@article{DonatiWeberKeller2022, author = {Donati, Luca and Weber, Marcus and Keller, Bettina G.}, title = {A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models}, volume = {63}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, doi = {10.1063/5.0127227}, pages = {123306-1 -- 123306-21}, year = {2022}, abstract = {Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential U(x) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) to reweight transition probabilities; the second method was originally developed to discretize the Fokker-Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses.}, language = {en} } @article{QuerRiberaBorrell2024, author = {Quer, Jannes and Ribera Borrell, Enric}, title = {Connecting Stochastic Optimal Control and Reinforcement Learning}, volume = {65}, journal = {Journal of Mathematical Physics}, number = {8}, doi = {10.1063/5.0140665}, year = {2024}, abstract = {In this paper the connection between stochastic optimal control and reinforcement learning is investigated. Our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem. By using a parameterised approach the optimal control problem becomes a stochastic optimization problem which still raises some open questions regarding how to tackle the scalability to high-dimensional problems and how to deal with the intrinsic metastability of the system. To explore new methods we link the optimal control problem to reinforcement learning since both share the same underlying framework, namely a Markov Decision Process (MDP). For the optimal control problem we show how the MDP can be formulated. In addition we discuss how the stochastic optimal control problem can be interpreted in the framework of reinforcement learning. At the end of the article we present the application of two different reinforcement learning algorithms to the optimal control problem and a comparison of the advantages and disadvantages of the two algorithms.}, language = {en} } @article{RayFackeldeySteinetal.2023, author = {Ray, Sourav and Fackeldey, Konstantin and Stein, Christoph and Weber, Marcus}, title = {Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane}, volume = {3}, journal = {Biophysica}, number = {2}, doi = {10.3390/biophysica3020017}, pages = {263 -- 275}, year = {2023}, abstract = {In our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the 𝜇-opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the 𝜇-opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe's parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane.}, language = {en} } @inproceedings{RichterBerner2022, author = {Richter, Lorenz and Berner, Julius}, title = {Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning}, volume = {162}, booktitle = {Proceedings of the 39th International Conference on Machine Learning, PMLR}, pages = {18649 -- 18666}, year = {2022}, abstract = {The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs), which allow the minimization of corresponding losses using gradient-based optimization methods. In respective numerical implementations it is therefore crucial to rely on adequate gradient estimators that exhibit low variance in order to reach convergence accurately and swiftly. In this article, we rigorously investigate corresponding numerical aspects that appear in the context of linear Kolmogorov PDEs. In particular, we systematically compare existing deep learning approaches and provide theoretical explanations for their performances. Subsequently, we suggest novel methods that can be shown to be more robust both theoretically and numerically, leading to substantial performance improvements.}, language = {en} } @article{delRazoWinkelmannKleinetal.2023, author = {del Razo, Mauricio and Winkelmann, Stefanie and Klein, Rupert and H{\"o}fling, Felix}, title = {Chemical diffusion master equation: formulations of reaction-diffusion processes on the molecular level}, volume = {64}, journal = {Journal of Mathematical Physics}, number = {1}, arxiv = {http://arxiv.org/abs/2210.02268}, doi = {10.1063/5.0129620}, year = {2023}, abstract = {The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects.}, language = {en} } @article{LueckeHeitzigKoltaietal.2023, author = {L{\"u}cke, Marvin and Heitzig, Jobst and Koltai, P{\´e}ter and Molkethin, Nora and Winkelmann, Stefanie}, title = {Large population limits of Markov processes on random networks}, volume = {166}, journal = {Stochastic Processes and their Applications}, arxiv = {http://arxiv.org/abs/2210.02934}, doi = {10.1016/j.spa.2023.09.007}, year = {2023}, abstract = {We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called "voter model" on Erdős-R{\´e}nyi random graphs, on the stochastic block model, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters.}, language = {en} } @inproceedings{SchneiderZschiedrichHammerschmidtetal.2022, author = {Schneider, Philipp-Immanuel and Zschiedrich, Lin and Hammerschmidt, Martin and Kuen, Lilli and Sekulic, Ivan and Kluge, Julien and Leykauf, Bastian and Krutzik, Markus and Burger, Sven}, title = {Boosting quantum optics experiments with Bayesian optimization}, volume = {12227}, booktitle = {Proc. SPIE}, doi = {10.1117/12.2632419}, pages = {122270F}, year = {2022}, language = {en} } @inproceedings{KruegerManleyZschiedrichetal.2022, author = {Kr{\"u}ger, Jan and Manley, Phillip and Zschiedrich, Lin and Hammerschmidt, Martin and Schneider, Philipp-Immanuel and K{\"o}ning, Rainer and Bodermann, Bernd}, title = {Untersuchung des Schwingungseinflusses auf gemessene Punktspreizfunktionen in der optischen Mikroskopie}, booktitle = {Proc. DGaO}, url = {http://nbn-resolving.de/urn:nbn:de:0287-2022-P005-6}, pages = {P5}, year = {2022}, language = {en} } @article{BoppPlockTuranetal.2024, author = {Bopp, Julian M. and Plock, Matthias and Turan, Tim and Pieplow, Gregor and Burger, Sven and Schr{\"o}der, Tim}, title = {Sawfish Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications}, volume = {12}, journal = {Adv. Opt. Mater.}, arxiv = {http://arxiv.org/abs/2210.04702}, doi = {10.1002/adom.202301286}, pages = {2301286}, year = {2024}, language = {en} } @inproceedings{ManleyKruegerZschiedrichetal.2022, author = {Manley, Phillip and Kr{\"u}ger, Jan and Zschiedrich, Lin and Hammerschmidt, Martin and Bodermann, Bernd and K{\"o}ning, Rainer and Schneider, Philipp-Immanuel}, title = {Elementary, my dear Zernike: model order reduction for accelerating optical dimensional microscopy}, volume = {266}, booktitle = {EPJ Web Conf.}, doi = {10.1051/epjconf/202226610010}, pages = {10010}, year = {2022}, language = {en} } @article{RaharinirinaFackeldeyWeber2022, author = {Raharinirina, N. Alexia and Fackeldey, Konstantin and Weber, Marcus}, title = {Qualitative Euclidean embedding of Disjoint Sets of Points}, year = {2022}, abstract = {We consider two disjoint sets of points with a distance metric, or a proximity function, associated with each set. If each set can be separately embedded into separate Euclidean spaces, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function (might require scaling).}, language = {en} } @article{BoegeFritzeGoergenetal.2023, author = {Boege, Tobias and Fritze, Ren{\´e} and G{\"o}rgen, Christiane and Hanselmann, Jeroen and Iglezakis, Dorothea and Kastner, Lars and Koprucki, Thomas and Krause, Tabea and Lehrenfeld, Christoph and Polla, Silvia and Reidelbach, Marco and Riedel, Christian and Saak, Jens and Schembera, Bj{\"o}rn and Tabelow, Karsten and Weber, Marcus}, title = {Research-Data Management Planning in the German Mathematical Community}, volume = {130}, journal = {Eur. Math. Soc. Mag.}, doi = {10.4171/mag/152}, pages = {40 -- 47}, year = {2023}, abstract = {In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians' research processes and discuss their usage all along the data life cycle.}, language = {en} } @article{ReidelbachBaiZoellneretal.2022, author = {Reidelbach, Marco and Bai, Mei and Z{\"o}llner, Martin Sebastian and Schneeberger, Michaela and Kubicek, Katharina and Kirchberg, Henning and Bressler, Christian and Thorwart, Michael and Herrmann, Carmen}, title = {Solvent dynamics of aqueous halides before and after photoionization}, journal = {Journal of Physical Chemistry}, year = {2022}, language = {en} } @misc{ReidelbachWeber2022, author = {Reidelbach, Marco and Weber, Marcus}, title = {MaRDI - The mathematical Research Data Initiative}, journal = {Aktionstag Forschungsdaten}, doi = {10.5281/zenodo.7397588}, year = {2022}, language = {en} } @article{BetzHammerschmidtZschiedrichetal.2024, author = {Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven and Binkowski, Felix}, title = {Efficient rational approximation of optical response functions with the AAA algorithm}, volume = {18}, journal = {Laser Photonics Rev.