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  <doc>
    <id>1603</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-10-12</completedDate>
    <publishedDate>2012-10-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Free Energy Calculation Using Mayer Cluster Expansion and Fluctuation Free Integration</title>
    <abstract language="eng">This work aims to develop a new algorithm to calculate the free energy of water molecules by using a deterministic way. &#13;
For this purpose, we assume a closed system confined to a physical volume, having water molecules in gas phase. &#13;
To calculate the free energy of this sytem we utilized Mayer cluster expansion and the fluctuation free integration &#13;
method.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-16031</identifier>
    <author>Burcu Tunga</author>
    <submitter>Burcu Tunga</submitter>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>12-35</number>
    </series>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="pacs" number="50.00.00">PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES</collection>
    <collection role="msc" number="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1603/freeenergycalc.pdf</file>
  </doc>
  <doc>
    <id>1779</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-02-22</completedDate>
    <publishedDate>2013-02-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computing the Minimal Rebinding Effect Included in a Given Kinetics</title>
    <abstract language="eng">The rebinding effect is a phenomenon which occurs when observing a ligand-receptor binding process.&#13;
On the macro scale this process comprises the Markov property. &#13;
This Makovian view is spoiled when switching to the atomistic scale of a binding process.&#13;
We therefore suggest a model which accurately describes the rebinding effect on the atomistic scale by allowing  ''intermediate'' bound states.&#13;
This allows us to define an indicator for the magnitude of rebinding and to formulate an optimization problem.&#13;
The results form our examples show good agreement with data form laboratory.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-17796</identifier>
    <identifier type="doi">10.1137/13091124X</identifier>
    <enrichment key="SourceTitle">Appeared in: Multiscale Model. Simul., 12  (2014) 318–334</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Marcus Weber</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Konstantin Fackeldey</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Rebinding</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Molecular Kinetics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Conformation Dynamics</value>
    </subject>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="EyeTracking">EyeTracking</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1779/ZR13-12.pdf</file>
  </doc>
  <doc>
    <id>4219</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-08-28</completedDate>
    <publishedDate>2013-08-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A square root approximation of transition rates for a Markov State Model</title>
    <abstract language="eng">Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular configuration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in configuration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional configuration space provides proof of concept and an example for which we compare the performance of different discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, finding discretizations of higher-dimensional configuration spaces in which metastable sets can be identified remains a challenge.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1137/120899959</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42195</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Matrix Anal. Appl. 34 (2013) pp. 738 - 756</enrichment>
    <author>Han Cheng Lie</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-43</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chains</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>meshfree methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Voronoi</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear programming</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="pacs" number="30.00.00">ATOMIC AND MOLECULAR PHYSICS</collection>
    <collection role="msc" number="60J10">Markov chains (discrete-time Markov processes on discrete state spaces)</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="msc" number="82B80">Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4219/zibtitlepage.pdf</file>
  </doc>
  <doc>
    <id>4316</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-11-26</completedDate>
    <publishedDate>2013-11-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On a Generalized Transfer Operator</title>
    <abstract language="eng">We introduce a generalized operator for arbitrary stochastic processes by using a pre-kernel, which is a generalization of the Markov kernel. For deterministic processes, such an operator is already known as the Frobenius-Perron operator, which is defined for a large class of measures. For Markov processes, there exists transfer operators being only well defined for stationary measures in $L^2$. Our novel generalized transfer operator is well defined for arbitrary stochastic processes, in particular also for deterministic ones. We can show that this operator is acting on $L^1$. For stationary measures, this operator is also an endomorphism of $L^2$ and, therefore, allows for a mathematical analysis in Hilbert spaces.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-43162</identifier>
    <author>Adam Nielsen</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-74</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transfer Operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pre Kernel</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Perron Frobenius Generalization</value>
