<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>10043</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>126</pageFirst>
    <pageLast>149</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>15959</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-08-19</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN</title>
    <abstract language="eng">Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system’s long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the&#13;
CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs.</abstract>
    <parentTitle language="eng">Computational Methods in Systems Biology. CMSB 2025</parentTitle>
    <identifier type="doi">10.1007/978-3-032-01436-8_8</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2025-06-09</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <author>Maryam Yousefian</author>
    <submitter>Alexander Sikorski</submitter>
    <author>Luca Donati</author>
    <author>Alexander Sikorski</author>
    <author>Marcus Weber</author>
    <author>Susanna Röblitz</author>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="donati">Donati, Luca</collection>
  </doc>
  <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>
