Special Issue "Entropy and Information Theory"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 20 December 2017

Special Issue Editors

Guest Editor
Prof. Dr. Abbe Mowshowitz

Department of Computer Science, The City College of New York, Convent Avenue at 138th Street, New York, NY 10031, USA
Website | E-Mail
Interests: network science; graph theory; entropy and information theory; discrete mathematics; virtual organization
Guest Editor
Prof. Dr. Matthias Dehmer

1 Department of Computer Science, Core Competence Center for Operations Research, Universität der Bundeswehr München, Neubiberg 85579, Germany
2 Institute for Bioinformatics and Translational Research, The Health and Life Sciences University (UMIT), Eduard Wallnoefer Zentrum 1, A-6060 Hall in Tyrol, Austria
Website | E-Mail
Interests: applied mathematics; bioinformatics; data mining; machine learning; systems biology; graph theory; complexity and information theory

Special Issue Information

Dear Colleagues,

The relationship between entropy and information theory has a long history and has led to many important results, as well as to applications in fields outside of mathematics and physics. This Special Issue will focus on applications of Shannon information theory to the measurement of entropy in mathematical systems and models, primarily those based on graphs or networks. Theoretical papers, as well as those reporting on experimental results, are welcome. Suggested topics include:

  • Information-theoretic measures on complex networks
  • Shannon Entropy measures on random graphs
  • Applications of information-theoretic measures in chemistry, biology, social sciences and the humanities

Prof. Dr. Abbe Mowshowitz
Prof. Dr. Matthias Dehmer
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 350 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entropy based information measures
  • entropy of graphs and networks
  • applications of entropy based information measures

Published Papers (2 papers)

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Research

Open AccessArticle Toward Measuring Network Aesthetics Based on Symmetry
Axioms 2017, 6(2), 12; doi:10.3390/axioms6020012
Received: 20 March 2017 / Revised: 3 May 2017 / Accepted: 3 May 2017 / Published: 6 May 2017
Cited by 1 | PDF Full-text (695 KB) | HTML Full-text | XML Full-text
Abstract
In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer’s perception. Here
[...] Read more.
In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer’s perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics. Full article
(This article belongs to the Special Issue Entropy and Information Theory)
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Open AccessArticle Expansion of the Kullback-Leibler Divergence, and a New Class of Information Metrics
Axioms 2017, 6(2), 8; doi:10.3390/axioms6020008
Received: 31 January 2017 / Revised: 25 March 2017 / Accepted: 27 March 2017 / Published: 1 April 2017
Cited by 1 | PDF Full-text (628 KB) | HTML Full-text | XML Full-text
Abstract
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces of this class of problem. This study takes an approach that simplifies many
[...] Read more.
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces of this class of problem. This study takes an approach that simplifies many aspects of these problems by presenting a structured, series expansion of the Kullback-Leibler divergence—a function central to information theory—and devise a distance metric based on this divergence. Using the Möbius inversion duality between multivariable entropies and multivariable interaction information, we express the divergence as an additive series in the number of interacting variables, which provides a restricted and simplified set of distributions to use as approximation and with which to model data. Truncations of this series yield approximations based on the number of interacting variables. The first few terms of the expansion-truncation are illustrated and shown to lead naturally to familiar approximations, including the well-known Kirkwood superposition approximation. Truncation can also induce a simple relation between the multi-information and the interaction information. A measure of distance between distributions, based on Kullback-Leibler divergence, is then described and shown to be a true metric if properly restricted. The expansion is shown to generate a hierarchy of metrics and connects this work to information geometry formalisms. An example of the application of these metrics to a graph comparison problem is given that shows that the formalism can be applied to a wide range of network problems and provides a general approach for systematic approximations in numbers of interactions or connections, as well as a related quantitative metric. Full article
(This article belongs to the Special Issue Entropy and Information Theory)
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