@article{KlusGelssPeitzetal., author = {Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Sch{\"u}tte, Christof}, title = {Tensor-based dynamic mode decomposition}, series = {Nonlinearity}, volume = {31}, journal = {Nonlinearity}, number = {7}, publisher = {IOP Publishing Ltd \& London Mathematical Society}, doi = {10.1088/1361-6544/aabc8f}, language = {en} } @article{GuptaGramatkeEinspanieretal.2017, author = {Gupta, Pooja and Gramatke, Annika and Einspanier, Ralf and Sch{\"u}tte, Christof and von Kleist, Max and Sharbati, Jutta}, title = {In silico cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, series = {Toxicology in Vitro}, volume = {41}, journal = {Toxicology in Vitro}, issn = {1438-0064}, pages = {179 -- 188}, year = {2017}, abstract = {Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence's real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50\% inhibitory concentration IC50 on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC50 values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA's in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master.}, language = {en} } @article{RuedrichSarichSchuette, author = {R{\"u}drich, S. and Sarich, Marco and Sch{\"u}tte, Christof}, title = {Utilizing hitting times for finding metastable sets in non-reversible Markov chains}, series = {Journal of Comp. Dynamics}, journal = {Journal of Comp. Dynamics}, language = {en} } @article{ConradGenzelCvetkovicetal., author = {Conrad, Tim and Genzel, Martin and Cvetkovic, Nada and Wulkow, Niklas and Leichtle, Alexander Benedikt and Vybiral, Jan and Kytyniok, Gitta and Sch{\"u}tte, Christof}, title = {Sparse Proteomics Analysis - a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data}, series = {BMC Bioinfomatics}, volume = {18}, journal = {BMC Bioinfomatics}, number = {160}, doi = {10.1186/s12859-017-1565-4}, abstract = {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.}, language = {en} } @article{VegaSchuetteConrad, author = {Vega, Iliusi and Sch{\"u}tte, Christof and Conrad, Tim}, title = {Finding metastable states in real-world time series with recurrence networks}, series = {Physica A: Statistical Mechanics and its Applications}, volume = {445}, journal = {Physica A: Statistical Mechanics and its Applications}, doi = {10.1016/j.physa.2015.10.041}, pages = {1 -- 17}, abstract = {In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with a complex time series example. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points.}, language = {en} } @article{GelssMateraSchuette, author = {Gelß, Patrick and Matera, Sebastian and Sch{\"u}tte, Christof}, title = {Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model}, series = {Journal of Computational Physics}, volume = {314}, journal = {Journal of Computational Physics}, doi = {10.1016/j.jcp.2016.03.025}, pages = {489 -- 502}, abstract = {In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased}, language = {en} } @article{KlusKoltaiSchuette, author = {Klus, Stefan and Koltai, Peter and Sch{\"u}tte, Christof}, title = {On the numerical approximation of the Perron-Frobenius and Koopman operator}, series = {Journal of Computational Dynamics}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2016003}, pages = {51 -- 77}, abstract = {Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review di� fferent methods that have been developed over the last decades to compute � infinite-dimensional approximations of these in� finite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and di� fferences between these approaches. The results will be illustrated using simple stochastic di� fferential equations and molecular dynamics examples.}, language = {en} } @article{HartmannSchuetteZhang, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Model reduction algorithms for optimal control and importance sampling of diffusions}, series = {Nonlinearity}, volume = {29}, journal = {Nonlinearity}, number = {8}, doi = {10.1088/0951-7715/29/8/2298}, pages = {2298 -- 2326}, abstract = {We propose numerical algorithms for solving optimal control and importance sampling problems based on simplified models. The algorithms combine model reduction techniques for multiscale diffusions and stochastic optimization tools, with the aim of reducing the original, possibly high-dimensional problem to a lower dimensional representation of the dynamics, in which only a few relevant degrees of freedom are controlled or biased. Specifically, we study situations in which either a reaction coordinate onto which the dynamics can be projected is known, or situations in which the dynamics shows strongly localized behavior in the small noise regime. No explicit assumptions about small parameters or scale separation have to be made. We illustrate the approach with simple, but paradigmatic numerical examples.}, language = {en} } @article{KlusSchuette, author = {Klus, Stefan and Sch{\"u}tte, Christof}, title = {Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator}, series = {Journal of Computational Dynamics}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {2}, doi = {10.3934/jcd.2016007}, pages = {139 -- 161}, abstract = {The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the system's behavior are the Perron-Frobenius operator and the Koopman operator. Due to the curse of dimensionality, computing the eigenfunctions of high-dimensional systems is in general infeasible. We will propose a tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional operators, namely Ulam's method and Extended Dynamic Mode Decomposition (EDMD). The aim of the tensor formulation is to approximate the eigenfunctions by low-rank tensors, potentially resulting in a significant reduction of the time and memory required to solve the resulting eigenvalue problems, provided that such a low-rank tensor decomposition exists. Typically, not all variables of a high-dimensional dynamical system contribute equally to the system's behavior, often the dynamics can be decomposed into slow and fast processes, which is also reflected in the eigenfunctions. Thus, the weak coupling between different variables might be approximated by low-rank tensor cores. We will illustrate the efficiency of the tensor-based formulation of Ulam's method and EDMD using simple stochastic differential equations.}, language = {en} } @misc{WeberFackeldeySchuette, author = {Weber, Marcus and Fackeldey, Konstantin and Sch{\"u}tte, Christof}, title = {Set-free Markov State Building}, issn = {1438-0064}, doi = {10.1063/1.4978501}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62167}, abstract = {Molecular dynamics (MD) simulations face challenging problems since the timescales of interest often are much longer than what is possible to simulate and even if sufficiently long simulation are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant timescales accessible via coarse grained representations that also allows for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.}, language = {en} }