7596
2020
eng
1
37
15
article
Public Library of Science
0
2020-11-12
2020-11-12
--
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
PLOS ONE
10.1371/journal.pone.0241133
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0241133
yes
PLOS ONE
Fabian Becker
Erlinda Körnig
Natasa Djurdjevac Conrad
Raphael A. Eser
Luzie Helfmann
Brigitta Schütt
Christof Schütte
Johannes Zonker
Numerical Mathematics
Schütte, Christof
Conrad, Natasa
Helfmann, Luzie
Zonker, Johannes
INNOSPREAD
Modeling and Simulation of Complex Processes
MathPlusEF5-1
7969
2021
eng
3
31
article
0
2021-03-02
--
--
Transition paths of marine debris and the stability of the garbage patches
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.
Chaos: An Interdisciplinary Journal of Nonlinear Science
2009.11234
https://doi.org/10.1063/5.0030535
yes
Philippe Miron
Francisco Beron-Vera
Luzie Helfmann
Péter Koltai
Numerical Mathematics
Helfmann, Luzie
Modeling and Simulation of Complex Processes
Stability and Tipping in Social Systems
6949
2018
eng
24
EPJ Data Science
1
7
article
EPJ Data Science
0
--
2018-07-13
--
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
10.1140/epjds/s13688-018-0153-9
yes
2018-07-02
EPJ Data Science
Natasa Djurdjevac Conrad
Natasa Djurdjevac Conrad
Luzie Helfmann
Johannes Zonker
Stefanie Winkelmann
Christof Schütte
Numerical Mathematics
Schütte, Christof
Conrad, Natasa
Winkelmann, Stefanie
Helfmann, Luzie
Zonker, Johannes
INNOSPREAD
7188
2019
2018
2019
eng
68
masterthesis
0
--
--
2019-01-29
Stochastic Modeling of Interacting Agent Systems
urn:nbn:de:0297-zib-71887
Christof Schütte
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Numerical Mathematics
Computational Molecular Design
Helfmann, Luzie
INNOSPREAD
Freie Universität Berlin
https://opus4.kobv.de/opus4-zib/files/7188/Masterarbeit_Helfmann.pdf
7339
2021
eng
1
32
1
16
article
0
--
--
--
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.
Communications in Applied Mathematics and Computational Science
1905.13525
10.2140/camcos.2021.16.1
2020-11-01
yes
urn:nbn:de:0297-zib-73456
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Ana Djurdjevac
Stefanie Winkelmann
Christof Schütte
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Schütte, Christof
Conrad, Natasa
Winkelmann, Stefanie
Helfmann, Luzie
INNOSPREAD
Modeling and Simulation of Complex Processes
7345
eng
reportzib
0
--
2019-06-11
--
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.
1438-0064
urn:nbn:de:0297-zib-73456
Comm. Appl. Math. Comp. Sci. 16(1):1-32, 2021
https://doi.org/10.2140/camcos.2021.16.1
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Ana Djurdjevac
Stefanie Winkelmann
Christof Schütte
ZIB-Report
19-21
Numerical Mathematics
Computational Molecular Design
Computational Systems Biology
Schütte, Christof
Conrad, Natasa
Winkelmann, Stefanie
Helfmann, Luzie
INNOSPREAD
https://opus4.kobv.de/opus4-zib/files/7345/main.pdf
8750
2022
eng
doctoralthesis
0
--
--
2022-07-06
Non-stationary Transition Path Theory with applications to tipping and agent-based models
The interesting dynamical regimes in agent-based models (ABMs) of social dynamics are the transient dynamics leading to metastable or absorbing states, and the transition paths between metastable states possibly caused by external influences. In this thesis, we are particularly interested in the pathways of rare and critical transitions such as the tipping of the public opinion in a population or the forming of social movements. For a detailed quantitative analysis of these transition paths, we consider the agent-based models as Markov chains and employ Transition Path Theory. Since ABMs are usually not considered in stationarity and possibly even forced, we generalize Transition Path Theory to time-dependent dynamics, for example on finite-time intervals or with periodically varying transition probabilities. We also specifically consider the case of dynamics with absorbing states and show how the transitions prior to absorption can be studied. These generalizations can also be useful in other application domains such as for studying tipping in climate models or transitions in molecular models with external stimuli. Another obstacle when analysing the dynamics of agent-based models is the large number of agents resulting in a high-dimensional state space for the model. However, the emergent dynamics of the ABM usually has significantly fewer degrees of freedom and many symmetries enabling a model reduction. On the example of two stationary ABMs we demonstrate how a long model simulation can be employed to find a lower-dimensional parametrization of the state space using a manifold learning algorithm called Diffusion Maps. In the considered models, agents adapt their binary behaviour to the local neighbourhood. When the interaction network consists of several densely connected communities, the dynamics result in a largely coherent behaviour in each community. The low-dimensional structure of the state space is therefore a hypercube. The corners represent metastable states with coherent agent behaviour in each group and the edges correspond to transition paths where agents in a community change their behaviour through a chain reaction. Finally, we can apply Transition Path Theory to the effective dynamics in the reduced space to reveal, for example, the dominant transition paths or the agents that are most indicative of an impending tipping event.
https://refubium.fu-berlin.de/handle/fub188/35660
http://dx.doi.org/10.17169/refubium-35374
publish
Christof Schütte
Luzie Helfmann
Luzie Helfmann
Helfmann, Luzie
Modeling and Simulation of Complex Processes
Stability and Tipping in Social Systems
Freie Universität Berlin
8166
2021
eng
3249
3271
230
article
0
2021-06-18
2021-06-18
--
Statistical analysis of tipping pathways in agent-based models
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.
