hypothesis testing with multiterminal data compression the multiterminal hypothesis testing h xy against h xy is considered where x n x n and y n y n are separately encoded at rates r 1 and r 2 respectively the problem is to determine the minimum beta n of the second kind of error probability under the condition that the first kind of error probability alpha n leq epsilon for a prescribed 0 a good lower bound theta l r 1 r 2 on the power exponent theta r 1 r 2 epsilon lim inf n rightarrow infty 1 n log beta n is given and several interesting properties are revealed the lower bound is tighter than that of ahlswede and csiszar furthermore in the special case of testing against independence this bound turns out to coincide with that given by them the main arguments are devoted to the special case with r 2 infty corresponding to full side information for y n y n in particular the compact solution is established to the complete data compression cases which are useful in statistics from the practical point of view

presenting an algorithm to find nash equilibrium in two person static games with many strategies this article attempts to present an algorithm to find nash equilibrium point in large two person static games in static games each player chooses his her strategy simultaneously with other players equilibrium can be easily recognized in static games with a limited number of strategies this paper focuses on two person games in which each player deals with many strategies after reviewing the literature this article considers concepts such as game equilibrium and rationalism in order to identify the problem and the required methodology to solve it eventually a heuristic meta heuristic algorithm will be presented to solve such problems which have been validated using a sample problem

remote vector gaussian source coding with decoder side information under mutual information and distortion constraints let x y z be zero mean jointly gaussian random vectors of dimensions nx ny and nz respectively let p be the set of random variables w such that w harr y harr x z is a markov string we consider the following optimization problem wisinp min i y z subject to one of the following two possible constraints 1 i x w z ges ri and 2 the mean squared error between x and xcirc e x w z is less than d the problem under the first kind of constraint is motivated by multiple input multiple output mimo relay channels with an oblivious transmitter and a relay connected to the receiver through a dedicated link while for the second case it is motivated by source coding with decoder side information where the sensor observation is noisy in both cases we show that jointly gaussian solutions are optimal moreover explicit water filling interpretations are given for both cases which suggest transform coding approaches performed in different transform domains and that the optimal solution for one problem is in general suboptimal for the other

theory of genetic algorithms ii models for genetic operators over the string tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling we present a theoretical framework for an asymptotically converging scaled genetic algorithm which uses an arbitrary size alphabet and common scaled genetic operators the alphabet can be interpreted as a set of equidistant real numbers and multiple spot mutation performs a scalable compromise between pure random search and neighborhood based change on the alphabet level we discuss several versions of the crossover operator and their interplay with mutation in particular we consider uniform crossover and gene lottery crossover which does not commute with mutation the vose liepins version of mutation crossover is also integrated in our approach in order to achieve convergence to global optima the mutation rate and the crossover rate have to be annealed to zero in proper fashion and unbounded power law scaled proportional fitness selection is used with logarithmic growth in the exponent our analysis shows that using certain types of crossover operators and large population size allows for particularly slow annealing schedules for the crossover rate in our discussion we focus on the following three major aspects based upon contraction properties of the mutation and fitness selection operators i the drive towards uniform populations in a genetic algorithm using standard operations ii weak ergodicity of the inhomogeneous markov chain describing the probabilistic model for the scaled algorithm iii convergence to globally optimal solutions in particular we remove two restrictions imposed in theorem 8 6 and remark 8 7 of theoret comput sci 259 2001 1 where a similar type of algorithm is considered as described here mutation need not commute with crossover and the fitness function which may come from a coevolutionary single species setting need not have a single maximum

distributed rate distortion with common components we describe a scheme for rate distortion with distributed encoding in which the sources to be compressed contain a common component we show that this scheme is optimal in some situations and that it strictly improves upon existing schemes which do not make full use of common components this establishes that independent quantization followed by independent binning is not optimal for the two encoder problem with a distortion constraint on one source we also show that independent quantization and binning is suboptimal for the three encoder problem in which the goal is to reproduce one of the sources losslessly this provides a counterexample that is fundamentally different from one provided earlier by korner and marton the proofs rely on the binary analogue of the entropy power inequality and the existence of a rate loss for the binary symmetric wyner ziv problem

