robustness of strong stability of semigroups abstract in this paper we study the preservation of strong stability of strongly continuous semigroups on hilbert spaces in particular we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points we characterize classes of perturbations preserving the strong stability of the semigroup in addition we improve recent results on preservation of polynomial stability of a semigroup under perturbations of its generator theoretic results are illustrated with an example where we consider the preservation of the strong stability of a multiplication semigroup

ergodicity of markov channels a markov channel is a discrete information channel that includes as special cases the finite state channels and finite state codes of information theory kieffer and rahe proved that one sided and two sided markov channels have the following property if the input source to a markov channel is asymptotically mean stationary ams then so is the resulting input output process and hence the ergodic theorem and the shannon mcmillan breiman theorem hold for the input output process kieffer and rahe also provided a sufficient condition for any ams ergodic source to yield an ams ergodic input output process new conditions for a markov channel to have this ergodicity property are presented and discussed here several relations are developed among various classes of channels including weakly ergodic indecomposable and strongly mixing channels some connections between markov channels and the theory of nonhomogeneous markov chains are also discussed

a fitting algorithm for markov modulated poisson processes having two arrival rates abstract point processes with fluctuating arrival rates arise in many current applications of queueing theory notably in communications modeling markov modulated poisson processes mmpp have been used to describe such processes because they incorporate a mechanism to account for the temporal inhomogeneity of the arrival rates yet yield analytically tractable queueing results an iterative statistical procedure is developed for fitting mmpp having two arrival rates to observational data the procedure is largely numerical experimental and is motivated by maximum likelihood estimation

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

a two state markov mixture model for a time series of epileptic seizure counts this paper discusses a model for a time series of epileptic seizure counts in which the mean of a poisson distribution changes according to an underlying two state markov chain the em algorithm dempster laird and rubin 1977 journal of the royal statistical society series b 39 1 38 is used to compute maximum likelihood estimators for the parameters of this two state mixture model and extensions are made allowing for nonstationarity the model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple poisson distribution and poisson regressions some simulation results are also presented to demonstrate the feasibility of this model

time phase bispectral analysis bispectral analysis a technique based on high order statistics is extended to encompass time dependence for the case of coupled nonlinear oscillators it is applicable to univariate as well as to multivariate data obtained respectively from one or more of the oscillators it is demonstrated for a generic model of interacting systems whose basic units are the poincare oscillators their frequency and phase relationships are explored for different coupling strengths both with and without gaussian noise the distinctions between additive linear or quadratic and parametric frequency modulated interactions in the presence of noise are illustrated

decay estimates of functions through singular extensions of vector valued laplace transforms abstract let x be a banach space and let f l r x whose laplace transform extends analytically to some region containing i r 0 possibly having a pole at the origin in this paper we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its laplace transform along the imaginary axis this technique is applied to obtain decay estimates of smooth orbits of bounded c 0 semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum these results are close to those given recently by c j k batty and t duyckaerts

asymptotically optimal classification for multiple tests with empirically observed statistics the decision problem of testing m hypotheses when the source is kth order markov and there are m or fewer training sequences of length n and a single test sequence of length n is considered k m n n are all given it is shown what the requirements are on m n n to achieve vanishing exponential error probabilities and how to determine or bound the exponent a likelihood ratio test that is allowed to produce a no match decision is shown to provide asymptotically optimal error probabilities and minimum no match decisions as an important serial case the binary hypotheses problem without rejection is discussed it is shown that for this configuration only one training sequence is needed to achieve an asymptotically optimal test

analyticity of entropy rate of hidden markov chains with continuous alphabet we first prove that under certain mild assumptions the entropy rate of a hidden markov chain observed when passing a finite state stationary markov chain through a discrete time continuous output channel is analytic with respect to the input markov chain parameters we then further prove under strengthened assumptions on the channel that the entropy rate is jointly analytic as a function of both the input markov chain parameters and the channel parameters in particular the main theorems establish the analyticity of the entropy rate for two representative channels 1 cauchy and 2 gaussian the analyticity results obtained are expected to be helpful in computation estimation of entropy rate of hidden markov chains and capacity of finite state channels with continuous output alphabet

stability theory for semigroups using l p l q fourier multipliers abstract we study polynomial and exponential stability for c 0 semigroups using the recently developed theory of operator valued l p l q fourier multipliers we characterize polynomial decay of orbits of a c 0 semigroup in terms of the l p l q fourier multiplier properties of its resolvent using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space we do not assume that the semigroup is uniformly bounded our results depend only on spectral properties of the generator as a corollary of our work on polynomial stability we reprove and unify various existing results on exponential stability and we also obtain a new theorem on exponential stability for positive semigroups

