#### Computational Science Technical Note CSTN-058

#
Spectral Analysis of Attractors in Random Boolean Network Models

##
K. A. Hawick

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Archived July 2008

**Abstract**

Circuits and loops in graph systems can be used to study the attractors in gene-regulatory networks. The number of such attractors
grows very rapidly with network size and even for small nets the properties of the set of attractors, including their length
distribution, are not well understood. This paper presents a Fourier spectral analysis of attractor lengths in a set of networks
using Kauffman's NK random boolean network model. This allows a systematic study of the bulk-average properties of the attractor
distribution for different network connectivities without resorting to computationally expensive exact enumeration techniques.
Networks with nodes of fixed degree and with distributions of different degree are studied. The length distribution of attractors
flattens out above a connectivity of $K=2$. It is hypothesised that discontinuities in the distribution are due to partial
unreachability that arise even in single component nets at low connectivities.

**Keywords:**
graph theory; random boolean network; gene-regulatory network; time-series; power spectrum.

**Full Document Text:**
PDF version.

**Citation Information:** BiBTeX database for CSTN Notes.

**BiBTeX reference:**

@INPROCEEDINGS{CSTN-058,
author = {K.A. Hawick},
title = {Spectral Analysis of Attractors in Gene-Regulatory Network Models},
booktitle = {Proc. 2009 International Conference on Foundations of Computer Science
(FCS 09)},
year = {2009},
pages = {61-67},
address = {Las Vegas, USA.},
month = {13-16 July},
organization = {WorldComp},
institution = {Computer Science, Massey University},
timestamp = {2008.08.09},
type = {Tech Note}
}

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