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Related papers: A Statistical Measure of Complexity

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I present my viewpoint on complexity, stressing general arguments and using a rather simple language.

Statistical Mechanics · Physics 2007-05-23 Giorgio Parisi

An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…

Statistical Mechanics · Physics 2007-05-23 Constantino Tsallis

This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…

Systems and Control · Electrical Eng. & Systems 2025-08-18 John W. Sheppard

The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…

Adaptation and Self-Organizing Systems · Physics 2009-11-19 Russell K. Standish

The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…

Functional Analysis · Mathematics 2007-07-16 A. A. Bosov

A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…

adap-org · Physics 2009-10-28 C. Adami , N. J. Cerf

This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…

Physics Education · Physics 2007-05-23 Rajesh R. Parwani

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…

Information Theory · Computer Science 2012-11-16 Carlos Gershenson , Nelson Fernandez

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the…

Chaotic Dynamics · Physics 2009-11-07 Raquel G. Catalan , Jose Garay , Ricardo Lopez-Ruiz

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of…

Information Theory · Computer Science 2013-08-21 David J. Galas , Nikita A. Sakhanenko , Alexander Skupin , Tomasz Ignac

A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…

Disordered Systems and Neural Networks · Physics 2007-05-23 D. B. Saakian

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…

Adaptation and Self-Organizing Systems · Physics 2016-04-01 Guillermo Santamaría-Bonfil , Nelson Fernández , Carlos Gershenson

We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s…

Statistics Theory · Mathematics 2010-12-10 Samer A. Abdallah , Mark D. Plumbley

In recent studies, new measures of complexity for nonlinear systems have been proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A {\bf 209} (1995) 321) or the SDL measure (Phys. Rev. E {\bf 59} (1999) 2). All these…

adap-org · Physics 2015-06-30 Ricard V. Sole , Bartolo Luque

This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity…

Computational Complexity · Computer Science 2007-07-11 Robert Gilman , Alexei G. Miasnikov , Alexey D. Myasnikov , Alexander Ushakov

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem…

Quantum Physics · Physics 2013-03-20 Amit Hagar , Giuseppe Sergioli

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…

Computational Complexity · Computer Science 2013-12-10 Nicolas Gauvrit , Hector Zenil , Jean-Paul Delahaye , Fernando Soler-Toscano

In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state…

Formal Languages and Automata Theory · Computer Science 2009-07-30 Yuan Gao , Sheng Yu

This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…

Quantum Physics · Physics 2014-10-27 Subhash Kak

A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…

Disordered Systems and Neural Networks · Physics 2007-05-23 D. B. Saakian