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

blind equalization of iir channels using hidden markov models and extended least squares in this paper we present a blind equalization algorithm for noisy iir channels when the channel input is a finite state markov chain the algorithm yields estimates of the iir channel coefficients channel noise variance transition probabilities and state of the markov chain unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length our algorithm is computationally inexpensive our algorithm is based on combining a recursive hidden markov model hmm estimator with a relaxed spr strictly positive real extended least squares els scheme in simulation studies we show that the algorithm yields satisfactory estimates even in low snr we also compare the performance of our scheme with a truncated fir scheme and the constant modulus algorithm cma which is currently a popular algorithm in blind equalization

on the relations between modeling approaches for speech recognition some relations among approaches that have been applied to estimating models for acoustic signals in speech recognition systems are examined in particular the modeling approaches based on maximum likelihood ml maximum mutual information mmi and minimum discrimination information mdi are studied it is shown that all three approaches can be formulated uniformly as mdi modeling approaches for simultaneous estimation of the acoustic models for all words in the vocabulary and that none of the approaches requires any model correctness assumption the three approaches differ in the effective source being modeled and in the probability distribution attributed to this source

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

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

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

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

new finite dimensional filters and smoothers for noisily observed markov chains new finite dimensional filters and smoothers that are related to the wonham filter of a noisily observed markov chain are obtained in particular finite dimensional recursive filters and smoothers are given for the number of jumps from state i to state j for the occupation time of state i and for a stochastic integral related to the drift in the observations these filters allow easy application of the em algorithm for the estimation of the parameters of the markov chain and observation process

partially hidden markov models partially hidden markov models phmm are introduced they differ from the ordinary hmms in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations as an illustration they are applied to black and white image compression where the hidden variables may be interpreted as representing noncausal pixels

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

remarks on linear and nonlinear filtering this communication tries to give some insight into relationships existing between viterbi and the forward backward algorithm used in the context of hidden markov models on the one hand and kalman filtering and rauch tung striebel smoothing on the other we give a unifying view which shows how those algorithms are related and give an example of a nonlinear hybrid system that can be filtered through a mixed algorithm

synchronization between main rhythmic processes in the human cardiovascular system for the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans namely the main heart rhythm respiration and the process whose fundamental frequency is close to 0 1 hz the analysis of the experimental records reveals synchronous regimes of different orders n m between all the three main rhythms the influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered

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

phase relationships between two or more interacting processes from one dimensional time series i basic theory a general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system using one dimensional time series only it is based on the introduction of angles and radii of return times maps and on studying the dynamics of the angles an explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data it is valid under conditions of weak forcing this correspondence is confirmed numerically for a nonstationary process in a forced van der pol system a model describing the angles behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived to establish from experimental data whether or not two or more interacting processes are synchronized is an old and important problem in the absence of noise the existence of synchronization between two processes in interacting limit cycle oscillators was originally taken to imply that their basic frequencies of oscillation are related as integer numbers i e are rationally connected 1 2 and that their instantaneous phases are permanently locked this definition suggests that the detection of whether or not synchronization exists can be established by computation of the ratio of basic frequencies in the fourier spectrum of the signal from one of the sub systems involved even in this simplest case however the finite observation time and the discreteness of the digitiza tion steps used in practice will make it appear that all fre quencies are rationally connected thereby complicating the reliable estimation of their ratio furthermore the noise that is invariably present in all real macroscopic systems means that only effective synchronization 3 can normally take place meaning that the phases can remain locked only dur ing finite time intervals and that the basic frequencies may no longer be rationally connected 4 serious difficulties may also arise due to the nonstationarity of experimental data in view of these problems modern techniques for estab lishing the presence or absence of synchronization are based on the assumption that the behavior of each subsystem can be considered separately and that their individual time series can be compared by a variety of techniques e g by compu tation of the phase difference between them this approach has been justified theoretically 3 6 and is widely used to detect synchronization not only in periodic noisy but also in

