非线性再生散度随机效应模型的极大似然估计及随机逼近算法

非线性再生散度随机效应模型包括了非线性随机效应模型和指数族非线性随机效应模型等．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings(简称MH) 算法,提出了模型参数极大似然估计的随机逼近算法．模拟研究和实例分析表明了该算法的可行性．     

含不可忽略缺失数据非线性再生散度模型参数的Bayes估计

给出协变量带有不可忽略缺失数据的非线性再生散度模型的Bayes方法,缺失数据机制由Logistic回归模型来确定.Gibbs抽样技术和Metropolis-Hastings算法(简称MH算法)用来得到模型参数、缺失数据机制中回归系数的联合Bayes估计,并用实例加以说明.     

中域效应模型中物种分布幅度梯度的影响

中域效应（Mid-domain effect）模型量化了几何限制对物种丰富度空间分布格局的影响．然而,目前的研究缺乏对该模型的生物学意义作进一步的阐明,以及对物种分布幅度的梯度变化进行数量评价．本文利用已发表的马达加斯加蝴蝶的多样性数据,通过模拟方法和物种幅度频度分布（RSFD）的分析,研究了几何限制和物种幅度非随机分布的共同效应．研究发现,尽管马达加斯加蝴蝶物种丰富度的分布格局满足中域效应模型,但并不符合该模型的特征RSFD变化．如果在模型中加入物种分布幅度的梯度变化,则能较好地模拟实际RSFD的变化,表明物种丰富度的空间格局确实存在物种分布幅度的梯度变化．同时还发现,物种分布幅度梯度的存在对最终丰富度格局影响不大,表明中域效应模型的生物学意义难以从物种分布幅度的行为上来解释．     

基于随机效应的兴安落叶松材积生长模拟

基于黑龙江省带岭林业局大青川林场80株人工兴安落叶松解析木数据和Logistic生长模型,分别考虑单木效应和样地效应,利用S-PLUS软件中的NLME过程拟合非线性材积生长模型,采用赤池信息准则(AIC)、贝叶斯信息准则(BIC)、对数似然值和似然比检验等模型评价指标对不同模型的精度进行比较.结果表明：当考虑单木效应影响时,b₁、b₂、b₃（分别代表Logistic模型中的渐进、尺度和形状的随机参数）同时作为随机参数时模型拟合效果最好; 当考虑样地效应影响时,b₁作为随机参数时模型拟合效果最好.基于单木效应和样地效应的混合模型的拟合精度高于基本模型（Logistic生长模型）,考虑单木效应影响的混合模型的精度高于考虑样地效应影响的模型.模型检验结果表明,随机效应模型不但能反映单木材积的总体平均变化趋势,还能反映个体之间的差异;随机效应模型通过校正随机参数值能提高模型的预测精度.     

Crow-Kimura模型中位点突变率对误差阈的随机效应

为了补充Eigen模型和Crow-Kimura模型的随机效应研究,Crow-Kimura模型中的位点突变率被处理成高斯分布随机变量,从而研究误差阈值的特征以及误差阈值的扩展与随机突变率涨落强度之间的关系. 准物种浓度和群体序参数分析表明,在位点突变率涨落较大时,误差阈值不再是相变点,而是平滑的转变区域. 定量分析表明,随机Crow-Kimura模型中转变区宽度与涨落强度之间的关系是非线性的. 将Crow-Kimura模型与Eigen模型的随机特征进行比较发现,在两个模型中适应值随机化使得转变区域的宽度和随机变量涨落强度之间的关系是线性的,而位点突变率随机化中两者的关系是非线性的（指数）. 对于随机化的Crow-Kimura模型,适应值随机化与位点突变率随机化引起的误差阈扩展效应相当. 对于随机Eigen模型,误差阈的扩展效应则主要是由位点突变率的随机化引起的. 之后,本文概述了Eigen模型和Crow Kimura模型中适应值和位点突变率随机化对误差阈值随机效应的影响,并讨论了上述结果对抗病毒策略、癌症治疗和动植物育种的重要意义.     