Eur. Phys. J. Spec. Top.
2103.02883
10.1140/epjs/s11734-021-00191-0
publish
yes
Luzie Helfmann
Luzie Helfmann
Jobst Heitzig
Péter Koltai
Jürgen Kurths
Christof Schütte
Schütte, Christof
Helfmann, Luzie
Modeling and Simulation of Complex Processes
Stability and Tipping in Social Systems
6709
2018
eng
7
article
0
--
--
--
Mathematical modeling of the spreading of innovations in the ancient world
eTopoi. Journal for Ancient Studies
ISSN 2192-2608
10.17171/4-7-1
yes
http://journal.topoi.org/index.php/etopoi/index
Natasa Djurdjevac Conrad
Erlinda Koernig
Daniel Fuerstenau
Ana Grabundzija
Luzie Helfmann
Martin Park
Wolfram Schier
Brigitta Schütt
Christof Schütte
Marcus Weber
Niklas Wulkow
Johannes Zonker
Numerical Mathematics
Schütte, Christof
Weber, Marcus
Conrad, Natasa
Helfmann, Luzie
Zonker, Johannes
INNOSPREAD
7718
2020
eng
3321
3366
30
article
0
2020-09-10
2020-09-10
--
Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics
Journal of Nonlinear Science
https://doi.org/10.1007/s00332-020-09652-7
yes
2020-08-23
Luzie Helfmann
Erlinda Körnig
Enric Ribera Borrell
Christof Schütte
Peter Koltai
Numerical Mathematics
Schütte, Christof
Helfmann, Luzie
Ribera Borrell, Enric
Modeling and Simulation of Complex Processes
Stability and Tipping in Social Systems
8762
2023
eng
1151
1160
4
53
article
0
--
2023-01-20
--
Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water
In this note, we apply Transition Path Theory (TPT) from Markov chains to shed light on the problem of Iceland-Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow to focus the attention on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, the more heterogeneously sampled chains do not, irrespective of whether observed or simulated trajectories are used. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about time-asymptotic aspects of the ISOW circulation.
Journal of Physical Oceanography
2208.09499
10.1175/JPO-D-22-0172.1
Yes
17.01.2023
Francisco Javier Beron-Vera
Luzie Helfmann
Maria Josefina Olascoaga
Luzie Helfmann
Philippe Miron
Numerical Mathematics
no-project
Helfmann, Luzie
Modeling and Simulation of Complex Processes
8976
2023
eng
19375
13
article
0
--
--
--
Modelling opinion dynamics under the impact of influencer and media strategies
Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation.
Scientific Reports
2301.13661
10.1038/s41598-023-46187-9
yes
Luzie Helfmann
Luzie Helfmann
Natasa Djurdjevac Conrad
Philipp Lorenz-Spreen
Christof Schütte
Numerical Mathematics
Schütte, Christof
Conrad, Natasa
Helfmann, Luzie
Modeling and Simulation of Complex Processes
MathPlusEF45-1
9267
eng
software
0
--
2023-01-01
--
Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies
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.
10.12752/9267
https://doi.org/10.1038/s41598-023-46187-9
Julia code
https://github.com/LuzieH/SocialMediaModel
https://github.com/LuzieH/SocialMediaModel
publish
Luzie Helfmann
Natasa Djurdjevac Conrad
Natasa Djurdjevac Conrad
Philipp Lorenz-Spreen
Christof Schütte
Numerical Mathematics
Schütte, Christof
Conrad, Natasa
Helfmann, Luzie
Modeling and Simulation of Complex Processes
MathPlusEF45-1
Zuse Institute Berlin (ZIB)
9131
2024
eng
369
article
0
2024-01-12
--
--
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.
Mathematical Biosciences
2307.01737
10.1016/j.mbs.2024.109143
publish
2024-01-10
yes
Alberto Montefusco
Winkelmann
Luzie Helfmann
Toluwani Okunola
Stefanie Winkelmann
Christof Schütte
Numerical Mathematics
Computational Systems Biology
Schütte, Christof
SFB1114-C3
Winkelmann, Stefanie
Helfmann, Luzie
Modeling and Simulation of Complex Processes
MathPlusAA1-5
Okunola, Toluwani
9118
eng
software
0
--
2021-05-11
--
cmdtools
Python implementation of severals tools (PCCA, AJC, SQRA, P/Q estimation) for the analysis of dynamical systems from the transfer operator perspective.
https://doi.org/10.5281/zenodo.4749331
https://doi.org/10.5281/zenodo.4749331
v1.0.1
Python package
https://github.com/zib-cmd/cmdtools
0
publish
Alexander Sikorski
Alexander Sikorski
Renata Sechi
Luzie Helfmann
Sikorski, Alexander
Helfmann, Luzie
Modeling and Simulation of Complex Processes
Zuse Institute Berlin (ZIB)