A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

This paper considers a generalized birth process {X^m(t), t > 0} and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to model such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.     

Testing concordance of clinical characteristics in familial studies with application to inflammatory bowel diseases

The etiology of chronic Inflammatory Bowel Diseases (IBD) remains unknown, with both genetic and environmental risk factors having been implicated. A recent collaborative study of IBD provides clinical data from families with three or more affected first-degree relatives. The scientific question is whether specific clinical characteristics aggregate among affected individuals within families. Gastroenterological researchers have examined the number of concordant familial pairs in familial aggregation studies, but methods and results have been discrepant. This article investigates concepts of concordance and gives a comprehensive statistical treatment for testing concordance of various clinical traits in familial studies. For dichotomous traits, the distribution of this statistic under the null hypothesis of no familial aggregation is obtained by three methods: asymptotic, probability generating function, and permutation. The permutation method is extended to analyze aggregation for non-dichotomous traits and co-aggregations between two traits. We apply the permutation method to analyze the aforementioned multiply-affected IBD family data. Evidence is found for familial clustering of various traits, some of which are not revealed in existing studies. Such analyses provide a basis for investigating the dependence of trait aggregation upon genetic or environmental risk factors.     

On a Birth-and-Death Process Induced Distribution

A type of distribution induced by the linear birth-and-death processes is useful in modeling certain biological phenomena. In addition to extending some existing results, new findings are presented concerning the mathematical properties of the distribution.     

A Markov Chain Model of Population Growth with an Application in Epidemiology

This paper is concerned with a class of population growth processes in discrete time; the simple epidemic process is considered as a specific example. A Markov chain model is constructed and standard Markov methods are used to study the main biological concepts. A simple and explicit formula is obtained for the transient distribution of the population size. Then, the cost of the process is defined and the joint probability generating function of its components is derived. Finally, the results are extended to the case where the inter-transition periods are bounded i.i.d. random variables.     

A random process may control the number of endemic species

The richness of endemic species is often recognized as an indication of the distinctiveness of certain local faunas and is used for the definition of conservation hotspots as well. Faunas of different animal taxa were considered in sets of contiguous geographical units. Comparing the faunas of different units in one set, we found an exponential increase in the number of endemics when plotted against the number of non-endemics. A model of independent stochastic population dynamics under the control of environmental oscillations produces random fluctuations in the ranges of species. Ranges of endemic species are supposedly narrower than ranges of co-occurring non-endemic species. In such a case, the flow of a random process leads to an exponential relationship between numbers of co-occurring endemic and non-endemic species. This process also produces an apparent positive correlation between total species number and the percentage of endemics.     

随机抽样对蛋白质相互作用网络度分布的影响

蛋白质相互作用(PPI)网络,是目前系统研究蛋白质层面细胞活动的重要工具,PPI网络的度分布是研究复杂网络性质的重要物理量。随着蛋白质相互作用数据量不断的增加,其数据的可靠性是否会对PPI网络的度分布造成影响,并不确定。本文对四种模式生物的PPI网络数据,按照5%的增长比率,随机删除PPI网络的边,来检验随机抽样对PPI网络度分布的影响。结果表明,各种实验数据的误差不会对真实PPI网络的度分布造成干扰,且在目前描述网络度分布的五种函数中,广延指数函数拟合程度最优。     

On the Green’s function for a one-dimensional random walk

The Green’s function of a random walk on a lattice is defined as the inverse of the operatorK-z1, whereK is the matrix of transition rates and z is an arbitrary complex parameter. The Green’s function for a symmetrical random walk in one dimension is here explicitly given in closed form for reflecting, periodic, and absorbing boundaries, and also for an infinite lattice.     

On models for binomial data with random numbers of trials

A binomial outcome is a count s of the number of successes out of the total number of independent trials n=s+f, where f is a count of the failures. The n are random variables not fixed by design in many studies. Joint modeling of (s, f) can provide additional insight into the science and into the probability pi of success that cannot be directly incorporated by the logistic regression model. Observations where n= 0 are excluded from the binomial analysis yet may be important to understanding how pi is influenced by covariates. Correlation between s and f may exist and be of direct interest. We propose Bayesian multivariate Poisson models for the bivariate response (s, f), correlated through random effects. We extend our models to the analysis of longitudinal and multivariate longitudinal binomial outcomes. Our methodology was motivated by two disparate examples, one from teratology and one from an HIV tertiary intervention study.     

Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.     

A stochastic model of tumor response to fractionated radiation: limit theorems and rate of convergence

The iterated birth and death Markov process is defined as an n-fold iteration of a birth and death Markov process describing kinetics of certain population combined with random killing of individuals in the population at moments tau 1,...,tau n with given survival probabilities s1,...,sn. A long-standing problem of computing the distribution of the number of clonogenic tumor cells surviving an arbitrary fractionated radiation schedule is solved within the framework of iterated birth and death Markov process. It is shown that, for any initial population size iota, the distribution of the size N of the population at moment t > or = tau n is generalized negative binomial, and an explicit computationally feasible formula for the latter is found. It is shown that if i --> infinity and sn --> 0 so that the product iota s1...sn tends to a finite positive limit, the distribution of random variable N converges to a probability distribution, which for t = tau n turns out to be Poisson. In the latter case, an estimate of the rate of convergence in the total variation metric similar to the classical Law of Rare Events is obtained.     

Modeling the dependence between the number of trials and the success probability in binary trials

A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics59, 955-961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta-binomial-Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.