Symmetry Studies and Dcompositions 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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| Format: | Article |
| Language: | English |
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MDPI AG
2006-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/8/2/88/ |
| _version_ | 1817989407370641408 |
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| author | Marlos Viana |
| author_facet | Marlos Viana |
| author_sort | Marlos Viana |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T00:46:33Z |
| format | Article |
| id | doaj.art-e1fcae069a354891912736ec587fdccf |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T00:46:33Z |
| publishDate | 2006-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e1fcae069a354891912736ec587fdccf2022-12-22T02:22:00ZengMDPI AGEntropy1099-43002006-06-01828810910.3390/e8020088Symmetry Studies and Dcompositions of EntropyMarlos VianaThis 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.http://www.mdpi.com/1099-4300/8/2/88/group representationcharacterscanonical decompositioninvarianceKullback's divergencevisual acuitySloan fonts. |
| spellingShingle | Marlos Viana Symmetry Studies and Dcompositions of Entropy Entropy group representation characters canonical decomposition invariance Kullback's divergence visual acuity Sloan fonts. |
| title | Symmetry Studies and Dcompositions of Entropy |
| title_full | Symmetry Studies and Dcompositions of Entropy |
| title_fullStr | Symmetry Studies and Dcompositions of Entropy |
| title_full_unstemmed | Symmetry Studies and Dcompositions of Entropy |
| title_short | Symmetry Studies and Dcompositions of Entropy |
| title_sort | symmetry studies and dcompositions of entropy |
| topic | group representation characters canonical decomposition invariance Kullback's divergence visual acuity Sloan fonts. |
| url | http://www.mdpi.com/1099-4300/8/2/88/ |
| work_keys_str_mv | AT marlosviana symmetrystudiesanddcompositionsofentropy |