TY - GEN A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Nataša T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia N2 - 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. T3 - ZIB-Report - 22-10 KW - mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86764 SN - 1438-0064 ER - TY - JOUR A1 - Kostré, Margarita A1 - Sunkara, Vikram A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia JF - Applied Network Science N2 - 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. KW - mesoscale spreading process KW - network inference KW - time-evolving network KW - romanization spreading KW - scarce data Y1 - 2022 U6 - https://doi.org/10.1007/s41109-022-00492-w VL - 7 PB - Springer Nature ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Köppl, Jonas A1 - Djurdjevac, Ana T1 - Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise JF - Entropy N2 - 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. Y1 - 2022 U6 - https://doi.org/10.3390/e24101352 VL - 24(10) ER - TY - JOUR A1 - Klus, Stefan A1 - Djurdjevac Conrad, Natasa T1 - Koopman-based spectral clustering of directed and time-evolving graphs JF - Journal of Nonlinear Science N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1007/s00332-022-09863-0 VL - 33 ER -