expectation consistent approximate inference we propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation the approximation can be understood as replacing an average over the original intractable distribution with a tractable one it requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution in this way we are able to use gaussian approximations for models with discrete or bounded variables which allow us to include non trivial correlations these are neglected in many other methods we test the framework on toy benchmark problems for binary variables on fully connected graphs and 2d grids and compare with other methods such as loopy belief propagation good performance is already achieved by using single nodes as tractable substructures significant improvements are obtained when a spanning tree is used instead

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

propagation of probabilities means and variances in mixed graphical association models abstract a scheme is presented for modeling and local computation of exact probabilities means and variances for mixed qualitative and quantitative variables the models assume that the conditional distribution of the quantitative variables given the qualitative is multivariate gaussian the computational architecture is set up by forming a tree of belief universes and the calculations are then performed by local message passing between universes the asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure approximate methods when these are not appropriately fulfilled are sketched it has earlier been shown how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation thereby paving the way for exploiting probability based models as parts of realistic systems for planning and decision support the purpose of this article is to extend this computational s

relationship of second order lacunarity hurst exponent brownian motion and pattern organization abstract second order lacunarity metrics are related to the hurst exponent h fractional brownian motion with h 0 5 is used as a benchmark for quantifying patterns local versus global correlation and implications for pattern organization are discussed

the low mach number limit for the full navier stokes fourier system we study the low mach number asymptotic limit for solutions to the full navier stokes fourier system supplemented with ill prepared data and considered on an arbitrary time interval convergencetowards the incompressible navier stokes equations is shown

coexistence versus extinction in the stochastic cyclic lotka volterra model cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity see e g b kerr m a riley m w feldman and b j m bohannan nature 418 171 2002 and b kirkup and m a riley nature 428 412 2004 through analytical methods supported by numerical simulations we address this issue by studying the properties of a paradigmatic non spatial three species stochastic system namely the rock paper scissors or cyclic lotka volterra model while the deterministic approach rate equations predicts the coexistence of the species resulting in regular yet neutrally stable oscillations of the population densities we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction after long enough time two of the three species die out as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time we also discuss the implications of our results for a broad class of competing population systems

a regularity criterion for the weak solutions to the navier stokes fourier system we show that any weak solution to the full navier stokes fourier system emanating from the data belonging to the sobolev space w 3 2 remains regular as long as the velocity gradient is bounded the proof is based on the weak strong uniqueness property and parabolic a priori estimates for the local strong solutions

low mach number limit of the full navier stokes equations the low mach number limit for classical solutions of the full navier stokes equations is here studied the combined effects of large temperature variations and thermal conduction are taken into account in particular we consider general initial data the equations lead to a singular problem depending on a small scaling parameter whose linearized system is not uniformly well posed yet it is proved that solutions exist and they are uniformly bounded for a time interval which is independent of the mach number ma 0 1 the reynolds number re 1 and the peclet number pe 1 based on uniform estimates in sobolev spaces and using a theorem of g metivier s schochet 30 we next prove that the penalized terms converge strongly to zero this allows us to rigorously justify at least in the whole space case the well known computations given in the introduction of p l lions book 26

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

approximate bayes learning of stochastic differential equations we introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector gaussian processes are used as flexible models for these functions and estimates are calculated directly from dense data sets using gaussian process regression we develop an approximate expectation maximization algorithm to deal with the unobserved latent dynamics between sparse observations the posterior over states is approximated by a piecewise linearized process of the ornstein uhlenbeck type and the maximum a posteriori estimation of the drift is facilitated by a sparse gaussian process approximation

variational mean field algorithm for efficient inference in large systems of stochastic differential equations this work introduces a gaussian variational mean field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations this new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating gaussian process a restriction of the moment equations to piecewise polynomial functions over time dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden markov models the algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well known inference methodologies

fluctuations and oscillations in a simple epidemic model we show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behavior in the endemic phase in a large parameter range the oscillations are due to resonant amplification of stochastic fluctuations a general mechanism first reported for predator prey dynamics in a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations this effect is apparent in simulations of the stochastic process in systems of variable size and can be understood from the phase diagram of the deterministic pair approximation equations the two mechanisms combined play a central role in explaining the ubiquity of oscillatory behavior in real data and in simulation results of epidemic and other related models

