brownian motion with restoring drift micro canonical ensemble and the thermodynamic limit we take up the old problem of micro canonical conditioning in the context of diffusion starting with a potential the schrodinger operator with ground state is carried by a conjugation into the diffusion generator with invariant density the latter motion is made micro canonical by first conditioning the path to be periodic and then further conditioning on the empirical mean square or particle number the thermodynamics are then studied by taking while d remains fixed the problem in this form owes its inception to mckean vaninsky cite mv2 who obtained the following result for with they showed the same type of diffusion appears in the thermodynamic limit but with drift arising from the shifted potential being such that the limiting mean square equals d their method of proof predicts the same outcome for so long as d is smaller than the canonical mean square while if the matter was unresolved the purpose of this note is to show a type of phase transition takes place in this case the conditioning is overcome in the limit and one sees the original stationary diffusion on the line the proof employs an entropy inequality due to csiszar 1

corrigendum to parameterized tractability of the maximum duo preservation string mapping problem theoret comput sci 646 2016 16 25 this is a corrigendum for our paper 1 as we have found that the first fpt algorithm for the maximum duo preservation string mapping problem we presented is incorrect however we show that by slightly modifying the color coding technique on which the algorithm is based we can fix the error thus giving a correct fpt algorithm for maximum duo preservation string mapping problem

convergence of the maximum a posteriori path estimator in hidden markov models in a hidden markov model hmm the underlying finite state markov chain cannot be observed directly but only by an additional process we are interested in estimating the unknown path of the markov chain the most widely used estimator is the maximum a posteriori path estimator map path estimator it can be calculated effectively by the viterbi 1967 algorithm as is e g frequently done in the field of coding theory correction of intersymbol interference and speech recognition we investigate component wise convergence of the map path estimator convergence is shown under the condition of unbounded likelihood ratios this condition is satisfied in the important case of hmms with additive white gaussian noise we also prove convergence if the markov chain has two states the so called viterbi paths are an important tool for obtaining these results

a dependent data extension of wald s identity and its application to sequential test performance computation the development of an exponential transformation of measure not restricted to independent identically distributed data is presented for a class of semi markov processes known as markov additive ma process the ma measure transformation is applied to obtain a new form of the wald identity to demonstrate the utility of this extension to ma processes the application of sequential tests with markov data to error probability performance analysis is investigated in particular it is demonstrated how previous work dealing with robust error probability evaluation in the presence of uncertain serial dependency can be applied to sequential tests

solving the maximum duo preservation string mapping problem with linear programming abstract in this paper we introduce the maximum duo preservation string mapping problem mpsm which is complementary to the minimum common string partition problem mcsp when each letter occurs at most k times in any input string the version of mpsm is called k mpsm in order to design approximation algorithms for mpsm we also introduce the constrained maximum induced subgraph problem cmis and the constrained minimum induced subgraph cnis problem we show that both cmis and cnis are np complete we also study the approximation algorithms for the restricted version of cmis which is called k cmis k 2 using linear programming method we propose an approximation algorithm for 2 cmis with approximation ratio 2 and an approximation algorithm for k cmis k 3 with approximation ratio k 2 based on approximation algorithms for k cmis we get approximation algorithms for k mpsm with the same approximation ratio

an asymptotically least favorable chernoff bound for a large class of dependent data processes it is desired to determine the worst case asymptotic error probability performance of a given detector operating in an environment of uncertain data dependency a class of markov data process distributions is considered which satisfy a one shift dependency bound and agree with a specified univariate distribution within this dependency contamination class the distribution structure which minimizes the exponential rate of decrease of detection error probabilities is identified this is a uniform least favorability principle because the least favorable dependency structure is the same for all bounded memoryless detectors the error probability exponential rate criterion used is a device of large deviations theory the results agree well with previous results obtained using pitman s asymptotic relative efficiency are which is a more tractable small signal performance criterion in contrast to are large deviations theory is closely related to finite sample error probabilities via the finite sample chernoff bounds and other exponentially tight bounds and other approximations

