Species extinction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects

Recently, the population dynamic systems with impulsive controls have been researched by many authors. However, most of them are reluctant to study the seasonal effects on prey. Thus, in this paper, an impulsively controlled two-prey one-predator system with the Beddington–DeAngelis type functional response and seasonal effects is investigated. By using the Floquet theory, the sufficient conditions for the existence of a globally asymptotically stable two-prey-free periodic solution are established. Further, it is proven that this system is permanent under some conditions via a comparison method involving multiple Lyapunov functions and meanwhile the conditions for extinction of one of the two prey and permanence of the remaining two species are given.     

Colon cancer prediction with genetic profiles using intelligent techniques

Micro array data provides information of expression levels of thousands of genes in a cell in a single experiment. Numerous efforts have been made to use gene expression profiles to improve precision of tumor classification. In our present study we have used the benchmark colon cancer data set for analysis. Feature selection is done using t‐statistic. Comparative study of class prediction accuracy of 3 different classifiers viz., support vector machine (SVM), neural nets and logistic regression was performed using the top 10 genes ranked by the t‐statistic. SVM turned out to be the best classifier for this dataset based on area under the receiver operating characteristic curve (AUC) and total accuracy. Logistic Regression ranks as the next best classifier followed by Multi Layer Perceptron (MLP). The top 10 genes selected by us for classification are all well documented for their variable expression in colon cancer. We conclude that SVM together with t-statistic based feature selection is an efficient and viable alternative to popular techniques.     

A periodicity result for a nonlinear functional integral equation

In this paper, we study the effect of introducing a delay in a model of cell proliferation considered originally by O. Arino and M. Kimmel (J. Math. Biol. 27, 341–354 (1989)). We prove that slow oscillations take place and periodic oscillations appear for appropriate values of a parameter.     

Microscopic Factors that Control β-Sheet Registry in Amyloid Fibrils Formed by Fragment 11-25 of Amyloid β Peptide: Insights from Computer Simulations

Short fragments of amyloidogenic proteins are widely used as model systems in studies of amyloid formation. Fragment 11-25 of the amyloid β protein involved in Alzheimer's disease (Aβ11-25) was recently shown to form amyloid fibrils composed of anti-parallel β-sheets. Interestingly, fibrils grown under neutral and acidic conditions were seen to possess different registries of their inter-β-strand hydrogen bonds. In an effort to explain the microscopic origin of this pH dependence, we studied Aβ11-25 fibrils using methods of theoretical modeling. Several structural models were built for fibrils at low and neutral pH levels and these were examined in short molecular dynamics simulations in explicit water. The models that displayed the lowest free energy, as estimated using an implicit solvent model, were selected as representative of the true fibrillar structure. It was shown that the registry of these models agrees well with the experimental results. At neutral pH, the main contribution to the free energy difference between the two registries comes from the electrostatic interactions. The charge group of the carboxy terminus makes a large contribution to these interactions and thus appears to have a critical role in determining the registry.     

Proportional Hazards Regression for the Analysis of Clustered Survival Data from Case–Cohort Studies

Summary Case–cohort sampling is a commonly used and efficient method for studying large cohorts. Most existing methods of analysis for case–cohort data have concerned the analysis of univariate failure time data. However, clustered failure time data are commonly encountered in public health studies. For example, patients treated at the same center are unlikely to be independent. In this article, we consider methods based on estimating equations for case–cohort designs for clustered failure time data. We assume a marginal hazards model, with a common baseline hazard and common regression coefficient across clusters. The proposed estimators of the regression parameter and cumulative baseline hazard are shown to be consistent and asymptotically normal, and consistent estimators of the asymptotic covariance matrices are derived. The regression parameter estimator is easily computed using any standard Cox regression software that allows for offset terms. The proposed estimators are investigated in simulation studies, and demonstrated empirically to have increased efficiency relative to some existing methods. The proposed methods are applied to a study of mortality among Canadian dialysis patients.     

Stabilization of telomeres in nonlinear models of proliferating cell lines

We analyse an age-structured model of telomere loss in a proliferating cell population. The cell population is divided into telomere classes, which shorten each round of division. The model consists of a nonlinear system of partial differential equations for the telomere classes. We prove that if the highest telomere class is exempted from mortality, then all the classes stabilize to a nontrivial equilibrium dependent on the initial state of cells in the highest telomere class.     

Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant

The relationship between spatial density and size of plants is an important topic in plant ecology. The self‐thinning rule suggests a ?3/2 power between average biomass and density or a ?1/2 power between stand yield and density. However, the self‐thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log‐linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self‐thinning rule to improve light interception.     

应用结构方程模型解析影响黄连木果实产量 和种子命运的因素

果实(种子)产量和质量是影响植物种群更新的重要因素。为了探明影响黄连木果实产量和种子命运的因素以及这些影响因素之间的相互作用, 作者于2009年对河南省济源市45株黄连木(Pistacia chinensis)结果样树的植株特征、果实特征、果实产量和种子命运等进行了测定, 并用结构方程模型进行综合分析。结果表明: (1)黄连木果实产量与树高、树冠面积和果序大小等特征成正相关, 但与胸径、果实大小相关性不显著; (2)与捕食者饱和假说的预测不一致, 单株果实产量对黄连木广肩小蜂(Eurytoma plotnikovi)的种子捕食率(即虫蛀率)无显著直接负向效应; (3)树高和果实大小对虫蛀率为显著直接正向效应, 胸径对虫蛀率为显著直接负向效应, 显示黄连木广肩小蜂对植株特征和果实特征有一定的选择能力; (4)空壳率与虫蛀率成显著负相关, 空壳果实越多, 越易逃避黄连木广肩小蜂的寄生, 空壳果实的存在对完好种子起到了一定保护作用, 可能是黄连木防御昆虫寄生的重要机制; (5)空壳率和虫蛀率对种子完好率有显著直接负向效应, 而胸径、果序大小和果实产量对完好率为间接正向效应, 树高和果实大小为间接负向效应。可见, 黄连木植株特征和果实特征均不同程度地影响其果实产量和昆虫寄生, 从而影响黄连木的种子质量和种群更新。     

Validation of the Boussinesq equation for use in traction field determination

Cell traction force plays an important role in many biological processes. Several traction force microscopy methods have been developed to determine cell traction forces based on the Boussinesq solution. This approach, however, is rooted in a half-space assumption. The purpose of this study was to determine the error induced in the half-space assumption using a finite element method (FEM). It demonstrates that displacement error between the FEM and the Boussinesq equation can be used to measure the accuracy of the Boussinesq equation, although singularity exists in the loading point. For one concentrated force, significant difference between the FEM and the Boussinesq equation occurs in the whole field; this difference decreases with an increase in the plate thickness. However, in the case of the balanced forces, the offset of the balanced forces decreases the errors in the middle area. Overall, this study demonstrates that increasing the thickness of the polyacrylamide gel is important for reducing the error of the Boussinesq equation when determining the displacement field of the gel under loads.