equations supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological nonequilibrium thermodynamics for a general nonisothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.

Neutrino mixing from the double tetrahedral group Tprime ; It is shown that it is possible to create successful models of flavor for both quarks and leptons using the discrete nonabelian group Tprime by itself. Two simple realizations are presented that can be used as the starting point for more general scenarios. In addition to the Minimal Supersymmetric Standard Model particle content, the models include three generations of right handed neutrinos and four scalar flavon fields. Three of the flavons are needed in the quark and charged lepton sector of the models and the fourth flavon participates only in the neutrino sector.

A Dark Energy Model Characterized by the Age of the Universe ; Quantum mechanics together with general relativity leads to the K'arolyh'azy relation and a corresponding energy density of quantum fluctuations of spacetime. Based on the energy density we propose a dark energy model, in which the age of the universe is introduced as the length measure. This dark energy is consistent with astronomical data if the unique numerical parameter in the dark energy model is taken to be a number of order one. The dark energy behaves like a cosmological constant at early time and drives the universe to an eternally accelerated expansion with powerlaw form at late time. In addition, we point out a subtlety in this kind of dark energy model.

Convergence rates of posterior distributions for noniid observations ; We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We apply our general results to several examples of infinitedimensional statistical models including nonparametric regression with normal errors, binary regression, Poisson regression, an interval censoring model, Whittle estimation of the spectral density of a time series and a nonlinear autoregressive model.

Minimal E6 Supersymmetric Standard Model ; We propose a Minimal E6 Supersymmetric Standard Model ME6SSM which allows Planck scale unification, provides a solution to the mu problem and predicts a new Z'. Above the conventional GUT scale MGUTsim 1016 GeV the gauge group corresponds to a leftright symmetric Supersymmetric PatiSalam model, together with an additional U1psi gauge group arising from an E6 gauge group broken near the Planck scale. Below MGUT the ME6SSM contains three reducible mathbf27 representations of the Standard Model gauge group together with an additional U1X gauge group, consisting of a novel and nontrivial linear combination of U1psi and two PatiSalam generators, which is broken at the TeV scale by the same singlet which also generates the effective mu term, resulting in a new low energy Z' gauge boson. We discuss the phenomenology of the new Z' gauge boson in some detail.

Topological Higher Gauge Theory from BF to BFCG theory ; We study generalizations of 3 and 4dimensional BFtheory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature the SigmaPhiEAmodel of 3dimensional gravity coupled to topological matter, and also a 4dimensional model of BFtheory coupled to topological matter.

Simulation of Spread and Control of Lesions in Brain ; A simulation model for the spread and control of lesions in the brain is constructed using a planar network graph representation for the Central Nervous System CNS. The model is inspired by the lesion structures observed in the case of Multiple Sclerosis MS, a chronic disease of the CNS. The initial lesion site is at the center of a unit square and spreads outwards based on the success rate in damaging edges axons of the network. The damaged edges send out alarm signals which, at appropriate intensity levels, generate programmed cell death. Depending on the extent and timing of the programmed cell death, the lesion may get controlled or aggravated akin to the control of wild fires by burning of peripheral vegetation. The parameter phase space of the model shows smooth transition from uncontrolled situation to controlled situation. The simulations show that the model is capable of generating a wide variety of lesion growth and arrest scenarios.

Discretely Holomorphic Parafermions in Lattice ZN Models ; We construct lattice parafermions local products of order and disorder operators in nearestneighbor ZN models on regular isotropic planar lattices, and show that they are discretely holomorphic, that is they satisfy discrete CauchyRiemann equations, precisely at the critical FateevZamolodchikov FZ integrable points. We generalize our analysis to models with anisotropic interactions, showing that, as long as the lattice is correctly embedded in the plane, such discretely holomorphic parafermions exist for particular values of the couplings which we identify as the anisotropic FZ points. These results extend to more general inhomogeneous lattice models as long as the covering lattice admits a rhombic embedding in the plane.

