TY - JOUR A1 - Becker, Fabian A1 - Djurdjevac Conrad, Natasa A1 - Eser, Raphael A. A1 - Helfmann, Luzie A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Zonker, Johannes T1 - The Furnace and the Goat—A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century CE JF - PLOS ONE Y1 - 2020 UR - https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0241133 U6 - https://doi.org/10.1371/journal.pone.0241133 VL - 15 SP - 1 EP - 37 PB - Public Library of Science ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Fuerstenau, Daniel A1 - Grabundzija, Ana A1 - Helfmann, Luzie A1 - Park, Martin A1 - Schier, Wolfram A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Weber, Marcus A1 - Wulkow, Niklas A1 - Zonker, Johannes T1 - Mathematical modeling of the spreading of innovations in the ancient world JF - eTopoi. Journal for Ancient Studies Y1 - 2018 U6 - https://doi.org/10.17171/4-7-1 SN - ISSN 2192-2608 VL - 7 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Helfmann, Luzie A1 - Zonker, Johannes A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach JF - EPJ Data Science N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1140/epjds/s13688-018-0153-9 VL - 7 IS - 1 PB - EPJ Data Science ET - EPJ Data Science ER - TY - JOUR A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Djurdjevac, Ana A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - From interacting agents to density-based modeling with stochastic PDEs JF - Communications in Applied Mathematics and Computational Science N2 - 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. Y1 - 2021 U6 - https://doi.org/10.2140/camcos.2021.16.1 VL - 16 IS - 1 SP - 1 EP - 32 ER - TY - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Djurdjevac, Ana A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - From interacting agents to density-based modeling with stochastic PDEs N2 - 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. T3 - ZIB-Report - 19-21 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73456 SN - 1438-0064 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 -