On the stability of a model of testosterone dynamics

We prove the global asymptotic stability of a well-known delayed negative-feedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length.Supported in part by AFOSR Grant F49620-01-1-0063, NIH Grant P20 GM64375, and Dimacs.E.D. Sontag: Supported in part by AFOSR Grant F49620-01-1-0063 and NIH Grant R01 GM46383.Acknowledgement We would like to thank Augusto Ponce for useful suggestions.     

Sensitivity analysis for nonrandom dropout: a local influence approach

Diggle and Kenward (1994, Applied Statistics 43, 49-93) proposed a selection model for continuous longitudinal data subject to nonrandom dropout. It has provoked a large debate about the role for such models. The original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests. Since then, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B 48, 133-169). The influence of perturbing a missing-at-random dropout model in the direction of nonrandom dropout is explored. The method is applied to data from a randomized experiment on the inhibition of testosterone production in rats.     

具有时滞的Schoener模型的全局稳定性

研究了具有时滞的Schoener竞争模型,通过构造一个合理的lyapunov函数,在一定条件下得到了该系统正解的全局稳定性．     

浑太森林流域径流过程模拟

基于浑河与太子河上游1998-2007年北口前站和南甸峪站水文数据以及清原、新宾和本溪县气象站点同期气象数据,应用DHSVM分布式水文模型模拟浑太流域的水文过程,验证模型的科学适用性,并提供最敏感模型参数的参考值.结果表明：浑河源区月径流模拟的Nash-Suttclife系数(E值)在率定期(1998-2002年)和验证期(2003-2007年)分别达到0.9675和0.8957,较好重现了研究区的月径流过程.太子河上游流域的年、月径流模拟值的E值均大于0.6,说明模型在浑太流域有较好的适用性、率定的参数方案有良好的可靠性.本文为无站点观测资料的流域水文研究建立了一个坚实的框架,并构建了合理的参数方案.     

自然植被净第一性生产力模型初探

本文根据植物的生理生态学特点及联系能量平衡方程和水量平衡方程的区域蒸散模式建立了联系植物生理生态学特点和水热平衡关系的植物的净第一性生产力模型：该模型的建立为宏观地确定地带性景观的生产潜力、植物净第一性生产力的区域分布和全球分布,以及全球变化的影响提供了理论基础,对于合理地利用气候资源,扬长避短,充分发挥气候生产潜力,最大限度地提高植物的产量具有重要的意义。     

温带阔叶红松林生态系统潜热通量模拟——气孔导度组合模型在Shuttleworth-Wallace双源模型中的应用

叶片水平的气孔导度组合模型已被成功扩展到冠层水平,并被应用于冬小麦生态系统潜热通量的模拟研究,但该研究仅基于1a的数据,有必要研究模型在更长时间尺度和其它生态系统类型的适用性.以长白山阔叶红松林(CBS)为研究对象,将组合模型进一步应用于Shuttleworth-Wallace双源模型,模拟了CBS 3a生长季内的潜热通量,利用涡度相关系统观测的潜热通量数据对模型进行验证,并对比了双源模型与单源模型的模拟结果.结果显示,双源模型较单源模型能取得更高的模拟精度,生长季不同时期的潜热通量模拟值和实测值的日变化较一致.对双源模型模拟值和实测潜热通量的相关分析显示,二者直线回归斜率和R2分别为0.96和0.72.对长白山阔叶红松林生态系统的蒸散和植被蒸腾的季节和年际变异分析发现,影响冠层蒸散和植被蒸腾季节动态的主要因素是饱和差和辐射,而影响它们年际动态的主要因素则是饱和差和温度.     

农业生产力模型初探

根据植物的生理生态学特点及诸气候要素建立了农业净第一性生产力模型:NPP=exp(rR_n(r~2 R_n~2 rR_n/(R_n r)(R_n~2 r~2)·(0.0015RDI 0.0013)) 用该模型对全球变化条件下的农业净第一性生产力的敏感性试验表明:我国农业净第一性生产力在气温升高2℃且降水不变或增加20％的情况下都有不同程度的提高,幅度为0.44％～12.88％,其中,在降水不变的情况下,湿润地区增加幅度最大,为5.46％～12.88％,在降水增加的情况下,干旱、半干旱地区增加幅度最大,为3.89％～10.92％;在温度升高2℃、降水减少20％的情况下,湿润地区农业生产力增加1.48％～14.63%,干旱、半干旱地区农业生产力降低0.44%～2.92％,干旱地区降低幅度较大,为1.04％～6.01％,表明水分为农业生产力的主要限制因子。     