    </subject>
    <collection role="ccs" number="">Stochastic processes (NEW)</collection>
    <collection role="pacs" number="31.00.00">Electronic structure of atoms and molecules: theory</collection>
    <collection role="msc" number="37-XX">DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]</collection>
    <collection role="msc" number="47N30">Applications in probability theory and statistics</collection>
    <collection role="msc" number="60Gxx">Stochastic processes</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="EyeTracking">EyeTracking</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4316/NFW_13.pdf</file>
  </doc>
  <doc>
    <id>7021</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>2018-08-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Spectral Clustering for Non-reversible Markov Chains</title>
    <abstract language="eng">Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g. the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We also extend this spectral clustering method to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension non-reversible Markov chains can be analyzed. Furthermore, the chains do not need to have a positive stationary distribution. In addition to metastabilities, dominant cycles and sinks can also be identified. This novel method is called GenPCCA  (i.e.&#13;
Generalized PCCA), since it includes the case of non reversible processes. &#13;
We also apply the method to real world eye tracking data.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-70218</identifier>
    <enrichment key="AcceptedDate">01.07.2018</enrichment>
    <enrichment key="SourceTitle">Comp. Appl. Math., pp 1-16, https://doi.org/10.1007/s40314-018-0697-0</enrichment>
    <author>Konstantin Fackeldey</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Alexander Sikorski</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-48</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>spectral clustering</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schur decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-reversible</value>
    </subject>
    <collection role="ccs" number="G.1.3">Numerical Linear Algebra</collection>
    <collection role="pacs" number="05.00.00">Statistical physics, thermodynamics, and nonlinear dynamical systems (see also 02.50.-r Probability theory, stochastic processes, and statistics)</collection>
    <collection role="msc" number="15A21">Canonical forms, reductions, classification</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7021/GenPCCA_FSW.pdf</file>
  </doc>
  <doc>
    <id>4257</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-09-27</completedDate>
    <publishedDate>2013-09-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient Conformational Analysis by Partition-of-Unity Coupling</title>
    <abstract language="eng">Obtaining a sufficient sampling of conformational space is a common problem in molecular simulation. We present the implementation of an umbrella-like adaptive sampling approach based on function-based meshless discretization of conformational space that is compatible with state of the art molecular dynamics code and that integrates an eigenvector-based clustering approach for conformational analysis and the computation of inter-conformational transition rates. The approach is applied to three example systems, namely n-pentane, alanine dipeptide, and a small synthetic host-guest system, the latter two including explicitly modeled solvent.</abstract>
    <parentTitle language="eng">Math Chem</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42570</identifier>
    <author>Alexander Bujotzek</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Ole Schütt</author>
    <author>Adam Nielsen</author>
    <author>Konstantin Fackeldey</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-58</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Meshfree</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Molecular Simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Partition of Unity</value>
    </subject>
    <collection role="ccs" number="G.4">MATHEMATICAL SOFTWARE</collection>
    <collection role="ccs" number="">Markov processes (NEW)</collection>
    <collection role="pacs" number="87.10.-e">General theory and mathematical aspects</collection>
    <collection role="msc" number="60Jxx">Markov processes</collection>
    <collection role="msc" number="92-08">Computational methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="Matheon-A19">Matheon-A19</collection>
    <collection role="projects" number="MIP_FORMATION">MIP_FORMATION</collection>
    <collection role="projects" number="NAMPAR">NAMPAR</collection>
    <collection role="projects" number="Salsa-Klimm">Salsa-Klimm</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4257/MolPyPUM.pdf</file>
  </doc>
  <doc>
    <id>6207</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>2017-01-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates</title>
    <abstract language="eng">In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine  a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-62075</identifier>
    <author>Jannes Quer</author>
    <submitter>Jannes Quer</submitter>
    <author>Luca Donati</author>
    <author>Bettina Keller</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Adaptive Importance Sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Molecular Dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Variance Reduction</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non Equilibrium Sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Metadynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Girsanov</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="37-XX">DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]</collection>
