<?xml version="1.0" encoding="utf-8"?>
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  <doc>
    <id>9555</id>
    <completedYear>2024</completedYear>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>41</pageFirst>
    <pageLast>58</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>De Gruyter</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-04-16</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions</title>
    <abstract language="eng">Markov processes serve as foundational models in many scientific disciplines,&#13;
such as molecular dynamics, and their simulation forms a common basis for&#13;
analysis. While simulations produce useful trajectories, obtaining macroscopic&#13;
information directly from microstate data presents significant challenges. This&#13;
paper addresses this gap by introducing the concept of membership functions&#13;
being the macrostates themselves. We derive equations for the holding times of&#13;
these macrostates and demonstrate their consistency with the classical definition.&#13;
Furthermore, we discuss the application of the ISOKANN method for learning&#13;
these quantities from simulation data. In addition, we present a novel method&#13;
for extracting transition paths based on the ISOKANN results and demonstrate&#13;
its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this&#13;
approach we provide a new perspective on analyzing the macroscopic behaviour&#13;
of Markov systems.</abstract>
    <parentTitle language="eng">Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023</parentTitle>
    <identifier type="arxiv">2404.10523</identifier>
    <identifier type="doi">10.1515/9783111376776-004</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2024-07-15</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Alexander Sikorski</author>
    <submitter>Alexander Sikorski</submitter>
    <editor>K. Fackeldey</editor>
    <author>Robert Julian Rabben</author>
    <author>Surahit Chewle</author>
    <author>Marcus Weber</author>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="persons" number="rabben">Rabben, Robert Julian</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="chewle">Chewle, Surahit</collection>
    <collection role="projects" number="NHR@ZIB">NHR@ZIB</collection>
    <collection role="projects" number="CCMAI">CCMAI</collection>
  </doc>
</export-example>
