Measuring the Complexity of Continuous Distributions
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico
Laboratorio de Hidroinformática, Universidad de Pamplona, 543050 Pamplona, Colombia
Grupo de Investigación en Ecología y Biogeografía, Universidad de Pamplona, 543050 Pamplona, Colombia
SENSEable City Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
MoBS Lab, Northeastern University, Boston, MA 02115, USA
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
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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.
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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.
Santamaría-Bonfil G, Fernández N, Gershenson C. Measuring the Complexity of Continuous Distributions. Entropy. 2016; 18(3):72.
Santamaría-Bonfil, Guillermo; Fernández, Nelson; Gershenson, Carlos. 2016. "Measuring the Complexity of Continuous Distributions." Entropy 18, no. 3: 72.
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