uniqueness of gradient gibbs measures with disorder we consider in a uniformly strictly convex potential regime two versions of random gradient models with disorder in model a the interface feels a bulk term of random fields while in model b the disorder enters through the potential acting on the gradients we assume a general distribution on the disorder with uniformly bounded finite second moments it is well known that for gradient models without disorder there are no gibbs measures in infinite volume in dimension d 2 while there are shift invariant gradient gibbs measures describing an infinite volume distribution for the gradients of the field as was shown by funaki and spohn commun math phys 185 1 36 1997 van enter and kulske proved in ann appl probab 18 1 109 119 2008 that adding a disorder term as in model a prohibits the existence of such gradient gibbs measures for general interaction potentials in d 2 in cotar and kulske ann appl probab 22 5 1650 1692 2012 we proved the existence of shift covariant random gradient gibbs measures for model a when d ge 3 the disorder is i i d and has mean zero and for model b when d ge 1 and the disorder has a stationary distribution in the present paper we prove existence and uniqueness of shift covariant random gradient gibbs measures with a given expected tilt u in mathbb r d and with the corresponding annealed measure being ergodic for model a when d ge 3 and the disordered random fields are i i d and symmetrically distributed and for model b when d ge 1 and for any stationary disorder dependence structure we also compute for both models for any gradient gibbs measure constructed as in cotar and kulske ann appl probab 22 5 1650 1692 2012 when the disorder is i i d and its distribution satisfies a poincare inequality assumption the optimal decay of covariances with respect to the averaged over the disorder gradient gibbs measure

fast planar oriented ripple search algorithm for hyperspace vq codebook this paper presents a fast codebook search method for improving the quantization complexity of full search vector quantization vq the proposed method is built on the planar voronoi diagram to label a ripple search domain then the appropriate codeword can easily be found just by searching the local region instead of global exploration in order to take a step further and obtain the close result full search vq would we equip the proposed method with a duplication mechanism that helps to bring down the possible quantizing distortion to its lowest level according to the experimental results the proposed method is indeed capable of providing better outcome at a faster quantization speed than the existing partial search methods moreover the proposed method only requires a little extra storage for duplication

on the exponential decay of the n point correlation functions and the analyticity of the pressure the goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n point correlation functions for certain unbounded models of kac type the methods are based on estimating higher order derivatives of the solution of the witten laplacian equation on 1 forms associated with the hamiltonian of the system we also provide a formula for the taylor coefficients of the pressure that is suitable for a direct proof of the analyticity

fast full search equivalent encoding algorithms for image compression using vector quantization three fast search routines to be used in the encoding phase of vector quantization vq image compression systems are presented these routines which are based on geometric considerations provide the same results as an exhaustive or full search examples show that the proposed algorithms need only 3 20 of the number of mathematical operations required by a full search and fewer than 50 of the operations required by recently proposed alternatives

on homogenization and scaling limit of some gradient perturbations of a massless free field we study the continuum scaling limit of some statistical mechanical models defined by convex hamiltonians which are gradient perturbations of a massless free field by proving a central limit theorem for these models we show that their long distance behavior is identical to a new homogenized continuum massless free field we shall also obtain some new bounds on the 2 point correlation functions of these models

finite range decomposition for families of gradient gaussian measures abstract let a family of gradient gaussian vector fields on z d be given we show the existence of a uniform finite range decomposition of the corresponding covariance operators that is the covariance operator can be written as a sum of covariance operators whose kernels are supported within cubes of diameters l k in addition we prove natural regularity for the subcovariance operators and we obtain regularity bounds as we vary within the given family of gradient gaussian measures

pde with random coefficients and euclidean field theory in this paper a new proof of an identity of giacomin olla and spohn is given the identity relates the 2 point correlation function of a euclidean field theory to the expectation of the green s function for a pde with random coefficients the euclidean field theory is assumed to have convex potential an inequality of brascamp and lieb therefore implies gaussian bounds on the fourier transform of the 2 point correlation function by an application of results from random pde the previously mentioned identity implies pointwise gaussian bounds on the 2 point correlation function

two fast nearest neighbor searching algorithms for image vector quantization in this paper two efficient codebook searching algorithms for vector quantization vq are presented the first fast search algorithm utilizes the compactness property of signal energy on transform domain and the geometrical relations between the input vector and every codevector to eliminate those codevectors that have no chance to be the closest codeword of the input vector it achieves a full search equivalent performance as compared with other fast methods of the same kind this algorithm requires the fewest multiplications and the least total times of distortion measurements then a suboptimal searching method which sacrifices the reconstructed signal quality to speed up the search of nearest neighbor is presented this algorithm performs the search process on predefined small subcodebooks instead of the whole codebook for the closest codevector experimental results show that this method not only needs less cpu time to encode an image but also encounters less loss of reconstructed signal quality than tree structured vq does

