limits of hypercyclic and supercyclic operators abstract an operator t on a complex separable infinite dimensional hilbert space h is hypercyclic if there is a vector y in h such that the orbit y ty t2y is dense in h it is shown that if t is hypercyclic then t does not have any eigenvalue and that the union of the spectrum of t and the unit circle is a connected set this result is used to obtain a spectral characterization of the norm closure of the class hc h of all hypercyclic operators acting on h as well as a formula for the distance from a given operator to hc h analogous results are obtained for the closely related class sc h of all supercyclic operators this paper includes some information about the structure of the set of all hypercyclic supercyclic vectors of a given hypercyclic supercyclic resp operator t

generalization in a multi state neural network the generalization ability of an extremely dilute feedback neural network with multi state neurons is studied by means of a deterministic noiseless parallel dynamics the overlap with any one of a macroscopic number of binary full activity concepts is determined when the network is trained with examples of variable activity according to a hebbian learning algorithm that favours stable symmetric mixture states explicit results about the phase diagram and the generalization error are obtained for a network with three state neurons which remain inactive below a threshold it is shown that the generalization ability can be considerably enhanced either by training the network with low activity examples or by means of a moderate increase in

theory of the dynamics of the hopfield model of associative memory we present an analysis of the parallel dynamics of the hopfield model of the associative memory of a neural network without recourse to the replica formalism a probabilistic method based on the signal to noise ratio is employed to obtain a simple recursion relation for the zero temperature as well as the finite temperature dynamics of the network the fixed points of the recursion relation and their basins of attraction are found to be in fairly satisfactory agreement with the numerical simulations of the model we also present some new numerical results which support our recursion relation and throw light on the nature of the ensemble of the network states which are optimized with respect to single spin flips

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

dynamics of ising random bond models neural network and random anisotropy axis model a discrete time retrieval dynamics for a class of random bond models with infinite range interactions is studied in a unified picture the hopfield model of neural networks with the hebb learning rule is considered together with the ising random anisotropy axis model in the strong anisotropy limit the main overlap magnetization the residual overlap and its dispersion as well as the correlation between the gaussian component of the residual overlap and the initial value of the latter obtained in the first step of a recursion relation are used to infer the structure of the recursion for large times a crucial assumption is the strong stationarity of the gaussian component the dynamics are discussed for finite alpha p n the storage ratio in the neural network problem or the ratio of random axis components per site in the limit where both p and n go to infinity the long time behaviour of the theory is shown to yield the equilibrium solution of an earlier work in mean field theory for a tri modal distribution of random axis components explicit results for the basins of attraction of either a ferromagnetic or a spin glass phase are obtained as well as the relaxation time with a square root power law decay near saturation

on the correct convergence of the em algorithm for gaussian mixtures it is well known that the em algorithm generally converges to a local maximum likelihood estimate however there have been many evidences to show that the em algorithm can converge correctly to the true parameters as long as the overlap of gaussians in the sample data is small enough this paper studies this correct convergence problem asymptotically on the em algorithm for gaussian mixtures it has been proved that the em algorithm becomes a contraction mapping of the parameters within a neighborhood of the consistent solution of the maximum likelihood when the measure of average overlap among gaussians in the original mixture is small enough and the number of samples is large enough that is if the initial parameters are set within the neighborhood the em algorithm will always converge to the consistent solution i e the expected result moreover the simulation results further demonstrate that this correct convergence neighborhood becomes larger as the average overlap becomes smaller

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

on the parallel dynamics for the little hopfield model we propose a method algorithm for calculation of the explicit formulas for evolution of the main and the residual overlaps it allows us to confirm the gardner derrida mottishaw second step formula for the main overlap and to go beyond to the next steps we discuss the dynamical status of the amit gutfreund sompolinsky formula for the main overlap and some computersimulation results

on universal subsets of banach spaces we prove that to most of the known hypercyclic operators a on separable banach spaces there exist compact compact convex compact connected subsets k of e such that each compact compact convex compact connected subset of e can be approximated with respect to hausdorff s distance by a n k for suitable n in mathbb n

dense lineability of sets of birkhoff universal functions with rapid decay let a be an unbounded arakelian set in the complex plane whose complement has infinite inscribed radius and be an increasing positive function on the positive real numbers we prove the existence of a dense linear manifold m of entire functions all of whose non zero members are birkhoff universal such that each function in m has overall growth faster than and in addition exp z f z 0 z z a for all 1 2 and f m with slightly more restrictive conditions on a we get that the last property also holds for the action tf of certain holomorphic operators t our results unify extend and complete recent work by several authors

