Related papers: Is a nonlocal diffusion strategy convenient for bi…
Whether an idea, information, infection, or innovation diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. Recent studies have shown that diffusion…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
We study the problem of decision-making in the setting of a scarcity of shared resources when the preferences of agents are unknown a priori and must be learned from data. Taking the two-sided matching market as a running example, we focus…
In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction…
In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in various applications. For example, these kernels have been…
This paper studies distributed resource allocation problem in multi-agent systems, where all the agents cooperatively minimize the sum of their cost functions with global resource constraints over stochastic communication networks. This…
This paper studies a strategic model of marketing and product diffusion in social networks. We consider two firms offering substitutable products which can improve their market share by seeding the key individuals in the market. Consumers…
We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…
We study how to allocate resources to participants who can strategically misrepresent their deservingness at a cost. A principal assigns item(s) (or money) among multiple agents on the basis of their costly signals. Each agent's signal…
In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain the global existence, uniqueness and longtime behaviour of solution of these two problems. The spreading-vanishing…
We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasi-species. By suggesting an analogy between the competition among strains and the…
Nonlocal cross-diffusion systems on the torus, arising in population dynamics and neuroscience, are analyzed. The global existence of weak solutions, the weak-strong uniqueness, and the localization limit are proved. The kernels are assumed…
This work studies a nonlocal extension of the Klausmeier vegetation model in $\mathbb{R}^N$ $(N \ge 1)$ that incorporates both local and nonlocal diffusion. The biomass dynamics are driven by a nonlocal convolution operator, representing…
A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving…
In this paper, we inspect well-known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns.…
We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order $0 < s < 1$, incorporating a nonlocal time component modeled by an integral kernel. After establishing well-posedness of the problem, we analyze…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
The role of dispersal on the stability and synchrony of a metacommunity is a topic of considerable interest in theoretical ecology. Dispersal is known to promote both synchrony, which enhances the likelihood of extinction, and spatial…