noncommutative maximal ergodic theorems for positive contractions let m be a von neumann algebra equipped with a normal semifinite faithful trace let t be a positive linear contraction on m such that t and such that the numerical range of t as an operator on l2 m is contained in a stoltz region with vertex 1 we show that junge and xu s noncommutative stein maximal ergodic inequality holds for the powers of t on lp m 1 p we apply this result to obtain the noncommutative analogue of a recent result of cohen concerning the iterates of the product of a finite number of conditional expectations

estimating the population size for capture recapture data with unequal catchability a point estimator and its associated confidence interval for the size of a closed population are proposed under models that incorporate heterogeneity of capture probability real data sets provided in edwards and eberhardt 1967 journal of wildlife management 31 87 96 and carothers 1973 journal of animal ecology 42 125 146 are used to illustrate this method and to compare it with other estimates the performance of the proposed procedure is also investigated by means of monte carlo experiments the method is especially useful when most of the captured individuals are caught once or twice in the sample for which case the jackknife estimator usually does not work well numerical results also show that the proposed confidence interval performs satisfactorily in maintaining the nominal levels

smooth stable invariant manifolds and arbitrary growth rates abstract for nonautonomous linear equations v a t v with a generalized exponential dichotomy we show that there is a smooth stable invariant manifold for the perturbed equation v a t v f t v provided that f is sufficiently small the generalized exponential dichotomies may exhibit stable and unstable behaviors with respect to arbitrary growth rates e c t for some function t we consider the general case of nonuniform exponential dichotomies and the result is obtained in banach spaces moreover we show that for an equivariant system the dynamics on the stable manifold in a certain class of graphs is also equivariant we emphasize that this result cannot be obtained by averaging over the symmetry

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

existence of nonuniform exponential dichotomies and a fredholm alternative abstract we consider linear equations x a t x in a banach space with nonuniform exponential dichotomies in r and r and we give an admissibility condition for the existence of nonuniform exponential dichotomies in the whole line under sufficiently small perturbations we also obtain a fredholm alternative for the existence of bounded solutions under nonlinear perturbations

characteristic exponents and invariant manifolds in hilbert space the multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds pesin theory are extended to differentiable dynamical systems on hilbert manifolds under some compactness assumptions the results apply to partial differential equations of evolution and also to non invertible maps of compact manifolds

on ergodic theorems for free group actions on noncommutative spaces we extend in a noncommutative setting the individual ergodic theorem of nevo and stein concerning measure preserving actions of free groups and averages on spheres s 2 n of even radius here we study state preserving actions of free groups on a von neumann algebra a and the behaviour of s 2 n x for x in noncommutative spaces l p a for the cesaro means this problem was solved by walker our approach is based on ideas of bufetov we prove a noncommutative version of rota alternierende verfahren theorem to this end we introduce specific dilations of the powers of some noncommutative markov operators

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

noncommutative maximal ergodic theorems this paper is devoted to the study of various maximal ergodic theorems in noncommutative spaces in particular we prove the noncommutative analogue of the classical dunford schwartz maximal ergodic inequality for positive contractions on and the analogue of stein s maximal inequality for symmetric positive contractions we also obtain the corresponding individual ergodic theorems we apply these results to a family of natural examples which frequently appear in von neumann algebra theory and in quantum probability

estimating the number of classes via sample coverage abstract assume that a random sample is drawn from a population with unknown number of classes and possibly unequal class probabilities a nonparametric estimation technique is proposed to estimate the number of classes using the idea of sample coverage which is defined as the sum of the cell probabilities of the observed classes since expected sample coverage can be well estimated we were motivated to find its role in the estimation of the number of classes this work generalizes the result of esty to a nonparametric approach and extends darroch and ratcliff to incorporate the heterogeneity of the class probabilities the coefficient of variation of the class sizes is shown to play an important role in the recommended estimation procedures the performance of the proposed estimators is investigated by means of monte carlo simulations

on stability of linear time varying infinite dimensional discrete time systems the asymptotic behaviour of linear time varying infinite dimensional discrete lime systems is considered the introduced notions are weak power equistability power equistability uniform power equistability l p equistability uniform l p equistability and l p x equistability it is shown that they are identical a generalization of the concept of spectral radius of a single operator is also proposed it is proven that any time varying system is uniformly power equistable if and only if the generalized spectral radius of the sequence of the operators which define the system considered is less than one

