<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>6177</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>52</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Importance sampling in path space for diffusion processes with slow-fast variables</title>
    <abstract language="eng">Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton–Jacobi–Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.</abstract>
    <parentTitle language="eng">Probability Theory and Related Fields</parentTitle>
    <identifier type="doi">10.1007/s00440-017-0755-3</identifier>
    <identifier type="url">http://rdcu.be/oA51</identifier>
    <note>If you are not subscribing to the journal please use the http link below as part of the Springer Nature SharedIt initiative</note>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Carsten Hartmann</author>
    <submitter>Regine Kossick</submitter>
    <author>Christof Schütte</author>
    <author>Marcus Weber</author>
    <author>Wei Zhang</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</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>
  </doc>
  <doc>
    <id>2148</id>
    <completedYear>1998</completedYear>
    <publishedYear>1998</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1689</pageFirst>
    <pageLast>1697</pageLast>
    <pageNumber/>
    <edition/>
    <issue>15</issue>
    <volume>19</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hybrid Monte Carlo with Adaptive Temperature in Mixed–Canonical Ensemble: Efficient conformational analysis of RNA</title>
    <parentTitle language="eng">J. Comp. Chem.</parentTitle>
    <identifier type="doi">10.1002/(SICI)1096-987X(19981130)19:15&lt;1689::AID-JCC2&gt;3.0.CO;2-J</identifier>
    <author>Alexander Fischer</author>
    <author>Frank Cordes</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
  </doc>
  <doc>
    <id>2289</id>
    <completedYear>2010</completedYear>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>031114</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>82</volume>
    <type>article</type>
    <publisherName>American Physical Society</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Observation uncertainty in reversible Markov chains</title>
    <parentTitle language="eng">Phys. Rev. E</parentTitle>
    <identifier type="doi">10.1103/PhysRevE.82.031114</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Ph. Metzner</author>
    <author>Marcus Weber</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
  </doc>
  <doc>
    <id>7345</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>2019-06-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From interacting agents to density-based modeling with stochastic PDEs</title>
    <abstract language="eng">Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing  ABM and SPDE models.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-73456</identifier>
    <enrichment key="SourceTitle">Comm. Appl. Math. Comp. Sci. 16(1):1-32, 2021</enrichment>
    <enrichment key="zib_relatedIdentifier">https://doi.org/10.2140/camcos.2021.16.1</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Ana Djurdjevac</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-21</number>
    </series>
    <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="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7345/main.pdf</file>
  </doc>
  <doc>
    <id>7339</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>32</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>16</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From interacting agents to density-based modeling with stochastic PDEs</title>
    <abstract language="eng">Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.</abstract>
    <parentTitle language="eng">Communications in Applied Mathematics and Computational Science</parentTitle>
    <identifier type="arxiv">1905.13525</identifier>
    <identifier type="doi">10.2140/camcos.2021.16.1</identifier>
    <enrichment key="AcceptedDate">2020-11-01</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73456</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Ana Djurdjevac</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</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="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>5167</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>A2654</pageFirst>
    <pageLast>A2672</pageLast>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>36</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Applications of the cross-entropy method to importance sampling and optimal control of diffusions</title>
    <parentTitle language="eng">Siam Journal on Scientific Computing</parentTitle>
    <identifier type="doi">10.1137/14096493X</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-49720</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>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="MIP_FORMATION">MIP_FORMATION</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
  </doc>
  <doc>
    <id>5141</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>69</pageFirst>
    <pageLast>78</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>113</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov State Models and Molecular Alchemy</title>
    <abstract language="deu">In recent years Markov State Models (MSMs) have attracted a consid-&#13;
erable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g., for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under con-&#13;
sideration. The performance of the reweighting scheme is illustrated for simple test cases including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.</abstract>
    <parentTitle language="eng">Molecular Physics</parentTitle>
    <identifier type="doi">10.1080/00268976.2014.944597</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-46718</enrichment>
    <author>Christof Schütte</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Adam Nielsen</author>
    <author>Marcus Weber</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MSM</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Reweighting</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Girsanov</value>
    </subject>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="EyeTracking">EyeTracking</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="TransRisk">TransRisk</collection>
  </doc>
  <doc>
    <id>6262</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>12</issue>
    <volume>146</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Set-Free Markov State Model Building</title>
    <parentTitle language="eng">Journal of Chemical Physics</parentTitle>
    <identifier type="doi">10.1063/1.4978501</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-62167</enrichment>
    <author>Marcus Weber</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Konstantin Fackeldey</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
  </doc>
  <doc>
    <id>4985</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>49</pageFirst>
    <pageLast>65</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1</volume>
    <type>incollection</type>
    <publisherName>European Mathematical Society</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Design of functional molecules</title>
    <parentTitle language="eng">MATHEON-Mathematics for Key Technologies</parentTitle>
    <enrichment key="Series">Series in Industrial and Applied Mathematics</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Christof Schütte</author>
    <editor>Peter Deuflhard</editor>
    <submitter>Erlinda Körnig</submitter>
    <author>Peter Deuflhard</author>
    <editor>Martin Grötschel</editor>
    <author>Frank Noé</author>
    <editor>Dietmar Hömberg</editor>
    <author>Marcus Weber</author>
    <editor>Ulrich Horst</editor>
    <editor>Jürg Kramer</editor>
    <editor>Volker Mehrmann</editor>
    <editor>Konrad Polthier</editor>
    <editor>Frank Schmidt</editor>
    <editor>Christof Schütte</editor>
    <editor>Martin Skutella</editor>
    <editor>Jürgen Sprekels</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
  </doc>
  <doc>
    <id>4671</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>2014-03-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov State Models and Molecular Alchemy</title>
    <abstract language="deu">In recent years Markov State Models (MSMs) have attracted a consid-&#13;
erable amount of attention with regard to modelling conformation changes&#13;
and associated function of biomolecular systems. They have been used&#13;
successfully, e.g., for peptides including time-resolved spectroscopic ex-&#13;
periments, protein function and protein folding , DNA and RNA, and&#13;
ligand-receptor interaction in drug design and more complicated multi-&#13;
valent scenarios. In this article a novel reweighting scheme is introduced&#13;
that allows to construct an MSM for certain molecular system out of an&#13;
MSM for a similar system. This permits studying how molecular proper-&#13;
ties on long timescales differ between similar molecular systems without&#13;
performing full molecular dynamics simulations for each system under con-&#13;
sideration. The performance of the reweighting scheme is illustrated for&#13;
simple test cases including one where the main wells of the respective en-&#13;
ergy landscapes are located differently and an alchemical transformation&#13;
of butane to pentane where the dimension of the state space is changed.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-46718</identifier>
    <identifier type="doi">10.1080/00268976.2014.944597</identifier>
    <enrichment key="SourceTitle">appeared in: Mol. Phys. 2014 (epub ahead of print)</enrichment>
    <author>Christof Schütte</author>
    <submitter>Adam Nielsen</submitter>
    <author>Adam Nielsen</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-05</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Girsanov Theorem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Stochastic Differential Equation</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Importance Sampling</value>
    </subject>
    <collection role="msc" number="60J70">Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="TransRisk">TransRisk</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4671/article_zib.pdf</file>
  </doc>
</export-example>