    <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="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="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="persons" number="quer">Quer, jannes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6207/AISZIB.pdf</file>
  </doc>
  <doc>
    <id>6216</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>2017-03-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Set-free Markov State Building</title>
    <abstract language="eng">Molecular dynamics (MD) simulations face challenging problems since&#13;
the timescales of interest often are much longer than what is possible&#13;
to simulate and even if sufficiently long simulation are possible the complex&#13;
nature of the resulting simulation data makes interpretation difficult.&#13;
Markov State Models (MSMs) help to overcome these problems by making&#13;
experimentally relevant timescales accessible via coarse grained representations&#13;
that also allows for convenient interpretation. However, standard&#13;
set-based MSMs exhibit some caveats limiting their approximation quality&#13;
and statistical significance. One of the main caveats results from the fact&#13;
that typical MD trajectories repeatedly re-cross the boundary between&#13;
the sets used to build the MSM which causes statistical bias in estimating&#13;
the transition probabilities between these sets. In this article, we present&#13;
a set-free approach to MSM building utilizing smooth overlapping ansatz&#13;
functions instead of sets and an adaptive refinement approach. This kind&#13;
of meshless discretization helps to overcome the recrossing problem and&#13;
yields an adaptive refinement procedure that allows to improve the quality&#13;
of the model while exploring state space and inserting new ansatz&#13;
functions into the MSM.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-62167</identifier>
    <identifier type="doi">10.1063/1.4978501</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal of Chemical Physics 146/12 (2017)</enrichment>
    <author>Marcus Weber</author>
    <submitter>Julia Boltze</submitter>
    <author>Konstantin Fackeldey</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-10</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <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>
    <file>https://opus4.kobv.de/opus4-zib/files/6216/ZR-17-10.pdf</file>
  </doc>
  <doc>
    <id>6219</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>2017-03-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Eigenvalues of non-reversible Markov chains – A case study</title>
    <abstract language="eng">Finite reversible Markov chains are characterized by a transition matrix P that has real eigenvalues and pi-orthogonal eigenvectors, where pi is the stationary distribution of P. This means, that a transition matrix with complex eigenvalues corresponds to a non-reversible Markov chain. This observation leads to the question, whether the imaginary part of that eigendecomposition corresponds to or indicates the “pattern” of the nonreversibility. This article shows that the direct relation between imaginary parts of eigendecompositions and the non-reversibility of a transition matrix is not given. It is proposed to apply the Schur decomposition of P instead of the eigendecomposition in order to characterize its nonreversibility.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-62191</identifier>
    <author>Marcus Weber</author>
    <submitter>Regine Kossick</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>17-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-reversible</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition matrix</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>detailed balance</value>
    </subject>
    <collection role="msc" number="60J10">Markov chains (discrete-time Markov processes on discrete state spaces)</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="82C35">Irreversible thermodynamics, including Onsager-Machlup theory</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6219/ZR-17-13.pdf</file>
  </doc>
  <doc>
    <id>7843</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>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>707</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-11-15</completedDate>
    <publishedDate>2002-11-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals</title>
    <abstract language="eng">Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol.</abstract>
    <identifier type="serial">02-40</identifier>
    <identifier type="opus3-id">708</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7074</identifier>
    <author>Frank Cordes</author>
    <author>Marcus Weber</author>
    <author>Johannes Schmidt-Ehrenberg</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Perron-Cluster Cluster Analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>curse of dimension</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hybrid Monte Carlo</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>significant dihedrals</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="MOLVIS">MOLVIS</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/707/ZR-02-40.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/707/ZR-02-40.pdf</file>
  </doc>
  <doc>
    <id>726</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-03-06</completedDate>
    <publishedDate>2003-03-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Improved Perron Cluster Analysis</title>
    <abstract language="eng">The problem of clustering data can often be transformed into the problem of finding a hidden block diagonal structure in a stochastic matrix. Deuflhard et al. have proposed an algorithm that state s the number $k$ of clusters and uses the sign structure of $k$ eigenvectors of the stochastic matrix to solve the cluster problem. Recently Weber and Galliat discovered that this system of eigenvectors can easily be transformed into a system of $k$ membership functions or soft characteristic functions describing the clusters. In this article we explain the corresponding cluster algorithm and point out the underlying theory. By means of numerical examples we explain how the grade of membership can be interpreted.</abstract>