4个常用的气候-植被分类模型对中国植被分布模拟的比较研究

 应用KAPPA一致性检验方法,比较研究了4个常用的气候植被分类模型：Penman模型、Holdridge生命地带系统、Kira模型和Thornthwaite模型对中国植被分布模拟的一致性和适用性。结果表明：这4个常用的气候 植被分类模型对中国植被区划一级分类的植被地理分布模拟效果较好。其中,Holdridge生命地带系统的KAPPA值达到0.57,模拟效果优于其它三者。但对特定地区,如青藏高原的植被地理分布,所有模型均需改进或引入新的影响因子才能较好地模拟二级植被区划的植被地理分布。1)Penman模型对温带草原和青藏高原的植被地理分布模拟的KAPPA值超过0.50,是4个模型中对青藏高原植被地理分布模拟效果最好的。2)Thornthwaite模型对热带雨林、季雨林植被地理分布模拟的KAPPA值达到0.40,可以弥补Holdridge生命地带系统对热带植被地理分布模拟精度的不足。3) Holdridge生命地带系统对中国植被地理分布模拟的效果最佳,但对西部季雨林、雨林区域(52)、西部草原亚区域(63)、青藏高原温性荒漠地带(86)和温性草原地带(84)的模拟程度不理想。4)Kira模型对亚热带常绿阔叶林植被地理分布的模拟效果可与Holdridge生命地带系统相媲美;对低海拔和湿润、湿润地区植被地理分布的模拟效果尚可,但在温带荒漠区与青藏高原区植被地理分布的模拟效果与实际相差较远。     

Watkinson时滞差分方程模型的全局渐近稳定性

考虑差分方程ｘｎ＋１＝λｘｎ／（１＋ａｘｎ－ｋ）＾ｐ＋ｂλｘｎ－ｍ,ｎ＝０,１,２,…,其中ａ,ｂ,ｐ＞０,λ＞１,ｋ,ｍ∈｛０,１,２,…｝,当ｋ＝ｍ＝０时,Ｗａｔｋｉｎｓｏｎ用此方程来描述热带地区季蜀黍属作物的生长规律,当Ｐ＝１时,此方程就是著名的含多个滞量的Ｌｏｇｉｓｔｉｃ微分方程的离散模拟,本文主要目的是研究该方程唯一正平衡解的全局渐近稳定性。     

Global stability and optimisation of a general impulsive biological control model

An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations, i.e. a meta-model, augmented by a discrete part describing periodic introductions of predators is considered. The existence of an invariant periodic solution that corresponds to prey eradication is shown and a condition ensuring its global asymptotic stability is given. An optimisation problem related to the preemptive use of augmentative biological control is then considered. It is assumed that the per time unit budget of biological control (i.e. the number of predators to be released) is fixed and the best deployment of this budget is sought in terms of release frequency. The cost function to be minimised is the time needed to reduce an unforeseen prey (pest) invasion occurring at a worst time instant under some harmless level. The analysis shows that the optimisation problem admits a countable infinite number of solutions. An argumentation considering the required robustness of the optimisation result with respect to the invasive prey population level and to the model parameters is then conducted. It is shown that the cost function is decreasing in the predator release frequency so that the best deployment of the biocontrol agents is to carry out as frequent introductions as possible.     

关于一类时滞人口模型的全局吸引性

给出了保证时滞人口模型N'(t)=r(t)N(t) t≤0的每一正解N(t)趋于正平衡点 N*=1(t→∞)的一族充分条件．改进了Joseph和Yu的相关结果．     

Regulation of type 1 inositol 1,4,5-trisphosphate-gated calcium channels by InsP3 and calcium: Simulation of single channel kinetics based on ligand binding and electrophysiological analysis.

Cytosolic calcium acts as both a coagonist and an inhibitor of the type 1 inositol 1,4,5-trisphosphate (InsP3)-gated Ca channel, resulting in a bell-shaped Ca dependence of channel activity (Bezprozvanny, I., J. Watras, and B.E. Ehrlich. 1991. Nature. 351:751-754; Finch, E.A., T.J. Turner, and S.M. Goldin. 1991. Science. 252: 443-446; Iino, M. 1990. J. Gen. Physiol. 95:1103-1122). The ability of Ca to inhibit channel activity, however, varies dramatically depending on InsP3 concentration (Combettes, L., Z. Hannaert-Merah, J.F. Coquil, C. Rousseau, M. Claret, S. Swillens, and P. Champeil. 1994. J. Biol. Chem. 269:17561-17571; Kaftan, E.J., B.E. Ehrlich, and J. Watras. 1997. J. Gen. Physiol. 110:529-538). In the present report, we have extended the characterization of the effect of cytosolic Ca on both InsP3 binding and InsP3-gated channel kinetics, and incorporated these data into a mathematical model capable of simulating channel kinetics. We found that cytosolic Ca increased the Kd of InsP3 binding approximately 3.5-fold, but did not influence the maximal number of binding sites. The ability of Ca to decrease InsP3 binding is consistent with the rightward shift in the bell-shaped Ca dependence of InsP3-gated Ca channel activity. High InsP3 concentrations are able to overcome the Ca-dependent inhibition of channel activity, apparently due to a low affinity InsP3 binding site (Kaftan, E.J., B.E. Ehrlich, and J. Watras. 1997. J. Gen. Physiol. 110:529-538). Constants from binding analyses and channel activity determinations were used to develop a mathematical model that fits the complex Ca-dependent regulation of the type 1 InsP3-gated Ca channel. This model accurately simulated both steady state data (channel open probability and InsP3 binding) and kinetic data (channel activity and open time distributions), and yielded testable predictions with regard to the regulation of this intracellular Ca channel. Information gained from these analyses, and our current molecular model of this Ca channel, will be important for understanding the basis and regulation of intracellular Ca waves and oscillations in intact cells.     