Nuclear physics with spherically symmetric supernova models ; Few years ago, Boltzmann neutrino transport led to a new and reliable generation of spherically symmetric models of stellar core collapse and postbounce evolution. After the failure to prove the principles of the supernova explosion mechanism, these sophisticated models continue to illuminate the close interaction between highdensity matter under extreme conditions and the transport of leptons and energy in general relativistically curved spacetime. We emphasize that very different input physics is likely to be relevant for the different evolutionary phases, e.g. nuclear structure for weak rates in collapse, the equation of state of bulk nuclear matter during bounce, multidimensional plasma dynamics in the postbounce evolution, and neutrino cross sections in the explosive nucleosynthesis. We illustrate the complexity of the dynamics using preliminary 3D MHD highresolution simulations based on parameterized deleptonization. With established spherically symmetric models we show that typical features of the different phases are reflected in the predicted neutrino signal and that a consistent neutrino flux leads to electron fractions larger than 0.5 in neutrinodriven supernova ejecta.

On the Dipole Swing and the Search for Frame Independence in the Dipole Model ; Smallx evolution in QCD is conveniently described by Mueller's dipole model which, however, does not include saturation effects in a way consistent with boost invariance. In this paper we first show that the recently studied zero and one dimensional toy models exhibiting saturation and explicit boost invariance can be interpreted in terms positive definite k k1 dipole vertices. Such k k1 vertices can in the full model be generated by combining the usual dipole splitting with k1 simultaneous dipole swings. We show that, for a system consisting of N dipoles, one needs to combine the dipole splitting with at most N1 simultaneous swings in order to generate all colour correlations induced by the multiple dipole interactions.

A Probability Model for Lifetime of Wireless Sensor Networks ; Considering a wireless sensor network whose nodes are distributed randomly over a given area, a probability model for the network lifetime is provided. Using this model and assuming that packet generation follows a Poisson distribution, an analytical expression for the complementary cumulative density function ccdf of the lifetime is obtained. Using this ccdf, one can accurately find the probability that the network achieves a given lifetime. It is also shown that when the number of sensors, N, is large, with an error exponentially decaying with N, one can predict whether or not a certain lifetime can be achieved. The results of this work are obtained for both multihop and singlehop wireless sensor networks and are verified with computer simulation. The approaches of this paper are shown to be applicable to other packet generation models and the effect of the area shape is also investigated.

Exact Static Solutions of a Generalized Discrete 4 Model Including ShortPeriodic Solutions ; For a fiveparameter discrete phi4 model, we derive various exact static solutions, including the staggered ones, in the form of the basic Jacobi elliptic functions sn, cn, and dn, and also in the form of their hyperbolic function limits such as kink tanh and singlehumped pulse sech solutions. Such solutions are admitted by the considered model in seven cases, two of which have been discussed in the literature, and the remaining five cases are addressed here. We also obtain sine, staggered sine as well as a large number of shortperiodic static solutions of the generalized 5parameter model. All the Jacobi elliptic, hyperbolic and trigonometric function solutions including the staggered ones are translationally invariant TI, i.e., they can be shifted along the lattice by an arbitrary x0, but among the shortperiodic solutions there are both TI and nonTI solutions. The stability of these solutions is also investigated. Finally, the constructed Jacobi elliptic function solutions reveal four new types of cubic nonlinearity with the TI property.

On the growth of linear perturbations ; We consider the linear growth of matter perturbations in various dark energy DE models. We show the existence of a constraint valid at z0 between the background and dark energy parameters and the matter perturbations growth parameters. For LambdaCDM gamma'0equiv fracdgammadz0 lies in a very narrow interval 0.0195 le gamma'0 le 0.0157 for 0.2 le Omegam,0le 0.35. Models with a constant equation of state inside General Relativity GR are characterized by a quasiconstant gamma'0, for Omegam,00.3 for example we have gamma'0approx 0.02 while gamma0 can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either gamma'00.02. A measurement of gammaz on small redshifts could help discriminate between various DE models even if their gamma0 is close, a possibility interesting for DE models outside GR for which a significant gamma'0 can be obtained.

