关于农药消解模型参数拟合优化算法的研究

参数拟合是数学建模的重要方面．本文对农药消解模型参数拟合的算法进行优化,用麦夸方法最优拟合消解方程y=c0e～-kt,给出参数和半衰期的数值解．理论和实例计算均表明：用麦夸方法得到的消解模型的预测值与实测值拟合度优于其他方法．优化的麦夸算法简便实用,且具有普遍适用性．     

进化规划在医用非线性曲线模型拟合中的应用

本文提出医用非线性曲线模型拟合的进化规划,并以指数曲线模型为例,选择了一组标样进行了模拟。结果表明,进行规划方法性能良好,可望成为各类医用非线性曲线拟合的有效工具。     

单纯形加速法拟合生态学中的非线性模型

本文以Logistic模型,Taylor幂法则模型,Holling功能反应模型,以及种群内禀增长力Rm等模型的拟合和参数估计为例,探讨单纯形加速法在生态模型优化拟合和参数估计中的应用.结果表明,单纯形加速法拟合生态学中的非线性模型不仅适用广泛,而且拟合过程是直接求原来非线性模型的最优拟合,因而优于生态学中通常使用的将原模型“线性化后再拟合”的方法,而与其它一些最优化方法,如:麦夸方法、枚举选优法等比较,由于单纯形法不需计算目标函数的偏导数,因而计算不受目标函数及其偏导函数复杂程度的限制,而且对于各种模型其求优计算过程十分相似,可以编制统一的计算程序.本研究所编制的计算机程序对于本文未提到的其它一些模型也是完全适用的,在应用时仅需修改定义目标函数的自定义函数语句即可.研究也发现,在求优过程中,只要搜索系数选择适当和实际数据合理,是可以保证寻优成功的.     

运用遗传算法拟合Logistic曲线的研究

Logistic方程是研究有限空间内种群增长规律的重要工具之一．本文运用遗传算法拟合logistic曲线,并且比较了各种方法的拟合结果,证明遗传算法具有较强的拟合非线性方程的能力,对生物实验及生态、生理学中诸多非线性曲线的参数估计具有普遍意义．     

改进的遗传算法在医用非线性曲线模型拟合中的应用

本文提出医用非线性曲线模型拟合改进的遗传算法,以指数曲线模型为例,选择了一组标样进行了模拟,结果表明,改进的遗传算法性能良好,可望成为各类医用非线性曲线拟合的有效手段。     

三次设计结合模矢法拟合Logistic曲线的研究

Ｌｏｇｉｓｔｉｃ曲线是种群动态的一个经典模型,针对传统拟合方法存在的缺陷和三次设计的优点,以及拟合过程是离差平方和最小──可看作是运筹学中无约束极值问题──的优化原则,本文提出新的方法－三次设计结合模大法的组合方法来拟合,结果表明该法能取长补短,拟合效果最佳,因此在一般非线性模型参数求解中具有普遍意义．     

运用改进单纯形法拟合Logistic曲线的研究

Ｌｏｇｉｓｔｉｃ方程是研究有限空间内种群增长规律的重要工具之一本文运用改进单纯形法最优拟合Ｌｏｇｉｓｔｉｃ曲线,结果表明改进单纯形法具有较强的拟合非线性方程的能力,对生物实验及生态、生理学中诸多非线性曲线的参数估计具有普遍意义．     

亚洲玉米螟产卵量增长曲线的一种新的拟合方法

本文用多项式方法与微分理论,提出逻辑斯蒂曲线的拟合新方法。应用这个方法建立了亚洲玉米螟产卵量动态模型,并阐述了计算参数方法。结果与其它方法相比,其优点是计算方便,而且拟合程度精确。用新方程作为预报虫害,可以提高预报效果。     

农业生产中四组数据的Logistic模型的参数确定

本文介绍了求非线性回归模型参数的基本理论,选择Logistic回归模型作为模型函数.以牧草再生长的数据集1为例,用Mathematica软件绘制了数据集1的点图.最后给出四组数据的拟合曲线和置信域.     

北京东灵山地区植物群落多样性研究一种-面积曲线的拟合与评价

 本文选择了10条曲线作为种—面积曲线的拟合模型,它们分别是 S=b+aA (1) S= b+alnA (2) S=(b+alnA)c (3) S=aln(A+1) (4) S=aln(bA+1) (5) S= aAb (6) S=aA/(1+bA) (7) S=c/(1+ae-bA) (8) S=c-ae-bA (9) S=a(1-e-bA) (10) 对其中的7个非线性模型给出了参数初值的计算方法,并用Gauss—Newton或Marquardt方法计算非线性最优解。又选择了剩余标准差(RSE)、相关指数(CRI)、偏差绝对值的平均值(AAD)和相对偏差绝对值的平均值(AARD)作为模型拟合优劣的4个评价指标。研究结果表明：1)7个非线性模型中参数初值的计算方法是可行的。从4个评价指标来看,它们的非线性最小二乘解都明显优于线性最小二乘解;2)10个模型的拟合效果都相当好,对5个样地及其各层拟合的共200个CRI中有71.5％大于0.9,89％大于0.8,其中曲线(3)和(9)最好,其次是(5)、(6)、(2),(1)和(10)最差;3)秩相关分析表明,3个评价指标RSE、AAD和AARD相互之间存在极强的正秩相关,因此在本研究中,它们的评价结果具很强的一致性。     

