TY - JOUR A1 - Peppert, Felix A1 - von Kleist, Max A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks JF - IEEE Transactions on Neural Networks and Learning Systems N2 - Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling. Y1 - 2022 U6 - https://doi.org/10.1109/TNNLS.2021.3072746 VL - 33 IS - 11 SP - 6194 EP - 6205 ER - TY - JOUR A1 - Bittracher, Andreas A1 - Mollenhauer, Mattes A1 - Koltai, Péter A1 - Schütte, Christof T1 - Optimal Reaction Coordinates: Variational Characterization and Sparse Computation JF - Multiscale Modelling & Simulation N2 - Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques. Y1 - 2023 U6 - https://doi.org/10.1137/21M1448367 VL - 21 IS - 2 SP - 449 EP - 488 ER - TY - JOUR A1 - Mollenhauer, Mattes A1 - Klus, Stefan A1 - Schütte, Christof A1 - Koltai, Péter T1 - Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence JF - Journal of Machine Learning Research N2 - We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition. Y1 - 2022 UR - https://jmlr.org/papers/v23/20-442.html VL - 23 IS - 327 SP - 1 EP - 34 ER - TY - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies N2 - This repository contains the Julia code accompanying the paper "Modelling opinion dynamics under the impact of influencer and media strategies", Scientific Reports, Vol.13, p. 19375, 2023. Y1 - 2023 U6 - https://doi.org/10.12752/9267 ER - TY - GEN A1 - Secker, Christopher T1 - Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists (Dataset) N2 - Virtual Screening Dataset for the paper "Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists" by Secker et al. (https://doi.org/10.1186/s13321-023-00746-4) Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-96220 ER - TY - JOUR A1 - Wehlitz, Nathalie A1 - Sadeghi, Mohsen A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Pavliotis, Grigorios A. A1 - Winkelmann, Stefanie T1 - Approximating particle-based clustering dynamics by stochastic PDEs JF - SIAM Journal on Applied Dynamical Systems N2 - This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number. Y1 - 2025 U6 - https://doi.org/10.1137/24M1676661 VL - 24 IS - 2 SP - 1231 EP - 1250 ER - TY - JOUR A1 - Kostré, Margarita A1 - Djurdjevac Conrad, Natasa A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - Exploration of Particle Swarm Optimisation Algorithm with Divergent Parameters JF - Natural Computing Y1 - 2024 ER - TY - JOUR A1 - Regényi, Enikő A1 - Mashreghi, Mir-Farzin A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - Exploring transcription modalities from bimodal, single-cell RNA sequencing data JF - NAR Genomics and Bioinformatics N2 - Abstract There is a growing interest in generating bimodal, single-cell RNA sequencing (RNA-seq) data for studying biological pathways. These data are predominantly utilized in understanding phenotypic trajectories using RNA velocities; however, the shape information encoded in the two-dimensional resolution of such data is not yet exploited. In this paper, we present an elliptical parametrization of two-dimensional RNA-seq data, from which we derived statistics that reveal four different modalities. These modalities can be interpreted as manifestations of the changes in the rates of splicing, transcription or degradation. We performed our analysis on a cell cycle and a colorectal cancer dataset. In both datasets, we found genes that are not picked up by differential gene expression analysis (DGEA), and are consequently unnoticed, yet visibly delineate phenotypes. This indicates that, in addition to DGEA, searching for genes that exhibit the discovered modalities could aid recovering genes that set phenotypes apart. For communities studying biomarkers and cellular phenotyping, the modalities present in bimodal RNA-seq data broaden the search space of genes, and furthermore, allow for incorporating cellular RNA processing into regulatory analyses. Y1 - 2024 U6 - https://doi.org/10.1093/nargab/lqae179 SN - 2631-9268 VL - 6 IS - 4 PB - Oxford University Press (OUP) ER - TY - CHAP A1 - Ribera Borrell, Enric A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Reinforcement Learning with Random Time Horizons T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/borrell25a/borrell25a.pdf VL - 267 SP - 5101 EP - 5123 ER - TY - GEN A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics N2 - Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings. T3 - ZIB-Report - 21-40 KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2021 SN - 1438-0064 ER - TY - JOUR A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning JF - Acta Numerica N2 - One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject. Y1 - 2023 U6 - https://doi.org/10.1017/S0962492923000016 VL - 32 SP - 517 EP - 673 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Helfmann, Luzie A1 - Okunola, Toluwani A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Partial mean-field model for neurotransmission dynamics JF - Mathematical Biosciences N2 - This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios. Y1 - 2024 U6 - https://doi.org/10.1016/j.mbs.2024.109143 VL - 369 ER -