exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

symmetric simple exclusion process with free boundaries we consider the one dimensional symmetric simple exclusion process with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle at a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate independently the rightmost particle dies we prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem

exact time dependent correlation functions for the symmetric exclusion process with open boundary as a simple model for single file diffusion of hard core particles we investigate the one dimensional symmetric exclusion process we consider an open semi infinite system where one end is coupled to an external reservoir of constant density rho and which initially is in a nonequilibrium state with bulk density rho 0 we calculate the exact time dependent two point density correlation function c k l t identical with and the mean and variance of the integrated average net flux of particles n t n 0 that have entered or left the system up to time t we find that the boundary region of the semi infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient the symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal time two point correlation functions some implications for the relaxational dynamics of entangled polymers and for single file diffusion in colloidal systems are discussed

exact results for one dimensional cellular automata with different types of updates we study two common types of time noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions we first construct the stationary states using the matrix product formalism this construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates using this connection we derive explicit relations between the densities and correlation functions for these different stationary states

symplectic tori in rational elliptic surfaces let e 1 p denote the rational elliptic surface with a single multiple fiber fp of multiplicity p we construct an infinite family of homologous non isotopic symplectic tori representing the primitive 2 dimensional homology class fp in e 1 p when p 1 as a consequence we get infinitely many non isotopic symplectic tori in the fiber class of the rational elliptic surface open image in new window we also show how these tori can be non isotopically embedded as homologous symplectic submanifolds in other symplectic 4 manifolds

lattice gas models in contact with stochastic reservoirs local equilibrium and relaxation to the steady state extending the results of a previous work we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials we establish here the local equilibrium structure of the stationary measures for these models further we prove as a law of large numbers that the time dependent empirical density field converges to a deterministic limit process which is the solution of the initial boundary value problem for a nonlinear diffusion equation

non isotopic symplectic tori in the same homology class for any pair of integers n 1 and q 2 we construct an infinite family of mutually non isotopic symplectic tori representing the homology class q f of an elliptic surface e n where f is the homology class of the fiber we also show how such families can be non isotopically and symplectically embedded into a more general class of symplectic 4 manifolds

maximum correntropy criterion for robust face recognition in this paper we present a sparse correntropy framework for computing robust sparse representations of face images for recognition compared with the state of the art l1norm based sparse representation classifier src which assumes that noise also has a sparse representation our sparse algorithm is developed based on the maximum correntropy criterion which is much more insensitive to outliers in order to develop a more tractable and practical approach we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state of the art methods in particular it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic roc curves while the computational cost is much lower than the src algorithms

the c loss function for pattern classification this paper presents a new loss function for neural network classification inspired by the recently proposed similarity measure called correntropy we show that this function essentially behaves like the conventional square loss for samples that are well within the decision boundary and have small errors and l0 or counting norm for samples that are outliers or are difficult to classify depending on the value of the kernel size parameter the proposed loss function moves smoothly from convex to non convex and becomes a close approximation to the misclassification loss ideal 0 1 loss we show that the discriminant function obtained by optimizing the proposed loss function in the neighborhood of the ideal 0 1 loss function to train a neural network is immune to overfitting more robust to outliers and has consistent and better generalization performance as compared to other commonly used loss functions even after prolonged training the results also show that it is a close competitor to the svm since the proposed method is compatible with simple gradient based online learning it is a practical way of improving the performance of neural network classifiers highlightswe propose a new classification method the method is based on the recently proposed similarity measure called correntropy the method is robust against overfitting and less sensitive to system parameters we obtain better performance as compared to several conventional classifiers

current fluctuations of the one dimensional symmetric simple exclusion process with step initial condition for the symmetric simple exclusion process on an infinite line we calculate exactly the fluctuations of the integrated current qt during time t through the origin when in the initial condition the sites are occupied with density a on the negative axis and with density b on the positive axis all the cumulants of qt grow like sqrt t in the range where q t sim sqrt t the decay exp qt3 t of the distribution of qt is non gaussian our results are obtained using the bethe ansatz and several identities derived recently by tracy and widom for exclusion processes on the infinite line

