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Volume explored by a branching random walk on general graphs

Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding—the branch...

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Autores principales: Bordeu, Ignacio, Amarteifio, Saoirse, Garcia-Millan, Rosalba, Walter, Benjamin, Wei, Nanxin, Pruessner, Gunnar
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6821755/
https://www.ncbi.nlm.nih.gov/pubmed/31666539
http://dx.doi.org/10.1038/s41598-019-51225-6
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author Bordeu, Ignacio
Amarteifio, Saoirse
Garcia-Millan, Rosalba
Walter, Benjamin
Wei, Nanxin
Pruessner, Gunnar
author_facet Bordeu, Ignacio
Amarteifio, Saoirse
Garcia-Millan, Rosalba
Walter, Benjamin
Wei, Nanxin
Pruessner, Gunnar
author_sort Bordeu, Ignacio
collection PubMed
description Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding—the branching random walk (BRW)—is required. Despite its wide range of applications, the properties of the volume explored by the BRW so far remained elusive, with exact results limited to one dimension. Here we present analytical results, supported by numerical simulations, on the scaling of the volume explored by a BRW in the critical regime, the onset of epidemics, in general environments. Our results characterise the spreading dynamics on regular lattices and general graphs, such as fractals, random trees and scale-free networks, revealing the direct relation between the graphs’ dimensionality and the rate of propagation of the viral process. Furthermore, we use the BRW to determine the spectral properties of real social and metabolic networks, where we observe that a lack of information of the network structure can lead to differences in the observed behaviour of the spreading process. Our results provide observables of broad interest for the characterisation of real world lattices, tissues, and networks.
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spelling pubmed-68217552019-11-05 Volume explored by a branching random walk on general graphs Bordeu, Ignacio Amarteifio, Saoirse Garcia-Millan, Rosalba Walter, Benjamin Wei, Nanxin Pruessner, Gunnar Sci Rep Article Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding—the branching random walk (BRW)—is required. Despite its wide range of applications, the properties of the volume explored by the BRW so far remained elusive, with exact results limited to one dimension. Here we present analytical results, supported by numerical simulations, on the scaling of the volume explored by a BRW in the critical regime, the onset of epidemics, in general environments. Our results characterise the spreading dynamics on regular lattices and general graphs, such as fractals, random trees and scale-free networks, revealing the direct relation between the graphs’ dimensionality and the rate of propagation of the viral process. Furthermore, we use the BRW to determine the spectral properties of real social and metabolic networks, where we observe that a lack of information of the network structure can lead to differences in the observed behaviour of the spreading process. Our results provide observables of broad interest for the characterisation of real world lattices, tissues, and networks. Nature Publishing Group UK 2019-10-30 /pmc/articles/PMC6821755/ /pubmed/31666539 http://dx.doi.org/10.1038/s41598-019-51225-6 Text en © The Author(s) 2019 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
Bordeu, Ignacio
Amarteifio, Saoirse
Garcia-Millan, Rosalba
Walter, Benjamin
Wei, Nanxin
Pruessner, Gunnar
Volume explored by a branching random walk on general graphs
title Volume explored by a branching random walk on general graphs
title_full Volume explored by a branching random walk on general graphs
title_fullStr Volume explored by a branching random walk on general graphs
title_full_unstemmed Volume explored by a branching random walk on general graphs
title_short Volume explored by a branching random walk on general graphs
title_sort volume explored by a branching random walk on general graphs
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6821755/
https://www.ncbi.nlm.nih.gov/pubmed/31666539
http://dx.doi.org/10.1038/s41598-019-51225-6
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