absence of absolutely continuous spectrum of floquet operators the spectrum of the floquet operator associated with time periodic perturbations of discrete hamiltonians is considered if the gap between successive eigenvalues j of the unperturbed hamiltonian grows as j j 1 j and the multiplicity of j grows asj with 0 asj tends to infinity then the corresponding floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough

stability of oscillators driven by ergodic processes the evolution of a quantum harmonic oscillator forced by a stationary ergodic process is considered under suitable conditions on the dynamics of this process it is shown that generically the spectrum of the associated quasienergy operator is continuous these results also apply to kicked harmonic oscillators where the amplitudes of the kicks are governed by a stationary ergodic process

diffusive energy growth in classical and quantum driven oscillators we study the long time stability of oscillators driven by time dependent forces originating from dynamical systems with varying degrees of randomness the asymptotic energy growth is related to ergodic properties of the dynamical system when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy for a system with good mixing properties we obtain a stronger result in the form of a central limit theorem if the autocorrelation decays slowly or does not decay the behavior can depend on subtle properties of the particular model we study this dependence in detail for a family of quasiperiodic forces the solution involves the analysis of a small denominator problem that can be treated by fairly elementary methods in the special case of a periodic force the quantum stability problem can be expressed in terms of spectral properties of the floquet operator in the presence of resonances the spectrum is absolutely continuous we find explicitly the eigenvalues and eigenfunctions for the nonresonant case

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

hidden markov models and disease mapping we present new methodology to extend hidden markov models to the spatial domain and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon this situation occurs commonly in many domains of application particularly in disease mapping we assume that the counts follow a poisson model at the lowest level of the hierarchy and introduce a finite mixture model for the poisson rates at the next level the novelty lies in the model for allocation to the mixture components which follows a spatially correlated process the potts model and in treating the number of components of the spatial mixture as unknown inference is performed in a bayesian framework using reversible jump markov chain monte carlo the model introduced can be viewed as a bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models performance of the model and comparison with an alternative well known markov random field specification for the poisson rates are de

some effects of duration on vowel recognition this study was designed to examine the role of duration in vowel perception by testing listeners on the identification of cvc syllables generated at different durations test signals consisted of synthesized versions of 300 utterances selected from a large multitalker database of hvd syllables hillenbrand et al j acoust soc am 97 3099 3111 1995 four versions of each utterance were synthesized 1 an original duration set vowel duration matched to the original utterance 2 a neutral duration set duration fixed at 272 ms the grand mean across all vowels 3 a short duration set duration fixed at 144 ms two standard deviations below the mean and 4 a long duration set duration fixed at 400 ms two standard deviations above the mean experiment 1 used a formant synthesizer while a second experiment was an exact replication using a sinusoidal synthesis method that represented the original vowel spectrum more precisely than the formant synthesizer findings included 1 duration

the evolution operator technique in solving the schrodinger equation and its application to disentangling exponential operators and solving the problem of a mass varying harmonic oscillator the authors present a method for finding the evolution operator for the schrodinger equation for the hamiltonian expressible as h t a1 t j4 a2 t j0 a3 t j where j j0 and j are the su 2 group generators such a method is applied to the disentangling technique for exponential operators which are not necessarily unitary as a demonstration of our general approach they solved the problem of a harmonic oscillator with a varying mass

a bayesian nonparametric approach to reliability abstract it is suggested that problems in a reliability context may be handled by a bayesian non parametric approach a stochastic process is defined whose sample paths may be assumed to be either increasing hazard rates or decreasing hazard rates by properly choosing the parameter functions of the process the posterior distribution of the hazard rates are derived for both exact and censored data bayes estimates of hazard rates c d f s densities and means are found under squared error type loss functions some simulation is done and estimates graphed to better understand the estimators finally estimates of the c d f from some data in a paper by kaplan and meier are constructed author

