@Article{EAJAM-1-132,
author = {Xi Chen, Wai-Ki Ching, Xiao-Shan Chen, Yang Cong and Nam-Kiu Tsing},
title = {Construction of Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix: A Maximum Entropy Rate Approach},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {1},
number = {2},
pages = {132--154},
abstract = {<p style="text-align: justify;">Modeling genetic regulatory networks is an important problem in genomic
research. Boolean Networks (BNs) and their extensions Probabilistic Boolean Networks
(PBNs) have been proposed for modeling genetic regulatory interactions. In a PBN, its
steady-state distribution gives very important information about the long-run behavior
of the whole network. However, one is also interested in system synthesis which requires
the construction of networks. The inverse problem is ill-posed and challenging, as there
may be many networks or no network having the given properties, and the size of the
problem is huge. The construction of PBNs from a given transition-probability matrix
and a given set of BNs is an inverse problem of huge size. We propose a maximum
entropy approach for the above problem. Newton’s method in conjunction with the
Conjugate Gradient (CG) method is then applied to solving the inverse problem. We
investigate the convergence rate of the proposed method. Numerical examples are also
given to demonstrate the effectiveness of our proposed method.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.080310.200910a},
url = {http://global-sci.org/intro/article_detail/eajam/10900.html}
}