Year: 2012
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 1 : pp. 1–18
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 $L_α$-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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.030511.060911a
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 1 : pp. 1–18
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Probabilistic Boolean Networks entropy stationary distribution sparsity transition probability matrix.
-
A new alternating direction method of multipliers for sparse Probabilistic Boolean Networks
Li, Xiao-Min | Peng, Zheng | Zhu, Wenxing2014 10th International Conference on Natural Computation (ICNC), (2014), P.790
https://doi.org/10.1109/ICNC.2014.6975938 [Citations: 0] -
On Generating Optimal Sparse Probabilistic Boolean Networks with Maximum Entropy from a Positive Stationary Distribution
Jiang, Hao | Chen, Xi | Qiu, Yushan | Ching, Wai-KiEast Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 P.353
https://doi.org/10.4208/eajam.191012.221112a [Citations: 1] -
A Look-Back-type restart for the restarted Krylov subspace methods for solving non-Hermitian linear systems
Imakura, Akira | Sogabe, Tomohiro | Zhang, Shao-LiangJapan Journal of Industrial and Applied Mathematics, Vol. 35 (2018), Iss. 2 P.835
https://doi.org/10.1007/s13160-018-0308-x [Citations: 3] -
A modified orthogonal matching pursuit for construction of sparse probabilistic boolean networks
Xiao, Guiyun | Bai, Zheng-Jian | Ching, Wai-KiApplied Mathematics and Computation, Vol. 424 (2022), Iss. P.127041
https://doi.org/10.1016/j.amc.2022.127041 [Citations: 2] -
Computational Intelligence in Emerging Technologies for Engineering Applications
Fault Detection and Isolation in Smart Grid Devices Using Probabilistic Boolean Networks
Rivera-Torres, Pedro J. | Llanes Santiago, Orestes2020
https://doi.org/10.1007/978-3-030-34409-2_10 [Citations: 5] -
The complex fluctuations of probabilistic Boolean networks
Gao, Yuan-ming | Xu, Peng | Wang, Xiang-hong | Liu, Wen-binBiosystems, Vol. 114 (2013), Iss. 1 P.78
https://doi.org/10.1016/j.biosystems.2013.07.008 [Citations: 7] -
The Construction of Sparse Probabilistic Boolean Networks: A Discrete Perspective
Fok, Christopher H. | Ching, Wai-Ki | Wong, Chi-Wing2023 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), (2023), P.222
https://doi.org/10.1109/BIBM58861.2023.10385616 [Citations: 0] -
Probabilistic Boolean network modeling of an industrial machine
Rivera Torres, Pedro J. | Serrano Mercado, E. I. | Anido Rifón, LuisJournal of Intelligent Manufacturing, Vol. 29 (2018), Iss. 4 P.875
https://doi.org/10.1007/s10845-015-1143-4 [Citations: 33] -
Reinforcement Learning with Probabilistic Boolean Network Models of Smart Grid Devices
Rivera Torres, Pedro Juan | Gershenson García, Carlos | Sánchez Puig, María Fernanda | Kanaan Izquierdo, Samir | Sayama, HirokiComplexity, Vol. 2022 (2022), Iss. 1
https://doi.org/10.1155/2022/3652441 [Citations: 2] -
Sparse solution of nonnegative least squares problems with applications in the construction of probabilistic Boolean networks
Wen, You‐Wei | Wang, Man | Cao, Zhiying | Cheng, Xiaoqing | Ching, Wai‐Ki | Vassiliadis, Vassilios S.Numerical Linear Algebra with Applications, Vol. 22 (2015), Iss. 5 P.883
https://doi.org/10.1002/nla.2001 [Citations: 8] -
Modeling preventive maintenance of manufacturing processes with probabilistic Boolean networks with interventions
Rivera Torres, Pedro J. | Serrano Mercado, Eileen I. | Llanes Santiago, Orestes | Anido Rifón, LuisJournal of Intelligent Manufacturing, Vol. 29 (2018), Iss. 8 P.1941
https://doi.org/10.1007/s10845-016-1226-x [Citations: 19] -
A Geometric Proximal Gradient Method for Sparse Least Squares Regression with Probabilistic Simplex Constraint
Xiao, Guiyun | Bai, Zheng-JianJournal of Scientific Computing, Vol. 92 (2022), Iss. 1
https://doi.org/10.1007/s10915-022-01873-0 [Citations: 2] -
Probabilistic Boolean network modeling and model checking as an approach for DFMEA for manufacturing systems
Rivera Torres, Pedro J. | Serrano Mercado, Eileen I. | Anido Rifón, LuisJournal of Intelligent Manufacturing, Vol. 29 (2018), Iss. 6 P.1393
https://doi.org/10.1007/s10845-015-1183-9 [Citations: 21] -
Bayesian selection probability estimation for probabilistic Boolean networks
Toyoda, Mitsuru
Asian Journal of Control, Vol. 21 (2019), Iss. 6 P.2513
https://doi.org/10.1002/asjc.2166 [Citations: 5]