}, arxiv = {http://arxiv.org/abs/2403.19404}, doi = {10.1002/lpor.202400584}, pages = {2400584}, year = {2024}, language = {en} } @misc{BetzHammerschmidtZschiedrichetal.2024, author = {Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven and Binkowski, Felix}, title = {Source code and simulation results: Efficient rational approximation of optical response functions with the AAA algorithm}, journal = {Zenodo}, doi = {10.5281/zenodo.10853692}, pages = {doi: 10.5281/zenodo.10853692}, year = {2024}, language = {en} } @article{SikorskiNiknejadWeberetal.2024, author = {Sikorski, Alexander and Niknejad, Amir and Weber, Marcus and Donati, Luca}, title = {Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies}, volume = {160}, journal = {Journal of Chemical Physics}, arxiv = {http://arxiv.org/abs/2311.09779}, doi = {10.1063/5.0187792}, pages = {104112}, year = {2024}, abstract = {Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.}, language = {en} } @inproceedings{SikorskiRabbenChewleetal.2025, author = {Sikorski, Alexander and Rabben, Robert Julian and Chewle, Surahit and Weber, Marcus}, title = {Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions}, booktitle = {Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023}, editor = {Fackeldey, K.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/2404.10523}, doi = {10.1515/9783111376776-004}, pages = {41 -- 58}, year = {2025}, abstract = {Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations produce useful trajectories, obtaining macroscopic information directly from microstate data presents significant challenges. This paper addresses this gap by introducing the concept of membership functions being the macrostates themselves. We derive equations for the holding times of these macrostates and demonstrate their consistency with the classical definition. Furthermore, we discuss the application of the ISOKANN method for learning these quantities from simulation data. In addition, we present a novel method for extracting transition paths based on the ISOKANN results and demonstrate its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this approach we provide a new perspective on analyzing the macroscopic behaviour of Markov systems.}, language = {en} } @article{MukherjeeKerteszZolnaietal.2025, author = {Mukherjee, Deshabrato and Kert{\´e}sz, Kriszti{\´a}n and Zolnai, Zsolt and Kov{\´a}cs, Zolt{\´a}n and De{\´a}k, Andr{\´a}s and P{\´a}link{\´a}s, Andr{\´a}s and Osv{\´a}th, Zolt{\´a}n and Olasz, D{\´a}niel and Romanenko, Alekszej and Fried, Mikl{\´o}s and Burger, Sven and S{\´a}fr{\´a}n, Gy{\"o}rgy and Petrik, Peter}, title = {Optimized Sensing on Gold Nanoparticles Created by Graded-Layer Magnetron Sputtering and Annealing}, volume = {425}, journal = {Sens. Actuators B Chem.}, doi = {10.1016/j.snb.2024.136875}, pages = {136875}, year = {2025}, language = {en} } @article{BetzBinkowskiKuenetal.2024, author = {Betz, Fridtjof and Binkowski, Felix and Kuen, Lilli and Burger, Sven}, title = {Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena}, volume = {26}, journal = {SoftwareX}, doi = {10.1016/j.softx.2024.101694}, pages = {101694}, year = {2024}, language = {en} } @inproceedings{SteyerCheginiPotseetal.2023, author = {Steyer, Joshua and Chegini, Fatemeh and Potse, Mark and Loewe, Axel and Weiser, Martin}, title = {Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model}, volume = {50}, booktitle = {2023 Computing in Cardiology Conference (CinC)}, publisher = {Computing in Cardiology}, issn = {2325-887X}, doi = {10.22489/CinC.2023.385}, year = {2023}, abstract = {Conduction velocity in cardiac tissue is a crucial electrophysiological parameter for arrhythmia vulnerability. Pathologically reduced conduction velocity facilitates arrhythmogenesis because such conduction velocities decrease the wavelength with which re-entry may occur. Computational studies on CV and how it changes regionally in models at spatial scales multiple times larger than actual cardiac cells exist. However, microscopic conduction within cells and between them have been studied less in simulations. In this work, we study the relation of microscopic conduction patterns and clinically observable macroscopic conduction using an extracellular-membrane-intracellular model which represents cardiac tissue with these subdomains at subcellular resolution. By considering cell arrangement and non-uniform gap junction distribution, it yields anisotropic excitation propagation. This novel kind of model can for example be used to understand how discontinuous conduction on the microscopic level affects fractionation of electrograms in healthy and fibrotic tissue. Along the membrane of a cell, we observed a continuously propagating activation wavefront. When transitioning from one cell to the neighbouring one, jumps in local activation times occurred, which led to lower global conduction velocities than locally within each cell.}, language = {en} }