A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

An Alternative Perspective

The need for a revised definition is discussed and a more simplified alternative is suggested.     

An Alternative Approach to Modelling the Assortative Mating Process

In this article we demonstrate how the difficulties encountered from consideration of two-sided assortation for a characteristic (or set of characteristics) in human populations can be overcome. This is achieved, essentially, by postulating a socio-environmental variable (based on an individual's lifetime experiences) over which individuals are mating assortatively. The value an individual has on this scale determines his mean value for the characteristic under consideration. In other words, there is a relationship between the characteristic and the socioenvironmental scale. As well, individuals may be mating assortatively for the characteristic under consideration (although not necessarily). Thus we achieve assortative mating for a single characteristic as a result of mixing, simultaneously, over more than just one variable. Expansions to more ‘mixing’ scales than a single socio-environmental variable are quite straightforward.     

Alternative Reading Frame Supports An Alternative Model for Retinoblastoma

The ubiqutin-proteasome system is the major pathway by which cells target proteins for degradation in a specific manner. The E3 ubiquitin ligase, which brings targeted proteins (substrates) and activated ubiquitin in close proximity, enabling covalent conjugation of ubiquitin to the substrate, is an essential component of this system. Of the E3 ligases, the cullin (CUL) ligases are of high interest because of their capacity to form multiple distinct E3 complexes to ubiquitinate a potentially large number of substrates. Of the six closely related cullins, very little is known about how specific substrates are recruited to CUL4-dependent ligases. A recent paper in Nature Cell Biology may shed some light on this issue as well as on the function of DDB1, a damaged-DNA binding protein that has long been associated with DNA repair.     

An Alternative Method for Meta-Analysis

In many fields of applications, test statistics are obtained by combining estimates from several experiments, studies or centres of a multi-centre trial. The commonly used test procedure to judge the evidence of a common overall effect can result in a considerable overestimation of the significance level, leading to a high rate of too liberal decisions. Alternative test statistics are presented and better approximating test distributions are derived. Explicitly discussed are the methods in the unbalanced heteroscedastic 1-way random ANOVA model and for the probability difference method, including interaction treatment by centres or studies. Numerical results are presented by simulation studies.     

An Alternative to the Flat Substrate Method of Preparing Electron Microscope Autoradiographs

Difficulty with flat substrate methods of preparing electron microscope autoradiographs has prompted reconsideration and refinement of a technique in which an electron microscope grid is placed beneath the specimen prior to dipping. This technique avoids the problems commonly associated with the direct application of emulsions to specimen grids, and should be considered as an alternative to flat substrate techniques when difficulty with these methods is encountered.     

An Alternative to Ewald Sums. Part 3: Implementation and Results

Abstract

This paper describes the implementation of a method for computing the Coulombic interaction in a periodic system. If the basic cell contains n charges the CPU time required to compute all forces and the total energy is O(n·log n) in contrast to Ewald's method with O(n ³/²).     

An Alternative Approach to Estimation in Two-Phase Sampling Using two Auxiliary Variables

Using two-phase sampling mechanism, two alternative estimators in the presence of the available knowledge on second auxiliary variable z are considered, when the population mean of the main auxiliary variable × is unknown. The suggested estimators are found to be more eficient than the ratio-type and regression-type estimators suggested by KIREGYERA (1980, 1984).