Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 206, Issue 1-2, Pages 49-61Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2005.04.016
Keywords
Boolean networks; spectral methods; phase transition; gene regulatory network; scale-free topology
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In this work we present results that can be used for analysis of Boolean networks. The results utilize Fourier spectra of the functions in the network. An accurate formula is given for Derrida plots of networks of finite size N based on a result on Boolean functions presented in another context. Derrida plots are widely used to examine the stability issues of Boolean networks. For the limit N (->) infinity, we give a computationally simple form that can be used as a good approximation for rather small networks as well. A formula for Derrida plots of random Boolean networks (RBNs) presented earlier in the literature is given an alternative derivation. It is shown that the information contained in the Derrida plot is equal to the average Fourier spectrum of the functions in the network. In the case of random networks the mean Derrida plot can be obtained from the mean spectrum of the functions. The method is applied to real data by using the Boolean functions found in genetic regulatory networks of eukaryotic cells in an earlier study. Conventionally, Derrida plots and stability analysis have been computed with statistical sampling resulting in poorer accuracy. (c) 2005 Elsevier B.V. All rights reserved.
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