Related papers: A graph based advection framework for climate-driv…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
Advection of entities induced by gradients in attractant concentration fields is observed via diffusiophoresis in colloids and via chemotaxis in microorganisms. Mathematically, both diffusiophoresis and chemotaxis follow similar…
Graph neural networks (GNNs) have shown remarkable success in learning representations for graph-structured data. However, GNNs still face challenges in modeling complex phenomena that involve feature transportation. In this paper, we…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…
Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in the…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster…
Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…
This paper develops and analyzes a diffusion-advection model coupling population dynamics with toxicant transport, incorporating a boundary protection zone. For both upstream and downstream protection zone configurations, we investigate the…
Estimating population-level prevalence and transmission dynamics of wildlife pathogens can be challenging, partly because surveillance data is sparse, detection-driven, and unevenly sequenced. Using highly pathogenic avian influenza A/H5…
We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche. This model consists of a system of coupled…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…
The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a…
As a result of climate change, many populations have to modify their range to follow the suitable areas - their "climate envelope" - often risking extinction. During this migration process, they may face absolute boundaries to dispersal,…
Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the…
Many biological, geophysical and technological systems involve the transport of resource over a network. In this paper we present an algorithm for calculating the exact concentration of resource at any point in space or time, given that the…
The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…