Measuring the Complexity of Continuous Distributions

Santamaría-Bonfil, Guillermo; Fernández, Nelson; Gershenson, Carlos

doi:10.3390/e18030072

Cited by 14 publications

(20 citation statements)

References 47 publications

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“…In this section, we describe the statistical measures of E, S, and C. Discrete measures were defined in a previous study presented in Fernández et al (2014), latter extended for continuous probability distributions (Santamaría-Bonfil et al, 2016). This package is limited to the aforementioned measures.…”

Section: Method: Emergence Selforganization and Complexitymentioning

confidence: 99%

“…This package is limited to the aforementioned measures. Proofs, advantages, and limitations are defined and discussed in Fernández et al (2014) and Santamaría-Bonfil et al (2016). Furthermore, for simplicity, differences between discrete and the continuous will be mentioned when necessary.…”

Section: Method: Emergence Selforganization and Complexitymentioning

confidence: 99%

“…In this manuscript, we present a package to calculate statistical measures of emergence E, self-organization S, and complexity C which are applicable to any dataset or probability distributions (Fernández et al, 2014;Santamaría-Bonfil et al, 2016). These are closely related to other Shannon-based measures (Lopez-Ruiz et al, 1995;Jost, 2006).…”

mentioning

confidence: 99%

“…Specifically, our main contributions are as follows: (a) a software bundle to compute discrete and continuous statistical complexity measures; (b) examples on how to use both measures to analyze probability distributions and different timescales; (c) code comments to enhance usability; (d) vector and matrix operations to improve the computation time. This package was coded in Octave GNU 4.0.3, checked for compatibility in Matlab2013a, and is publicly available at the web repository Entropy-based Complexity 1 (Santamaría-Bonfil, 2016). In Appendices A and B, code snippets of the function are provided.…”

mentioning

confidence: 99%

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A Package for Measuring Emergence, Self-organization, and Complexity Based on Shannon Entropy

2017

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Section: Method: Emergence Selforganization and Complexitymentioning

confidence: 99%

Section: Method: Emergence Selforganization and Complexitymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A Package for Measuring Emergence, Self-organization, and Complexity Based on Shannon Entropy

2017

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“…In their contribution, Santamaría-Bonfil, Fernández and Gershenson [10] start by reminding the reader of the above noted measures based as they were on discrete Shannon information. They then suggest a novel approach and measures for the above basic notions of complexity based on differential entropy.…”

Section: The Contributionsmentioning

confidence: 99%

Information and Self-Organization

Haken

Portugali

2016

Entropy

116

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The process of "self-organization" takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. In domains such as physics, chemistry or biology, the phrase, "far from equilibrium", refers to systems that are "far from thermal equilibrium", while in other disciplines, the term refers to the property of being "away from the resting state". Such systems are "complex" in the sense that they are composed of many interacting components, parts, elements, etc., and "open" in the sense that they exchange with their environment matter, energy, and information. Here, "information" may imply Shannon information [1], as a measure of the capacity of a channel through which a message passes, pragmatic information, as the impact of a message on recipients, or semantic information, as the meaning conveyed by a message.An attempt to bring these lines of thought together was made by Hermann Haken in his 1988 book Information and Self-Organization [2]. In the meantime, a number of authors have studied the interplay between information and self-organization in a variety of fields. Though the selection of the relevant authors and topics is surely not complete, we believe that this special issue mirrors the state of these interdisciplinary approaches fairly well. In fact, the various papers of this Special Issue expose the different ways processes of self-organization are linked with the various forms of information. As will be seen below, a study of such links has consequences on a number of research domains, ranging from physics and chemistry, through the life sciences and cognitive science, including human behavior and action, to our understanding of society, economics, and the dynamics of cities and urbanization.As will be seen below, the contributions to this Special Issue shed light on the various facets of information and self-organization. And since these various facets do not lend themselves to a topic-oriented order, and since a reader may prefer one over another, we present the papers in an alphabetic order that follows the family name of the first author of each article. The ContributionsA central theme in the theories of complexity is the self-organized bottom-up transition from the local micro-scale of a system's elementary parts to the global macro-scale of the system as a whole. In a way, the various theories of complexity differ in their conceptualization of this scale-dependent transition. Harald Atmanspacher [3] approaches this issue from the perspective of his notions of contextual emergence and the associated process of partitioning; both notions are related to the property that complex systems are open in the sense that they exchange matter, energy and information with

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Review and comparison of two meta-model-based uncertainty propagation analysis methods in groundwater applications: polynomial chaos expansion and Gaussian process emulation

Rajabi

2019

Stoch Environ Res Risk Assess

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Measuring the Complexity of Continuous Distributions

Cited by 14 publications

References 47 publications

A Package for Measuring Emergence, Self-organization, and Complexity Based on Shannon Entropy

A Package for Measuring Emergence, Self-organization, and Complexity Based on Shannon Entropy

Information and Self-Organization

Review and comparison of two meta-model-based uncertainty propagation analysis methods in groundwater applications: polynomial chaos expansion and Gaussian process emulation

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