2 research outputs found
Understanding the romanization spreading on historical interregional networks in Northern Tunisia
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
Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs
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