基于植被指数的典型草原区生物量模型——以内蒙古锡林浩特市为例

利用遥感估测地上生物量是国内外生态学与地理学的研究热点。但基于植被指数的生物量回归模型结果差异较大,究竟哪种植被指数与哪种模型更适合典型草原的生物量反演,是现代草地遥感急需解决的问题之一。该文基于TM影像数据的不同植被指数(VI)差异性,分别选取了RVI(比值植被指数)、NDVI(归一化差异植被指数)、SAVI(土壤调节植被指数)、MASVI(修改型土壤调整植被指数)和RSR(简化比率植被指数)5种植被指数,与同期的内蒙古典型草原区地面实测地上生物量做相关分析,分别建立了5种植被指数与地上生物量的线性及3种非线性(对数、二次多项式、三次多项式)回归模型。研究结果表明:对于中国北方典型草原区而言,地上生物量与5种植被指数(RVI、NDVI、SAVI、MSAVI和RSR)均呈现出显著相关,但地上生物量与后4种植被指数是正相关,与RVI为负相关;利用5种植被指数(RVI、NDVI、SAVI、MSAVI和RSR)监测草地植被生物量的复相关系数均大于0.6,充分说明利用植被指数检测典型草原生物量是一种简单可行的方法;NDVI建立的生物量回归模型,其复相关系数大于其它4类植被指数(RVI、SAVI、MSAVI和RSR),说明NDVI-生物量模型优于植被指数RVI、SAVI、MSAVI和RSR 模型,其模拟地表生物量的效果好;对于TM影像来说,植被生物量的线性模型与3种非线性模型(三次多项式生物量模型、二次多项式生物量模型、对数模型)都表现出较好的模拟效果,都通过了0.01的显著性检验,而且该研究的结果显示出三次多项式生物量回归模型最优,其次是二次多项式生物量模型,再次是线性模型,相对较差的是对数模型。通过NDVI-生物量三次多项式回归模型模拟锡林浩特草原的生物量,可以看出整个研究区的地上生物量基本上是东高西低、东南高西北低的趋势,这与研究区的地形、气候及土地利用等多种因素有关。     

植被叶面积指数遥感监测模型

叶面积指数是植被定量遥感的重要参数,区域的时序列叶面积指数揭示了区域生态的演化过程,反演方法上主要是通过植被指数建立相关模型实现的,对于不同地区或不同气候带而言,模型的通用性以及各种植被指数在模型中的灵敏度都需做进一步的探讨。以江苏省宜兴市作为研究区,采用2002年8月22日获得的Landsat-5TM图像数据和2003年8月23～26日采用LAI-2000进行的野外实测植被叶面积指数(LAI)数据,分别探讨了植被指数(VI)与LAI的一元、多元线性回归模型和非线性回归模型,其中的非线性回归模型包括对数、指数、乘幂和多项式回归模型。结果表明,VI与LAI之间的最佳回归模型为多元线性回归模型,R2达0.864;采用逐步选择剔除法,遴选出了用于回归模型的植被指数为RVI、PVI、SAVIL=0.35、MSAVI、ARVIγ=1、ARVIγ=0.5和SARVI。经模型LAI=-ln((VI-VI∞)/(VIg-VI∞))/KVI检验,预测值(y)与实测值(x)的拟合度较好y=0.5345x 1.3304,R2为0.7379。RVI与LAI的三次多项式回归模型也较好,R2为0.7806。再次为RVI与LAI的一元线性回归模型,R2为0.7726,比值植被指数RVI在反演叶面积指数模型中具有较高的灵敏度。     

降水量和温度对植被覆盖指数影响的空间非平稳性特征——以新疆伊犁河谷地区为例

多变量空间相关分析多基于时间序列数据,对数据时长与统计要求严格,空间非平稳性特征分析可以利用单期数据分析多变量之间的相关性。通过空间变系数回归模型分析了2006年和2011年的新疆伊犁地区降水量和温度对植被覆盖度指数影响的空间变化特征,利用局部线性地理加权回归(GWR)方法估计得到了回归系数曲面,揭示出变量间相互影响的空间异质性,同时利用线性回归最小二乘估计进行了对比。结果表明:(1)空间变系数回归模型可以用于变量间的空间相关分析;(2)局部线性GWR估计方法明显优于线性回归最小二乘估计;(3)拟合结果表明,伊犁地区降水量和温度对植被覆盖指数的影响具有显著的空间非平稳性特征;(4)模型估计误差是降水、气温之外的地形、地貌及人类活动等多种因素造成的,需进一步研究。方法可为具有空间非平稳性特征变量间空间相关性分析以及植被覆盖指数的空间模拟分布提供思路和方法。     

