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  <doc>
    <id>629</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-02-23</completedDate>
    <publishedDate>2001-02-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hierarchical Uncoupling-Coupling of Metastable Conformations</title>
    <abstract language="eng">Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.</abstract>
    <identifier type="serial">01-03</identifier>
    <identifier type="opus3-id">630</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6296</identifier>
    <enrichment key="SourceTitle">Appeared in: Computational Methods for Macromolecules: Challenges and Applications. Proc. of the 3rd Int. Workshop on Methods for Macromolecular Modeling, New York, Oct. 12-14, 2000. T. Schlick, Gan, H. H. (eds.) Springer 2002. LNCSE 24, pp. 235-259</enrichment>
    <author>Alexander Fischer</author>
    <author>Christof Schütte</author>
    <author>Peter Deuflhard</author>
    <author>Frank Cordes</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-03</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>almost invariant sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bridge sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hierarchical annealing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hybrid Monte Carlo</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>$n$-pentane molecule</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>ratio of normalizing co</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="msc" number="82B80">Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]</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/629/ZR-01-03.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/629/ZR-01-03.pdf</file>
  </doc>
  <doc>
    <id>572</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>reportzib</type>
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    <completedDate>2000-03-01</completedDate>
    <publishedDate>2000-03-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Uncoupling-Coupling Technique for Markov Chain Monte Carlo Methods</title>
    <abstract language="eng">Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. By determining almost invariant sets of the associated Markov operator, the Monte Carlo sampling splits by a hierarchical annealing process into the essential regions of the state space; therefore UCMC aims at avoiding the typical metastable behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. The correct weighting factors for the various Markov chains are obtained via a coupling matrix, that connects the samplings from the different almost invariant sets. The underlying mathematical structure of this approach is given by a general examination of the uncoupling-coupling procedure. Furthermore, the overall algorithmic scheme of UCMC is applied to the $n$-pentane molecule, a well-known example from molecular dynamics.</abstract>
    <identifier type="serial">00-04</identifier>
    <identifier type="opus3-id">573</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5720</identifier>
    <author>Alexander Fischer</author>
    <series>
      <title>ZIB-Report</title>
      <number>00-04</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>almost invariant sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bridge sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hierarchical annealing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chains</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Monte Carlo</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>$n$-pentane molecule</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>ratio of no</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="msc" number="82B80">Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/572/ZR-00-04.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/572/ZR-00-04.pdf</file>
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