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  <doc>
    <id>5120</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2014-08-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Utilizing hitting times for ﬁnding metastable sets in non-reversible Markov chains</title>
    <abstract language="eng">Techniques for ﬁnding metastable or almost invariant sets have been investigated, e.g., for deterministic dynamical systems in set-oriented numerics, for stochastic processes in molecular dynamics, and for random walks on complex networks. Most prominent algorithms are based on spectral apporaches and identify metastable sets via the doimant eigenvalues of the transfer operator associated with the dynamical system under consideration. These algorithms require the dominant eigenvalues to be real-valued. However, for many types of dynamics, e.g. for non-reversible Markov chains, this condition is not met. In this paper we utilize the hitting time apporach to metastable sets and demonstrate how the wellknown statements about optimal metastable decompositions of reversible chains can be reformulated for non-reversible chains if one switches from a spectral approach to an exit time approach. The performance of the resulting algorithm is illustrated by numerical experiments on random walks on complex networks.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-51209</identifier>
    <enrichment key="SourceTitle">To appear in: Journal of Comput. Dynamics</enrichment>
    <author>Marco Sarich</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-32</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hitting times</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-reversible Markov chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>directed networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>random walk</value>
    </subject>
    <collection role="msc" number="37M99">None of the above, but in this section</collection>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="Salsa-Klimm">Salsa-Klimm</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5120/ZIB-Report_14-32.pdf</file>
  </doc>
</export-example>
