existence and global attractivity of positive periodic solutions of functional differential equations with feedback control sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback controldxdt b t x t f t x email protected 1 t x email protected n t u email protected t email protected t u t a t x email protected t the method involves the application of krasnoselskii s fixed point theorem and estimates of uniform upper and lower bounds of solutions when these results are applied to some special delay population models with multiple delays some new results are obtained and some known results are generalized

robust covariate adjusted log rank statistics and corresponding sample size formula for recurrent events data recurrent events data are frequently encountered in clinical trials this article develops robust covariate adjusted log rank statistics applied to recurrent events data with arbitrary numbers of events under independent censoring and the corresponding sample size formula the proposed log rank tests are robust with respect to different data generating processes and are adjusted for predictive covariates it reduces to the kong and slud 1997 biometrika 84 847 862 setting in the case of a single event the sample size formula is derived based on the asymptotic normality of the covariate adjusted log rank statistics under certain local alternatives and a working model for baseline covariates in the recurrent event data context when the effect size is small and the baseline covariates do not contain significant information about event times it reduces to the same form as that of schoenfeld 1983 biometrics 39 499 503 for cases of a single event or independent event times within a subject we carry out simulations to study the control of type i error and the comparison of powers between several methods in finite samples the proposed sample size formula is illustrated using data from an rhdnase study

existence and global stability of periodic solutions of a discrete predator prey system with delays with the help of continuation theorem in coincidence degree theory and lyapunov functions we derive sufficient and realistic conditions that guarantee the existence of a positive periodic solution for a delayed discrete predator prey system and also obtain sufficient conditions for the global stability of positive periodic solutions

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

a two state markov mixture model for a time series of epileptic seizure counts this paper discusses a model for a time series of epileptic seizure counts in which the mean of a poisson distribution changes according to an underlying two state markov chain the em algorithm dempster laird and rubin 1977 journal of the royal statistical society series b 39 1 38 is used to compute maximum likelihood estimators for the parameters of this two state mixture model and extensions are made allowing for nonstationarity the model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple poisson distribution and poisson regressions some simulation results are also presented to demonstrate the feasibility of this model

oscillation and global attractivity in a delay periodic host macroparasite model abstract in this paper we shall consider the nonlinear delay host macroparasite model with periodic coefficients with common period by means of a continuation theorem in coincidence degree theory we establish a sufficient condition for the existence of a positive periodic solution m t with strictly positive components also we establish some sufficient conditions for oscillation of all positive solutions about the positive periodic solution m t and establish a sufficient condition for the global attractivity of m t

on the existence of periodic solutions of a neutral delay model of single species population growth abstract in this paper we employ some new techniques to study the existence of positive periodic solutions of the neutral delay model n t n t a t t n t b t n t t c t n t t our result gives a correct answer to the open problem 9 2 due to y kuang 1993 delay differential equations with applications in population dynamics academic press new york

linearized oscillation theory for a nonlinear nonautonomous delay differential equation oscillation properties of two following equations are compared a scalar nonlinear delay differential equation y t k 1m rk t f k y hk t 0 with rk t o hk t t and a linear delay differential equation x t k 1m rk t x hk t 0 coefficients rk t and delays are not assumed to be continuous as an application explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics

multiple positive periodic solutions of nonlinear functional differential system with feedback control abstract in this paper we employ avery henderson fixed point theorem to study the existence of positive periodic solutions to the following nonlinear nonautonomous functional differential system with feedback control dx dt r t x t f t x t u t t du dt h t u t g t x t t we show that the system above has at least two positive periodic solutions under certain growth condition imposed on f

oscillation of continuous and discrete diffusive delay nicholson s blowflies models in this paper we consider the continuous and the discrete delay diffusive nicholson s blowflies models with different types of boundary conditions our aim is to give some sufficient conditions for oscillation of all positive solutions about the positive steady state we show that these conditions have essentially first order character by reducing the problem of oscillation of the boundary value problem to that of first order delay differential or difference equation

a linearized oscillation result for odd order neutral delay differential equations abstract consider the odd order nonlinear neutral equation d n dt n x t p t g x t q t h x t 0 we establish a linearized oscillation result of this equation when p t 1 which answers partially an open problem proposed by gyori and ladas

the mackey glass model of respiratory dynamics review and new results a b s t r a c t since the celebrated mackey glass model of respiratory dynamics was introduced in 1977 many results on its qualitative behavior have been obtained including oscillation stability and chaos the paper reviews some known properties and presents new results for more general models equations with time dependent parameters several delays a positive periodic equilibrium and distributed delays the problems considered in the paper involve existence positivity and permanence of solutions oscillation and global asymptotic stability in addition some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined the paper generalizes and unifies existing results and provides an outlook on further studies

