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  <doc>
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    <language>eng</language>
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    <completedDate>--</completedDate>
    <publishedDate>2022-12-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning</title>
    <abstract language="eng">One of the main challenges in molecular dynamics is overcoming the “timescale barrier”, a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics, and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behavior on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory as well as the algorithmic development from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and&#13;
improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in MD. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-88637</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Christof Schütte</author>
    <submitter>Ekaterina Engel</submitter>
    <author>Stefan Klus</author>
    <author>Carsten Hartmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-25</number>
    </series>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlusAA1-15">MathPlusAA1-15</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8863/ZIB-Report-22-25.pdf</file>
  </doc>
  <doc>
    <id>8676</id>
    <completedYear/>
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    <language>eng</language>
    <pageFirst/>
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    <completedDate>--</completedDate>
    <publishedDate>2022-05-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia</title>
    <abstract language="eng">Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process.&#13;
	However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-86764</identifier>
    <author>Margarita Kostré</author>
    <submitter>Margarita Kostre</submitter>
    <author>Vikram Sunkara</author>
    <author>Christof Schütte</author>
    <author>Nataša Djurdjevac Conrad</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data</value>
    </subject>
    <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="sunkara">Sunkara, Vikram</collection>
    <collection role="persons" number="kostre">Kostre, Margarita</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="projects" number="MathPlusEF5-2">MathPlusEF5-2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8676/ZIBReportKostre.pdf</file>
  </doc>
  <doc>
    <id>8523</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
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    <pageNumber/>
    <edition/>
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    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-12-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics</title>
    <abstract language="eng">Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Enric Ribera Borrell</author>
    <submitter>Jannes Quer</submitter>
    <author>Jannes Quer</author>
    <author>Lorenz Richter</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>importance sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare event simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>neural networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metadynamics</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="68-XX">COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="persons" number="ribera.borrell">Ribera Borrell, Enric</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="richter">Richter, Lorenz</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8523/improving_is_strategies_via_metadynamics.pdf</file>
  </doc>
  <doc>
    <id>8279</id>
    <completedYear/>
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    <language>eng</language>
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    <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>8267</id>
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    <language>eng</language>
    <pageFirst/>
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    <type>reportzib</type>
    <publisherName/>
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    <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>7966</id>
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    <language>eng</language>
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    <completedDate>--</completedDate>
    <publishedDate>2020-09-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Inferring Gene Regulatory Networks from Single Cell RNA-seq Temporal Snapshot Data Requires Higher Order Moments</title>
    <abstract language="eng">Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. &#13;
&#13;
In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. &#13;
&#13;
We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver.  &#13;
&#13;
There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-79664</identifier>
    <author>Vikram Sunkara</author>
    <submitter>vikram sunkara</submitter>
    <author>N. Alexia Raharinirina</author>
    <author>Felix Peppert</author>
    <author>Max von Kleist</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-25</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7966/RAHARINIRINA et al 2020.pdf</file>
  </doc>
  <doc>
    <id>7868</id>
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    <language>eng</language>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2020-06-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A probabilistic algorithm for aggregating vastly undersampled large Markov chains</title>
    <abstract language="eng">Model reduction of large Markov chains is an essential step in a wide array of techniques for understanding complex systems and for efficiently learning structures from high-dimensional data. We present a novel aggregation algorithm for compressing such chains that exploits a specific low-rank structure in the transition matrix which, e.g., is present in metastable systems, among others. It enables the recovery of the aggregates from a vastly undersampled transition matrix which in practical applications may gain a speedup of several orders of mag- nitude over methods that require the full transition matrix. Moreover, we show that the new technique is robust under perturbation of the transition matrix. The practical applicability of the new method is demonstrated by identifying a reduced model for the large-scale traffic flow patterns from real-world taxi trip data.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-78688</identifier>
    <identifier type="url">https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/7587</identifier>
    <enrichment key="SourceTitle">Appeard in: Physica D</enrichment>
    <author>Andreas Bittracher</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-21</number>
    </series>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7868/ZR-20-21.pdf</file>
  </doc>
  <doc>
    <id>7843</id>
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    <language>eng</language>
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    <completedDate>--</completedDate>
    <publishedDate>2020-06-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs</title>
    <abstract language="eng">Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation.  &#13;
&#13;
&#13;
One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a $\mu$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). &#13;
&#13;
MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1080/08927022.2020.1839660</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-78437</identifier>
    <enrichment key="SourceTitle">Molecular Simulation, 46:18, 1443-1452</enrichment>
    <submitter>Vikram Sunkara</submitter>
    <author>Sourav Ray</author>
    <author>Vikram Sunkara</author>
    <author>Christof Schütte</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Opioid, Ligand-Receptor Interaction, Binding Kinetics, Molecular Dynamics, Metadynamics, SQRA</value>
    </subject>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="projects" number="MathPlusAA1-1">MathPlusAA1-1</collection>
    <collection role="projects" number="MathPlus - AA6">MathPlus - AA6</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7843/Ray et al_06_2020.pdf</file>
  </doc>
  <doc>
    <id>7345</id>
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    <language>eng</language>
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    <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>
  </doc>
  <doc>
    <id>6617</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-12-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Data-driven Computation of Molecular Reaction Coordinates</title>
    <abstract language="eng">The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated&#13;
on a realistic peptide system.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66179</identifier>
    <author>Andreas Bittracher</author>
    <submitter>Paulina Bressel</submitter>
    <author>Ralf Banisch</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-77</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction coordinate</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>coarse graining</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition manifold</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transfer operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Galerkin method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>meshfree basis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>data-driven</value>
    </subject>
    <collection role="msc" number="60H35">Computational methods for stochastic equations [See also 65C30]</collection>
    <collection role="msc" number="70K70">Systems with slow and fast motions</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="SFB-1114-B3">SFB-1114-B3</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6617/ZIB-Report_17-77.pdf</file>
  </doc>
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