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On Construction of Sparse Probabilistic Boolean Networks

Published online by Cambridge University Press:  28 May 2015

Xi Chen ,
Hao Jiang  and
Wai-Ki Ching
Xi Chen*
Affiliation:
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Hao Jiang*
Affiliation:
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Wai-Ki Ching*
Affiliation:
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
*
Corresponding author. Email: dlkcissy@hku.hk
Corresponding author. Email: haohao@hkusuc.hku.hk
Corresponding author. Email: wching@hku.hk
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Abstract

In this paper we envisage building Probabilistic Boolean Networks (PBNs) from a prescribed stationary distribution. This is an inverse problem of huge size that can be subdivided into two parts — viz. (i) construction of a transition probability matrix from a given stationary distribution (Problem ST), and (ii) construction of a PBN from a given transition probability matrix (Problem TP). A generalized entropy approach has been proposed for Problem ST and a maximum entropy rate approach for Problem TP respectively. Here we propose to improve both methods, by considering a new objective function based on the entropy rate with an additional term of La-norm that can help in getting a sparse solution. A sparse solution is useful in identifying the major component Boolean networks (BNs) from the constructed PBN. These major BNs can simplify the identification of the network structure and the design of control policy, and neglecting non-major BNs does not change the dynamics of the constructed PBN to a large extent. Numerical experiments indicate that our new objective function is effective in finding a better sparse solution.

Keywords

65C2092B05Probabilistic Boolean Networksentropystationary distributionsparsitytransition probability matrix
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 1 , February 2012 , pp. 1 - 18
Copyright
Copyright © Global-Science Press 2012

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