random coin tossing a sequence of heads and tails is produced by repeatedly selecting a coin from two possible coins and tossing it the second coin is tossed at renewal times in a renewal process and the first coin is tossed at all other times the first coin is fair prob heads 1 2 and the second coin is known either to be fair or to have known bias 0 1 prob heads letting u k prob there is a renewal at time k we show that if k 0 u k 2 we can determine using only the sequence of heads and tails produced if the second coin had bias or 0 if we show that this is not possible

fractal measures of first passage time of a simple random walk abstract we consider random walks starting at the site i 1 on a one dimensional lattice segment with an absorbing boundary at i 0 and a reflecting boundary at i l we find that the typical value of first passage time fpt is independent of system size l while the mean value diverges linearly with l the qth moment of the fpt diverges with system size as l2q 1 for q 1 2 for a finite but large l the fpt distribution has an 1 t tail cut off by an exponential of the form exp t l2 however if l is set equal to infinity the distribution has an algebraic tail given by t 1 2 we find that the generalised dimensions d q have a nontrivial dependence on q this shows that the fpt distribution is a multifractal we also calculate the singularity spectrum f

t t 1 transformation is not loosely bernoulli the t t problem open since 1971 is to demonstrate that the t t transformation a naturally arising k transformation is not bernoulli it is shown here not even to be loosely bernoulli

ergodic properties of color records abstract in a series of papers culminating in the dissertation of the second author under the direction of p w kasteleyn several rigorous results have been obtained concerning the color sequence seen by a random walker on a stochastically black white colored lattice and this under the sole assumption that the coloring is stationary ergodic and independent of the walking in this article we investigate the ergodic properties of the color record process and their implications for the behavior of the sequence nk k 0 of successive times needed for the walker to go from the kth to the k 1 st black point as an example of the type of results obtained we show that if a certain induced color record process is strongly mixing in the ergodic theoretic sense then the average nk tends to the inverse of the density of black points as k tends to infinity and similarly that the distribution of nk tends to a limit that can be explicitly calculated in terms of the distribution of n0 for a certain class of stochastic colorings and random walks we are able to verify that the induced color record process is indeed strongly mixing our main goal however is to clarify the nature of the ergodic properties and thereby provide a tool for future use in the study of color records

image compression using address vector quantization a novel vector quantization scheme called the address vector quantizer a vq is proposed it is based on exploiting the interblock correlation by encoding a group of blocks together using an address codebook the address codebook consists of a set of address codevectors where each codevector represents a combination of addresses indexes each element of this codevector is an address of an entry in the lbg codebook representing a vector quantized block the address codebook consists of two regions one is the active addressable region and the other is the inactive nonaddressable region during the encoding process the codevectors in the address codebook are reordered adaptively in order to bring the most probable address codevectors into the active region when encoding an address codevector the active region of the address codebook is checked and if such an address combination exist its index is transmitted to the receiver otherwise the address of each block is transmitted individually the quality snr value of the images encoded by the proposed a vq method is the same as that of a memoryless vector quantizer but the bit rate would be reduced by a factor of approximately two when compared to a memoryless vector quantizer

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

strong invariance for local times let y 1 y 2 be a sequence of i i d random variables with distribution p y 1 k p k k 1 2 e y 1 0 e y 1 2 2 put t n y 1 y n and n x n k 0 k n t k x extending the result of revesz 1981 it is shown that for appropriate skorohod construction we have 1 mathop text sup limits x in mathbb z text l x n sigma 2 text sigma text 2 n x n o n 1 mathord left vphantom 1 4 varepsilon right kern nulldelimiterspace 4 varepsilon text a text s text provided all moments e y 1 m m 0 exists where l is the local time of a wiener process certain rate of convergence is given also under weaker conditions and for l x n 2 2 n x n too when x is fixed

dynamical spin system exact solution and mean recurrence time abstract a model involving a chain of n 2 spins si 1 i 1 n evolvi ng syncronously in discrete time t via a nonlinear autonomous transformation si t 1 si t si 1 t i 1 n 1 sn t 1 sn t is presented the transformation equations are solved explicitly and the detailed decomposition of state space into ergodic sets is found on the assumption of equally likely initial states the mean recurrence time is calculated and its variance is discussed the model displays a strikingly sensitive dependence on the number of spins and this is reflected in the staircase behavior of the mean recurrence time remarks are made regarding the connection between the behavior of the model and the ground states of a related two dimensional ising model

