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Article: On construction of sparse probabilistic boolean networks

TitleOn construction of sparse probabilistic boolean networks
Authors
KeywordsProbabilistic Boolean Networks
Entropy
Stationary distribution
Sparsity
Transition probability matrix
Issue Date2012
PublisherGlobal Science Press. The Journal's web site is located at http://www.global-sci.org/eajam/
Citation
East Asian Journal of Applied Mathematics, 2012, v. 2 n. 1, p. 1-18 How to Cite?
AbstractIn 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 $L_{alpha}$-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.
Persistent Identifierhttp://hdl.handle.net/10722/145891
ISSN
2015 Impact Factor: 0.489
2015 SCImago Journal Rankings: 0.424
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, Xen_US
dc.contributor.authorJiang, Hen_US
dc.contributor.authorChing, WKen_US
dc.date.accessioned2012-03-27T09:00:57Z-
dc.date.available2012-03-27T09:00:57Z-
dc.date.issued2012en_US
dc.identifier.citationEast Asian Journal of Applied Mathematics, 2012, v. 2 n. 1, p. 1-18en_US
dc.identifier.issn2079-7362-
dc.identifier.urihttp://hdl.handle.net/10722/145891-
dc.description.abstractIn 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 $L_{alpha}$-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.-
dc.languageengen_US
dc.publisherGlobal Science Press. The Journal's web site is located at http://www.global-sci.org/eajam/-
dc.relation.ispartofEast Asian Journal of Applied Mathematicsen_US
dc.subjectProbabilistic Boolean Networks-
dc.subjectEntropy-
dc.subjectStationary distribution-
dc.subjectSparsity-
dc.subjectTransition probability matrix-
dc.titleOn construction of sparse probabilistic boolean networksen_US
dc.typeArticleen_US
dc.identifier.emailChen, X: dlkcissy@hku.hken_US
dc.identifier.emailJiang, H: haohao@hkusuc.hku.hk-
dc.identifier.emailChing, WK: wching@hku.hk-
dc.identifier.authorityChing, WK=rp00679en_US
dc.identifier.doi10.4208/eajam.030511.060911a-
dc.identifier.hkuros198817en_US
dc.identifier.volume2en_US
dc.identifier.issue1-
dc.identifier.spage1en_US
dc.identifier.epage18en_US
dc.identifier.isiWOS:000325516600001-
dc.publisher.placeHong Kong-

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