asymptotic normality of the maximum likelihood estimator for general hidden markov models hidden markov models hmms have during the last decade become a widespread tool for modeling sequences of dependent random variables inference for such models is usually based on the maximum likelihood estimator mle and consistency of the mle for general hmms was recently proved by leroux in this paper we show that under mild conditions the mle is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the fisher information

asymptotic normality of the maximum likelihood estimator in state space models state space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way inference in such models has been studied by bickel ritov and ryden who consider hidden markov models which are special kinds of state space models and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions in this paper we generalize the results of bickel ritov and ryden to state space models where the latent process is a continuous state markov chain satisfying regularity conditions which are fulfilled if the latent process takes values in a compact space

hitting probabilities and large deviations let fyngn2z be a sequence of random variables in r d and let a r d then pfyn 2 a for some ng is the hitting probability of the set a by the sequence fyng we consider the asymptotic behavior as m 1 o fpfyn 2 ma some ng pfhitting mag whenever 1 the probability law of yn n satises the large deviation principle and 2 the central tendency of yn n is directed away from the given set a for a particular function i w e showpfyn 2 ma some n ge m i a

moderate deviations for empirical measures of markov chains lower bounds we obtain upper bounds for moderate deviations of empirical measures of markov chains with general state space in the topology under the minimal assumption of geometric ergodicity the regeneration split chain method and a result on projective systems are employed in the proof

maximum likelihood estimation for multivariate observations of markov sources parameter estimation for multivariate functions of markov chains a class of versatile statistical models for vector random processes is discussed the model regards an ordered sequence of vectors as noisy multivariate observations of a markov chain mixture distributions are a special case the foundations of the theory presented here were established by baum petrie soules and weiss a powerful representation theorem by fan is employed to generalize the analysis of baum em et al to a larger class of distributions

on a conjecture about slender context free languages we prove that every slender context free language is a union of paired loops thus confirming a conjecture of pa un and salomaa to appear a series of consequences of this result are inferred most of them also left as open problems in recent papers about slender languages

large deviation bounds for functionals of viterbi paths in a number of applications the underlying stochastic process is modeled as a finite state discrete time markov chain that cannot be observed directly and is represented by an auxiliary process the maximum a posteriori map estimator is widely used to estimate states of this hidden markov model through available observations the map path estimator based on a finite number of observations is calculated by the viterbi algorithm and is often referred to as the viterbi path it was recently shown in and see also and that under mild conditions the sequence of estimators of a given state converges almost surely to a limiting regenerative process as the number of observations approaches infinity this in particular implies a law of large numbers for some functionals of hidden states and finite viterbi paths the aim of this paper is to provide the corresponding large deviation estimates

branching random walk in random environment phase transitions for local and global growth rates let n be the infinite particle system on whose evolution is as follows at each unit of time each particle independently is replaced by a new generation the size of a new generation descending from a particle at sitex has distributionf x and each of its members independently jumps to sitex 1 with probability 1 h 2 h 0 1 the sequence f x is i i d with uniformly bounded second moment and is kept fixed during the evolution the initial configuration 0 is shift invariant and ergodic two quantities are considered

on lengths of words in context free languages we consider slender languages that is languages for which the number of words of the same length is bounded from above by a constant we prove that the slenderness problem is decidable for context free languages and that the maximal number of words of the same length in a given context free language is computable some effective representations of slender context free languages as well as other related decidability problems are investigated

