Symmetry studies and decompositions of entropy
type: Item
instance of: scholarly article
title: Symmetry studies and decompositions of entropy
zbMATH Open document ID: 1135.94319
published in: Entropy
publication date: 2008-05-22T00:00:00Z
review text: Summary: This paper describes a group-theoretic method for decomposing the entropy of a finite ensemble when symmetry considerations are of interest. The cases in which the elements in the ensemble are indexed by \(1, 2, \dots, n\) and by the permutations of a finite set are considered in detail and interpreted as particular cases of ensembles with elements indexed by a set subject to the actions of a finite group. Decompositions for the entropy in binary ensembles and in ensembles indexed by short DNA words are discussed. Graphical descriptions of the decompositions of the entropy in geological samples are illustrated. The decompositions derived in the present cases follow from a systematic data analytic tool to study entropy data in the presence of symmetry considerations.
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 37A35
Mathematics Subject Classification ID: 54C70
Mathematics Subject Classification ID: 92C20
zbMATH DE Number: 5278285
zbMATH Keywords: group representation
zbMATH Keywords: characters
zbMATH Keywords: canonical decomposition
zbMATH Keywords: invariance
zbMATH Keywords: Kullback's divergence
zbMATH Keywords: visual acuity, Sloan fonts
author: Marlos A. G. Viana
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e8020088
OpenAlex ID: W2053484202
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DOI: 10.3390/E8020088
description: scientific article; zbMATH DE number 5278285