ramp loss linear programming support vector machine the ramp loss is a robust but non convex loss for classification compared with other non convex losses a local minimum of the ramp loss can be effectively found the effectiveness of local search comes from the piecewise linearity of the ramp loss motivated by the fact that the l1 penalty is piecewise linear as well the l1 penalty is applied for the ramp loss resulting in a ramp loss linear programming support vector machine ramp lpsvm the proposed ramp lpsvm is a piecewise linear minimization problem and the related optimization techniques are applicable moreover the l1 penalty can enhance the sparsity in this paper the corresponding misclassification error and convergence behavior are discussed generally the ramp loss is a truncated hinge loss therefore ramp lpsvm possesses some similar properties as hinge loss svms a local minimization algorithm and a global search strategy are discussed the good optimization capability of the proposed algorithms makes ramp lpsvm perform well in numerical experiments the result of ramp lpsvm is more robust than that of hinge svms and is sparser than that of ramp svm which consists of the k penalty and the ramp loss

knots links and 4 manifolds in this paper we investigate the relationship between isotopy classes of knots and links in s and the di eomorphism types of homeomorphic smooth 4 manifolds as a corollary of this initial investigation we begin to uncover the surprisingly rich structure of di eomorphism types of manifolds homeomorphic to the k3 surface in order to state our theorems we need to view the seiberg witten invariant of a smooth 4 manifold as a multivariable laurent polynomial to do this recall that the seiberg witten invariant of a smooth closed oriented 4 manifold x with b2 x 1 is an integer valued function which is de ned on the set of spinc structures over x cf w km ko1 t1 in case h1 x z has no 2 torsion which will be the situation in this paper there is a natural identi cation of the spinc structures of x with the characteristic elements of h2 x z in this case we view the seiberg witten invariant as

small deviations from local equilibrium for a process which exhibits hydrodynamical behavior i the symmetric simple exclusion process on with sources at l l e is considered the stationary measure l is studied in the limit asl diverges the first order correction to its limit is proven to be of order 1 l and it is explicitly computed the result is in agreement with the analysis of the model from the hydrodynamical point of view initiated in ref 1

exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra we study the partially asymmetric exclusion process with open boundaries we generalize the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid for all values of the asymmetry parameter q due to the relationship between the matrix algebra and the q deformed quantum harmonic oscillator algebra we find that q hermite polynomials along with their orthogonality properties and generating functions are of great utility we employ two distinct sets of q hermite polynomials one for q 1 it turns out that these correspond to two distinct regimes the previously studied case of forward bias q 1 where the boundaries support a current opposite in direction to the bulk bias for the forward bias case we confirm the previously proposed phase diagram whereas the case of reverse bias produces a new phase in which the current decreases exponentially with system size

correntropy properties and applications in non gaussian signal processing the optimality of second order statistics depends heavily on the assumption of gaussianity in this paper we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure a close relationship between correntropy and m estimation is established connections and differences between correntropy and kernel methods are presented as such correntropy has vastly different properties compared with second order statistics that can be very useful in non gaussian signal processing especially in the impulsive noise environment examples are presented to illustrate the technique

hydrodynamics of stationary non equilibrium states for some stochastic lattice gas models we consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials the unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non reversible we study the structure of the stationary measure in the hydrodynamic limit as the microscopic lattice size goes to infinity in particular we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by fick s law

one dimensional partially asymmetric simple exclusion process with open boundaries orthogonal polynomials approach the stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered the so called matrix product ansatz is employed this enables us to construct the stationary state in the form of the product of the matrices d and e noticing the fact that the matrix c d e for the model is related to certain q orthogonal polynomials the model is analysed for a wide range of parameters the current and the correlation length are evaluated in the thermodynamic limit it turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

non equilibrium current fluctuations in stochastic lattice gases we study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles more precisely we establish a large deviation principle for a space time fluctuation j of the empirical current with a rate functional i j we then estimate the probability of a fluctuation of the average current over a large time interval this probability can be obtained by solving a variational problem for the functional i we discuss several possible scenarios interpreted as dynamical phase transitions for this variational problem they actually occur in specific models we finally discuss the time reversal properties of i and derive a fluctuation relationship akin to the gallavotti cohen theorem for the entropy production

entropy of open lattice systems we investigate the behavior of the gibbs shannon entropy of the stationary nonequilibrium measure describing a one dimensional lattice gas of l sites with symmetric exclusion dynamics and in contact with particle reservoirs at different densities in the hydrodynamic scaling limit l the leading order o l behavior of this entropy has been shown by bahadoran to be that of a product measure corresponding to strict local equilibrium we compute the first correction which is o 1 the computation uses a formal expansion of the entropy in terms of truncated correlation functions for this system the k th such correlation is shown to be o l k 1 this entropy correction depends only on the scaled truncated pair correlation which describes the covariance of the density field it coincides in the large l limit with the corresponding correction obtained from a gaussian measure with the same covariance

