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A Statistical Measure of Complexity

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TLDR
A measure of complexity based on a probabilistic description of physical systems is proposed that can be applied to many physical situations and to different descriptions of a given system.
Abstract
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.

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Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

TL;DR: The theoretical foundations of the permutation entropy are analyzed, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.
Journal ArticleDOI

What is a complex graph

TL;DR: It is argued that a complex graph contains many different subgraphs, and different measures that quantify this complexity are presented, for instance C1e, the relative number of non-isomorphic one-edge-deleted sub graphs (i.e. DECK size).
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Time Scales of a Chaotic Semiconductor Laser With Optical Feedback Under the Lens of a Permutation Information Analysis

TL;DR: Analysis of the intrinsic time scales of the chaotic dynamics of a semiconductor laser subject to optical feedback by estimating quantifiers derived from a permutation information approach finds that permutation entropy and permutation statistical complexity allow the extraction of important characteristics of the dynamics of the system.
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An image encryption scheme based on quantum logistic map

TL;DR: The security and performance analysis and reliability analysis of the proposed image encryption scheme based on the quantum logistic map are encouraging and it can be concluded that, the proposed scheme is efficient and secure.
References
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Journal ArticleDOI

A mathematical theory of communication

TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Journal Article

The mathematical theory of communication

TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.
Journal ArticleDOI

Information Theory and Statistical Mechanics. II

TL;DR: In this article, the authors consider statistical mechanics as a form of statistical inference rather than as a physical theory, and show that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle.
Book

Thermodynamics and an Introduction to Thermostatics

H.B. Callen
TL;DR: The Canonical Formalism Statistical Mechanics in the Entropy Representation as discussed by the authors is a generalization of statistical mechanics in the Helmholtz Representation, and it has been applied to general systems.
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