Related papers: Graphon Limits of Graph Reaction--Diffusion Equati…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling among others system of self-gravitating particles when one…
The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are…
A nonsplit graph is a directed graph where each pair of nodes has a common incoming neighbor. We show that the radius of such graphs is in $O(\log \log n)$, where $n$ is the number of nodes. We then generalize the result to products of…
The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are…
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…
We study the problem of generating graph signals from unknown distributions defined over given graphs, relevant to domains such as recommender systems or sensor networks. Our approach builds on generative diffusion models, which are well…
In this paper, we present an approach to characterising fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential…
This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve uniform H\"{o}lder regularity in terms of $L^p$-bound on the…
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
We study the network reconstruction problem for an epidemic reaction-diffusion. These models are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion. We…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
The degree-restricted random process is a natural algorithmic model for generating graphs with degree sequence D_n=(d_1, \ldots, d_n): starting with an empty n-vertex graph, it sequentially adds new random edges so that the degree of each…
Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…
Graph burning is a discrete-time process that models the propagation of information in a network. Initially, we have an undirected graph of unburned vertices. At each time step, an unburned vertex is chosen to burn; additionally, unburned…
Point process is the dominant paradigm for modeling event sequences occurring at irregular intervals. In this paper we aim at modeling latent dynamics of event propagation in graph, where the event sequence propagates in a directed weighted…
The group classification of a class of variable coefficient reaction-diffusion equations with exponential nonlinearities is carried out up to both the equivalence generated by the corresponding generalized equivalence group and the general…