@article{HelfmannHeitzigKoltaietal., author = {Helfmann, Luzie and Heitzig, Jobst and Koltai, P{\´e}ter and Kurths, J{\"u}rgen and Sch{\"u}tte, Christof}, title = {Statistical analysis of tipping pathways in agent-based models}, series = {Eur. Phys. J. Spec. Top.}, volume = {230}, journal = {Eur. Phys. J. Spec. Top.}, doi = {10.1140/epjs/s11734-021-00191-0}, pages = {3249 -- 3271}, abstract = {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.}, language = {en} } @article{BeckerDjurdjevacConradEseretal., author = {Becker, Fabian and Djurdjevac Conrad, Natasa and Eser, Raphael A. and Helfmann, Luzie and Sch{\"u}tt, Brigitta and Sch{\"u}tte, Christof and Zonker, Johannes}, title = {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}, series = {PLOS ONE}, volume = {15}, journal = {PLOS ONE}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0241133}, pages = {1 -- 37}, language = {en} } @article{HelfmannRiberaBorrellSchuetteetal., author = {Helfmann, Luzie and Ribera Borrell, Enric and Sch{\"u}tte, Christof and Koltai, Peter}, title = {Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics}, series = {Journal of Nonlinear Science}, volume = {30}, journal = {Journal of Nonlinear Science}, doi = {https://doi.org/10.1007/s00332-020-09652-7}, pages = {3321 -- 3366}, language = {en} } @misc{HelfmannDjurdjevacConradDjurdjevacetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Djurdjevac, Ana and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {From interacting agents to density-based modeling with stochastic PDEs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73456}, abstract = {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.}, language = {en} } @article{DjurdjevacConradHelfmannZonkeretal., author = {Djurdjevac Conrad, Natasa and Helfmann, Luzie and Zonker, Johannes and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach}, series = {EPJ Data Science}, volume = {7}, journal = {EPJ Data Science}, number = {1}, edition = {EPJ Data Science}, publisher = {EPJ Data Science}, doi = {10.1140/epjds/s13688-018-0153-9}, pages = {24}, abstract = {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.}, language = {en} } @article{DjurdjevacConradFuerstenauGrabundzijaetal., author = {Djurdjevac Conrad, Natasa and Fuerstenau, Daniel and Grabundzija, Ana and Helfmann, Luzie and Park, Martin and Schier, Wolfram and Sch{\"u}tt, Brigitta and Sch{\"u}tte, Christof and Weber, Marcus and Wulkow, Niklas and Zonker, Johannes}, title = {Mathematical modeling of the spreading of innovations in the ancient world}, series = {eTopoi. Journal for Ancient Studies}, volume = {7}, journal = {eTopoi. Journal for Ancient Studies}, issn = {ISSN 2192-2608}, doi = {10.17171/4-7-1}, language = {en} }