This paper presents a novel approach to the supervised classification of structured objects such as sequences, trees and graphs, when the input instances are characterized by probability distributions. Distances between distributions are computed via the JensenShannon (JS) divergence, which offers several advantages over the L2 distance or the Kullback-Leibler divergence. The JS divergence indu...

We say that a function f (with values in either R or C) is supported on a set A if it is zero on the complement of this set. The support of f , which we denote by supp(g), is the minimal closed set on which f is supported, equivalently, it is the closure of the set on which f is non-zero. We note that if f ∈ L1(R) is real-valued then the support of f̂ is symmetric around zero (since the real par...

Convexity is a key concept in information theory, namely via the many implications of Jensen’s inequality, such as the non-negativity of the Kullback-Leibler divergence (KLD). Jensen’s inequality also underlies the concept of Jensen-Shannon divergence (JSD), which is a symmetrized and smoothed version of the KLD. This paper introduces new JSD-type divergences, by extending its two building bloc...

Shannon gave a lower bound in 1959 on the binary rate of spherical codes of given minimum Euclidean distance ρ. Using nonconstructive codes over a finite alphabet, we give a lower bound that is weaker but very close for small values of ρ. The construction is based on the Yaglom map combined with some finite sphere packings obtained from nonconstructive codes for the Euclidean metric. Concatenat...

We present a proof that the Shannon switching game on a graph with distinguished vertices A and B has a winning strategy for player Short iff the graph has a subgraph connecting A to B with two edge disjoint spanning trees. This theorem was first proved by Lehman in [11]. The difficulty is that his proof is phrased in terms of matroids and appears very difficult. However, I was able to cull a n...

We present a notion of frame multiresolution analysis on the Heisenberg group, abbreviated by FMRA, and study its properties. Using the irreducible representations of this group, we shall define a sinc-type function which is our starting point for obtaining the scaling function. Further, we shall give a concrete example of a wavelet FMRA on the Heisenberg group which is analogous to the Shannon...

The calculation of a statistical measure of complexity and the Fisher-Shannon information in nuclei is carried out in this work. We use the nuclear shell model in order to obtain the fractional occupation probabilities of nuclear orbitals. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the number of nucleons is observed. The shell structur...