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Mutual information in random Boolean models of regulatory networks
Andre S Ribeiro1, Stuart A Kauffman, Jason Lloyd-Price
1Institute for Biocomplexity and Informatics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4.
Average pairwise mutual information quantifies coordination in complex networks. In random Boolean networks (RBNs), N peaks near critical states, driven by indirect correlations in large systems.
Area of Science:
- Complex Systems
- Network Science
- Computational Biology
Background:
- Mutual information measures coordination between elements in time series.
- Average pairwise mutual information () globally assesses system dynamics coordination.
- Random Boolean networks (RBNs) model complex interacting systems like genetic networks.
Purpose of the Study:
- Investigate average pairwise mutual information () in RBNs.
- Analyze as a function of Boolean rule distribution and network structure.
- Determine how network size (N) affects coordination measures.
Main Methods:
- Utilized efficient numerical methods for calculating .
- Studied random Boolean networks (RBNs) with random link placement.
- Analyzed the behavior of N as N approaches infinity and for finite systems.
Main Results:
- N exhibits a discontinuity at critical RBN parameter values for infinite N.
- For finite systems, N peaks near the critical value, slightly in the disordered regime.
- Indirect correlations between elements in different chains drive high N values.
Conclusions:
- Criticality in RBNs is associated with a discontinuity in average pairwise mutual information.
- System coordination in RBNs is influenced by both direct and indirect correlations.
- The study provides insights into the dynamics and coordination of complex networks.
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