variations on a theme by mark kac mark kac s theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations most of which are formulated in terms of 0 1 processes whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0 this condition is dropped in part of the variations two others refer to the variance of the recurrence time and two to the poincare cycle of a dynamical system most variations consist in inequalities and formal identities for the mean first arrival time and subsequent recurrence times for the given state

algebraic ℤ actions of entropy rank one we investigate algebraic z d actions of entropy rank one namely those for which each element has finite entropy such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery this leads to numerous alternative characterizations of entropy rank one both geometric and algebraic we then compute the measure entropy of a class of skew products where the fiber maps are elements from an algebraic z d action of entropy rank one this leads via the relative variational principle to a formula for the topological entropy of continuous skew products as the maximum of a finite number of topological pressures we use this to settle a conjecture concerning the relational entropy of commuting toral automorphisms

ergodic and bernoulli properties of analytic maps of complex projective space we examine the measurable ergodic theory of analytic maps f of complex projective space we focus on two different classes of maps ueda maps of p n and rational maps of the sphere with parabolic orbifold and julia set equal to the entire sphere we construct measures which are invariant ergodic weak or strong mixing exact or automorphically bernoulli with respect to these maps we discuss topological pressure and measures of maximal entropy h f h top f log deg f we find analytic maps of p 1 and p 2 which are one sided bernoulli of maximal entropy including examples where the maximal entropy measure lies in the smooth measure class further we prove that for any integer d 1 there exists a rational map of the sphere which is one sided bernoulli of entropy log d with respect to a smooth measure

on the bernoulli property for certain partially hyperbolic diffeomorphisms abstract we address the classical problem of equivalence between kolmogorov and bernoulli property of smooth dynamical systems in a natural class of volume preserving partially hyperbolic diffeomorphisms homotopic to anosov derived from anosov on 3 torus we prove that kolmogorov and bernoulli properties are equivalent in our approach we propose to study the conditional measures of volume along central foliation to recover fine ergodic properties for partially hyperbolic diffeomorphisms as an important consequence we obtain that there exists an almost everywhere conjugacy between any volume preserving derived from anosov diffeomorphism of 3 torus and its linearization our results also hold in higher dimensional case when central bundle is one dimensional and stable and unstable foliations are quasi isometric

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

long time tails in a random diffusion model letw w x x zd be a positive random field with i i d distribution given its realization letxt be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w 1 xt the processx xt t 0 combined withw on a common probability space is an example of random walk in random environment we consider the quantities t d dt e x t 2 m 1t and t w d dt ew x t 2 m 1t here ew is expectation overx at fixedw and e ew dw is the expectation over bothx andw we prove the following long time tail results 1 limt td 2 t v2md 2 3 d 2 d 2 and 2 limt td 4 st w zs weakly in path space with zs s 0 the gaussian process with ezs 0 and ezrzs v2md 2 4 d d 2 r s d 2 herem and v2 are the mean and variance of w 0 under the main surprise is that fixingw changes the power of the long time tail fromd 2 tod 4 since delta t me mu 0 w 1 x 0 m 1 w 1 x t m 1 with 0 the stationary measure for the environment process our result 1 exhibits a long time tail in an equilibrium autocorrelation function

anisotropic diffusion with generalized diffusion coefficient function for defect detection in low contrast surface images in this paper an anisotropic diffusion model with a generalized diffusion coefficient function is presented for defect detection in low contrast surface images and especially aims at material surfaces found in liquid crystal display lcd manufacturing a defect embedded in a low contrast surface image is extremely difficult to detect because the intensity difference between the unevenly illuminated background and the defective region is hardly observable and no clear edges are present between the defect and its surroundings the proposed anisotropic diffusion model provides a generalized diffusion mechanism that can flexibly change the curve of the diffusion coefficient function it adaptively carries out a smoothing process for faultless areas and performs a sharpening process for defect areas in an image an entropy criterion is proposed as the performance measure of the diffused image and then a stochastic evolutionary computation algorithm particle swarm optimization pso is applied to automatically determine the best parameter values of the generalized diffusion coefficient function experimental results have shown that the proposed method can effectively and efficiently detect small defects in various low contrast surface images

image recovery using the anisotropic diffusion equation a new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales the diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter a new discrete realization is developed for the simultaneous removal of noise and preservation of edges

