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Faculty of mathematics, physics & computer science

Dynamical Systems and Data – Prof. Dr Péter Koltai

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  • MatherCoherent (by R. Chemnitz)
    Cohrent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. This package implements a Fourier-Galerkin discretization of the so-called Mather-semigroup to compute coherent sets of quasiperiodically driven flows on the torus
    in a trajectory-free manner.

    R. Chemnitz, M. Engel, P. Koltai. Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups. Preprint. arxiv:2403.19274. 2024.

  • DynamicPLaplacian (by A. de Diego)
    The dynamic p-Laplacian provides solutions (for p approaching 1 from above) to the dynamic isoperimetric problem,
    which in turn characterizes coherent sets in fluid flows. This package is a loose collection of methods to produce the figures of the work:

    A. de Diego Unanue, G. Froyland, O. Junge, P. Koltai. A dynamic p-Laplacian. Preprint. arxiv:2308.05947. 2023.

  • SPoNet (by M. Lücke)
    The package provides an efficient implementation of popular discrete-state spreading processes on networks of
    interacting agents. It can be used to describe the time-evolution of certain opinions in a population, or the spreading of infectious diseases.

    M. Lücke, S. Winkelmann, J. Heitzig, N. Molkenthin, P. Koltai. Learning interpretable collective variables for spreading processes on networks. Physical Review E 109, L022301, 2024. DOI: 10.1103/PhysRevE.109.L022301

  • PyTMRC (by A. Bittracher and M. Mollenhauer)
    The Python Transition Manifold Reaction Coordinate package for computing reaction coordinates of high-dimensional stochastic systems is based on the transition manifold data analysis framework. Based on: 

    A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, Ch. Schütte. Transition Manifolds of Complex Metastable Systems. Journal of Nonlinear Science 28(2): 471–512, 2018. DOI: 10.1007/s00332-017-9415-0.

    A. Bittracher, S. Klus, B. Hamzi, P. Koltai, Ch. Schütte. Dimensionality Reduction of Complex Metastable Systems via
    Kernel Embeddings of Transition Manifolds. Journal of Nonlinear Science 31, 3. 2021. DOI: 10.1007/s00332-020-09668-z.

  • PyTPT (by L. Helfmann and E. Ribera Borrell)
    Python package for the Transition Path Theory (TPT) analysis of stationary Markov chains, periodically driven Markov chains, and for time-inhomogeneous Markov chains over finite time intervals. Based on:

    L. Helfmann, E. Ribera Borrell, Ch. Schütte, P. Koltai. Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics. Journal of Nonlinear Science 30, 3321-3366, 2020. DOI: 10.1007/s00332-020-09652-7.

  • SINAR (by N. Wulkow)
    Matlab code for learning sparse nonlinear autoregressive models from trajectory data; in particular with an application in opinion dynamics. Based on: 

    N. Wulkow, P. Koltai, Ch. Schütte. Memory-based reduced modelling and data-based estimation of opinion spreading. Journal of Nonlinear Science 31, 19, 2021. DOI: 10.1007/s00332-020-09673-2.

  • pyDiffMap (by R. Banisch, E. H. Thiede, Z. Trstanova)
    An open-source project to develop a robust and accessible diffusion map code for public use. Includes implementations
    of target measure diffusion maps and local kernel diffusion maps. Based on:

    ​R. Banisch, Z. Trstanova, A. Bittracher, S. Klus, P. Koltai. Diffusion maps tailored to arbitrary non-degenerate Itô processes. Applied and Computational Harmonic Analysis 48(1), 242-265, 2020. DOI: 10.1016/j.acha.

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