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<export-example>
  <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>6486</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>2017-09-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics</title>
    <abstract language="eng">We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64868</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-08-15</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <author>Péter Koltai</author>
    <submitter>Paulina Bressel</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-49</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov state model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-equilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>two timescale master equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-stationary forcing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <collection role="msc" number="34E13">Multiple scale methods</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="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6486/ZIB-Report_17-49.pdf</file>
  </doc>
  <doc>
    <id>5786</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition>145</edition>
    <issue/>
    <volume>174103</volume>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-03-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On metastability and Markov state models for non-stationary molecular dynamics</title>
    <abstract language="eng">We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, “meta- stable” sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.</abstract>
    <parentTitle language="eng">The Journal of Chemical Physics</parentTitle>
    <subTitle language="deu">2016 Editor's Choice of The Journal of Chemical Physics</subTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57869</identifier>
    <identifier type="doi">10.1063/1.4966157</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Appeared in: The Journal of Chemical Physics 145 (2016)</enrichment>
    <author>Peter Koltai</author>
    <submitter>Erlinda Koernig</submitter>
    <author>Giovanni Ciccotti</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-11</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>coherent set,</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov state model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-equilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</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="60J35">Transition functions, generators and resolvents [See also 47D03, 47D07]</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</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="projects" number="no-project">no-project</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5786/ZIB_16-11_new.pdf</file>
  </doc>
  <doc>
    <id>6607</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>2017-12-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From Metastable to Coherent Sets - time-discretization schemes</title>
    <abstract language="eng">Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in  $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66074</identifier>
    <author>Konstantin Fackeldey</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Peter Névir</author>
    <author>Henning Rust</author>
    <author>Axel Schild</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-74</number>
    </series>
    <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="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6607/ZIB-Report_17-74.pdf</file>
  </doc>
</export-example>