    <identifier type="serial">03-04</identifier>
    <identifier type="opus3-id">727</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7260</identifier>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-04</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic matrices</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>almost invariant sets</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/726/ZR-03-04.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/726/ZR-03-04.pdf</file>
  </doc>
  <doc>
    <id>741</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-07-01</completedDate>
    <publishedDate>2003-07-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Robust Perron Cluster Analysis in Conformation Dynamics</title>
    <abstract language="eng">The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.</abstract>
    <identifier type="serial">03-19</identifier>
    <identifier type="opus3-id">742</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7415</identifier>
    <enrichment key="SourceTitle">Appeared in : Linear Algebra and Its Applications, Special Issue on Matrices and Mathematical Biology, Vol. 398c, 161-184 (2005)</enrichment>
    <author>Peter Deuflhard</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-19</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chains</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster algorithms</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Perron cluster analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>conformation dynamics</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="91C20">Clustering [See also 62D05]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/741/ZR_03_19_erratum.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/741/ZR-03-19.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/741/ZR-03-19.pdf</file>
  </doc>
  <doc>
    <id>851</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-03-14</completedDate>
    <publishedDate>2005-03-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">ZIBgridfree - Adaptive Conformation Analysis with qualified Support of Transition States and Thermodynamic Weights</title>
    <abstract language="eng">This paper introduces a new algorithm of conformational analysis based on mesh-free methods as described in [M. Weber. Mehless methods in Conformation Dynamics.(2005)]. The adaptive decomposition of the conformational space by softly limiting functions avoids trapping effects and allows adaptive refinement strategies. These properties of the algorithm makes ZIBgridfree particularly suitable for the complete exploration of high-dimensional conformational space. The adaptive control of the algorithm benefits from the tight integration of molecular simulation and conformational analysis. An emphasized part of the analysis is the Robust Perron Cluster Analysis (PCCA+) based on the work of Peter Deuflhard and Marcus Weber. PCCA+ supports an almost-characteristic cluster definition with an outstanding mapping of transition states. The outcome is expressed by the metastable sets of conformations, their thermodynamic weights and flexibility.</abstract>
    <identifier type="serial">05-17</identifier>
    <identifier type="opus3-id">851</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8514</identifier>
    <author>Marcus Weber</author>
    <author>Holger Meyer</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Molecular Dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Meshfree Methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Conformation Analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quality Functions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="37A60">Dynamical systems in statistical mechanics [See also 82Cxx]</collection>
    <collection role="msc" number="60J22">Computational methods in Markov chains [See also 65C40]</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/851/ZR-05-17.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/851/ZR-05-17.ps</file>
  </doc>
  <doc>
    <id>5550</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">G-PCCA: Spectral Clustering for Non-reversible Markov Chains</title>
    <abstract language="eng">Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, because reversibility implies a real-valued spectrum. We extend this spectral clustering method also to non-reversible Markov chains and give some illustrative examples. The main idea is to replace the eigenvalue problem by a real-valued Schur decomposition. By this extension, non-reversible Markov chains can be analyzed. Furthermore, the chains need not have a positive stationary distribution. And additionally to metastabilities, dominant cycles and sinks can be identified, too.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-55505</identifier>
    <author>Marcus Weber</author>
    <submitter>Konstantin Fackeldey</submitter>
    <author>Konstantin Fackeldey</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-35</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="EyeTracking">EyeTracking</collection>
    <collection role="projects" number="Salsa-Klimm">Salsa-Klimm</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5550/ZR-15-35.pdf</file>
  </doc>
  <doc>
    <id>5573</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>2015-08-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Finding dominant structures of nonreversible Markov processes</title>
    <abstract language="eng">Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-55739</identifier>
    <identifier type="doi">10.1137/15M1032272</identifier>
    <enrichment key="SourceTitle">Appeared in: Multiscale Modeling and Simulation 14(4): 1319-1340</enrichment>
    <author>Natasa Djurdjevac Conrad</author>
    <submitter>Erlinda Koernig</submitter>
