@article{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}, series = {Communications in Applied Mathematics and Computational Science}, volume = {16}, journal = {Communications in Applied Mathematics and Computational Science}, number = {1}, doi = {10.2140/camcos.2021.16.1}, pages = {1 -- 32}, 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} } @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{DjurdjevacConradKoepplDjurdjevac, author = {Djurdjevac Conrad, Natasa and K{\"o}ppl, Jonas and Djurdjevac, Ana}, title = {Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise}, series = {Entropy}, volume = {24(10)}, journal = {Entropy}, doi = {10.3390/e24101352}, abstract = {We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents' movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents' spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.}, language = {en} } @article{SarichDjurdjevacConradBruckneretal.2014, author = {Sarich, Marco and Djurdjevac Conrad, Natasa and Bruckner, Sharon and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Modularity revisited: A novel dynamics-based concept for decomposing complex networks}, series = {Journal of Computational Dynamics}, volume = {1}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2014.1.191}, pages = {191 -- 212}, year = {2014}, language = {en} } @article{WulkowConradDjurdjevacConradetal., author = {Wulkow, Hanna and Conrad, Tim and Djurdjevac Conrad, Natasa and M{\"u}ller, Sebastian A. and Nagel, Kai and Sch{\"u}tte, Christof}, title = {Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts}, series = {PLOS One}, volume = {16}, journal = {PLOS One}, number = {4}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0249676}, language = {en} } @article{DjurdjevacConradBrucknerConradetal.2012, author = {Djurdjevac Conrad, Natasa and Bruckner, Stefanie and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Random Walks on Complex Modular Networks}, series = {Journal of Numerical Analysis, Industrial and Applied Mathematics}, volume = {6}, journal = {Journal of Numerical Analysis, Industrial and Applied Mathematics}, number = {1-2}, publisher = {European Society of Computational Methods in Sciences and Engineering}, pages = {29 -- 50}, year = {2012}, language = {en} } @misc{DjurdjevacConradBanischSchuette, author = {Djurdjevac Conrad, Natasa and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Modularity of Directed Networks: Cycle Decomposition Approach}, issn = {1438-0064}, doi = {10.3934/jcd.2015.2.1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51166}, abstract = {The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.}, language = {en} } @misc{BanischDjurdjevacConradSchuette, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof}, title = {Reactive flows and unproductive cycles for random walks on complex networks}, issn = {1438-0064}, doi = {10.1140/epjst/e2015-02417-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54239}, abstract = {We present a comprehensive theory for analysis and understanding of transition events between an initial set A and a target set B for general ergodic finite-state space Markov chains or jump processes, including random walks on networks as they occur, e.g., in Markov State Modelling in molecular dynamics. The theory allows us to decompose the probability flow generated by transition events between the sets A and B into the productive part that directly flows from A to B through reaction pathways and the unproductive part that runs in loops and is supported on cycles of the underlying network. It applies to random walks on directed networks and nonreversible Markov processes and can be seen as an extension of Transition Path Theory. Information on reaction pathways and unproductive cycles results from the stochastic cycle decomposition of the underlying network which also allows to compute their corresponding weight, thus characterizing completely which structure is used how often in transition events. The new theory is illustrated by an application to a Markov State Model resulting from weakly damped Langevin dynamics where the unproductive cycles are associated with periodic orbits of the underlying Hamiltonian dynamics.}, language = {en} } @article{DjurdjevacConradWeberSchuette, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, series = {Multiscale Modeling and Simulation}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, language = {en} } @misc{BanischSchuetteDjurdjevacConrad, author = {Banisch, Ralf and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Module Detection in Directed Real-World Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49849}, abstract = {We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network.