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Relevant components in critical random Boolean networks

Kaufman, Viktor ; Drossel, Barbara (2024)
Relevant components in critical random Boolean networks.
In: New Journal of Physics, 2006, 8 (10)
doi: 10.26083/tuprints-00020624
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Relevant components in critical random Boolean networks
Language: English
Date: 13 February 2024
Place of Publication: Darmstadt
Year of primary publication: 9 October 2006
Place of primary publication: London
Publisher: IOP Publishing
Journal or Publication Title: New Journal of Physics
Volume of the journal: 8
Issue Number: 10
Collation: 16 Seiten
DOI: 10.26083/tuprints-00020624
Corresponding Links:
Origin: Secondary publication DeepGreen

Random Boolean networks (RBNs) were introduced in 1969 by Kauffman as a model for gene regulation. By combining analytical arguments and efficient numerical simulations, we evaluate the properties of relevant components of critical RBNs independently of update scheme. As known from previous study, the number of relevant components grows logarithmically with network size. We find that in most networks all relevant nodes with more than one relevant input sit in the same component, while all other relevant components are simple loops. As the proportion of nonfrozen nodes with two relevant inputs increases, the number of relevant components decreases and the size and complexity of the largest complex component grows. We evaluate the probability distribution of different types of complex components in an ensemble of networks and confirm that it becomes independent of network size in the limit of large network size. In this limit, we determine analytically the frequencies of occurrence of complex components with different topologies.

Identification Number: Artikel-ID: 228
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-206242
Classification DDC: 500 Science and mathematics > 530 Physics
Divisions: 05 Department of Physics > Institute for Condensed Matter Physics
Date Deposited: 13 Feb 2024 10:10
Last Modified: 13 Feb 2024 10:10
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/20624
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