    <author>Marcus Weber</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonreversible Markov processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastable sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cycle decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schur decomposition</value>
    </subject>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="msc" number="82C26">Dynamic and nonequilibrium phase transitions (general)</collection>
    <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="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <collection role="projects" number="EyeTracking">EyeTracking</collection>
    <collection role="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5573/ZIB-Report_15-40.pdf</file>
  </doc>
  <doc>
    <id>5329</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2014-12-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computing the nearest reversible Markov chain</title>
    <abstract language="eng">Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-53292</identifier>
    <author>Adam Nielsen</author>
    <submitter>Adam Nielsen</submitter>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-48</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Reversible Markov Chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convex Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MSM</value>
    </subject>
    <collection role="msc" number="15-XX">LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY</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="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="BMS-Nielsen">BMS-Nielsen</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5329/ZR-14-48.pdf</file>
  </doc>
  <doc>
    <id>4972</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>2014-04-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Applications of the cross-entropy method to importance sampling and optimal control of diffusions</title>
    <abstract language="eng">We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-49720</identifier>
    <identifier type="doi">10.1137/14096493X</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Appeared in: Siam Journal on Scientific Computing 36 (2014) A 2654-A2672</enrichment>
    <author>Wei Zhang</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Han Wang</author>
    <author>Carsten Hartmann</author>
    <author>Marcus Weber</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>important sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross-entropy method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>change of measure</value>
    </subject>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="93E20">Optimal stochastic control</collection>
    <collection role="msc" number="94A17">Measures of information, entropy</collection>
    <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="projects" number="NonequiMSM">NonequiMSM</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4972/ZIB-Report_14-10.pdf</file>
  </doc>
  <doc>
    <id>5662</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>2015-11-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Estimating exit rates in rare event dynamical systems via extrapolation</title>
    <abstract language="eng">In this article we present a new idea for approximating exit rates for diffusion processes living in a craggy landscape. We are especially interested in the exit rates of a process living in a metastable regions. Due to the fact that Monte Carlo simulations perform quite poor and are very computational expensive in this setting we create several similar situations with a smoothed potential. For this we introduce a new parameter $\lambda \in [0,1]$ ($\lambda = 1$ very smoothed potential, $\lambda=0$ original potential) into the potential which controls the influence the smoothing. We then sample the exit rate for different parameters $\lambda$ the exit rate from a given region. Due to the fact that $\lambda$ is connected to the exit rate we can use this dependency to approximate the real exit rate. The method can be seen as something between hyperdynamics and temperature accelerated MC.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-56622</identifier>
    <author>Marcus Weber</author>
    <submitter>Jannes Quer</submitter>
    <author>Jannes Quer</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-54</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare event sampling, smoothing, membership functions, perturbed potential</value>
    </subject>
    <collection role="ccs" number="G.3">PROBABILITY AND STATISTICS</collection>
    <collection role="pacs" number="31.00.00">Electronic structure of atoms and molecules: theory</collection>
    <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="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="projects" number="SFB765-C2">SFB765-C2</collection>
    <collection role="persons" number="quer">Quer, jannes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5662/Homotopy.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/5662/ConExitTimes-2.pdf</file>
  </doc>
  <doc>
    <id>4671</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>2014-03-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov State Models and Molecular Alchemy</title>
    <abstract language="deu">In recent years Markov State Models (MSMs) have attracted a consid-&#13;
erable amount of attention with regard to modelling conformation changes&#13;
and associated function of biomolecular systems. They have been used&#13;
successfully, e.g., for peptides including time-resolved spectroscopic ex-&#13;
periments, protein function and protein folding , DNA and RNA, and&#13;
ligand-receptor interaction in drug design and more complicated multi-&#13;
valent scenarios. In this article a novel reweighting scheme is introduced&#13;
that allows to construct an MSM for certain molecular system out of an&#13;
MSM for a similar system. This permits studying how molecular proper-&#13;