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

mackey glass model of hematopoiesis with monotone feedback revisited for the blood cell production modeldxdt ax t f 0 q n q n x n t t we review known results permanence of solutions oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non autonomous generalizations of this equation with both concentrated and distributed delays

calabi yau manifolds motivations and constructions the possible ways of compacitification of thee8 e8 superstring theory to four dimensions are reviewed the phenomenological need forn 1 supersymmetry is argued on quite general grounds to favour the choice of a calabi yau manifold for the compact internal manifold the massless spectrum after compactification is derived in full detail revealing beside the usual particles others that may have great phenomenological impact the technical aspects of the construction of such manifolds are examined and the methods of calculation of the relevant topological properties are given a big family of such constructions giving rise to many new calabi yau manifolds is presented and its relevance to the search of a phenomenologically acceptable solution is discussed

on oscillation of a generalized logistic equation with several delays abstract for a scalar delay generalized logistic equation y t k 1 m r k t y t 1 y h k t k 1 y h k t k k 1 explicit oscillation conditions are established for all the cases of parameters k i e sublinear superlinear and also mixed ones coefficients rk t and delays hk t are not assumed to be continuous

existence and global attractivity of positive periodic solutions for the impulsive delay nicholson s blowflies model in this paper we shall consider the following nonlinear impulsive delay population model 0 1 x t d t x t p t x t m w e a t x t m w a e t 0 t t k x t k 1 b k x t k k 1 2 where m is a positive integer d t a t and p t are positive periodic continuous functions with period w 0 in the nondelay case m 0 we show that 0 1 has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate linear periodic impulsive perturbations the impulsive delay equation 0 1 preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

mackey glass model of hematopoiesis with non monotone feedback stability oscillation and control for the blood cell production model with a unimodal hump feedback email protected t email protected q ny email protected q n y n email protected we review the known results and investigate generalizations of this equation permanence oscillation and stability of the positive equilibrium are studied for non autonomous equations including equations with a distributed delay in addition a linear control is introduced and possibilities to stabilize an otherwise unstable positive equilibrium are explored

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

almost periodic solutions of lasota wazewska type delay differential equation sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a single species model given by the nonautonomous lasota wazewska type delay differential equations x t txt ptfxt in which 0 p t 0 t are continuous almost periodic functions and f is a decreasing positive c1 function conditions of the uniform asymptotical stability for some associated nonautonomous delay differential equations x t txt ptxt are also discussed

existence of positive periodic solutions of nonlinear discrete model exhibiting the allee effect in this paper we shall consider the discrete nonlinear delay population model with allee effectx n 1 x n exp a n b n x p n w c n x q n w where a n b n and c n are positive sequences of period w and p and q are positive integers by using the coincidence degree theorem as well as some priori estimates we will establish a sufficient condition for the existence of positive periodic solution x n

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

existence and global attractivity of a positive periodic solution of a delayed periodic respiration model in this paper we consider the following delayed periodic differential equation x t v t x t x n t t t q t x n t t t t t which describes a dynamic disease involving respiratory disorders using the method of coincidence degree we first show the existence of a positive periodic solution this result greatly extends the existing ones then several sufficient conditions for the global attractivity of this periodic solution are established these results are independent of each other and in general are much better than the existing ones

global attractivity in population dynamics we established sufficient conditions for the global attractivity of the positive equilibrium of the delay differential equation n t mu n t i 1m pi exp n t i t 0 m 1 for m 1 equation 1 was used by wazewska czyzewska and lasota as a model for the survival of red blood cells in an animal