}, language = {en} } @phdthesis{DjurdjevacConrad, author = {Djurdjevac Conrad, Natasa}, title = {Methods for analyzing complex networks using random walker}, language = {en} } @article{BanischDjurdjevacConrad, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa}, title = {Cycle-flow-based module detection in directed recurrence networks}, series = {EPL (Europhysics Letters)}, volume = {108}, journal = {EPL (Europhysics Letters)}, number = {6}, doi = {10.1209/0295-5075/108/68008}, language = {en} } @article{LorenzWolfBraunetal., author = {Lorenz, Philipp and Wolf, Frederik and Braun, Jonas and Djurdjevac Conrad, Natasa and H{\"o}vel, Philipp}, title = {Capturing the Dynamics of Hashtag-Communities}, series = {International Workshop on Complex Networks and their Applications}, journal = {International Workshop on Complex Networks and their Applications}, doi = {10.1007/978-3-319-72150-7_33}, pages = {401 -- 413}, language = {en} } @misc{DjurdjevacConradWeberSchuette, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, issn = {1438-0064}, doi = {10.1137/15M1032272}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55739}, abstract = {Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.}, language = {en} } @article{DjurdjevacConradBanischSchuette, author = {Djurdjevac Conrad, Natasa and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Modularity of Directed Networks: Cycle Decomposition Approach}, series = {Journal of Computational Dynamics 2 (2015) pp. 1-24}, journal = {Journal of Computational Dynamics 2 (2015) pp. 1-24}, doi = {10.3934/jcd.2015.2.1}, abstract = {The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.}, language = {en} } @article{BanischDjurdjevacConradSchuette, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof}, title = {Reactive flows and unproductive cycles for random walks on complex networks}, series = {The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387}, journal = {The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387}, doi = {10.1140/epjst/e2015-02417-8}, 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{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{ThielDjurdjevacConradNtinietal., author = {Thiel, Denise and Djurdjevac Conrad, Natasa and Ntini, Evgenia and Peschutter, Ria and Siebert, Heike and Marsico, Annalisa}, title = {Identifying lncRNA-mediated regulatory modules via ChIA-PET network analysis}, series = {BMC Bioinformatics}, volume = {20}, journal = {BMC Bioinformatics}, number = {1471-2105}, doi = {10.1186/s12859-019-2900-8}, abstract = {Background: Although several studies have provided insights into the role of long non-coding RNAs (lncRNAs), the majority of them have unknown function. Recent evidence has shown the importance of both lncRNAs and chromatin interactions in transcriptional regulation. Although network-based methods, mainly exploiting gene-lncRNA co-expression, have been applied to characterize lncRNA of unknown function by means of 'guilt-by-association', no strategy exists so far which identifies mRNA-lncRNA functional modules based on the 3D chromatin interaction graph. Results: To better understand the function of chromatin interactions in the context of lncRNA-mediated gene regulation, we have developed a multi-step graph analysis approach to examine the RNA polymerase II ChIA-PET chromatin interaction network in the K562 human cell line. We have annotated the network with gene and lncRNA coordinates, and chromatin states from the ENCODE project. We used centrality measures, as well as an adaptation of our previously developed Markov State Models (MSM) clustering method, to gain a better understanding of lncRNAs in transcriptional regulation. The novelty of our approach resides in the detection of fuzzy regulatory modules based on network properties and their optimization based on co-expression analysis between genes and gene-lncRNA pairs. This results in our method returning more bona fide regulatory modules than other state-of-the art approaches for clustering on graphs. Conclusions: Interestingly, we find that lncRNA network hubs tend to be significantly enriched in evolutionary conserved lncRNAs and enhancer-like functions. We validated regulatory functions for well known lncRNAs, such as MALAT1 and the enhancer-like lncRNA FALEC. In addition, by investigating the modular structure of bigger components we mine putative regulatory functions for uncharacterized lncRNAs.}, language = {en} } @article{WinkelmannZonkerSchuetteetal., author = {Winkelmann, Stefanie and Zonker, Johannes and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading}, series = {Mathematical Biosciences}, volume = {336}, journal = {Mathematical Biosciences}, publisher = {Elsevier}, doi = {10.1016/j.mbs.2021.108619}, abstract = {Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.