bayesian poisson process partition calculus with an application to bayesian levy moving averages this article develops and describes how to use results concerning disintegrations of poisson random measures these results are fashioned as simple tools that can be tailor made to address inferential questions arising in a wide range of bayesian nonparametric and spatial statistical models the poisson disintegration method is based on the formal statement of two results concerning a laplace functional change of measure and a poisson palm fubini calculus in terms of random partitions of the integers 1 n the techniques are analogous to but much more general than techniques for the dirichlet process and weighted gamma process developed in ann statist 12 1984 351 3571 and ann inst statist math 41 1989 227 245 in order to illustrate the flexibility of the approach large classes of random probability measures and random hazards or intensities which can be expressed as functionals of poisson random measures are described we describe a unified posterior analysis of classes of discrete random probability which identifies and exploits features common to all these models the analysis circumvents many of the difficult issues involved in bayesian nonparametric calculus including a combinatorial component this allows one to focus on the unique features of each process which are characterized via real valued functions h the applicability of the technique is further illustrated by obtaining explicit posterior expressions for levy cox moving average processes within the general setting of multiplicative intensity models in addition novel computational procedures similar to efficient procedures developed for the dirichlet process are briefly discussed for these models

on quantum stability for systems under quasiperiodic perturbations we prove that the spectrum defined in terms of the autocorrelation function of a harmonic subject to a quasiperiodic perturbation is at resonance transient absolutely continuous covering the whole line in the nonresonant case and under some supplementary diophantine condition it is pure point coinciding with the spectrum of a special almost periodic function

floquet spectrum for two level systems in quasiperiodic time dependent fields we study the time evolution ofn level quantum systems under quasiperiodic time dependent perturbations the problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged hilbert space or equivalently of a generalized floquet operator we discuss criteria for the appearance of pure point as well as continuous spectrum corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior we discuss two types of mechanisms that lead to instability the first one is due to near resonances while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation we treat explicitly an example of this type the stability of the pure point spectrum under small perturbations is proven using kam techniques

the use of acoustic cues for phonetic identification effects of spectral degradation and electric hearing although some cochlear implant ci listeners can show good word recognition accuracy it is not clear how they perceive and use the various acoustic cues that contribute to phonetic perceptions in this study the use of acoustic cues was assessed for normal hearing nh listeners in optimal and spectrally degraded conditions and also for ci listeners two experiments tested the tense lax vowel contrast varying in formant structure vowel inherent spectral change and vowel duration and the word final fricative voicing contrast varying in f1 transition vowel duration consonant duration and consonant voicing identification results were modeled using mixed effects logistic regression these experiments suggested that under spectrally degraded conditions nh listeners decrease their use of formant cues and increase their use of durational cues compared to nh listeners ci listeners showed decreased use of spectral cues like formant structure and formant change and consonant voicing and showed greater use of durational cues especially for the fricative contrast the results suggest that although nh and ci listeners may show similar accuracy on basic tests of word phoneme or feature recognition they may be using different perceptual strategies in the process

some remarks concerning stability for nonstationary quantum systems the problem of characterizing stability and instability for general nonstationary quantum systems is investigated some characterizations are reported and some elementary properties of a topological characterization are established then it is proven by considering a simple example that there are nonperiodic driven systems whose orbits are neither precompact nor leave on average any compact set autocorrelation measures are computed and the possible roles of the generalizes quasienergy operator and energy growth are briefly discussed

posterior propriety and computation for the cox regression model with applications to missing covariates full likelihood bayesian approaches in which a gamma process prior is specified for the cumulative baseline hazard we examine characterizations of posterior propriety under completely observed data settings as well as for missing covariates latent variables are introduced to facilitate a straightforward gibbs sampling scheme in the bayesian computation a real dataset is presented to illustrate the proposed methodology

the nested dirichlet process in multicenter studies subjects in different centers may have different outcome distributions this article is motivated by the problem of nonparametric modeling of these distributions borrowing information across centers while also allowing centers to be clustered starting with a stick breaking representation of the dirichlet process dp we replace the random atoms with random probability measures drawn from a dp this results in a nested dp prior which can be placed on the collection of distributions for the different centers with centers drawn from the same dp component automatically clustered together theoretical properties are discussed and an efficient markov chain monte carlo algorithm is developed for computation the methods are illustrated using a simulation study and an application to quality of care in u s hospitals

asymptotics for posterior hazards an important issue in survival analysis is the investigation and the modeling of hazard rates within a bayesian nonparametric framework a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure in this paper we provide a comprehensive analysis of the asymptotic behavior of such models we investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate the general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals

multifractal analysis and randomness of almost periodic forced two level systems numerical results of multifractal analysis of the quantum dynamics of forced two level systems under some almost periodic time dependence are reported the aims are to check the presence of multifractal characteristics of these systems and also to inspect if different degrees of aperiodicities in the force are transferred to the system dynamics although the dynamics present signatures of the randomness of the perturbation it does not follow strictly its autocorrelation type the wavelet transform is the tool used to carry out the multifractal analysis

unitary transformation approach to the exact solutions of time dependent quantum systems with su 1 1 dynamical group a unitary transformation is introduced to determine the exact solution of the time dependent quantum system as examples two quantum systems with hamiltonian including the quadratic term of generators of su 1 1 are solved analytically

size biased sampling of poisson point processes and excursions some general formulae are obtained for size biased sampling from a poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function these formulae explain why in certain cases gamma and stable the size biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking residual allocation scheme defined by independent beta random variables an application is made to length biased sampling of excursions of a markov process away from a recurrent point of its statespace with emphasis on the brownian and bessel cases when the associated inverse local time is a stable subordinator results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by brownian motion

two estimators of the mean of a counting process with panel count data we study two estimators of the mean function of a countingprocess based on panel count data the setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly different times duringa study following a model proposed by schick and yu we allow the number of observation times and the observation times themselves to be random variables our goal is to estimate the mean function of the counting process we show that the estimator of the mean function proposed by sun and kalbfleisch can be viewed as a pseudo maximum likelihood estimator when a non homogeneous poisson process model is assumed for the counting process we establish consistency of both the nonparametric pseudo maximum likelihood estimator of sun and kalbfleisch and the full maximum likeli hood estimator even if the underlying counting process is not a poisson process we also derive the asymptotic distribution of both estimators at a fixed time t and compare the resulting theoretical relative efficiency with finite sample relative efficiency by way of a limited monte carlo study

analytic controllability of time dependent quantum control systems the question of controllability is investigated for a quantum control system in which the hamiltonian operator components carry explicit time dependence which is not under the control of an external agent we consider the general situation in which the state moves in an infinite dimensional hilbert space a drift term is present and the operators driving the state evolution may be unbounded however considerations are restricted by the assumption that there exists an analytic domain dense in the state space on which solutions of the controlled schrodinger equation may be expressed globally in exponential form the issue of controllability then naturally focuses on the ability to steer the quantum state on a finite dimensional submanifold of the unit sphere in hilbert space and thus on analytic controllability a relatively straightforward strategy allows the extension of lie algebraic conditions for strong analytic controllability derived earlier for the simpler time independent system in which the d

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

computational methods for multiplicative intensity models using weighted gamma processes proportional hazards marked point processes and panel count data we develop computational procedures for a class of bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures a key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of bayesian hierarchical models using the dirichlet process using this fact along with an approximation for the weighted gamma process we show that with some care one can adapt efficient algorithms used for the dirichlet process to this setting we discuss blocked gibbs sampling procedures and polya urn gibbs samplers we illustrate our methods with applications to proportional hazard models poisson spatial regression models recurrent events and panel count data

generalized adiabatic product expansion a nonperturbative method of solving the time dependent schrodinger equation we outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general possibly non hermitian hamiltonian for a class of such hamiltonians this expansion involves a finite number of terms and our method gives the exact solution of the corresponding time dependent schrodinger equation we apply this method to study the dynamics of a general nondegenerate two level quantum system a time dependent classical harmonic oscillator and a degenerate system consisting of a spin 1 particle interacting with a time dependent electric field e t through the stark hamiltonian h j e 2

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

poisson gamma random field models for spatial statistics summary doubly stochastic bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models inhomogeneous gamma process random fields and more generally markov random fields with infinitely divisible distributions are used to construct positively autocorrelated intensity measures for spatial poisson point processes these in turn are used to model the number and location of individual events a data augmentation scheme and markov chain monte carlo numerical methods are employed to generate samples from bayesian posterior and predictive distributions the methods are developed in both continuous and discrete settings and are applied to a problem in forest ecology

on form preserving transformations for the time dependent schrodinger equation in this paper we point out a close connection between the darboux transformation and the group of point transformations which preserve the form of the time dependent schrodinger equation tdse in our main result we prove that any pair of time dependent real potentials related by a darboux transformation for the tdse may be transformed by a suitable point transformation into a pair of time independent potentials related by a usual darboux transformation for the stationary schrodinger equation thus any real potential solvable via a time dependent darboux transformation can alternatively be solved by applying an appropriate form preserving point transformation of the tdse to a time independent potential the pre eminent role of the latter type of transformations in the solution of the tdse is illustrated with a family of quasi exactly solvable time dependent anharmonic potentials

non stochasticity of time dependent quadratic hamiltonians and the spectra of canonical transformations the authors study the quantum mechanical evolution generated by hamiltonians which are quadratic polynomials in q and p with time dependent coefficients this evolution is determined by a unitary implementation of the phase flow of the corresponding classical hamiltonian in the case of quadratic hamiltonians which are periodic in time the floquet operator is shown to have either a pure point spectrum or a purely transient absolutely continuous spectrum thus the motion is non stochastic in a simple model of a quadratic hamiltonian with random time dependence the quantum mechanical motion is shown to be non stochastic almost surely

a class of hazard rate mixtures for combining survival data from different experiments mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism the present article introduced a new class of vectors of random hazard rate functions that are expressed as kernel mixtures of dependent completely random measures this leads to define dependent nonparametric prior processes that are suitably tailored to draw inferences in the presence of heterogenous observations besides its flexibility an important appealing feature of our proposal is analytical tractability we are indeed able to determine some relevant distributional properties and a posterior characterization that is also the key for devising an efficient markov chain monte carlo sampler for illustrative purposes we specialize our general results to a class of dependent extended gamma processes we finally display a few numerical examples including both simulated and real two sample datasets these allow us to identify the effect of a borrow

aggregate data studies of disease risk factors summary statistical methods are proposed for estimating relative rate parameters based on estimated disease rates and covariate data from random samples of individuals from each of several cohorts a random effects model is used to derive mean and variance models for estimated disease rates estimating equations for relative rate parameters are then developed by replacing cohort covariate averages by corresponding sample averages the asymptotic distribution of regression parameter estimates is derived and the asymptotic bias is shown to be small even if covariates are contaminated by classical random measurement errors provided the covariate sample size in each cohort is not small simulation studies motivated by international data on diet and breast cancer provide insights into the properties of the proposed estimators

asymptotic behavior of the quantum harmonic oscillator driven by a random time dependent electric field this paper investigates the evolution of the state vector of a charged quantum particle in a harmonic oscillator driven by a time dependent electric field the external field randomly oscillates and its amplitude is small but it acts long enough so that we can solve the problem in the asymptotic framework corresponding to a field amplitude which tends to zero and a field duration which tends to infinity we describe the effective evolution equation of the state vector which reads as a stochastic partial differential equation we explicitly describe the transition probabilities which are characterized by a polynomial decay of the probabilities corresponding to the low energy eigenstates and give the exact statistical distribution of the energy of the particle

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

evaluation of a strategy for automatic formant tracking variations on an automatic formant tracking strategy developed at alberta will be compared to manual formant measurements from two databases of vowels spoken by men women and children in texas or michigan correct vowel formant candidates for f1 f2 and f3 may be found roughly 85 90 percent of the time for adult male speakers using autocorrelation lpc with the following settings f3 maximum at 3000 hz lpc order of 14 sampling rate of 10 khz j markel and a gray linear prediction of speech springer new york 1975 experience shows good results are also often found with females and children s speech provided the sampling rate and f3 maximum are scaled appropriately for each speaker our new basic strategy involves analyzing each utterance at several distinct sampling rates and coordinated f3 cutoff frequencies with a fixed lpc order each scaling choice provides an independent set of candidates that is post processed by a simple tracking algorithm a correlation measure between a spectrogram of the original signal and one resynthesized from each estimated track set is defined this measure is combined with other heuristic figures of merit based on e g continuity formant ranges and bandwidths to choose the best analysis

unitary transformation approach to the cyclic evolution of su 1 1 and su 2 time dependent systems and geometrical phases using the time dependent unitary transformation instead of the invariant operator the solutions of su 1 1 and su 2 time dependent quantum systems are obtained it is shown that the evolution operator is decomposed into the product form of two unitary operators in such a way that one of them has the same periodicity as the hamiltonian and the other correspond to the floquet operator which gives the cyclic states and their associated phases over one period of the evolution the non adiabatic berry s or aharonov anandan phases are determined totally by such a unitary transformation

synthesis fidelity and time varying spectral change in vowels recent studies have shown that synthesized versions of american english vowels are less accurately identified when the natural time varying spectral changes are eliminated by holding the formant frequencies constant over the duration of the vowel a limitation of these experiments has been that vowels produced by formant synthesis are generally less accurately identified than the natural vowels after which they are modeled to overcome this limitation a high quality speech analysis synthesis system straight was used to synthesize versions of 12 american english vowels spoken by adults and children vowels synthesized with straight were identified as accurately as the natural versions in contrast with previous results from our laboratory showing identification rates 9 12 lower for the same vowels synthesized using the cascade formant model consistent with earlier studies identification accuracy was not reduced when the fundamental frequency was held constant across the vowel however elimination o

symmetric effective mass schrodinger equations we outline a general method of obtaining exact solutions of symmetric schrodinger equations with a position dependent effective mass using this method exact solutions of some symmetric potentials have been obtained we have also discussed the construction of isospectral symmetric potentials

time dependent diffeomorphisms as quantum canonical transformations and the time dependent harmonic oscillator quantum canonical transformations corresponding to time dependent diffeomorphisms of the configuration space are studied a special class of these transformations which correspond to time dependent dilatations is used to identify a previously unknown class of exactly solvable time dependent harmonic oscillators the caldirola kanai oscillator belongs to this class for a general time dependent harmonic oscillator it is shown that choosing the dilatation parameter to satisfy the classical equation of motion one obtains the solution of the schrodinger equation a simple generalization of this result leads to the reduction of the schrodinger equation to a second order ordinary differential equation whose special case is the auxiliary equation of the lewis riesenfeld invariant theory the time evolution operator is expressed in terms of a positive real solution of this equation in a closed form and the time dependent position and momentum operators are calculated

bayesian nonparametric statistical inference for poisson point processes a random measure is said to be selected by a weighted gamma prior probability if the values it assigns to disjoint sets are independent gamma random variables with positive multipliers if the intensity measure of a nonhomogeneous poisson point process is selected by a weighted gamma prior probability and if a sample is drawn from the poisson point process having this intensity measure then the posterior random intensity measure given the observations is also selected by a weighted gamma prior probability if the measure space is euclidean and if the true intensity measure is continuous and finite the centered posterior process rescaled by the square root of the sample size will converge weakly in skorohod topology to a wiener process subject to a change of time scale

reducibility of quantum harmonic oscillator on rd with differential and quasi periodic in time potential abstract we improve the results in the following two aspects by grebert and paturel in 28 and prove that a linear schrodinger equation on r d with harmonic potential x 2 and small t quasiperiodic potential as i u t u x 2 u e v t x u 0 t x r r d reduces to an autonomous system for most values of the frequency vector r n firstly we assume the potential v is only in c t n h s r d with large enough secondly the condition on s is better than 28 as a consequence any solution of such a linear pde is almost periodic in time and remains bounded in some suitable sobolev norms

bayesian semiparametric dynamic frailty models for multiple event time data many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly such as infection hospitalization recurrence of disease or tumor onset to analyze such data it is necessary to account for within subject dependency in the multiple event times motivated by data from studies of palpable tumors this article proposes a dynamic frailty model and bayesian semiparametric approach to inference the widely used shared frailty proportional hazards model is generalized to allow subject specific frailties to change dynamically with age while also accommodating nonproportional hazards parametric assumptions on the frailty distribution are avoided by using dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty by centering the semiparametric model on a conditionally conjugate dynamic gamma model we facilitate posterior computation and lack of fit assessments of the parametric model our proposed method is demonstrated using data from a cancer chemoprevention study

pure point spectrum of the floquet hamiltonian for the quantum harmonic oscillator under time quasi periodic perturbations we prove that the 1 d quantum harmonic oscillator is stable under spatially localized time quasi periodic perturbations on a set of diophantine frequencies of positive measure this proves a conjecture raised by enss veselic in their 1983 paper ev in the general quasi periodic setting the motivation of the present paper also comes from construction of quasi periodic solutions for the corresponding nonlinear equation

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

transient and recurrent spectrum abstract we deal primarily with spectral analysis of an abstract self adjoint operator h on a hilbert space h we propose a further refinement of the absolutely continuous subspace h ac into the transient absolutely continuous subspace h tac which is the closure of those with e ith o t n for all n and the recurrent absolutely continuous subspace h rac h ac h tac we discuss general features of this breakup in a subsequent paper we construct analytic almost periodic functions v on so that h d 2 dx 2 v x on l 2 has only recurrent absolutely continuous spectrum in the sense that h rac h

absolute continuity of the floquet spectrum for a nonlinearly forced harmonic oscillator we prove that the floquet spectrum of the time periodic schrodinger equation corresponding to a mildly nonlinear resonant forcing is purely absolutely continuous for suitably small