shape preserving local histogram modification a novel approach for shape preserving contrast enhancement is presented in this paper contrast enhancement is achieved by means of a local histogram equalization algorithm which preserves the level sets of the image this basic property is violated by common local schemes thereby introducing spurious objects and modifying the image information the scheme is based on equalizing the histogram in all the connected components of the image which are defined based both on the grey values and spatial relations between pixels in the image and following mathematical morphology constitute the basic objects in the scene we give examples for both grey value and color images

ornstein zernike theory for finite range ising models above t c we derive a precise ornstein zernike asymptotic formula for the decay of the two point function 0 x in the general context of finite range ising type models on d the proof relies in an essential way on the a priori knowledge of the strict exponential decay of the two point function and by the sharp characterization of phase transition due to aizenman barsky and fernandez goes through in the whole of the high temperature region c as a byproduct we obtain that for every c the inverse correlation length is an analytic and strictly convex function of direction

exact histogram specification while in the continuous case statistical models of histogram equalization specification would yield exact results their discrete counterparts fail this is due to the fact that the cumulative distribution functions one deals with are not exactly invertible otherwise stated exact histogram specification for discrete images is an ill posed problem invertible cumulative distribution functions are obtained by translating the problem in a k dimensional space and further inducing a strict ordering among image pixels the proposed ordering refines the natural one experimental results and statistical models of the induced ordering are presented and several applications are discussed image enhancement normalization watermarking etc

on the relaxation properties of stochastic ginzburg landau type models abstract considering the project of studying the basic properties of commonly used stochastic nonlinear dynamical systems we investigate and present new properties of the relaxation to equilibrium of stochastic ginzburg landau type models with polynomial interaction with nonlocal nonlinear terms in our approach we map the initial stochastic model on a imaginary time quantum field theory we show that with a suitable nonlocality a two particle bound state appears below the two particle threshold even if all the coefficients in the polynomial interaction are positive the existence of such a bound state changes the relaxation rate to equilibrium and so it is an experimentally observable effect of physical interest moreover we show that the bound state masses are sensitive to changes in the rate of nonlocality which may favor other phenomena related to the low lying spectrum of the dynamics generator our results involve a perturbative analysis supported by previous rigorous results in the computation of the bound state mass we use a bethe salpeter equation in the ladder approximation

an energy based model for the image edge histogram specification problem in this correspondence we present an original energy based model that achieves the edge histogram specification of a real input image and thus extends the exact specification method of the image luminance or gray level distribution recently proposed by coltuc et al our edge histogram specification approach is stated as an optimization problem in which each edge of a real input image will tend iteratively toward some specified gradient magnitude values given by a target edge distribution or a normalized edge histogram possibly estimated from a target image to this end a hybrid optimization scheme combining a global and deterministic conjugate gradient based procedure and a local stochastic search using the metropolis criterion is proposed herein to find a reliable solution to our energy based model experimental results are presented and several applications follow from this procedure

anderson parabolic model for a quasi stationary medium we study the anderson parabolic model for a random medium which is a product of an i i d space like random field and a white noise the model has long range space time correlations and is intermediate between the stationary case and the turbulent one which were studied in previous works under some natural assumptions on the distribution of the space potential we prove existence and uniqueness and derive the long time asymptotics for the annealed moments and the semi annealed ones for which expectation is taken only w r t the white noise a conjecture for the fully quenched case is discussed on a simplified model

image enhancement by entropy maximization and quantization resolution upconversion this article introduces a new contrast enhancement algorithm of tone preserving entropy maximization its design objective is to present the maximal amount of information content in the enhanced image or being optimal in an information theoretical sense while preventing the loss of tone continuity the resulting optimization problem can be graph theoretically modeled as the construction of the k edges maximum weight path and it can be solved efficiently by dynamic programming moreover the proposed algorithm is made more effective by being combined with a preprocess of image restoration that aims to correct quantization errors caused by the analog to digital conversion of image signals empirical evidences are provided to demonstrate the superior visual quality obtained by the new image enhancement algorithm

