TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Chemnitz, Robin A1 - Kostre, Margarita A1 - Schweigart, Fleur A1 - Fless, Friederike A1 - Schütte, Christof A1 - Ducke, Benjamin T1 - A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia JF - PLoS ONE N2 - Romanisation is a multi-faceted historical phenomenon with profound and lasting cultural impact on the ancient world. In the modern-day territory of Tunisia, this is particularly manifest during the first four centuries AD, under the reign of the Roman Empire. We derive a reduced, operational concept of Romanisation as a cultural diffusion process that is observable in the archaeological remains of the Roman era settlement system. We then introduce a novel mathematical model that computes spatio-temporal approximations for the Romanisation of the settlement system. The model is based on the concept of temporal road activation and makes minimal assumptions regarding input data quality. The results of our study contribute to the understanding of the time dynamics of the region’s road network, under the influence of Romanisation. Our model can be applied in similar archaeological research scenarios, to generate spatio-temporal backbones for the analysis of otherwise intractably complex social processes. Y1 - 2024 U6 - https://doi.org/10.1371/journal.pone.0309752 VL - 19 IS - 9 ER - TY - CHAP A1 - Kostre, Margarita A1 - Sunkara, Vikram A1 - Djurdjevac Conrad, Natasa T1 - Inference of historical influence networks T2 - International Conference on Complex Networks & Their Applications Proceedings N2 - 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. Y1 - 2021 U6 - https://doi.org/10.12752/8558 SP - 110 EP - 113 ET - International Conference on Complex Networks & Their Applications ER - TY - JOUR A1 - Kostre, Margarita A1 - Schütte, Christof A1 - Noé, Frank A1 - del Razo Sarmina, Mauricio T1 - Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs JF - Multiscale Modeling & Simulation N2 - Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications. Y1 - 2021 U6 - https://doi.org/10.1137/20M1352739 VL - 19 IS - 4 SP - 1659 EP - 1683 PB - Society for Industrial and Applied Mathematics ER -