人类本性的嬗变与理性信息人假设的现代意义——信息人社会与势科学理论研究之三

基于势科学理论的理性信息人假设从根本上揭示了现代社会人的量性、向性和对称性的复杂本质,其最重要的理论意义和实践价值在于：为社会科学特别是管理学和经济学研究,在一维经济人假设基础上摆脱只能应用低抽象性的运筹学和数理统计带来的种种困惑,从而为应用更高抽象性的数学工具铺垫了逻辑基础,为社会科学在基于信息相互作用的科学化研究开辟了有效路径。     

TESTING SYMMETRY USING A TRIMMED LONGEST RUN STATISTIC

A distribution‐free test is proposed for the symmetry of a continuous distribution about a specified median. The test is based on a longest run statistic on the upper portion of the sequence of ordered ‘centred’ observations in magnitude. The probability distribution of the longest run statistic is derived, and a computationally simple and accurate approximation of the right‐tail probabilities of this statistic is given. This approximation is based on a partial fraction expansion of the corresponding generating function and is derived for use with large samples. The powers of the proposed test, some variations of the test, and other rival tests are investigated under a wide variety of asymmetric alternatives. Simulations indicate that the proposed test is competitive with other tests in terms of power performance.     

Optimal detection of Fechner-asymmetry

We consider a general class of skewed univariate densities introduced by Fechner [1897. Kollectivmasslehre. Engleman, Leipzig], and derive optimal testing procedures for the null hypothesis of symmetry within that class. Locally and asymptotically optimal (in the Le Cam sense) tests are obtained, both for the case of symmetry with respect to a specified location as for the case of symmetry with respect to some unspecified location. Signed-rank based versions of these tests are also provided. The efficiency properties of the proposed procedures are investigated by a derivation of their asymptotic relative efficiencies with respect to the corresponding Gaussian parametric tests based on the traditional Pearson–Fisher coefficient of skewness. Small-sample performances under several types of asymmetry are investigated via simulations.     

对称性视域中的《唯批》和《哲学笔记》原著解读

《唯物主义和经验批判主义（对一种反动哲学的批判）》与《哲学笔记》在马克思主义哲学发展史上虽具有里程碑意义，但新时代下二者在基本思想、主要观点、理论影响、公众评价等多方面亦存在着“矛盾问题域”。这就需要试用对称性方法，将两者结合起来，对列宁原著中的哲学思想进行更全面、更深入地解读，以便进一步挖掘原著深遂的思想和价值，揭示其内在联系和重大意义。     

Application of box-cox transformations to discrimination for the two-class problem

The performance of Box-Cox power transformations in classification using Hinkley's (1975) method is studied. Misclassification probabilities before and after transformation are compared. It is found that the use of Box-Cox transformations can sometimes substantially reduce the error probabilities. Estimates of error probabilities are obtained and certain properties are derived. Examples for a number of distributions are given.     

现代汉语中的对举结构

对举结构有内部对举和外部对举。对举后往往产生新的结构义,在意义上、功能上都具有整体性。对举结构充分体现了对称规律对语法规则的完善和制约作用。     

Bayesian estimation methods for contingency tables

Summary A method of inputting prior opinion in contingency tables is described. The method can be used to incorporate beliefs of independence or symmetry but extensions are straightforward. Logistic normal distributions that express such beliefs are used as priors of the cell probabilities and posterior estimates are derived. Empirical Bayes methods are also discussed and approximate posterior variances are provided. The methods are illustrated by a numerical example.     

基于马尔可夫域变模型的上海股市收益率非线性特征分析

针对股市收益率在不同时期内具有不同的均值、波动性和持续性等非线性特征，引入马尔可夫域变模型（MRSM）对上海股市收益率的均值与波动性的对应关系以及高、低收益率状态转换特征进行分析，结果表明马尔可夫域变模型与GARCH类模型相比较，显著地提高了对股票市场行为的描述能力。它不仅可以从动态角度明确刻画金融市场的“收益与风险”相对称的特征，而且可测定不同状态持续的可能性和由一种状态转向另一种状态的概率。     

广义相对论的超维观念和降维方法

广义相对论运用降维方法研究空间弯曲导致的超维空间。球状有限无界闭合空间的提出实际上赋予超维物理意义。球状空间不同的对称性导致对空间第 4维的不同理解 :镜像对称使“无界”变为“镜界” ,“穿越赤道”变为“自我碰撞” ;中心对称使第 4维成为与原有 3维一样实在的空间维。弯曲状况不同的空间并存可以明显表现超 3维空间。近似开放空间的不均匀收缩导致局部闭合为“空洞” ,可作为显示超维的模型。宇宙可能包含无数并存的空间 ;具体时空的有限性 ,不能作为否认宇宙时空无限性的依据     

Measure of Asymmetry for Square Contingency Tables Having Ordered Categories

For the analysis of square contingency tables with nominal categories, Tomizawa and coworkers have considered measures that represent the degree of departure from symmetry. This paper proposes a measure that represents the degree of asymmetry for square contingency tables with ordered categories (instead of those with nominal categories). The measure proposed is expressed using the Cressie–Read power-divergence or Patil–Taillie diversity index, defined for the cumulative probabilities that an observation falls in row (column) category i or below and column (row) category j (> i ) or above. The measure depends on the order of listing the categories. It should be useful for comparing the degree of asymmetry in several tables with ordered categories. The relationship between the measure and the normal distribution is shown.