joint coding and embedding techniques for multimedia images hiding data in digital images is a technique for secret data communication it involves embedding important data into a cover image in digital form with minimal perceptible degradation in this paper we first propose an improved data hiding method for side match vector quantization smvq compressed images which utilizes the codeword pairing procedure to modulate the index code of each image block in order to take it a step further and obtain a larger embedding capacity we remodel the first proposed method into a new one with the power of variable rate data embedding through the use of a multiple base notational system according to the experimental results the two proposed methods are indeed capable of providing a larger embedding capacity without causing noticeable distortions of stego images in comparison with previous methods moreover our methods also maintain a low compression bit rate without auxiliary data

a renormalisation group method i gaussian integration and normed algebras this paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields fermion fields or both our immediate motivation is a specific model involving both boson and fermion fields which arises as a representation of the continuous time weakly self avoiding walk in this paper we define normed algebras suitable for a renormalisation group analysis and develop methods for performing analysis on these algebras we also develop the theory of gaussian integration on these normed algebras and prove estimates for gaussian integrals the concepts and results developed here provide a foundation for the continuation of the method presented in subsequent papers in the series

stochastic differential equations with fuzzy drift and diffusion a new framework for the fuzzification of stochastic differential equations is presented it allows for a detailed description of the model uncertainty and the non predictable stochastic law of natural systems e g in ecosystems even the probability law of the random dynamic changes due to unobservable influences like anthropogenic disturbances or climate variation the fuzziness of the stochastic system is modelled by a fuzzy set of stochastic differential equations which is identified with a fuzzy set of initial conditions time dependent drift and diffusion functions using appropriate function spaces the extension principle leads to a consistent theory providing fuzzy solutions in terms of fuzzy sets of processes fuzzy states fuzzy moments and fuzzy probabilities

strict convexity of the free energy for a class of non convex gradient models we consider a gradient interface model on the lattice with interaction potential which is a non convex perturbation of a convex potential we show using a one step multiple scale analysis the strict convexity of the surface tension at high temperature this is an extension of funaki and spohn s result 8 where the strict convexity of potential was crucial in their proof

the short distance behavior of φ 4 3 we consider the 3 4 quantum field theory on a torus and study the short distance behavior we reproduce the standard result that the singularities can be removed by a simple mass renormalization for the resulting model we give anl p bound on the short distance regularity of the correlation functions to obtain these results we develop a systematic treatment of the generating functional for correlations using a renormalization group method incorporating background fields

mayer expansions and the hamilton jacobi equation we review the derivation of wilson s differential equation in infinitely many variables which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal integration out is performed we show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic the resulting series solutions are generalizations of the mayer expansion in statistical mechanics the differential equation approach gives a remarkable identity for connected parts and precise estimates which include criteria for convergence of iterated mayer expansions applications include the yukawa gas in two dimensions past the 4 threshold and another derivation of some earlier results of gopfert and mack

motion by mean curvature from the ginzburg landau interface model we consider the scalar field t with a reversible stochastic dynamics which is defined by the standard dirichlet form relative to the gibbs measure with formal energy the potential v is even and strictly convex we prove that under a suitable large scale limit the t field becomes deterministic such that locally its normal velocity is proportional to its mean curvature except for some anisotropy effects as an essential input we prove that for every tilt there is a unique shift invariant ergodic gibbs measure for the field

a virtual image cryptosystem based upon vector quantization we propose a new image cryptosystem to protect image data it encrypts the original image into another virtual image since both original and virtual images are significant our new cryptosystem can confuse illegal users besides the camouflage this new cryptosystem has three other benefits first our cryptosystem is secure even if the illegal users know that our virtual image is a camouflage second this cryptosystem can compress image data finally our method is more efficient than a method that encrypts the entire image directly

a renormalisation group method v a single renormalisation group step this paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and or fermion fields and comprises the core of the method in the renormalisation group method increasingly large scales are studied in a progressive manner with an interaction parametrised by a field polynomial which evolves with the scale under the renormalisation group map in our context the progressive analysis is performed via a finite range covariance decomposition perturbative calculations are used to track the flow of the coupling constants of the evolving polynomial but on their own perturbative calculations are insufficient to control error terms and to obtain mathematically rigorous results in this paper we define an additional non perturbative coordinate which together with the flow of coupling constants defines the complete evolution of the renormalisation group map we specify conditions under which the non perturbative coordinate is contractive under a single renormalisation group step our framework is essentially combinatorial but its implementation relies on analytic results developed earlier in the series of papers the results of this paper are applied elsewhere to analyse the critical behaviour of the 4 dimensional continuous time weakly self avoiding walk and of the 4 dimensional n component varphi 4 model in particular the existence of a logarithmic correction to mean field scaling for the susceptibility can be proved for both models together with other facts about critical exponents and critical behaviour

