We consider two notions describing how one finite graph may be larger than another. Using them, we prove several theorems for such pairs that compare the number of spanning trees, the return probabilities of random walks, and the number of independent sets, among other combinatorial quantities. Our methods involve inequalities for determinants, for traces of functions of operators, and for entr...

We characterize pairs of convex sets A, Bin the k-dimensional space with the property that every probability distribution (p 1 ,. • • , P~<) has a repsesentation p, =a;· b;, a EA, bE B. Minimal pairs with this property are antiblocking pairs of convex corners. This result is closely related to a new entropy concept. The main application is an information theoretic characterization of perfect gr...

Several counterparts of Bayesian networks based on different paradigms have been proposed in evidence theory. Nevertheless, none of them is completely satisfactory. In this paper we will present a new one, based on a recently introduced concept of conditional independence. We define a conditioning rule for variables, and the relationship between conditional independence and irrelevance is studi...

Classically, Shannon entropy was formalized over discrete probability distributions. However, the concept of entropy can be extended to continuous distributions through a quantity known as continuous (or differential) entropy. The most common definition for continuous entropy is seemingly straightforward; however, further analysis reveals a number of shortcomings that render it far less useful ...

This article presents new sensitivity measures in reliability-oriented global analysis. The obtained results show that the contrast and newly proposed (entropy two others) effectively describe influence of input random variables on probability failure Pf. measure builds Sobol, using variance binary outcome as either a success (0) or (1). In Bernoulli distribution, Pf(1 ? Pf) discrete entropy—Pf...

In this paper the notion of robust entropy and subsequently, robust entropy rate for a family of discrete time uncertain sources is introduced. When the uncertainty is described by a relative entropy constraint between the set of uncertain source densities and a given nominal source density, the solution to this robust notion of information is presented and its connection with other notions of ...

This paper extends maximum entropy estimation of discrete probability distributions to the continuous case. This transition leads to a nonparametric estimation of a probability density function, preserving the maximum entropy principle. Furthermore, the derived density estimate provides a minimum mean integrated square error. In a second step it is shown, how boundary conditions can be included...

Abstract. We study a system of conservation laws that describes multispecies kinematic flows with an emphasis on models of multiclass traffic flow and of the creaming of oil-in-water dispersions. The flux can have a spatial discontinuity which models abrupt changes of road surface conditions or of the cross-sectional area in a settling vessel. For this system, an entropy inequality is proposed ...

The coin-position entanglement generated by the evolution operator of a discrete–time quantum walk is quantified, using the von Neumann entropy of the reduced density operator (entropy of entanglement). In the case of a single walker, the entropy of entanglement converges, in the long time limit, to a well defined value which depends on the initial state. Exact expressions are obtained for loca...

Information entropy is one of crucial concepts in modern information theory and related fields. Over the years a large number of methods for reliable estimation of information entropy have been invented. In this paper we introduce a method for the estimation entropy of binary streams based on binary decision diagrams. Binary decision diagrams are an efficient method of representation of discret...