a novel 3 d color histogram equalization method with uniform 1 d gray scale histogram the majority of color histogram equalization methods do not yield uniform histogram in gray scale after converting a color histogram equalized image into gray scale the contrast of the converted image is worse than that of an 1 d gray scale histogram equalized image we propose a novel 3 d color histogram equalization method that produces uniform distribution in gray scale histogram by defining a new cumulative probability density function in 3 d color space test results with natural and synthetic images are presented to compare and analyze various color histogram equalization algorithms based upon 3 d color histograms we also present theoretical analysis for nonideal performance of existing methods

asymptotics of even even correlations in the ising model we consider finite range ferromagnetic ising models on mathbb z d in the regime beta beta mathrm scriptscriptstyle c we analyze the behavior of the prefactor to the exponential decay of mathrm cov sigma a sigma b for arbitrary finite sets a and b of even cardinality as the distance between a and b diverges

curve fitting and identification of physical spectra a modification of the trust region gauss newton method for the identification of physical spectra is described and analysed local convergence results are presented

one particle subspaces in the stochastic xy model we study the spectrum of the generatorh of the glauber dynamics for a model of planar rotators on a lattice in the case of a high temperature 1 we construct two so called one particle subspacesh forh and describe the spectrum of the generator in these subspaces as a consequence we find time asymptotics of the correlations for the glauber dynamics

large deviations for the 2d ising model a lower bound without cluster expansions we show that a lower large deviation bound for the block spin magnetization in the 2d ising model can be pushed all the way forward toward its correct wulff value for all c

large deviations and continuum limit in the 2d ising model we study the 2d ising model in a rectangular box l of linear size o l we determine the exact asymptotic behaviour of the large deviations of the magnetization p t2 l ae t when l 1 for values of the parameters of the model corresponding to the phase coexistence region where the order parameter m is strictly positive we study in particular boundary eects due to an arbitrary real valued boundary magnetic field using the self duality of the model a large part of the analysis consists in deriving properties of the covariance function hae 0 ae t i as t 1 at dual values of the parameters of the model to do this analysis we establish new results about the high temperature representation of the model these results are valid for dimensions d 2 and up to the critical temperature they give a complete non perturbative exposition of the high temperature representation we then study the gibbs measure conditioned by p t2 l ae t im l l l ic with 0 c 1 4 and im m m we construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperi metric type

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

a local limit theorem for triple connections in subcritical bernoulli percolation we prove a local limit theorem for the probability of a site to be connected by disjoint paths to three points in subcritical bernoulli percolation on mathbb z d d geq2 in the limit where their distances tend to infinity

adaptive image contrast enhancement using generalizations of histogram equalization this paper proposes a scheme for adaptive image contrast enhancement based on a generalization of histogram equalization he he is a useful technique for improving image contrast but its effect is too severe for many purposes however dramatically different results can be obtained with relatively minor modifications a concise description of adaptive he is set out and this framework is used in a discussion of past suggestions for variations on he a key feature of this formalism is a cumulation function which is used to generate a grey level mapping from the local histogram by choosing alternative forms of cumulation function one can achieve a wide variety of effects a specific form is proposed through the variation of one or two parameters the resulting process can produce a range of degrees of contrast enhancement at one extreme leaving the image unchanged at another yielding full adaptive equalization

fast ordering algorithm for exact histogram specification this paper provides a fast algorithm to order in a meaningful strict way the integer gray values in digital quantized images it can be used in any exact histogram specification based application our algorithm relies on the ordering procedure based on the specialized variational approach this variational method was shown to be superior to all other state of the art ordering algorithms in terms of faithful total strict ordering but not in speed indeed the relevant functionals are in general difficult to minimize because their gradient is nearly flat over vast regions in this paper we propose a simple and fast fixed point algorithm to minimize these functionals the fast convergence of our algorithm results from known analytical properties of the model our algorithm is equivalent to an iterative nonlinear filtering furthermore we show that a particular form of the variational model gives rise to much faster convergence than other alternative forms we demonstrate that only a few iterations of this filter yield almost the same pixel ordering as the minimizer thus we apply only few iteration steps to obtain images whose pixels can be ordered in a strict and faithful way numerical experiments confirm that our algorithm outperforms by far its main competitors

