Entropies, dimensions et représentation d'observations
Entropies of vague information sources
The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entropy - the main of them regard the formal aspects of the fundamental concepts. Namely their rather additive...
Entropy at a weight-per-symbol and embeddings of Markov chains.
Entropy generation in a model of reversible computation
We present a model in which, due to the quantum nature of the signals controlling the implementation time of successive unitary computational steps, physical irreversibility appears in the execution of a logically reversible computation.
Entropy jumps for isotropic log-concave random vectors and spectral gap
We prove a quantitative dimension-free bound in the Shannon-Stam entropy inequality for the convolution of two log-concave distributions in dimension d in terms of the spectral gap of the density. The method relies on the analysis of the Fisher information production, which is the second derivative of the entropy along the (normalized) heat semigroup. We also discuss consequences of our result in the study of the isotropic constant of log-concave distributions (slicing problem).
Entropy lower bounds related to a problem of universal coding and prediction.
Entropy of complete fuzzy partitions
Entropy of random walk range
We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd. We show that for d≥3, the entropy is of order n. For d=2, the entropy is of order n/log2n. These values are essentially governed by the size of the boundary of the trace.
∈-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms
Entropy of -sums and -products of - fuzzy numbers
In the paper the entropy of – fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of – fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of –sums and –products of – fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters without the...
Entropy of Type (a, ß) and Other Generalized Measures in Information Theory.
Entropy-like functionals: conceptual background and some results
We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy considered in the author’s previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded.
Enumeration of binary trees and universal types.
Epsilon-rates, epsilon-quantiles, and group coding theorems for finitely additive information sources
Equivalences between elliptic curves and real quadratic congruence function fields
In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...
Ergodic behavior of graph entropy.
Ergodic decomposition of entropy
Ergodic theory, entropy, and coding problems of information theory
Ergodicity and extremality of AMS sources and channels.
Errata to my paper "On some functional equations and their applications".