Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

例析五华话的量词重叠

五华话的量词重叠形式颇有特色,有"从"形式、"一AA哩"形式、"A实A哩"形式。三种重叠形式在句法功能和语法意义方面有一定的差异。     

An Informational Approach to the Sinusoidal Law of Photon Polarization

The photon polarization law po ＝ sin2θ is derived from a simple informational consideration by twomethods: The first is via an intuitive principle of mininum Fisher information, the second is via a symmetry andinvariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herselfas deepas possible while obeying some regular conditions.     

Hypothesis testing for the generalized multivariate modified Bessel model

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T²-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T²-statistic for the Behrens–Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model.     

关于渐近中位无偏估计的渐近效率(英文)

本文在几种重要的分布族中,给出了渐近中位无偏估计的渐近效率的一种定义。给出了如下一些结果：在单参数族中,提出了构造渐近有效的渐近中位无偏估计的一种方法,在具有共同支撑集的分布族中,论证了渐近中位无偏有效估计与ＢＡＮ估计之间的等价值;而在非共同支撑集的截断族中,对一般的参数向量函数构造了它们的渐近中位无偏估计,并且计算出了它们的渐近效率。     

Net information measures for modified Yukawa and Hulthén potentials

The dimensional analyses of the position and momentum variances‐based quantum mechanical Heisenberg uncertainty measure, as well as the entropic information measures given by the Shannon information entropy sum and the product of Fisher information measures are carried out for two widely used nonrelativistic isotropic exponential‐cosine screened Coulomb potentials generated by multiplying the superpositions of (i) Yukawa‐like, ?Z(e^?μr/r), and (ii) Hulthén‐like, ?Zμ(1/(e^μr ? 1)), potentials by cos(bμr) followed by addition of the term a/r², where a and b ≥ 0, μ are the screening parameters and Z, in case of atoms, denotes the nuclear charge. Under the spherical symmetry, all the information measures considered are shown to be independent of the scaling of the set [μ, Z] at a fixed value of μ/Z, a, and b and the other parameters defining the superpositions of the potentials. Numerical results are presented, which support the validity of the scaling properties. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

分类器系统综述

分类器系统(Classifier System)是一种基于遗传算法(GA)的规则系统,本文综述了分类器系统的基本原理和研究状况,并提出了需进一步研究的问题.     

余江话的"里"尾

余江话的“里”尾可加在名词、动词、形容词性成分或动词性结构后面构成名词,能起到区别事物、表示词性变化、指小、亲昵或纯粹作名词的标志等作用;在使用原则上名词“里”尾与普通话“子”尾同中有异;“里”尾名词所指事物范围广(可分为人名、人品、疾病、人体、服饰、家俱生活用品、房屋建筑、动物及其他等九类)。“里”尾亦可加在形容性成分后构成形式多样的形容词的生动形式,有表示词性变化、附加评价意义、扩大语法功能等作用。“里”尾还能通过特定的形式,与个体量词、集合量词、部分量词、容器量词、度量量词及自主量词等结合,表示相应的语法意义。     

浅谈汉语陪伴型名量词的起源

对从甲骨卜辞以来的文献资料加以考察可以看出,汉语陪伴名量词在“S.VP1.O.VP2”的句法结构的VP2位置上形成。推动其形成的原因在于,汉语音节变化导致谓语位置的单音节数词不能再形成一个自然音步而必须后附一个语义表达上并不起作用的词。