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

rational maps are d adic bernoulli freire lopes and mafine proved that for any rational map f there exists a natural invariant measure f 5 maiine showed there exists an n 0 such that fn af is measurably conjugate to the one sided dn shift with bernoulli measure d 15 in this paper we show that f uf is conjugate to the one sided bernoulli d shift this verifies a conjecture of freire lopes and maine 5 and lyubich 11

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

tail triviality for sums of stationary random variables we study tail sigma fields and loss of memory associated with sums of stationary integer valued random variables an application concerns convergence in distribution of interarrival times in zero one sequences

symmetric duality for mathematical programming in complex spaces with f convexity abstract under f convexity f concavity f pseudoconvexity f pseudoconcavity appropriate duality results for a pair of wolfe and mond weir type symmetric dual nonlinear programming problems in complex spaces are established these results are then used to develop second order f convexity f concavity second order f pseudoconvexity f pseudoconcavity and appropriate second order symmetric dual nonlinear programming problems in complex spaces

mixing properties for random walk in random scenery consider the lattice z d d geq 1 together with a stochastic black white coloring of its points and on it a random walk that is independent of the coloring a local scenery perceived at a given time is a pattern of colors seen by the walker in a finite box around his current position under weak assumptions on the probability distributions governing walk and coloring we prove asymptotic independence of local sceneries perceived at times 0 and n in the limit as n rightarrow infty and at times 0 and t k in the limit as k rightarrow infty where t k is the random k th hitting time of a black point an immediate corollary of the latter result is the convergence in distribution of the interarrival times between successive black hits i e of t k 1 t k as k rightarrow infty the limit distribution is expressed in terms of the distribution of the first hitting time t 1 the proof uses coupling arguments and ergodic theory

reconstructing a random scenery observed with random errors along a random walk path we show that an i i d uniformly colored scenery on observed along a random walk path with bounded jumps can still be reconstructed if there are some errors in the observations we assume the random walk is recurrent and can reach every point with positive probability at time k the random walker observes the color at her present location with probability 1 and an error y k with probability the errors y k k 0 are assumed to be stationary and ergodic and independent of scenery and random walk if the number of colors is strictly larger than the number of possible jumps for the random walk and is sufficiently small then almost all sceneries can be almost surely reconstructed up to translations and reflections

entropy and dyadic equivalence of random walks on a random scenery abstract for any 1 1 measure preserving map t of a probability space consider the t t 1 endomorphism and the corresponding decreasing sequence of algebras we demonstrate that if the decreasing sequence of algebras generated by t t 1 and s s 1 are isomorphic then t and s must have equal entropies as a consequence if the t t 1 endomorphism is isomorphic to the s s 1 endomorphism then the entropy of t is equal to the entropy of s central to this is a relationship between feldman s f metric 1976 israel j math 24 16 38 and vershik s v metric 1970 dokl akad nauk sssr193 748 751

second order symmetric duality for nonlinear minimax mixed integer programs abstract wolfe type second order minimax mixed integer dual programs are formulated and a symmetric duality theorem is e established under separability and bonvexity boncavity of the kernel function k x y mond weir type symmetric duality is also discussed under weaker bonvexity assumptions moreover self duality theorems for these pairs are obtained assuming k x y to be skew symmetric

retrieving random media benjamini asked whether the scenery reconstruction methods of matzinger see e g 21 22 20 can be done in polynomial time in this article we give the following answer for a 2 color scenery and simple random walk with holding we prove that a piece of the scenery of length of the order 3 n around the origin can be reconstructed up to a reflection and a small translation with high probability from the first 2 310 n observations with a constant 0 independent of n thus the number of observations needed is polynomial in the length of the piece of scenery which we reconstruct the probability that the reconstruction fails tends to 0 as n

