Exact Common Information

This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity $G(X;Y)=\min_{X\to W \to Y} H(W)$ as a natural bound on the exact common information and study its properties and computation. We then introduce the exact common information rate, which is the minimum description rate of the common randomness for the exact generation of a 2-DMS $(X,Y)$. We give a multiletter characterization for it as the limit $\bar{G}(X;Y)=\lim_{n\to \infty}(1/n)G(X^n;Y^n)$. While in general $\bar{G}(X;Y)$ is greater than or equal to the Wyner common information, we show that they are equal for the Symmetric Binary Erasure Source. We do not know, however, if the exact common information rate has a single letter characterization in general

Using string-matching to analyze hypertext navigation

A method of using string-matching to analyze hypertext navigation was developed, and evaluated using two weeks of website logfile data. The method is divided into phases that use: (i) exact string-matching to calculate subsequences of links that were repeated in different navigation sessions (common trails through the website), and then (ii) inexact matching to find other similar sessions (a community of users with a similar interest). The evaluation showed how subsequences could be used to understand the information pathways users chose to follow within a website, and that exact and inexact matching provided complementary ways of identifying information that may have been of interest to a whole community of users, but which was only found by a minority. This illustrates how string-matching could be used to improve the structure of hypertext collections

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose-Einstein condensation are discussed.Comment: 13 pages, 7 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://obelix.physik.uni-osnabrueck.de/~schnack

Isoscaling and the high Temperature limit

This study shows that isoscaling, usually studied in nuclear reactions, is a phenomenon common to all cases of fair sampling. Exact expressions for the yield ratio $R_{21}$ and approximate expressions for the isoscaling parameters $\alpha$ and $\beta$ are obtained and compared to experimental results. It is concluded that nuclear isoscaling is bound to contain a component due to sampling and, thus, a words of caution is issued to those interested in extracting information about the nuclear equation of state from isoscaling.Comment: 7 pages, 1 figur