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

duality and exact correlations for a model of heat conduction we study a model of heat conduction with stochastic diffusion of energy we obtain a dual particle process which describes the evolution of all the correlation functions an exact expression for the covariance of the energy exhibits long range correlations in the presence of a current we discuss the formal connection of this model with the simple symmetric exclusion process

lagrangian tori in homotopy elliptic surfaces let e 1 k denote the symplectic four manifold homotopy equivalent to the rational elliptic surface corresponding to a fibred knot k in s 3 constructed by r fintushel and r j stern in 1998 we construct a family of nullhomologous lagrangian tori in e 1 k and prove that infinitely many of these tori have complements with mutually non isomorphic fundamental groups if the alexander polynomial of k has some irreducible factor which does not divide t n 1 for any positive integer n we also show how these tori can be non isotopically embedded as nullhomologous lagrangian submanifolds in other symplectic 4 manifolds

energy profile fluctuations in dissipative nonequilibrium stationary states the exact large deviation function ldf for the fluctuations of the energy density field is computed for a chain of ising or more generally potts spins driven by a zero temperature dissipative glauber dynamics and sustained in a nontrivial stationary regime by an arbitrary energy injection mechanism at the boundary of the system it is found that this ldf is independent of the dynamical details of the energy injection and that the energy fluctuations unlike conservative systems in a nonequilibrium state are not spatially correlated in the stationary regime

exact large deviation functional of a stationary open driven diffusive system the asymmetric exclusion process we consider the asymmetric exclusion process asep in one dimension on sites i 1 n in contact at sites i 1 and i n with infinite particle reservoirs at densities a and b as a and b are varied the typical macroscopic steady state density profile x x a b obtained in the limit n l b a exhibits shocks and phase transitions here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile rho x text p n rho x sim exp l mathcal f a b rho x rho a rho b so that mathcal f is the large deviation functional a quantity similar to the free energy of equilibrium systems we find as in the symmetric purely diffusive case q 1 treated in an earlier work that mathcal f is in general a non local functional of x unlike the symmetric case however the asymmetric case exhibits ranges of the parameters for which mathcal f rho x is not convex and others for which mathcal f rho x has discontinuities in its second derivatives at x x in the latter ranges the fluctuations of order 1 sqrt n in the density profile near x are then non gaussian and cannot be calculated from the large deviation function

a robust regression framework with laplace kernel induced loss this work proposes a robust regression framework with nonconvex loss function two regression formulations are presented based on the laplace kernel induced loss lk loss moreover we illustrate that the lk loss function is a nice approximation for the zero norm however nonconvexity of the lk loss makes it difficult to optimize a continuous optimization method is developed to solve the proposed framework the problems are formulated as dc difference of convex functions programming the corresponding dc algorithms dcas converge linearly furthermore the proposed algorithms are applied directly to determine the hardness of licorice seeds using near infrared spectral data with noisy input experiments in eight spectral regions show that the proposed methods improve generalization compared with the traditional support vector regressions svr especially in high frequency regions experiments on several benchmark data sets demonstrate that the proposed methods achieve better results than the traditional regression methods in most of data sets we have considered

large deviation probabilities for correlated gaussian processes and intermittent dynamical systems in its classical version the theory of large deviations makes quantitative statements about the probability of outliers when estimating time averages if time series data are identically independently distributed we study large deviation probabilities ldps for time averages in short and long range correlated gaussian processes and show that long range correlations lead to subexponential decay of ldps a particular deterministic intermittent map can depending on a control parameter also generate long range correlated time series we illustrate numerically in agreement with the mathematical literature that this type of intermittency leads to a power law decay of ldps the power law decay holds irrespective of whether the correlation time is finite or infinite and hence irrespective of whether the central limit theorem applies or not