ties on long timescales differ between similar molecular systems without&#13;
performing full molecular dynamics simulations for each system under con-&#13;
sideration. The performance of the reweighting scheme is illustrated for&#13;
simple test cases including one where the main wells of the respective en-&#13;
ergy landscapes are located differently and an alchemical transformation&#13;
of butane to pentane where the dimension of the state space is changed.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-46718</identifier>
    <identifier type="doi">10.1080/00268976.2014.944597</identifier>
    <enrichment key="SourceTitle">appeared in: Mol. Phys. 2014 (epub ahead of print)</enrichment>
    <author>Christof Schütte</author>
    <submitter>Adam Nielsen</submitter>
    <author>Adam Nielsen</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-05</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Girsanov Theorem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Stochastic Differential Equation</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Importance Sampling</value>
    </subject>
    <collection role="msc" number="60J70">Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="TransRisk">TransRisk</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4671/article_zib.pdf</file>
  </doc>
  <doc>
    <id>6607</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>2017-12-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From Metastable to Coherent Sets - time-discretization schemes</title>
    <abstract language="eng">Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in  $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66074</identifier>
    <author>Konstantin Fackeldey</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Peter Névir</author>
    <author>Henning Rust</author>
    <author>Axel Schild</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-74</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6607/ZIB-Report_17-74.pdf</file>
  </doc>
  <doc>
    <id>679</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-03-15</completedDate>
    <publishedDate>2002-03-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Characterization of Transition States in Conformational Dynamics using Fuzzy Sets</title>
    <abstract language="eng">Recently, a novel approach for the analysis of molecular dynamics on the basis of a transfer operator has been introduced. Therein conformations are considered to be disjoint metastable clusters within position space of a molecule. These clusters are defined by almost invariant characteristic functions that can be computed via {\em Perron Cluster} analysis. The present paper suggests to replace crisp clusters with {\em fuzzy} clusters, i.e. to replace characteristic functions with membership functions. This allows a more sufficient characterization of transiton states between different confor conformations and therefore leads to a better understanding of molecular dynamics. Fur thermore, an indicator for the uniqueness of metastable fuzzy clusters and a fast algorithm for the computation of these clusters are described. Numerical examples are included.</abstract>
    <identifier type="serial">02-12</identifier>
    <identifier type="opus3-id">680</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6791</identifier>
    <author>Marcus Weber</author>
    <author>Tobias Galliat</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>biochemical conformations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>conformational dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cluster analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition states</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>fuzzy sets</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="03E72">Fuzzy set theory</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="msc" number="92-08">Computational methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/679/ZR-02-12.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/679/ZR-02-12.pdf</file>
  </doc>
  <doc>
    <id>961</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-07-23</completedDate>
    <publishedDate>2007-07-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Conformation-based transition state theory</title>
    <abstract language="eng">For the treatment of equilibrated molecular systems in a heat bath we propose a transition state theory that is based on conformation dynamics. In general, a set-based discretization of a Markov operator ${\cal P}^\tau$ does not preserve the Markov property. In this article, we propose a discretization method which is based on a Galerkin approach. This discretization method preserves the Markov property of the operator and can be interpreted as a decomposition of the state space into (fuzzy) sets. The conformation-based transition state theory presented here can be seen as a first step in conformation dynamics towards the computation of essential dynamical properties of molecular systems without time-consuming molecular dynamics simulations.</abstract>
    <identifier type="serial">07-18</identifier>
    <identifier type="opus3-id">961</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9612</identifier>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamical systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition state theory</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>rare events</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="msc" number="82B80">Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/961/ZR_07_18.pdf</file>
  </doc>
  <doc>
    <id>876</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-09-28</completedDate>
    <publishedDate>2005-09-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Conformation Kinetics as a Reduced Model for Transition Pathways</title>
