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Open AccessArticle

Measuring the Complexity of Continuous Distributions

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Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
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Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
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Laboratorio de Hidroinformática, Universidad de Pamplona, 543050 Pamplona, Colombia
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Grupo de Investigación en Ecología y Biogeografía, Universidad de Pamplona, 543050 Pamplona, Colombia
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SENSEable City Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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MoBS Lab, Northeastern University, Boston, MA 02115, USA
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ITMO University, 199034 St. Petersburg, Russia
*
Authors to whom correspondence should be addressed.
Academic Editors: Hermann Haken and Juval Portugali
Entropy 2016, 18(3), 72; https://doi.org/10.3390/e18030072
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)
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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MDPI and ACS Style

Santamaría-Bonfil, G.; Fernández, N.; Gershenson, C. Measuring the Complexity of Continuous Distributions. Entropy 2016, 18, 72. https://doi.org/10.3390/e18030072

AMA Style

Santamaría-Bonfil G, Fernández N, Gershenson C. Measuring the Complexity of Continuous Distributions. Entropy. 2016; 18(3):72. https://doi.org/10.3390/e18030072

Chicago/Turabian Style

Santamaría-Bonfil, Guillermo; Fernández, Nelson; Gershenson, Carlos. 2016. "Measuring the Complexity of Continuous Distributions" Entropy 18, no. 3: 72. https://doi.org/10.3390/e18030072

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