Related papers: Transmission problems: regularity theory, interfac…
In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different times. The flow is transient, and may transition between…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…
The increasing prominence of temporal networks in online social platforms and dynamic communication systems has made influence maximization a critical research area. Various diffusion models have been proposed to capture the spread of…
Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease…
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…
Researchers have attempted to model information diffusion and topic trends and lifecycle on online social networks. They have investigated the role of content, social connections and communities, familiarity and behavioral similarity in…
This work is devoted to radiative transfer equations with long-range interactions. Such equations arise in the modeling of high frequency wave propagation in random media with long-range dependence. In the regime we consider, the singular…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second order geometry and Ito integration on manifolds, allows us to give a natural and effective…
Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
This paper explores the computational complexity of diffusion-based language modeling. We prove a dichotomy based on the quality of the score-matching network in a diffusion model. In one direction, a network that exactly computes the score…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
We study networks of processes that all execute the same finite state protocol and that communicate through broadcasts. The processes are organized in a graph (a topology) and only the neighbors of a process in this graph can receive its…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the…