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A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…
This paper is concerned with the numerical approximation of the Dirichlet initial-boundary-value problem of nonlinear pseudo-parabolic equations with spectral methods. Error estimates for the semidiscrete Galerkin and collocation schemes…
Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a…
We consider a metric measure space with a local regular Dirichlet form. We establish necessary and sufficient conditions for upper heat kernel bounds with sub-diffusive space-time exponent to hold. This characterization is stable under…
Given a network represented by a graph $G=(V,E)$, we consider a dynamical process of influence diffusion in $G$ that evolves as follows: Initially only the nodes of a given $S\subseteq V$ are influenced; subsequently, at each round, the set…
We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…
Graph models are relevant in many fields, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, i.e. a varying number of…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their…
There has been significant interest in the networking community on the impact of cascade effects on the diffusion of networking technology upgrades in the Internet. Thinking of the global Internet as a graph, where each node represents an…
This paper presents a novel application of graph neural networks for modeling and estimating network heterogeneity. Network heterogeneity is characterized by variations in unit's decisions or outcomes that depend not only on its own…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…
Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on…
Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions…
We discuss a multiscale Galerkin approximation scheme for a system of coupled quasilinear parabolic equations. These equations arise from the upscaling of a pore scale filtration combustion model under the assumptions of large Damkh\"oler…
We prove equivalent conditions for two-sided sub-Gaussian estimates of heat kernels on metric measure spaces.
Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…
Diffusion models are a class of generative models that have demonstrated remarkable success in tasks such as image generation. However, one of the bottlenecks of these models is slow sampling due to the delay before the onset of trajectory…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…