a phase transition in random coin tossing suppose that a coin with bias theta is tossed at renewal times of a renewal process and a fair coin is tossed at all other times let mu theta be the distribution ofthe observed sequence of coin tosses and let u n denote the chance of a renewal at time n harris and keane showed that if sum n 1 infty u n 2 infty then mu theta and mu 0 are singular while if sum n 1 infty u n 2 infty and theta is small enough then mu theta is absolutely continuous with respect to mu 0 they conjectured that absolute continuity should not depend on theta but only on the square summability of u n we show that in fact the power law governing the decay of u n is crucial and for some renewal sequences u n there is a phase transition at a critical parameter theta c in 0 1 for theta theta c the measures mu theta and mu 0 are mutually absolutely continuous but for theta theta c they are singular we also prove that when u n o n 1 the measures mu theta for theta in 1 1 are all mutually absolutely continuous

pseudo invexity and symmetric duality in nonlinear fractional programming abstract the purpose of this paper is to study the symmetric dual fractional programming problem for pseudo invex functions and arbitrary cones several known results are obtained as special cases

on multiobjective second order symmetric duality with cone constraints abstract a pair of wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions these results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets i e the sets of integers this paper points out certain omissions and inconsistencies in the earlier work of mishra s k mishra multiobjective second order symmetric duality with cone constraints european journal of operational research 126 2000 675 682 and mishra and wang s k mishra s y wang second order symmetric duality for nonlinear multiobjective mixed integer programming european journal of operational research 161 2005 673 682

a cell dynamical system model of chemical turbulence a cellular automaton like caricature of chemical turbulence on an infinite one dimensional lattice is studied the model exhibits apparently turbulent space time patterns to make this statement precise the following problems or points are discussed 1 the infinite system size limit of such cell dynamical systems and its observability is defined 2 it is proved that the invariant state in the large system size limit of the turbulent phase exhibits spatial patterns governed by a gibbs random field 3 potential characteristics of turbulent space time patterns are critically surveyed and a working definition of weak turbulence is proposed 4 it is proved that the invariant state of the turbulent phase is actually weak turbulent furthermore we conjecture that the turbulent phase of our model is an example of a k system that is not bernoulli

non differentiable second order symmetric duality in mathematical programming with f convexity abstract a pair of wolfe type non differentiable second order symmetric primal and dual problems in mathematical programming is formulated the weak and strong duality theorems are then established under second order f convexity assumptions symmetric minimax mixed integer primal and dual problems are also investigated

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

mond weir type second order symmetric duality in non differentiable minimax mixed integer programming problems abstract a pair of mond weir type non differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated symmetric and self duality theorems are then established under second order f pseudo convexity assumptions several known results including that of gulati and ahmad eur j oper res 101 1997 122 hou and yang j math anal appl 255 2001 491 and mond and schechter bull aust math soc 53 1996 177 as well as others are obtained as special cases

higher order nondifferentiable symmetric duality with generalized f convexity a pair of nondifferentiable higher order wolfe type symmetric dual models is formulated and usual duality theorems are established under higher order f convexity assumption symmetric minimax mixed integer primal and dual problems are also discussed

non differentiable higher order symmetric duality in mathematical programming with generalized invexity a pair of non differentiable higher order symmetric dual model in mathematical programming is formulated the weak and strong duality theorems are established under higher order invexity assumption symmetric minimax mixed integer primal and dual problems are also investigated

stretched exponential relaxation in the biased random voter model we study the relaxation properties of the voter model with i i d random bias we prove under mild conditions that the disorder averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent d d where 0 2 depends on the transition rates of the non biased voter model under an additional assumption we show that the above upper bound is optimal the main ingredient of our proof is a result of donsker and varadhan

on a pair of nonlinear mixed integer programming problems abstract we consider maximin and minimax nonlinear mixed integer programming problems which are nonsymmetric in duality sense under weaker pseudo convex pseudo concave assumptions we show that the supremum infimum of the maximin problem is greater than or equal to the infimum supremum of the minimax problem as a particular case this result reduces to the weak duality theorem for minimax and symmetric dual nonlinear mixed integer programming problems further this is used to generalize available results on minimax and symmetric duality in nonlinear mixed integer programming

symmetric duality for minimax nonlinear mixed integer programming abstract a pair of symmetric dual minimax integer programming problems is formulated and an appropriate duality theorem is established under the pseudoconvexity pseudoconcavity assumption on the kernel function k x y this model removes certain inconsistencies in an earlier model and helps to study self duality as well