subcritical percolation with a line of defects we consider the bernoulli bond percolation process pp p on the nearest neighbor edges of zd which are open independently with probability p pc except for those lying on the first coordinate axis for which this probability is p define p p limn n 1logpp p 0 ne1 and p p p we show that there exists p c p c p d such that p p p if p p c moreover p c p 2 p c p 3 p and p c p d p for d 4 we also analyze the behavior of p p p as p p c in dimensions d 2 3 finally we prove that when p p c the following purely exponential asymptotics holds pp p 0 ne1 de p p n 1 o 1 for some constant d d p p uniformly for large values of n this work gives the first results on the rigorous analysis of pinning type problems that go beyond the effective models and don t rely on exact computations

invariant distributions and scaling limits for some diffusions in time varying random environments we consider a family of one dimensional diffusions in dynamical wiener mediums which are random perturbations of the ornstein uhlenbeck diffusion process we prove quenched and annealed convergences in distribution and under weigh ted total variation norms we find two kind of stationary probability measures which are either the standard normal distribution or a quasi invariant measure depending on the environment and which is naturally connected to a random dynamical system we apply these results to the study of a model of time inhomogeneous brox s diffusions which generalizes the diffusion studied by brox ann probab 14 4 1206 1218 1986 and those investigated by gradinaru and offret ann inst henri poincare probab stat 2011 we point out two distinct diffusive behaviours and we give the speed of convergences in the quenched situations

approximation of subadditive functions and convergence rates in limiting shape results for a nonnegative subadditive function h on mathbb z d with limiting approximation g x lim n h nx n it is of interest to obtain bounds on the discrepancy between g x and h x typically of order x nu with nu 1 for certain subadditive h x particularly those which are expectations associated with optimal random paths from 0 to x in a somewhat standardized way a more natural and seemingly weaker property can be established every x is in a bounded multiple of the convex hull of the set of sites satisfying a similar bound we show that this convex hull property implies the desired bound for all x applications include rates of convergence in limiting shape results for first passage percolation standard and oriented and longest common subsequences and bounds on the error in the exponential decay approximation to the off axis connectivity function for subcritical bernoulli bond percolation on the integer lattice

a note on the diffusion of directed polymers in a random environment a simple martingale argument is presented which proves that directed polymers in random environments satisfy a central limit theorem ford 3 and if the disorder is small enough this simplifies and extends an approach by j imbrie and t spencer

random walk in markovian environment we prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on z d we assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is markovian with strong spatial and temporal mixing properties

entropic repulsion of an interface in an external field we consider an interface above an attractive hard wall in the complete wetting regime and submitted to the action of an external increasing convex potential and study its delocalization as the intensity of this potential vanishes our main motivation is the analysis of critical prewetting which corresponds to the choice of a linear external potential we also present partial results on critical prewetting in the two dimensional ising model as well as a few weak results on pathwise estimates for the pure wetting problem for effective interface models

almost sure central limit theorem for directed polymers and random corrections we consider a general model of directed polymers on the lattice weakly coupled to a random environment we prove that the central limit theorem holds almost surely for the discrete time random walk x t associated to the polymer moreover we show that the random corrections to the cumulants of x t are finite starting from some dimension depending on the index of the cumulants and that there are corresponding random corrections of order in the asymptotic expansion of the expectations of smooth functions of x t full proofs are carried out for the first two cumulants we finally prove a kind of local theorem showing that the ratio of the probabilities of the events to the corresponding probabilities with no randomness in the region of moderate deviations from the average drift bt are for almost all choices of the environment uniformly close as to a functional of the environment as seen from t y

