a hybrid lower bound for parameter estimation of signals with multiple change points change point estimation has received much attention in the literature as it plays a significant role in several signal processing applications however the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters namely the parameters associated with the noise distribution and the change point locations in this paper we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters specifically we propose a hybrid cramer rao weiss weinstein bound and derive its associated closed form expressions numerical simulations assess the tightness of the proposed bound in the case of gaussian and poisson observations

inhomogeneous and modulated gamma processes summary two classes of point processes the inhomogeneous and modulated gamma processes are defined asymptotic test statistics of stationarity are derived for modulated gamma processes some examples are studied in detail and applied to two sets of data

a dynamic approach to the statistical analysis of point processes summary an approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented bayesian inference for processes with explanatory variables is derived in terms of on line estimation filtering and prediction limiting equations for the time continuous intensity rate are obtained and solved for the no covariates case examples are provided and the approach is applied in a numerical example similar approaches include the work of koch spreij 1983 and snyder 1975 6 which also use a dynamic model with a system equation these approaches based on filtering theory for time continuous processes provide good probabilistic descriptions their main problem is the difficulty in applying the results in the presence of covariates even in simple problems the purpose of this paper is to provide tractable yet reasonable solutions to the inference problem of point processes with explanatory variables azzalini 1982 warns about the complications of exact calculations required by filtering theory even in the absence of covariates the approach is based on and to some extent generalizes work on survival data gamerman 1991 inference is considered in terms of on line and smoothed or filtered estimation of model parameters and prediction of future occurrences based on past information in 2 the model is stated and inference procedures derived in 3 the model with no covariates is considered in detail and limiting equations for any continuous rate

global existence and asymptotic properties of the solution to a two species chemotaxis system abstract this paper deals with the cauchy problem for a two species chemotactic keller segel system u t u 1 u w v t v 2 v w w t w w 1 u 2 v in r 2 0 where 0 1 2 and 1 2 are real numbers we obtain the global existence of solutions if u 0 1 v 0 1 and w 0 2 are small and the asymptotic behavior of the small data solution as follows if 0 the solution is asymptotic to a self similar solution for large time if 0 the solution behaves like a multiple of the heat kernel as t

estimation in change point hazard rate models summary this paper discusses the estimation of parameters in hazard rate models with a changepoint due to the irregularity of the models the classical maximum likelihood method and the method of moments cannot be used a consistent estimator of the change point is obtained by examining the properties of the density represented as a mixture the performance of the estimator is checked via simulation

on power adaptation in adaptive signaling systems the shannon capacity of a fading channel under an average power constraint with channel side information at the transmitter and receiver is only negligibly larger than the capacity of the same channel when constant power transmission is employed however power adaptation has been shown to be quite useful in practical systems where it has been conjectured that it allows for compensation of the effect of rate quantization here an average bit error probability constraint is employed instead of the conventional instantaneous bit error probability constraint when the set of rates available to the transmitter is unrestricted in practical systems necessary conditions for jointly optimal power and rate allocation are derived and used to demonstrate that power adaptation is of limited utility however when the rates available to the transmitter are restricted to the nonnegative integers for the example of uncoded quadrature amplitude modulation over frequency nonselective rayleigh fading channels a 0 5 0 75 db loss in power efficiency is incurred when employing only a single power level for each constellation and a 0 5 bits symbol loss in rate is incurred when constant power transmission is employed

bootstrap confidence regions for the intensity of a poisson point process abstract bootstrap methods are developed for constructing confidence regions for the intensity function of a nonstationary poisson process several different resampling algorithms are suggested ranging from resampling a poisson process with intensity equal to that estimated nonparametrically from the data to resampling the data points themselves in the same manner that the bootstrap is used in problems involving independent and identically distributed observations for each different bootstrap method various percentile t ways of constructing confidence bands are described the effectiveness of these different approaches is demonstrated both theoretically and numerically for real and simulated data issues such as bias correction are addressed

practical aspects of dft based frequency division multiplexing for data transmission a practical implementation of digital frequency division multiplexing is presented the design goals are the use of very few modulation schemes two or three uniform reliability across the subchannels and the avoidance of peak power violation the ftdm fourier transform division multiplexing method is used to design signals for transmission data are encoded in the frequency domain fourier transformed to yield a real sequence and a signal is transmitted whose sampled values when inverse fourier transformed yield the original code spectral characteristics for the code are easily obtained because it is designed in the frequency domain

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

global solutions and self similar solutions of semilinear parabolic equations with nonlinear gradient terms abstract in this paper we consider the cauchy problem of semilinear parabolic equations with nonlinear gradient terms a x u q 1 u u p we prove the existence of global solutions and self similar solutions for small initial data moreover for a class of initial data we show that the global solutions behave asymptotically like self similar solutions as t

the analysis of neuronal discharge sequences change point estimation and comparison of variances a key problem in neurophysiology is to determine whether after presentation of a stimulus there has been a modification in the discharge of a recorded neuron and if so an attempt is made to estimate the latency of the response the estimation problem can be considered as that of the estimation of a change point in a sequence of random variables the gamma distribution is adequate to model the distribution of intervals between action potentials for different types of neurons simulations show that the maximum likelihood estimator based on this model is efficient and robust an additional problem in the case of experiments in which a movement follows the stimulus is to determine whether a response is related to the stimulus or to the movement a test based on the comparison of marginal scales of a bivariate distribution is proposed the whole procedure has been tested in simulation and with real examples

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

global existence and asymptotic behavior in a two species chemotaxis system with logistic source abstract in this work we consider the two species chemotaxis system with logistic source we present the global existence of generalized solutions under appropriate regularity assumptions on the initial data in addition the asymptotic behavior of the solutions is studied and our results generalize and improve some well known results in the literature

large time behavior of the vorticity of two dimensional viscous flow and its application to vortex formation we consider the cauchy problem for the two dimensional vorticity equation we show that the solution behaves like a constant multiple of the gauss kernel having the same total vorticity as time tends to infinity no particular structure of initial data 0 x 0 is assumed except the restriction that the reynolds numberr 0 dx v is small wherev is the kinematic viscosity applying a time dependent scale transformation we show a stability of burgers vortex which physically implies formation of a concentrated vortex

joint optimization of transmission rate and outer loop snr target adaptation over fading channels joint optimization of signal to noise ratio snr target and transmission rate adaptation is examined for multilevel quadrature amplitude modulation mqam over flat fading channels to maximize the spectral efficiency subject to an average transmit power constraint we propose an adaptive transmission scheme in which the outer loop snr target and data rate are adapted to bit error rate ber where total or truncated channel inversion strategies are exploited for the fast inner loop power control we obtain the optimal solutions for both continuous and discrete rate adaptation and consider cases where diversity combining is performed in the receiver we show that by using this ber based adaptive scheme spectral efficiency can be improved compared with optimal snr based variable rate variable power mqam we also show that for continuous rate adaptation the optimal snr target monotonically increases with ber while it descends within a ber range with constant rate

global existence and asymptotic behavior of solutions to a two species chemotaxis system with two chemicals in this paper we investigate the competitive parabolic elliptic parabolic elliptic two species chemotaxis system with two chemicals in a smooth bounded domain rn n 1 the existence of global bounded classical solution is proved under mild assumptions on the initial data and appropriate conditions on the strength of the damping death effects moreover for the case when both competition parameters a1 and a2 lie in 0 1 it is shown that such solution stabilizes to spatially homogeneous equilibria in the large time limit

global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening abstract this paper deals with nonnegative solutions of the neumann initial boundary value problem for the parabolic chemotaxis system u t u u v u u 2 x t 0 v t v v u x t 0 in bounded convex domains r n n 1 with smooth boundary it is shown that if the ratio is sufficiently large then the unique nontrivial spatially homogeneous equilibrium given by u v 1 is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data u 0 v 0 such that u 0 0 the above problem possesses a uniquely determined global classical solution u v with u v t 0 u 0 v 0 which satisfies u t 1 l 0 and v t 1 l 0 as t

on asymptotic behaviors of solutions to parabolic systems modelling chemotaxis abstract this paper deals with large time behaviors of solutions to a keller segel system which possesses self similar solutions by taking into account the invariant properties of the equation with respect to a scaling and translations we show that suitably shifted self similar solutions give more precise asymptotic profiles of general solutions at large time the convergence rate is also computed in details

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

a new approach toward stabilization in a two species chemotaxis model with logistic source abstract this paper aims at providing an alternative approach to study global dynamic properties for a two species chemotaxis model with the main novelty being that both populations mutually compete with the other on account of the lotka volterra dynamics more precisely we consider the following neumann initial boundary value problem u t d 1 u 1 u w 1 u 1 u a 1 v x t 0 v t d 2 v 2 v w 2 v 1 a 2 u v x t 0 0 d 3 w w u v x t 0 in a bounded domain r n n 1 with smooth boundary where d 1 d 2 d 3 1 2 1 2 a 1 a 2 are positive constants when a 1 0 1 and a 2 0 1 it is shown that under some explicit largeness assumptions on the logistic growth coefficients 1 and 2 the corresponding neumann initial boundary value problem possesses a unique global bounded solution which moreover approaches a unique positive homogeneous steady state u v w of above system in the large time limit the respective decay rate of this convergence is shown to be exponential when a 1 1 and a 2 0 1 if 2 is suitable large for all sufficiently regular nonnegative initial data u 0 and v 0 with u 0 0 and v 0 0 the globally bounded solution of above system will stabilize toward 0 1 1 as t in algebraic

asymptotic stability of a two species chemotaxis system with non diffusive chemoattractant abstract we study the behavior of two biological populations u and v attracted by the same chemical substance whose behavior is described in terms of second order parabolic equations the model considers a logistic growth of the species and the interactions between them are relegated to the chemoattractant production the system is completed with a third equation modeling the evolution of chemical we assume that the chemical w is a non diffusive substance and satisfies an ode more precisely u t u u 1 w w 1 u 1 u x t 0 v t v v 2 w w 2 v 1 v x t 0 w t h u v w x t 0 under appropriate boundary and initial conditions in an n dimensional open and bounded domain we consider the cases of positive chemo sensitivities not necessarily constant elements the chemical production function h increases as the concentration of the species u and v increases we first study the global existence and uniform boundedness of the solutions by using an iterative approach the asymptotic stability of the homogeneous steady state is a consequence of the growth of h i and the size of i finally some examples of the theoretical results are presented for particular functions h and i

an improved bayesian information criterion for multiple change point models in multiple change point analysis inferring the number of change points is often achieved by minimizing a selection criterion that trades off data fidelity with complexity we address the open problem of defining a selection criterion adapted to the context of multiple change point analysis our approach is inspired by the schwarz seminal formulation of the bayesian information criterion bic similarly we introduce priors here describing the occurrence of change points and we use the laplace approximation to derive a closed form expression of the criterion differently from this previous work we take advantage of the a priori information introduced instead of asymptotically eliminating the dependence on priors results obtained on simulated series show a substantial gain in performance versus recent alternative criteria used in multiple change point analysis results also show that the a priori information introduced in our criterion on the regularity of interevent times is the main driver of this s

asymptotically self similar global solutions of a general semilinear heat equation we consider the general nonlinear heat equation partial t u delta u a u p 1 1 u g u u 0 varphi on 0 infty times i r n where a in i r p 1 1 2 n and g satisfies certain growth conditions we prove the existence of global solutions for small initial data with respect to a norm which is related to the structure of the equation we also prove that some of those global solutions are asymptotic for large time to self similar solutions of the single power nonlinear heat equation i e with g equiv 0

boundedness and asymptotic stability of solutions to a two species chemotaxis system with consumption of chemoattractant this paper deals with a two competing species chemotaxis system with consumption of chemoattractant ut d1 u u 1 w w 1u 1 u a1v x t 0 vt d2 v v 2 w w 2v 1 a2u v x t 0 wt d3 w u v w x t 0 under homogeneous neumann boundary conditions in a bounded domain rn rn n 1n 1 with smooth boundary where the initial data u0 v0 c0 2 and w0 w1 w0 w1 are non negative and the parameters d1 d2 d3 0d1 d2 d3 0 1 2 0 1 2 0 a1 a2 0a1 a2 0 and 0 0 the chemotactic function i w i w i 1 2i 1 2 is smooth and satisfying some conditions it is proved that the corresponding initial boundary value problem possesses a unique global bounded classical solution if one of the following cases hold for i 1 2i 1 2 i i w 0 i 0 i w 0 i 0 and w0 l did3n 1 0 i 2did3n 1 0 iarctan di d32n 1did3 ii 0 w0 l d33 n 1 i l 0 w0 l min 2didi d3 1 moreover we prove asymptotic stabilization of solutions in the sense that if a1 a2 0 1 a1 a2 0 1 and u0 0 v0u0 0 v0 then any global bounded solution exponentially converge to 1 a11 a1a2 1 a21 a1a2 0 as t t if a1 1 a2 0a1 1 a2 0 and v0 0v0 0 then any global bounded solution exponentially converge to 0 1 0 0 1 0 as t t if a1 1 a2 0a1 1 a2 0 and v0 0v0 0 then any global bounded solution algebraically converge to 0 1 0 0 1 0 as t t

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

global solutions in a high dimensional two species chemotaxis model with lotka volterra competitive kinetics abstract this paper deals with the two species chemotaxis system with logistic source u t u 1 u w 1 u 1 u a 1 v x t 0 v t v 2 v w 2 v 1 a 2 u v x t 0 w t w w u v x t 0 under homogeneous neumann boundary condition in a smooth bounded domain r n n 1 it is proved that in convex domains the problem possesses a unique global bounded solution if 1 and 2 are large enough moreover we establish the existence of global weak solution for any 1 0 and 2 0

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

eventual smoothness and asymptotics in a three dimensional chemotaxis system with logistic source abstract we prove existence of global weak solutions to the chemotaxis system u t u u v u u 2 v t v v u under homogeneous neumann boundary conditions in a smooth bounded convex domain r n for arbitrarily small values of 0 additionally we show that in the three dimensional setting after some time these solutions become classical solutions provided that is not too large in this case we also consider their large time behaviour we prove decay if 0 and the existence of an absorbing set if 0 is sufficiently small

degrees of freedom in adaptive modulation a unified view we examine adaptive modulation schemes for flat fading channels where the data rate transmit power and instantaneous ber are varied to maximize spectral efficiency subject to an average power and ber constraint both continuous rate and discrete rate adaptation are considered as well as average and instantaneous ber constraints we find the general form of power ber and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions the optimal adaptation of these parameters is to increase the power and data rate and decrease the ber as the channel quality improves surprisingly little spectral efficiency is lost when the power or rate is constrained to be constant hence the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted

inference and prediction for a general order statistic model with unknown population size abstract suppose that the first n order statistics from a random sample of n positive random variables are observed where n is unknown this the general order statistic model has been applied to the study of market penetration capture recapture burn in in repairable systems software reliability growth the estimation of the number of individuals exposed to radiation and the estimation of the number of unseen species inference is to be made about the unknown parameters especially n and future observations are to be predicted a bayes empirical bayes approach to inference is presented this permits the comparison of competing perhaps nonnested models for the distribution of the random variables in a natural way it also provides easily implemented inference and prediction procedures that avoid the difficulties of non bayesian methods one such difficulty is that the maximum likelihood estimator of n may be infinite results are given for the case in which vague prior information about the model

boundedness and stabilization in a two dimensional two species chemotaxis navier stokes system with competitive kinetics abstract this paper deals with the two species chemotaxis navier stokes system with lotka volterra competitive kinetics n 1 t u n 1 n 1 1 n 1 c 1 n 1 1 n 1 a 1 n 2 in 0 n 2 t u n 2 n 2 2 n 2 c 2 n 2 1 a 2 n 1 n 2 in 0 c t u c c n 1 n 2 c in 0 u t u u u p n 1 n 2 u 0 in 0 under homogeneous neumann boundary conditions in a bounded domain r 2 with smooth boundary this system consists of two models which were attracting mathematical interests one is a chemotaxis navier stokes system which is known as a challenging model the other is a two species chemotaxis system with lotka volterra competitive kinetics which has a complicated form both systems were recently well investigated however the above mixed system seems to be not studied yet this paper gives results for global existence boundedness and stabilization of solutions to the above system

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

existence and uniqueness theorem on mild solutions to the keller segel system in the scaling invariant space we prove the existence and uniqueness of solutions u v to the keller segel system of parabolic parabolic type in rn for n 3 in the scaling invariant class u lq 0 t lr rn v lr 0 t h r rn where 2 q n r 2 2 q n r 2 provided the initial data u0 v0 is chosen as u0 ln 2 rn v0 h 2 n 2 rn for n 2 n 2 1 2 in particular our uniqueness result holds for all n 2 even though we impose an assumption only on u such as lq 0 t lr rn for 2 q n r 2 with n 2 r as for the marginal case when r n 2 we show that if n 3 and if u c 0 t ln 2 rn v c 0 t ln rn then u v is the only solution

the likelihood ratio test for a change point in simple linear regression summary we consider likelihood ratio tests to detect a change point in simple linear regression a when the alternative specifies that only the intercept changes and b when the alternative permits the intercept and the slope to change approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable the approximations are compared with simulations in order to assess their accuracy for the model in which only the intercept is allowed to change a confidence region for the change point and an approximate joint confidence region for the change point the difference in intercepts and the slope are obtained by inversion of the appropriate likelihood ratio tests

global bounded solutions and their asymptotic properties under small initial data condition in a two dimensional chemotaxis system for two species abstract in this paper a fully parabolic chemotaxis system for two species u t u u w x t 0 v t v v w x t 0 w t w u w v w x t 0 is considered under homogeneous neumann boundary conditions in a smooth bounded domain r 2 we obtain the global boundedness and asymptotic behavior with small initial data condition in critical space more precisely it is proved that one can find a small e 0 0 such that for any initial data u 0 v 0 w 0 satisfying u 0 l 1 e 0 and w 0 l 2 e 0 the solution of the problem above is global in time and bounded in addition u v w converges to the steady state m 1 m 2 m 1 1 m 2 as t where m 1 1 u 0 and m 2 1 v 0

global existence and asymptotic stability of solutions to a two species chemotaxis system with any chemical diffusion abstract this paper deals with the two species chemotaxis system u t u u 1 w w 1 u 1 u in 0 v t v v 2 w w 2 v 1 v in 0 w t d w h u v w in 0 where is a bounded domain in r n with smooth boundary n n h i are functions satisfying some conditions negreanu tello 2014 2015 12 13 proved global existence and asymptotic behavior of solutions to the above system when 0 d 1 the main purpose of the present paper is to remove the restriction of 0 d 1

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12