栖息地永久性破坏的比例对物种多度稳定值影响的迭代算法

为了分析栖息地破坏程度对集合群落中物种多度稳定值的影响,基于Tilman等[1, 2]提出的多物种竞争的集合群落模型,设计了一种通用的迭代算法用以分析栖息地永久性破坏的比例对物种多度稳定值的影响。针对Tilman等[2]提出的物种多度与其扩散能力或者与其竞争能力相互关系的四种模型,也即：（1）物种竞争力越强则其多度稳定值越大,所有物种死亡率相同;（2）所有物种不论竞争力如何,其多度稳定值相同、死亡率也相同;（3）物种竞争力越弱则其多度稳定值越大,所有物种死亡率相同;（4）物种多度的稳定值相同,但物种竞争力越弱其死亡率越高。先前的研究已经阐明了在前2种模型中栖息地永久性破坏的比例对物种多度稳定值的影响;而对于模型3,因为其数学表达式较为复杂,先前的研究者不得不使用模型3的简化式来考察栖息地永久性破坏的比例对物种多度稳定值的影响;而对于模型4,由于其数学表达式更为复杂,栖息地永久性破坏的比例对物种多度稳定值的影响未能被以往的研究所阐明。本文所使用的迭代算法可以阐明四种模型中任何一种模型条件下栖息地永久性破坏的比例对物种多度稳定值的影响。我们发现对于模型1和2迭代算法所得到的物种多度稳定值与通过数学解析式分析的结果完全一致,同时通过使用迭代算法还阐明了模型4中栖息地永久性破坏的比例对物种多度稳定值的影响。假设栖息地永久性破坏的比例达到了能够导致第s个物种灭绝的水平,起初幸存物种竞争力的排序为s 1 ~ s 3 ~ s 5 ~ … ~ s 6 ~ s 4 ~ s 2,但是随着栖息地永久性破坏的比例不断增大,当其快达到（但还未达到）能够导致第s 1个物种灭绝的水平,物种竞争力的排序将变为s 2 ~ s 4 ~ s 6 ~ … ~ s 5 ~ s 3 ~ s 1。模型4中栖息地永久性破坏的比例对物种多度稳定值的影响与模型2中栖息地永久性破坏程度对物种多度稳定值的影响几乎一致,唯一不同是模型2中所有物种栖息地稳定值的曲线有一个共同的交点,而模型4中所有物种栖息地稳定值的曲线交点不唯一。此外,还使用迭代算法考对比了模型3原始数学表达式和简化式两种情况下栖息地永久性破坏的比例对物种多度稳定值的影响,发现结果略有不同。     

连续近交下家猪微卫生基因组杂合度与经济性状的相关性研究

从已这位于家猪０１、０２、１１、１３、１７、１８号染色体上的遗传标记中选用５６个具有足够覆盖率的微卫生标记,对１个连续５个代近交家系共１９２个头家猪进行了基因组扫描.平均微卫生标记杂合度估计基因组杂合度（ＧＨ）。ＧＨ对于屠宰重（ＳＷＴ）和日均屠宰重（ＡＤＳＧ）为显著正相关效应,对于背膘厚（ＢＦＤＰ）的相关效应不显著且方向也不一致。ＧＨ的相关效应随近交世代递增而呈非线性变化趋势;ＧＨ对于ＳＷＴ和ＡＤＳＧ的相关效应在近交前２世代呈上升趋势。２代分别到达最大值（２２．４３kg和０．１３２kg/d）,此后随近交世代的递增而递减;ＧＨ对于ＢＦＤＰ的相关效应随世代递增而非线性递减。微卫星杂合度的相关效应在不同染色体间存在较大差异,对ＳＷＴ和ＡＳＤＧ均表现为正效应,其中又以１３号染色体标记杂合度的相关效应为最大（６．３０kg和０．０３２kg／d)其次依镒为１号、１７号、１８号、２号和１１号。各染色体微卫星标记杂合度对于ＢＦＤＰ的相关效应估值的标准误差大,且效应方向不一致（１８号染色体来正效应,其余染色体为负效应）,由引得到如下３点启示,第一,对于经济性状重要的基因（e.g.QTL)不同是均衡分布于各杂染色体上,此差异可能反应出生物性状决定在染色体以及分子分上上的差异;第二,由于基因,基因互作和且背景效应的复杂性,基因（组）杂合度与性能间不为简单的相关,学可能由于标记数目不够或是标记选择不适当而误导;第三,由于高度近交（如连续同胞交配）下较高的连锁不平衡所致,有害基因可能以较高的概率民中性标记连锁遗传,由此可能部分或全部抵消杂合优势的表现,甚至出现杂合劣势。     

