谈谈昆虫生态学中的数学模型(一)

<正> 一、什么是数学模型 “数学模型”有不同的定义。不过,无论如何定义它,总应包括两个基本点:①数学模型是由一定的数学符号按照一定的数学结构组成的。由于数学是“辩证的辅助工具和表现方式”,所以数学模型一般都具有普适性,这一点使得数学模型同“概念模型”和“物理模型”相区别。②数学模型是用来反映客观事物之间的关系以及预测其变化规律的。所以,一个好的生态学数学模型在解决具体生态学问题时,每个     

生物数学方法

将数学知识应用于生物科学产生了生物数学的边缘科学。按研究对象和任务的不同,生物数学可分为数学生物学和生物数学两个分支。数学生物学主要是指生物各个学科应用数学方法所形成的一些新的生物学分支,例如数值分类学、数量进化论、数学生态学,数量遗传学、数量生理学、数量仿生学等等;生物数学主要是指用于生物科学研究的一些数学理论和方法,诸如生物统计学、生物概率论、生物数学模型、电子计算机     

谈谈昆虫生态学中的数学模型(二)

<正> 四、昆虫生态学中的数学模型有哪些类型 数学在昆虫生态学中的应用是极其广泛的,很难精确指出昆虫生态学中的数学模型一共有多少类型。事实上,关于数学模型的种类,各种教科书和文献所做的论述是五花八门的。这里,我们先从基本数学模型空间介绍起,就是说,从三个数学模型谱(spectrums of mathematicalmodels)来谈这个问题,供大家讨论。 第一个模型谱 确定性模型(deterministicmodels)与随机模型(stochastic models)谱。确定性模型是用来处理必然现象的。所谓必然现     

《数学生态学模型与研究方法》简介

《数学生态学模型与研究方法》一书,由中国科学院数学研究所陈兰荪编著,此书1988年由科学出版社出版。全书共404页,书末附参考文献62篇并备有附录,该书利用常微分方程的理论和方法,讨论了生态学模型的建立及其研究方     

书讯

☆陈兰荪著《数学生态学模型与研究方法》一书,即将由科学出版社出版。它将结合作者自己的研究成果详细介绍生态学中微分方程模型及差分方程的建立方法,以及如何去研究模型所涉及的稳定性、全局稳定性、时滞影响、极限所与空间周期解问题,还介绍了混沌现象的研究近况。 (吕虹) ☆一本兼及确定性模型及随机模型并可作为教学参考书的专著《生态数学模型》将由海洋出版社出版,作者为张炳根。全书共13万字,并含有习题。(鲁长海)     

邻体干扰模型的改进及其在营林中的应用

本文研究了植物群落中优势种个体间的相互干扰问题。在前人工作基础上提出了邻体干扰指数的改进模型及野外资料搜集方法。保证了数学模型的逻辑一致性,增加了生态学的解释意义。本文还讨论了邻体干扰效应模型的选择问题,进而得出了约束条件下的材积增长的数学优化模型。以四川省重庆市缙云山马尾松林为例,进行了实例研究。     

注重实验生态学改进人工气候箱应用的研究

实验生态学的研究是数学生态学和理论生态学发展的基础,而实验生态学中常用的人工气候箱的设置和应用尤为重要,文中报道了对上述设备进行完善和改进的研究.     

邻体干扰模型的改进及其在营林中的应用

 本文研究了植物群落中优势种个体间的相互干扰问题。在前人工作基础上提出了邻体干扰指数的改进模型及野外资料搜集方法。保证了数学模型的逻辑一致性,增加了生态学的解释意义。本文还讨论了邻体干扰效应模型的选择问题,进而提出了约束条件下的材积增长的数学优化模型。以四川省重庆市缙云山马尾松林为例,进行了实例研究。     

应用生态学的现状与发展

应用生态学可定义为研究协调人类与生物、资源、环境之间关系以达到和谐目的的科学。生态学已成为包含上百个分支的庞大学科, 当前的弱点和存在问题主要是:缺乏科学的严格性、实验技能和应用技术薄弱以及生态学在迅速扩展过程中正失去自身的学科边界。数学和计算机技术在生态学研究和实践中的应用, 生态实验、宏观生态学研究和生态工程技术的研究和发展可能是未来应用生态学研究最活跃的领域。     

《基础数学生态学》简介

现代生态学的研究中,数学愈来愈起着重要的作用。有人曾将生态学描述成为实质上是一门数学,虽然似乎有些过激,但可见其份量。由于生物科学的思维方式与数学的高度抽象、严格的逻辑推理的思维方式差异甚大,因而许多生物科学家对数学有某种恐畏(math anxiety)。John Vandermere教授为大家带来了福音,他于1981年出版了《基础数学生态学》一书。     

昆虫数学形态学研究及其应用展望

数学形态学是用数学方法描述或分析一个物体图象的形状的理论和方法,是图象处理和图象识别技术的发展,但在生物学当中的应用还很有限。本文介绍了一个新的分支学科——昆虫数学形态学,包括三方面的内容：①昆虫数学形态学技术研究,涉及昆虫图象数字化技术和昆虫图象处理与识别技术;②昆虫数学形态学理论研究,主要以昆虫图象的解释和理解研究及昆虫数学形态学与分类学等学科的关系研究为主;③昆虫和昆虫数学形态学应用基础研究,涉及昆虫数学形态学数据库及其分析软件开发,昆虫图象的机器学习和计算机视觉等内容。昆虫数学形态学理论和方法与计算机视觉技术相结合,在害虫虫情监测、昆虫多媒体专家系统的构建等方面具有广阔的应用前景。     