}, language = {en} } @article{DjurdjevacConradSarichSchuette2012, author = {Djurdjevac Conrad, Natasa and Sarich, Marco and Sch{\"u}tte, Christof}, title = {Estimating the eigenvalue error of Markov State Models}, series = {Multiscale Modeling \& Simulation}, volume = {10}, journal = {Multiscale Modeling \& Simulation}, number = {1}, doi = {10.1137/100798910}, pages = {61 -- 81}, year = {2012}, language = {en} } @inproceedings{DjurdjevacConradSarichSchuette2010, author = {Djurdjevac Conrad, Natasa and Sarich, Marco and Sch{\"u}tte, Christof}, title = {On Markov State Models for Metastable Processes}, series = {Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010}, booktitle = {Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010}, year = {2010}, 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} } @inproceedings{KostreSunkaraDjurdjevacConrad, author = {Kostre, Margarita and Sunkara, Vikram and Djurdjevac Conrad, Natasa}, title = {Inference of historical influence networks}, series = {International Conference on Complex Networks \& Their Applications Proceedings}, booktitle = {International Conference on Complex Networks \& Their Applications Proceedings}, edition = {International Conference on Complex Networks \& Their Applications}, doi = {10.12752/8558}, pages = {110 -- 113}, abstract = {We study the romanization process of northern Africa from 50 BC till 300 AD. Our goal is to infer the communication strength between different subregions, based on the evolution of the status of cities. Herefore, we use the general inverse infection model, that infers the weights of a known underlying network, given observations of the spreading on this network. As infection process we choose the SI metapopulation model, where I stands for a city with a Roman status. To solve the minimization problem we use the particle swarm optimization algorithm with a specific choice of parameters.}, language = {de} } @article{HelfmannConradLorenzSpreenetal., author = {Helfmann, Luzie and Conrad, Natasa Djurdjevac and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Modelling opinion dynamics under the impact of influencer and media strategies}, series = {Scientific Reports}, volume = {13}, journal = {Scientific Reports}, doi = {10.1038/s41598-023-46187-9}, pages = {19375}, abstract = {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.}, language = {en} } @article{ZonkerPadillaIglesiasDjurdjevacConrad, author = {Zonker, Johannes and Padilla-Iglesias, Cecilia and Djurdjevac Conrad, Natasa}, title = {Insights into drivers of mobility and cultural dynamics of African hunter-gatherers over the past 120 000 years}, series = {Royal Society Open Science}, volume = {10}, journal = {Royal Society Open Science}, number = {11}, doi = {10.1098/rsos.230495}, abstract = {Humans have a unique capacity to innovate, transmit and rely on complex, cumulative culture for survival. While an important body of work has attempted to explore the role of changes in the size and interconnectedness of populations in determining the persistence, diversity and complexity of material culture, results have achieved limited success in explaining the emergence and spatial distribution of cumulative culture over our evolutionary trajectory. Here, we develop a spatio-temporally explicit agent-based model to explore the role of environmentally driven changes in the population dynamics of hunter-gatherer communities in allowing the development, transmission and accumulation of complex culture. By modelling separately demography- and mobility-driven changes in interaction networks, we can assess the extent to which cultural change is driven by different types of population dynamics. We create and validate our model using empirical data from Central Africa spanning 120 000 years. We find that populations would have been able to maintain diverse and elaborate cultural repertoires despite abrupt environmental changes and demographic collapses by preventing isolation through mobility. However, we also reveal that the function of cultural features was also an essential determinant of the effects of environmental or demographic changes on their dynamics. Our work can therefore offer important insights into the role of a foraging lifestyle on the evolution of cumulative culture.}, language = {en} } @misc{ZonkerPadillaIglesiasDjurdjevacConrad, author = {Zonker, Johannes and Padilla-Iglesias, Cecilia and Djurdjevac Conrad, Natasa}, title = {Supplementary code and data for Royal Society Open Science Manuscript rsos.230495}, doi = {10.12752/9254}, abstract = {In this repository are all files necessary to run the agent-based model of the paper "Insights into drivers of mobility and cultural dynamics of African hunter-gatherers over the past 120 000 years", Royal Society Open Science, 10(11), 2023.}, language = {en} } @misc{HelfmannDjurdjevacConradLorenzSpreenetal., author = {Helfmann, Luzie and Djurdjevac Conrad, Natasa and Lorenz-Spreen, Philipp and Sch{\"u}tte, Christof}, title = {Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies}, doi = {10.12752/9267}, abstract = {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.