特征捆绑的计算模型

特征捆绑问题一直是认知科学和神经科学中的一个重要问题．本文通过将噪声神经元模型的思想、贝叶斯方法和脉冲神经网络模型相结合,并引入竞争机制,提出了一个特征捆绑的计算模型．Bayesian Linking Field模型,对视感知中的特征捆绑问题进行研究．实验证明本研究的模型很好地完成了视觉感知中特征捆绑的任务,并给感知研究带来了新的思路．     

生物膜的分子模型是怎样演进的

膜是生物界最通常的特征之一,是细胞重要的组成部分,也是科学家研究的重要领域之一。主要从历史的角度介绍科学家研究膜的过程。根据科学家研究的特点,将膜的研究划分为早期科学家对膜理化特性的探讨和细胞膜分子模型的构建2个阶段,在细胞膜分子模型构建阶段又划分为“三明治”模型、单位膜模型、液态镶嵌模型3个时期。通过介绍对膜的研究过程揭示,人类对生物膜的认识是一个不断积累、不断创新的过程;是一个物理、化学和生物学知识相互渗透的过程。     

湿地养分截留功能的空间模拟Ⅰ.模型的概念和方法

运用河口湿地来削减氮磷入海通量,防止近海水体富营养分,首先对辽河三角洲湿地净化系统进行了理论分析,并建立了相应的概念模型,然后依靠野外实验数据,为湿地的营养物去除功能建立了一个空间模型,该模型包括两大部分：一是灌渠子系统,二是苇田子系统,前者使用的是一个非线性回归模型,后者则以分率为基础的简单模型,该模型在个别灌区试运行后,推到整个苇田研究区。     

短时记忆的神经网络模型

提出一个带有指针环路的短时记忆神经网络模型,模型包含两个神经网络,其中一个是与长时记忆共有的存贮内容表达网络,另一个为短时指针神经元环路,由于指针环路仅作为记忆内容的临时指针,因此,仅用很少的存贮单元即可完成各种短时记忆任务,计算机仿真证明,本模型确能表现出短时记忆的存贮容量有限和组块编码两个基本特征。     

数学生态学随机模型

本文引入了数学生态学随机模型,建立了这类模型的向后和向前方程,最后给出了一个例子。     

一类微生物食物链模型的持续生存

讨论了一类n维微生物食物链模型的持续生存问题,假设模型中微生物的增长率具有Monod内在代谢形式．证明了模型有一个解平面．并且模型所有的解以此解平面为ω极限集,因此所有的解是有界的;并证明了满足一定条件时,n维食物链模型是持久的．     

外源输入对大亚湾大鹏澳浮游生物影响的模拟研究

本文通过建立一个简单的浮游植物、浮游动物和营养盐动力学数值模型,根据大亚湾大鹏澳秋季一个月的连续观测资料,利用线性回归分析法来求得上述动力学数值模型的一些主要参数,结果表明,降雨及陆源输入是导致该海区营养盐增加的一个重要因子;根据上述参数进行的数值模拟结果与实测结果基本吻合,同时也表明,降雨及陆源输入对该海区浮游植物和浮游动物的分布规律影响较大。     

湿地水文生态学模型的理论与方法

定量模拟生态模式与水文机制间的关系是当前生态学、水文学和湿地科学的一个热点研究领域。本文介绍了湿地水文生态学的概念、多学科理论体系以及跨学科特征,概括了湿地水文生态模型构建原理与方法,及国内外研究进展和特点。分析了湿地水文生态模型存在的尺度冲突、模型变量选择与模型不确定性,缺少有效校验方法等主要问题。指出湿地水文生态模型未来发展中与新兴交叉学科和地学信息技术耦合的特征由当前数学模型为主逐步过渡到物理模型的趋势。本文还以内陆平原淡水湿地为例,构建了以生境湿度特征为核心的湿地水文生态概念模型,同时设计了一个在集水区尺度上基于RS和GIS方法的湿地水文生态模型范式,以便于增加对此类模型的理解和认识。     

