Discriminant versus rough sets approach to vague data analysis

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.     

不协调目标信息系统知识约简的比较研究

研究不协调目标信息系统的各种知识约简之间的关系。证明分布约简既是β上分布约简，也是β下分布约简，并且在一定条件下,β上、下分布约简与不协调目标信息系统的分配约简和最大分布约简等价。     

Direct approach to quantum extensions of Fisher information

By manipulating classical Fisher information and employing various derivatives of density operators, and using entirely intuitive and direct methods, we introduce two families of quantum extensions of Fisher information that include those defined via the symmetric logarithmic derivative, via the right logarithmic derivative, via the Bogoliubov-Kubo-Mori derivative, as well as via the derivative in terms of commutators, as special cases. Some fundamental properties of these quantum extensions of Fisher information are investigated, a multi-parameter quantum Cramér-Rao inequality is established, and applications to characterizing quantum uncertainty are illustrated.      

用平均有效信息量评价环境噪声的尝试

本文认为噪声是一种声信息，因此，运用信息理论建立起了一种新的环境噪声评价量模式－平均有效信息量，通过实际应用，表明其能较地反映了环境噪声水平。     

Inference for earthquake models: A self-correcting model

Questions of asymptotic inference are discussed for a point process model in which the conditional intensity function increases monotonically between events and drops by determined (nonrandom) amounts after each event. Parameter estimates are shown to be consistent and, except under the null hypothesis of a Poisson process, normally distributed. Under the null hypothesis, however, the Hessian matrix is not asymptotically constant, and the limiting distribution of the likelihood ratio statistics is not χ², but has a form related to that of the Cramer-von Mises ω² statistic for the test of goodness of fit.     

On the impact of an event

Given an information structure a function that measures how the inferences made by the agents spread among the states is defined; it specifies for each event its impact at each state, for each agent. Several properties are established. Received November 1994/Revised version September 1996     

Limiting properties of some measures of information

In this paper we investigate the limiting behaviour of the measures of information due to Csiszár, Rényi and Fisher. Conditions for convergence of measures of information and for convergence of Radon-Nikodym derivatives are obtained. Our results extend the results of Kullback (1959,Information Theory and Statistics, Wiley, New York) and Kirmani (1971,Ann. Inst. Statist. Math.,23, 157–162).     

Operator-valued free Fisher information and modular frames

We introduce the operator-valued free Fisher information for a random variable in an operator-valued noncommutative probability space and point out its relations to the amalgamated freeness. Using M. Frank and D. Larson's modular frame notion we can construct the conjugate variable for an operator-valued semicircle variable with conditional expectation covariance. Then we obtain its free Fisher information and show it is equal to the index of the conditional expectation. At last the conjugate variable with respect to a modular frame operator for a semicircle variable is also constructed.

     

Statistical thermodynamic formalism in the solution of information theory problems

This is the first of several papers dealing with the application of statistical thermodynamic methodology to the solution of coding and communication theory problems. Emphasis is placed on the various ensemble techniques of statistical mechanics, the words or samples of a message taking the place of molecules in the prototype physical system. Analogs of temperature, internal energy, pressure, chemical potential, volume, entropy, etc., are developed. The isomorphism with thermodynamics is complete and these quantities transform (for example, by partial differentiation) in exactly the same way as the prototype physical quantities. The methods are nicely applicable to coding cases involving sources with memory, in which case, correlation can be discussed in terms of analog coupling energies between signals or words so that the store of many-body-problem techniques can be used. In addition, the manipulative freedom stemming from the possibility of choosing from a multiplicity of ensembles constrained by intensive parameters proves a distinct advantage. A concrete example dealing with the choice of a compact code for a nonextended source with memory is presented. The compact code is derived, and some discussion is given concerning the breadth of its power spectrum. In a following paper, its autocorrelation function within the framework of pulse code modulation is derived and transformed by Wiener theory so that the power spectrum is directly exhibited (along with the spectra for several other cases).Research supported under AFOSR Grant No. 70-1877. The present work is contribution No. 2643 of the Department of Chemistry, University of California-Los Angeles.