TY - JOUR A1 - Wulkow, Niklas A1 - Koltai, Péter A1 - Sunkara, Vikram A1 - Schütte, Christof T1 - Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory JF - J. Stat. Phys. N2 - We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples. Y1 - 2021 ER - TY - JOUR A1 - Wulkow, Niklas A1 - Koltai, Péter A1 - Schütte, Christof T1 - Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading JF - Journal of Nonlinear Science N2 - We investigate opinion dynamics based on an agent-based model and are interested in predicting the evolution of the percentages of the entire agent population that share an opinion. Since these opinion percentages can be seen as an aggregated observation of the full system state, the individual opinions of each agent, we view this in the framework of the Mori–Zwanzig projection formalism. More specifically, we show how to estimate a nonlinear autoregressive model (NAR) with memory from data given by a time series of opinion percentages, and discuss its prediction capacities for various specific topologies of the agent interaction network. We demonstrate that the inclusion of memory terms significantly improves the prediction quality on examples with different network topologies. Y1 - 2021 U6 - https://doi.org/10.1007/s00332-020-09673-2 VL - 31 ER - TY - JOUR A1 - Wulkow, Niklas A1 - Telgmann, Regina A1 - Hungenberg, Klaus-Dieter A1 - Schütte, Christof A1 - Wulkow, Michael T1 - Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples JF - Macromolecular Theory and Simulations N2 - Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered. Y1 - 2021 U6 - https://doi.org/10.1002/mats.202100017 VL - 30 ER - TY - JOUR A1 - Conrad, Tim A1 - Genzel, Martin A1 - Cvetkovic, Nada A1 - Wulkow, Niklas A1 - Vybiral, Jan A1 - Kutyniok, Gitta A1 - Schütte, Christof T1 - Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data JF - BMC Bioinformatics N2 - Motivation: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested how MS spectra dier between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust to noise and outliers, and the identied feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based on the theory of Compressed Sensing that allows to identify a minimal discriminating set of features from mass spectrometry data-sets. We show how our method performs on artificial and real-world data-sets. Y1 - 2017 U6 - https://doi.org/10.1186/s12859-017-1565-4 VL - 18 IS - 160 SP - 1 EP - 20 ER - TY - JOUR A1 - Conrad, Tim A1 - Genzel, Martin A1 - Cvetkovic, Nada A1 - Wulkow, Niklas A1 - Leichtle, Alexander Benedikt A1 - Vybiral, Jan A1 - Kytyniok, Gitta A1 - Schütte, Christof T1 - Sparse Proteomics Analysis – a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data JF - BMC Bioinfomatics N2 - Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA),based on thet heory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets. Y1 - 2017 U6 - https://doi.org/10.1186/s12859-017-1565-4 VL - 18 IS - 160 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Fuerstenau, Daniel A1 - Grabundzija, Ana A1 - Helfmann, Luzie A1 - Park, Martin A1 - Schier, Wolfram A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Weber, Marcus A1 - Wulkow, Niklas A1 - Zonker, Johannes T1 - Mathematical modeling of the spreading of innovations in the ancient world JF - eTopoi. Journal for Ancient Studies Y1 - 2018 U6 - https://doi.org/10.17171/4-7-1 SN - ISSN 2192-2608 VL - 7 ER -