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

sample sizes based on the log rank statistic in complex clinical trials the log rank test is frequently used to compare survival curves while sample size estimation for comparison of binomial proportions has been adapted to typical clinical trial conditions such as noncompliance lag time and staggered entry the estimation of sample size when the log rank statistic is to be used has not been generalized to these types of clinical trial conditions this paper presents a method of estimating sample sizes for the comparison of survival curves by the log rank statistic in the presence of unrestricted rates of noncompliance lag time and so forth the method applies to stratified trials in which the above conditions may vary across the different strata and does not assume proportional hazards power and duration as well as sample sizes can be estimated the method also produces estimates for binomial proportions and the tarone ware class of statistics

global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics in this paper we shall consider the following nonlinear impulsive delay differential equation x t v t x t xn t m n xn t m t a e t 0 t tk x tk 1 1 bk x tk k 1 2 where m and n are positive integers v t and t are positive periodic continuous functions with period 0 in the nondelay case m 0 we show that the above equation has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate periodic impulsive perturbations the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

sample size calculations for the two sample problem using the multiplicative intensity model in this paper we propose formulae for calculating the expected number of events or alternatively the required trial duration for clinical trials involving two treatment groups in which patients may potentially experience multiple events and the data will be analysed using a multiplicative intensity mi model we use a partial likelihood based approach and examine in detail two mi models one that includes a binary treatment variable as the only covariate and a three state markov process model in which a binary time varying covariate is added to the previous model for the simpler model our formula coincides with those derived by cook using full likelihood methods we present applications of the derived formulae to chronic granulomatous disease and breast cancer data sets

sample size calculations for comparative clinical trials with over dispersed poisson process data this paper develops a new formula for sample size calculations for comparative clinical trials with poisson or over dispersed poisson process data the criteria for sample size calculations is developed on the basis of asymptotic approximations for a two sample non parametric test to compare the empirical event rate function between treatment groups this formula can accommodate time heterogeneity inter patient heterogeneity in event rate and also time varying treatment effects an application of the formula to a trial for chronic granulomatous disease is provided

oscillation theorems for first order nonlinear neutral functional differential equations abstract this paper discusses a class of first order nonlinear neutral differential equations with variable coefficients and variable deviations sharp conditions are established for all solutions of the equations to be oscillatory linearized oscillation criteria of the equations are also given

positive periodic solutions of discrete three level food chain model of holling type ii with the help of differential equations with piecewise constant arguments we first derive a discrete analogy of continuous three level food chain model of holling type ii which is governed by difference equations with periodic coefficients a set of sufficient conditions is derived for the existence of positive periodic solutions with strictly positive components by using the continuation theorem in coincidence degree theory particularly the upper and lower bounds of the periodic solutions are also established

oscillation and global attractivity in hematopoiesis model with periodic coefficients in this paper we shall consider the nonlinear delay differential equation p t email protected t p m email protected 1 p n email protected email protected t p t where k is a positive integer b t and c t are positive periodic functions of period w in the nondelay case we shall show that has a unique positive periodic solution email protected t and we will study the global attractivity of email protected t in the delay case we shall establish some sufficient conditions for oscillation of all positive solutions of about email protected t and establish some sufficient conditions for the global attractivity of email protected t our results in this paper extend as well as improve the results in the autonomous case

a note on stability of mackey glass equations with two delays abstract if the mackey glass equation x t r t a x h t 1 x g t x t with a 1 and 0 incorporates not one but two variable delays some new phenomena arise there may exist non oscillatory about the positive equilibrium unstable solutions the effect of possible absolute stability for certain a and disappears we obtain sufficient conditions for local and global stability of the positive equilibrium and illustrate the stability tests as well as new effects of two different delays with examples

boundedness and persistence of delay differential equations with mixed nonlinearity for a nonlinear equation with several variable delays x t k 1 m f k t x h 1 t x h l t g t x t where the functions fk increase in some variables and decrease in the others we obtain conditions when a positive solution exists on 0 as well as explore boundedness and persistence of solutions finally we present sufficient conditions when a solution is unbounded examples include the mackey glass equation with non monotone feedback and two variable delays its solutions can be neither persistent nor bounded unlike the well studied case when these two delays coincide

semiparametric transformation models for point processes in this article we propose a family of semiparametric transformation models for point processes with positive jumps of arbitrary sizes these models offer great flexibilities in formulating the effects of covariates on the mean function of the point process while leaving the stochastic structure completely unspecified we develop a class of estimating equations for the baseline mean function and the vector valued regression parameter based on censored point processes and covariate data these equations can be solved easily by the standard newton raphson algorithm the resultant estimator of the regression parameter is consistent and asymptotically normal with a covariance matrix that can be estimated consistently furthermore the estimator of the baseline mean function is uniformly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function we demonstrate through extensive simulation studies that the proposed inference procedu

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

periodic solution of a delayed predator prey system without dominating instantaneous negative feedback by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator prey system without dominating instantaneous negative feedback indeed our result are applicable to statedependent delays