一阶时间序列模型的诊断

本文研究用条件均值与条件方差的非参数估计识别非线性时间序列模型的方法。并通过模拟考察了上述条件量对于模型识别的效果，指出对于一阶模型，条件均值是一个很好识别指标，本文最后还给出了确定模型阶数为一阶的方法，从而解决了一阶模型的识别问题。     

线画图形质地辨认的一个神经网络模型

本文提出了一个能辨认线画质地的神经网络模型,并在IBM-PC机上对它进行了成功的模拟.该模型可与真实的视觉系统建立起很好的对应关系,因此可以认为它是对视觉系统质地辨认过程的一个机器再现.另外,本文推广了原广义Gabor函数模型,得到了一个适合于描写网络层次视觉功能的单细胞感受野的数学描述.     

卡尔文循环的数学模型

本文运用常微分方程组的数学方法,建立了卡尔文循环的数学模型。     

Periodicity computation of generalized mathematical biology problems involving delay differential equations

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann–Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.     

生物种群动态微分方程模型参数估计方法

本文以数值分析和最优化技术的有机结合为基础,提出了一种新的对动态微分方程模型直接进行数据拟合和参数估计方法,并以Logistic微分方程、生物种间竞争关系微分方程以及一种复合形态的Logistic微分方程为例进行了数据拟合试验．结果表明,该方法对各种动态微分方程模型均能进行最优拟合分析并求解其参数．同时发现,以前有的作者〔1,2,3,4,5〕提出的方法所得到的参数估计值存在系统误差且误差较大．     

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.     

Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory

A functional differential equation which is nonlinear and involves forward and backward deviating arguments is solved numerically. The equation models conduction in a myelinated nerve axon in which the myelin completely insulates the membrane, so that the potential change jumps from node to node. The equation is of first order with boundary values given at t=±. The problem is approximated via a difference scheme which solves the problem on a finite interval by utilizing an asymptotic representation at the endpoints, cubic interpolation and iterative techniques to approximate the delays, and a continuation method to start the procedure. The procedure is tested on a class of problems which are solvable analytically to access the scheme's accuracy and stability, then applied to the problem that models propagation in a myelinated axon. The solution's dependence on various model parameters of physical interest is studied. This is the first numerical study of myelinated nerve conduction in which the advance and delay terms are treated explicitly.Supported in part by NSF Grant MCS8301724 and by a Biomedical Research Support Grant 2SO7RR0706618 from NIH     

Stochastic modeling of drug resistance in cancer

One of the main causes of failure in the treatment of cancer is the development of drug resistance by the cancer cells. Employing multi-drug therapeutic strategies is a promising way to prevent resistance and improve the chances of treatment success. We formulate and analyse a stochastic model for multi-drug resistance and investigate the dependence of treatment outcomes on the initial tumor load, mutation rates and the turnover rate of cancerous cells. We elucidate the general principles of the emergence and evolution of resistant cells inside the tumor, before and after the start of treatment. We discover that for non-mutagenic drugs, pre-existence contributes more to resistance generation than the treatment phase; this result holds for the case where all drugs are applied simultaneously, and is not applicable for sequential therapy models. The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling. J. Math. Biol. 48(4), 375-422]. Also, we find that treatment success is independent on the turnover rate for one drug, and it depends strongly on it for multi-drug therapies. For low-turnover rates, increasing the number of drugs will increase the probability of successful therapy. For very high-turnover rates, increasing the number of drugs used does not significantly increase the chances of treatment success.     

A model for the interaction of two chemicals

We describe a method for studying the interaction of two anesthetic agents, Morphine and Midazolam, acting simultaneously in the same individual. Representing the levels of the two chemicals by diffusion processes, we assume their interaction is governed by a linear combination of the separate components. Pharmacological data is used to estimate the model parameters and, in particular, to determine the coefficient in the linear combination. This leads to the conclusion that the two chemicals have a counteractive effect.     

Mathematical Models for Hantavirus Infection in Rodents

Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.     

一个生物种群非线性泛函微分方程模型整体解的聚集性

自然界的种群,如鱼类、鸟类和有蹄兽类有聚集成群的现象,研究种群的聚集性是生物数学中的一个有趣的课题．本文讨论了一个有关生物种群的非线性泛函微分方程模型整体解的聚集性和稳定性问题．