@Article{EAJAM-2-353, author = {}, title = {On Generating Optimal Sparse Probabilistic Boolean Networks with Maximum Entropy from a Positive Stationary Distribution}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.191012.221112a}, url = {http://global-sci.org/intro/article_detail/eajam/10882.html} }