基于遥感图像不同辐射校正水平的植被覆盖度估算模型

选用南京市SPOT 5 HRG图像的地物反射率(PAC)、表观反射率(TOA)和灰度值（DN）影像,提取了4种植被指数（VI）,即归一化植被指数（NDVI）、转换植被指数（TVI）、土壤调节植被指数（SAVI）和修正的土壤调节植被指数（MSAVI）,与地面实测的植被覆盖度进行了回归分析,并建立了36个VI-VFC关系模型.结果表明：在所有模型中,基于PAC级影像提取的NDVI和TVI的3次多项式模型最优;其次为基于DN级影像提取的SAVI和MSAVI的3次多项式模型,在VFC>0.8时其精度略高于前两种模型.这4个模型在植被中等密集区域（VFC＝0.4～0.8）的精度高于植被稀疏区域（VFC=0～0.4）.所建模型可通过中间模型的联结,进行推广使用.在基于VI-VFC关系建模过程中,基于遥感影像不同辐射校正水平提取植被指数,有利于充分挖掘遥感影像信息,进而提高VFC估算的精度.     

甘蔗蔗汁品质性状的回归分析及模型

本文对47份不同甘蔗基因型的蔗汁品质性状进行简单回归和逐步回归分析.结果表明,蔗汁蔗糖分(Suc)与锤度(BX)、温度校正后锤度(BX′)、蔗汁旋光读数(0Z)以及转光度(pol)之间均呈线性回归,简单回归模型均达极显著水平(P＜0.01),决定系数(R2)分别为0.9393、0.9199、0.9861及0.9839.通过逐步回归分析和残差分析建立多重线性回归方程为Suc=0.05706 0.21488BX 0.181030Z,方差分析表明多重线性回归模型达极显著水平(P＜0.01),决定系数为0.9931.t测验表明,蔗汁蔗糖分的模型预测值与实测值间的差异不显著,相对误差平均为0.49%.     

纽结理论与分子生物学：数学家与生物学家的科学二重奏

纽结理论是拓扑学的一个分支,其研究历史较为悠久。1833—1932的一百年间,纽结理论的发展联结着高斯(K.F.Gauss)、登恩(M.Dehn)和亚历山大(J.w.Aloxander)等著名数学家的名字。亚历山大采用了简捷的多项式来区分各种纽结,这类多项式被称为纽结的不变量。遗憾的是,亚历山大多项式不能区分镜像对称纽结。     

上海郊区甘蓝田鳞翅目害虫的复合动态经济阈值

本文研究了上海郊区甘蓝田鳞翅目害虫复合体(菜青虫Pieris rapae,小菜蛾Plutella xylostella,甜菜夜蛾Spodoptera exigua和斜纹夜蛾ProdenJd litura等。)的动态经济阈值模型,该模型主要包括：(1)叶片生长动态与有效积温回归模型,考虑甘蓝品种和叶片层次等因子;(2)鳞翅目幼虫的高龄菜青虫等价取食系数(ICE),考虑甘蓝叶片层次和虫龄等因子;(3)甘蓝产量损失率模型,考虑甘蓝品种、生育期和叶片层次等因子。以经济允许产量损失率作为决策参数(“黄苗”品种为3.2%,“夏光”品种为1.7%)。由于系统纳入了害虫株内为害分布这一因素,本模型确定的经济阈值具有较宽的值域。下限接于现有经济阈值,上限则大大超过它们。田间应用表明在不影响甘蓝产量的情况下,防治成本平均降低45%。     

基于TM影像的表层土壤有机碳空间格局

土壤有机碳是土壤肥力的核心指标之一,理解其空间分布格局对促进精准农业的发展和科学施肥具有重要意义.本研究旨在检验TM影像结合地面采样数据分析黑龙江省黑土分布区表层土壤有机碳空间分布格局的可行性.结果表明:1)表层土壤有机碳浓度与TM5波段呈显著正相关(r=0.553,P＜0.01),与TM4、TM5波段影像像素值之间满足二次多项式回归关系(R2=0.6791,P＜0.05);2)回归模型对表层土壤有机碳空间分布格局具有较好的预测效果(R2=0.7097,P＜0.05);3)海拔高于200 m的地区表层土壤有机碳浓度显著高于海拔低于200 m的地区(P＜0.05).     

