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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>895</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-12-29</completedDate>
    <publishedDate>2005-12-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Identification of Metastabilities in Monomolecular Conformation Kinetics</title>
    <abstract language="eng">The identification of metastable conformations of molecules plays an important role in computational drug design. One main difficulty is the fact that the underlying dynamic processes take place in high dimensional spaces. Although the restriction of degrees of freedom to a few dihedral angles significantly reduces the complexity of the problem, the existing algorithms are time-consuming. They are based on the approximation of transition probabilities by an extensive sampling of states according to the Boltzmann distribution. We present a method which can identify metastable conformations without sampling the complete distribution. Our algorithm is based on local transition rates and uses only pointwise information about the potential energy surface. In order to apply the cluster algorithm PCCA+, we compute a few eigenvectors of the rate matrix by the Jacobi-Davidson method. Interpolation techniques are applied to approximate the thermodynamical weights of the clusters. The concluding example illustrates our approach for epigallocatechine, a molecule which can be described by seven dihedral angles.</abstract>
    <identifier type="serial">06-01</identifier>
    <identifier type="opus3-id">895</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8956</identifier>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastable conformations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>potential energy surface</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition rates</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>eigenvectors</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>clustering</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="80A30">Chemical kinetics [See also 76V05, 92C45, 92E20]</collection>
    <collection role="msc" number="82B41">Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]</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="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/895/ZR-06-01.pdf</file>
  </doc>
  <doc>
    <id>2262</id>
    <completedYear>2007</completedYear>
    <publishedYear>2007</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>126</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations</title>
    <parentTitle language="eng">Journal of Chemical Physics</parentTitle>
    <identifier type="doi">10.1063/1.2404953</identifier>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
  </doc>
  <doc>
    <id>2247</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>57</pageFirst>
    <pageLast>66</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Robust Perron Cluster Analysis for Various Applications in Computational Life Science</title>
    <parentTitle language="eng">Computational Life Sciences</parentTitle>
    <author>Marcus Weber</author>
    <author>Susanna Kube</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
  </doc>
  <doc>
    <id>2261</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>339</pageFirst>
    <pageLast>342</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1048</volume>
    <type>conferenceobject</type>
    <publisherName>AIP Conference Proceedings</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computation of equilibrium densities in metastable dynamical systems by domain decomposition</title>
    <parentTitle language="eng">Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008</parentTitle>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
  </doc>
  <doc>
    <id>2452</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>593</pageFirst>
    <pageLast>596</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1048</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Preserving the Markov Property of Reduced Reversible Markov Chains</title>
    <parentTitle language="eng">Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008</parentTitle>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
  </doc>
  <doc>
    <id>2455</id>
    <completedYear>2007</completedYear>
    <publishedYear>2007</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>396</pageFirst>
    <pageLast>416</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>6</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stable Computation of Probability Densities of Metastable Dynamical Systems</title>
    <parentTitle language="eng">SIAM J. Multiscale Model. Simul.</parentTitle>
    <author>Marcus Weber</author>
    <author>Susanna Kube</author>
    <author>Lionel Walter</author>
    <author>Peter Deuflhard</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</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>
  </doc>
  <doc>
    <id>2619</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1947</pageFirst>
    <pageLast>1962</pageLast>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>228</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics</title>
    <parentTitle language="eng">Journal of Computational Physics</parentTitle>
    <identifier type="doi">10.1016/j.jcp.2008.11.016</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-9604</enrichment>
    <author>Susanna Kube</author>
    <author>Caroline Lasser</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
  </doc>
  <doc>
    <id>876</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-09-28</completedDate>
    <publishedDate>2005-09-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Conformation Kinetics as a Reduced Model for Transition Pathways</title>
    <abstract language="eng">The complexity of molecular kinetics can be reduced significantly by a restriction to metastable conformations which are almost invariant sets of molecular dynamical systems. With the Robust Perron Cl uster Analysis PCCA+, developed by Weber and Deuflhard, we have a tool available which can be used to identify these conformations from a transition probability matrix. This method can also be applied to the corresponding transition rate matrix which provides important information concerning transition pathways of single molecules. In the present paper, we explain the relationship between these tw o concepts and the extraction of conformation kinetics from transition rates. Moreover, we show how transition rates can be approximated and conclude with numerical examples.</abstract>
    <identifier type="serial">05-43</identifier>
    <identifier type="opus3-id">876</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8763</identifier>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-43</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>conformation kinetics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition rates</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Robust Perron Cluster Analysis</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="60J75">Jump processes</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</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/876/ZR-05-43.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>
  <doc>
    <id>960</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-07-23</completedDate>
    <publishedDate>2007-07-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics</title>
    <abstract language="eng">Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy.</abstract>
    <identifier type="serial">07-17</identifier>
    <identifier type="opus3-id">960</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9604</identifier>
    <enrichment key="SourceTitle">A rev. vers. appeared in: Journal of Computational Physics 228 (2009) pp. 1947-1962. doi:10.1016/j.jcp.2008.11.016</enrichment>
    <author>Susanna Kube</author>
    <author>Caroline Lasser</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Metropolis Monte Carlo</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quadrature</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>oscillating functions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62D05">Sampling theory, sample surveys</collection>
    <collection role="msc" number="65D30">Numerical integration</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</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/960/ZR_07_17.pdf</file>
  </doc>
</export-example>