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

consistent and asymptotically normal parameter estimates for hidden markov models hidden markov models are today widespread for modeling of various phenomena it has recently been shown by leroux that the maximum likelihood estimate mle of the parameters of a such a model is consistent and local asymptotic normality has been proved by bickel and ritov in this paper we propose a new clans of estimates which are consistent asymptoti cally normal and almost as good an the mle

strongly consistent code based identification and order estimation for constrained finite state model classes observations are made of data generated by a stationary ergodic finite alphabet information source according to an unknown statistical model two modeling problems the identification problem and the order estimation problem are considered it is required that the given model class in the identification problem and each given model class in the order estimation problem be a constrained finite state model class which is a type that includes many model classes of information theoretic interest strongly consistent decision rules are exhibited in both the identification problem and the order estimation problem the decision rules are code based in that a model class is chosen based on how well a certain code for that class encodes the observed data the code used for a model class is based on the maximum likelihood code for that class and asymptotic code performance is gauged by means of a key property of divergence rate distance

bayesian estimation of switching arma models abstract switching arma processes have recently appeared as an efficient modelling to nonlinear time series models because they can represent multiple or heterogeneous dynamics through simple components the levels of dependence between the observations are double at a first level the parameters of the model are selected by a markovian procedure at a second level the next observation is generated according to a standard time series model when the model involves a moving average structure the complexity of the resulting likelihood function is such that simulation techniques like those proposed by shephard 1994 biometrika 81 115 131 and billio and monfort 1998 journal of statistical planning and inference 68 65 103 are necessary to derive an inference on the parameters of the model we propose in this paper a bayesian approach with a non informative prior distribution developed in mengersen and robert 1996 bayesian statistics 5 oxford university press oxford pp 255 276 and robert and titterington 1998 statistics and computing 8 2 145 158 in the setup of mixtures of distributions and hidden markov models respectively the computation of the bayes estimates relies on mcmc techniques which iteratively simulate missing states innovations and parameters until convergence the performances of the method are illustrated on several simulated examples this work also extends the papers by chib and greenberg 1994 journal of econometrics 64 183 206 and chib 1996 journal of econometrics 75 1 79 97 which deal with arma and hidden markov models respectively

on classification with empirically observed statistics and universal data compression classification with empirically observed statistics is studied for finite alphabet sources efficient universal discriminant functions are described and shown to be related to universal data compression it is demonstrated that if one of the probability measure of the two classes is not known it is still possible to define a universal discrimination function which performs as the optimal likelihood ratio discriminant function which can be evaluated only if the probability measures of the two classes are available if both of the probability measures are not available but training vectors from at least one of the two classes are available it is demonstrated that no discriminant function can perform efficiency of the length of the training vectors does not grow at least linearly with the length of the classified vector a universal discriminant function is introduced and shown to perform efficiently when the length of the training vectors grows linearly with the length of the classified sequence in the sense that it yields an error exponent that is arbitrarily close to that of the optimal discriminant function

an algorithm for the design of labeled transition finite state vector quantizers a finite state vector quantizer fsvq is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder it can be viewed as an adaptive vector quantizer with backward estimation a vector generalization of an aqb system recently a family of algorithms for the design of fsvq s for waveform coding application has been introduced these algorithms first design an initial set of vector quantizers together with a next state function giving the rule by which the next quantizer is selected the codebooks of this initial fsvq are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm the next state function however is not modified from its initial form in this paper we present two extensions of the fsvq design algorithms first the algorithm for fsvq design for waveform coders is extended to fsvq design of linear predictive coded lpc speech parameter vectors using an itakura saito distortion measure second we introduce a new technique for the iterative improvement of the next state function based on an algorithm from adaptive stochastic automata theory the design algorithms are simulated for an lpc fsvq and the results are compared with each other and to ordinary memoryless vector quantization several open problems suggested by the simulation results are presented