nonequilibrium measures which exhibit a temperature gradient study of a model we give some rules to define measures which could describe heat flow in homogeneous crystals we then study a particular model which is explicitly solvable the one dimensional nearest neighborhood ising model we analyze two cases in the first one the spins at the two boundaries interact with reservoirs at different temperatures in the thermodynamical limit the measure we introduce converges locally to gibbs measures and a temperature profile is so derived we obtain an explicit expression for the thermal conductivity coefficient which depends on the temperature in the second case we study the asymptotic behavior starting from an initial state in which each half of the space is at a different temperature we find again a temperature profile which asymptotically obeys the heat equation with the thermal conductivity coefficient previously derived from a mathematical point of view the analysis of the invariant measure is made possible by studying a time reversed process related to a graphical representation of an associated process this provides us with an explicit formula for then fold correlation function and we study the limiting behavior using both this representation for proving an exchangeability result and a donsker type spacetime renormalization procedure

fuzzy support vector machines a support vector machine svm learns the decision surface from two distinct classes of the input points in many applications each input point may not be fully assigned to one of these two classes in this paper we apply a fuzzy membership to each input point and reformulate the svms such that different input points can make different contributions to the learning of decision surface we call the proposed method fuzzy svms fsvms

statistical behavior and consistency of classification methods based on convex risk minimization we study how closely the optimal bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function the measurement of closeness is characterized by the loss function used in the estimation we show that such a classification scheme can be generally regarded as a nonmaximum likelihood conditional in class probability estimate and we use this analysis to compare various convex loss functions that have appeared in the literature furthermore the theoretical insight allows us to design good loss functions with desirable properties another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization this study sheds light on the good performance of some recently proposed linear classification methods including boosting and support vector machines it also shows their limitations and suggests possible improvements

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

finite size corrections to the large deviation function of the density in the one dimensional symmetric simple exclusion process the symmetric simple exclusion process is one of the simplest out of equilibrium systems for which the steady state is known its large deviation functional of the density has been computed in the past both by microscopic and macroscopic approaches here we obtain the leading finite size correction to this large deviation functional the result is compared to the similar corrections for equilibrium systems

large deviations for a stochastic model of heat flow we investigate a one dimensional chain of 2n harmonic oscillators in which neighboring sites have their energies redistributed randomly the sites n and n are in contact with thermal reservoirs at different temperature and kipnis et al j statist phys 27 65 74 1982 proved that this model satisfies fourier s law and that in the hydrodynamical scaling limit when n the stationary state has a linear energy density profile bar theta u u 1 1 we derive the large deviation function s u for the probability of finding in the stationary state a profile u different from bar theta u the function s has striking similarities to but also large differences from the corresponding one of the symmetric exclusion process like the latter it is nonlocal and satisfies a variational equation unlike the latter it is not convex and the gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state we also briefly discuss more general models and find the features common in these two and other models whose s is known

existence of nonequilibrium steady state for a simple model of heat conduction this paper contains rigorous results for a simple stochastic model of heat conduction similar to the kmp knipnis marchiori presutti model but with possibly energy dependent interaction rates we prove the existence and uniqueness of nonequilibrium steady states their relation to lebesgue measure and exponential convergence to steady states from suitable initial conditions

direct evaluation of dynamical large deviation rate functions using a variational ansatz we describe a simple form of importance sampling designed to bound and compute large deviation rate functions for time extensive dynamical observables in continuous time markov chains we start with a model defined by a set of rates and a time extensive dynamical observable we construct a reference model a variational ansatz for the behavior of the original model conditioned on atypical values of the observable direct simulation of the reference model provides an upper bound on the large deviation rate function associated with the original model an estimate of the tightness of the bound and if the ansatz is chosen well the exact rate function the exact rare behavior of the original model does not need to be known in advance we use this method to calculate rate functions for currents and counting observables in a set of network and lattice models taken from the literature straightforward ansatze yield bounds that are tighter than bounds obtained from level 2 5 of large deviations via approximations that involve uniform scalings of rates we show how to correct these bounds in order to recover the rate functions exactly our approach is complementary to more specialized methods and offers a physically transparent framework for approximating and calculating the likelihood of dynamical large deviations

current reservoirs in the simple exclusion process we consider the symmetric simple exclusion process in the interval n n with additional birth and death processes respectively on n k n k 0 and n n k the exclusion is speeded up by a factor n2 births and deaths by a factor n assuming propagation of chaos a property proved in a companion paper de masi et al http arxiv org abs 1104 3447 we prove convergence in the limit n to the linear heat equation with dirichlet condition on the boundaries the boundary conditions however are not known a priori they are obtained by solving a non linear equation the model simulates mass transport with current reservoirs at the boundaries and the fourier law is proved to hold

