@article{delRazoDibakSchuetteetal.2021, author = {del Razo, Mauricio J. and Dibak, Manuel and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics}, volume = {155}, journal = {The Journal of Chemical Physics}, number = {12}, doi = {10.1063/5.0060314}, year = {2021}, language = {en} } @article{GelssKlusSchusteretal.2021, author = {Gelss, Patrick and Klus, Stefan and Schuster, Ingmar and Sch{\"u}tte, Christof}, title = {Feature space approximation for kernel-based supervised learning}, volume = {221}, journal = {Knowledge-Based Sytems}, publisher = {Elsevier}, doi = {https://doi.org/10.1016/j.knosys.2021.106935}, year = {2021}, language = {en} } @article{BittracherMoschnerKokschetal.2021, author = {Bittracher, Andreas and Moschner, Johann and Koksch, Beate and Netz, Roland and Sch{\"u}tte, Christof}, title = {Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis}, volume = {94}, journal = {The European Physical Journal B}, doi = {10.1140/epjb/s10051-021-00200-0}, year = {2021}, language = {en} } @article{HelfmannHeitzigKoltaietal.2021, author = {Helfmann, Luzie and Heitzig, Jobst and Koltai, P{\´e}ter and Kurths, J{\"u}rgen and Sch{\"u}tte, Christof}, title = {Statistical analysis of tipping pathways in agent-based models}, volume = {230}, journal = {Eur. Phys. J. Spec. Top.}, arxiv = {http://arxiv.org/abs/2103.02883}, doi = {10.1140/epjs/s11734-021-00191-0}, pages = {3249 -- 3271}, year = {2021}, abstract = {Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.}, language = {en} } @article{SikorskiWeberSchuette2021, author = {Sikorski, Alexander and Weber, Marcus and Sch{\"u}tte, Christof}, title = {The Augmented Jump Chain}, volume = {4}, journal = {Advanced Theory and Simulations}, number = {4}, publisher = {Wiley-VCH}, arxiv = {http://arxiv.org/abs/2008.04624}, doi = {10.1002/adts.202000274}, year = {2021}, abstract = {Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated.}, language = {en} }