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 - THES A1 - Helfmann, Luzie T1 - Stochastic Modeling of Interacting Agent Systems Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71887 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 - 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 - 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 - Helfmann, Luzie A1 - Ribera Borrell, Enric A1 - Schütte, Christof A1 - Koltai, Peter T1 - Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics JF - Journal of Nonlinear Science Y1 - 2020 U6 - https://doi.org/https://doi.org/10.1007/s00332-020-09652-7 VL - 30 SP - 3321 EP - 3366 ER - TY - JOUR A1 - Miron, Philippe A1 - Beron-Vera, Francisco A1 - Helfmann, Luzie A1 - Koltai, Péter T1 - Transition paths of marine debris and the stability of the garbage patches JF - Chaos: An Interdisciplinary Journal of Nonlinear Science N2 - We used transition path theory (TPT) to infer "reactive" pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the NOAA Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific Garbage Patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1063/5.0030535 VL - 31 IS - 3 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 - JOUR A1 - Helfmann, Luzie A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Kurths, Jürgen A1 - Schütte, Christof T1 - Statistical analysis of tipping pathways in agent-based models JF - Eur. Phys. J. Spec. Top. N2 - Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach. Y1 - 2021 U6 - https://doi.org/10.1140/epjs/s11734-021-00191-0 VL - 230 SP - 3249 EP - 3271 ER - TY - GEN A1 - Sikorski, Alexander A1 - Sechi, Renata A1 - Helfmann, Luzie T1 - cmdtools N2 - Python implementation of severals tools (PCCA, AJC, SQRA, P/Q estimation) for the analysis of dynamical systems from the transfer operator perspective. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.5281/zenodo.4749331 ER -