论社会结构的对称与非对称

对作为自然界中一种普遍现象和联系的对称与非对称，自然科学已进行了较为深入持久的研究，并且取得了可喜的成绩。但对称与非对称是否也存在于人类社会，它们在自然界中所形成的规律，是否也适用于人类社会？本文试图通过对社会结构中的对称与非对称现象及其规律的考察，进一步揭示社会发展的内在原因和外在表现，以及对称、非对称与社会规律的关系。     

Global Markov models for eukaryote nucleotide data

We discuss the quite remarkable global Markovian structure of the nucleotides in eukaryotic DNA strands with special emphasis on (i) the similarity property for intra- species chromosomes and (ii) the reversibility property for the two (complementary) strands of a chromosome.     

对称——东山魁夷绘画生涯中重要的美学语言

以东山魁夷的作品为立足点,从理论的角度分析、着手,从对称美是日本画家东山魁夷之画面构成的主要表现手段为基础论据,论证了对称是东山魁夷绘画生涯中重要的美学语言之理论的成立.并点到为止地揭示了对称也是东山魁夷绘画成功的一个"秘密".     

A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951 Freeman , G. H. , Halton , J. H. ( 1951 ). Note on an exact treatment of contingency tables, goodness of fit and other problems of significance . Biometrika 38 : 141 – 149 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948 Bowker , A. H. ( 1948 ). A test for symmetry in contingency tables . Journal of the American Statistical Association 43 : 572 – 574 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Hollander, 1971 Hollander , M. ( 1971 ). A nonparametric test for bivariate symmetry . Biometrika 58-1 : 203 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]; and its improvement given in Krampe and Kuhnt, 2007 Krampe , A. , Kuhnt , S. ( 2007 ). Bowker's test for symmetry and modifications within the algebraic framework . Computational Statistics and Data Analysis 51 : 4124 – 4142 .[Crossref], [Web of Science ®] , [Google Scholar]). Our proposal represents a competitive option as a test for symmetry.     

On Robust and Efficient Estimation of the Center of Symmetry

In this article, a class of estimators of the center of symmetry based on the empirical characteristic function is examined. In the spirit of the Hodges–Lehmann estimator, the resulting procedures are shown to be a function of the pairwise averages. The proposed procedures are also shown to have an equivalent representation as the minimizers of certain distances between two corresponding kernel density estimators. An alternative characterization of the Hodges–Lehmann estimator is established upon the use of a particularly simple choice of kernel.     

The Characterization of the Symmetric Lorenz Curves by Doubly Truncated Mean Function

We characterize symmetric Lorenz curves by the relation m(x, μ²/x) = μ (where μ =E(X) and m(x, y) = E(X | x ≤ X ≤ y) is the doubly truncated mean function). We establish that the points of the r.v. which generate the symmetric points on the Lorenz curve are x and μ²/x, and that all the distribution functions defined on the same support which are generators of the symmetric Lorenz curves have the same mean. We obtain the conditions under which doubly truncated distributions generate symmetrical Lorenz curves.     

Antipodally symmetric distributions for orientation statistics

The conventional antipodally symmetric Bingham matrix distribution on the Stiefel manifold is generalized. Large sample maximum likelihood estimation and uniformity tests are discussed, and a parametric model for axial orientations (X-shapes) is suggested. A generalization of the Khatri-Mardia matrix distribution is developed to provide a model suitable for hybrids (T-shapes).     

物质世界演化机制:从对称性到对称性破缺

日本三位科学家因在量子物理世界中发现自发对称性破缺机制而同时获得2008年诺贝尔物理学奖,它引起科学家对宇宙起源和物质演化机制的关注和认识.本文对传统的对称性理论进行了系统梳理,从科学思维方法的角度探讨宇宙起源和物质演化机制的认识逻辑,围绕对称性和非对称性、以及对称性破缺的理论思维和辩证思维的特点进行了分析,并探讨了从对称性到对称性破缺认识过程中的认识论价值和方法论意义.     

A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs

Measures of distributional symmetry based on quantiles, L-moments, and trimmed L-moments are briefly reviewed, and (asymptotic) sampling properties of commonly used estimators considered. Standard errors are estimated using both analytical and computer-intensive methods. Simulation is used to assess results when sampling from some known distributions; bootstrapping is used on sample data to estimate standard errors, construct confidence intervals, and test a hypothesis of distributional symmetry. Symmetry measures based on 2- or 3-trimmed L-moments have some advantages over other measures in terms of their existence. Their estimators are generally well behaved, even in relatively small samples.     

A class of copulas with piecewise linear horizontal sections

We introduce the class of bivariate copulas with piecewise linear horizontal sections whose graph is composed, at most, of two segments. It is a wide class of copulas which contains some known copulas. We study several properties of the copulas in the new class concerning absolute continuity, singular components, measures of association, concordance ordering, dependence concepts and symmetry. Finally, we provide several examples.