Homotopy Analysis Method for Solving Biological Population Model

In this paper,the homotopy analysis method (HAM) is applied to solve generalized biological populationmodels.The fractional derivatives are described by Caputo's sense.The method introduces a significant improvementin this field over existing techniques.Results obtained using the scheme presented here agree well with the analyticalsolutions and the numerical results presented in Ref.[6].However,the fundamental solutions of these equations stillexhibit useful scaling properties that make them attractive for applications.

Can we reestablish a self-sustaining population?A case study on reintroduced Crested Ibis with population viability analysis

Background:One of the most challenging tasks in wildlife conservation and management is clarifying which and how external and intrinsic factors influence wildlife demography and long-term viability.The wild population of the Crested Ibis(Nipponia nippon)has recovered to approximately 4400,and several reintroduction programs have been carried out in China,Japan and Korea.Population viability analysis on this endangered species has been limited to the wild population,showing that the long-term population growth is restricted by the carrying capacity and inbreeding.However,gaps in knowledge of the viability of the reintroduced population and its drivers in the release environment impede the identification of the most effective population-level priorities for aiding in species recovery.Methods:The field monitoring data were collected from a reintroduced Crested Ibis population in Ningshan,China from 2007 to 2018.An individual-based VORTEX model(Version 10.3.5.0)was used to predict the future viability of the reintroduced population by incorporating adaptive patterns of ibis movement in relation to catastrophe frequency,mortality and sex ratio.Results:The reintroduced population in Ningshan County is unlikely to go extinct in the next 50 years.The popula-tion size was estimated to be 367,and the population genetic diversity was estimated to be 0.97.Sensitivity analysis showed that population size and extinction probability were dependent on the carrying capacity and sex ratio.The carrying capacity is the main factor accounting for the population size and genetic diversity,while the sex ratio is the primary factor responsible for the population growth trend.Conclusions:A viable population of the Crested Ibis can be established according to population viability analysis.Based on our results,conservation management should prioritize a balanced sex ratio,high-quality habitat and low mortality.

Analytic algorithms for Some Models of Nonlinear Age–Structured Population Dynamics and Epidemiology

Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and accuracy of the methods.

Thought and Method on Establishing the Prediction Model of TCM Dominant Population with Advanced Digestive Tract Malignant Tumors based on TCM Tumor Registration Platform

Advanced digestive tract malignant tumors,represented by advanced colorectal cancer,advanced gastric cancer and advanced esophageal cancer,have insidious onsets and high mortality.Western medicine based on targeted therapy greatly can improves the benefit and efficacy for patients through population stratification,but its population is limited.Traditional Chinese medicine(TCM)has a long history in treatment of tumors,which is an important part of comprehensive treatment of tumors.Clinical observation has shown that different patients could get different efficacy from TCM treatment.Based on real world registration studies,patients with advanced colorectal cancer,advanced gastric cancer or advanced esophageal cancer who had received TCM treatment were observed and followed,and a TCM dominant population that achieved significant efficacy was screened out to carry out multivariate regression analysis,further explore key factors that affect survival in advanced digestive tract malignant tumors,and establish a prediction model of TCM dominant population.It will provide reference for the follow-up TCM treatment,and provide reference for development of individualized treatment plans,making the TCM treatment for advanced digestive tract malignant tumors more targeted,and helping to improve the benefit rate in TCM.

Effects of life-history components on population dynamics of the rare endangered plant <i>Davidia involucrata</i>

In order to estimate the most effect stage and process on population growth and effective conserve the rare endangered plant Davidia involucrata, we analyzed the dynamics and the contributions of life-history components on population dynamics based on Lefkovitch matrix model and sensitivity analysis. The life cycle of Davidia involucrata was divided into six stages (seed, seedling, juvenile, immature, early adult and late adult) based on the species characteristics and published literature data, the survival rates in each life-history stage were simulated using a static life table, and the fecundity of each stage was determined according to sample information. The results showed that the structure of the observed population was not ideal, and the numbers of seedlings and coppice shoots was similar. The population growth rate was influenced largely by individual growth process, and asexual reproduction made a larger contribution to population growth than sexual reproduction. However, sexual reproduction was more important than asexual reproduction, because most asexual reproducing individuals (the coppice shoots) were derived mainly from human destruction (e.g. felling trees). The most important stage was stage V (late adult), associated with seed production and germination. Therefore, conservation of Davidia involucrata populations should focus on stage V and sexual reproduction, in order to improve the seed production and germination rate, and to promote population stability and development.

