<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>4878</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>350</pageFirst>
    <pageLast>376</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">Characterization of Rare Events in Molecular Dynamics</title>
    <parentTitle language="eng">Entropy (Special Issue)</parentTitle>
    <identifier type="doi">10.3390/e16010350</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-42410</enrichment>
    <enrichment key="SourceTitle">Appeared in: Entropy (Special Issue), 16 (2013), pp. 350-376</enrichment>
    <author>Carsten Hartmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Ralf Banisch</author>
    <author>Marco Sarich</author>
    <author>Thomas Badowski</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
  </doc>
  <doc>
    <id>4880</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>258</pageFirst>
    <pageLast>286</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">Markov State Models for Rare Events in Molecular Dynamics</title>
    <parentTitle language="eng">Entropy (Special Issue)</parentTitle>
    <identifier type="doi">10.3390/e16010258</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-42420</enrichment>
    <enrichment key="PeerReviewed">Yes</enrichment>
    <author>Marco Sarich</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Ralf Banisch</author>
    <author>Carsten Hartmann</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
  </doc>
  <doc>
    <id>6685</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>471</pageFirst>
    <pageLast>512</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>28</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2017-10-12</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics</title>
    <abstract language="eng">We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.</abstract>
    <parentTitle language="eng">Jounal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1007/s00332-017-9415-0</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-63822</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Stefan Klus</author>
    <author>Ralf Banisch</author>
    <author>Michael Dellnitz</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
  </doc>
  <doc>
    <id>5549</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reactive flows and unproductive cycles for random walks on complex networks</title>
    <parentTitle language="eng">The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387</parentTitle>
    <identifier type="doi">10.1140/epjst/e2015-02417-8</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-54239</enrichment>
    <author>Ralf Banisch</author>
    <submitter>Regine Kossick</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="projects" number="ECMath-CH7">ECMath-CH7</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>5423</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>2015-03-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reactive flows and unproductive cycles for random walks on complex networks</title>
    <abstract language="eng">We present a comprehensive theory for analysis and understanding of transition events between an initial set A and a target set B for general ergodic finite-state space Markov chains or jump processes, including random walks on networks as they occur, e.g., in Markov State Modelling in molecular dynamics. The theory allows us to decompose the probability flow generated by transition events between the sets A and B into the productive part that directly flows from A to B through reaction pathways and the unproductive part that runs in loops and is supported on cycles of the underlying network. It applies to random walks on directed networks and nonreversible Markov processes and can be seen as an extension of Transition Path Theory. Information on reaction pathways and unproductive cycles results from the stochastic cycle decomposition of the underlying network which also allows to compute their corresponding weight, thus characterizing completely which structure is used how often in transition events. The new theory is illustrated by an application to a Markov State Model resulting from weakly damped Langevin dynamics where the unproductive cycles are associated with periodic orbits of the underlying Hamiltonian dynamics.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-54239</identifier>
    <identifier type="doi">10.1140/epjst/e2015-02417-8</identifier>
    <enrichment key="SourceTitle">Appeared in: The European Physical Journal Special Topics, vol. 224, issue 12 ,(2015) pp. 2369-2387</enrichment>
    <author>Ralf Banisch</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-19</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Complex networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular transition networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition path theory</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cycle decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reactive trajectories</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markow State Methods</value>
    </subject>
    <collection role="msc" number="05C81">Random walks on graphs</collection>
    <collection role="msc" number="90B15">Network models, stochastic</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="projects" number="ECMath-CH7">ECMath-CH7</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="DynOOCompNet">DynOOCompNet</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5423/ZIB-Report_15-19.pdf</file>
  </doc>
  <doc>
    <id>5116</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>2014-08-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modularity of Directed Networks: Cycle Decomposition Approach</title>
    <abstract language="eng">The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-51166</identifier>
    <identifier type="doi">10.3934/jcd.2015.2.1</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal of Computational Dynamics 2 (2015) pp. 1-24</enrichment>
    <author>Natasa Djurdjevac Conrad</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Ralf Banisch</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-31</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>directed networks, modules, cycle decomposition, measure of node communication</value>
    </subject>
    <collection role="msc" number="05C81">Random walks on graphs</collection>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="94C15">Applications of graph theory [See also 05Cxx, 68R10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5116/ZIB-Report_14-31.pdf</file>
  </doc>
  <doc>
    <id>5197</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modularity of Directed Networks: Cycle Decomposition Approach</title>
    <abstract language="eng">The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.</abstract>
    <parentTitle language="eng">Journal of Computational Dynamics 2 (2015) pp. 1-24</parentTitle>
    <identifier type="doi">10.3934/jcd.2015.2.1</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-51166</enrichment>
    <author>Natasa Djurdjevac Conrad</author>
    <submitter>Christof Schütte</submitter>
    <author>Ralf Banisch</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="DynOOCompNet">DynOOCompNet</collection>
  </doc>
  <doc>
    <id>6382</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>2017-05-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics</title>
    <abstract language="eng">We consider complex dynamical systems showing metastable behavior but no local&#13;
separation of fast and slow time scales. The article raises the question of whether&#13;
such systems exhibit a low-dimensional manifold supporting its effective dynamics.&#13;
For answering this question, we aim at finding nonlinear coordinates, called reaction&#13;
coordinates, such that the projection of the dynamics onto these coordinates preserves&#13;
the dominant time scales of the dynamics. We show that, based on a specific&#13;
reducibility property, the existence of good low-dimensional reaction coordinates&#13;
preserving the dominant time scales is guaranteed. Based on this theoretical framework,&#13;
we develop and test a novel numerical approach for computing good reaction&#13;
coordinates. The proposed algorithmic approach is fully local and thus not prone to&#13;
the curse of dimension with respect to the state space of the dynamics. Hence, it is&#13;
a promising method for data-based model reduction of complex dynamical systems&#13;
such as molecular dynamics.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-63822</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="AcceptedDate">2017-09-23</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Stefan Klus</author>
    <author>Ralf Banisch</author>
    <author>Michael Dellnitz</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-22</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>slow dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>effective dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition manifold</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>embedding</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transfer operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction coordinate</value>
    </subject>
    <collection role="msc" number="47B38">Operators on function spaces (general)</collection>
    <collection role="msc" number="60H35">Computational methods for stochastic equations [See also 65C30]</collection>
    <collection role="msc" number="82C31">Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6382/ZIB-Report_17-22.pdf</file>
  </doc>
  <doc>
    <id>4984</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>2014-05-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Module Detection in Directed Real-World Networks</title>
    <abstract language="eng">We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-49849</identifier>
    <author>Ralf Banisch</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Natasa Djurdjevac Conrad</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Module identification and classification</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cycle decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>communication</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>directed networks</value>
    </subject>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="94C15">Applications of graph theory [See also 05Cxx, 68R10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMath-CH7">ECMath-CH7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4984/ZIB-Report_14-13.pdf</file>
  </doc>
  <doc>
    <id>4241</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-09-11</completedDate>
    <publishedDate>2013-09-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Characterization of Rare Events in Molecular Dynamics</title>
    <abstract language="eng">A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski's equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42410</identifier>
    <enrichment key="SourceTitle">Appeared in Entropy (Special Issue), 16 (1)</enrichment>
    <author>Carsten Hartmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Ralf Banisch</author>
    <author>Marco Sarich</author>
    <author>Thomas Badowski</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-51</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>moleculare dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal pathways</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamic programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>change of measure</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cumulant generating function</value>
    </subject>
    <collection role="msc" number="49M20">Methods of relaxation type</collection>
    <collection role="msc" number="60J45">Probabilistic potential theory [See also 31Cxx, 31D05]</collection>
    <collection role="msc" number="82C31">Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]</collection>
    <collection role="msc" number="93E20">Optimal stochastic control</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4241/ZIB-Report13-51.pdf</file>
  </doc>
  <doc>
    <id>4242</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-09-11</completedDate>
    <publishedDate>2013-09-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov State Models for Rare Events in Molecular Dynamics</title>
    <abstract language="eng">Rare but important transition events between long lived states are a key feature of many molecular systems. In many cases the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible even on the most powerful computers because of the immensely long simulation timescales needed. Recently a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs), has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore we introduce a novel approach to using MSMs for the eﬃcient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42420</identifier>
    <enrichment key="SourceTitle">Appeared in: Entropy (spec. issue)  16 (2013) 258-286</enrichment>
    <author>Marco Sarich</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Ralf Banisch</author>
    <author>Carsten Hartmann</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-52</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov state models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>long timescales</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <collection role="msc" number="49M29">Methods involving duality</collection>
    <collection role="msc" number="60J28">Applications of continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="60J35">Transition functions, generators and resolvents [See also 47D03, 47D07]</collection>
    <collection role="msc" number="93E20">Optimal stochastic control</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4242/ZIB-Report13-52.pdf</file>
  </doc>
  <doc>
    <id>6617</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>2017-12-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data-driven Computation of Molecular Reaction Coordinates</title>
    <abstract language="eng">The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated&#13;
on a realistic peptide system.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66179</identifier>
    <author>Andreas Bittracher</author>
    <submitter>Paulina Bressel</submitter>
    <author>Ralf Banisch</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-77</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction coordinate</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>coarse graining</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition manifold</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transfer operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Galerkin method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>meshfree basis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>data-driven</value>
    </subject>
    <collection role="msc" number="60H35">Computational methods for stochastic equations [See also 65C30]</collection>
    <collection role="msc" number="70K70">Systems with slow and fast motions</collection>
    <collection role="msc" number="82C31">Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6617/ZIB-Report_17-77.pdf</file>
  </doc>
  <doc>
    <id>6643</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>108</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Cycle-flow-based module detection in directed recurrence networks</title>
    <parentTitle language="eng">EPL (Europhysics Letters)</parentTitle>
    <identifier type="doi">10.1209/0295-5075/108/68008</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Ralf Banisch</author>
    <submitter>Marcus Weber</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="projects" number="SparseApproxiTN">SparseApproxiTN</collection>
  </doc>
</export-example>