on the entropy rate of hidden markov processes observed through arbitrary memoryless channels this paper studies the entropy rate of hidden markov processes hmps which are generated by observing a discrete time binary homogeneous markov chain through an arbitrary memoryless channel a fixed point functional equation is derived for the stationary distribution of an input symbol conditioned on all past observations while the existence of a solution to the fixed point functional equation is guaranteed by martingale theory its uniqueness follows from the fact that the solution is the fixed point of a contraction mapping the entropy or differential entropy rate of the hmp can then be obtained through computing the average entropy of each input symbol conditioned on past observations in absence of an analytical solution to the fixed point functional equation a numerical method is proposed in which the fixed point functional equation is first converted to a discrete linear system using uniform quantization and then solved efficiently the accuracy of the computed entropy rate is shown to be proportional to the quantization interval unlike many other numerical methods this numerical solution is not based on averaging over a sample path of the hmp

a filtered em algorithm for joint hidden markov model and sinusoidal parameter estimation derives finite dimensional discrete time filters for estimating the parameters of discrete time finite state markov chains imbedded in a mixture of gaussian white noise and deterministic signals of known functional form with unknown parameters the filters that are derived estimate quantities used in the expectation maximization em algorithm for maximum likelihood ml estimation of the markov chain parameters transition probabilities and state levels as well as the parameters of the deterministic interference two types of deterministic signals are considered periodic or almost periodic signals with unknown frequency components amplitudes and phases and polynomial drift in the states of the markov process with the coefficients of the polynomial unknown the filter based em algorithm has negligible memory requirements in comparison implementing the em algorithm using smoothed variables forward backward variables requires memory proportional to the number of observations in addition the filters are suitable for multiprocessor implementation unlike the forward backward algorithm

on the parameters estimation of continuous time arma processes from noisy observations recently an iterative algorithm has been presented for estimating the parameters of partially observed continuous time processes 1 in this note we concentrate on continuous time arma processes observed in white noise a maximum a posteriori map estimator is defined for the trajectory of the parameters random process this approach enables the map estimation of randomly slowly varying parameters and extends the conventional treatment of time invariant parameters the iterative algorithm derived for the map estimation increases the posterior probability of the parameters in each iteration and converges to a stationary point of the posterior probability functional each iteration involves a standard linear smoother followed by a finite dimensional linear system and thus is easily implemented

two types of phase synchronization destruction in this paper we report that there are two different types of destruction of the phase synchronization ps regime of chaotic oscillators depending on the parameter mismatch as well as in the case of the classical synchronization of periodic oscillators when the parameter mismatch of the interacting chaotic oscillators is small enough the ps breaking takes place without the destruction of the phase coherence of chaotic attractors of oscillators alternatively due to the large frequency detuning the ps breaking is accomplished by loss of the phase coherence of the chaotic attractors

detecting synchronization of self sustained oscillators by external driving with varying frequency we propose a method for detecting the presence of a synchronization of a self sustained oscillator by external driving with linearly varying frequency the method is based on a continuous wavelet transform of the signals of the self sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals we apply the method to a driven van der pol oscillator and to experimental data of human heart rate variability and respiration

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

theorems of katznelson tzafriri type for semigroups of operators let s be a locally compact abelian semigroup and t a bounded representation of s by linear bounded operators in a banach space x with spectrum sp t let spu t be the intersection of sp t with the set of unitary characters of s we prove that if s r or if t is norm continuous and if f is a function in l1 s which is of spectral synthesis with respect to spu t then inft s sf s t t s ds 0

application of the conditional population mixture model to image segmentation the problem of image segmentation is considered in the context of a mixture of probability distributions the segments fall into classes a probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function a numerical example is given choice of the number of classes using akaike s information criterion aic for model identification is illustrated

the strong ergodic theorem for densities generalized shannon mcmillan breiman theorem let xi x2 be a stationary process with probability densities f x1 x2 xn with respect to lebesgue measure or with respect to a markov measure with a stationary transition measure it is shown that the sequence of relative entropy densities 1 n log f xi x2 x0 converges almost surely this long conjectured result extends the l convergence obtained by moy perez and kieffer and generalizes the shannon mcmillanbreiman theorem to nondiscrete processes the heart of the proof is a new martingale inequality which shows that logarithms of densities are l dominated

optimal rates of decay for operator semigroups on hilbert spaces abstract we investigate rates of decay for c 0 semigroups on hilbert spaces under assumptions on the resolvent growth of the semigroup generator our main results show that one obtains the best possible estimate on the rate of decay that is to say an upper bound which is also known to be a lower bound under a comparatively mild assumption on the growth behaviour this extends several statements obtained by batty et al 2016 6 in fact for a large class of semigroups our condition is not only sufficient but also necessary for this optimal estimate to hold even without this assumption we obtain a new quantified asymptotic result which in many cases of interest gives a sharper estimate for the rate of decay than was previously available and for semigroups of normal operators we are able to describe the asymptotic behaviour exactly we illustrate the strength of our theoretical results by using them to obtain sharp estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary

phase relationships between two or more interacting processes from one dimensional time series ii application to heart rate variability data the recently proposed approach to detect synchronization from univariate data is applied to heart rate variability hrv data from ten healthy humans the approach involves introducing angles for return times map and studying their behavior for filtered human hrv data it is demonstrated that i in many of the subjects studied interactions between different processes within the cardiovascular system can be considered as weak and the angles can be well described by the derived model ii in some of the subjects the strengths of the interactions between the processes are sufficiently large that the angles map has a distinctive structure which is not captured by our model iii synchronization between the processes involved can often be detected iv the instantaneous radii are rather disordered

regions of cardiorespiratory synchronization in humans under paced respiration cardiorespiratory synchronization under paced respiration is studied systematically as the respiration frequency is changed between 3 and 30 breaths per min we plot a one dimensional cut of the classical picture of synchronization regions along the line defining the current breathing amplitude the existence of n m synchronization regions of finite width is demonstrated for each of six subjects studied the statistics of the different types of synchronization and their stability are discussed

optimal energy decay in a one dimensional wave heat system with infinite heat part abstract using recent results in the theory of c 0 semigroups due to batty et al 2016 5 we study energy decay in a one dimensional coupled wave heat system with finite wave part and infinite heat part our main result provides a sharp estimate for the rate of energy decay of a certain class of classical solutions the present paper can be thought of as a natural sequel to a recent work by batty et al 2016 6 which studied a similar wave heat system with finite wave and heat parts using a celebrated result due to borichev and tomilov

length distribution of laminar phases for type i intermittency in the presence of noise we consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type i intermittency and random dynamics we analytically deduce the laws for the distribution of the laminar phases with the law for the mean length of the laminar phases versus the critical parameter deduced earlier w h kye and c m kim phys rev e 62 6304 2000 being the corollary fact of the developed theory we find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations we discuss also how this mechanism is expected to take place in other relevant physical circumstances

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

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

time scale synchronization of chaotic oscillators this paper presents the result of the investigation of chaotic oscillator synchronization a new approach to detect the synchronized behaviour of chaotic oscillators has been proposed this approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators this approach has been applied for the coupled rossler and lorenz systems

l p tauberian theorems and l p rates for energy decay abstract we prove l p analogues of the classical tauberian theorem of ingham and karamata and its variations giving rates of decay these results are applied to derive l p decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains by constructing some examples of critical behaviour we show that the l p rates of decay obtained in this way are best possible under our assumptions

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

the consistency of the bic markov order estimator the bayesian information criterion bic estimates the order of a markov chain with finite alphabet a from observation of a sample path x 1 x 2 x n as that value k k that minimizes the sum of the negative logarithm of the kth order maximum likelihood and the penalty term a k a 1 2 log n we show that k equals the correct order of the chain eventually almost surely as n oo thereby strengthening earlier consistency results that assumed an apriori bound on the order a key tool is a strong ratio typicality result for markov sample paths we also show that the bayesian estimator or minimum description length estimator of which the bic estimator is regarded as an approximation fails to be consistent for the uniformly distributed i i d process

synchronization of spectral components and its regularities in chaotic dynamical systems the chaotic synchronization regime in coupled dynamical systems is considered it has been shown that theonset of a synchronous regime is based on the appearance of a phase relation between the interacting chaoticoscillator frequency components of fourier spectra the criterion of synchronization of spectral components aswell as the measure of synchronization has been discussed the universal power law has been described themain results are illustrated by coupled rossler systems van der pol and van der pol duf ng oscillators doi 10 1103 physreve 71 056204 pacs numberssd 05 45 xt 05 45 tpi introduction

asymptotics and approximation of large systems of ordinary differential equations abstract in this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations under the mild assumption that the so called characteristic function of our system is completely monotonic we obtain a drastically simplified condition which ensures boundedness of the associates semigroup if the characteristic function satisfies certain additional conditions we deduce sharp rates of convergence to equilibrium we moreover address the important and delicate issue of the role of the infinite system in understanding the asymptotic behaviour of large but finite systems and we provide a precise way of obtaining size independent rates of convergence for families of finite dimensional systems finally we illustrate our abstract results in the setting of the well known platoon problem

