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Sample space reducing cascading processes produce the full spectrum of scaling exponents

Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce power laws with arbitrary exponents. We demons...

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Detalles Bibliográficos
Autores principales: Corominas-Murtra, Bernat, Hanel, Rudolf, Thurner, Stefan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5593845/
https://www.ncbi.nlm.nih.gov/pubmed/28894107
http://dx.doi.org/10.1038/s41598-017-09836-4
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author Corominas-Murtra, Bernat
Hanel, Rudolf
Thurner, Stefan
author_facet Corominas-Murtra, Bernat
Hanel, Rudolf
Thurner, Stefan
author_sort Corominas-Murtra, Bernat
collection PubMed
description Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce power laws with arbitrary exponents. We demonstrate analytically that the frequency distributions of states are power laws with exponents that coincide with the multiplication parameter of the cascading process. In addition, we show that imposing energy conservation in SSR cascades allows us to recover Fermi’s classic result on the energy spectrum of cosmic rays, with the universal exponent −2, which is independent of the multiplication parameter of the cascade. Applications of the proposed process include fragmentation processes or directed cascading diffusion on networks, such as rumour or epidemic spreading.
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spelling pubmed-55938452017-09-13 Sample space reducing cascading processes produce the full spectrum of scaling exponents Corominas-Murtra, Bernat Hanel, Rudolf Thurner, Stefan Sci Rep Article Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce power laws with arbitrary exponents. We demonstrate analytically that the frequency distributions of states are power laws with exponents that coincide with the multiplication parameter of the cascading process. In addition, we show that imposing energy conservation in SSR cascades allows us to recover Fermi’s classic result on the energy spectrum of cosmic rays, with the universal exponent −2, which is independent of the multiplication parameter of the cascade. Applications of the proposed process include fragmentation processes or directed cascading diffusion on networks, such as rumour or epidemic spreading. Nature Publishing Group UK 2017-09-11 /pmc/articles/PMC5593845/ /pubmed/28894107 http://dx.doi.org/10.1038/s41598-017-09836-4 Text en © The Author(s) 2017 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Corominas-Murtra, Bernat
Hanel, Rudolf
Thurner, Stefan
Sample space reducing cascading processes produce the full spectrum of scaling exponents
title Sample space reducing cascading processes produce the full spectrum of scaling exponents
title_full Sample space reducing cascading processes produce the full spectrum of scaling exponents
title_fullStr Sample space reducing cascading processes produce the full spectrum of scaling exponents
title_full_unstemmed Sample space reducing cascading processes produce the full spectrum of scaling exponents
title_short Sample space reducing cascading processes produce the full spectrum of scaling exponents
title_sort sample space reducing cascading processes produce the full spectrum of scaling exponents
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5593845/
https://www.ncbi.nlm.nih.gov/pubmed/28894107
http://dx.doi.org/10.1038/s41598-017-09836-4
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