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.
Un contraste de normalidad basado en la energía informacional.
En este trabajo se presenta un contraste de normalidad basado en la Energía Informacional de forma paralela al obtenido por Vasicek (1976) basándose en la Entropía de Shannon. Se estima la potencia de este contraste para diversas alternativas comparándola con la de otros contrastes de normalidad. Estos resultados permiten afirmar que este contraste es preferido en algunos casos a algunos contrastes clásicos.
Una medida de incertidumbre probabilística para sucesos difusos.
El objetivo de este artículo es proponer una medida de incertidumbre asociada a un conjunto difuso, de un referencial finito, que generalice la entropía de Shannon; es decir, que además de considerar la distribución de probabilidades definida en el referencial considere también la función de pertenencia del conjunto difuso.Posteriormente se estudian algunas propiedades de la medida propuesta.
Une condition asymptotique pour le calcul de constantes de Sobolev logarithmiques sur la droite
On présente une formule explicite pour la constante de Sobolev logarithmique correspondant à des diffusions réelles ou à des processus entiers de vie et de mort, sous l’hypothèse que certaines quantités, naturellement associées à des inégalités de Hardy dans ce contexte, approchent leur supremum au bord de leur domaine de définition. La preuve se ramène au cas de la constante de Poincaré, à l’aide de comparaisons exactes entre entropie et variances appropriées.
Universally typical sets for ergodic sources of multidimensional data
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an with...
Velocity and Entropy of Motion in Periodic Potentials
This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti.We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities.The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.