Struggles with Survey Weighting and Regression Modeling ; The general principles of Bayesian data analysis imply that models for survey responses should be constructed conditional on all variables that affect the probability of inclusion and nonresponse, which are also the variables used in survey weighting and clustering. However, such models can quickly become very complicated, with potentially thousands of poststratification cells. It is then a challenge to develop general families of multilevel probability models that yield reasonable Bayesian inferences. We discuss in the context of several ongoing public health and social surveys. This work is currently openended, and we conclude with thoughts on how research could proceed to solve these problems.

Dynamics in nonlocal linear models in the FriedmannRobertsonWalker metric ; A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.

Observational semantics of the Prolog Resolution Box Model ; This paper specifies an observational semantics and gives an original presentation of the Byrd box model. The approach accounts for the semantics of Prolog tracers independently of a particular Prolog implementation. Prolog traces are, in general, considered as rather obscure and difficult to use. The proposed formal presentation of its trace constitutes a simple and pedagogical approach for teaching Prolog or for implementing Prolog tracers. It is a form of declarative specification for the tracers. The trace model introduced here is only one example to illustrate general problems relating to tracers and observing processes. Observing processes know, from observed processes, only their traces. The issue is then to be able to reconstitute, by the sole analysis of the trace, part of the behaviour of the observed process, and if possible, without any loss of information. As a matter of fact, our approach highlights qualities of the Prolog resolution box model which made its success, but also its insufficiencies.

A quantum mechanical model of the Riemann zeros ; In 1999 Berry and Keating showed that a regularization of the 1D classical Hamiltonian H xp gives semiclassically the smooth counting function of the Riemann zeros. In this paper we first generalize this result by considering a phase space delimited by two boundary functions in position and momenta, which induce a fluctuation term in the counting of energy levels. We next quantize the xp Hamiltonian, adding an interaction term that depends on two wave functions associated to the classical boundaries in phase space. The general model is solved exactly, obtaining a continuum spectrum with discrete bound states embbeded in it. We find the boundary wave functions, associated to the BerryKeating regularization, for which the average Riemann zeros become resonances. A spectral realization of the Riemann zeros is achieved exploiting the symmetry of the model under the exchange of position and momenta which is related to the duality symmetry of the zeta function. The boundary wave functions, giving rise to the Riemann zeros, are found using the RiemannSiegel formula of the zeta function. Other Dirichlet Lfunctions are shown to find a natural realization in the model.

Minimal gauge inflation ; We consider a gauge inflation model in the simplest orbifold M4 x S1Z2 with the minimal nonAbelian SU2 hidden sector gauge symmetry. The inflaton potential is fully radiatively generated solely by gauge selfinteractions. Following the virtue of gauge inflation idea, the inflaton, a part of the five dimensional gauge boson, is automatically protected by the gauge symmetry and its potential is stable against quantum corrections. We show that the model perfectly fits the recent cosmological observations, including the recent WMAP 5year data, in a wide range of the model parameters. In the perturbative regime of gauge interactions g4D 12pi R MP with the moderately compactified radius 10 R MP 100 the anticipated magnitude of the curvature perturbation power spectrum and the value of the corresponding spectral index are in perfect agreement with the recent observations. The model also predicts a large fraction of the gravitational waves, negligible nonGaussianity, and high enough reheating temperature.

Classical Solutions of Ghost Condensation Models ; Motivated by ideas obtained from both ghost condensation and gravitational Higgs mechanism, we attempt to find classical solutions in the unitary gauge in general ghost condensation models. It is shown that depending on the form of scalar fields in an action, there are three kinds of exact solutions, which are anti de Sitter spacetime, polynomially expanding universes and flat Minkowski spacetime. We briefly comment on gravitational Higgs mechanism in these models where we have massive gravitons of 5 degrees of freedom and 1 unitary scalar field NambuGoldstone boson after spontaneous symmetry breakdown of general coordinate reparametrization invariance. The models at hand are free from the problem associated with the nonunitary propagating mode.