properties of the maximum a posteriori path estimator in hidden markov models a hidden markov model hmm consists of a nonobservable markov chain x x0 x1 and a measured process y y 0 y1 whose distribution is determined by x to estimate the hidden path of x up to time n x0 x1 xn by the observations y 0 y1 yn usually the maximum a posteriori probability path estimator map path estimator is applied an effective means for calculating this estimator is the viterbi algorithm which is widely employed in the fields of coding theory correction of intersymbol interference and text recognition here properties of the map estimator are derived under a certain condition c it is shown that the limiting process u u0 u1 is a regenerative process particularly this means that u has an asymptotic distribution satisfies the central limit theorem and possesses a mean error furthermore condition c is satisfied for a broad class of hmms including the most important case for applications the hmm with additive white gaussian noise

closure properties of slender languages abstract we investigate languages where the number of words of every length is bounded from above by a constant independent of the length the issues involved are very basic in the theory of formal languages and moreover have arisen in some recent studies in cryptography this paper deals with closure properties of such slender languages with respect to a number of operations some of them introduced very recently closure is considered both in general and with respect to slender languages in the families of the chomsky hierarchy

parameterized tractability of the maximum duo preservation string mapping problem in this paper we investigate the parameterized complexity of the maximum duo preservation string mapping problem the complementary of the minimum common string partition problem we show that this problem is fixed parameter tractable when parameterized by the number k of conserved duos by first giving a parameterized algorithm based on the color coding technique and then presenting a reduction to a kernel of size o k 6

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

language theoretic problems arising from richelieu cryptosystems abstract classical cryptosystems of the type richelieu or garbage in between give rise to ideas and notions so far neglected in the theory of formal languages this paper investigates such notions mainly from the point of view of decidability

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

revisiting the parameterized complexity of maximum duo preservation string mapping abstract in the maximum duo preservation string mapping max duo psm problem the input consists of two related strings a and b of length n and a nonnegative integer k the objective is to determine whether there exists a mapping m from the set of positions of a to the set of positions of b that maps only to positions with the same character and preserves at least k duos which are pairs of adjacent positions we develop a randomized algorithm that solves max duo psm in 4 k n o 1 time and a deterministic algorithm that solves this problem in 6 855 k n o 1 time the previous best known deterministic algorithm for this problem has 8 e 2 k o k n o 1 running time beretta et al 2016 1 2 we also show that max duo psm admits a problem kernel of size o k 3 improving upon the previous best known problem kernel of size o k 6

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

determinant sums for undirected hamiltonicity we present a monte carlo algorithm for hamiltonicity detection in an n vertex undirected graph running in o 1 657 n time to the best of our knowledge this is the first superpolynomial improvement on the worst case runtime for the problem since the o 2 n bound established for the traveling salesman problem tsp over 50 years ago r bellman j assoc comput mach 9 1962 pp 61 63 m held and r m karp j soc indust appl math 10 1962 pp 196 210 o f n suppresses polylogarithmic functions in f n it answers in part the first open problem in woeginger s 2003 survey on exact algorithms for np hard problems for bipartite graphs we improve the bound to o sqrt 2 n subset o 1 415 n time both the bipartite and the general algorithm can be implemented to use space polynomial in n we combine several recently resurrected ideas to get the results our main technical contribution is a new algebraic characterization of hamiltonian graphs we introduce an ex

markov additive processes i eigenvalue properties and limit theorems on etudie d un point de vue general les proprietes d existence et de regularite des valeurs propres et des fonctions propres de l operateur de feynman kac

exact filters for the estimation of the number of transitions of finite state continuous time markov processes the problem of estimating the number of transitions of finite state continuous time markov processes observed by a noisy sensor is considered a finite dimensional exact filter is derived and using the em algorithm an extension of the baum welch algorithm for the discrete time case an application is made to the problem of estimating the unknown transition matrix of a finite state continuous time markov process