dichotomies for linear evolutionary equations in banach spaces abstract in this paper we present a characterization for the existence of an exponential dichotomy for a linear evolutionary system on a banach space the theory we present here applies to general time varying linear equations in banach spaces as a result it gives a description of the behavior of the nonlinear dynamics generated by certain nonlinear evolutionary equations in the vicinity of a compact invariant set in the case of dissipative systems our theory applies to the study of the flow in the vicinity of the global attractor the theory formulated here holds for linear evolutionary systems which are uniformly contracting and applies to the study of the linearization of nonlinear equations of the following type a parabolic pdes including systems of reaction diffusion equations and the navier stokes equations b hyperbolic pdes including the nonlinear wave equation and the nonlinear schrodinger equation with dissipation c retarded differential equations and d certain neutral differential delay equations

a general class of recapture models based on the conditional capture probabilities we propose an mhotb model for population size estimation in capture recapture studies the tb part is based on equality constraints for the conditional capture probabilities leading to an extremely rich model class observed and unobserved heterogeneity are dealt with by means of a logistic parameterization in order to explore the model class we introduce a penalized version of the likelihood the conditional likelihood and penalized conditional likelihood are maximized by means of efficient em algorithms simulations and two real data examples illustrate the approach

harmonic analysis on quantum tori this paper is devoted to the study of harmonic analysis on quantum tori we consider several summation methods on these tori including the square fej r means square and circular poisson means and bochner riesz means we first establish the maximal inequalities for these means then obtain the corresponding pointwise convergence theorems in particular we prove the noncommutative analogue of the classical stein theorem on bochner riesz means the second part of the paper deals with fourier multipliers on quantum tori we prove that the completely bounded l p fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension finally we present the littlewood paley theory associated with the circular poisson semigroup on quantum tori we show that the hardy spaces in this setting possess the usual properties of hardy spaces as one can expect these include the quantum torus analogue of fefferman s h 1 bmo duality theorem and interpolation theorems our analysis is based on the recent developments of noncommutative martingale ergodic inequalities and littlewood paley stein theory

averaging theorems for the large time behavior of the solutions of nonautonomous systems abstract we obtain some averaging theorems for the large time behavior of an evolution family u t s t s 0 acting on a banach space it is known that if a trajectory u t 0 x 0 is asymptotically stable then its p mean tends to zero we will show here that if the uniformly weighted p means of all the trajectories starting on the unit sphere are bounded then u t s t s 0 is uniformly exponentially stable while the converse statement is a simple verification discrete time versions of this result are given also variants for the uniform exponential blow up are obtained thus we generalize some known results obtained by r datko a pazy and v pata

strong nonuniform behaviour a datko type characterization abstract we obtain a datko type characterization of several classes of a strong nonuniform exponential behaviour we consider separately the case of exponential contractions expansions and dichotomies in addition we consider both discrete and continuous time as a nontrivial application of our work we study the robustness property of strong nonuniform exponential contractions expansions and dichotomies

exponential stability of operators and operator semigroups extending earlier results of datko pazy and littman on c0 semigroups and of przyluski and weiss on operators we prove the following let t be a bounded linear operator on a banach space x and let r t denotes its spectral radius let e be a banach function space over n with the property that limn 0 n 1 e if for each x x and x x the map n x tnx belongs to e then r t 0 for all t 0 if n 0 x tnx for all x x 1 then r t 1 assuming a 2 condition on a further improvement is obtained for locally bounded semigroups t t t t 0 we obtain similar results in terms of the maps t t t x

on weak exponential stability of evolution operators in banach spaces abstract the aim of this paper is to give some characterizations for weak exponential stability properties of evolution operators in banach spaces variants for weak exponential stability of some well known results in uniform stability theory buse and niculescu 2009 1 daleckij and krein 1974 2 datko 1973 3 rolewicz 1986 7 stoica and megan 2009 8 are obtained

on identifiability in capture recapture models we study the issue of identifiability of mixture models in the context of capture recapture abundance estimation for closed populations such models are used to take account of individual heterogeneity in capture probabilities but their validity was recently questioned by link 2003 biometrics 59 1123 1130 on the basis of their nonidentifiability we give a general criterion for identifiability of the mixing distribution and apply it to establish identifiability within families of mixing distributions that are commonly used in this context including finite and beta mixtures our analysis covers binomial and geometrically distributed outcomes in an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models

