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  Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

Zierenberg, J., Wilting, J., Priesemann, V., & Levina, A. (2020). Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence. Physical Review E, 101(2): 022301, pp. 1-13. doi:10.1103/PhysRevE.101.022301.

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Zierenberg, J, Author
Wilting, J, Author
Priesemann, V, Author
Levina, A1, 2, Author              
Affiliations:
1Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time by multiple sources. In particular, we consider a (microscopic) branching network (probabilistic cellular automaton) with annealed connectivity disorder, record the macroscopic activity, and then approximate this activity by a (macroscopic) branching process. In this framework we analytically calculate the effect of coalescence on the collective dynamics. We show that coalescence leads to a universal nonlinear scaling function for the conditional expectation value of successive network activity. This allows us to quantify the difference between the microscopic model parameter and established estimates of the macroscopic branching parameter. To overcome this difference, we propose a nonlinear estimator that correctly infers the microscopic model parameter for all system sizes.

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Language(s): eng - English
 Dates: 2020-02
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevE.101.022301
 Degree: -

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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: 13 Volume / Issue: 101 (2) Sequence Number: 022301 Start / End Page: 1 - 13 Identifier: ISSN: 1539-3755
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012