random walks in random environments random walks in random environments and their diffusion analogues have been a source of surprising phenomena and challenging problems especially in the non reversible situation since they began to be studied in the 1970s we review the model available results and techniques and point out several gaps in the understanding of these processes

ornstein zernike theory for the bernoulli bond percolation on mathbb z d we derive a precise ornstein zernike asymptotic formula for the decay of the two point function p p 0 x of the bernoulli bond percolation on the integer lattice z d in any dimension d 2 in any direction x and for any subcritical value of p p c d

uniqueness of the stochastic dynamics for continuous spin systems on a lattice abstract we prove the uniqueness of the stochastic dynamics associated with gibbs measures on infinite products of compact riemannian manifolds

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

an almost sure invariance principle for random walks in a space time random environment we consider a discrete time random walk in a space time i i d random environment we use a martingale approach to show that the walk is diffusive in almost every fixed environment we improve on existing results by proving an invariance principle and considering environments with an l2 averaged drift we also state an a s invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean under an ergodic invariant measure for the environment chain

ornstein zernike asymptotics for a general two particle lattice operator we study the asymptotic behavior of correlations for a general two particle operator mathcal t acting on the hilbert space ell 2 mathbb z d times mathbb z d for all dimension d 1 2 mathcal t is written as the sum of a main term and a small interacting term a form which appears in many problems if the interacting term is small we give a complete description of the asymptotics for large t of the correlations mathcal t t f 1 f 2 t 1 2 ldots for f 1 f 2 in some suitable class the asymptotics is of the ornstein zernike type i e exponential with a power law factor which is t d for d 3 but for d 1 2 it can be anomalous and is determined by the interacting term

quenched invariance principle for random walks with time dependent ergodic degenerate weights we study a continuous time random walk xx on zdzd in an environment of dynamic random conductances taking values in 0 0 we assume that the law of the conductances is ergodic with respect to space time shifts we prove a quenched invariance principle for the markov process xx under some moment conditions on the environment the key result on the sublinearity of the corrector is obtained by moser s iteration scheme

illumination insensitive image representation via synergistic weighted center surround receptive field model and weber law a novel illumination insensitive texture feature descriptor weber synergistic center surround pattern is presented we model differential synergistic excitation pattern synergistic straight orientation pattern and synergistic diagonal orientation pattern we discuss different scale and direction weighted coefficients in detail we mine higher order spatial information of weighted wscp image representation under complex illumination condition is a great challenge in computer vision field motivated by weber law and synergistic center surround receipt field model we propose an illumination insensitive feature descriptor named as weber synergistic center surround pattern wscp including three components differential synergistic excitation pattern dsep synergistic straight orientation pattern ssop and synergistic diagonal orientation pattern sdop to further enhance the discriminative power of wscp we present a scale and orientation weighted wscp wwscp which fully considers the inner and outer layer pixels excitation distributions as well as their orientation information importance to acquire more discriminative and rich features we utilize the spatiograms to describe patterns instead of the conventional histograms which can obtain higher order spatial information in the final classification stage we present a novel distance measurement model called weighted similarity measurement model wsmm to improve classification accuracy by sufficiently utilizing the information contents and orientation distributions of each pattern extensive experimental comparisons between our methods and other state of the art methods are conducted on cmupie yale b yale b ext feret photex alot and rawfoot databases and performance results have verified the effectiveness and efficiency of our proposed methods on the robustness to illumination variations

a finite volume version of aizenman higuchi theorem for the 2d ising model in the late 1970s in two celebrated papers aizenman and higuchi independently established that all infinite volume gibbs measures of the two dimensional ferromagnetic nearest neighbor ising model at inverse temperature beta geq 0 are of the form alpha mu beta 1 alpha mu beta where mu beta and mu beta are the two pure phases and 0 leq alpha leq 1 we present here a new approach to this result with a number of advantages a we obtain an optimal finite volume quantitative analogue implying the classical claim b the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon c this new approach might be applicable to systems for which the classical method fails