equivalence of truncated count mixture distributions and mixtures of truncated count distributions summary this article is about modeling count data with zero truncation a parametric count density family is considered the truncated mixture of densities from this family is different from the mixture of truncated densities from the same family whereas the former model is more natural to formulate and to interpret the latter model is theoretically easier to treat it is shown that for any mixing distribution leading to a truncated mixture a usually different mixing distribution can be found so that the associated mixture of truncated densities equals the truncated mixture and vice versa this implies that the likelihood surfaces for both situations agree and in this sense both models are equivalent zero truncated count data models are used frequently in the capture recapture setting to estimate population size and it can be shown that the two horvitz thompson estimators associated with the two models agree in particular it is possible to achieve strong results for mixtures of truncated poisson densities including reliable global construction of the unique npmle nonparametric maximum likelihood estimator of the mixing distribution implying a unique estimator for the population size the benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities which is less appealing for the practitioner but theoretically easier mixtures of truncated count densities form a convex linear model for which a developed theory exists including global maximum likelihood theory as well as algorithmic approaches once the problem has been solved in this class it might readily be transformed back to the original problem by means of an explicitly given mapping applications of these ideas are given particularly in the case of the truncated poisson family

estimating the number of species a review how many kinds are there suppose that a population is partitioned into c classes in many situations interest focuses not on estimation of the relative sizes of the classes but on estimation of c itself for example biologists and ecologists may be interested in estimating the number of species in a population of plants or animals numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue and linguists may be interested in estimating the size of an author s vocabulary in this article we review the problem of statistical estimation of c many approaches have been proposed some purely data analytic and others based in sampling theory in the latter case numerous variations have been considered the population may be finite or infinite if finite samples may be taken with replacement multinomial sampling or without replacement hypergeometric sampling or by bernoulli sampling if infinite sampling may be multinomial or bernoulli or the sample may be th

iterates of a product of conditional expectation operators abstract let f be a probability space and let t p 1 p 2 p d be a finite product of conditional expectations with respect to the sub algebras f 1 f 2 f d we show that for every f l p 1 p 2 the sequence t n f converges a e with lim n t n f e f f 1 f 2 f d a e

a penalized nonparametric maximum likelihood approach to species richness estimation we propose a class of penalized nonparametric maximum likelihood estimators npmles for the species richness problem we use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem the estimators are constructed using a conditional likelihood that is simpler than the full likelihood we show that the full likelihood npmle solution given by norris and pollock can be found with great accuracy by using an appropriate penalty term on the conditional likelihood so it is an element of our class of estimators a simple and fast algorithm for the penalized npmle is developed it can be used to greatly speed up computation of the unconditional npmle it can also be used to find profile mixture likelihoods based on our goal of attaining high stability while retaining sensitivity we propose an adaptive quadratic penalty function a systematic simulation study using a wide range of scenarios establishes the success of this method relative to its competi

on uniform exponential stability for skew evolution semiflows on banach spaces the aim of this paper is to give several characterizations for the property of stability for skew evolution semiflows on banach spaces thus we obtain generalizations of some well known results due to barbashin datko and rolewicz in the case of evolution equations in banach spaces a unified treatment in the uniform setting is provided

the performance of mixture models in heterogeneous closed population capture recapture summarydorazio and royle 2003 biometrics59 351 364 investigated the behavior of three mixture models for closed population capture recapture analysis in the presence of individual heterogeneity of capture probability their simulations were from the beta binomial distribution with analyses from the beta binomial the logit normal and the finite mixture latent class models in this response simulations from many different distributions give a broader picture of the relative value of the beta binomial and the finite mixture models and provide some preliminary insights into the situations in which these models are useful

a generalization of chao s estimator for covariate information this note generalizes chao s estimator of population size for closed capture recapture studies if covariates are available chao s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size if observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of chao s estimator the key element in this development is the understanding and placement of chao s estimator in a truncated poisson likelihood it is shown that a truncated poisson likelihood with log link with all counts truncated besides ones and twos is equivalent to a binomial likelihood with logit link this enables the development of a generalized chao estimator as the estimated expected value of the frequency of zero counts under a truncated all counts truncated except ones and twos poisson regression model if the regression model accounts for the heterogeneity entirely the generalized chao estimator is asymptotically unbiased a simulation study illustrates the potential in gain of bias reduction comparisons of the generalized chao estimator with the homogeneous zero truncated poisson regression approach are supplied as well the method is applied to a surveillance study on the completeness of farm submissions in great britain

capture recapture estimation with samples of size one using frequency data summary one way in which a capture recapture experiment can be designed is to count each capture occasion as a separate sample and tally the number of individuals caught once twice and so on this paper discusses the estimators currently used for this type of experiment and suggests some new ones each of the estimators is categorized by its derivation following this their properties are discussed particularly their bias and variance with the aim of choosing one or two of the estimators which are the best to use especially in handling a heterogeneous population it is found that the bias adjusted estimator of chao 1989 is the best to use when the number of captures is relatively small and that the estimator of darroch ratcliff 1980 should be used otherwise