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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
54/2008

Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

Thimo Rohlf

Abstract

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter.

If a node is active, with probability $p$ an existing link is deleted, with probability $1-p$ the node's threshold is increased, if it is frozen, with probability $p$ it acquires a new link, with probability $1-p$ the node's threshold is decreased.

For any $p < 1$, we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity $\bar{K}_{evo}$ than networks without threshold adaptation ($p =1$). While $\bar{K}_{evo}$ and evolved out-degree distributions are independent from $p$ for $p <1$, in-degree distributions become broader when $p \to 1$, indicating crossover to a power-law. In this limit, time scale separation between threshold adaptions and rewiring also leads to strong correlations between thresholds and in-degree.

Finally, evidence is presented that networks converge to self-organized criticality for large $N$, and possible applications to problems in the context of the evolution of gene regulatory networks and development of neuronal networks are discussed.

Received:
Aug 18, 2008
Published:
Aug 19, 2008
PACS:
05.45.-a, 05.65.+b, 89.75.-k
Keywords:
dynamical network, self-organized criticality, adaptation

Related publications

inJournal
2008 Repository Open Access
Thimo Rohlf

Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

In: epl, 84 (2008) 1, p. 10004