On the effects of spatial heterogeneity on the persistence of interacting species

 The dynamics of two interacting theoretical populations inhabiting a heterogeneous environment are modelled by a system of two weakly coupled reaction–diffusion equations having spatially dependent reaction terms. Longterm persistence of both populations is guaranteed by an invasibility condition, which is itself expressed via the signs of certain eigenvalues of related linear elliptic operators with spatially dependent lowest order coefficients. The effects of change in these coefficients upon the eigenvalues are here exploited to study the effects of spatial heterogeneity on the persistence of interacting species through two particular ecological topics of interest. The first concerns when the location of favorable hunting grounds within the overall environment does or does not affect the success of a predator in predator–prey models, while the second concerns cases of competition models in which the outcome of competition in a spatially varying environment differs from that which would be expected in a spatially homogeneous environment. Received: 9 June 1997     

Solving the brain synchrony eigenvalue problem: conservation of temporal dynamics (fMRI) over subjects doing the same task

Brain measures often show highly structured temporal dynamics that synchronize when observers are doing the same task. The standard method for analysis of brain imaging signals (e.g. fMRI) uses the GLM for each voxel indexed against a specified experimental design but does not explicitly involve temporal dynamics. Consequently, the design variables that determine the functional brain areas are those correlated with the design variation rather than the common or conserved brain areas across subjects with the same temporal dynamics given the same stimulus conditions. This raises an important theoretical question: Are temporal dynamics conserved across individuals experiencing the same stimulus task? This general question can be framed in a dynamical systems context and further be posed as an eigenvalue problem about the conservation of synchrony across all brains simultaneously. We show that solving the problem results in a non-arbitrary measure of temporal dynamics across brains that scales over any number of subjects, stabilizes with increasing sample size, and varies systematically across tasks and stimulus conditions.     

Effective gene prediction by high resolution frequency estimator based on least-norm solution technique

Linear algebraic concept of subspace plays a significant role in the recent techniques of spectrum estimation. In this article, the authors have utilized the noise subspace concept for finding hidden periodicities in DNA sequence. With the vast growth of genomic sequences, the demand to identify accurately the protein-coding regions in DNA is increasingly rising. Several techniques of DNA feature extraction which involves various cross fields have come up in the recent past, among which application of digital signal processing tools is of prime importance. It is known that coding segments have a 3-base periodicity, while non-coding regions do not have this unique feature. One of the most important spectrum analysis techniques based on the concept of subspace is the least-norm method. The least-norm estimator developed in this paper shows sharp period-3 peaks in coding regions completely eliminating background noise. Comparison of proposed method with existing sliding discrete Fourier transform (SDFT) method popularly known as modified periodogram method has been drawn on several genes from various organisms and the results show that the proposed method has better as well as an effective approach towards gene prediction. Resolution, quality factor, sensitivity, specificity, miss rate, and wrong rate are used to establish superiority of least-norm gene prediction method over existing method.     

一类扩散循环系统正解的存在性与稳定性

利用上下解方法及全藕合线性互惠系统的最大值原理,研究了一类非线性椭圆系统,给出了其正解存在的充分必要条件,同时也得到了其正解局部稳定的某些结果．     

Movement toward better environments and the evolution of rapid diffusion

We study a reaction-diffusion-advection model for two ecologically equivalent competitors with different dispersal strategies inhabiting a spatially heterogeneous environment. The competitors represent different phenotypes of the same species. One is assumed to disperse by simple diffusion, the other by diffusion together with directed movement toward more favorable environments. We show that under suitable conditions on the underlying spatial domain, the competitor that moves toward more favorable environments may have a competitive advantage even if it diffuses more rapidly than the other competitor. This is in contrast with the case in which both competitors disperse by pure diffusion, where the competitor that diffuses more slowly always has the advantage. We determine competitive advantage by examining the invasibility, i.e. stability or instability, of steady states with only one competitor present. The mathematical approach is a perturbation analysis of principal eigenvalues.     

复合茶园节肢动物类群特征值关系研究

为深入了解影响茶园节肢动物群落多样性的因子,本文对在茶园地面种植长节耳草Hedyotis uncinella Hook & Arn(茜草科,耳草属)的复合茶园茶树生境节肢动物类群多样性指数、物种丰富度、类群均匀度、物种优势度指数和类群优势集中性指数5个主要特征值之间的关系进行了因子分析与通径分析。结果显示:茶树生境节肢动物类群5个主要特征值可综合为三个主份量。第一主份量代表类群多样性指数和均匀性;第二主份量集中体现物种丰富度;第三主份量代表优势度指数,它们对方差的贡献率分别为50.279%、26.920%和22.466%。复合茶园节肢动物类群多样性与节肢动物类群丰富度和天敌类群丰富度呈极显著的正相关,而同类群优势集中性呈极显著的负相关。因此,要提高茶园节肢动物类群的多样性可通过营造复合茶园生境来增加节肢动物类群物种丰富度和天敌类群物种丰富度而减少物种优势集中性来实现。