高山姬鼠幼仔的生长发育和产热特征

根据高山姬鼠幼仔56 d 的生长资料初步分析了其生长发育规律;用电子天平测量了体重的增长过程; 用开放式呼吸仪测定了静止代谢率(Resting metabolic rate,RMR)、非颤抖性产热(Nonshivering thermogenesis, NST)以及肺皮蒸发失水(Evaporative water loss,EWL)。依据逻辑斯蒂曲线的拐点,高山姬鼠的体重生长可划分为加速生长相和减速生长相。幼仔的体温在17 日龄前逐渐升高,35 日龄时接近成体水平;静止代谢率和非颤抖性产热在17 日龄前随日龄逐渐增大,17 日龄后与体重成异速增长关系,RMR 在49 日龄时接近成体水平,NST 在6 日龄内即被激活;蒸发失水在断乳前较断乳后为高。高山姬鼠为典型的晚成性发育动物。高山姬鼠较短的妊娠期、较大的胎仔数、较长的哺乳期与其食物资源较丰富有关。     

一种确定rm的简单方法的验证与分析

本文对一种测定蚜虫和螨的内禀增长率(rm)的简单方法进行了验证与分析。这种方法不要求详细的生殖力表资料,计算rm的公式如下:rm=0.74 ln(Md)/d。式中,d表示生殖前期,即从出生到第一次生殖之间的天数;Md表示在2d期间每个雌虫繁殖的平均雌性后代数。这种方法是Wyatt和White提出的。我们的研究表明:当Md小于1,这种方法不宜采用;当Md大于1和2d期间的繁殖贡献接近或大于70％时,可以用这种方法计算rm;不过,所有蚜虫和螨种群在2d期间对rm的繁殖贡献是否能够达到70％或70％以上还有待研究。研究繁殖分布特征对于这种简单方法的实际应用有重要意义。     

Bayesian lasso for semiparametric structural equation models

There has been great interest in developing nonlinear structural equation models and associated statistical inference procedures, including estimation and model selection methods. In this paper a general semiparametric structural equation model (SSEM) is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables. A basis representation is used to approximate these nonparametric functions in the structural equation and the Bayesian Lasso method coupled with a Markov Chain Monte Carlo (MCMC) algorithm is used for simultaneous estimation and model selection. The proposed method is illustrated using a simulation study and data from the Affective Dynamics and Individual Differences (ADID) study. Results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model.     

The evolution of altruism between siblings: Hamilton's rule revisited

This paper explores the validity of Hamilton's rule in the case of other-only altruism in which the benefits are shared by other members of the sibling group excluding the donor. It presents a model of competition between two alleles which code for different kinds of altruism. It derives a simple replicator equation for allele frequencies under conditions of strong selection. This equation does not depend on the size of the sibling group. In mathematical form, the equation is similar to Hamilton's original rule in the case of inbreeding, although the causal mechanism is different. The paper derives a simple criterion to determine whether there will be a polymorphism in which both alleles coexist permanently. Such an event is rare and victory will normally go to the allele with the higher value of 1/2b-c, where b is the total benefit which an offspring confers on its siblings and c is the cost to the donor. The paper also considers how an offspring will behave in particular circumstances. Using a specialized version of the basic model, it shows how, in the absence of polymorphism, natural selection should take the system towards the point of 50% marginal altruism. With this type of altruism, an offspring will perform any act for which the expected cost to the donor is at most half the expected benefit to its siblings. Acts which do not satisfy this criterion are not performed. This accords with Haldane's quip that he would sacrifice his own life for two of his brothers, but not for less. Numerical simulation is used to explore these issues in greater depth. The paper also examines briefly the implications of heterozygote advantage for Hamilton's rule. It concludes with a brief discussion of the connection between other-only altruism and whole-group altruism, in which the donor gains some benefit from its actions.     

Numerical integration of the master equation in some models of stochastic epidemiology

The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation--up to a desired precision--in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1.     

Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

Alpha functions are commonly used to describe different receptor channel kinetics (non-NMDA, GABA_A and GABA_B). In this paper we show that they may be represented as solutions to simple ordinary differential equations. This alternative method is compared with the commonly used direct summation of the alpha function conductances in a high-level neuronal circuit model. A parametric study shows that the differential equation method greatly speeds up the previous summation method. The forward Euler method used to solve this differential equation is shown to be accurate for this type of simulation. The modelling of NMDA receptor channel kinetics is also discussed. Received: 18 December 1992/Accepted in revised form: 28 June 1993     

A continuous cable method for determining the transient potential in passive dendritic trees of known geometry

Models using cable equations are increasingly employed in neurophysiological analyses, but the amount of computer time and memory required for their implementation are prohibitively large for many purposes and many laboratories. A mathematical procedure for determining the transient voltage response to injected current or synaptic input in a passive dendritic tree of known geometry is presented that is simple to implement since it is based on one equation. It proved to be highly accurate when results were compared to those obtained analytically for dendritic trees satisfying equivalent cylinder constraints. In this method the passive cable equation is used to express the potential for each interbranch segment of the dendritic tree. After applying boundary conditions at branch points and terminations, a system of equations for the Laplace transform of the potential at the ends of the segments can be readily obtained by inspection of the dendritic tree. Except for the starting equation, all of the equations have a simple format that varies only with the number of branches meeting at a branch point. The system of equations is solved in the Laplace domain, and the result is numerically inverted back to the time domain for each specified time point (the method is independent of any time increment t). The potential at any selected location in the dendritic tree can be obtained using this method. Since only one equation is required for each interbranch segment, this procedure uses far fewer equations than comparable compartmental approaches. By using significantly less computer memory and time than other methods to attain similar accuracy, this method permits extensive analyses to be performed rapidly on small computers. One hopes that this will involve more investigators in modeling studies and will facilitate their motivation to undertake realistically complex dendritic models.