a non gaussian fixed point for φ4 in 4 e dimensions we consider the 4 quantum field theory in four dimensions the gaussian part of the measure is modified to simulate 4 e dimensions where e is small and positive we give a renormalization group analysis for the infrared behavior of the resulting model we find that the gaussian fixed point is unstable but that there is a hyperbolic non gaussian fixed point a distance e away in a neighborhood of this fixed point we construct the stable manifold

hierarchy oriented searching algorithms using alternative duplicate codewords for vector quantization mechanism in this paper we will show those algorithms that speed up the search of a closest codeword over a given codebook the mechanism is based on a multilevel concept constructed as a hierarchical organization for a given codebook with size n existing n codewords there are only log email protected levels that need to be constructed in order to find the closest codeword where k is a parameter selection to optimize the comparisons in the course of the searching theoretically the comparisons required to find the closest codeword are on average email protected log email protected which is substantially faster than that of a full search job besides in order to approach the perfect match with the exact one among the codewords a duplicate mechanism is also applied to our algorithm so that the lowest possible distortion is achieved as is observed from the results of the experiments the estimation of comparisons in our execution without codeword duplicate is on average about email protected log email protected n times the full search method it is worth noting that the larger the size of the codebook the more the speed increases in particular there are two classifications non duplicate and duplicate method which are associated with the codewords distribution in the dominated set which were experimented on some tables the duplicate is manipulated by the training set containing six popular image data to demonstrate the efficiency of our scheme also the time requirement to find the closest codeword is effectively reduced especially in the case of a large sized codebook therefore our scheme offers a novel exploration and achieves a faster performance in the closest codeword searching for vector quantization of image data

construction of the two dimensional sine gordon model for β 8π we present a rigorous renormalization group construction of the two dimensional massless and massive quantum sine gordon models in finite volume for the range 0 8 we prove analyticity in the coupling constant which implies the convergence of perturbation theory the field correlation functions and their generating functional are analyzed and shown to have the short distance asymptotics of the free field theory in the massive case the bounds are uniform in volume and we also obtain uniform estimates on the long distance decay of correlations

multiscale representation of generating and correlation functions for some models of statistical mechanics and quantum field theory we consider models of statistical mechanics and quantum field theory in the euclidean formulation which are treated using renormalization group methods and where the action is a small perturbation of a quadratic action we obtain multiscale formulas for the generating and correlation functions aftern renormalization group transformations which bring out the relation with thenth effective action we derive and compare the formulas for different rgs the formulas for correlation functions involve 1 two propagators which are determined by a sequence of approximate wave function renormalization constants and renormalization group operators associated with the decomposition into scales of the quadratic form and 2 field derivatives of the nth effective action for the case of the block field function rg the formulas are especially simple and for asymptotic free theories only the derivatives at zero field are needed the formulas have been previously used directly to obtain bounds on correlation functions using information obtained from the analysis of effective actions the simplicity can be traced to an orthogonality of scales property which follows from an implicit wavelet structure other commonly used rgs do not have the orthogonality of scales property

grad o perturbations of massless gaussian fields we investigate weak perturbations of the continuum massless gaussian measure by a class of approximately local analytic functionals and use our general results to give a new proof that the pressure of the dilute dipole gas is analytic in the activity

witten laplacian method for the decay of correlations the aim of this paper is to apply direct methods to the study of integrals that appear naturally in statistical mechanics and euclidean field theory we provide weighted estimates leading to the exponential decay of the two point correlation functions for certain classical convex unbounded models the methods involve the study of the solutions of the witten laplacian equations associated with the hamiltonian of the system

an improvement on codebook search for vector quantization presents a simple but effective algorithm to speed up the codebook search in a vector quantization scheme when a mse criterion is used a considerable reduction in the number of operations is achieved this algorithm was originally designed for image vector quantization in which the samples of the image signal pixels are positive although it can be used with any positive negative signal with only minor modifications

quantum diffusion of the random schrodinger evolution in the scaling limit ii the recollision diagrams we consider random schrodinger equations on mathbb r d for d 3 with a homogeneous anderson poisson type random potential denote by the coupling constant and t the solution with initial data 0 the space and time variables scale as x sim lambda 2 kappa 2 t sim lambda 2 kappa with 0 0 d we prove that in the limit 0 the expectation of the wigner distribution of t converges weakly to the solution of a heat equation in the space variable x for arbitrary l2 initial data the proof is based on a rigorous analysis of feynman diagrams in the companion paper 10 the analysis of the non repetition diagrams was presented in this paper we complete the proof by estimating the recollision diagrams and showing that the main terms i e the ladder diagrams with renormalized propagator converge to the heat equation