旋转回归结合非线性规划在优化提取丝瓜籽油工艺参数的应用

采用通用旋转回归组合设计结合非线性规划探讨以石油醚为溶剂微波辅助浸提丝瓜籽油的最优化生产工艺参数(溶剂体积、水浴浸提时间、微波处理时间、微波处理温度).结果表明:二次多项式方程能较好地说明参试因子与丝瓜籽油得率之间的数值关系.具有显著的回归关系(p-值<0.05),不存在失拟现象(p-值约为0.5).根据这一数量关系模型应用非线性规划获取最优化生产工艺参数(溶剂体积为60ml;水浴浸提时间为180分;微波处理时间为160.4064秒;微波处理温度为86.32436°).验证试验说明这一最优化试验因子组合具有较高的提取率(18.55071     

北京西山静福寺地区鸟类多度分布格局

物种多度格局分析对理解群落结构具有重要意义。采用分割线段模型对北京西山静福寺地区鸟类群落物种数量关系进行拟合研究,并运用秩相关性分析对模型进行相关系数检验,结果表明:(1)该地区鸟类群落多度格局模型与分割线段模型显著相关,利用分割线段模型可以良好的拟合该地区鸟类群落多度格局;(2)鸟类多度分布格局具有时间和空间的双重属性;(3)月尺度上,1月与其他月份差异显著,森林群落间差异不显著;(4)季尺度上,冬季与春、秋两季差异显著,落叶阔叶林与针阔混交林差异显著,针叶林与落叶阔叶林、针阔混交林差异都不显著;(5)年尺度上,年变化差异不显著。     

Moment arms and musculotendon lengths estimation for a three-dimensional lower-limb model

This paper presents a set of polynomial expressions that can be used as regression equations to estimate length and three-dimensional moment arms of 43 lower-limb musculotendon actuators. These equations allow one to find, at a low computational cost, the musculotendon geometric parameters required for numerical simulation of large musculoskeletal models. Nominal values for these biomechanical parameters were established using a public-domain musculoskeletal model of the lower limb (IEEE Trans. Biomed. Eng. 37 (1990) 757). To fit these nominal values, regression equations with different levels of complexity were generated, based on the number of generalized coordinates of the joints spanned by each musculotendon actuator. Least squares fitting was used to identify regression equation coefficients. The goodness of the fit and confidence intervals were assessed, and the best fitting equations selected.     

Race: A population concept

Abstract

The conceptual model presented allows for the identification and organization of different kinds of fertility policies and programs, as they affect fertility, and the relevant elements of the sociocultural variables, dichotomized into “structural” and “cultural” components, that can be associated with fertility. Support for the model was obtained by “fitting” Puerto Rican fertility policies and programs, and structural and cultural components, to the model. Seventeen regression equations using polynomials to the third degree are used for the statistical interpretation of the Puerto Rican data. The results indicate that the use and interpretation of the model and some of the polynomial regression analyses are successful.     

甘蔗实生苗的数量性状相关及选种标准的数学模型研究

本文用25个甘蔗杂交组合的2500丛实生苗的数量性状茎径、茎数、株高和锤度,进行净相关分析、各性状分级频率统计、多项式回归分析及多项式方程求解分析,结果表明：（1）各对数量性状的总体单相关,除茎数与锤度单相关接近显著外,其余均达到极显著水平;各对数量性状的二级净相关,茎数与锤度达显著水平,其余的均达极显著水平;这四个数量性状的复相关系数也达到极显著水平.表现为甘蔗数量性状间是互相影响、互为矛盾,构成品质、产量性状间的矛盾与统一.（2）经标准化的茎数（x′2）、株高（x′3）和锤度（x′4）分别依茎径（x1）真值回归的三次多项式回归方程为,x′2=10.543-14.534x′1＋6.55x2^2-0.968x1^3; x′3=-0.573-1.654x1＋1.249x1^2-0.185x1^3;x′4=-2.926＋3.502x1-1.221x1^2＋0.116x1^3.根据这些方程的升降性,分别组成联立方程组,寻找出这四个数量性状的数学摸型入选标准的最适值分别约为：茎径2.4cm、茎数4条/丛、株高180cm、锤度20.0%.最后根据茎径的标准差,求得甘蔗实生苗数量性状的入选标准数学模型值.     

Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.     

