The software Randentropy is designed to estimate inequality in a random system where several individuals interact moving among many communities and producing dependent quantities of an attribute. overall assessed by computing the Random Theil’s Entropy. Firstly, estimates piecewise homogeneous Markov chain identifying change-points relative transition probability matrices. Secondly, it multivar...

We critique the measure of complexity introduced by Shiner, Davison, and Landsberg [Phys. Rev. E 59, 1459 (1999)]. In particular, we point out that it is over universal, in the sense that it has the same dependence on disorder for structurally distinct systems. We then give counterexamples to the claim that complexity is synonymous with being out of equilibrium: equilibrium systems can be struc...

We present a coding measure which is based on the statistical properties of the stop codons, and that is able to estimate accurately the variation of coding content along an anonymous sequence. As the stop codons play the same role in all the genomes (with very few exceptions) the measure turns out to be species-independent. We show results both for prokaryotic and for eukaryotic genomes, indic...

A “concurrency measure” provides an objective means of comparing the level of parallelism achievable by a distributed computation. To date such measures have only been applicable after a computation has successfully terminated. This paper develops a notion of “observed concurrency” that can be continuously evaluated as a computation proceeds. It is suitable for nested parallelism and evaluation...

Consider n points distributed uniformly in [0, 1]d. Form a graph by connecting two points if their mutual distance is no greater than r(n). This gives a random geometric graph, G(Xn; r(n)), which is connected for appropriate r(n). We show that the spectral measure of the transition matrix of the simple random walk (srw) on G(Xn; r(n)) is concentrated, and in fact converges to that of the graph ...

The intersection exponent for simple random walk in two and three dimensions gives a measure of the rate of decay of the probability that paths do not intersect. In this paper we show that the intersection exponent for random walks is the same as that for Brownian motion and show in fact that the probability of nonintersection up to distance n is comparable (equal up to multiplicative constants...