}, language = {en} } @misc{KostreSunkaraSchuetteetal., author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Nataša}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86764}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{KostreSunkaraSchuetteetal.2022, author = {Kostr{\´e}, Margarita and Sunkara, Vikram and Sch{\"u}tte, Christof and Djurdjevac Conrad, Natasa}, title = {Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia}, series = {Applied Network Science}, volume = {7}, journal = {Applied Network Science}, publisher = {Springer Nature}, doi = {10.1007/s41109-022-00492-w}, pages = {18}, year = {2022}, abstract = {Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.}, language = {en} } @article{KlusDjurdjevacConrad, author = {Klus, Stefan and Djurdjevac Conrad, Natasa}, title = {Koopman-based spectral clustering of directed and time-evolving graphs}, series = {Journal of Nonlinear Science}, volume = {33}, journal = {Journal of Nonlinear Science}, doi = {10.1007/s00332-022-09863-0}, pages = {8}, abstract = {While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and social network analysis, clustering directed graphs remains notoriously difficult. Two of the main challenges are that the eigenvalues and eigenvectors of graph Laplacians associated with directed graphs are in general complex-valued and that there is no universally accepted definition of clusters in directed graphs. We first exploit relationships between the graph Laplacian and transfer operators and in particular between clusters in undirected graphs and metastable sets in stochastic dynamical systems and then use a generalization of the notion of metastability to derive clustering algorithms for directed and time-evolving graphs. The resulting clusters can be interpreted as coherent sets, which play an important role in the analysis of transport and mixing processes in fluid flows.}, language = {en} } @article{DjurdjevacConradChemnitzKostreetal., author = {Djurdjevac Conrad, Natasa and Chemnitz, Robin and Kostre, Margarita and Schweigart, Fleur and Fless, Friederike and Sch{\"u}tte, Christof and Ducke, Benjamin}, title = {A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia}, language = {en} } @article{LorenzSpreenWolfBraunetal., author = {Lorenz-Spreen, Philipp and Wolf, Frederik and Braun, Jonas and Ghoshal, Gourab and Djurdjevac Conrad, Natasa and H{\"o}vel, Philipp}, title = {Tracking online topics over time: understanding dynamic hashtag communities}, series = {Computational Social Networks}, volume = {5}, journal = {Computational Social Networks}, number = {9}, doi = {10.1186/s40649-018-0058-6}, abstract = {Background: Hashtags are widely used for communication in online media. As a condensed version of information, they characterize topics and discussions. For their analysis, we apply methods from network science and propose novel tools for tracing their dynamics in time-dependent data. The observations are characterized by bursty behaviors in the increases and decreases of hashtag usage. These features can be reproduced with a novel model of dynamic rankings. Hashtag communities in time: We build temporal and weighted co-occurrence networks from hashtags. On static snapshots, we infer the community structure using customized methods. On temporal networks, we solve the bipartite matching problem of detected communities at subsequent timesteps by taking into account higher-order memory. This results in a matching protocol that is robust toward temporal fluctuations and instabilities of the static community detection. The proposed methodology is broadly applicable and its outcomes reveal the temporal behavior of online topics. Modeling topic-dynamics: We consider the size of the communities in time as a proxy for online popularity dynamics. We find that the distributions of gains and losses, as well as the interevent times are fat-tailed indicating occasional, but large and sudden changes in the usage of hashtags. Inspired by typical website designs, we propose a stochastic model that incorporates a ranking with respect to a time-dependent prestige score. This causes occasional cascades of rank shift events and reproduces the observations with good agreement. This offers an explanation for the observed dynamics, based on characteristic elements of online media.}, language = {en} } @article{NiemannKlusConradetal., author = {Niemann, Jan-Hendrik and Klus, Stefan and Conrad, Natasa Djurdjevac and Sch{\"u}tte, Christof}, title = {Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems}, series = {Physica D: Nonlinear Phenomena}, volume = {460}, journal = {Physica D: Nonlinear Phenomena}, doi = {https://doi.org/10.1016/j.physd.2024.134052}, pages = {134052}, abstract = {Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend on potentially nonlinear control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.}, language = {en} } @article{NiemannUramWolfetal., author = {Niemann, Jan-Hendrik and Uram, Samuel and Wolf, Sarah and Conrad, Natasa Djurdjevac and Weiser, Martin}, title = {Multilevel Optimization for Policy Design with Agent-Based Epidemic Models}, series = {Computational Science}, volume = {77}, journal = {Computational Science}, doi = {10.1016/j.jocs.2024.102242}, pages = {102242}, abstract = {Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples.}, language = {en} }