critical region for droplet formation in the two dimensional ising model we study the formation dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence specifically we consider the 2d ising model in volumes of size l2 inverse temperature c and overall magnetization conditioned to take the value m l2 2m vl where c 1 is the critical temperature m m is the spontaneous magnetization and vl is a sequence of positive numbers we find that the critical scaling for droplet formation dissolution is when vl3 2l 2 tends to a definite limit specifically we identify a dimensionless parameter proportional to this limit a non trivial critical value c and a function such that the following holds for c there is a single wulff shaped droplet containing a fraction c 2 3 of the magnetization deficit and there are no other droplets beyond the scale of log l moreover and are related via a universal equation that apparently is independent of the details of the system

a continuation method for nonlinear regression many iterative regression methods only perform well near a solution one may construct a modified problem with a free parameter k which has a known solution for a particular k by suitably deforming this problem through k space one may always remaining close to an intermediate solution eventually solve the original problem the continuation method was used to perform three nonlinear least squares regressions where the conventional newton methods failed to converge in particular the third problem was associated with experimental kinetic data and differential equations which needed to be integrated numerically no satisfactory answers were obtainable from the gauss newton method while the continuation parameter variation method showed its robustness by converging for a large range of initial values

the threshold effects for the two particle hamiltonians on lattices for a wide class of two body energy operators h k on the d dimensional lattice d d 3 k being the two particle quasi momentum we prove that if the following two assumptions i and ii are satisfied then for all nontrivial values k k 0 the discrete spectrum of h k below its threshold is non empty the assumptions are i the two particle hamiltonian h 0 corresponding to the zero value of the quasi momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and ii the one particle free hamiltonians in the coordinate representation generate positivity preserving semi groups

asymptotics of decay of correlations for lattice spin fields at high temperatures i the ising model we find the asymptotic decrease of correlations y zv 1 y in the ising model at high temperatures for the case when monomials a and b both are odd using the saddle point method we find the asymptotics of the correlations for any dimension for even monomials a b we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases 1 1 and the vectory has an arbitrary direction 2 y is directed along a fixed axis and arbitrary here we use besides the saddle point method some arguments from scattering theory

automatic exact histogram specification for contrast enhancement and visual system based quantitative evaluation histogram equalization which aims at information maximization is widely used in different ways to perform contrast enhancement in images in this paper an automatic exact histogram specification technique is proposed and used for global and local contrast enhancement of images the desired histogram is obtained by first subjecting the image histogram to a modification process and then by maximizing a measure that represents increase in information and decrease in ambiguity a new method of measuring image contrast based upon local band limited approach and center surround retinal receptive field model is also devised in this paper this method works at multiple scales frequency bands and combines the contrast measures obtained at different scales using lp norm in comparison to a few existing methods the effectiveness of the proposed automatic exact histogram specification technique in enhancing contrasts of images is demonstrated through qualitative analysis and the proposed image contrast measure based quantitative analysis

nonlocal interactions and the excitation spectrum in lattice quantum scalar field models we determine the effects of nonlocal nonlinear interactions on the excitation spectrum of lattice quantum field scalar models we consider perturbations of a quantized discrete string formally self adjoint hamiltonian operator on the lattice d and with a large mass coefficient for the quadratic term the low lying energy momentum spectrum has an isolated dispersion curve and a two particle first band we analyse a ladder approximation of the bethe salpeter equation on the lattice for a weak perturbation of the type d 6 6 v 6 0 and consider the spectral interval starting at zero and extending to near the three particle threshold for space dimension d 1 2 and v 1 4 we find that a bound state occurs either below if 1 0 but not both this agrees with recent results where bound states were obtained for the stochastic dynamics generator associated with the relaxation rate to equilibrium in weakly coupled stochastic ginzburg landau models with continuous time and on a spatial lattice d these results are in contrast however with those obtained for v 2 3 for this case surprisingly we show that stable particles exist simultaneously above and below the band for d 1 2 regardless of the sign of the coupling 2 if v 3 2 2 the ladder analysis is inconclusive if d 3 4 no bound states exist in the spectral region we consider

