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  <doc>
    <id>4219</id>
    <completedYear/>
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    <language>eng</language>
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    <edition/>
    <issue/>
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    <type>reportzib</type>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-08-28</completedDate>
    <publishedDate>2013-08-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A square root approximation of transition rates for a Markov State Model</title>
    <abstract language="eng">Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular configuration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in configuration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional configuration space provides proof of concept and an example for which we compare the performance of different discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, finding discretizations of higher-dimensional configuration spaces in which metastable sets can be identified remains a challenge.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1137/120899959</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42195</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Matrix Anal. Appl. 34 (2013) pp. 738 - 756</enrichment>
    <author>Han Cheng Lie</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-43</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chains</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>meshfree methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Voronoi</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear programming</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="pacs" number="30.00.00">ATOMIC AND MOLECULAR PHYSICS</collection>
    <collection role="msc" number="60J10">Markov chains (discrete-time Markov processes on discrete state spaces)</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="msc" number="82B80">Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]</collection>
    <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="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4219/zibtitlepage.pdf</file>
  </doc>
  <doc>
    <id>4257</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
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    <pageNumber/>
    <edition/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-09-27</completedDate>
    <publishedDate>2013-09-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient Conformational Analysis by Partition-of-Unity Coupling</title>
    <abstract language="eng">Obtaining a sufficient sampling of conformational space is a common problem in molecular simulation. We present the implementation of an umbrella-like adaptive sampling approach based on function-based meshless discretization of conformational space that is compatible with state of the art molecular dynamics code and that integrates an eigenvector-based clustering approach for conformational analysis and the computation of inter-conformational transition rates. The approach is applied to three example systems, namely n-pentane, alanine dipeptide, and a small synthetic host-guest system, the latter two including explicitly modeled solvent.</abstract>
    <parentTitle language="eng">Math Chem</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42570</identifier>
    <author>Alexander Bujotzek</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Ole Schütt</author>
    <author>Adam Nielsen</author>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-58</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Meshfree</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Molecular Simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Partition of Unity</value>
    </subject>
    <collection role="ccs" number="G.4">MATHEMATICAL SOFTWARE</collection>
    <collection role="ccs" number="">Markov processes (NEW)</collection>
    <collection role="pacs" number="87.10.-e">General theory and mathematical aspects</collection>
    <collection role="msc" number="60Jxx">Markov processes</collection>
    <collection role="msc" number="92-08">Computational methods</collection>
    <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="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <collection role="projects" number="MIP_FORMATION">MIP_FORMATION</collection>
    <collection role="projects" number="NAMPAR">NAMPAR</collection>
    <collection role="projects" number="Salsa-Klimm">Salsa-Klimm</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4257/MolPyPUM.pdf</file>
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  <doc>
    <id>6035</id>
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    <language>eng</language>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-05-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes</title>
    <abstract language="eng">In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60353</identifier>
    <identifier type="doi">10.1137/16M1091162</identifier>
    <author>Jakob Witzig</author>
    <submitter>Jakob Witzig</submitter>
    <author>Isabel Beckenbach</author>
    <author>Leon Eifler</author>
    <author>Konstantin Fackeldey</author>
    <author>Ambros Gleixner</author>
    <author>Andreas Grever</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non-reversible Markov Processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NESS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</collection>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="msc" number="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="beckenbach">Beckenbach, Isabel</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="SparseApproxiTN">SparseApproxiTN</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6035/ZR-16-39-revised2.pdf</file>
  </doc>
  <doc>
    <id>6029</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>248</pageFirst>
    <pageLast>265</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>16</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2018-02-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes</title>
    <abstract language="eng">In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.</abstract>
    <parentTitle language="eng">Multiscale Modeling and Simulation</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1137/16M1091162</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-60353</enrichment>
    <enrichment key="SourceTitle">Multiscale Modeling and Simulation</enrichment>
    <enrichment key="AcceptedDate">2017-10-18</enrichment>
    <author>Jakob Witzig</author>
    <submitter>Jakob Witzig</submitter>
    <author>Isabel Beckenbach</author>
    <author>Leon Eifler</author>
    <author>Konstantin Fackeldey</author>
    <author>Ambros Gleixner</author>
    <author>Andreas Grever</author>
    <author>Marcus Weber</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NESS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non-reversible Markov Processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Programming</value>
    </subject>
    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</collection>
    <collection role="msc" number="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="beckenbach">Beckenbach, Isabel</collection>
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    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="SparseApproxiTN">SparseApproxiTN</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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