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

better than uniform approximation on closed sets by harmonic functions with singularities we work in the euclidean space r n where unless the contrary is stated n 2 the euclidean norm of a point x r n is denoted by x if r 0 the we denote the open ball of centre x and radius r by b x r and we write b 0 x r b x r x

genericity of wild holomorphic functions and common hypercyclic vectors abstract let t be the translation operator by in the space of entire functions h c defined by t f z f z we prove that there is a residual set g of entire functions such that for every f g and every c 0 the sequence t n f is dense in h c that is g is a residual set of common hypercyclic vectors functions for the family t c 0 also we prove similar results for many families of operators as multiples of differential operator multiples of backward shift weighted backward shifts

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

bayesian texture classification based on contourlet transform and byy harmony learning of poisson mixtures as a newly developed 2 d extension of the wavelet transform using multiscale and directional filter banks the contourlet transform can effectively capture the intrinsic geometric structures and smooth contours of a texture image that are the dominant features for texture classification in this paper we propose a novel bayesian texture classifier based on the adaptive model selection learning of poisson mixtures on the contourlet features of texture images the adaptive model selection learning of poisson mixtures is carried out by the recently established adaptive gradient bayesian ying yang harmony learning algorithm for poisson mixtures it is demonstrated by the experiments that our proposed bayesian classifier significantly improves the texture classification accuracy in comparison with several current state of the art texture classification approaches

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

a lot of counterexamples to liouville s theorem abstract we prove in this paper that given 0 1 2 there exists a linear manifoldmof entire functions satisfying thatmis dense in the space of all entire functions and in addition limz exp z f j z 0 on any plane strip for everyf mand for every derivation indexj moreover it is shown the existence of an entire function with infinite growth index satisfying the latter property

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

improved kinetic renormalisation group approach to diffusion limited aggregation an improved kinetic renormalisation group approach to diffusion limited aggregation is presented this approach is based on the growth process itself and accounts for the dispersity in the growth probabilities it yields the multifractal spectrum d q with better values at smaller q on the 2d square lattice the authors find df 1 694 for the fractal dimensions of the cluster and that of its interface and d 1 1 01 for the information dimension the former agrees with the simulation results df approximately 1 70 and the latter compares very well with the exact value d 1 1

parameter estimation of poisson mixture with automated model selection through byy harmony learning finite mixture is widely used in the fields of information processing and data analysis however its model selection i e the selection of components in the mixture for a given sample data set has been still a rather difficult task recently the bayesian ying yang byy harmony learning has provided a new approach to the gaussian mixture modeling with a favorite feature that model selection can be made automatically during parameter learning in this paper based on the same byy harmony learning framework for finite mixture we propose an adaptive gradient byy learning algorithm for poisson mixture with automated model selection it is demonstrated well by the simulation experiments that this adaptive gradient byy learning algorithm can automatically determine the number of actual poisson components for a sample data set with a good estimation of the parameters in the original or true mixture where the components are separated in a certain degree moreover the adaptive gradient byy learning algorithm is successfully applied to texture classification

the byy annealing learning algorithm for gaussian mixture with automated model selection bayesian ying yang byy learning has provided a new mechanism that makes parameter learning with automated model selection via maximizing a harmony function on a backward architecture of the byy system for the gaussian mixture however since there are a large number of local maxima for the harmony function any local searching algorithm such as the hard cut em algorithm does not work well in order to overcome this difficulty we propose a simulated annealing learning algorithm to search the global maximum of the harmony function being expressed as a kind of deterministic annealing em procedure it is demonstrated by the simulation experiments that this byy annealing learning algorithm can efficiently and automatically determine the number of clusters or gaussians during the learning process moreover the byy annealing learning algorithm is successfully applied to two real life data sets including iris data classification and unsupervised color image segmentation

a dynamical characterization of sub arakelian subsets abstract we are going to characterize those sets which can be covered by an arakelian set in terms of dynamical properties of entire functions via similarities moreover if we consider the set of universal entire functions via similarities that are bounded on such a sub arakelian set then it is shown that its algebraic size is as large as possible as a consequence we prove that the set of universal entire functions bounded on every straight line is algebraically large

unsupervised learning of categorical data with competing models this paper considers the unsupervised learning of high dimensional binary feature vectors representing categorical information a cognitively inspired framework referred to as modeling fields theory mft is utilized as the basic methodology a new mft based algorithm referred to as accelerated maximum a posteriori map is proposed accelerated map allows simultaneous learning and selection of the number of models the key feature of accelerated map is a steady increase of the regularization penalty resulting in competition among models the differences between this approach and other mixture learning and model selection methodologies are described the operation of this algorithm and its parameter selection are discussed numerical experiments aimed at finding performance limits are conducted the performance with real world data is tested by applying the algorithm to a text categorization problem and to the clustering congressional voting data