on the decay rate for the wave equation with viscoelastic boundary damping abstract we consider the wave equation with a boundary condition of memory type under natural conditions on the acoustic impedance of the boundary a corresponding semigroup of contractions is known to exist with the help of quantified tauberian theorems we establish energy decay rates via resolvent estimates on the generator of the semigroup using a variational approach we reduce resolvent estimates to estimates for a sesquilinear form induced by an operator characteristic function arising form the matrix representation of the generator under not too strict additional assumptions on the acoustic impedance we establish an upper bound on the resolvent for the wave equation on the interval or the disc we prove our estimates to be sharp

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

on universal coding for classes of composite and remote sources with memory corresp weakly minimax universal codes for composite sources whose channel analog has asymptotically decreasing input memory and anticipation adima are examined in particular weak universal codes of all rates with respect to an arbitrary distortion measure are shown to exist for adima composite sources when the switch processes belong to a bar d compact class these results are immediately applicable to universal coding for classes of remote sources

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

frequency domain approach for the polynomial stability of a system of partially damped wave equations in this paper we study the stability of a system of wave equations which are weakly coupled and partially damped using a frequency domain approach based on the growth of the resolvent on the imaginary axis we establish the polynomial energy decay rate for smooth initial data we show that the behavior of the system is sensitive to the arithmetic property of the ratio of the wave propagation speeds of the two equations

likelihood ratio tests for hidden markov models summary we consider hidden markov models as a versatile class of models for weakly dependent random phenomena the topic of the present paper is likelihood ratio testing for hidden markov models and we show that under appropriate conditions the standard asymptotic theory of likelihood ratio tests is valid such tests are crucial in the specification of multivariate gaussian hidden markov models which we use to illustrate the applicability of our general results finally the methodology is illustrated by means of a real data set

capacity of gaussian channels with duty cycle and power constraints in many wireless communication systems radios are subject to a duty cycle constraint that is a radio can only actively transmit signals over a fraction of the time for example it is desirable to have a small duty cycle in some low power systems a half duplex radio cannot keep transmitting if it wishes to receive useful signals and a cognitive radio needs to listen and detect primary users frequently this paper studies the capacity of point to point scalar discrete time gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint an idealized duty cycle constraint is first studied which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword independent input with a unique discrete distribution is shown to achieve the channel capacity in many situations numerically optimized on off signaling can achieve much higher rate than gaussian signaling over a deterministic transmission schedule this is in part because the positions of nontransmissions in a codeword can convey information a more realistic duty cycle constraint is also studied where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for the capacity achieving input is correlated over time and is hard to compute a lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first order markov input process whose stationary distribution is also discrete and can be computed efficiently the results in this paper suggest that under various duty cycle constraints departing from the usual paradigm of intermittent packet transmissions may yield substantial gain

operators l1 r x and the norm continuity problem for semigroups we present a new method for constructing c0 semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator norm topology are controlled simultaneously it allows us to show that a there exists a c0 semigroup which is continuous in the operator norm topology for no t 0 1 such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines b there exists a c0 semigroup which is continuous in the operator norm topology for no t r such that the resolvent of its generator has a decay along vertical lines arbitrarily close to a logarithmic one these examples rule out any possibility of characterizing norm continuity of semigroups on arbitrary banach spaces in terms of resolvent norm decay on vertical lines

recursive estimation of parameters in markov modulated poisson processes a hidden markov regime is a markov process that governs the time or space dependent distributions of an observed stochastic process recursive algorithms can be used to estimate parameters in mixed distributions governed by a markov regime the authors derive a recursive algorithm for estimation of parameters in a markov modulated poisson process also called a cox point process by this the authors mean a doubly stochastic poisson process with a time dependent intensity that can take on a finite number of different values the intensity switches randomly between the possible values according to a markov process the authors consider two different ways to observe the markov modulated poisson process in the first model the observations consist of the observed time intervals between events and in the second model they use the total number of events in successive intervals of fixed length they derive an algorithm for recursive estimation of the poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study the estimates of the switch intensities are based on the observed conditional switch probabilities

