Inclusion-induced boundary layers in lipid vesicles

The equilibrium shapes of lipid vesicles are perturbed by rigid inclusions. In a two-dimensional vesicle, that may also model a cylindrically elongated tubule, the shape modifications can be determined analytically, and turn out to be significant even far from the inclusion. On the contrary, previous numerical work has given evidence that in the three-dimensional case the shape perturbations decay quite rapidly and are negligible a few inclusion radii away. In this paper, we use the tools of asymptotic analysis to derive analytically the shape of the boundary layer induced by the inclusion. As a result, we are able to determine the dominant part of the free-energy perturbation that, in turn, allows to identify the vesicle points where the inclusion prefers to sit.     

Probabilistic analysis of a genealogical model of animal group patterns

Many social animals live in stable groups, and it has been argued that kinship plays a major role in their group formation process. In this study we present the mathematical analysis of a recent model which uses kinship as a main factor to explain observed group patterns in a finite sample of individuals. We describe the average number of groups and the probability distribution of group sizes predicted by this model. Our method is based on the study of recursive equations underlying these quantities. We obtain asymptotic equivalents for probability distributions and moments as the sample size increases, and we exhibit power-law behaviours. Computer simulations are also utilized to measure the extent to which the asymptotic approximation can be applied with confidence.     

Analysis of a distributed model of leg coordination

Using tools from discrete dynamical systems theory, we begin a systematic analysis of a distributed model of leg coordination with both biological and robotic applications. In this paper, we clarify the role of individual coordination mechanisms by studying a system of two leg oscillators coupled in one direction by each of the three major mechanisms that have been described for the stick insect Carausius morosus. For each mechanism, we derive analytical return maps, and analyze the behavior of these return maps under iteration in order to determine the asymptotic phase relationship between the two legs. We also derive asymptotic relative phase densities for each mechanism and compare these densities to those obtained from numerical simulations of the model. Our analysis demonstrates that, although each of these mechanisms can individually compress a range of initial conditions into a narrow band of relative phase, this asymptotic relative phase relationship is, in general, only neutrally stable. We also show that the nonlinear dependence of relative phase on walking speed along the body in the full hexapod model can be explained by our analysis. Finally, we provide detailed parameter charts of the range of behavior that each mechanism can produce as coupling strength and walking speed are varied. Received: 22 June 1999 / Accepted in revised form: 7 September 1999     

Incorporating extra information in experimental design for bioassay

In a bioassay, under certain experimental circumstances, information on concentration (dose rate) and time to response for some subjects can be combined in a single analysis. An underlying logistic random variable is assumed and the resulting mixed- (continuous-quantal) response model is analyzed by likelihood methods. The estimation procedure for the mean and the variance is described, and expressions for asymptotic variances are obtained. A comparison of results from the mixed model and from the standard quantal-response model shows that there is a substantial reduction in the variance of the estimators for the mixed model. On the basis of the table of asymptotic variances, some design implications are discussed. An example from insect pheromone research is used to illustrate the main ideas.     

A constrained-likelihood approach to marker-trait association studies

Marker-trait association analysis is an important statistical tool for detecting DNA variants responsible for genetic traits. In such analyses, an analysis model of the mean genetic effects of the genotypes is often specified. For instance, the effect of the disease allele on the trait is often specified to be dominant, recessive, additive, or multiplicative. Although this model-based approach is powerful when the analysis model is correctly specified, it has been found to have low power sometimes when the specified model is incorrect. We introduce an approach that does not require the specification of a particular genetic model. This approach is built upon a constrained maximum likelihood in which the mean genetic effect of the heterozygous genotype is required to not exceed those of the two homozygous genotypes. The asymptotic distribution of the likelihood-ratio statistic is derived for two special cases. A simulation study suggests that this new approach has power comparable to that of the model-based method when the analysis model is correctly specified. This approach uses one marker at a time (i.e., it is a single-marker analysis). However, given the latest findings that powerful inferential procedures for haplotype analyses can be constructed from single-marker analyses, we expect this approach to be useful for haplotype analyses.     

Exact inference for matched case-control studies

In an epidemiological study with a small sample size or a sparse data structure, the use of an asymptotic method of analysis may not be appropriate. In this paper we present an alternative method of analyzing data for case-control studies with a matched design that does not rely on large-sample assumptions. A recursive algorithm to compute the exact distribution of the conditional sufficient statistics of the parameters of the logistic model for such a design is given. This distribution can be used to perform exact inference on model parameters, the methodology of which is outlined. To illustrate the exact method, and compare it with the conventional asymptotic method, analyses of data from two case-control studies are also presented.     

Regular gaits and optimal velocities for motor proteins

It has been observed in numerical experiments that adding a cargo to a motor protein can regularize its gait. Here we explain these results via asymptotic analysis on a general stochastic motor protein model. This analysis permits a computation of various observables (e.g., the mean velocity) of the motor protein and shows that the presence of the cargo also makes the velocity of the motor nonmonotone in certain control parameters (e.g., ATP concentration). As an example, we consider the case of a single myosin-V protein transporting a cargo and show that, at realistic concentrations of ATP, myosin-V operates in the regime which maximizes motor velocity. Our analysis also suggests an experimental regimen which can test the efficacy of any specific motor protein model to a greater degree than was heretofore possible.     

