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Formalization of Shannon’s Theorems
Journal of Automated Reasoning, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reynald Affeldt +2 more
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Shannon entropy as a new measure of aromaticity, Shannon aromaticity
Physical Chemistry Chemical Physics, 2010Based on the local Shannon entropy concept in information theory, a new measure of aromaticity is introduced. This index, which describes the probability of electronic charge distribution between atoms in a given ring, is called Shannon aromaticity (SA).
Siamak, Noorizadeh, Ehsan, Shakerzadeh
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Symmetry and the Shannon entropy
Information Sciences, 1981Abstract Some equivalent systems of postulates characterizing the Shannon entropy of a finite discrete complete probability distribution are proposed.
Prem Nath, Man Mohan Kaur
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The Shannon Capacity of a Union
COMBINATORICA, 1998For an undirected graph \(G=(V,E)\), let \(G^n\) denote the graph whose vertex set is \(V^n\) in which two distinct vertices \((u_1,\dots,u_n)\) and \((v_1,\dots,v_n)\) are adjacent iff for all \(1\leq i\leq n\) either \(u_i=v_i\) or \(u_iv_i\in E\). The Shannon capacity \(c(G)\) of \(G\) is \(\lim_{n\to \infty}(\alpha(G^n))^{1/n}\), where \(\alpha(G^n)
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On the Shannon measure of entropy
Information Sciences, 1981Abstract This paper deals with the axiomatic characterization of Shannon's entropy for generalized probability distributions (A. Renyi, 1961). Also the author has extended Shannon's entropy to subsets of n-dimensional Euclidean space, n = 1,2,3,…. Finally, he has introduced a functional equation, which is a generalization of the one due to T.
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SHANNON INFORMATION IN COMPLETE GENOMES
Journal of Bioinformatics and Computational Biology, 2004Shannon information in the genomes of all completely sequenced prokaryotes and eukaryotes are measured in word lengths of two to ten letters. It is found that in a scale-dependent way, the Shannon information in complete genomes are much greater than that in matching random sequences — thousands of times greater in the case of short words. Furthermore,
Chang-Heng Chang +5 more
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On a characterization of the Shannon entropy
Kybernetika, 1991It is studied a new characterization of the Shannon entropy using less restrictive assumptions on symmetry than extreme symmetry and block symmetry of \textit{M. M. Kaur} and \textit{P. Nath} [Inf. Control 53, 9-20 (1982; Zbl 0511.94012)].
Marzena Kosno, Dominik Szynal
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On the Shannon capacity of a graph
IEEE Transactions on Information Theory, 1979Author's summary: It is proved that the Shannon zero-error capacity of the pentagon is \(\sqrt{5}\). The method is then generalized to obtain upper bounds on the capacity of an arbitrary graph. A well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of
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