on the spectrum of an hamiltonian in fock space discrete spectrum asymptotics a model operator h associated with the energy operator of a system describing three particles in interaction without conservation of the number of particles is considered the location of the essential spectrum of h is described the existence of infinitely many eigenvalues resp the finiteness of eigenvalues below the bottom ess h of the essential spectrum of h is proved for the case where the associated friedrichs model has a threshold energy resonance resp a threshold eigenvalue for the number n z of eigenvalues of h lying below z ess h the following asymptotics is found lim limits z to tau rm ess h 0 frac n z log z tau rm ess h u 0 0 u 0 infty

spectral analysis of a stochastic ising model in continuum we consider an equilibrium stochastic dynamics of spatial spin systems in r d involving both a birth and death dynamics and a spin flip dynamics as well using a gen eral approach to the spectral analysis of corresponding markov generator we estimate the spectral gap and construct one particle invariant subspaces for the generator

spectral analysis of weakly coupled stochastic lattice ginzburg landau models we consider the relaxation to equilibrium of solutions t 0 of stochastic dynamical langevin equations with white noise and weakly coupled ginzburg landau interactions using a feynman kac formula which relates stochastic expectations to correlation functions of a spatially non local imaginary time quantum field theory we obtain results on the joint spectrum of h where h is the self adjoint positive generator of the semi group associated with the dynamics and p j j 1 d are the self adjoint generators of the group of lattice spatial translations we show that the low lying energy momentum spectrum consists of an isolated one particle dispersion curve and for the mass spectrum energy momentum at zero momentum besides this isolated one particle mass we show using a bethe salpeter equation the existence of an isolated two particle bound state if the coefficient of the quartic term in the polynomial of the ginzburg landau interaction is negative and d 1 2 otherwise there is no two particle bound state asymptotic values for the masses are obtained

exact order based feature descriptor for illumination robust image matching we present a novel method for a feature descriptor called an exact order based descriptor eod the proposed method consists of three steps first to resolve ordering ambiguity for pixels of the same intensity an exact order image is created by changing the discrete intensity into a k dimensional continuous value second exact order based features are generated globally and locally finally the eod is constructed by combining the global and local exact order features using the discrete cosine transform experimental results show that the proposed method outperforms other state of the art descriptors over a number of images

phase separation in random cluster models iii circuit regularity we study the droplet that results from conditioning the subcritical fortuin kasteleyn random cluster model on the presence of an open circuit encircling the origin and enclosing an area of at least or exactly n 2 in this paper we prove that the resulting circuit is highly regular we define a notion of a regeneration site in such a way that for any such site v the circuit cuts through the radial line segment through v only at v we show that provided that the conditioned circuit is centred at the origin in a natural sense the set of regeneration sites reaches into all parts of the circuit with maximal distance from one such site to the next being at most logarithmic in n with high probability the result provides a flexible control on the conditioned circuit that permits the use of surgical techniques to bound its fluctuations and as such it plays a crucial role in the derivation of bounds on the local fluctuation of the circuit carried out in hammond arxiv 1001 1527 2009 arxiv 1001 1528 2009

spatial mutual information and pagerank based contrast enhancement and quality aware relative contrast measure this paper proposes a novel algorithm for global contrast enhancement using a new definition of spatial mutual information smi of gray levels of an input image and pagerank algorithm the gray levels are used to represent nodes in pagerank algorithm and the weights between the nodes are computed according to their dependence and spatial spread over the image which is quantified by using smi the rank vector of gray levels resulted from pagerank algorithm is used in mapping input gray levels to output the damping factor of the pagerank algorithm is utilized to control the level of perceived global contrast on the output image furthermore a new metric is proposed for image quality aware relative contrast measurement between input and output images experimental results show that the proposed algorithm consistently produces good results

gaussian fluctuations of connectivities in the subcritical regime of percolation we consider thed dimensional bernoulli bond percolation model and prove the following results for allp pc the finite volume conditional measures defined by requiring the existence of a dual path between opposing faces of the boundary converge in the infinite volume limit to the standard bernoulli measure