the gaussian many help one distributed source coding problem jointly gaussian memoryless sources are observed at n distinct terminals the goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations say the first one at the decoder subject to a quadratic fidelity criterion our main result is a precise characterization of the rate distortion region when the covariance matrix of the sources satisfies a tree structure condition in this situation a natural analog digital separation scheme optimally trades off the distributed quantization rate tuples and the distortion in the reconstruction each encoder consists of a point to point gaussian vector quantizer followed by a slepian wolf binning encoder we also provide a partial converse that suggests that the tree structure condition is fundamental

on the optimality of binning for distributed hypothesis testing we study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data the aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value for related problems in distributed source coding schemes based on random binning perform well and are often optimal for distributed hypothesis testing however the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process we show that despite this complication binning is optimal for a class of problems in which the goal is to test against conditional independence we then use this optimality result to give an outer bound for a more general class of instances of the problem

nonstationary markov chains and convergence of the annealing algorithm we study the asymptotic behavior as timet of certain nonstationary markov chains and prove the convergence of the annealing algorithm in monte carlo simulations we find that in the limitt a nonstationary markov chain may exhibit phase transitions nonstationary markov chains in general and the annealing algorithm in particular lead to biased estimators for the expectation values of the process we compute the leading terms in the bias and the variance of the sample means estimator we find that the annealing algorithm converges if the temperaturet t goes to zero no faster thanc log t t0 ast with a computable constantc andt0 the initial time the bias and the variance of the sample means estimator in the annealing algorithm go to zero likeo t 1 e for some 0 e 1 with e 0 only in very special circumstances our results concerning the convergence of the annealing algorithm and the rate of convergence to zero of the bias and the variance of the sample means estimator provide a rigorous procedure for choosing the optimal annealing schedule this optimal choice reflects the competition between two physical effects a the adiabatic effect whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state and b the super cooling effect whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state s but may do so extremely slowly

improved source coding exponents via witsenhausen s rate we provide a novel upper bound on witsenhausen s rate the rate required in the zero error analogue of the slepian wolf problem our bound is given in terms of a new information theoretic functional defined on a certain graph and is derived by upper bounding complementary graph entropy we use the functional along with graph entropy to give a single letter lower bound on the error exponent for the slepian wolf problem under the vanishing error probability criterion where the decoder has full i e unencoded side information we demonstrate that our error exponent can beat the expurgated source coding exponent of csiszar and korner for some sources that have zeroes in the channel matrix connecting the source with the side information an extension of our scheme to the lossy case i e wyner ziv is given for the case in which the side information is a deterministic function of the source the exponent of our improved scheme agrees with the sphere packing bound exactly thus determining the reliability function an application of our functional to zero error channel capacity is also given

vector gaussian multiple description with two levels of receivers the problem of l multiple descriptions of a stationary and ergodic gaussian source with two levels of receivers is investigated each of the first level receivers receive an arbitrary subset k of the l descriptions k l the second level receiver receives all l descriptions all the receivers both at the first level and the second level reconstruct the source using the subset of descriptions they receive the corresponding reconstructions are subject to quadratic distortion constraints our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met we show that an analog digital separation architecture involving joint gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios these scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k 2 and l 3

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

statistical inference under multiterminal data compression this paper presents a survey of the literature on the information theoretic problems of statistical inference under multiterminal data compression with rate constraints significant emphasis is put on problems 1 multiterminal hypothesis testing 2 multiterminal parameter estimation and 3 multiterminal pattern classification in either case of positive rates or zero rates in addition the paper includes three new results i e the converse theorems for all problems of multiterminal hypothesis testing multiterminal parameter estimation and multiterminal pattern classification at the zero rate

