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We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
The metric dimension of a graph is the minimum size of a set of vertices such that each vertex is uniquely determined by the distances to the vertices of that set. Our aim is to upper-bound the order $n$ of a graph in terms of its diameter…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…
We establish a universal framework for concentration inequalities based on invariance under diffeomorphism groups. Given a probability measure $\mu$ on a space $E$ and a diffeomorphism $\psi: E \to F$, concentration properties transfer…
Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [A…
We study a metric on the set of finite graphs in which two graphs are considered to be similar if they have similar bounded dimensional "factors". We show that limits of convergent graph sequences in this metric can be represented by…
Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which…
In the paper we are dealing with metric measure spaces of diameter at most one and of total measure one. Gromov introduced the sampling compactification of the set of these spaces. He asked whether the metric measure space invariants extend…
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph -- in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs.…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept is similar to those from Chen, Gao and Ren (2017) and Zhang (2002). Rather than focusing, as in these earlier works, on…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
In 1989, Ne\v{s}et\v{r}il and Pudl\'ak posed the following challenging question: Do planar posets have bounded Boolean dimension? We show that every poset with a planar cover graph and a unique minimal element has Boolean dimension at most…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…