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Article: Construction of Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix: A Maximum Entropy Rate Approach

TitleConstruction of Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix: A Maximum Entropy Rate Approach
Authors
KeywordsBoolean networks
Conjugate gradient method
Genetic regulatory networks
Inverse problem
Markov chains
Issue Date2011
PublisherGlobal Science Press. The Journal's web site is located at http://www.global-sci.org/eajam/
Citation
East Asian Journal of Applied Mathematics, 2011, v. 1 n. 2, p. 132-154 How to Cite?
AbstractModeling 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.
Persistent Identifierhttp://hdl.handle.net/10722/133320
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.authorChing, WKen_US
dc.contributor.authorChen, XSen_US
dc.contributor.authorCong, Yen_US
dc.contributor.authorTsing, NKen_US
dc.date.accessioned2011-05-11T08:30:55Z-
dc.date.available2011-05-11T08:30:55Z-
dc.date.issued2011en_US
dc.identifier.citationEast Asian Journal of Applied Mathematics, 2011, v. 1 n. 2, p. 132-154en_US
dc.identifier.issn2079-7362-
dc.identifier.urihttp://hdl.handle.net/10722/133320-
dc.description.abstractModeling 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.-
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.subjectBoolean networks-
dc.subjectConjugate gradient method-
dc.subjectGenetic regulatory networks-
dc.subjectInverse problem-
dc.subjectMarkov chains-
dc.titleConstruction of Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix: A Maximum Entropy Rate Approachen_US
dc.typeArticleen_US
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=2079-7362&volume=1&issue=2&spage=132&epage=154&date=2011&atitle=Construction+of+Probabilistic+Boolean+Networks+from+a+Prescribed+Transition+Probability+Matrix:+A+Maximum+Entropy+Rate+Approach-
dc.identifier.emailChen, X: dlkcissy@hotmail.comen_US
dc.identifier.emailChing, WK: wching@hku.hken_US
dc.identifier.emailTsing, NK: nktsing@hku.hk-
dc.identifier.doi10.4208/eajam.080310.200910a-
dc.identifier.hkuros185021en_US
dc.identifier.volume1en_US
dc.identifier.issue2-
dc.identifier.spage132en_US
dc.identifier.epage154en_US
dc.identifier.isiWOS:000208793100003-

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