一类Hopfield型时滞神经网络模型的全局渐近稳定性

用拓扑度和Lyapunov泛函方法，讨论了一类具有时滞的Hopfield神经网络平衡点的存在性及其全局渐近稳定性．所获得的若干判别条件，都去掉了有关文献中关于激活函数的可微性和有界性限制，增强了模型的适用性．     

Reduction of slow-fast asymptotically autonomous systems with applications to gradostat models

Two distinguishing features characterize the population dynamic models considered in the present work. On the one hand, we consider several interacting organization levels associated to different time scales. On the other hand, the environment tends to be constant in the long term. The mathematical representation of these properties leads to slow-fast asymptotically autonomous systems. These characteristics add some realism in the models. However, the analytical study of this class of systems is generally hard to perform.Here we present a reduction technique that can be included among the so-called approximate aggregation methods. The existence of different time scales, together with the long term features, are used to build up a simpler system, which can be described by means of a lower number of state variables. The asymptotic behavior of the simplified model helps to study the original one.The reduction procedure is formulated in a general way. Following, two illustrations of asymptotically autonomous models with two time scales, in a gradostat, are given: a consumer–resource model and a competition model. Finally, a wider range of applications is suggested.     

Heuristic Bayesian Segmentation for Discovery of Coexpressed Genes within Genomic Regions

Segmentation aims to separate homogeneous areas from the sequential data, and plays a central role in data mining. It has applications ranging from finance to molecular biology, where bioinformatics tasks such as genome data analysis are active application fields. In this paper, we present a novel application of segmentation in locating genomic regions with coexpressed genes. We aim at automated discovery of such regions without requirement for user-given parameters. In order to perform the segmentation within a reasonable time, we use heuristics. Most of the heuristic segmentation algorithms require some decision on the number of segments. This is usually accomplished by using asymptotic model selection methods like the Bayesian information criterion. Such methods are based on some simplification, which can limit their usage. In this paper, we propose a Bayesian model selection to choose the most proper result from heuristic segmentation. Our Bayesian model presents a simple prior for the segmentation solutions with various segment numbers and a modified Dirichlet prior for modeling multinomial data. We show with various artificial data sets in our benchmark system that our model selection criterion has the best overall performance. The application of our method in yeast cell-cycle gene expression data reveals potential active and passive regions of the genome.     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach

Our starting point is a selection-mutation equation describing the adaptive dynamics of a quantitative trait under the influence of an ecological feedback loop. Based on the assumption of small (but frequent) mutations we employ asymptotic analysis to derive a Hamilton-Jacobi equation. Well-established and powerful numerical tools for solving the Hamilton-Jacobi equations then allow us to easily compute the evolution of the trait in a monomorphic population when this evolution is continuous but also when the trait exhibits a jump. By adapting the numerical method we can, at the expense of a significantly increased computing time, also capture the branching event in which a monomorphic population turns dimorphic and subsequently follow the evolution of the two traits in the dimorphic population. From the beginning we concentrate on a caricatural yet interesting model for competition for two resources. This provides the perhaps simplest example of branching and has the great advantage that it can be analyzed and understood in detail.     

Hypothesis testing under mixture models: application to genetic linkage analysis

In this paper we propose a new class of statistics to test a simple hypothesis against a family of alternatives characterized by a mixture model. Unlike the likelihood ratio statistic, whose large sample distribution is still unknown in this situation, these new statistics have a simple asymptotic distribution to which to refer under the null hypothesis. Simulation results suggest that it has adequate power in detecting the alternatives. Its application to genetic linkage analysis in the presence of the genetic heterogeneity that motivated this work is emphasized.     

The effect of time delays on Caribbean coral-algal interactions

The analysis of ecological models often focuses on their asymptotic behavior, but there is increasing recognition that it is important to understand the role of transient behavior. By introducing a time delay into a model of coral-algal interactions in Caribbean coral reefs that exhibits alternative stable states (a favorable coral rich state and a degraded coral-depleted state), we demonstrate the criticality of understanding the basins of attraction for stable equilibria in addition to the systems' asymptotic behavior. Specifically, we show that although the introduction of a time delay into the model does not change the asymptotic stability of the stable equilibria, there are significant changes to their basins of attraction. An understanding of these effects is necessary when determining appropriate reef management options. We then demonstrate that this is a general phenomenon by considering similar behavior underlying the changes in the basins of attraction in a simple Lotka-Volterra model of competition.     

Latent group detection in functional partially linear regression models

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities.     

The effects of conditioning on probands to correct for multiple ascertainment.

Cannings and Thompson suggested conditioning on the phenotypes of the probands to correct for ascertainment in the analysis of pedigree data. The method assumes single ascertainment and can be expected to yield asymptotically biased parameter estimates except in this specific case. However, because the method is easy to apply, we investigated the degree of bias in the more typical situation of multiple ascertainment, in the hope that the bias might be small and that the method could be applied more generally. To explore the utility of conditioning on probands to correct for multiple ascertainment, we calculated the asymptotic value of the segregation ratio for two versions of the simple Mendelian segregation model on sibship data. For both versions, we found that this asymptotic value decreased approximately linearly as the ascertainment probability increased. When ascertainment was complete, the segregation-ratio estimates were zero, not just asymptotically but for finite sample size as well. In some cases, conditioning on probands actually resulted in greater parameter bias than no ascertainment correction at all. These results hold for a variety of sibship-size distributions, several modes of inheritance, and a wide range of population prevalences of affected individuals.