广义神经传播方程非协调类Wilson元的超收敛分析及外推

在半离散格式下研究了广义神经传播方程的非协调类Wilson有限元方法．利用该单元相容误差比协调误差高一阶的特殊性质和双线性元的高精度分析技巧,得到了相应的超逼近性质和超收敛结果．进一步地,构造了一个新的外推格式,并借助于该单元相容误差比协调误差高两阶的特殊性质,由此导出了能量模意义下具有O（h3）阶的外推效果．     

一类神经传播方程的特征差分方法与分析

首先对给定的方程进行恒等变换,再把MMOCAA差分方法与UNO插值相结合,提出了方程的MMOCAA-UNO差分方法,避免了基于k次Lagrange插值的MMOCAA差分方法在方程的解的陡峭前沿附近产生振荡．通过引入插值算子等方法给出了格式的误差估计．数值实验说明理论分析的正确性和格式的有效性．     

食物链种群模型的格子Boltzmann方法模拟

用格子Boltzmann方法求解用反应一扩散方程组描述的食物链种群模型．我们用一维和二维方程组进行数值实验,模拟结果与现有的数值实验结果很好地吻合,反映了格子Boltzmann方法的高效性和稳定性,并就二维格子、Boltzmann格式,通过其等价的差分格式,由极值原理证明了该格式的稳定性．     

具有时滞的非自治差分竞争系统的渐近行为研究(英文)

提出了一个具有时滞的非自治差分竞争系统.分别利用差分不等式及Lyapunov离散函数技巧,得到了系统永久持续生存和正解全局吸引的充分条件.数值模拟验证了理论结果的正确性.     

非线性拟双曲方程的交替方向变网格有限元方法

研究在神经传播过程中的一类非线性拟双曲方程的初边值问题,提出了一种三维交替方向变网格有限元格式,应用微分方程先验估计的理论和技巧,得到了最佳阶的L^2模误差估计结果。并作了数值实验。指明方法是高效可行的．     

广义神经传播方程的一个各向异性非协调有限元超收敛分析

在神经传播过程中,神经传递信号及它关于时间和空间的变化率,在数学上表现为一类非线性拟双曲方程.本文在各向异性条件下,讨论了该方程的一个非协调有限元逼近,给出了半离散格式下解关于L∞(||·||h)模的最优误差估计.利用插值算予与Ritz-Vblterra投影的一致性得到了关于神经传递信号的超逼近性质,同时基于插值后处理技术还导出了它的整体超收敛.     

区间离散时滞广义系统的鲁棒稳定性

讨论了一类区间离散时滞广义系统的鲁棒稳定性问题,在给出区间离散时滞广义系统的等价描述之后,基于系统参数矩阵不等式,分别得出了时滞独立和时滞依赖情况下区间离散广义系统稳定的充分条件,数值例子说明了该方法的有效性．     

一类食饵具有S-型变收获率的非自治离散捕食系统渐近行为

建立并研究了一类具有S-型变收获率的非自治离散捕食系统,应用差分不等式、Brouwer不动点定理和分析技巧分别建立了系统的持久生存性,正周期解的存在性及全局渐近稳定性的充分条件,我们还给出了具体验证例子及相应的数值模拟结果.     

离散时间的互惠系统的正周期解的存在性

利用重合度理论中的延拓定理研究了一类具有周期系数的离散时间的差分互惠系统模型．得到了该系统正周期解存在的充分条件．     

一种处理人体骨骼肌肉层各向异性导电性的数值方法

重点讨论了应用电磁场数值计算方法求解心电图正问题和逆问题中人体骨骼肌肉层的各向异性导电性的处理方法．文中应用有限元和边界元结合的方法,构造了一个包含不同的纤维方向组合的骨骼肌肉层的三维胸腔模型,并在此模型下引入了局部坐标内的各向异性导电率向整体坐标转换的方法．据此进行的模拟计算结果以图像的方式清晰地展示了各向异性导电性对体表电位图的影响．     

Kinetics of the Opening and Closing of Individual Excitability-Inducing Material Channels in a Lipid Bilayer

The kinetics of the opening and closing of individual ion-conducting channels in lipid bilayers doped with small amounts of excitability-inducing material (EIM) are determined from discrete fluctuations in ionic current. The kinetics for the approach to steady-state conductance during voltage clamp are determined for lipid bilayers containing many EIM channels. The two sets of measurements are found to be consistent, verifying that the voltage-dependent conductance of the many-channel EIM system arises from the opening and closing of individual EIM channels. The opening and closing of the channels are Poisson processes. Transition rates for these processes vary exponentially with applied potential, implying that the energy difference between the open and closed states of an EIM channel is linearly proportional to the transmembrane electric field. A model incorporating the above properties of the EIM channels predicts the observed voltage dependence of ionic conductance and conductance relaxation time, which are also characteristic of natural electrically excitable membranes.     

ANCESTRAL CHARACTER ESTIMATION UNDER THE THRESHOLD MODEL FROM QUANTITATIVE GENETICS

Evolutionary biology is a study of life's history on Earth. In researching this history, biologists are often interested in attempting to reconstruct phenotypes for the long extinct ancestors of living species. Various methods have been developed to do this on a phylogeny from the data for extant taxa. In the present article, I introduce a new approach for ancestral character estimation for discretely valued traits. This approach is based on the threshold model from evolutionary quantitative genetics. Under the threshold model, the value exhibited by an individual or species for a discrete character is determined by an underlying, unobserved continuous trait called “liability.” In this new method for ancestral state reconstruction, I use Bayesian Markov chain Monte Carlo (MCMC) to sample the liabilities of ancestral and tip species, and the relative positions of two or more thresholds, from their joint posterior probability distribution. Using data simulated under the model, I find that the method has very good performance in ancestral character estimation. Use of the threshold model for ancestral state reconstruction relies on a priori specification of the order of the discrete character states along the liability axis. I test the use of a Bayesian MCMC information theoretic criterion based approach to choose among different hypothesized orderings for the discrete character. Finally, I apply the method to the evolution of feeding mode in centrarchid fishes.     