Statistical analysis for genome-wide association study

In the past few years, genome-wide association study （GWAS） has made great successes in identifying genetic susceptibility loci underlying many complex diseases and traits. The findings provide important genetic insights into understanding pathogenesis of diseases. In this paper, we present an overview of widely used approaches and strategies for analysis of GWAS, offered a general consideration to deal with GWAS data. The issues regarding data quality control, population structure, association analysis, multiple comparison and visual presentation of GWAS results are discussed; other advanced topics including the issue of missing heritability, meta-analysis, setbased association analysis, copy number variation analysis and GWAS cohort analysis are also briefly introduced.

MODELLING AND STABILITY ANALYSIS OF POPULATION GROWTH WITH SPATIAL DIFFUSION

In recent years, population growth models with spatial diffusion have beenextensively studied by many authors (for example, see [1-5]). In this paper, a populationgrowth model is considered with a discrete age-dependence and spatial diffusion, and isinvestigated in a semigroup framework. The spectral properties of the population oper-ator are given. On the basis of such spectral consideration, the asymptotic behaviourof the semigroup generated by the population operator is obtained. Finally, a nonlinearpopulation growth model is considered and its stability is analyzed.

一维p-Laplacian方程Neumann边值问题正解的存在性和多解性

本文利用时间映像分析法考虑了一类源自人口问题中的稳态反应扩散方程Neumann边值问题{|u'(t)|^(p-2)u'(t))'+λ(au-bu^(2)-c)=0,0<t<1,u'(0)=u'(1)=0多个正解的存在性.其中,1/λ>0为扩散系数,1<p≤2,a>0,b>0,c>0.进一步,当确定了a,b,c,1/λ的值时,本文证明了上述问题多个正解的存在性和解的精确个数,所得结果推广并改进了已有文献的相关结果.

东北三省碳排放影响因素分析和趋势预测——基于STIRPAT模型和情景分析法

东北三省是“双碳”目标下碳减排工作的重点区域。利用STIRPAT(可拓展的随机性环境影响评估)模型对2000—2021年东北三省各省的碳排放影响因素进行分析,并利用情景分析法预测截止到2040年以前、均衡情景下东北三省各省的碳排放趋势。模型分析结果表明:各省只存在导致碳排放量增加的影响因素;能源消费总量、碳排放强度、人均GDP是各省的共同影响因素;各省的影响因素是不同的组合;各省影响因素的促进作用存在省份差异性。预测结果表明:碳排放量同期数值由高到低依次为辽宁省、黑龙江省、吉林省;各省的碳排放量曲线都呈现出倒“U”形并能够看出明显的峰值;黑龙江省和吉林省碳达峰的时间都为2012年,而辽宁省碳达峰的时间为2025年。针对分析和预测结果,提出能源、社会经济、区域协调3个方面的建议。

基于优化支持向量回归的磨古倾倒变形体参数反分析研究

岩土体力学参数的确定将直接影响对倾倒变形体稳定性的分析判断,野外原位监测数据作为反映倾倒变形体现场条件的重要信息,利用原位监测数据能有效地获得倾倒变形体岩土体参数.本文针对雅砻江两河口近坝库区磨古倾倒变形体,提出以海洋捕猎者优化算法对支持向量回归反分析模型参数进行寻优,构建MPA-SVR岩土体参数反分析模型.以倾倒变形体现场安全监测数据为输入信息,反分析得到适用于两河口磨古倾倒变形体折断带的力学参数,其反分析结果可为变形体稳定性分析提供重要数据基础.结果表明磨古倾倒变形体不同高程监测点具有相似的变形规律,变形速率发展趋势与水位变化趋势一致,变形累计值整体呈增长趋势,变形尚未完全收敛;随着分期蓄水进程的推进,倾倒变形体水动力作用特征明显,反分析得到的折断带力学参数逐渐降低,从第二阶段蓄水到第三阶段蓄水,折断带黏聚力下降3.68%,内摩擦角下降1.98%.

Analysis and control of a non-smooth population model with impulsive effects

In this paper, a non-smooth population model with impulsive effects is proposed by combining discontinuity and non-smoothness. According to the qualitative theory of differential equations, the global analysis of the model is discussed. Using the theory of impulsive differential equations, the existence conditions of order one periodic solution are obtained. And the impulsive controllers are designed to make the pest populations stay at the refuge level. Some simulations are carried out to prove the results.