scaling limit for a class of gradient fields with nonconvex potentials we consider gradient fields x x d whose law takes the gibbs boltzmann form z 1 exp x y v v x where the sum runs over nearest neighbors we assume that the potential v admits the representation v log d exp 1 2 2 where is a positive measure with compact support in 0 hence the potential v is symmetric but nonconvex in general while for strictly convex v s the translation invariant ergodic gradient gibbs measures are completely characterized by their tilt a nonconvex potential as above may lead to several ergodic gradient gibbs measures with zero tilt still every ergodic zero tilt gradient gibbs measure for the potential v above scales to a gaussian free field

finite range decomposition for gaussian measures with improved regularity abstract we consider a family of gradient gaussian vector fields on the torus z l n z d adams koteck muller and independently bauerschmidt established the existence of a uniform finite range decomposition of the corresponding covariance operators i e the covariance can be written as a sum of covariance operators supported on increasing cubes with diameter l k we improve this result and show that the decay behaviour of the kernels in fourier space can be controlled then we show the regularity of the integration map that convolves functionals with the partial measures of the finite range decomposition in particular the new finite range decomposition avoids the loss of regularity which arises in the renormalisation group approach to anisotropic problems in statistical mechanics

critical φ 4 3 e the euclidean 4 3 e model in r3 corresponds to a perturbation by a 4 interaction of a gaussian measure on scalar fields with a covariance depending on a real parameter e in the range 0 e 1 for e 1 one recovers the covariance of a massless scalar field in r3 for e 0 4 is a marginal interaction for 0 e 0 sufficiently small there exists a non gaussian fixed point with one unstable direction of the renormalization group iterations we construct the stable critical manifold near this fixed point and prove that under renormalization group iterations the critical theories converge to the fixed point

the renormalization group according to balaban ii large fields this is an expository account of balaban s approach to the renormalization group the method is illustrated with a treatment of the ultraviolet problem for the scalar 4 model on a toroidal lattice in dimension d 3 in this paper we control the large field contribution to the partition function

renormalization group flow of a hierarchical sine gordon model by partial differential equations we use a renormalization group differential equation to rigorously control the renormalization group flow in a hierarchical lattice sine gordon field theory in the kosterlitz thouless phase

an improvement of the minimum distortion encoding algorithm for vector quantization in this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords and about 25 40 percent for a tree search vector quantizer similar improvement can be achieved in other vector quantization systems

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

multiscale formalism for correlation functions of fermions infrared analysis of the tridimensional gross neveu model we present a multiscale formalism for fermionic systems with a smooth uv cutoff establishing a trivial link between the correlation functions and the effective potential flow and study the k point truncated functions of the tridimensional gross neveu model a new efficient method is used to bound these correlation functions and show polynomial tree decay for long distances we are guided by a block lattice mechanism with a property of orthogonality between terms in different scales which leads to simple formulas for the correlations

decay of correlations and uniqueness of gibbs lattice systems with nonquadratic interaction the aim of this paper is to develop the classical lattice models with unbounded spin to the case of nonquadratic polynomial interaction we demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the fast decay of correlations for gibbs measure

quantum diffusion of the random schrodinger evolution in the scaling limit we consider random schrodinger equations on r d for d 3 with a homogeneous anderson poisson type random potential denote by the coupling constant and psi t the solution with initial data psi 0 the space and time variables scale as x sim lambda 2 varkappa 2 text and t sim lambda 2 varkappa text with 0 varkappa varkappa 0 left d right we prove that in the limit 0 the expectation of the wigner distribution of psi t converges weakly to the solution of a heat equation in the space variable x for arbitrary l 2 initial data

a complete renormalization group trajectory between two fixed points we give a rigorous nonperturbative construction of a massless discrete trajectory for wilson s exact renormalization group the model is a three dimensional euclidean field theory with a modified free propagator the trajectory realizes the mean field to critical crossover from the ultraviolet gaussian fixed point to an analog recently constructed by brydges mitter and scoppola of the wilson fisher nontrivial fixed point

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques

towards a nonperturbative renormalization group analysis we prove that a certain class of convex gradient models in high dimensional spaces without the presence of a small parameter renormalizes to a free field as a consequence we establish a certain asymptotic formula for the partition function in some ways this is a realization of gawedzki and kupiainen s idea to use correlation inequalities to augment the rigorous renormalization group methods we use the more particular suggestion of spencer to use certain inequalities of brascamp and lieb and also the formulation of the correlation functions in terms of the solutions to some partial differential equations given by helffer and sjostrand