local limit theorem for randomly deforming billiards we study limit theorems in the context of random perturbations of dispersing billiards in finite and infinite measure in the context of a planar periodic lorentz gas with finite horizon we consider random perturbations in the form of movements and deformations of scatterers we prove a central limit theorem for the cell index of planar motion as well as a mixing local limit theorem for piecewise holder continuous observables in the context of the infinite measure random system we prove limit theorems regarding visits to new obstacles and self intersections as well as decorrelation estimates the main tool we use is the adaptation of anisotropic banach spaces to the random setting

multiobjective higher order symmetric duality involving generalized cone invex functions in this paper a pair of mond weir type multiobjective higher order symmetric dual programs over arbitrary cones is formulated and usual duality results are established under higher order k preinvexity k pseudoinvexity assumptions symmetric minimax mixed integer primal and dual problems are also discussed

random walks on lattices with points of two colours i abstract this paper is concerned with random walks on lattices with two kinds of points black and white the colours of the points are random variables with a translation invariant but otherwise arbitrary joint probability distribution the steps of the walk are independent of the colours we study the stochastic properties of the length of the subwalk from the starting point to a first black point and of subwalks between points visited in succession and establish a number of exact relations these relations can be applied to a trapping problem by identifying the black points with imperfect traps an example is discussed

on the choice of the parameters for anisotropic diffusion in image processing anisotropic diffusion filtering is highly dependent on some crucial parameters such as the conductance function the gradient threshold parameter and the stopping time of the iterative process the various alternative options at each stage of the algorithm are examined and evaluated and the best choice is selected an automatic stopping criterion is proposed that takes into consideration the quality of the preserved edges as opposed to just the level of smoothing achieved the proposed scheme is evaluated with the help of real and simulated images and compared with other state of the art schemes using objective criteria

a long time tail for random walk in random scenery consider a simple random walk on d whose sites are colored black or white independently with probabilityq resp 1 q walk and coloring are independent letn k be the number of steps by the walk between itskth and k 1 th visits to a black site i e the length of itskth white run and let k e n k q 1 our main result is a proof that lim k k d 2 k 1 q q d 2 2 d 2 d 2 since it is known thatq 1 k e n 1 n k 1 b e n 1 b e n k 1 b withb the event that the origin is black exhibits a long time tail in the run length autocorrelation function numerical calculations of k 1 k 100 ind 1 2 and 3 show that there is an oscillatory behavior of k for smallk this damps exponentially fast following which the power law sets in fairly rapidly we prove that if the coloring is not independent but is convex in the sense of fkg then the decay of k cannot be faster than

local variance controlled forward and backward diffusion for image enhancement and noise reduction in order to improve signal to noise ratio snr and contrast to noise ratio this paper introduces a local variance controlled forward and backward lvcfab diffusion algorithm for edge enhancement and noise reduction in our algorithm an alternative fab diffusion algorithm is proposed the results for the alternative fab algorithm show better algorithm behavior than other existing diffusion fab approaches furthermore two distinct discontinuity measures and the alternative fab diffusion are incorporated into a lvcfab diffusion algorithm where the joint use of the two measures leads to a complementary effect for preserving edge features in digital images this lvc mechanism adaptively modifies the degree of diffusion at any image location and is dependent on both local gradient and inhomogeneity qualitative experiments based on general digital images and magnetic resonance images show significant improvements when the lvcfab diffusion algorithm is used versus the existing anisotropic diffusion and the previous fab diffusion algorithms for enhancing edge features and improving image contrast quantitative analyses based on peak snr confirm the superiority of the proposed lvcfab diffusion algorithm

finite size scaling of the time dependent structure factor in the one dimensional glauber model abstract we study the time dependent structure factor of the one dimensional glauber model upon instantaneous cooling results obtained earlier by reiss mazenko and widom and bray are linked together next finite size scaling in the limit of zero temperature long times small wave vectors and large systems is established the scaling function is compared with numerical simulation results obtained by vinals and jasnow in the case of a two dimensional glauber model quenched into the region of phase separation

asymptotically brownian skew products give non loosely bernoulli k automorphisms a quite natural exponential mixing condition on a real valued cocyclef implies that the cocycle is asymptotically approximable by brownian motion to a degree better thant 1 2 this in turn implies that the skew extension by a positive entropy ergodic flow using the cocycle is not loosely bernoulli in complete analogy to kalikow st t 1 argument kal