Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-9131 Wissenschaftlicher Artikel Montefusco, Alberto; Helfmann, Luzie; Okunola, Toluwani; Winkelmann, Stefanie; Schütte, Christof Partial mean-field model for neurotransmission dynamics 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. 2024 Mathematical Biosciences 369 10.1016/j.mbs.2024.109143 Numerical Mathematics OPUS4-7339 Wissenschaftlicher Artikel Helfmann, Luzie; Djurdjevac Conrad, Natasa; Djurdjevac, Ana; Winkelmann, Stefanie; Schütte, Christof From interacting agents to density-based modeling with stochastic PDEs Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. 2021 31 Communications in Applied Mathematics and Computational Science 16 1 1 32 10.2140/camcos.2021.16.1 Numerical Mathematics OPUS4-7345 misc Helfmann, Luzie; Djurdjevac Conrad, Natasa; Djurdjevac, Ana; Winkelmann, Stefanie; Schütte, Christof From interacting agents to density-based modeling with stochastic PDEs Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models. 2019 urn:nbn:de:0297-zib-73456 Numerical Mathematics OPUS4-6949 Wissenschaftlicher Artikel Djurdjevac Conrad, Natasa; Helfmann, Luzie; Zonker, Johannes; Winkelmann, Stefanie; Schütte, Christof Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution. EPJ Data Science EPJ Data Science 2018 24 EPJ Data Science 7 1 10.1140/epjds/s13688-018-0153-9 Numerical Mathematics