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  <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>920</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-05-09</completedDate>
    <publishedDate>2006-05-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">ConfJump : a fast biomolecular sampling method which drills tunnels through high mountains</title>
    <abstract language="eng">In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.</abstract>
    <identifier type="serial">06-26</identifier>
    <identifier type="opus3-id">920</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9204</identifier>
    <author>Lionel Walter</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-26</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Monte Carlo simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rough potential energy function</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular dynamics</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="37A60">Dynamical systems in statistical mechanics [See also 82Cxx]</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="92E10">Molecular structure (graph-theoretic methods, methods of differential topology, etc.)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/920/ZR-06-26.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/920/ZR-06-26.ps</file>
  </doc>
  <doc>
    <id>4972</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>2014-04-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Applications of the cross-entropy method to importance sampling and optimal control of diffusions</title>
    <abstract language="eng">We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-49720</identifier>
    <identifier type="doi">10.1137/14096493X</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Appeared in: Siam Journal on Scientific Computing 36 (2014) A 2654-A2672</enrichment>
    <author>Wei Zhang</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Han Wang</author>
    <author>Carsten Hartmann</author>
    <author>Marcus Weber</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>important sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross-entropy method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>change of measure</value>
    </subject>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="93E20">Optimal stochastic control</collection>
    <collection role="msc" number="94A17">Measures of information, entropy</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4972/ZIB-Report_14-10.pdf</file>
  </doc>
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