An SVD approach to identifying meta-stable states of Markov chains

dc.contributor.authorFritzsche, David
dc.contributor.authorMehrmann, Volker
dc.contributor.authorSzyld, Daniel
dc.contributor.authorVirnik, Elena
dc.date.accessioned2021-12-17T10:06:59Z
dc.date.available2021-12-17T10:06:59Z
dc.date.issued2006-08-04
dc.description.abstractBeing one of the key tools in conformation dynamics, the identification of meta-stable states of Markov chains has been subject to extensive research in recent years, especially when the Markov chains represent energy states of biomolecules. Some previous work on this topic involved the computation of the eigenvalue cluster close to one, as well as the corresponding eigenvectors and the stationary probability distribution of the associated stochastic matrix. Later, since the eigenvalue cluster algorithm turned out to be non-robust, an optimisation approach was developed. As a possible less costly alternative, we present an SVD approach to identifying meta-stable states of a stochastic matrix, where we only need the second largest singular vector. We outline some theoretical background and discuss the advantages of this strategy. Some simulated and real numerical examples illustrate the effectiveness of the proposed algorithm.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15592
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14365
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherMarkov chainsen
dc.subject.otherconformation dynamicsen
dc.subject.othersingular value decompositionen
dc.titleAn SVD approach to identifying meta-stable states of Markov chainsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2006, 15en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200015A18 Eigenvalues, singular values, and eigenvectorsen
tub.subject.msc200015A51 Stochastic matricesen
tub.subject.msc200060J10 Markov chains with discrete parameteren
tub.subject.msc200060J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.)en
tub.subject.msc200065F15 Eigenvalues, eigenvectorsen

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