@article{MoellerIsbilirSungkawornetal.2020, author = {M{\"o}ller, Jan and Isbilir, Ali and Sungkaworn, Titiwat and Osberg, Brenda and Karathanasis, Christos and Sunkara, Vikram and Grushevsky, Eugene O and Bock, Andreas and Annibale, Paolo and Heilemann, Mike and Sch{\"u}tte, Christof and Lohse, Martin J.}, title = {Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision}, volume = {16}, journal = {Nature Chemical Biology}, doi = {10.1038/s41589-020-0566-1}, pages = {946 -- 954}, year = {2020}, language = {en} } @article{BittracherSchuette2021, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A probabilistic algorithm for aggregating vastly undersampled large Markov chains}, volume = {416}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2020.132799}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75874}, year = {2021}, language = {en} } @article{BittracherKlusHamzietal.2021, author = {Bittracher, Andreas and Klus, Stefan and Hamzi, Boumediene and Sch{\"u}tte, Christof}, title = {Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds}, volume = {31}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-020-09668-z}, year = {2021}, abstract = {We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.}, language = {en} } @article{KlusNueskePeitzetal.2020, author = {Klus, Stefan and N{\"u}ske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Sch{\"u}tte, Christof}, title = {Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume = {406}, journal = {Physica D: Nonlinear Phenomena}, doi = {10.1016/j.physd.2020.132416}, year = {2020}, language = {en} } @book{Reuter2020, author = {Reuter, Bernhard}, title = {Generalisierte Markov-Modellierung}, publisher = {Springer Spektrum, Wiesbaden}, isbn = {978-3-658-29711-4}, doi = {10.1007/978-3-658-29712-1}, year = {2020}, abstract = {Markov State Models (MSM) sind der Goldstandard zur Modellierung biomolekularer Dynamik, da sie die Identifizierung und Analyse metastabiler Zust{\"a}nde erm{\"o}glichen. Die robuste Perron-Cluster-Cluster-Analyse (PCCA+) ist ein verbreiteter Spectral-Clustering-Algorithmus, der f{\"u}r das Clustering hochdimensionaler MSM verwendet wird. Da die PCCA+ auf reversible Prozesse beschr{\"a}nkt ist, wird sie zur Generalisierten PCCA+ (G-PCCA) verallgemeinert, die geeignet ist, nichtreversible Prozesse aufzukl{\"a}ren. Bernhard Reuter untersucht hier mittels G-PCCA die nichtthermischen Auswirkungen von Mikrowellen auf die Proteindynamik. Dazu f{\"u}hrt er molekulardynamische Nichtgleichgewichtssimulationen des Amyloid-β-(1-40)-Peptids durch und modelliert diese.}, language = {de} } @misc{BittracherSchuette2020, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A weak characterization of slow variables in stochastic dynamical systems}, volume = {304}, journal = {Advances in Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, E.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_6}, pages = {132 -- 150}, year = {2020}, language = {en} } @misc{MollenhauerSchusterKlusetal.2020, author = {Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces}, volume = {304}, journal = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, K.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_5}, pages = {109 -- 131}, year = {2020}, language = {en} } @article{KoltaiLiePlonka2019, author = {Koltai, P{\´e}ter and Lie, Han Cheng and Plonka, Martin}, title = {Fr{\´e}chet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic dynamics}, volume = {32}, journal = {Nonlinearity}, number = {11}, doi = {10.1088/1361-6544/ab1f2a}, pages = {4232 -- 4257}, year = {2019}, abstract = {We prove the Fr{\´e}chet differentiability with respect to the drift of Perron-Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron-Frobenius and Koopman operators.}, language = {en} } @article{KlusHusicMollenhaueretal.2019, author = {Klus, Stefan and Husic, Brooke E. and Mollenhauer, Mattes and Noe, Frank}, title = {Kernel methods for detecting coherent structures in dynamical data}, volume = {29}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {12}, doi = {10.1063/1.5100267}, year = {2019}, language = {en} } @misc{Kostre2019, type = {Master Thesis}, author = {Kostr{\´e}, Margarita}, title = {Hybrid Models and Simulations of Reaction-Diffusion Processes}, school = {Zuse Institute Berlin (ZIB)}, pages = {77}, year = {2019}, abstract = {In this thesis,we are interested in multiscale models for particle-based reaction diffusion (PBRD) simulations,where we focus on coupling particle-based simulations to macroscopic chemical reservoirs. These reservoirs are given by a mean concentration of chemical species that can vary in time and space. We model these reservoirs as reaction-diffusion partial differential equations (PDEs). The goal of this work is to achieve a mathematically consistent coupling between the PBRD simulations and the reaction-diffusion PDEs.}, language = {en} }