@Article{EAJAM-2-353,
author = {Hao Jiang, Xi Chen, Yushan Qiu and Wai-Ki Ching},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.191012.221112a},
url = {http://global-sci.org/intro/article_detail/eajam/10882.html}
}