表征心室复极不一致有效参数的仿真研究

建立了从心内膜到心外膜的一维心肌几何模型,采用心肌双域模型建立心电电位的仿真模型,通过改变缺血程度构造不同的心室复极不一致状态,利用有限差分法求解控制方程,模拟了心电兴奋在心室复极不一致状态下形成的心电电位,并从中提取QT离散度和兴奋恢复间期(activation-recovery interval,ARI)离散度。分析结果显示：缺血区与正常区电位的QT间期没有明显差异,QT离散度接近于零,不能有效地表征心室肌复极不一致;缺血区ARI明显区别于正常区,ARI离散度与缺血程度有很好的对应关系,可以用来表征心室复极不一致。     

一类具有非单调发生率SIS流行病模型的分析

该文讨论了具有非单调发生率SIS流行病模型,分别建立了带有分布时滞和离散时滞形式的感染个体的恢复时滞模型,同时分析了系统平衡态的稳定性．     

具有综合控制策略的离散宿主病原体模型(英文)

研究了具有综合控制策略的离散宿主病原体模型,并考虑了固定时刻脉冲效应和状态依赖脉冲效应对综合控制策略的影响.对于固定时刻脉冲的模型,分析了宿主根除、宿主病原体共存以及宿主爆发周期解的存在性和稳定性,并给出了宿主根除周期解全局稳定的充分条件.对于状态依赖的脉冲离散模型,数值研究说明宿主最大振幅不超过经济临界值的周期解的存在性以及相应动态行为的复杂性.     

具有分布时滞离散Cohen-Grossberg神经网络的周期解

讨论了一类具有分布时滞离散Cohen-Grossberg神经网络模型,利用M-矩阵理论与适合的Lypunov函数,得到该类模型周期解的存在性与全局指数稳定性．     

基于细胞自动机的实体肿瘤生长动态建模

基于细胞自动机方法,建立了一种简单的实体肿瘤免疫性系统模型,用来模拟实体肿瘤生长过程中的情况．我们基于二维随机、离散细胞自动机计算方法,在生物细胞水平上,建立了一种肿瘤免疫性系统生长模型．该模型考虑了免疫反应的宏观性质,描绘了癌细胞和机体免疫系统之间的细胞相互作用,表现了围绕在肿瘤机体周围,免疫系统细胞的免疫作用发展情况．我们研究了常规细胞自动机模型,设计出实体肿瘤模型随机演化生长规则．最终,构建离散细胞自动机肿瘤免疫性系统模型,并做了相应的数值仿真试验．通过对仿真模型不同参数的调整,最终的仿真结果表明,该模型能反映肿瘤免疫性系统基本的相关性质．     

基于c-均值聚类的粗糙集神经网络在心脏病诊断中的应用

采用c-均值聚类法将决策表中的连续条件属性进行离散化,用粗糙集处理离散化后的决策表系统得到简化规则,然后将规则集输入BP神经网络进行训练,并对测试集进行预测.以此模型对一组有关心脏病诊断的数据进行处理,得到的预测判准率达85%,而单独使用粗糙集或BPNN进行预测,则判准率分别为76%和82%;若在粗糙集和BPNN联用模型中,对原始数据采用传统的等距离离散化和等频率离散化等离散化方法,预测判准率则分别只有53%和77%.     

一类神经传播方程的特征差分方法和最佳阶l^2误差估计

给出矩形域上一类神经传播方程的特征差分,利用沿特征线方向构造差分逼近格式的方法和技巧．对给定的模型进行离散数值逼近和数值分析．特别是在沿特征线方向构造离散差分格式的过程中,可能会出现离散点在定义域之外的问题．本文提供了一个新的有效的差分逼近的处理方法,得到了该方法的三。一模误差估计．     

桔全爪螨产卵动态模型的研究

以桔全爪螨(Panonychus citri(McG.)),雌成螨,在15℃,20℃,25℃,30℃,35℃ 5个温度条件下的逐日产卵量为基础,建立桔全爪螨产卵动态横拟模型。首先建立以温度为自变量的离散概率模型.并对此模型作了分析,考虑到离散概率模型不具备动态性,我们在第二部分采用了灰色系统动态建模法,建立了温度为25℃的条件下桔全爪螨产卵的动态模型,以此动态模型为基础,我们在第三部分进一步建立以有效积温和平均温度为自变量的桔全爪螨的产卵动态模拟模型.     

