A General Framework of Generating Estimation Functions for Computing the Mutual Information of Terms

Computing statistical dependence of terms in textual documents is a widely studied subject and a core problem in many areas of science. This study focuses on such a problem and explores the techniques of estimation using the expected mutual information measure. A general framework is established for tackling a variety of estimations: (i) general forms of estimation functions are introduced; (ii) a set of constraints for the estimation functions is discussed; (iii) general forms of probability distributions are defined; (iv) general forms of the measures for calculating mutual information of terms (MIT) are formalised; (v) properties of the MIT measures are studied and, (vi) relations between the MIT measures are revealed. Four estimation methods, as examples, are proposed and mathematical meanings of the individual methods are respectively interpreted. The methods may be directly applied to practical problems for computing dependence values of individual term pairs. Due to its generality, our method is applicable to various areas, involving statistical semantic analysis of textual dat

Fermions Tunneling from Apparent Horizon of FRW Universe

In the paper [arXiv:0809.1554], the scalar particles' Hawking radiation from the apparent horizon of Friedmann-Robertson-Walker(FRW) universe was investigated by using the tunneling formalism. They obtained the Hawking temperature associated with the apparent horizon, which was extensively applied in investigating the relationship between the first law of thermodynamics and Friedmann equations. In this paper, we calculate Fermions' Hawking radiation from the apparent horizon of FRW universe via tunneling formalism. Applying WKB approximation to the general covariant Dirac equation in FRW spacetime background, the radiation spectrum and Hawking temperature of apparent horizon are correctly recovered, which supports the arguments presented in the paper [arXiv:0809.1554].Comment: 8 pages, no figure