joint exact histogram specification and image enhancement through the wavelet transform histogram specification equalization is an important tool for tasks such as image enhancement and normalization although this problem has exact solution for continuous images in the case of digital images it is ill posed recently an exact pixel ordering method based solely on local image intensity was proposed yet still with some limitations especially since it ignores the important image edge information in this paper we present a wavelet based method that simultaneously achieves the exact histogram specification and good image enhancement performance it does so through a carefully designed strict pixel ordering process during which the wavelet coefficients are fine tuned for the image enhancement purpose compared to previous work this approach takes into account not only local mean intensity values but also local edge information other advantages include fast pixel ordering good statistical models and better image enhancement performance experimental results and comparison with state of the art methods are presented

continuity and anomalous fluctuations in random walks in dynamic random environments numerics phase diagrams and conjectures we perform simulations for one dimensional continuous time random walks in two dynamic random environments with fast independent spin flips and slow simple symmetric exclusion decay of space time correlations respectively we focus on the asymptotic speeds and the scaling limits of such random walks we observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment we compare our data with well known results for static random environment we observe that the non diffusive regime known so far only for the static case can occur in the dynamical setup too such anomalous fluctuations give rise to a new phase diagram further we discuss possible consequences for more general static and dynamic random environments

the threshold effects for a family of friedrichs models under rank one perturbations a family of friedrichs models under rank one perturbations h p p 3 0 associated to a system of two particles on the three dimensional lattice z3 is considered we prove the existence of a unique eigenvalue below the bottom of the essential spectrum of h p for all non trivial values of p under the assumption that h 0 has either a threshold energy resonance virtual level or a threshold eigenvalue the threshold energy expansion for the fredholm determinant associated to a family of friedrichs models is also obtained

on the spectrum of the generator of an infinite system of interacting diffusions we study the spectrum of the operator generating an infinite dimensional diffusion process t in space here is a natural t invariant measure on which is a gibbs distribution corresponding to a formal hamiltonian h of an anharmonic crystal with a value of the inverse temperature 0 for small enough we establish the existence of an l invariant subspace such that has a distinctive character related to a quasi particle picture in particular has a lebesgue spectrum separated from the rest of the spectrum of l and concentrated near a point 1 0 giving the smallest non zero eigenvalue of a limiting problem associated with 0

interband spectrum of weakly coupled stochastic lattice ginzburg landau models we analyze the excitation spectrum of the generator associated with the relaxation rate to equilibrium in weakly coupled stochastic ginzburg landau models on a spatial lattice z d the spectrum has a quasiparticle interpretation depending on d and on the specific interaction by solving the bethe salpeter equation in the ladder approximation we show the existence of a stable particle above the upper envelope of the two particle band possessing a concave dispersion curve this result furthers our knowledge about the spectrum of the stochastic dynamics generator

directed polymers in a random environment some results on fluctuations we consider a polymer model on where to each edgee is associated a random variable v e a polymer configuration is represented by a directed pathr and has a weight exp e r e with 1 t the inverse temperature we extend some rigorous results that have been obtained for the ground state of this model to finite temperatures in particular we obtain some upper and lower bounds on sample to sample free energy fluctuations and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations

random walks in quenched i i d space time random environment are always a s diffusive we consider a general model of discrete time random walk x t on the lattice 1 in a random environment t x t x 1 with i i d components t x previous results on the a s validity of the central limit theorem for the quenched model required a small stochasticity condition in this paper we show that the result holds provided only that an obvious non degeneracy condition is met the proof is based on the analysis of a suitable generating function which allows to estimate l 2 norms by contour integrals

continuation methods theory and applications this paper surveys in a tutorial fashion theoretical and applications aspects of the confirmation method for the solution of large scale system engineering problems the continuation method is motivated and defined the existence of the method is formulated in terms of degree theory a la algebraic topology examples are given throughout the paper and applications to engineering and economic problems are cited and described