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

design of clinical trials for recurrent events with periodic monitoring this paper presents a design for randomized clinical trials in which incomplete data are collected on the occurrence of potentially recurrent events through periodic monitoring in particular events are assumed to arise according to a point process but information is available at the times of monitoring only if one or more events has occurred since the preceding monitoring point the event process is modelled via a piecewise poisson process and a proportional rates model is introduced to represent the difference in event rates between treatment groups the design was developed on the basis of a wald type test derived from the generalized estimating equations of liang and zeger biometrika 73 13 22 1986 robustification of the variance of the estimator of the treatment effect was considered under a random effects model with a semi parametric mixture distribution the design was adopted to address issues which arose in an osteoporosis trial conducted in japan

existence and global attractivity of positive periodic solutions of functional differential equations with impulses abstract sufficient and realistic conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with impulses d y t d t y t f t y t 1 t y t n t a e t 0 t t k y t k y t k b k y t k k 1 2 the method involves the application of the gaines and mawhin s coincidence degree theory the constructing suitable lyapunov functionals and estimations of uniform upper bounds on solutions when these results are applied to some special delay population models some new results are obtained and some known results are generalized in particular our results indicate that under the appropriate linear periodic impulsive perturbations the above impulsive delay differential equation preserves the original periodicity and global attractivity of the nonimpulsive delay differential equation d y t d t y t f t y t 1 t y t n t

power sample size calculations for generalized linear models an approach for estimating power sample size is described within the framework of generalized linear models this approach is based on an asymptotic approximation to the power of the score test under contiguous alternatives and is applicable to tests of composite null hypotheses an implementation is described for the special case of logistic regression models simulation studies are presented which indicate that the asymptotic approximation to the finite sample situation is good over a range of parameter configurations

positive periodic solutions of a class of delay differential system with feedback control with the help of continuation theorem based on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for the delay differential system with feedback control when these results are applied to some special delay population models some new results are obtained and some known results are generalized

oscillatory and asymptotic behavior of positive periodic solutions of nonlinear discrete model exhibiting the allee effect in this paper we shall consider the discrete nonlinear delay population model with allee effectx n 1 x n exp a n b n x p email protected c n x q email protected where a n b n and c n are positive sequences of period w and p and q are positive integers we will establish some sufficient conditions for the oscillation of all positive solutions about its positive periodic solution x n and prove that every nonoscillatory solution converges to x n monotonically as n

complex symplectic geometry and compact locally hyper kahlerian manifolds complex symplectic geometry is the study of complex manifolds admitting a global closed nondegenerate holomorphic two form compact simply connected complex symplectic manifolds are of interest for various reasons for example they always admit a ricci flat metric in this work the close relationship between the complex geometry of such manifolds and their riemannian structures is exploited in order to obtain results in both directions riemannian techniques are used to obtain results on the complex automorphism group and the problem of constructing examples of compact locally hyper kahlerian manifolds with prescribed holonomy groups is discussed

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

gauging discrete symmetries recent developments in quantum gravity theory have led to the suggestion that various discrete symmetries in particular charge parity cp should be gauged that is interpreted as elements of some connected lie group as the parity operator is related to a space time isometry however it is far from clear that this suggestion has any real meaning we give a simple geometric construction in terms of which it is meaningful to gauge discrete symmetries provided that certain nontrivial conditions are satisfied by the space time manifold by the gauge group and by the discrete symmetry itself

sample size calculations for studies with correlated observations correlated data occur frequently in biomedical research examples include longitudinal studies family studies and ophthalmologic studies in this paper we present a method to compute sample sizes and statistical powers for studies involving correlated observations this is a multivariate extension of the work by self and mauritsen 1988 biometrics 44 79 86 who derived a sample size and power formula for generalized linear models based on the score statistic for correlated data we appeal to a statistic based on the generalized estimating equation method liang and zeger 1986 biometrika 73 13 22 we highlight the additional assumptions needed to deal with correlated data some special cases that are commonly seen in practice are discussed followed by simulation studies

power and sample size calculation for paired recurrent events data based on robust nonparametric tests the purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data the developed formula is based on robust non parametric tests for comparing the marginal mean function of events between paired samples this calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model we evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations homogeneous or nonhomogeneous processes marginal hazard rates censoring rate accrual and follow up times as well as the sensitivity analysis for the assumption of the frailty distribution the use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern taiwan copyright 2017 john wiley sons ltd

oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics abstract in this paper we shall consider the nonlinear delay differential equation where m and n are positive integers and v t and t are positive periodic functions of period in the nondelay case we shall show that has a unique positive periodic solution x t and provides sufficient conditions for the global attractivity of x t in the delay case we shall present sufficient conditions for the oscillation of all positive solutions of about x t and establish sufficient conditions for the global attractivity of x t

existence and global attractivity of unique positive periodic solution for a model of hematopoiesis sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis then some criteria are established for the existence uniqueness and global attractivity of almost periodic solutions of almost periodic system

efficiency lost by analyzing counts rather than event times in poisson and overdispersed poisson regression models abstract inference for point processes is most efficient if the event times for each individual are available sometimes the study design is such that only aggregated data are collected consisting of the number of events or recurrences for each individual over the observation period this article discusses the loss in efficiency of an analysis of the aggregated counts versus an analysis of the actual event times one particular case is exemplified that in which the purpose of the experiment or trial is to compare the effects of treatments and the loss in efficiency in the estimator of the treatment effect is computed the specific point process considered here is the nonhomogeneous poisson process with a proportional intensity model for the treatment effects random effects models are also considered with estimation via a quasi likelihood approach the quasi likelihood analysis proposed here is an extension of such techniques for the homogeneous poisson process the resulting estimating equations for

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

stability conditions for scalar delay differential equations with a non delay term abstract the problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non autonomous equations which include a non delay term and one or more delayed terms first we demonstrate that introducing a non delay term with a non negative coefficient can destroy stability of the delay equation next sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained the nonlinear results are applied to the mackey glass model of respiratory dynamics

periodic solution of a delayed predator prey system with michaelis menten type functional response by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator prey system with michaelis menten type functional response indeed our results are applicable to state dependent delays

mixed poisson likelihood regression models for longitudinal interval count data summary in many longitudinal studies it is desired to estimate and test the rate over time of a particular recurrent event often only the event counts corresponding to the elapsed time intervals between each subject s successive observation times and baseline covariate data are available the intervals may vary substantially in length and number between subjects so that the corresponding vectors of counts are not directly comparable a family of poisson likelihood regression models incorporating a mixed random multiplicative component in the rate function of each subject is proposed for this longitudinal data structure a related empirical bayes estimate of random effect parameters is also described these methods are illustrated by an analysis of dyspepsia data from the national cooperative gallstone study

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

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided

global linearized stability theory for delay differential equations abstract for nonlinear delay differential equations where nonlinearities are approximated by linear functions we discuss a rather general global stability principle several examples which extend and improve known global stability results are presented

a practical approach to computing power for generalized linear models with nominal count or ordinal responses data analysts facing study design questions on a regular basis could derive substantial benefit from a straightforward and unified approach to power calculations for generalized linear models many current proposals for dealing with binary ordinal or count outcomes are conceptually or computationally demanding limited in terms of accommodating covariates and or have not been extensively assessed for accuracy assuming moderate sample sizes here we present a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non continuous outcome the model is fit to an appropriate expanded data set using easily calculated weights that represent response probabilities given the assumed values of the parameters the variance covariance matrix resulting from this fit is then used in conjunction with an established non central chi square approximation to the distribution of the wald statistic alternatively the model can be re fit under the null hypothesis to approximate power based on the likelihood ratio statistic we provide guidelines for constructing a representative expanded data set to allow close approximation of unconditional power based on the assumed joint distribution of the covariates relative to prior proposals the approach proves particularly flexible for handling one or more continuous covariates without any need for discretizing we illustrate the method for a variety of outcome types and covariate patterns using simulations to demonstrate its accuracy for realistic sample sizes

oscillation properties of a logistic equation with several delays abstract for a scalar delay logistic equation y t y t k 1 m r k t 1 y h k t k h k t t the oscillation properties are established which are well known for a linear delay differential equation such as comparison theorems explicit nonoscillation and oscillation conditions dependence of the solution sign on the initial function and the initial value

gauge theory in witten s approach to the generation problem in witten s topological theory of the generation problem gauge groups are identified with thee 8 centraliser of the holonomy group of the internal manifold here we show that this amounts to interpreting gauge groups as generalised symmetry groups of the internal levi civita connection we then give techniques for computing centralisers in exceptional groups taking into account the fact that holonomy groups are frequently disconnected these techniques allow us to deal with compact locally irreducible ricci flat riemannian manifolds of all holonomy types and dimensions