a minimum discrimination information approach for hidden markov modeling an iterative approach for minimum discrimination information mdi hidden markov modeling of information sources is proposed the approach is developed for sources characterized by a given set of partial covariance matrices and for hidden markov models hmms with gaussian autoregressive output probability distributions pds the approach aims at estimating the hmm which yields the mdi with respect to all sources that could have produced the given set of partial covariance matrices each iteration of the mdi algorithm generates a new hmm as follows first a pd for the source is estimated by minimizing the discrimination information measure with respect to the old model over all pds which satisfy the given set of partial covariance matrices then a new model that decreases the discrimination information measure between the estimated pd of the source and the pd of the old model is developed the problem of estimating the pd of the source is formulated as a standard constrained minimization problem in the euclidean space the estimation of a new model given the pd of the source is done by a procedure that generalizes the baum algorithm the mdi approach is shown to be a descent algorithm for the discrimination information measure and its local convergence is proved

approximation of partial sums of arbitrary i i d random variables and the precision of the usual exponential upper bound this paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary i i d random variables the introduction of a single truncation allows the usual exponential upper bound to apply usefully whenever the summands are arbitrary i i d random variables more specifically let n be a fixed natural number and let z z 1 z 2 z n be arbitrary i i d random variables we construct a function f z n derived from the probability of occurrence of one or more large summands plus an upper bound of exponential type such that for some constant c 0 independent of z n and a and all real a c f z 2 n a formula math zj na 2f z n a furthermore examples show that the upper and lower bounds are achievable

a constructive proof of the existence of viterbi processes since the early days of digital communication hidden markov models hmms have now been also routinely used in speech recognition processing of natural languages images and in bioinformatics in an hmm x t y t t 1 observations x 1 x 2 are assumed to be conditionally independent given a markov process y 1 y 2 which itself is not observed moreover the conditional distribution of x t depends solely on y t central to the theory and applications of hmm is the viterbi algorithm to find a maximum a posteriori probability map estimate v x 1 t v 1 v 2 vt of y 1 t given observed data x 1 t maximum a posteriori paths are also known as the viterbi paths or alignments recently attempts have been made to study behavior of the viterbi alignments when t thus it has been shown that in some cases a well defined limiting viterbi alignment exists while innovative these attempts have relied on rather strong assumptions and involved proofs which are existential this work proves the existence of infinite viterbi alignments in a more constructive manner and for a very general class of hmms

length considerations in context free languages abstract in this paper we investigate languages containing at most a bounded number of words of each length we first show that the context free languages for which the number of words of every length is bounded by a fixed polynomial are exactly the bounded context free languages in the sense of ginsburg 1966 thus we present a length characterization for bounded context free languages we then study slender context free languages i e those containing at most a constant number of words of each length recently ilie proved that every such language can be described by a finite union of terms of the form uv i wx i y ilie 1994 we provide a completely different proof of this using constructive methods this enables us to prove that thinness and slenderness are decidable our proofs are based upon a novel characterization of languages in terms of the structure of the infinite paths in their prefix closure this characterization seems to be interesting in itself and can be expanded to more general families of languages

a recursive algorithm for the bayes solution of the smoothing problem the optimum fixed interval smoothing problem is solved using a bayesian approach assuming that the signal is markov and is corrupted by independent noise not necessarily additive a recursive algorithm to compute the a posteriori smoothed density is obtained using this recursive algorithm the smoothed estimate of a binary markov signal corrupted by an independent noise in a nonlinear manner is determined demonstrating that the bayesian approach presented in this paper is not restricted to the gauss markov problem

markov additive processes and perron frobenius eigenvalue inequalities we present a method for proving perron frobenius eigenvalue inequalities the method is to apply jensen s inequality to the change in a random evolution over a regenerative cycle of the underlying finite state markov chain one of the primary benefits of the method is that it readily gives necessary and sufficient conditions for strict inequality it also gives insights into some of the conjectures of j e cohen ney and nummelin s hypothesis 2 arises here as a condition for strict inequality and we explore its ramifications in detail for a special family of markov additive processes which we call fluid models this leads to a connection between hypothesis 2 and the condition p t p irreducible which arose in the work of cohen friedland kato and kelly

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture