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  <doc>
    <id>4195</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-08-07</completedDate>
    <publishedDate>2013-08-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1</title>
    <abstract language="eng">Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are&#13;
used for modelling situations in which the evolution of a process is partly random and&#13;
partly controllable. These MDP theories allow for computing the optimal control policy&#13;
for processes that can continuously or frequently be observed, even if only partially.&#13;
However, they cannot be applied if state observation is very costly and therefore rare&#13;
(in time). We present a novel MDP theory for rare, costly observations and derive the&#13;
corresponding Bellman equation. In the new theory, state information can be derived&#13;
for a particular cost after certain, rather long time intervals. The resulting information&#13;
costs enter into the total cost and thus into the optimization criterion. This approach&#13;
applies to many real world problems, particularly in the medical context, where the&#13;
medical condition is examined rather rarely because examination costs are high. At the&#13;
same time, the approach allows for efficient numerical realization. We demonstrate the&#13;
usefulness of the novel theory by determining, from the national economic perspective,&#13;
optimal therapeutic policies for the treatment of the human immunodefficiency virus&#13;
(HIV) in resource-rich and resource-poor settings. Based on the developed theory and&#13;
models, we discover that available drugs may not be utilized efficiently in resource-poor&#13;
settings due to exorbitant diagnostic costs.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-41955</identifier>
    <identifier type="doi">10.4310/CMS.2014.v12.n5.a4</identifier>
    <enrichment key="SourceTitle">Appeared In: Comm. in Mathematical Sciences 12 (2014) 859-877</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-34</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>information costs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hidden state</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bellmann equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal therapeutic policies</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>diagnostic frequency</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>resource-poor</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>resource-rich</value>
    </subject>
    <collection role="msc" number="49N30">Problems with incomplete information [See also 93C41]</collection>
    <collection role="msc" number="60J27">Continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="60J28">Applications of continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="90C40">Markov and semi-Markov decision processes</collection>
    <collection role="msc" number="93B07">Observability</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>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4195/ZR-13-34.pdf</file>
  </doc>
  <doc>
    <id>6099</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>2016-11-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling</title>
    <abstract language="eng">Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments  and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by  Galerkin projection methods is presented.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60999</identifier>
    <enrichment key="SourceTitle">AIP - Journal of Chemical Physics 145 (2016)</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-60</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction-diffusion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic chemical kinetics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>chemical master equation</value>
    </subject>
    <collection role="ccs" number="">Stochastic processes (NEW)</collection>
    <collection role="msc" number="60J27">Continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="82C22">Interacting particle systems [See also 60K35]</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>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6099/ZIB-report_SpatiotemporalCME.pdf</file>
  </doc>
  <doc>
    <id>6095</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>21</issue>
    <volume>145</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2016-12-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Spatiotemporal Master Equation: Approximation of Reaction-Diffusion Dynamics via Markov State Modeling</title>
    <abstract language="eng">Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest.We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.</abstract>
    <parentTitle language="eng">Journal of Chemical Physics</parentTitle>
    <identifier type="doi">10.1063/1.4971163</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">http://scitation.aip.org/content/aip/journal/jcp/145/21/10.1063/1.4971163</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-60999</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>6096</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>11</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV/1 in Resource-Poor Settings</title>
    <abstract language="eng">An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention’ may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention’ for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that ‘treatment-for-prevention’ may be further improved using either of the two analyzed treatment paradigms.</abstract>
    <parentTitle language="eng">PloS Computational Biology</parentTitle>
    <identifier type="doi">10.1371/journal.pcbi.1004200</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Sulav Duwal</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>2659</id>
    <completedYear>2012</completedYear>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>259</pageFirst>
    <pageLast>282</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>134</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal control of molecular dynamics using Markov state models</title>
    <parentTitle language="eng">Math. Program. (Series B)</parentTitle>
    <identifier type="url">http://publications.imp.fu-berlin.de/1107/</identifier>
    <identifier type="doi">10.1007/s10107-012-0547-6</identifier>
    <author>Christof Schütte</author>
    <author>Stefanie Winkelmann</author>
    <author>Carsten Hartmann</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
  </doc>
  <doc>
    <id>2669</id>
    <completedYear>2012</completedYear>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>859</issue>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov Control Processes with Rare State Observation</title>
    <parentTitle language="eng">Communications in Mathematical Sciences</parentTitle>
    <identifier type="url">http://publications.imp.fu-berlin.de/1176/</identifier>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
  </doc>
  <doc>
    <id>2670</id>
    <completedYear>2012</completedYear>
    <publishedYear>2012</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">Markov Control with Rare State Observation</title>
    <parentTitle language="eng">International Journal of Biomathematics and Biostatistics</parentTitle>
    <identifier type="url">http://publications.mi.fu-berlin.de/1177/</identifier>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
  </doc>
  <doc>
    <id>6949</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>24</pageNumber>
    <edition>EPJ Data Science</edition>
    <issue>1</issue>
    <volume>7</volume>
    <type>article</type>
    <publisherName>EPJ Data Science</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach</title>
    <abstract language="eng">Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.</abstract>
    <parentTitle language="eng">EPJ Data Science</parentTitle>
    <identifier type="doi">10.1140/epjds/s13688-018-0153-9</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-07-02</enrichment>
    <enrichment key="SourceTitle">EPJ Data Science</enrichment>
    <author>Natasa Djurdjevac Conrad</author>
    <submitter>Natasa Djurdjevac Conrad</submitter>
    <author>Luzie Helfmann</author>
    <author>Johannes Zonker</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
  </doc>
  <doc>
    <id>7575</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>8</volume>
    <type>book</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stochastic Dynamics in Computational Biology</title>
    <parentTitle language="eng">Frontiers in Applied Dynamical Systems: Reviews and Tutorials</parentTitle>
    <identifier type="isbn">978-3-030-62386-9</identifier>
    <identifier type="doi">10.1007/978-3-030-62387-6</identifier>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</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="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
  </doc>
  <doc>
    <id>7730</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>31</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-03-16</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Agent-based modeling: Population limits and large timescales</title>
    <abstract language="eng">Modeling, simulation and analysis of interacting agent systems is a broad field of research, with  existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (ODEs and SDEs, respectively) for medium to large populations. By means of an appropriately adapted transfer operator approach we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations. This approach has the potential to drastically reduce computational effort for the analysis of ABMs.</abstract>
    <parentTitle language="eng">Chaos: An Interdisciplinary Journal of Nonlinear Science</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-77309</identifier>
    <identifier type="doi">10.1063/5.0031373</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-02-28</enrichment>
    <author>Jan-Hendrik Niemann</author>
    <submitter>Jan-Hendrik Niemann</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Sarah Wolf</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="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="MathPlus-EF4-3">MathPlus-EF4-3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7730/AgentInteractionJumpProcess.pdf</file>
  </doc>
  <doc>
    <id>7345</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>2019-06-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From interacting agents to density-based modeling with stochastic PDEs</title>
    <abstract language="eng">Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing  ABM and SPDE models.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-73456</identifier>
    <enrichment key="SourceTitle">Comm. Appl. Math. Comp. Sci. 16(1):1-32, 2021</enrichment>
    <enrichment key="zib_relatedIdentifier">https://doi.org/10.2140/camcos.2021.16.1</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Ana Djurdjevac</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-21</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7345/main.pdf</file>
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  <doc>
    <id>7339</id>
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    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
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    <pageFirst>1</pageFirst>
    <pageLast>32</pageLast>
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    <edition/>
    <issue>1</issue>
    <volume>16</volume>
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    <title language="eng">From interacting agents to density-based modeling with stochastic PDEs</title>
    <abstract language="eng">Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.</abstract>
    <parentTitle language="eng">Communications in Applied Mathematics and Computational Science</parentTitle>
    <identifier type="arxiv">1905.13525</identifier>
    <identifier type="doi">10.2140/camcos.2021.16.1</identifier>
    <enrichment key="AcceptedDate">2020-11-01</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73456</enrichment>
    <author>Luzie Helfmann</author>
    <submitter>Luzie Helfmann</submitter>
    <author>Natasa Djurdjevac Conrad</author>
    <author>Ana Djurdjevac</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="INNOSPREAD">INNOSPREAD</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>5220</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>859</pageFirst>
    <pageLast>877</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1</title>
    <abstract language="eng">Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are used for modelling situations in which the evolution of a process is partly random and partly controllable. These MDP theories allow for computing the optimal control policy for processes that can continuously or frequently be observed, even if only partially. However, they cannot be applied if state observation is very costly and therefore rare (in time). We present a novel MDP theory for rare, costly observations and derive the corresponding Bellman equation. In the new theory, state information can be derived for a particular cost after certain, rather long time intervals. The resulting information costs enter into the total cost and thus into the optimization criterion. This approach applies to many real world problems, particularly in the medical context, where the medical condition is examined rather rarely because examination costs are high. At the same time, the approach allows for efficient numerical realization. We demonstrate the usefulness of the novel theory by determining, from the national economic perspective, optimal therapeutic policies for the treatment of the human immunodeficiency virus (HIV) in resource-rich and resource-poor settings. Based on the developed theory and models, we discover that available drugs may not be utilized efficiently in resource-poor settings due to exorbitant diagnostic costs.</abstract>
    <parentTitle language="eng">Communications in Mathematical Sciences</parentTitle>
    <identifier type="doi">10.4310/CMS.2014.v12.n5.a4</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-41955</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMath-CH6">ECMath-CH6</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>5216</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>2</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov Control Processes with Rare State Observation: Sensitivity Analysis with Respect to Optimal Treatment Strategies against HIV-1</title>
    <abstract language="eng">We present the theory of “Markov decision processes (MDP) with rare state observation” and apply it to optimal treatment scheduling and diagnostic testing to mitigate HIV-1 drug resistance development in resource-poor countries. The developed theory assumes that the state of the process is hidden and can only be determined by making an examination. Each examination produces costs which enter into the considered cost functional so that the resulting optimization problem includes finding optimal examination times. This is a realistic ansatz: In many real world applications, like HIV-1 treatment scheduling, the information about the disease evolution involves substantial costs, such that examination and control are intimately connected. However, a perfect compliance with the optimal strategy can rarely be achieved. This may be particularly true for HIV-1 resistance testing in resource-constrained countries. In the present work, we therefore analyze the sensitivity of the costs with respect to deviations from the optimal examination times both analytically and for the considered application. We&#13;
discover continuity in the cost-functional with respect to the examination times. For the HIV-application, moreover, sensitivity towards small deviations from the optimal examination rule depends on the disease state. Furthermore, we compare the optimal rare-control strategy to (i) constant control strategies (one action for the remaining time) and to (ii) the permanent control of the original, fully observed MDP. This comparison is&#13;
done in terms of expected costs and in terms of life-prolongation. The proposed rare-control strategy offers a clear benefit over a constant control, stressing the usefulness of medical testing and informed decision making. This indicates that lower-priced medical tests could improve HIV treatment in resource-constrained settings and warrants further investigation.</abstract>
    <parentTitle language="eng">International Journal of Biomathematics and Biostatistics</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
  </doc>
  <doc>
    <id>6426</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hybrid Models for Chemical Reaction Networks: Multiscale Theory and Application to Gene Regulatory Systems</title>
    <abstract language="eng">Well-mixed stochastic chemical kinetics are properly modelled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows to express various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-64264</identifier>
    <enrichment key="SourceTitle">The Journal of Chemical Physics 147 (2017)</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-29</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6426/ZIB-report_HybridModels.pdf</file>
  </doc>
  <doc>
    <id>6501</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>114115-1</pageFirst>
    <pageLast>114115-18</pageLast>
    <pageNumber/>
    <edition/>
    <issue>11</issue>
    <volume>147</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems</title>
    <abstract language="eng">Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.</abstract>
    <parentTitle language="eng">The Journal of Chemical Physics</parentTitle>
    <identifier type="doi">10.1063/1.4986560</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-64264</enrichment>
    <enrichment key="FulltextUrl">http://scitation.aip.org/content/aip/journal/jcp/147/11/10.1063/1.4986560</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</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="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
  </doc>
  <doc>
    <id>8267</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-06-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics</title>
    <abstract language="eng">Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact ﬁrst- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the ﬁltered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to eﬃciently compare diﬀerent spatial coarse graining approaches for a speciﬁc model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a ﬁltered stochastic signal.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-82674</identifier>
    <identifier type="doi">10.1016/j.mbs.2021.108760</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SourceTitle">Mathematical Biosciences 343:108760</enrichment>
    <author>Ariane Ernst</author>
    <submitter>Ariane Ernst</submitter>
    <author>Christof Schütte</author>
    <author>Stephan Sigrist</author>
    <author>Stefanie Winkelmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-15</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear reaction networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross-correlation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>neurotransmission</value>
    </subject>
    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</collection>
    <collection role="msc" number="92-XX">BIOLOGY AND OTHER NATURAL SCIENCES</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8267/ZIBReport.pdf</file>
  </doc>
  <doc>
    <id>8270</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>343</volume>
    <type>article</type>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics</title>
    <abstract language="eng">Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact ﬁrst- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the ﬁltered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to eﬃciently compare diﬀerent spatial coarse graining approaches for a speciﬁc model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a ﬁltered stochastic signal.</abstract>
    <parentTitle language="eng">Mathematical Biosciences</parentTitle>
    <identifier type="doi">10.1016/j.mbs.2021.108760</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-82674</enrichment>
    <enrichment key="AcceptedDate">2021-10-25</enrichment>
    <author>Ariane Ernst</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Stephan Sigrist</author>
    <author>Stefanie Winkelmann</author>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
  </doc>
  <doc>
    <id>8274</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>607</issue>
    <volume>13</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2023-01-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design</title>
    <abstract language="eng">We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.</abstract>
    <parentTitle language="eng">Scientific Reports</parentTitle>
    <identifier type="doi">10.1038/s41598-023-27699-w</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2023-01-06</enrichment>
    <author>Arne Thies</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Vikram Sunkara</author>
    <author>Sourav Ray</author>
    <author>Hanna Wulkow</author>
    <author>M. Özgür Celik</author>
    <author>Fatih Yergöz</author>
    <author>Christof Schütte</author>
    <author>Christoph Stein</author>
    <author>Marcus Weber</author>
    <author>Stefanie Winkelmann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</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>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
  </doc>
  <doc>
    <id>8279</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
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    <edition/>
    <issue/>
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    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-07-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design</title>
    <abstract language="eng">Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. &#13;
We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. &#13;
The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. &#13;
We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. &#13;
These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-82797</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Sourav Ray</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Arne Thies</author>
    <author>Vikram Sunkara</author>
    <author>Hanna Wulkow</author>
    <author>Özgür Celik</author>
    <author>Fatih Yergöz</author>
    <author>Christof Schütte</author>
    <author>Christoph Stein</author>
    <author>Marcus Weber</author>
    <author>Stefanie Winkelmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-19</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8279/ZIB-Report.pdf</file>
  </doc>
  <doc>
    <id>8602</id>
    <completedYear>2023</completedYear>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>837</pageFirst>
    <pageLast>861</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>83</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-04-28</completedDate>
    <publishedDate>2023-04-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures</title>
    <abstract language="eng">The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257–2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.</abstract>
    <parentTitle language="eng">SIAM Journal on Applied Mathematics</parentTitle>
    <identifier type="arxiv">2201.02613</identifier>
    <identifier type="doi">10.1137/22M1488831</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2022-12-13</enrichment>
    <author>Alberto Montefusco</author>
    <submitter>Alberto Montefusco</submitter>
    <author>Christof Schütte</author>
    <author>Stefanie Winkelmann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
  </doc>
  <doc>
    <id>9723</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1231</pageFirst>
    <pageLast>1250</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>24</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Approximating particle-based clustering dynamics by stochastic PDEs</title>
    <abstract language="eng">This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.</abstract>
    <parentTitle language="eng">SIAM Journal on Applied Dynamical Systems</parentTitle>
    <identifier type="arxiv">2407.18952</identifier>
    <identifier type="doi">10.1137/24M1676661</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Nathalie Wehlitz</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Mohsen Sadeghi</author>
    <author>Alberto Montefusco</author>
    <author>Christof Schütte</author>
    <author>Grigorios A. Pavliotis</author>
    <author>Stefanie Winkelmann</author>
    <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>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="unger">Unger, Nathalie</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
  </doc>
  <doc>
    <id>9131</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>369</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-01-12</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Partial mean-field model for neurotransmission dynamics</title>
    <abstract language="eng">This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.</abstract>
    <parentTitle language="deu">Mathematical Biosciences</parentTitle>
    <identifier type="arxiv">2307.01737</identifier>
    <identifier type="doi">10.1016/j.mbs.2024.109143</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2024-01-10</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Alberto Montefusco</author>
    <submitter> Winkelmann</submitter>
    <author>Luzie Helfmann</author>
    <author>Toluwani Okunola</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
  </doc>
  <doc>
    <id>10070</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>13</issue>
    <volume>26</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-06-27</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Investigating Endogenous Opioids Unravels the Mechanisms Behind Opioid-Induced Constipation, a Mathematical Modeling Approach</title>
    <abstract language="eng">Endogenous opioids, such as Endomorphin-2, are not typically associated with severe constipation, unlike pharmaceutical opioids, which induce opioid-induced constipation (OIC) by activating μ-opioid receptors in the gastrointestinal tract. In this study, we present a mathematical model, which integrates the serotonergic and opioid pathways, simulating the interaction between serotonin and opioid signaling within the enteric nervous system (ENS). The model explores the mechanisms underlying OIC, with a focus on the change in adenylyl cyclase (AC) activity, cAMP accumulation, and the distinct functionalities of Endomorphin-2 compared to commonly used pharmaceutical opioids. We study the effects of Morphine, Fentanyl, and Methadone and contrast them with Endomorphin-2. Our findings reveal that opioids do not perturb the signaling of serotonin, but only the activity of AC, suggesting that serotonin levels have no influence on improving opioid-induced constipation. Furthermore, this study reveals that the primary difference between endogenous and pharmaceutical opioids is their degradation rates. This finding shows that modulating opioid degradation rates significantly improves cAMP recovery. In conclusion, our insights steer towards exploring opioid degrading enzymes, localized to the gut, as a strategy for mitigating OIC.</abstract>
    <parentTitle language="eng">International Journal of Molecular Sciences</parentTitle>
    <identifier type="doi">10.3390/ijms26136207</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2025-06-24</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Celvic Coomber</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Surahit Chewle</author>
    <author>Christopher Secker</author>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <author>Vikram Sunkara</author>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="institutes" number="scp">Supercomputing</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="persons" number="coomber">Coomber, Celvic</collection>
    <collection role="persons" number="chewle">Chewle, Surahit</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
    <collection role="persons" number="secker">Secker, Christopher</collection>
    <collection role="projects" number="CCMAI">CCMAI</collection>
    <collection role="projects" number="MathPlusAA1-19">MathPlusAA1-19</collection>
  </doc>
  <doc>
    <id>8155</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>336</volume>
    <type>article</type>
    <publisherName>Elsevier</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-04-19</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading</title>
    <abstract language="eng">Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.</abstract>
    <parentTitle language="eng">Mathematical Biosciences</parentTitle>
    <identifier type="doi">10.1016/j.mbs.2021.108619</identifier>
    <identifier type="arxiv">2205.05000</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-04-07</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Johannes Zonker</author>
    <author>Christof Schütte</author>
    <author>Natasa Djurdjevac Conrad</author>
    <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>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusEF5-1">MathPlusEF5-1</collection>
  </doc>
  <doc>
    <id>8405</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>49</issue>
    <volume>112</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations</title>
    <parentTitle language="eng">Letters in Mathematical Physics</parentTitle>
    <identifier type="arxiv">arXiv:2109.13616</identifier>
    <identifier type="doi">10.1007/s11005-022-01539-w</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2022-04-21</enrichment>
    <author>Mauricio del Razo</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Daniela Frömberg</author>
    <author>Arthur Straube</author>
    <author>Christof Schütte</author>
    <author>Felix Höfling</author>
    <author>Stefanie Winkelmann</author>
    <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>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <collection role="persons" number="delrazo">del Razo Sarmina, Mauricio</collection>
    <collection role="projects" number="DFG-OpenMultiscaleBiochem">DFG-OpenMultiscaleBiochem</collection>
  </doc>
  <doc>
    <id>8412</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>9888</pageFirst>
    <pageLast>9893</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-10-05</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles</title>
    <abstract language="eng">The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller.&#13;
The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.</abstract>
    <parentTitle language="deu">J. Phys. Chem. Lett.</parentTitle>
    <identifier type="doi">10.1021/acs.jpclett.1c03016</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Arthur Straube</author>
    <submitter>Arthur Straube</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Christof Schütte</author>
    <author>Felix Höfling</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vas">Distributed Algorithms and Supercomputing</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-18">MathPlusAA1-18</collection>
  </doc>
  <doc>
    <id>8954</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>362</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-05-26</completedDate>
    <publishedDate>2023-06-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Rate-limiting recovery processes in neurotransmission under sustained stimulation</title>
    <abstract language="deu">At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution.</abstract>
    <parentTitle language="deu">Mathematical Biosciences</parentTitle>
    <identifier type="arxiv">2302.01635</identifier>
    <identifier type="doi">10.1016/j.mbs.2023.109023</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-05-20</enrichment>
    <author>Ariane Ernst</author>
    <submitter>Ariane Ernst</submitter>
    <author>Nathalie Unger</author>
    <author>Christof Schütte</author>
    <author>Alexander Walter</author>
    <author>Stefanie Winkelmann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-5">MathPlusAA1-5</collection>
    <collection role="persons" number="unger">Unger, Nathalie</collection>
  </doc>
  <doc>
    <id>10262</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data-driven Reduction of Transfer Operators for Particle Clustering   Dynamics</title>
    <abstract language="eng">We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics.</abstract>
    <identifier type="arxiv">2601.02932</identifier>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Nathalie Wehlitz</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Grigorios Pavliotis</author>
    <author>Christof Schütte</author>
    <author>Stefanie Winkelmann</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="unger">Unger, Nathalie</collection>
  </doc>
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