通光散汤对小鼠哮喘模型气道高反应性和气道炎症的影响

目的观察通光散对小鼠哮喘模型气道反应和气道炎症的影响。方法35只6周龄BALB／c小鼠随机分为哮喘模型组、正常对照组和药物实验组。模型组和药物组以鸡卵白蛋白（OVA）致敏、激发;药物组在最后一次致敏后每天灌胃给予通光散汤0．72mL（相当于0．04g生药）;对照组以等体积的Ns代替OVA致敏、激发。末次激发48h后处理小鼠：无创法测定小鼠的气道高反应性,观察气道阻力变化;支气管肺泡灌洗液（BALF）行细胞学分类;观察肺组织的病理变化。结果①药物组小鼠气道阻力的变化与模型组相比明显下降,差异显著（P＜0．05）;②药物组BALF白细胞总数和Eos（％）与模型组相比明显降低（P＜0．05）。③模型组小鼠肺脏组织支气管、血管黏膜下和周围肺组织有明显的炎症细胞浸润,大量炎症细胞向支气管和血管迁移,上皮细胞部分有脱落,部分可见黏液栓,血管壁明显水肿;治疗组小鼠肺组织炎性细胞浸润和管腔黏液分泌情况较模型组明显减轻,气道粘液的分泌量得到明显的控制。结论通光散汤对小鼠哮喘模型气道高反应性和气道炎症有显著抑制作用。     

基于免疫进化算法（IEA）的鹤望兰(Strelitzia reginae)叶面积指数(LAI)模拟

免疫进化算法（IEA）是基于遗传算法（GA）的一种“加强局部搜索,兼顾全局搜索”的进化算法。利用免疫进化算法（IEA）对鹤望兰叶面积指数（IAI）进行模拟,平均相对误差为3．44％,取得满意的结果,对鹤望兰栽培管理有一定的实际意义。免疫进化算法用于鹤望兰叶面积指数模拟简便、易行,为鹤望兰叶面积指数模拟模型的建立及参数优化开辟了一条新途径。     

多观测序列HMM2的Baum-Welch算法

介绍了在观测噪声和马尔可夫链不相互独立的条件下二阶隐马尔可夫模型（second-orderHMM：HMM2）的结构．研究了在多观测序列不相互独立的情况下HMM2的学习算法,并由此导出了该模型的参数重估公式．     

Details of local dispersion improve the fit of neighborhood competition models

I performed a series of greenhouse experiments to explore how patterns in the dispersion of local competitors affect the reproductive performance of Capsella bursa-pastoris, Poa annua and Senecio vulgaris. I manipulated the density and relative frequency of competitors in each of three concentric rings surrounding a central plant, thereby creating a variety patterns by which local competitors were distributed. Neighborhood competition models were used to predict the seed output of these central plants. For both Senecio vulgaris and Capsella bursa-pastoris, I found that models which incorporated the dispersion of competitors, as well as the relative emergence date of plants, performed substantially better than those that considered only the distance between the central plant and each of its competitors. I was unable to measure the seed output of Poa annua but neither emergence data nor the dispersion of competitors were important in determining its final dry-weight. Present address: Department of Biology, Box 1137, Washington University, 1 Brookings Drive, St. Louis, MO 63130, USA     

Langmuir wave in weakly inhomogeneous relativistic plasma

The evolution of a Langmuir wave in a weakly inhomogeneous relativistic plasma with a positive density gradient is considered. It is shown that, at relativistic phase velocities, the wave evolution even at the tail of the electron distribution, where it is close to linear in the nonrelativistic case, results in the wave transformation into a hybrid of two waves with different spatial periods. Nonlinear dispersion relations for different stages of the wave evolution are derived.     

REML estimation of variance parameters in nonlinear mixed effects models using the SAEM algorithm

Nonlinear mixed effects models are now widely used in biometrical studies, especially in pharmacokinetic research or for the analysis of growth traits for agricultural and laboratory species. Most of these studies, however, are often based on ML estimation procedures, which are known to be biased downwards. A few REML extensions have been proposed, but only for approximated methods. The aim of this paper is to present a REML implementation for nonlinear mixed effects models within an exact estimation scheme, based on an integration of the fixed effects and a stochastic estimation procedure. This method was implemented via a stochastic EM, namely the SAEM algorithm. The simulation study showed that the proposed REML estimation procedure considerably reduced the bias observed with the ML estimation, as well as the residual mean squared error of the variance parameter estimations, especially in the unbalanced cases. ML and REML based estimators of fixed effects were also compared via simulation. Although the two kinds of estimates were very close in terms of bias and mean square error, predictions of individual profiles were clearly improved when using REML vs. ML. An application of this estimation procedure is presented for the modelling of growth in lines of chicken.     

