人体外形的相似性

本文首先提出了人体相似性的概念和定义, 并进行了数学论证, 导出了标准人体的数学表达方法,然后, 根据90名志愿者的样本具体计算说明了标准人体尺寸的适用性。本文提出的标准人体尺寸处理方法, 可供人种和体型分类、人体模型与服装设计时确定人体各部尺寸, 为利用人体其他节段估测人全身尺寸的可能性提供参考。最后指出, 表示人体尺寸间相互关系的人体常数是存在的; 在设计人体模型时, 不管模型的比例如何, 所设计模型的人体常数需保持与所代表的人群样本的人体常数一致。     

A mathematical framework for protein structure comparison

Comparison of protein structures is important for revealing the evolutionary relationship among proteins, predicting protein functions and predicting protein structures. Many methods have been developed in the past to align two or multiple protein structures. Despite the importance of this problem, rigorous mathematical or statistical frameworks have seldom been pursued for general protein structure comparison. One notable issue in this field is that with many different distances used to measure the similarity between protein structures, none of them are proper distances when protein structures of different sequences are compared. Statistical approaches based on those non-proper distances or similarity scores as random variables are thus not mathematically rigorous. In this work, we develop a mathematical framework for protein structure comparison by treating protein structures as three-dimensional curves. Using an elastic Riemannian metric on spaces of curves, geodesic distance, a proper distance on spaces of curves, can be computed for any two protein structures. In this framework, protein structures can be treated as random variables on the shape manifold, and means and covariance can be computed for populations of protein structures. Furthermore, these moments can be used to build Gaussian-type probability distributions of protein structures for use in hypothesis testing. The covariance of a population of protein structures can reveal the population-specific variations and be helpful in improving structure classification. With curves representing protein structures, the matching is performed using elastic shape analysis of curves, which can effectively model conformational changes and insertions/deletions. We show that our method performs comparably with commonly used methods in protein structure classification on a large manually annotated data set.     

基于成串刺激计算立即释放囊泡池（RRP）大小的改进方法

突触囊泡的立即释放囊泡池（RRP）概念已被广泛用于突触传递的分析. 基于这些囊泡池中囊泡性质是均匀的假设，通过外推成串刺激累积诱发的突触后兴奋性电流，已经开发了几种确定RRP大小的方法. 然而，使用不同刺激频率确定这些成串刺激得到的RRP大小结果不同. 这种频率依赖性显示了这些估算方法的不完备性，与RRP的定义相矛盾. 因此，我们提出了基于成串刺激计算RRP大小的改进算法. 假设RRP的填充率正比于RRP释放的部分，并且矫正RRP的未使用部分，给出RRP释放过程的完整数学描述，得到具体的解析结果. 与已知的两种常用方法做比较，该方法很好地描述了RRP的释放和填充过程，得到了比较良好的RRP大小和囊泡释放概率大小的评估. 该方法不受刺激频率的条件限制，可以很好地适用于不能给予高频刺激的细胞.     

Defining linear segments in protein structure

The analysis of protein structure using secondary structure line segments has been widely used in many structure analysis and prediction methods over the past 20 years. Its use in methods that compare protein structures at this level of representation is becoming more important as an increasing number of protein structures become determined through structural genomic programmes. The standard method used to define line segments is to fit an axis through each secondary structure element. This approach has difficulties, however, both with inconsistent definitions of secondary structure and the problem of fitting a single straight line to a bent structure. The procedure described here avoids these problems by finding a set of line segments independently of any external secondary structure definition. This allows the segments to be used as a novel basis for secondary structure definition by taking the average rise/residue along each axis to characterise the segment. This practice has the advantage that secondary structures are described by a single (continuous) value that is not restricted to the conventional classes of alpha-helix, 310 and beta-strand. This latter property allows structures without "classic" secondary structures to be encoded as line segments that can be used in comparison algorithms. When compared over a large number of pairs of homologous proteins, the current method was found to be slightly more consistent than a widely used method based on hydrogen bonds.     

为什么在物种概念上难以达成共识?

生物学家通常认为物种是生命多样性的基本单位。然而, 尽管近一个世纪以来生物学家们不断地讨论物种概念问题, 但到目前为止仍然难以形成共识。大多数生物学家关注如何定义物种主要是因为它有非常重要的实践意义, 所以, 不同学者提出的物种概念在很大程度上是基于实践应用上的可操作性, 并且其视角难免受其专业见地以及对形成新物种的进化过程的认识所影响。物种代表了进化过程的一个阶段, 而且不同的“物种”可能处于物种形成这个进化过程的不同阶段。鉴于“定义”实际上是一种类似协议的约定或界定, 任何定义都是一种带有局限性的概括, 因此我们可能很难建立一个与分类实践中千变万化的情况都能完全匹配协调的物种定义。已经提出来的那些物种概念或定义都有其合理性, 但是也没有一个是完美无缺的。认识到这一点很重要, 否则就可能会因为固执地坚持某一特定的物种概念而在物种界定和进化研究中自觉或不自觉地引入错误甚至制造混乱。     

Dynamic structure theory: A structural approach to social and biological systems

The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.     

An algebraic representation of RNA secondary structures.

This paper develops mathematical methods for describing and analyzing RNA secondary structures. It was motivated by the need to develop rigorous yet efficient methods to treat transitions from one secondary structure to another, which we propose here may occur as motions of loops within RNAs having appropriate sequences. In this approach a molecular sequence is described as a vector of the appropriate length. The concept of symmetries between nucleic acid sequences is developed, and the 48 possible different types of symmetries are described. Each secondary structure possible for a particular nucleotide sequence determines a symmetric, signed permutation matrix. The collection of all possible secondary structures is comprised of all matrices of this type whose left multiplication with the sequence vector leaves that vector unchanged. A transition between two secondary structures is given by the product of the two corresponding structure matrices. This formalism provides an efficient method for describing nucleic acid sequences that allows questions relating to secondary structures and transitions to be addressed using the powerful methods of abstract algebra. In particular, it facilitates the determination of possible secondary structures, including those containing pseudoknots. Although this paper concentrates on RNA structure, this formalism also can be applied to DNA.     

An Algebraic Representation of RNA Secondary Structures

Abstract

This paper develops mathematical methods for describing and analyzing RNA secondary structures. It was motivated by the need to develop rigorous yet efficient methods to treat transitions from one secondary structure to another, which we propose here may occur as motions of loops within RNAs having appropriate sequences. In this approach a molecular sequence is described as a vector of the appropriate length. The concept of symmetries between nucleic acid sequences is developed, and the 48 possible different types of symmetries are described. Each secondary structure possible for a particular nucleotide sequence determines a symmetric, signed permutation matrix. The collection of all possible secondary structures is comprised of all matrices of this type whose left multiplication with the sequence vector leaves that vector unchanged. A transition between two secondary structures is given by the product of the two corresponding structure matrices. This formalism provides an efficient method for describing nucleic acid sequences that allows questions relating to secondary structures and transitions to be addressed using the powerful methods of abstract algebra. In particular, it facilitates the determination of possible secondary structures, including those containing pseudoknots. Although this paper concentrates on RNA structure, this formalism also can be applied to DNA