一类具有垂直传染和预防接种的传染病模型的稳定性

考虑了垂直传染和预防接种因素对传染病流行影响的SEIRS模型,主要研究了系统的平衡点及其稳定性,得出当预防接种水平超过某一个阈值时疾病可以根除,若接种水平低于阈值时疾病将流行.     

The importance of assessing parameter sensitivity when using biophysical models: a case study using plethodontid salamanders

Landscapes are continually changing due to numerous assaults, including habitat alteration, anthropogenic disturbances, and climate change. Understanding how species will respond to these changes is of critical importance for conservation and management. Mechanistic models, such as biophysical models (BPMs), are an increasingly popular tool to predict how local population dynamics or species’ distributions may be altered in response to environmental and climate changes. By mechanistically modeling relationships between environmental conditions, physiology and behavior, it is possible to make accurate predictions about how species may respond. However, BPMs are often difficult to implement due to lack of appropriate, species-specific data that is biologically realistic or relevant. In this study, we present a BPM for the salamander Plethodon jordani and assess how adding more biological realism has potential to alter model predictions about annual energy budgets. Additionally, we conducted local and global sensitivity analyses to evaluate the importance of accurately specifying model parameter values and functional relationships. We found that the addition of biological realism resulted in greater model complexity as well as substantially different estimates of energy balance. Correct parameterization of biophysical models is also critical, as small changes in parameter values can result in disproportionately large changes in downstream model estimates. Our model highlights the overall importance of using ecologically relevant and specific data for input parameters, as well as careful assessment of parameter sensitivity. We encourage researchers to be aware of the data they are using to parameterize BPMs, and urge the collection of system-specific data that is relevant in spatial and temporal scale. We also recommend greater and more transparent use of sensitivity analyses to provide a better understanding of the model, as well as greater confidence in model predictions.     

Global stability of an SIR epidemic model with information dependent vaccination

We study the global behavior of a non-linear susceptible-infectious-removed (SIR)-like epidemic model with a non-bilinear feedback mechanism, which describes the influence of information, and of information-related delays, on a vaccination campaign. We upgrade the stability analysis performed in d’Onofrio et al. [A. d’Onofrio, P. Manfredi, E. Salinelli, Vaccinating behavior, information, and the dynamics of SIR vaccine preventable diseases, Theor. Popul. Biol. 71 (2007) 301] and, at same time, give a special example of application of the geometric method for global stability, due to Li and Muldowney. Numerical investigations are provided to show how the stability properties depend on the interplay between some relevant parameters of the model.     

具有周期系数和连续时滞的扩散模型的周期解

本文讨论了具有周期系数和连续时滞的竞争扩散模型,得到了保证其存在唯一周期解及全局渐近稳定的充分条件．     

Global Potential Energy Minima of SPC/E Water Clusters without and with Induced Polarization Using a Genetic Algorithm

The global minimum potential energy structures of water clusters, (H₂O) _n , n = 2-14, have been calculated for the SPC/E (Simple Point Charge/Extended) model and a recent fluctuating charge version of the latter using a simple genetic algorithm. The SPC/E cluster geometries are in good agreement with previous TIP3P (Transferable Intermolecular Potential-3 Point) and TIP4P (Transferable Intermolecular Potential-4 Point) calculations as well as the interpretation of experimental measurements. In contrast to this, the polarizable version of the SPC/E model, which is based on the fluctuating charge approach, deviates rather strongly for n=6 with few exceptions. However, comparing the polarizable model to ab initio results for identical cluster geometries we find reasonable agreement for the magnitude of the average molecular dipole moment, the corresponding energy per molecule, and the average oxygen-oxygen distance as functions of n.Electronic Supplementary Material available.     

分布时滞竞争模型的周期解

研究了分布时滞竞争模型周期解,利用Gaines与Mawhin的重合度理论,通过构造恰当的Lyapunov函数得到模型正周期解的存在性、唯一性及全局稳定性。     

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.     

Dielectric properties of E. coli cell as simulated by the three-shell spheroidal model

Dielectric properties of E. coli cell have been re-studied by means of the three-shell spheroidal model, where the three shells correspond to the outer membrane, the periplasmic space and the inner membrane, respectively. With the model, a curve-fitting procedure has been developed to analyze the dielectric spectra. Although E. coli cell has been studied before, its special morphological structure was taken into account more comprehensively than any previous model in the present work. Dielectric properties of various cell components have been estimated from the observed dielectric spectra, especially the permittivity of the outer membrane, which was evaluated quantitatively for the first time. The values of epsilon(om) were 12 for kappa(om) of 0 to 10(-4) S/m and 34 for kappa(om) of 10(-3) S/m. The specific capacitance of the inner membrane was 0.6-0.70 microF/cm(2). The relative permittivity and the conductivity of the cytoplasm were about 100 and 0.22 S/m, respectively, and the conductivity of the periplasmic space was 2.2-3.2 S/m.