Related papers: Internal DLA on Sierpinski gasket graphs
We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…
The present work investigates clustering of a graph-based representation of industrial connections derived from international trade data by Hidalgo et al (2007) and confirms existence of around ten industrial clusters that are reasonably…
The inward diffusion of particles, often observed in magnetospheric plasmas (either naturally created stellar ones or laboratory devices) creates a spontaneous density gradient, which seemingly contradicts the entropy principle. We…
We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1-block…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
Dynamic graph neural networks (DyGNNs) have demonstrated powerful predictive abilities by exploiting graph structural and temporal dynamics. However, the existing DyGNNs fail to handle distribution shifts, which naturally exist in dynamic…
Irregular (Irr) galaxies are gas-rich objects with recent or ongoing star formation. In absence of spiral density waves, star formation occurs largely stochastically. The scattered star-forming regions tend to be long-lived and migrate…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
Deep surface photometry reveals a faint, diffuse baryonic component in a significant fraction of galaxy groups, permeating the intragroup space. This intragroup light (IGL) is primarily formed by stars removed from their host galaxies…
The Diffusion-Limited Cluster-Cluster Aggregation (DLCA) model is modified by including cluster deformations using the {\it bond fluctuation} algorithm. From 3$d$ computer simulations, it is shown that, below a given threshold value $c_g$…
Transformer models have become foundational across a wide range of scientific and engineering domains due to their strong empirical performance. A key capability underlying their success is in-context learning (ICL): when presented with a…
In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer…
Diffusion probabilistic models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data, for instance, for computer vision, audio, natural language processing, or biomolecule…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
We continue the study of the properties of graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$, for various choices of $F$ and $r$. This is…
The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart,…