多基因离散性状QTL连锁分析方法

动物中有许多重要的离散性状,与常规的数量性状类似,其遗传基础受多基因控制并受到环境因子的修饰。由于多基因离散性状的表型特殊性,利用常规的QTL连锁分析方法很难获得理想的统计效果,相应地发展了许多基于广义线性模型框架内的非线性方法。本文就目前离散性状的QTL连锁分析方法作简要综述,并对可预期的改进方法进行了展望。     

Comparing the rates of speciation and extinction between phylogenetic trees

Over the past decade or so it has become increasingly popular to use reconstructed evolutionary trees to investigate questions about the rates of speciation and extinction. Although the methodology of this field has grown substantially in its sophistication in recent years, here I will take a step back to present a very simple model that is designed to investigate the relatively straightforward question of whether the tempo of diversification (speciation and extinction) differs between two or more phylogenetic trees, without attempting to attribute a causal basis to this difference. It is a likelihood method, and I demonstrate that it generally shows type I error that is close to the nominal level. I also demonstrate that parameter estimates obtained with this approach are largely unbiased. As this method can be used to compare trees of unknown relationship, it will be particularly well‐suited to problems in which a difference in diversification rate between clades is suspected, but in which these clades are not particularly closely related. As diversification methods can easily take into account an incomplete sampling fraction, but missing lineages are assumed to be missing at random, this method is also appropriate for cases in which we have hypothesized a difference in the process of diversification between two or more focal clades, but in which many unsampled groups separate the few of interest. The method of this study is by no means an attempt to replace more sophisticated models in which, for instance, diversification depends on the state of an observed or unobserved discrete or continuous trait. Rather, my intention is to provide a complementary approach for circumstances in which a simpler hypothesis is warranted and of biological interest.     

A general method for dealing with misclassification in regression: the misclassification SIMEX

We have developed a new general approach for handling misclassification in discrete covariates or responses in regression models. The simulation and extrapolation (SIMEX) method, which was originally designed for handling additive covariate measurement error, is applied to the case of misclassification. The statistical model for characterizing misclassification is given by the transition matrix Pi from the true to the observed variable. We exploit the relationship between the size of misclassification and bias in estimating the parameters of interest. Assuming that Pi is known or can be estimated from validation data, we simulate data with higher misclassification and extrapolate back to the case of no misclassification. We show that our method is quite general and applicable to models with misclassified response and/or misclassified discrete regressors. In the case of a binary response with misclassification, we compare our method to the approach of Neuhaus, and to the matrix method of Morrissey and Spiegelman in the case of a misclassified binary regressor. We apply our method to a study on caries with a misclassified longitudinal response.     

时标上一捕食二食饵系统的周期解（英文）

研究时标上一捕食二食饵系统.运用时标上Gaines和Mawhin的连续拓扑度定理,得到了系统存在周期解的新的充分条件.其研究方法可以广泛地运用来研究微分或者差分方程的周期解存在性问题.     

Inter-Hemispheric Oscillations in Human Sleep

Sleep is generally categorized into discrete stages based on characteristic electroencephalogram (EEG) patterns. This traditional approach represents sleep architecture in a static way, but it cannot reflect variations in sleep across time and across the cortex. To investigate these dynamic aspects of sleep, we analyzed sleep recordings in 14 healthy volunteers with a novel, frequency-based EEG analysis. This approach enabled comparison of sleep patterns with low inter-individual variability. We then implemented a new probability dependent, automatic classification of sleep states that agreed closely with conventional manual scoring during consolidated sleep. Furthermore, this analysis revealed a previously unrecognized, interhemispheric oscillation during rapid eye movement (REM) sleep. This quantitative approach provides a new way of examining the dynamic aspects of sleep, shedding new light on the physiology of human sleep.     

Convected element method for simulation of angiogenesis

We describe a novel Convected Element Method (CEM) for simulation of formation of functional blood vessels induced by tumor-generated growth factors in a process called angiogenesis. Angiogenesis is typically modeled by a convection-diffusion-reaction equation defined on a continuous domain. A difficulty arises when a continuum approach is used to represent the formation of discrete blood vessel structures. CEM solves this difficulty by using a hybrid continuous/discrete solution method allowing lattice-free tracking of blood vessel tips that trace out paths that subsequently are used to define compact vessel elements. In contrast to more conventional angiogenesis modeling, the new branches form evolving grids that are capable of simulating transport of biological and chemical factors such as nutrition and anti-angiogenic agents. The method is demonstrated on expository vessel growth and tumor response simulations for a selected set of conditions, and include effects of nutrient delivery and inhibition of vessel branching. Initial results show that CEM can predict qualitatively the development of biologically reasonable and fully functional vascular structures. Research is being carried out to generalize the approach which will allow quantitative predictions.     

Hypothesis testing for the genetic background of quantitative traits

The testing of Bayesian point null hypotheses on variance component models have resulted in a tough assignment for which no clear and generally accepted method exists. In this work we present what we believe is a succeeding approach to such a task. It is based on a simple reparameterization of the model in terms of the total variance and the proportion of the additive genetic variance with respect to it, as well as on the explicit inclusion on the prior probability of a discrete component at origin. The reparameterization was used to bypass an arbitrariness related to the impropriety of uninformative priors onto unbounded variables while the discrete component was necessary to overcome the zero probability assigned to sets of null measure by the usual continuous variable models. The method was tested against computer simulations with appealing results.