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Entropy 2016, 18(3), 72; doi:10.3390/e18030072

Measuring the Complexity of Continuous Distributions

1
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
2
Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
3
Laboratorio de Hidroinformática, Universidad de Pamplona, 543050 Pamplona, Colombia
4
Grupo de Investigación en Ecología y Biogeografía, Universidad de Pamplona, 543050 Pamplona, Colombia
5
SENSEable City Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
6
MoBS Lab, Northeastern University, Boston, MA 02115, USA
7
ITMO University, 199034 St. Petersburg, Russia
*
Authors to whom correspondence should be addressed.
Academic Editors: Hermann Haken and Juval Portugali
Received: 30 October 2015 / Revised: 8 February 2016 / Accepted: 16 February 2016 / Published: 26 February 2016
(This article belongs to the Special Issue Information and Self-Organization)
View Full-Text   |   Download PDF [701 KB, uploaded 26 February 2016]   |  

Abstract

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. Given that the measures were based on Shannon’s information, the novel continuous complexity measures describe how a system’s predictability changes in terms of the probability distribution parameters. This allows us to calculate the complexity of phenomena for which distributions are known. We find that a broad range of common parameters found in Gaussian and scale-free distributions present high complexity values. We also explore the relationship between our measure of complexity and information adaptation. View Full-Text
Keywords: complexity; emergence; self-organization; information; differential entropy; probability distributions complexity; emergence; self-organization; information; differential entropy; probability distributions
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Santamaría-Bonfil, G.; Fernández, N.; Gershenson, C. Measuring the Complexity of Continuous Distributions. Entropy 2016, 18, 72.

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