关于基本物理常数之间的定量关系

本研究揭示出了基本物理常数之间的定量关系。基本物理常数是通过两个普适的数学常数”和em（e＆在本文中代表数学常数e）相联系的。由此一个基本物理常数可以由其它的基本物理常数和这两个数学常数计算得到。例如,普朗克常数h可以通过电子的电荷m。和质量,光速c以及数学常数”和e＆来计算,即h=2×10-12咖。c3π3-3e数。     

Computational methods in synthetic biology

We discuss how a theoretical synthetic biology research programme may liberate empiricism in biological sciences beyond the unaided human brain. Because synthetic biological systems are relatively small and largely independent of evolutionary contexts, they can be represented with mathematical models strongly founded on first principles of molecular biology and laws of statistical thermodynamics. A universal mathematical formalism for describing synthetic constructs may then be plausibly used to explain in unambiguous, quantitative terms how biological phenotypic complexity emerges as a result of well-defined biomolecular interactions. SynBioSS, a publicly available software package, is described that implements this mathematical formalism.     

A history of the study of solid tumour growth: The contribution of mathematical modelling

A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elucidate and interpret these experimental findings. Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development. This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time. Most importantly these mathematical investigations are interwoven with the associated experimental work, showing the crucial relationship between experimental and theoretical approaches, which together have moulded our understanding of tumour growth and contributed to current anti-cancer treatments. Thus, a selection of mathematical publications, including the influential theoretical studies by Burton, Greenspan, Liotta et al., McElwain and co-workers, Adam and Maggelakis, and Byrne and co-workers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radio-sensitivity, Folkman on angiogenesis, Dorie et al. on cell migration and a wide variety of other crucial discoveries. In this way the development of this field of research through the interactions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease.     

Mathematical Model for Skeletal Muscle to Simulate the Concentric and Eccentric Contraction

Skeletal muscles are responsible for the relative motion of the bones at the joints and provide the required strength. They exhibit highly nonlinear mechanical behaviour and are described by nonlinear hyperelastic constitutive relations. It is distinct from other biological soft tissue. Its hyperelastic or viscoelastic behaviour is modelled by using CE, SEE, and PEE. Contractile element simulates the behaviour of skeletal muscle when it is subjected to eccentric and concentric contraction. This research aims to estimate the stress induced in skeletal muscle in eccentric and concentric contraction with respect to the predefined strain. With the use of mathematical model for contraction of skeletal muscle for eccentric and concentric contraction, the stress induced in the skeletal muscle is estimated in this research. Mathematical model is developed for the muscle using EMG signals and Force-velocity relationship calculated. With the use of force-velocity of contraction of muscle, mathematical model is developed. This can be useful to understand the mechanical behaviour of skeletal muscles in eccentric and concentric contraction with clinical relevance. Authors are further working to develop the mathematical model with torsion force with proper activation function of muscle and experimentation for extraction of the anisotropic mechanical properties of skeletal muscle.     

Adding Cognition to the Formula for Culturally Relevant Instruction in Mathematics

Although equity is one of the goals of the mathematics reform movement, there has been little research done to develop programs that meet the needs of specific cultural groups. By studying how mathematical knowledge is developed in the course of everyday life, it is possible to change mathematics instruction to enhance mathematical achievement. In a series of research projects with Native Hawaiian children, ethnographic information and cognitive studies of mathematical thinking guided a program to develop culturally relevant mathematics teaching. The approach taken in this study is compared to other recent efforts to develop culturally relevant instruction in mathematics.     

An optimal stopping approach for onset of fish migration

Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration.     

Systems biology and cancer: promises and perils

Systems biology uses systems of mathematical rules and formulas to study complex biological phenomena. In cancer research there are three distinct threads in systems biology research: modeling biology or biophysics with the goal of establishing plausibility or obtaining insights, modeling based on statistics, bioinformatics, and reverse engineering with the goal of better characterizing the system, and modeling with the goal of clinical predictions. Using illustrative examples we discuss these threads in the context of cancer research.     

农业废弃物养分循环利用技术模式评估模型的研究进展

农业废弃物的养分循环利用技术模式是实现农业循环经济的重要手段,其评估模型为优化养分循环利用技术提供了重要支撑。本文总结了农业废弃物养分循环技术模式评估框架、评估模型及评价指标、模型的数据源及其不确定性分析,以及模型应用尺度的研究进展。当前,常用于评估养分流动的模型主要是过程数学模型和产业生态学模型。过程数学模型和产业生态学模型在评估结果的可靠性和模拟尺度上存在较大差异,前者主要集中在实验室或中试规模,精度较高;后者可以实现从微观到宏观的多尺度模拟,数据的获取方式导致其具有较高的不确定性。最后,本文对农业废弃物养分循环利用技术评估模型的研究进行展望,提出为了在区域尺度上实现对农业生产系统废弃物资源化利用技术的准确评估,可以将过程数学模型与工业生态学模型相结合,建立可靠的模型框架和数据库,同时,在工厂、农场、村落、乡镇、区域等地理尺度进行模型拓展研究。