an inequality for rational functions with applications to some statistical estimation problems the well known baum eagon inequality 1967 provides an effective iterative scheme for finding a local maximum for homogeneous polynomials with positive coefficients over a domain of probability values however in many applications the goal is to maximize a general rational function in view of this the baum eagon inequality is extended to rational functions some of the applications of this inequality to statistical estimation problems are briefly described

a randomized algorithm for the capacity of finite state channels inspired by ideas from the field of stochastic approximation we propose a randomized algorithm to compute the capacity of a finite state channel with a markovian input when the mutual information rate of the channel is concave with respect to the chosen parameterization the proposed algorithm proves to be convergent to the capacity of the channel almost surely with the derived convergence rate we also discuss the convergence behavior of the algorithm without the concavity assumption

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

on the universality of the lz based decoding algorithm a universal decoder for a family of channels is a decoder that can be designed without prior knowledge of the particular channel in the family over which transmission takes place and it yet attains the same random coding error exponent as the optimal decoder tuned to the channel in use we study ziv s 1985 decoding algorithm which is based on lempel ziv 1978 incremental string parsing and demonstrate that while it was originally proposed as a universal decoder for the family of finite state channels with deterministic but unknown transitions it is in fact universal for the broader class of all finite state channels we also demonstrate that the generalized likelihood decoder may not be universal even for finite families for which a universal decoder always exists

detection of synchronization from univariate data using wavelet transform a method is proposed for detecting from univariate data the presence of synchronization of a self sustained oscillator by external driving with varying frequency the method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other we apply our method to a driven asymmetric van der pol oscillator experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series in the latest case the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure

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

zero lyapunov exponent in the vicinity of the saddle node bifurcation point in the presence of noise we consider a behavior of the zero lyapunov exponent in the vicinity of the bifurcation point that occurs as the result of the interplay between dynamical mechanisms and random dynamics we analytically deduce the laws for the dependence of this lyapunov exponent on the control parameter both above and below the bifurcation point the developed theory is applicable both to the systems with the random force and to the deterministic chaotic oscillators we find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations we also discuss how the revealed regularities are expected to take place in other relevant physical circumstances

limited rate channel state feedback for multicarrier block fading channels the capacity of a fading channel can be substantially increased by feeding back channel state information from the receiver to the transmitter if the feedback rate is limited what state information to feed back and how to encode it are important questions this paper studies power loading in a multicarrier system using no more than one bit of feedback per subchannel the subchannels can be correlated and full channel state information is assumed at the receiver first a simple model with n parallel two state good bad memoryless subchannels is considered where the channel state feedback is used to select a fixed number of subchannels to activate the optimal feedback scheme is the solution to a vector quantization problem and the associated performance for large n is characterized using a rate distortion function as n increases the loss in forward rate from the asymptotic rate distortion value is shown to decrease as logn n and logn n with optimal variable and fixed length feedback codes respectively these results are subsequently extended to parallel rayleigh block fading subchannels where the feedback designates a set of subchannels to be activated with equal power rate distortion feedback codes are proposed for designating subsets of good subchannels with signal to noise ratios snrs that exceed a threshold the associated performance is compared with that of a simpler lossless source coding scheme which designates groups of good subchannels where both the group size and threshold are optimized the rate distortion codes can provide a significant increase in forward rate at low snrs

optimal polynomial decay of functions and operator semigroups we characterize the polynomial decay of orbits of hilbert space c 0 semigroups in resolvent terms we also show that results of the same type for general banach space semigroups and functions obtained recently in batty and duyckaerts j evol eq 8 765 780 2008 are sharp this settles a conjecture posed in batty and duyckaerts 2008

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

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

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

cartesian hidden markov models with applications the author introduces the concept of a cartesian hidden markov model chmm which consists of a markov chain assuming values in the cartesian product of a finite number of elementary state sets the states are observed via a multivariable probabilistic mapping again assuming values in a cartesian product of finite sets of observables the chmm can be reduced to an ordinary i e scalar hmm by conventional nonlinear techniques the forms of the forward backward algorithm which gives the fixed interval smoothed maximum a posteriori map estimates of the states and the viterbi algorithm which gives the map fixed interval sequence are straightforward generalizations of the scalar case two applications of chmms in the area of frequency tracking are briefly indicated