Symmetry Studies and Decompositions of Entropy

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...

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Published inEntropy (Basel, Switzerland) Vol. 8; no. 2; pp. 88 - 109
Main Author Viana, Marlos
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 14.06.2006
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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.
AbstractList 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.
Author Viana, Marlos
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Cites_doi 10.1214/ss/1177013114
10.1214/lnms/1215540653
10.1214/aoms/1177706800
10.1007/978-94-009-4109-0
10.1111/j.2517-6161.1988.tb01707.x
10.1007/978-1-4613-8528-8
10.2307/3211873
10.1364/JOSAA.22.002483
10.1214/aos/1176343004
10.1214/cbms/1462061029
10.1111/j.2517-6161.1991.tb01808.x
10.1080/09500340600715185
10.1214/lnms/1215467407
10.1002/9780470316559
10.1023/A:1026285429743
10.1007/978-1-4684-9458-7
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References ref_14
ref_13
ref_10
ref_19
ref_18
ref_17
ref_16
ref_15
James (ref_12) 1957; 28
Perlman (ref_22) 1987; 2
Doi (ref_26) 1991; 88
Hannan (ref_11) 1965; 2
Ferris (ref_24) 1993; 15
Viana (ref_9) 2003; 5
ref_25
ref_23
ref_20
ref_1
Andersson (ref_21) 1975; 3
ref_3
ref_2
Lakshminarayanan (ref_8) 2005; 22
ref_27
ref_5
ref_4
ref_7
ref_6
References_xml – volume: 2
  start-page: 421
  year: 1987
  ident: ref_22
  article-title: Group symmetry covariance models
  publication-title: Statistical Science
  doi: 10.1214/ss/1177013114
– ident: ref_19
  doi: 10.1214/lnms/1215540653
– ident: ref_5
– volume: 28
  start-page: 993
  year: 1957
  ident: ref_12
  article-title: The relationship algebra of an experimental design
  publication-title: Annals of Mathematical Statistics
  doi: 10.1214/aoms/1177706800
– ident: ref_25
  doi: 10.1007/978-94-009-4109-0
– ident: ref_15
  doi: 10.1111/j.2517-6161.1988.tb01707.x
– ident: ref_18
  doi: 10.1007/978-1-4613-8528-8
– volume: 2
  start-page: 1
  year: 1965
  ident: ref_11
  article-title: Group representations and applied probability
  publication-title: Journal of Applied Probability
  doi: 10.2307/3211873
– volume: 22
  start-page: 2843
  year: 2005
  ident: ref_8
  article-title: Dihedral representations and statistical geometric optics I: Spherocylindrical lenses
  publication-title: J. Optical Society of America A
  doi: 10.1364/JOSAA.22.002483
– ident: ref_1
– volume: 3
  start-page: 132
  year: 1975
  ident: ref_21
  article-title: Invariant normal models
  publication-title: Annals of Statistics
  doi: 10.1214/aos/1176343004
– ident: ref_23
– ident: ref_17
  doi: 10.1214/cbms/1462061029
– ident: ref_6
– ident: ref_14
  doi: 10.1111/j.2517-6161.1991.tb01808.x
– ident: ref_4
– ident: ref_10
  doi: 10.1080/09500340600715185
– ident: ref_27
– ident: ref_2
– volume: 15
  start-page: 735
  year: 1993
  ident: ref_24
  article-title: Relative letter and position difficulty on visual acuity charts from the early treatment diabetic retinopathy study
  publication-title: Am J Ophthalmol
– ident: ref_16
  doi: 10.1214/lnms/1215467407
– ident: ref_7
  doi: 10.1002/9780470316559
– ident: ref_13
– volume: 5
  start-page: 439
  year: 2003
  ident: ref_9
  article-title: Invariance conditions for random curvature models
  publication-title: Methodology and Computing in Applied Probability
  doi: 10.1023/A:1026285429743
– ident: ref_3
  doi: 10.1007/978-1-4684-9458-7
– ident: ref_20
– volume: 88
  start-page: 9282
  year: 1991
  ident: ref_26
  article-title: Importance of purine and pyrimidine content of local nucleotide sequences (six bases long) for evolution of human immunodeficiency virus type 1
  publication-title: Evolution
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