boundary driven zero range processes in random media the stationary states of boundary driven zero range processes in random media with quenched disorder are examined and the motion of a tagged particle is analyzed for symmetric transition rates also known as the random barrier model the stationary state is found to be trivial in absence of boundary drive out of equilibrium two further cases are distinguished according to the tail of the disorder distribution for strong disorder the fugacity profiles are found to be governed by the paths of normalized stable subordinators the expectations of integrated functions of the tagged particle position are calculated for three types of routes

current fluctuations in one dimensional diffusive systems with a step initial density profile we show how to apply the macroscopic fluctuation theory mft of bertini de sole gabrielli jona lasinio and landim to study the current fluctuations of diffusive systems with a step initial condition we argue that one has to distinguish between two ways of averaging the annealed and the quenched cases depending on whether we let the initial condition fluctuate or not although the initial condition is not a steady state the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem we show how the equations of the mft can be solved in the case of non interacting particles the symmetry of these equations can be used to deduce the distribution of the current for several other models from its knowledge derrida and gerschenfeld in j stat phys 136 1 15 2009 for the symmetric simple exclusion process in the range where the integrated current q t sim sqrt t we show that the non gaussian decay exp q t 3 t of the distribution of q t is generic

nonconvex online support vector machines in this paper we propose a nonconvex online support vector machine svm algorithm lasvm nc based on the ramp loss which has the strong ability of suppressing the influence of outliers then again in the online learning setting we propose an outlier filtering mechanism lasvm i based on approximating nonconvex behavior in convex optimization these two algorithms are built upon another novel svm algorithm lasvm g that is capable of generating accurate intermediate models in its iterative steps by leveraging the duality gap we present experimental results that demonstrate the merit of our frameworks in achieving significant robustness to outliers in noisy data classification where mislabeled training instances are in abundance experimental evaluation shows that the proposed approaches yield a more scalable online svm algorithm with sparser models and less computational running time both in the training and recognition phases without sacrificing generalization performance we also point out the relation between nonconvex optimization and min margin active learning

temporal asymmetry of fluctuations in the nonequilibrium fpu model abstract the large deviation theory recently developed by bertini de sole gabrielli jona lasinio and landim is meant to extend the onsager machlup theory to nonequilibrium phenomena and predicts that the fluctuations of densities and currents in certain stochastic processes are not symmetric with respect to the time reversal operation in this paper several notions of fluctuations are introduced for deterministic systems and it is observed that temporally asymmetric not necessarily large fluctuations are ubiquitous even in the context of time reversal invariant dynamics of particle systems in nonequilibrium states to illustrate these ideas the nonequilibrium fpu chain devised by lepri livi and politi is studied in detail

large deviation functional of the weakly asymmetric exclusion process we obtain the large deviation functional of a density profile for the asymmetric exclusion process of l sites with open boundary conditions when the asymmetry scales like l 1 we recover as limiting cases the expressions derived recently for the symmetric ssep and the asymmetric asep cases in the asep limit the nonlinear differential equation one needs to solve can be analysed by a method which resembles the wkb method

numerical simulation of polynomial speed convergence phenomenon we provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for markov processes the hybrid method that we introduce is based on the coupling technique and renewal theory we propose to replace some estimates in classical results about the ergodicity of markov processes by numerical simulations when the corresponding analytical proof is difficult after that all remaining conclusions can be derived from rigorous analysis then we apply our results to seek numerical justification for the ergodicity of two 1d microscopic heat conduction models the mixing rate of these two models are expected to be polynomial but very difficult to prove in both examples our numerical results match the expected polynomial mixing rate well

dynamical large deviations for the boundary driven weakly asymmetric exclusion process 1 introduction the analysis of the large deviations is asymptotic as the number of degrees of freedom diverges for the stationary nonequilibrium states of interacting particle systems have recently proved to be an important step in the physical description of such states and a rich source of mathematical problems referring to 4 8 for two recent reviews on this topic we briefly outline its basic points we discuss only stochastic lattice gases for which the underlying random fluctuations ensure the necessary ergodicity for a rigorous analysis the stationary nonequilibrium states are characterized by a flow of mass through the system and the corresponding dynamics are not reversible the main difference with respect to reversible equilibrium states follows in equilibrium the invariant measure which determines the thermodynamic properties is given for free by the gibbs distribution specified by the hamiltonian on the contrary in nonequilibrium states the construction of the stationary state requires the solution of a dynamical problem since we are interested only in the macroscopic description only the thermodyamic observables are relevant for lattice gases there is only one of such observable which is the empirical density in equilibrium states the thermodynamic functional like the free energy can then be identified 6 22 24 with the large deviation rate function for the empirical density when the