响应面法优化豆粕固态发酵工艺的研究

采用SAS 9.1.3中的响应面分析法（中心组合一致精度设计）对影响豆粕固态发酵中蛋白质水解的四个主要因素（料水比,加酶量,发酵时间,接种量）进行了优化,考察了各因素及其交互作用对大豆蛋白水解度的影响。通过模拟二次多项式回归预测模型并建立了影响因素与响应值（水解度）之间的函数关系,即回归方程,根据回归方程寻优得出,当料水比1：1.00,加酶量2.55％,发酵时间65h,接种量1.00％时水解度可达13.3％,且比优化前提高了56％。     

Musculotendon lengths and moment arms for a three-dimensional upper-extremity model

Generating muscle-driven forward dynamics simulations of human movement using detailed musculoskeletal models can be computationally expensive. This is due in part to the time required to calculate musculotendon geometry (e.g., musculotendon lengths and moment arms), which is necessary to determine and apply individual musculotendon forces during the simulation. Modeling upper-extremity musculotendon geometry can be especially challenging due to the large number of multi-articular muscles and complex muscle paths. To accurately represent this geometry, wrapping surface algorithms and/or other computationally expensive techniques (e.g., phantom segments) are used. This paper provides a set of computationally efficient polynomial regression equations that estimate musculotendon length and moment arms for thirty-two (32) upper-extremity musculotendon actuators representing the major muscles crossing the shoulder, elbow and wrist joints. Equations were developed using a least squares fitting technique based on geometry values obtained from a validated public-domain upper-extremity musculoskeletal model that used wrapping surface elements (Holzbaur et al., 2005). In general, the regression equations fit well the original model values, with an average root mean square difference for all musculotendon actuators over the represented joint space of 0.39 mm (1.1% of peak value). In addition, the equations reduced the computational time required to simulate a representative upper-extremity movement (i.e., wheelchair propulsion) by more than two orders of magnitude (315 versus 2.3 s). Thus, these equations can assist in generating computationally efficient forward dynamics simulations of a wide range of upper-extremity movements.     

Implementation of Rao's one-sample polynomial growth curve model using SAS

Longitudinal data are frequently treated with the classic analysis of variance and regression models. However, these models assume independence of observations. Hoel (1964) demonstrated that the use of least-squares methods on intercorrelated serial observations results in the rejection of the null hypothesis much too frequently. Although appropriate models for analyzing longitudinal data have been available for quite some time, they have remained inaccessible due to cumbersome matrix manipulations. We implement Rao's (1959) one-sample polynomial growth curve model using the programming capability and matrix language of SAS, which involves testing the goodness-of-fit and calculation of confidence bands for polynomial growth curves fit to data at equally spaced time points. Confidence intervals for the parameters themselves are also computed. The method and program (presented in the Appendix) are illustrated with examples involving mandibular ramus height in 12 young male rhesus monkeys. The data set, which spans a 4 year period (yearly observations), is fit adequately by a quadratic equation. The data spanning a 2 year period (half-year observations) are fit adequately by the linear equation. These examples illustrate the considerable widening of confidence bands that occurs when polynomial equations having more terms than are needed to meet the goodness-of-fit requirement are considered.     

Operon dynamics with state dependent transcription and/or translation delays

This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of the paper is a model where points are also subject to some random motion. Conservation equations for moment measures are leveraged to analyze the stationary regime of the point processes of infected and susceptible individuals. A heuristic factorization of the third moment measure is then proposed to obtain simple polynomial equations allowing one to derive closed form approximations for the fraction of infected individuals in the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. A key take-away from this phase diagram is that the extinction of the epidemic is not always aided by a decrease in the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected individuals when the epidemic survives. The simulations also show that the proposed phase diagram accurately predicts the parameter regions where the mean survival time of the epidemic increases (resp. decreases) with motion rate.

     

The lower and upper critical temperatures in male Japanese

Critical temperatures were determined by a new estimating system called the polynomial equation method. Its consists of polynomial regression equations of metabolic rate on ambient and body temperatures and conversion equations enable to convert metabolic rate value into temperature value. Nine young adult males were tested using the system. Metabolic rate was calculated indirectly with a reference to protein metabolism and the critical temperatures were determined as follows; the lower critical air temperature to be 26.2 C, the upper critical air temperature to be 47.0 degrees C, the lower and upper mean skin temperature to be 29.2 degrees C and 36.5 degrees C, and the lower and upper critical rectal temperature to be 35.5 degrees C and 37.9 degrees C, respectively. The polynomial equation method has an advantage over the intersect method since it allows estimation of several kinds of critical temperature.