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

reliability in source coding with side information we study error exponents for source coding with side information both achievable exponents and converse bounds are obtained for the following two cases lossless source coding with coded information and lossy source coding with full side information wyner ziv these results recover and extend several existing results on source coding error exponents and are tight in some circumstances our bounds have a natural interpretation as a two player game between nature and the code designer with nature seeking to minimize the exponent and the code designer seeking to maximize it in the wyner ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events the gaussian and binary erasure cases are examined in detail

linear codes for sources and source networks error exponents universal coding for slepian wolf source networks the error exponents obtained by korner marton and the author are shown to be universally attainable by linear codes also improved exponents are derived for linear codes with large rates specializing the results to simple discrete memoryless sources reveals their relationship to the random coding and expurgated bounds for channels with additive noise one corollary is that there are universal linear codes for this class of channels which attain the random coding error exponent for each channel in the class the combinatorial approach of csiszar korner marton is used in particular all results are derived from a lemma specifying good encoders in terms of purely combinatorial properties

weak convergence and non linear ergodic theorems for reversible semigroups of non lipschitzian mappings abstract letgbe a semitopological semigroup letcbe a closed convex subset of a uniformly convex banach spaceewith afrechetdifferentiable norm and t tt t g be a continuous representation ofgas asymptotically nonexpansive type mappings ofcinto itself such that the common fixed point setf t of t incis nonempty we prove in this paper that ifgis right reversible then for every almost orbitu of t formula consists of at most one point further formula is nonempty for eachx cif and only if there exists a nonexpansive retractionpofcontof t such thatpts tsp pfor alls gandp x is in the closed convex hull of tsx s g x c this result is applied to study the problem of weak convergence of the net u t t g to a common fixed point of t

theory of genetic algorithms i we investigate spectral and geometric properties of the mutation crossover operator in a genetic algorithm with general size alphabet by computing spectral estimates we show how the crossover operator enhances the averaging procedure of the mutation operator in the random generator phase of the genetic algorithm by mapping our model to the multi set model often investigated in the literature we compute corresponding spectral estimates for mutation crossover in the multi set model ii various types of unscaled or scaled fitness selection mechanisms are considered such as proportional fitness selection rank selection and tournament fitness selection we allow fitness selection mechanisms where the fitness of an individual or creature depends upon the population it resides in we investigate contracting properties of these fitness selection mechanisms and combine them with the crossover operator to obtain a model for genetic drift this has applications to the study of genetic algorithms with zero or extremely low mutation rate iii we discuss a variety of convergent simulated annealing type algorithms with mutation crossover as generator matrix iv the theory includes proof of strong ergodicity for various types of scaled genetic algorithms using common fitness selection methods if the mutation rate converges to a positive value and the other operators of the genetic algorithm converge then the limit probability distribution over populations is fully positive at uniform populations whose members have not necessarily optimal fitness v in what follows suppose the mutation rate converges to zero sufficiently slow to assure weak ergodicity of the inhomogeneous markov chain describing the genetic algorithm unbounded power law scaling for the fitness selection is used mutation and crossover commute and the fitness function is injective which is a minor restriction in regard to function optimization va if a certain integrable convergence condition is satisfied such that the selection pressure increases fast then there is essentially no other restriction on the crossover operation and the algorithm asymptotically behaves as the following take the best search algorithm 1 mutate in every step with rate decreasing to zero and 2 map any population to the uniform population with the best creature the take the best search algorithm is investigated and its convergence is shown depending upon population size the take the best search algorithm does or does not necessarily converge to the optimal solution vb if population size is larger than length of genome and a certain logarithmic convergence condition is satisfied such that the selection pressure increases slowly but sufficiently fast then the algorithm asymptotically converges to the optimal solution

linear analysis of genetic algorithms original article can be found at http www sciencedirect com science journal 03043975 copyright elsevier b v doi 10 1016 s0304 3975 98 00004 8 full text of this article is not available in the uhra

the effect of multiple optima on the simple ga run time complexity genetic algorithms are stochastic search algorithms that have been applied to optimization problems in this paper we analyze the run time complexity of a genetic algorithm when we are interested in one of a set of distinguished solutions one such case occurs when multiple optima exist we define the worst case scenario and derive a probabilistic worst case bound on the number of iterations required to find one of these multiple solutions of interest

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem