distributional results for means of normalized random measures with independent increments we consider the problem of determining the distribution of means of random probability measures which are obtained by normalizing increasing additive processes a solution is found by resorting to a well known inversion formula for characteristic functions due to gurland moreover expressions of the posterior distributions of those means in the presence of exchangeable observations are given finally a section is devoted to the illustration of two examples of statistical relevance

chemotaxis with logistic source very weak global solutions and their boundedness properties abstract we consider the chemotaxis system u t u u v g u x t 0 0 v v u x t 0 in a smooth bounded domain r n where 0 and g generalizes the logistic function g u a u b u with 1 a 0 and b 0 a concept of very weak solutions is introduced and global existence of such solutions for any nonnegative initial data u 0 l 1 is proved under the assumption that 2 1 n moreover boundedness properties of the constructed solutions are studied inter alia it is shown that if b is sufficiently large and u 0 l has small norm in l for some n 2 then the solution is globally bounded finally in the case that additionally n 2 holds a bounded set in l can be found which eventually attracts very weak solutions emanating from arbitrary l 1 initial data the paper closes with numerical experiments that illustrate some of the theoretically established results

some uniqueness and exact multiplicity results for a predator prey model in this paper we consider positive solutions of a predator prey model with diffusion and under homogeneous dirichlet boundary conditions it turns out that a certain parameter m in this model plays a very important role a good understanding of the existence stability and number of positive solutions is gained when m is large in particular we obtain various results on the exact number of positive solutions our results for large m reveal interesting contrast with that for the well studied casem 0 i e the classical lotka volterra predator prey model

pattern formation in the brusselator system in the paper we deal with a reaction diffusion system well known as the brusselator model and some improved results for the steady states of this model are presented we first give an a priori estimates positive upper and lower bounds of positive steady states then we obtain the non existence and existence of positive non constant steady states as the parameters and b are varied which means some certain conditions under which the pattern formation occurs or not

positive steady states of the holling tanner prey predator model with diffusion this paper is concerned with the holling tanner prey predator model with diffusion subject to the homogeneous neumann boundary condition we obtain the existence and non existence of positive non constant steady states

stationary patterns caused by cross diffusion for a three species prey predator model we study a system arising from a three component prey predator model with prey dependent and ratio dependent functional responses where cross diffusion is included in such a way that predator chases the prey and the prey runs away from the predator we prove that the cross diffusion can generate the stationary patterns nonconstant positive steady states

bifurcation analysis of a predator prey system involving group defence a class of odes of generalized gause type modeling predator prey interaction is considered the prey are assumed to exhibit a phenomenon called group defence that is predation is decreased or even eliminated due to the ability of the prey to defend or disguise themselves as their numbers increase using the carrying capacity of the environment as the bifurcation parameter it is shown that the model undergoes a sequence of bifurcations that includes a homoclinic bifurcation as well as a hopf bifurcation conditions that hold even in the case of no group defence that ensure a subcritical hopf bifurcation and also the spontaneous appearance of a semistable periodic orbit that splits into a pair one stable and one unstable of periodic orbits are given ecological ramifications are considered unlike the classical model sufficient enrichment of the environment combined with group defence leads to extinction of the predator deterministically for almost all initial conditions providing strong support fo

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

disclosure control of microdata abstract national statistical offices meet an increasing demand for the dissemination of microdata this trend can be at variance with the care taken not to disclose data about individuals therefore the risk of disclosure of each microdata set to be released should be assessed if this risk is too high measures have to be taken to protect the data set this article describes the disclosure problem and explains why it is a real problem using the concept of uniqueness some theory is developed that can help establish the risk of identification it turns out that useful microdata sets can only be released if some of the disclosure risks are dealt with by legal arrangements rather than by restrictions on the data to be released

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

non constant positive steady states of a predator prey system with non monotonic functional response and diffusion this paper deals with non constant positive steady state solutions of a predator prey system with non monotonic functional response also called holling type iv interaction terms and diffusion under the homogeneous neumann boundary condition we first establish positive upper and lower bounds for such solutions and then study their non existence global existence and bifurcation

very weak global solutions to a parabolic parabolic chemotaxis system with logistic source abstract in this paper we study this chemotaxis system u t u u v g u x t 0 v t v v u x t 0 defined in a convex smooth and bounded domain of r n with n 1 and endowed with homogeneous neumann boundary conditions being 0 and g a sort of logistic function obeying growth technical restrictions specifically once an appropriate definition of very weak solution is given our main result deals with the global existence of such solutions for any nonnegative initial data u 0 v 0 c 0 c 2 and under zero flux boundary condition on v 0

steady states of a predator prey model with prey taxis abstract we study the steady states of a predator prey model with prey taxis incorporating holling type ii functional response under the homogeneous neumann boundary condition the stability of equilibrium points and the existence of non constant steady states are investigated we obtain that the prey tactic sensitivity coefficient delays the stability of the unique positive constant solution but for other equilibrium points stability the prey tactic sensitivity coefficient does not influence on it furthermore we derive some sufficient conditions relative to the prey tactic sensitivity coefficient which confines the existence of steady states and find that even if the interaction coefficient is sufficiently large there also exist non constant positive steady states under some conditions

global analysis in a predator prey system with nonmonotonic functional response a predator prey system with nonmonotonic functional response is considered global qualitative and bifurcation analyses are combined to determine the global dynamics of the model the bifurcation a

how far do chemotaxis driven forces influence regularity in the navier stokes system the chemotaxis navier stokes system nt u n n n c c ct u c c nf c ut u u u p n u 0 0 1 is considered under boundary conditions of homogeneous neumann type for n and c and dirichlet type for u in a bounded convex domain r with smooth boundary where w and and f are sufficiently smooth given functions generalizing the prototypes const and f s s for s 0 it is known that for all suitably regular initial data n0 c0 and u0 satisfying 0 6 n0 0 c0 0 and u0 0 a corresponding initial boundary value problem admits at least one global weak solution which can be obtained as the pointwise limit of a sequence of solutions to appropriately regularized problems the present paper shows that after some relaxation time this solution enjoys further regularity properties and thereby complies with the concept of eventual energy solutions which is newly introduced here and which inter alia requires that two quasi dissipative inequalities are ultimately satisfied moreover it is shown that actually for any such eventual energy solution n c u there exists a waiting time t0 0 with the property that n c u is smooth in t0 and that n x t n0 c x t 0 and u x t 0 hold as t uniformly with respect to x this resembles a classical result on the three dimensional navier stokes system asserting eventual smoothness of arbitrary weak solutions thereof which additionally fulfill the associated natural energy inequality in consequence our results inter alia indicate that under the considered boundary conditions the possibly destabilizing action of chemotactic cross diffusion in does not substantially affect the regularity properties of the fluid flow at least on large time scales

global existence and boundedness in a keller segel stokes system involving a tensor valued sensitivity with saturation the 3d case abstract in this paper we continue to deal with the initial boundary value problem for the coupled keller segel stokes system n t u n n n s x n c c x t 0 t c t u c c c n x t 0 t u t p u n x t 0 t u 0 x t 0 t where r d is a bounded domain with smooth boundary and the chemotactic sensitivity s is not a scalar function but rather attains values in r d d and satisfies s x n c c s 1 n with some c s 0 and 0 when d 2 our previous work j differential equations 2015 has established the existence of global bounded classical solutions under the subcritical assumption 0 which is consistent with the corresponding results of the fluid free system but the method seems to be invalid in the three dimensional setting in this paper for the case d 3 we develop a new method to establish the existence and boundedness of global classical solutions for arbitrarily large initial data under the assumption 1 2 which is slightly stronger than the corresponding subcritical assumption 1 3 on the fluid free system where such an assumption is essentially necessary and sufficient for the existence of global bounded solutions the key idea here is to establish the general l p regularity of u from a rather low l p regularity of n which will be obtained by a new combinational functional

blow up in a higher dimensional chemotaxis system despite logistic growth restriction abstract we study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype u t u u v u u x t 0 0 v m t u x t 0 in a ball r n with parameters 0 0 0 and 1 and m t 1 u x t d x it is shown that when n 5 and 3 2 1 2 n 2 then there exist initial data such that the smooth local in time solution of blows up in finite time this indicates that even superlinear growth restrictions may be insufficient to rule out a chemotactic collapse as is known to occur in the corresponding system without any proliferation

estimation of sums of random variables examples and information bounds this paper concerns the estimation of sums of functions of observable and unobservable variables lower bounds for the asymptotic variance and a convolution theorem are derived in general finite and infinite dimensional models an explicit relationship is established between efficient influence functions for the estimation of sums of variables and the estimation of their means certain plug in estimators are proved to be asymptotically efficient in finite dimensional models while u v estimators of robbins are proved to be efficient in infinite dimensional mixture models examples include certain species network and data confidentiality problems

stability and hopf bifurcation in a predator prey system with several parameters a predator prey system depending on several parameters which also allows for a satiation effect of the predator is investigated for stability of equilibria hopf bifurcation global existence of limit cycles global attrractivity of equilibria and codimension two bifurcations throughout the main interest is in results yielding explicit dependence on the parameters involved

finite time blowup and global in time unbounded solutions to a parabolic parabolic quasilinear keller segel system in higher dimensions abstract in this paper we consider quasilinear keller segel type systems of two kinds in higher dimensions in the case of a nonlinear diffusion system we prove an optimal with respect to possible nonlinear diffusions generating explosion in finite time of solutions finite time blowup result in the case of a cross diffusion system we give results which are optimal provided one assumes some proper non decay of a nonlinear chemical sensitivity moreover we show that once we do not assume the above mentioned non decay our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross diffusion terms to this end we provide an example interesting by itself of global in time unbounded solutions to the nonlinear cross diffusion keller segel system with chemical sensitivity decaying fast enough in a range of parameters in which there is a finite time blowup result in a corresponding case without nonlinear cross diffusion

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

decay estimates of the coupled chemotaxis fluid equations in r 3 abstract in this paper we are concerned with a chemotaxis navier stokes model arising from biology which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations with transport and external force the optimal convergence rates of classical solutions to the chemotaxis navier stokes system for small initial perturbation around constant states are obtained by pure energy method under the assumption the initial data belong to h s h n n 3 0 s 3 2 the h s 0 s 3 2 negative sobolev norms are shown to be preserved along time evolution compared to the result in 5 we obtain the optimal decay rates of the higher order spatial derivatives of the solutions

qualitative analysis for a diffusive predator prey model with a transmissible disease in the prey population in this paper we study a diffusive predator prey model with a transmissible disease in the prey population we offer a complete discussion of the dynamical properties under the homogeneous neumann boundary condition we analyze local and global stabilities of nonnegative constant steady states and long time behaviors of the positive solutions moreover we study the existence nonexistence and bifurcation of nonconstant positive stationary solutions finally some numerical simulations are presented to support and strengthen our analytical analysis

multiscale models of taxis driven patterning in bacterial populations spatially distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants in the past decade a great deal has been learned about signal transduction metabolism and movement in e coli and other bacteria but translating the individual level behavior into population level dynamics is still a challenging problem however this is a necessary step because it is computationally impractical to use a strictly cell based model to understand patterning in growing populations since the total number of cells may reach 10 12 10 14 in some experiments in the past phenomenological equations such as the patlak keller segel equations have been used in modeling the cell movement that is involved in the formation of such patterns but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation significant progress has been made for

global analysis of a system of predator prey equations we study a class of ode s modelling the interaction of one predator and one prey the prey is assumed to be asocial in the sense that there is a threshold below which it will die even in the absence of predators knowledge of the separatrices of the flow and the local nature of the equilibrium points yields an analogue of the kolmogorov theorem a more detailed study of the direction of hopf bifurcation and uniqueness of limit cycles together with recent work on their continuation allows us to exhibit a very rich dynamics for both this system as well as for the more classical case of a prey without threshold we briefly discuss the implications of this work for ecology

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

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

stationary patterns of strongly coupled prey predator models abstract we study some elliptic systems arising from 3 component predator prey models where cross diffusions are included in such a way that predator chases the prey and the prey runs away from the predator we establish the existence and non existence of non constant positive solutions our results show that the cross diffusions can create the stationary patterns

a general monotone scheme for elliptic systems with applications to ecological models we consider weakly coupled elliptic systems of the type with each f i being either an increasing or a decreasing function of each u j assuming the existence of coupled super and subsolutions we prove the existence of solutions and provide a constructive iteration scheme to approximate the solutions we then apply our results to study the steady states of two species interaction in the volterra lotka model with diffusion

a strongly coupled predator prey system with non monotonic functional response abstract the predator prey system with non monotonic functional response is an interesting field of theoretical study in this paper we consider a strongly coupled partial differential equation model with a non monotonic functional response a holling type iv function in a bounded domain with no flux boundary condition we prove a number of existence and non existence results concerning non constant steady states patterns of the underlying system in particular we demonstrate that cross diffusion can create patterns when the corresponding model without cross diffusion fails

dynamics and patterns of a diffusive leslie gower prey predator model with strong allee effect in prey abstract this paper is devoted to study the dynamical properties and stationary patterns of a diffusive leslie gower prey predator model with strong allee effect in the prey population we first analyze the nonnegative constant equilibrium solutions and their stabilities and then study the dynamical properties of time dependent solutions moreover we investigate the stationary patterns induced by diffusions turing pattern our results show that the impact of the strong allee effect essentially increases the system spatiotemporal complexity

coexistence states for a diffusive one prey and two predators model with b d functional response abstract in this paper we study a diffusive one prey and two predators system with beddington deangelis functional response the sufficient and necessary conditions for the existence of coexistence states are obtained by means of the fixed point index theory in addition the stability and uniqueness of coexistence states are investigated finally we give the sufficient conditions for extinction and permanence of the time dependent system

non constant positive steady state of one resource and two consumers model with diffusion abstract in this paper a predator prey reaction diffusion system with one resource and two consumers is considered assume that one consumer species exhibits holling ii functional response while the other consumer species exhibits beddington deangelis functional response and they compete for the common resource first it is proved that the unique positive constant steady state is stable for the ode system and the reaction diffusion system second a prior estimates of positive steady state is given finally the non existence of non constant positive steady state the existence and bifurcation of non constant positive steady state are studied

assessing identification risk in survey microdata using log linear models this article considers the assessment of the risk of identification of respondents in survey microdata in the context of applications at the united kingdom uk office for national statistics ons the threat comes from the matching of categorical key variables between microdata records and external data sources and from the use of log linear models to facilitate matching while the potential use of such statistical models is well established in the literature little consideration has been given to model specification or to the sensitivity of risk assessment to this specification in numerical work not reported here we have found that standard techniques for selecting log linear models such as chi squared goodness of fit tests provide little guidance regarding the accuracy of risk estimation for the very sparse tables generated by typical applications at ons for example tables with millions of cells formed by cross classifying six key variables with sample sizes of 10 or 100 000 in this articl

existence of weak and regular solutions for keller segel system with degradation coupled to fluid equations abstract we establish the global well posedness for the following chemotaxis fluid system t n u n n n c n q t c u c c c n t u u u p u n u 0 in r d d 2 3 where 0 q 2 1 d and 0 1 for either q 2 d 1 2 or q 2 d 0 3 we prove the global existence of regular solutions in case that q 2 1 d and 0 very weak solutions are constructed as well

qualitative analysis for a diffusive predator prey model in this paper we study the qualitative properties of a diffusive predator prey model subject to the homogeneous neumann boundary condition by a comparison argument and iteration technique under some hypotheses we prove that the positive constant steady state is globally asymptotically stable we also establish the existence and non existence of non constant positive steady states stationary patterns by use of the degree theory and the a priori estimates

strategy and stationary pattern in a three species predator prey model abstract in this paper we study a strongly coupled system of partial differential equations which models the dynamics of a two predator one prey ecosystem in which the prey exercises a defense switching mechanism and the predators collaboratively take advantage of the prey s strategy we demonstrate the emergence of stationary patterns for this system and show that it is due to the cross diffusion that arises naturally in the model as far as the authors are aware this is the first example of stationary patterns in a predator prey system arising solely from the effect of cross diffusion

uniqueness and stability of a predator prey model with c m functional response in this paper we are concerned with positive solutions of a predator prey model with crowley martin functional response under dirichlet boundary conditions first we establish the existence of positive solutions when a c is close to 1 1 next the stability properties of nonnegative solutions are discussed by spectral analysis in addition we obtain a complete understanding of the uniqueness and non uniqueness of positive solutions by the lyapunov schmidt procedure and the perturbation technique at last some numerical simulations are presented to supplement the analytic results in one dimension

existence and decay of global smooth solutions to the coupled chemotaxis fluid model abstract in this paper we consider a coupled chemotaxis fluid model in r 3 which describes the so called chemotaxis boycott effect arising from the interplay of chemotaxis and diffusion of nutrients or signaling chemicals in bacterial suspensions it is shown that the cauchy problem has a unique global in time solution n c u x t on r 3 0 provided the invariant initial norm u 0 c 0 l 3 n 0 l 3 2 is suitably small or the diffusion coefficients of cells substrate and fluid i e are large enough we also show that the invariant norm u c t l 3 3 n t l 3 2 3 2 is monotone decreasing in t for all t 0

positive steady state solutions of the noyes field model for belousov zhabotinskii reaction abstract in the paper we investigate the noyes field model for belousov zhabotinskii reaction and study positive steady state solutions of this model with the homogeneous neumann boundary condition we obtain the existence and non existence of non constant positive steady state solutions

priors for random count matrices derived from a family of negative binomial processes abstractwe define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns the three distributions we consider are derived from the gamma poisson gamma negative binomial and beta negative binomial processes which we refer to generically as a family of negative binomial processes because the models lead to closed form update equations within the context of a gibbs sampler they are natural candidates for nonparametric bayesian priors over count matrices a key aspect of our analysis is the recognition that although the random count matrices within the family are defined by a row wise construction their columns can be shown to be independent and identically distributed iid this fact is used to derive explicit formulas for drawing all the columns at once moreover by analyzing these matrices combinatorial structure we describe how to sequentially construct a column iid random count matrix one row at a time and derive the predictive d

are gibbs type priors the most natural generalization of the dirichlet process discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in bayesian inference here we focus on the family of gibbs type priors a recent elegant generalization of the dirichlet and the pitman yor process priors these random probability measures share properties that are appealing both from a theoretical and an applied point of view i they admit an intuitive predictive characterization justifying their use in terms of a precise assumption on the learning mechanism ii they stand out in terms of mathematical tractability iii they include several interesting special cases besides the dirichlet and the pitman yor processes the goal of our paper is to provide a systematic and unified treatment of gibbs type priors and highlight their implications for bayesian nonparametric inference we deal with their distributional properties the resulting estimators frequentist asymptotic validation and the construction of time dependent versions applications mainly concerning mixture models and species sampling serve to convey the main ideas the intuition inherent to this class of priors and the neat results they lead to make one wonder whether it actually represents the most natural generalization of the dirichlet process

negative binomial process count and mixture modeling the seemingly disjoint problems of count and mixture modeling are united under the negative binomial nb process a gamma process is employed to model the rate measure of a poisson process whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an nb process for count modeling a draw from the nb process consists of a poisson distributed finite number of distinct atoms each of which is associated with a logarithmic distributed number of data samples we reveal relationships between various count and mixture modeling distributions and construct a poisson logarithmic bivariate distribution that connects the nb and chinese restaurant table distributions fundamental properties of the models are developed and we derive efficient bayesian inference it is shown that with augmentation and normalization the nb process and gamma nb process can be reduced to the dirichlet process and hierarchical dirichlet process respectively these relationships highlight theoretical structural and computational advantages of the nb process a variety of nb processes including the beta geometric beta nb marked beta nb marked gamma nb and zero inflated nb processes with distinct sharing mechanisms are also constructed these models are applied to topic modeling with connections made to existing algorithms under poisson factor analysis example results show the importance of inferring both the nb dispersion and probability parameters

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

holder estimates for local solutions of some doubly nonlinear degenerate parabolic equations abstract we prove interior and boundary holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is u t div u m 1 du p 2 du

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

a measure of disclosure risk for microdata protection against disclosure is important for statistical agencies releasing microdata files from sample surveys simple measures of disclosure risk can provide useful evidence to support decisions about release we propose a new measure of disclosure risk the probability that a unique match between a microdata record and a population unit is correct we argue that this measure has at least two advantages first we suggest that it may be a more realistic measure of risk than two measures that are currently used with census data second we show that consistent inference in a specified sense may be made about this measure from sample data without strong modelling assumptions this is a surprising finding in its contrast with the properties of the two similar established measures as a result this measure has potentially useful applications to sample surveys in addition to obtaining a simple consistent predictor of the measure we propose a simple variance estimator and show that it is consistent we also consider the extension of inference to allow for certain complex sampling schemes we present a numerical study based on 1991 census data for about 450 000 enumerated individuals in one area of great britain we show that the theoretical results on the properties of the point predictor of the measure of risk and its variance estimator hold to a good approximation for these data

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space abstract we study three dimensional incompressible magnetohydrodynamic equations in bounded domains or a half space we present new regularity criteria of weak solutions a pair of weak solutions u b become regular if u satisfies serrin s type conditions when we consider no slip or slip boundary conditions for the velocity field u and slip boundary conditions for the magnetic field b in either bounded domains or a half space in addition in the case of a half space with no slip boundary conditions for u and slip boundary conditions for b we demonstrate that if tangential components of u and normal component of b satisfy serrin s type conditions then a pair of weak solutions u b become regular

boundedness and decay property in a three dimensional keller segel stokes system involving tensor valued sensitivity with saturation in this paper we consider the following keller segel stokes system nt u n d n n ns x n c c n n2 ct u c c c n ut p u n u 0 in a bounded domain r3 with smooth boundary where w1 d is a given function satisfying d n cdnm 1 for all n 0 with certain cd 0 and s is a given function with values in r3 3 which fulfills s x n c cs 1 n with some cs 0 and 0 it is proved that under the conditions m 13 and 65 m and proper regularity hypotheses on the initial data the corresponding initial boundary problem possesses at least one global bounded weak solution in addition it is shown that if 0 then all solution components satisfy n t 0 c t 0andu t 0inl as t

turing patterns of a strongly coupled predator prey system with diffusion effects abstract the main purpose of this work is to investigate the effects of cross diffusion in a strongly coupled predator prey system by a linear stability analysis we find the conditions which allow a homogeneous steady state stable for the kinetics to become unstable through a turing mechanism in particular it is shown that turing instability of the reaction diffusion system can disappear due to the presence of the cross diffusion which implies that the cross diffusion induced stability can be regarded as the cross stability of the corresponding reaction diffusion system furthermore we consider the existence and non existence results concerning non constant positive steady states patterns of the system we demonstrate that cross diffusion can create non constant positive steady state solutions these results exhibit interesting and very different roles of the cross diffusion in the formation and the disappearance of the turing instability

qualitative analysis of a prey predator model with stage structure for the predator in this paper we propose a diffusive prey predator model with stage structure for the predator we first analyze the stability of the nonnegative steady states for the reduced ode system and then study the same question for the corresponding reaction diffusion system with homogeneous neumann boundary conditions we find that a hopf bifurcation occurs in the ode system but no turing pattern happens in the reaction diffusion system however when a natural cross diffusion term is included in the model we can prove the emergence of stationary patterns i e nonconstant positive stationary solutions for this system moreover these stationary patterns do not exist in the considered parameter regime when there is no cross diffusion

analysis of a prey predator model with disease in prey abstract in this paper a system of reaction diffusion equations arising in eco epidemiological systems is investigated the equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases a number of existence and non existence results about the non constant steady states of a reaction diffusion system are given it is proved that if the diffusion coefficient of the predator is treated as bifurcation parameter non constant positive steady state solutions may bifurcate from the constant steady state solution under some conditions

existence of positive solutions for a prey predator model with refuge and diffusion abstract we are concerned with a prey predator reaction diffusion model with monotonic functional response and specific refuge size we discuss both existence and nonexistence of positive solutions of the model by using fixed point index theory and bifurcation theory as the main argument tools we also discuss bifurcation solutions of which stability is established by using spectrum analysis methods moreover we analyze the effects of refuge size on the dynamics of the model

stationary patterns created by cross diffusion for the competitor competitor mutualist model abstract in this paper we consider a competitor competitor mutualist model with cross diffusion we prove some existence and non existence results concerning non constant positive steady states patterns in particular we demonstrate that the cross diffusion can create patterns when the corresponding model without cross diffusion fails

stationary patterns for a prey predator model with prey dependent and ratio dependent functional responses and diffusion abstract we study a reaction diffusion system arising from a three species prey predator model with prey dependent and ratio dependent functional responses the main aim of this paper is to study the global existence and bifurcation of non constant positive steady states in particular we will show that even though the unique positive constant steady state is stable for the ode dynamics non constant positive steady states exist for the reaction diffusion system this demonstrates that stationary patterns arise as a result of diffusion

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

pattern formation of a coupled two cell brusselator model abstract in this paper we study the stationary problems for the coupled two cell brusselator model as follows d 1 u 1 b 1 u b u 2 v c w u in d 2 v u u 2 v in d 1 w 1 b 1 w b w 2 z c u w in d 2 z w w 2 z in u v w z 0 on we first study the stability of the unique positive constant solution u v w z 1 1 1 1 then we give a priori estimate positive upper and lower bounds to the positive solution at last we obtain the non existence and existence of positive non constant solutions as parameters d 1 d 2 and b varied

positive solutions of a diffusive predator prey model with modified leslie gower and holling type ii schemes abstract in this paper we investigate the existence multiplicity and stability of positive solutions to a prey predator model with modified leslie gower and holling type ii schemes p u u a 1 b u c 1 v u k 1 in v v a 2 c 2 v u k 2 in u 0 v 0 in u v 0 on where r n n 1 is a bounded domain with a smooth boundary the parameters a i b c i k i i 1 2 are positive numbers u and v are the respective populations of prey and predator here we say u v with u v 0 is a positive solution of problem p if u v is a solution of p and u v 0 in

a qualitative study on general gause type predator prey models with constant diffusion rates abstract in this paper we study the qualitative behavior of non constant positive solutions on a general gause type predator prey model with constant diffusion rates under homogeneous neumann boundary condition we show the existence and non existence of non constant positive steady state solutions by the effects of the induced diffusion rates in addition we investigate the asymptotic behavior of spatially inhomogeneous solutions local existence of periodic solutions and diffusion driven instability in some eigenmode

global stability and pattern formation in a nonlocal diffusive lotka volterra competition model abstract a diffusive lotka volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed the nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species it is shown that when there is no nonlocal intraspecific competition the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive lotka volterra competition model regardless of the strength of nonlocal interspecific competition global stability of nonnegative constant equilibria are proved using lyapunov or upper lower solution methods on the other hand strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity for the weak competition case the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

non constant positive steady states of the sel kov model abstract this paper deals with the reaction diffusion system known as the sel kov model with the homogeneous neumann boundary condition this model has been applied to various problems in chemistry and biology we first give a priori estimates positive upper and lower bounds of positive steady states and then study the non existence bifurcation and global existence of non constant positive steady states as the parameters and are varied

quasisolutions and dynamics of time periodic nonquasimonotone reaction diffusion systems abstract in this paper using the upper lower solution method we investigate the properties of periodic quasisolutions for time periodic nonquasimonotone reaction diffusion systems and present some existence asymptotic behavior results for two ecological models