expectation propagation for continuous time stochastic processes we consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints we cast the problem in a bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference giving rise to an expectation propagation type algorithm for non linear diffusion processes this is achieved by leveraging moment closure approximations we then show how the approximation can be extended to a wide class of discrete state markov jump processes by making use of the chemical langevin equation our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems

a rigorous derivation of the chemical master equation it is widely believed that the chemical master equation has no rigorous microphysical basis and hence no a priori claim to validity this view is challenged here through arguments purporting to show that the chemical master equation is exact for any gas phase chemical system that is kept well stirred and thermally equilibrated

a suggested generalization for the lacunarity index abstract nowadays lacunarity is a well accepted concept to complement fractality studies of complex sets lacunarity features are used to assess the largeness of gaps or holes of complex signals and images as it stands the lacunarity analysis used is an index averaging the behavior of small and large size structures in a given set the aim of this work is to propose a generalized lacunarity concept on the basis of generalized moments in this form the lacunarity index depending on a discrimination parameter is oriented to quantify lacunarity associated with objects of different size textbook and real images are used to illustrate the ability of the generalized lacunarity index for displaying interesting features of real complex sets

gaussian processes for classification mean field algorithms we derive a mean field algorithm for binary classification with gaussian processes that is based on the tap approach originally proposed in statistical physics of disordered systems the theory also yields an approximate leave one out estimator for the generalization error which is computed with no extra computational cost we show that from the tap approach it is possible to derive both a simpler naive mean field theory and support vector machines svms as limiting cases for both mean field algorithms and support vector machines simulation results for three small benchmark data sets are presented they show that one may get state of the art performance by using the leave one out estimator for model selection and the built in leave one out estimators are extremely precise when compared to the exact leave one out estimate the second result is taken as strong support for the internal consistency of the mean field approach

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

3d unsteady navier stokes problem with memory and subdifferential boundary condition abstract we consider a mathematical model which describes the motion of a 3d unsteady fluid flow governed by the navier stokes system and subjected to mixed boundary conditions with a given velocity on one part of the boundary and nonlinear slip conditions with a memory term reminiscent of coulomb s friction law on the other part we establish first some regularity properties and estimates for a simplified model then we prove the existence of a solution to our problem by using a successive approximation technique and compactness arguments based on helly s theorem for the velocity field

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

a suggested lacunarity expression for sierpinski carpets a suggested approximate expression for lacunarity is proposed some numerical investigations show that the old expression fails in describing the homogeneity of elimination for some sierpinski carpets

low mach number limit for the non isentropic navier stokes equations abstract we study the low mach number limit of the local in time solutions to the compressible navier stokes equations with zero heat conductivity coefficient as the mach number tends to zero a uniform existence result for the one dimensional initial boundary value problem is proved provided that the initial data are well prepared in the sense that the temporal derivatives up to order two are bounded initially

self referred approach to lacunarity this paper describes an approach to lacunarity which adopts the pattern under analysis as the reference for the sliding window procedure the superiority of such a scheme with respect to more traditional methodologies especially when dealing with finite size objects is established and illustrated through applications to diffusion limited aggregation pattern characterization it is also shown that given the enhanced accuracy and sensitivity of this scheme the shape of the window becomes an important parameter with advantage for circular windows

existence for non isothermal fluid flows with tresca s friction and cattaneo s heat law abstract we consider a two dimensional non isothermal incompressible fluid flow involving heat transfer and friction the problem is described by the non stationary navier stokes system and by the hyperbolic heat equation derived from cattaneo s heat flux law which allows to overcome the paradox of infinite propagation speed we assume a strong coupling due to temperature dependent viscosity and velocity dependent heat capacity moreover we consider tresca s friction boundary conditions for the flow we prove an existence result for this problem by using a fixed point technique

