The Analogues of Entropy and of Fisher's Information Measure in Free Probability Theory III: The Absence of Cartan Subalgebras.
The analogues of entropy and of Fisher's information measure in free probability theory, II.
The Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions.
The entropy and redundancy of normalized database structures
The entropy of Łukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
The entropy of Łukasiewicz-languages
The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
The fundamental equation of information and its generalizations.
The irrelevant information principle for collective probabilistic reasoning
Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, , as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach...
The mutual information estimation in the sampling with replacement
The mutual information. Estimation in the sampling without replacement
The Shannon information on a Markov chain approximately normally distributed
The Shannon kernel of a non-negative information function.
The uncertainty measure of hierarchical quotient space structure.
The Uncertainty Principle: A Mathematical Survey.
Théorème ergodique presque sous-additif et convergence en moyenne de l'information
Time-frequency representations : wavelet packets and optimal decomposition
Tropical probability theory and an application to the entropic cone
In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.