large deviations in weakly interacting boundary driven lattice gases one dimensional boundary driven lattice gases with local interactions are studied in the weakly interacting limit the density profiles and the correlation functions are calculated to first order in the interaction strength for zero range and short range processes differing only in the specifics of the detailed balance dynamics furthermore the effective free energy large deviation function and the integrated current distribution are also found to this order from the former we find that the boundary drive generates long range correlations only for the short range dynamics while the latter provides support to an additivity principle recently proposed by bodineau and derrida

antishocks in the asep with open boundaries conditioned on low current we study the time evolution of the asep on a finite lattice with l sites and open boundaries conditioned on an atypically low current up to a finite time t by an exact computation we show that for a one parameter family of boundary densities and a special value of the conditioned current an initial product measure with an antishock at site k evolves into a convex combination of such antishocks at sites k the weights p k t k 0 are shown to be the transition probabilities of simple biased random walk with reflecting boundaries we compute explicitly these transition rates our result implies that the antishock remains microscopically stable under the locally conditioned dynamics

robust truncated hinge loss support vector machines the support vector machine svm has been widely applied for classification problems in both machine learning and statistics despite its popularity however svm has some drawbacks in certain situations in particular the svm classifier can be very sensitive to outliers in the training sample moreover the number of support vectors svs can be very large in many applications to circumvent these drawbacks we propose the robust truncated hinge loss svm rsvm which uses a truncated hinge loss the rsvm is shown to be more robust to outliers and to deliver more accurate classifiers using a smaller set of svs than the standard svm our theoretical results show that the rsvm is fisher consistent even when there is no dominating class a scenario that is particularly challenging for multicategory classification similar results are obtained for a class of margin based classifiers

robust support vector machines based on the rescaled hinge loss function abstract the support vector machine svm is a popular classifier in machine learning but it is not robust to outliers in this paper based on the correntropy induced loss function we propose the rescaled hinge loss function which is a monotonic bounded and nonconvex loss that is robust to outliers we further show that the hinge loss is a special case of the proposed rescaled hinge loss then we develop a new robust svm based on the rescaled hinge loss after using the half quadratic optimization method we find that the new robust svm is equivalent to an iterative weighted svm which can help explain the robustness of iterative weighted svm from a loss function perspective experimental results confirm that the new robust svm not only performs better than svm and the existing robust svms on the datasets that have outliers but also presents better sparseness than svm

on the convergence of entropy for stationary exclusion processes with open boundaries we prove that for a wide class of stochastic lattice gases in contact with reservoirs despite long range correlations the leading order term of the gibbs shannon entropy in the nonequilibrium stationary state is given by the local equilibrium entropy

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

current large deviations for asymmetric exclusion processes with open boundaries we study the large deviation functional of the current for the weakly asymmetric simple exclusion process in contact with two reservoirs we compare this functional in the large drift limit to the one of the totally asymmetric simple exclusion process in particular to the jensen varadhan functional conjectures for generalizing the jensen varadhan functional to open systems are also stated

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

static large deviations for a reaction diffusion model we consider the superposition of a symmetric simple exclusion dynamics speeded up in time with a spin flip dynamics in a one dimensional interval with periodic boundary conditions we prove the large deviations principle for the empirical measure under the stationary state we deduce from this result that the stationary state is concentrated on the stationary solutions of the hydrodynamic equation which are stable

dissipation and large thermodynamic fluctuations the results of recent work of kipnis olla and varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation including non equilibrium steady states as a fluctuation dissipation hypothesis the basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation it is shown that this hypothesis leads to a nonlinear version of onsager machlup fluctuation theory that had previously been proposed by graham a direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints onsager s principle of least dissipation following graham the theory leads also to a generalized potential analogous to an equilibrium free energy for the nonequilibrium steady state and an associated static variational principle finally a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large deviations theory on a formal analogy with the results of freidlin and wentzell for finite dimensional systems