离散型二维竞争系统的渐近稳定性

研究了离散型二维竞争系统的渐近稳定性,得到了这类生物模型关于正平衡点渐近稳定的一系列充分条件。     

基于反馈控制离散Lotka-Volterra竞争模型的持续生存和稳定性

针对一类具有偏离自变量的离散Lotka-Volterra竞争模型,考虑到不可避免的外界扰动,通过引入反馈控制,基于一定的分析技巧得到该系统持久性与全局稳定性的充分条件.生态意义上表明:在外界扰动下,具有偏离自变量的离散Lotka-Volterra竞争模型仍能持续生存并保持全局稳定发展.     

Discrete event, multi-level simulation of metabolite channeling

Typically differential equations are employed to simulate cellular dynamics. To develop a valid continuous model based on differential equations requires accurate parameter estimations; an accuracy which is often difficult to achieve, due to the lack of data. In addition, processes in metabolic pathways, e.g. metabolite channeling, seem to be of a rather qualitative and discrete nature. With respect to the available data and to the perception of the underlying system, a discrete rather than a continuous approach to modeling and simulation seems more adequate. A discrete approach does not necessarily imply a more abstract view on the system. If we move from macro to micro and multi-level modeling, aspects of subsystems and their interactions, which have been only implicitly represented, become an explicit part of the model. To start exploring discrete event phenomena within metabolite channeling we choose the tryptophan synthase. Based on a continuous macro model, a discrete event, multi-level model is developed which allows us to analyze the interrelation between structural and functional characteristics of the enzymes.     

A general population-genetic model for the production by population structure of spurious genotype-phenotype associations in discrete, admixed or spatially distributed populations

In linkage disequilibrium mapping of genetic variants causally associated with phenotypes, spurious associations can potentially be generated by any of a variety of types of population structure. However, mathematical theory of the production of spurious associations has largely been restricted to population structure models that involve the sampling of individuals from a collection of discrete subpopulations. Here, we introduce a general model of spurious association in structured populations, appropriate whether the population structure involves discrete groups, admixture among such groups, or continuous variation across space. Under the assumptions of the model, we find that a single common principle--applicable to both the discrete and admixed settings as well as to spatial populations--gives a necessary and sufficient condition for the occurrence of spurious associations. Using a mathematical connection between the discrete and admixed cases, we show that in admixed populations, spurious associations are less severe than in corresponding mixtures of discrete subpopulations, especially when the variance of admixture across individuals is small. This observation, together with the results of simulations that examine the relative influences of various model parameters, has important implications for the design and analysis of genetic association studies in structured populations.     

Preservation of dynamic properties in qualitative modeling frameworks for gene regulatory networks

Mathematical modeling often helps to provide a systems perspective on gene regulatory networks. In particular, qualitative approaches are useful when detailed kinetic information is lacking. Multiple methods have been developed that implement qualitative information in different ways, e.g., in purely discrete or hybrid discrete/continuous models. In this paper, we compare the discrete asynchronous logical modeling formalism for gene regulatory networks due to R. Thomas with piecewise affine differential equation models. We provide a local characterization of the qualitative dynamics of a piecewise affine differential equation model using the discrete dynamics of a corresponding Thomas model. Based on this result, we investigate the consistency of higher-level dynamical properties such as attractor characteristics and reachability. We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different. In particular, the dynamics of the piecewise affine differential equation model is not a simple refinement of the dynamics of the Thomas model     

Bayesian Analysis Using a Simple Likelihood Model Outperforms Parsimony for Estimation of Phylogeny from Discrete Morphological Data

Despite the introduction of likelihood-based methods for estimating phylogenetic trees from phenotypic data, parsimony remains the most widely-used optimality criterion for building trees from discrete morphological data. However, it has been known for decades that there are regions of solution space in which parsimony is a poor estimator of tree topology. Numerous software implementations of likelihood-based models for the estimation of phylogeny from discrete morphological data exist, especially for the Mk model of discrete character evolution. Here we explore the efficacy of Bayesian estimation of phylogeny, using the Mk model, under conditions that are commonly encountered in paleontological studies. Using simulated data, we describe the relative performances of parsimony and the Mk model under a range of realistic conditions that include common scenarios of missing data and rate heterogeneity.     

