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  <doc>
    <id>933</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-07-06</completedDate>
    <publishedDate>2006-07-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stable computation of probability densities for metastable dynamical systems</title>
    <abstract language="eng">Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.</abstract>
    <identifier type="serial">06-39</identifier>
    <identifier type="opus3-id">933</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9331</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Multisc. Mod. Sim. 2007, 6(2), pp. 396-416</enrichment>
    <author>Marcus Weber</author>
    <author>Lionel Walter</author>
    <author>Susanna Kube</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamical systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular conformations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>aggregation/disaggregation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>domain decomposition</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</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="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/933/ZR-06-39.pdf</file>
  </doc>
  <doc>
    <id>946</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-12-19</completedDate>
    <publishedDate>2006-12-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems</title>
    <abstract language="eng">In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.</abstract>
    <identifier type="serial">07-03</identifier>
    <identifier type="opus3-id">946</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9467</identifier>
    <author>Marcus Weber</author>
    <author>Susanna Kube</author>
    <author>Alexander Riemer</author>
    <author>Alexander Bujotzek</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-03</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamical systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stationary distribution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster analysis</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</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="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/946/ZR-07-03.pdf</file>
  </doc>
  <doc>
    <id>929</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-06-27</completedDate>
    <publishedDate>2006-06-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Coarse Grained Molecular Kinetics</title>
    <abstract language="eng">The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.</abstract>
    <identifier type="serial">06-35</identifier>
    <identifier type="opus3-id">929</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9299</identifier>
    <enrichment key="SourceTitle">Appeared as : "A coarse grained method for the identification of transition rates between molecular conformations" in Journal of Chemical Physics, 126(2) 2007</enrichment>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-35</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="65P99">None of the above, but in this section</collection>
    <collection role="msc" number="80A30">Chemical kinetics [See also 76V05, 92C45, 92E20]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/929/ZR-06-35.pdf</file>
  </doc>
</export-example>