高原鼠兔种群密度与生境因子作用关系

高原鼠兔(Ochotona curzoniae)是青藏高原上的小型哺乳动物,一定数量内的高原鼠兔可以提高高寒草地的生物多样性,改善土壤结构,有利于维持生态系统的稳定性。但当其种群密度过大时,可能会导致草地退化。探究高原鼠兔种群密度的影响因素能够为科学防控高原鼠兔提供理论依据。本研究从气象、土壤、植被、地形及人类活动多角度探究16个生境因子对高原鼠兔种群密度的影响,通过主成分分析及Pearson相关性分析从16个生境因子中筛选出年均温、植被高度、海拔及土壤硬度为主要建模因子,并采用广义加性模型(GAM)分析高原鼠兔种群密度与4个建模因子之间的作用关系,构建高原鼠兔种群密度预测模型。结果显示:本研究构建的GAM模型拟合度较高(R^(2)=0.946),可以较好地评估青藏高原地区高原鼠兔的潜在致灾风险;土壤硬度与高原鼠兔种群密度之间存在显著负相关;海拔、植被高度和年均温度均与高原鼠兔种群密度之间存在非线性关系,并且海拔为3800~4000 m、植被高度为6~8 cm、年均温度为-2~0℃时高原鼠兔种群密度达到最大。

婺源蓝冠噪鹛种群生存力分析

为了解蓝冠噪鹛(Pterorhinus courtoisi)的灭绝风险,预测未来种群变化趋势,采用Vortex 10.5.0模型对蓝冠噪鹛进行种群生存力分析,并模拟不同参数对蓝冠噪鹛种群数量的影响,探索制约蓝冠噪鹛种群增长的主要因子,为该物种的保护管理提供科学依据。结果显示:在标准状态下(考虑近交、灾难因素),蓝冠噪鹛灭绝概率为73%,内禀增长率(R)为0.1480,周期增长率(λ)为1.1595,净生殖率(R0)为1.5046,雌性和雄性的平均世代时间(T)为2.76 a。在9个参数敏感度分析中,性别比例、1岁后雄性死亡率和天敌灾害发生频率3个参数是影响种群数量变化的主要参数。结果表明,在复杂的环境条件下蓝冠噪鹛仍有灭绝风险,其保护工作仍面临较大压力。控制天敌捕食压力、提高蓝冠噪鹛雄鸟成活率,将有益于蓝冠噪鹛种群增长。

基于CC-MPA特征优选算法的小麦条锈病遥感监测

为了弥补一次性建模分析的缺陷,提高小麦条锈病遥感监测模型的运行效率和精度,根据模型集群分析(Model population analysis,MPA)算法的特点,综合利用光谱区间选择算法和光谱点选择算法的优势,提出了一种联合相关系数(Correlation coefficient,CC)与MPA的特征变量优选算法。在利用CC算法对全波段光谱进行特征变量选择的基础上,分别利用基于MPA思想开发的竞争性自适应重加权采样法(Competitive adaptive reweighted sampling,CARS)和变量组合集群分析法(Variable combination population analysis,VCPA)进一步优选对小麦条锈病敏感的特征变量,并利用偏最小二乘回归(Partial least squares regression,PLSR)算法构建了小麦条锈病遥感监测的CC-CARS和CC-VCPA模型。结果表明:联合CC MPA算法优选的特征变量构建的CC-CARS和CC-VCPA模型精度均高于CC、CARS和VCPA算法。3组验证集样本中,CC-CARS模型预测病情指数(Disease index,DI)与实测DI间的R^(2)_(V)较CC模型和CARS模型至少分别提高了6.78%和6.66%,RMSEV至少分别降低了15.31%和10.98%,RPD至少分别提高了18.08%和12.34%。CC VCPA模型预测DI与实测DI间的R^(2)_(V)较CC模型和VCPA模型至少分别提高了9.58%和0.73%,RMSEV至少分别降低了20.78%和3.86%,RPD至少分别提高了26.22%和4.02%。基于CC-MPA的光谱特征优选算法是一种有效的特征选择方法,尤其是利用CC-VCPA方法选择的特征变量数更少,模型预测效果更好,研究结果对光谱特征优选及提高作物病害遥感监测精度具有重要的参考价值。