a probabilistic approach to parallel dynamics for the little hopfield model presents new results on a probabilistic approach to parallel dynamics of the little hopfield model the authors propose a truncated auxiliary dynamics method to control a feedback noise in this symmetrical neural network with full connection it allows them to propose an ansatz for derivation of the explicit recurrence relations for the main and residual noisy overlap evolution for arbitrary discrete moment t

a nonlinear age and maturity structured model of population dynamics i basic theory a nonlinear model of age and maturity structured population dynamics is analyzed the population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth the existence and asymptotic behavior of solutions are studied

on bayesian analysis of mixtures with an unknown number of components discussion author s reply new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

statistical properties of bit plane probability model and its application in supervised texture classification the modeling of wavelet subband histograms via the product bernoulli distributions pbd has received a lot of interest and the pbd model has been applied successfully in texture image retrieval in order to fully understand the usefulness and effectiveness of the pbd model and its associated signature namely the bit plane probability bp signature on image processing applications we discuss and investigate some of their statistical properties these properties would help to clarify the sufficiency of the bp signature to characterize wavelet subbands which in turn justifies its use in real time applications we apply the bp signature on supervised texture classification problem and experimental results suggest that the weighted l1 norm rather than the standard l1 norm should be used for the bp signature comparative classification experiments show that our method outperforms the current state of the art generalized gaussian density approaches

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

retrieval dynamics of associative memory of the hopfield type the authors have investigated the dynamics of retrieval processes of an associative memory of the hopfield type 1982 for synchronous dynamics they have generalized the theory of amari and maginu 1988 which enables them to treat the intermediate processes of memory retrieval in terms of a few simple macrovariables to the finite temperature case the resulting phase diagram in the equilibrium limit agrees qualitatively well with that from equilibrium statistical mechanics they have carried out monte carlo simulations to clarify the limit of applicability of their theory they have found that their basic assumption an independent gaussian distribution of the noise term with a time dependent variance is satisfied if the network succeeds in retrieval when retrieval fails the distribution of noise is non gaussian from very early stages of time development for asynchronous dynamics they propose a time dependent ginzburg landau approach which simply expresses a downhill motion of the network in the free energy landscape the resulting flow diagram in a phase space describes the behaviour of the network when it is close to equilibrium

texture classification using spectral histograms based on a local spatial frequency representation we employ a spectral histogram as a feature statistic for texture classification the spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage the distance between two spectral histograms is measured using spl chi sup 2 statistic the spectral histogram with the associated distance measure exhibits several properties that are necessary for texture classification a filter selection algorithm is proposed to maximize classification performance of a given dataset our classification experiments using natural texture images reveal that the spectral histogram representation provides a robust feature statistic for textures and generalizes well comparisons show that our method produces a marked improvement in classification performance finally we point out the relationships between existing texture features and the spectral histogram suggesting that the latter may provide a unified texture feature

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

asymptotic convergence rate of the em algorithm for gaussian mixtures it is well known that the convergence rate of the expectation maximization em algorithm can be faster than those of convention first order iterative algorithms when the overlap in the given mixture is small but this argument has not been mathematically proved yet this article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of xu and jordan 1996 it has been proved that the asymptotic convergence rate of the em algorithm for gaussian mixtures locally around the true solution is o e0 5 e where e 0 is an arbitrarily small number o x means that it is a higher order infinitesimal as x 0 and e is a measure of the average overlap of gaussians in the mixture in other words the large sample local convergence rate for the em algorithm tends to be asymptotically superlinear when e tends to zero

the use of a mixture model in the analysis of count data a mixture model is presented for the analysis of data on premature ventricular contractions the analysis is shown to be straightforward and the conclusions relatively simple

on a universality property of certain integral operators in this paper we establish a universality property of fourier and hankel convolution operators and dunkl transforms

universality of holomorphic functions bounded on closed sets in this note the existence of translation universal entire functions which are bounded on certain closed subsets is characterized in terms of topological and geometrical properties of such subsets corresponding results are also stated in the space of holomorphic functions on the unit disk and in the space of harmonic functions on the plane moreover it is shown the existence of entire functions which are bounded on many rays and simultaneously are universal with respect to a prescribed infinite order differential operator