zero relaxation and dissipation limits for hyperbolic conservation laws we are interested in hyperbolic systems of conservation laws with relaxation and dissipation particularly the zero relaxation limit such a limit is of interest in several physical situations including gas flow near thermo equilibrium kinetic theory with small mean free path and viscoelasticity with vanishing memory in this article we study hyperbolic systems of two conservation laws with relaxation for the stable case where the equilibrium speed is subcharacteristic with respect to the frozen speeds we illustrate for a model in viscoelasticity that no oscillation develops for the nonlinear system in the zero relaxation limit for the marginally stable case where the equilibrium speed may equal one of the frozen speeds we show for a model in phase transitions that no oscillation arises when the dissipation is present and goes to zero more slowly than the relaxation our analysis includes the construction of suitable entropy pairs to derive energy estimates we need such energy estimates not only for the compactness properties but also for the deviation from the equilibrium of the solutions for the relaxation systems the theory of compensated compactness is then applied to study the oscillation in the zero relaxation limit 1993 john wiley sons inc

fully nonparametric estimation of scalar diffusion models we propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process we show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter the asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens we prove almost sure consistency and weak convergence to mixtures of normal laws where the mixing variates depend on the chronological local time of the underlying diffusion process that is the random time spent by the process in the vicinity of a generic spatial point the estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes

non isothermal navier stokes system with mixed boundary conditions and friction law uniqueness and regularity properties abstract we consider an unsteady non isothermal fluid flow subjected to non homogeneous dirichlet conditions on a part of the boundary and tresca s friction law on the other part for this problem an existence result has been proved recently in boukrouche et al 2014 but uniqueness has been left as an open question starting from the approximation of the problem based on a regularization of the free boundary condition due to friction combined with a special penalty method we establish some sharp a priori estimates leading to better regularity properties for the velocity field and to the uniqueness of the solutions finally we study the regularity of the pressure field and of the stress tensor

low mach number limit of the full compressible navier stokes maxwell system abstract this paper deals with the low mach number limit of the full compressible navier stokes maxwell system it is justified rigorously that for the well prepared initial data the solutions of the full compressible navier stokes maxwell system converge to that of the incompressible navier stokes maxwell system as the mach number tends to zero

nonparametric estimation of diffusions a differential equations approach we consider estimation of scalar functions that determine the dynamics of diffusion processes it has been recently shown that nonparametric maximum likelihood estimation is ill posed in this context we adopt a probabilistic approach to regularize the problem by the adoption of a prior distribution for the unknown functional a gaussian prior measure is chosen in the function space by specifying its precision operator as an appropriate differential operator we establish that a bayesian gaussian conjugate analysis for the drift of one dimensional nonlinear diffusions is feasible using high frequency data by expressing the loglikelihood as a quadratic function of the drift with sufficient statistics given by the local time process and the end points of the observed path computationally efficient posterior inference is carried out using a finite element method we embed this technology in partially observed situations and adopt a data augmentation approach whereby we iteratively generate missing data paths and draws from the unknown functional our methodology is applied to estimate the drift of models used in molecular dynamics and financial econometrics using high and low frequency observations we discuss extensions to other partially observed schemes and connections to other types of nonparametric inference

efficient statistical inference for stochastic reaction processes we address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available using an asymptotic system size expansion for the backward equation we derive an efficient approximation for this problem we demonstrate the validity of our approach on model systems and generalize our method to the case when some state variables are not observed

low mach number limit for the full compressible navier stokes equations with cattaneo s heat transfer law abstract in this paper we study the low mach number limit for the full compressible navier stokes equations with cattaneo s heat transfer law it is rigorously justified that in the framework of classical solutions with small density temperature and heat flux variations the solutions of the full compressible navier stokes equations with cattaneo s heat transfer law converge to that of the incompressible navier stokes equations as the mach number tends to zero

low mach number limit of full navier stokes equations in a 3d bounded domain abstract this paper studies the low mach number limit of the full compressible navier stokes equations in a three dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the neumann boundary condition respectively the uniform estimates in the mach number for the strong solutions are derived in a short time interval provided that the initial density and temperature are close to the constant states and satisfy the bounded derivative conditions thus the solutions of the full compressible navier stokes equations converge to the one of the isentropic incompressible navier stokes equations as the mach number vanishes