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Entropy 2006, 8(2), 88-109; doi:10.3390/e8020088

Symmetry Studies and Decompositions of Entropy

The University of Illinois at Chicago Eye Center, 1855 W. Taylor St., Chicago, IL 60612, USA.
Received: 13 January 2006 / Accepted: 24 April 2006 / Published: 14 June 2006
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Abstract

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,...,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.
Keywords: group representation; characters; canonical decomposition; invariance; Kullback's divergence; visual acuity; Sloan fonts. group representation; characters; canonical decomposition; invariance; Kullback's divergence; visual acuity; Sloan fonts.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Viana, M. Symmetry Studies and Decompositions of Entropy. Entropy 2006, 8, 88-109.

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