Weber, Marcus
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Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.
MaRDMO Plugin
(2023)
MaRDMO, a plugin for the Research Data Management Organiser, was developed in the Mathematical Research Data Initiative to document interdisciplinary workflows using a standardised scheme. Interdisciplinary workflows recorded this way are published directly on the MaRDI portal. In addition, central information is integrated into the MaRDI knowledge graph. Next to the documentation, MaRDMO offers the possibility to retrieve existing interdisciplinary workflows from the MaRDI Knowledge Graph to allow the reproduction of the initial work and to provide scientists with new researchimpulses. Thus, MaRDMO creates a community-driven knowledge loop that could help to overcome the replication crisis.
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.
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.
We have investigated how Langevin dynamics is affected by the friction
coefficient using the novel algorithm ISOKANN, which combines the transfer
operator approach with modern machine learning techniques. ISOKANN describes
the dynamics in terms of an invariant subspace projection of the Koopman
operator defined in the entire state space, avoiding approximations due to
dimensionality reduction and discretization. Our results are consistent with
the Kramers turnover and show that in the low and moderate friction regimes,
metastable macro-states and transition rates are defined in phase space, not
only in position space.
Crystallization is a complex phenomenon with far-reaching implications for the production and formulation of active pharmaceutical ingredients. Understanding this process is critical for achieving control over key physicochemical properties that can affect, for example, the bioavailability and stability of a drug. In this study, we were able to reveal intricate and diverse dynamics of the formation of metastable intermediates of paracetamol crystallization varying with the choice of solvent. We demonstrate the efficacy of our novel approach utilizing an objective function-based non-negative matrix factorization technique for the analysis of time-resolved Raman spectroscopy data, in conjunction with time-lapse photography. Furthermore, we emphasize the crucial importance of integrating Raman spectroscopy with supplementary experimental instrumentation for the mathematical analysis of the obtained spectra.
Extracting the kinetic properties of a system whose dynamics depend on the pH of the environment with which it exchanges energy and atoms requires sampling the Grand Canonical Ensemble. As an alternative, we present a novel strategy that requires simulating only the most recurrent Canonical Ensembles that compose the Grand Canonical Ensemble. The simulations are used to estimate the Gran Canonical distribution for a specific pH value by reweighting and to construct the transition rate matrix by discretizing the Fokker-Planck equation by Square Root Approximation and robust Perron Cluster Cluster Analysis. As an application, we have studied the tripeptide Ala-Asp-Ala.