Related papers: Corrected mean-field model for random sequential a…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
The goal of random sequential adsorption (RSA), a time-dependent packing method, is to create a regular or asymmetric covering of an empty space that can fit in the allocated space without overlapping. The density of coverage tends to reach…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…
The medial axis of a smoothly embedded surface in $\mathbb{R}^3$ consists of all points for which the Euclidean distance function on the surface has at least two minima. We generalize this notion to the mid-sphere axis, which consists of…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in $d$-dimensional Euclidean space $\mathbb{R}^d$ in the infinite-time or saturation limit…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
The random packing fraction of binary particles in D-dimensional Euclidean space R^D is studied using a geometric approach. First, the binary packing fraction of assemblies with small size difference are studied, using the excluded volume…
Metropolis nested sampling evolves a Markov chain from a current livepoint and accepts new points along the chain according to a version of the Metropolis acceptance ratio modified to satisfy the likelihood constraint, characteristic of…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Interacting particles on graphs are routinely used to study magnetic behaviour in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs…
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…
Subgraph pattern detection aims to uncover complex interaction structures in graphs. However, state-of-the-art graph neural network (GNN)-based solutions assume centralized access to the entire graph. When graphs are instead distributed…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…