长汀生态恢复区不同混交比例针阔混交林内马尾松种群动态及其驱动机制

[目的]分析我国亚热带生态恢复典型先锋物种马尾松在不同混交比例针阔混交林内的种群动态及其驱动机制,为深入理解亚热带植被重建与恢复进程奠定基础。[方法]基于福建省长汀县生态恢复区4块不同混交比例针阔混交林内马尾松种群调查数据,构建积分投影模型并运用弹性分析、生命表响应试验等方法,探究混交林内马尾松种群动态及其驱动机制。[结果]针阔混交林内马尾松种群整体表现为持续衰退状态(种群增长率λ<1),随着阔叶树种在林分中相对多度增加,马尾松个体平均存活率和平均繁殖率以及λ均呈先上升后下降趋势。弹性分析表明,个体存活对混交林内马尾松种群增长最重要,小径级个体正生长利于种群发展,繁殖对种群增长的影响较为有限。随着阔叶树种相对多度增加,对马尾松种群增长最重要的个体逐渐由幼苗转变为成年树,种群维持风险逐渐增大。生命表响应试验显示,个体生长差异是不同混交林间马尾松种群增长差异的主要来源。[结论]随着阔叶树种混交比例上升,马尾松种群内幼苗和幼年树的比例和重要性持续降低,成年树的比例和重要性不断增加,不同生活史阶段个体生命率的差异化响应驱动马尾松种群动态变化。

基于VSPAI的近红外光谱小麦蛋白质分析方法研究

基于模型集群分析思想,利用变量选择比自适应迭代法(VSPAI)结合偏最小二乘法(PLS)建立了小麦蛋白质含量的近红外光谱预测模型。VSPAI利用蒙特卡罗采样法随机选取样本子集,运用PLS建立样本子集的回归模型,并计算各变量回归系数的平均值和标准差,求出每个变量的初始权重,并与加权自助采样法相结合选取最佳特征变量。结果表明,VSPAI-PLS模型与竞争性自适应重加权采样结合PLS、变量组合集群分析结合PLS、变量组合集群分析迭代保留信息变量法结合PLS、引导软阈值算法结合PLS模型相比,VSPAI-PLS模型的预测精度提高了39.9%、5.9%、25.4%、46.9%。综上,将VSPAI-PLS模型应用于小麦蛋白质的近红外光谱无损检测具备可行性。

基于狄利克雷多项式过程模型与K-means结合的菌群分析

群体分型是一种有助于更好的理解人类身心健康等复杂生物学问题的有效方法,聚类是一种为了对样本分组来降低复杂性的定义肠型的方法,而传统K-means聚类算法的K值选取无法确定,本文在传统K-means聚类算法的基础上进行了改进,并公开数据集上进行了验证,实验表明改进算法能够解决K值选取无法确定的问题,且聚类结果的稳定性、准确性和聚类质量都得到显著提高。将改进后的模型运用于肠道菌群OTUs数据,发现不仅能够有效地区分2-型糖尿病患者样本间的相似性,而且能鉴定出影响菌群结构异质性最大的OTUs菌,为临床解决2-型糖尿病问题提供了一种新的思路。

基于KANO模型的电子血压仪用户需求分析与设计

随着人们生活方式的转变以及老龄化进程的加速,我国高血压人群愈发庞大。文章以高血压人群为研究对象,研究该群体对电子血压仪的功能需求,以提出电子血压仪的设计策略。首先,通过问卷调研法和访谈法获得用户需求。其次,使用KANO模型对用户需求属性进行分类与整理。再次,对需求属性进行归类,并利用Better-Worse系数分析确定用户满意度的敏感程度。最后,对数据进行分析解读,从而确定不同功能需求的优先级。通过对高血压人群的需求分析,为今后电子血压仪提供新的设计思路与参考。

MPA方法在不同高度桥墩地震响应分析中的适用性研究

桥梁通常是线路中的控制工程,其抗震性能显得尤为重要。作为梁桥重要组成部分的桥墩,往往是地震作用下容易受到损伤的构件。结合西部山区梁桥的典型桥墩结构形式,基于纤维模型的有限元方法建立桥墩的非线性数值分析模型。采用MPA方法对不同高度桥墩的地震响应进行分析,以非线性时程分析方法的计算结果为基准研究MPA方法的适用性。计算表明MPA方法在分析高阶模态参与程度较高的高墩构件时适用性较差。

Forecasting Number of Students in University Department: Modeling Approach

In this study, the mathematical models of dynamics of student populations in the university departments are formulated. As a case study, we employ the data of registration section from Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Thailand, from calendar year 2006 to 2010. Using regression analysis, descriptive model and explanatory model are derived. The descriptive model is linear with R2 = 0.8864. Using log-transformation, the explanatory model gives the nonlinear approximation with R2 = 0.8293. The model predicts that the number of students of Department of Mathematics, KMUTNB has a tendency to linearly increase with slope of 20 with 95% CI (6.8417, 33.1583). The application of the models in educational management is discussed.