Overman, A.R. and Scholtz, R.V. III. Mathematical models of crop growth and yield

This book comprises six chapters: Introduction (34 pp.), Seasonalresponse models (60 pp.), Growth response models (91 pp.), Mathematicalcharacteristics of models (97 pp.), Pasture systems (22 pp.)and Nonlinear regression for mathematical models (20 pp.). Eachchapter ends with exercises and references. The book has a subjectindex. I found     

On the nonlinear dynamic plane base-rotator models of DNA: Base-base interaction and dissipation

Nonlinear mechanical plane base-rotator models of DNA are considered. Various expressions for the potential energy of interaction between complementary bases are analyzed. Dissipative functions are introduced into these models: the external function describing the motion of the bases in a solvent and the function describing the internal friction in the molecule. Particle-like solutions of the model without dissipation are obtained and the influence of dissipation on these (soliton) excitations is studied.     

Control of neuromuscular blockade with Gaussian process models

This paper presents Nonlinear Model Predictive Control (NMPC) of neuromuscular blockade induced by atracurium on patients subject to general anesthesia. In order to tackle the high levels of uncertainty in the process behavior, probabilistic and non-parametric Gaussian process models are used in the NMPC approach. The proposed control structure was tested in a bank of models that represent patients subject to general anesthesia under elective surgery. All patients models were stabilized and yield a satisfactory performance.     

An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations

The thresholds for mathematical epidemiology models specify the critical conditions for an epidemic to grow or die out. The reproductive number can provide significant insight into the transmission dynamics of a disease and can guide strategies to control its spread. We define the mean number of contacts, the mean duration of infection, and the mean transmission probability appropriately for certain epidemiological models, and construct a simplified formulation of the reproductive number as the product of these quantities. When the spread of the epidemic depends strongly upon the heterogeneity of the populations, the epidemiological models must account for this heterogeneity, and the expressions for the reproductive number become correspondingly more complex. We formulate several models with different heterogeneous structures and demonstrate how to define the mean quantities for an explicit expression for the reproductive number. In complex heterogeneous models, it seems necessary to define the reproductive number for each structured subgroup or cohort and then use the average of these reproductive numbers weighted by their heterogeneity to estimate the reproductive number for the total population.     

Neoplasms of the reproductive tract: the role of hormone exposure

Cancers of the reproductive system are a major source of morbidity and mortality among women worldwide. Because the uterus, ovaries, and cervix are hormonally responsive tissues, exposure to endogenous or exogenous sex steroids can profoundly affect the carcinogenic process. Animal models developed to date provide valuable but imperfect systems in which to study neoplasms of the reproductive tract. Nonhuman primate models share the unique primate-specific endometrial physiology of humans, but rarely develop neoplasms of the reproductive tract. Therefore a surrogate marker approach is required for the study of hormonally induced cancer risk in primates. Rodents provide practical models in which tumorigenesis can be assayed in a short time and, with appropriate interpretation, can be used for assessment of risk, prevention, and therapeutic strategies. In addition to the spontaneous strain-dependent incidence of female reproductive cancers, the classical chemical and hormonal carcinogenesis models, and the use of xenograft approaches, novel genetically modified animals provide unique insights into relevant molecular mechanisms. Caveats in the use of rodent models include anatomical differences from the human reproductive tract, the greater possibility of different metabolic responses to hormonal agents than humans, strain variations in tumor type and hormonal responsiveness, and unexpected tumor phenotypes in genetically modified animals. Reported nonmammalian models are limited primarily to the study of ovarian carcinogenesis. Recent progress in the understanding of cervical carcinogenesis is encouraging. Unmet needs in this area of research include models of early events in ovarian carcinogenesis and strongly predictive models of endometrial cancer risk. Nonhuman primates remain indispensable for the study of some aspects of reproductive pathophysiology, but the best understanding of carcinogenesis in the reproductive tract requires a broad approach using complementary human, nonhuman primate, and nonprimate studies.     

Locally adaptive function estimation for binary regression models

In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and uses latent utility representations of binary regression models for efficient block sampling from the full conditionals of nonlinear functions.