Displaying similar documents to “Optimal quantization for the one–dimensional uniform distribution with Rényi- α -entropy constraints”

Joint Range of Rényi entropies

Peter Harremoës (2009)

Kybernetika

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The exact range of the joined values of several Rényi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied. Like in the case when only two orders of the Rényi entropies are studied, one can parametrize the boundary of the range. An explicit formula for a tight upper or lower bound for one order of entropy in terms of another order of entropy cannot be given.

Time weighted entropies

Jörg Schmeling (2000)

Colloquium Mathematicae

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For invertible transformations we introduce various notions of topological entropy. For compact invariant sets these notions are all the same and equal the usual topological entropy. We show that for non-invariant sets these notions are different. They can be used to detect the direction in time in which the system evolves to highest complexity.

Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro Caputo, Paolo Dai Pra, Gustavo Posta (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known...