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  <doc>
    <id>7587</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>416</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A probabilistic algorithm for aggregating vastly undersampled large Markov chains</title>
    <parentTitle language="eng">Physica D: Nonlinear Phenomena</parentTitle>
    <identifier type="urn">urn:nbn:de:0297-zib-75874</identifier>
    <identifier type="doi">https://doi.org/10.1016/j.physd.2020.132799</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-78688</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
  </doc>
  <doc>
    <id>7588</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>31</volume>
    <type>article</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-12-18</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds</title>
    <abstract language="eng">We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.</abstract>
    <parentTitle language="eng">Journal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1007/s00332-020-09668-z</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Stefan Klus</author>
    <author>Boumediene Hamzi</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="MathPlusAA1-1">MathPlusAA1-1</collection>
  </doc>
  <doc>
    <id>7790</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>132</pageFirst>
    <pageLast>150</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>304</volume>
    <type>incollection</type>
    <publisherName>Springer International</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A weak characterization of slow variables in stochastic dynamical systems</title>
    <parentTitle language="eng">Advances in Dynamics, Optimization and Computation.&#13;
Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday</parentTitle>
    <identifier type="isbn">978-3-030-51264-4</identifier>
    <identifier type="doi">10.1007/978-3-030-51264-4_6</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <editor>Oliver Junge</editor>
    <author>Christof Schütte</author>
    <editor>O. Schütze</editor>
    <editor>Gary Froyland</editor>
    <editor>S. Ober-Blobaum</editor>
    <editor>E. Padberg-Gehle</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>7868</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2020-06-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A probabilistic algorithm for aggregating vastly undersampled large Markov chains</title>
    <abstract language="eng">Model reduction of large Markov chains is an essential step in a wide array of techniques for understanding complex systems and for efficiently learning structures from high-dimensional data. We present a novel aggregation algorithm for compressing such chains that exploits a specific low-rank structure in the transition matrix which, e.g., is present in metastable systems, among others. It enables the recovery of the aggregates from a vastly undersampled transition matrix which in practical applications may gain a speedup of several orders of mag- nitude over methods that require the full transition matrix. Moreover, we show that the new technique is robust under perturbation of the transition matrix. The practical applicability of the new method is demonstrated by identifying a reduced model for the large-scale traffic flow patterns from real-world taxi trip data.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-78688</identifier>
    <identifier type="url">https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/7587</identifier>
    <enrichment key="SourceTitle">Appeard in: Physica D</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-21</number>
    </series>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7868/ZR-20-21.pdf</file>
  </doc>
  <doc>
    <id>8210</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>94</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis</title>
    <parentTitle language="eng">The European Physical Journal B</parentTitle>
    <identifier type="doi">10.1140/epjb/s10051-021-00200-0</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Johann Moschner</author>
    <author>Beate Koksch</author>
    <author>Roland Netz</author>
    <author>Christof Schütte</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
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