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  <doc>
    <id>346</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1998-01-21</completedDate>
    <publishedDate>1998-01-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains</title>
    <abstract language="eng">The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule.</abstract>
    <identifier type="serial">SC-98-03</identifier>
    <identifier type="opus3-id">347</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3469</identifier>
    <enrichment key="SourceTitle">Appeared in: Lin. Alg. Appl. 315 (2000) 39-59</enrichment>
    <author>Peter Deuflhard</author>
    <author>Wilhelm Huisinga</author>
    <author>Alexander Fischer</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-03</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>essential molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nearly reducible</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nearly completely decomposable</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nearly uncoupled Markov chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>almost invariant aggregates</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trans</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="15A18">Eigenvalues, singular values, and eigenvectors</collection>
    <collection role="msc" number="60J10">Markov chains (discrete-time Markov processes on discrete state spaces)</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="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/346/SC-98-03.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/346/SC-98-03.pdf</file>
  </doc>
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