On Generating Optimal Sparse Probabilistic Boolean Networks with Maximum Entropy from a Positive Stationary Distribution
Year: 2012
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 353–372
Abstract
To understand a genetic regulatory network, two popular mathematical models, Boolean Networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been proposed. Here we address the problem of constructing a sparse Probabilistic Boolean Network (PBN) from a prescribed positive stationary distribution. A sparse matrix is more preferable, as it is easier to study and identify the major components and extract the crucial information hidden in a biological network. The captured network construction problem is both ill-posed and computationally challenging. We present a novel method to construct a sparse transition probability matrix from a given stationary distribution. A series of sparse transition probability matrices can be determined once the stationary distribution is given. By controlling the number of nonzero entries in each column of the transition probability matrix, a desirable sparse transition probability matrix in the sense of maximum entropy can be uniquely constructed as a linear combination of the selected sparse transition probability matrices (a set of sparse irreducible matrices). Numerical examples are given to demonstrate both the efficiency and effectiveness of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.191012.221112a
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 353–372
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Boolean Networks (BNs) Entropy Probabilistic Boolean Networks (PBNs) genetic regulatory networks sparsity stationary probability distribution transition probability matrix.