almost sure central limit theorem for a markov model of random walk in dynamical random environment we consider a model of random walk on 2 in a dynamical random environment described by a field t x t x 1 the random walk transition probabilities are taken as p x t 1 y x t x t p 0 y x c y x x we assume that the variables t x t x 1 are i i d that both p 0 u and c u s are finite range in u and that the random term c u is small and with zero average we prove that the c l t holds almost surely with the same parameters as for p 0 for all 2 for 3 there is a finite random i e dependent on correction to the average of x t and there is a corresponding random correction of order to the c l t for 5 there is a finite random correction to the covariance matrix of x t and a corresponding correction of order to the c l t proofs are based on some new l p estimates for a class of functionals of the field

computer simulations for some one dimensional models of random walks in fluctuating random environment we report some results of computer simulations for two models of random walks in random environment rwre on the one dimensional lattice mathbb z for fixed space time configuration of the environment quenched rwre a markov model with markov dependence in time and a quasi stationary model with long range space time correlations we compare with the corresponding results for a model with i i d in space time environment in the range of times available to us the quenched distributions of the random walk displacement are far from gaussian but as the behavior is similar for all three models one cannot exclude asymptotic gaussianity which is proved for the model with i i d environment we also report results on the random drift and on some time correlations which show a clear power decay

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

lace expansion for the ising model the lace expansion has been a powerful tool for investigating mean field behavior for various stochastic geometrical models such as self avoiding walk and percolation above their respective upper critical dimension in this paper we prove the lace expansion for the ising model that is valid for any spin spin coupling for the ferromagnetic case we also prove that the expansion coefficients obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace expansion coefficients for self avoiding walk as a result we obtain gaussian asymptotics of the critical two point function for the nearest neighbor model with d gg 4 and for the spread out model with d 4 and l gg 1 without assuming reflection positivity

interface surface tension and reentrant pinning transition in the 2d ising model we develop a new way to look at the high temperature representation of the ising model up to the critical temperature and obtain a number of interesting consequences in the two dimensional case it is possible to use these tools to prove results on phase separation lines in the whole phase coexistence regime by way of a duality transformation we illustrate the power of these techniques by studying an ising model with a boundary magnetic field in which a reentrant pinning transition takes place more precisely we show that the typical configurations of the model can be described at the macroscopic level by interfaces which are solutions of the corresponding thermodynamic variational problem this variational problem is solved explicitly there exist values of the boundary magnetic field and temperatures 0 t 2 but is pinned for t 1 t 3 it is not pinned an important property of the surface tension which is used in this paper is the sharp triangle inequality about which we report some new results the techniques used in this work are robust and can be used in a variety of different situations

naturalness preserved enhancement algorithm for non uniform illumination images image enhancement plays an important role in image processing and analysis among various enhancement algorithms retinex based algorithms can efficiently enhance details and have been widely adopted since retinex based algorithms regard illumination removal as a default preference and fail to limit the range of reflectance the naturalness of non uniform illumination images cannot be effectively preserved however naturalness is essential for image enhancement to achieve pleasing perceptual quality in order to preserve naturalness while enhancing details we propose an enhancement algorithm for non uniform illumination images in general this paper makes the following three major contributions first a lightness order error measure is proposed to access naturalness preservation objectively second a bright pass filter is proposed to decompose an image into reflectance and illumination which respectively determine the details and the naturalness of the image third we propose a bi log transformation which is utilized to map the illumination to make a balance between details and naturalness experimental results demonstrate that the proposed algorithm can not only enhance the details but also preserve the naturalness for non uniform illumination images

two particle spectrum of the generator for stochastic model of planar rotators at high temperatures we study two particle spectrum branches of the generator in the stochastic model of planar rotators using the construction of a special basis in two particle invariant subspaces we prove that the branches of the spectrum are in a small neighborhood of the point 2 we prove the existence of two bound states in addition to the continuous part of the spectrum in the one dimensional case