    <abstract language="eng">The complexity of molecular kinetics can be reduced significantly by a restriction to metastable conformations which are almost invariant sets of molecular dynamical systems. With the Robust Perron Cl uster Analysis PCCA+, developed by Weber and Deuflhard, we have a tool available which can be used to identify these conformations from a transition probability matrix. This method can also be applied to the corresponding transition rate matrix which provides important information concerning transition pathways of single molecules. In the present paper, we explain the relationship between these tw o concepts and the extraction of conformation kinetics from transition rates. Moreover, we show how transition rates can be approximated and conclude with numerical examples.</abstract>
    <identifier type="serial">05-43</identifier>
    <identifier type="opus3-id">876</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8763</identifier>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-43</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>conformation kinetics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition rates</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Robust Perron Cluster Analysis</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="60J75">Jump processes</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/876/ZR-05-43.pdf</file>
  </doc>
  <doc>
    <id>925</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-06-15</completedDate>
    <publishedDate>2006-06-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">ConFlow? A new space-based Application for complete Conformational Analysis of Molecules</title>
    <abstract language="eng">Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.</abstract>
    <identifier type="serial">06-31</identifier>
    <identifier type="opus3-id">925</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9258</identifier>
    <author>Holger Meyer</author>
    <author>Sebastian Moll</author>
    <author>Frank Cordes</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-31</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>conformational-analysis in-silico-screening drug-design</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="92-08">Computational methods</collection>
    <collection role="msc" number="92C40">Biochemistry, molecular biology</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/925/ZR-06-31.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/925/ZR-06-31.ps</file>
  </doc>
  <doc>
    <id>929</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-06-27</completedDate>
    <publishedDate>2006-06-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Coarse Grained Molecular Kinetics</title>
    <abstract language="eng">The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.</abstract>
    <identifier type="serial">06-35</identifier>
    <identifier type="opus3-id">929</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9299</identifier>
    <enrichment key="SourceTitle">Appeared as : "A coarse grained method for the identification of transition rates between molecular conformations" in Journal of Chemical Physics, 126(2) 2007</enrichment>
    <author>Susanna Kube</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-35</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65C40">Computational Markov chains</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="65P99">None of the above, but in this section</collection>
    <collection role="msc" number="80A30">Chemical kinetics [See also 76V05, 92C45, 92E20]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/929/ZR-06-35.pdf</file>
  </doc>
  <doc>
    <id>960</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-07-23</completedDate>
    <publishedDate>2007-07-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics</title>
    <abstract language="eng">Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy.</abstract>
    <identifier type="serial">07-17</identifier>
    <identifier type="opus3-id">960</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9604</identifier>
    <enrichment key="SourceTitle">A rev. vers. appeared in: Journal of Computational Physics 228 (2009) pp. 1947-1962. doi:10.1016/j.jcp.2008.11.016</enrichment>
    <author>Susanna Kube</author>
    <author>Caroline Lasser</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Metropolis Monte Carlo</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quadrature</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>oscillating functions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62D05">Sampling theory, sample surveys</collection>
    <collection role="msc" number="65D30">Numerical integration</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/960/ZR_07_17.pdf</file>
  </doc>
  <doc>
    <id>8279</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>2021-07-07</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>6035</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>2016-05-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes</title>
    <abstract language="eng">In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60353</identifier>
    <identifier type="doi">10.1137/16M1091162</identifier>
    <author>Jakob Witzig</author>
    <submitter>Jakob Witzig</submitter>
    <author>Isabel Beckenbach</author>
    <author>Leon Eifler</author>
    <author>Konstantin Fackeldey</author>
    <author>Ambros Gleixner</author>
    <author>Andreas Grever</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non-reversible Markov Processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NESS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</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="62-XX">STATISTICS</collection>
    <collection role="msc" number="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="beckenbach">Beckenbach, Isabel</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="SparseApproxiTN">SparseApproxiTN</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6035/ZR-16-39-revised2.pdf</file>
  </doc>
</export-example>
