Related papers: Is a nonlocal diffusion strategy convenient for bi…

Distributed resource allocation is a central task in network systems such as smart grids, water distribution networks, and urban transportation systems. When solving such problems in practice it is often important to have nonasymptotic…

This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection…

One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…

We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the…

In this paper we propose a method for sparse dynamic allocation of resources to bound the risk of spreading processes, such as epidemics and wildfires, using convex optimization and dynamic programming techniques. Here, risk is defined as…

Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…

Predicting species persistence within ecological communities is a fundamental challenge for both empirical and theoretical ecology. Existing methods span from mechanistic models, whose parameters are difficult to estimate from data, to…

Diffusion models have recently shown significant potential in solving decision-making problems, particularly in generating behavior plans -- also known as diffusion planning. While numerous studies have demonstrated the impressive…

We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP…

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…

We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…

Some aspects of nonlocal dynamics on directed and undirected networks for an initial value problem whose Jacobian matrix is a variable-order fractional power of a Laplacian matrix are discussed here. This is a new extension to…

In this work, we introduce a compartmental advection-diffusion network model to describe the propagation of stress in a population situated in two interconnected spatial zones during a disaster situation. The model accounts for interactions…

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have…

Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…

Cellular sheaves and sheaf Laplacians provide a far-reaching generalization of graphs and graph Laplacians, resulting in a wide array of applications ranging from machine learning to multi-agent control. In the context of multi-agent…

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how…

The competition for resources is a defining feature of microbial communities. In many contexts, from soils to host-associated communities, highly diverse microbes are organized into metabolic groups or guilds with similar resource…

Our investigation focuses on the asymptotic spreading behavior of the Fisher-KPP equation with a mixed local-nonlocal operator in the diffusion (see the work by X. Cabr\'e and J.-M. Roquejoffre, 2013, ref.[8]) to the setting of mixed…