Plant Dynamics,Birth-Jump Processes,and Sharp Traveling Waves

Motivated by the importance of understanding the dynamics of the growth and dispersal of plants in various environments, we introduce and analyze a discrete agent-based model based on a birth-jump process, which exhibit wave-like solutions. To rigorously analyze these traveling wave phenomena, we derive the diffusion limit of the discrete model and prove the existence of traveling wave solutions (sharp and continuously differentiable) assuming a logarithmic-type growth. Furthermore, we provide a variational speed for the minimum speed of the waves and perform numerical experiments that confirm our results.     

Revisiting “The Evolution of Reciprocity in Sizable Groups”: Continuous reciprocity in the repeated n-person prisoner's dilemma

For many years in evolutionary science, the consensus view has been that while reciprocal altruism can evolve in dyadic interactions, it is unlikely to evolve in sizable groups. This view had been based on studies which have assumed cooperation to be discrete rather than continuous (i.e., individuals can either fully cooperate or else fully defect, but they cannot continuously vary their level of cooperation). In real world cooperation, however, cooperation is often continuous. In this paper, we re-examine the evolution of reciprocity in sizable groups by presenting a model of the n-person prisoner's dilemma that assumes continuous rather than discrete cooperation. This model shows that continuous reciprocity has a dramatically wider basin of attraction than discrete reciprocity, and that this basin's size increases with efficiency of cooperation (marginal per capita return). Further, we find that assortative interaction interacts synergistically with continuous reciprocity to a much greater extent than it does with discrete reciprocity. These results suggest that previous models may have underestimated reciprocity's adaptiveness in groups. However, we also find that the invasion of continuous reciprocators into a population of unconditional defectors becomes realistic only within a narrow parameter space in which the efficiency of cooperation is close to its maximum bound. Therefore our model suggests that continuous reciprocity can evolve in large groups more easily than discrete reciprocity only under unusual circumstances.     

A comparative method for both discrete and continuous characters using the threshold model

The threshold model developed by Sewall Wright in 1934 can be used to model the evolution of two-state discrete characters along a phylogeny. The model assumes that there is a quantitative character, called liability, that is unobserved and that determines the discrete character according to whether the liability exceeds a threshold value. A Markov chain Monte Carlo algorithm is used to infer the evolutionary covariances of the liabilities for discrete characters, sampling liability values consistent with the phylogeny and with the observed data. The same approach can also be used for continuous characters by assuming that the tip species have values that have been observed. In this way, one can make a comparative-methods analysis that combines both discrete and continuous characters. Simulations are presented showing that the covariances of the liabilities are successfully estimated, although precision can be achieved only by using a large number of species, and we must always worry whether the covariances and the model apply throughout the group. An advantage of the threshold model is that the model can be straightforwardly extended to accommodate within-species phenotypic variation and allows an interface with quantitative-genetics models.     

Continuum or discrete patch landscape models for savanna birds? Towards a pluralistic approach

Conceptualising landscapes as a mosaic of discrete habitat patches is fundamental to landscape ecology, metapopulation theory and conservation biology. An emerging question in ecology is: when is the discrete patch model more appropriate than alternative and conceptually appealing models such as the continuum model? There is limited empirical testing of the utility of alternative landscape models compared to the discrete patch model for a range of species. In this paper, we constructed three alternative sets of models for testing the effect of landscape structure on diversity and abundance of a suite of woodland birds in a savanna landscape of northern Australia: the null model (only site‐scale habitat variables, landscape context not important), the continuum model, and the discrete patch model. We utilised high‐spatial resolution satellite images to quantify spatial gradients in tree cover density (the continuum model), and to then aggregate the fine‐scale heterogeneity in tree cover into discrete patches of trees, with grass cover forming the “matrix” (the discrete patch‐model). We then evaluated the relative importance of the alternative models using generalised linear models and an information theoretic approach. We found that the importance of the models varied among species, with no single model dominant. Species that move between open grassy areas and woody shelter responded well to the continuum model, reflecting the importance of gradients in density of forage (grasses) and cover (trees), while the discrete model performed best for species that forage in all vegetation strata, and nest predominantly in dense woody vegetation. This finding supports a pluralistic approach, highlighting the need for adopting and testing more than one landscape model in savanna landscapes, and in other landscapes that do not have a well defined patch structure.     

A dynamic theory of coordination of discrete movement

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.