Related papers: Diffusion-driven instability of topological signal…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practise, many systems for which Turing patterning is important…
We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving Dirac fermions that behave as massless relativistic particles. These Dirac fermions are responsible for achieving a…
A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these…
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks.…
Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$. The stability of these Dirac rings is…
Drifting pattern domains (DPDs), moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this…
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…
We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials…
In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite…
Distributed diffusion is a powerful algorithm for multi-task state estimation which enables networked agents to interact with neighbors to process input data and diffuse information across the network. Compared to a centralized approach,…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
Models of simple excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This subject is a topic of practical relevance to diverse fields, ranging from neuroscience to…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…