Related papers: Random assignment problems on ${2d}$ manifolds
This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints.…
Random 2-cell embeddings of a given graph $G$ are obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces, $\mathbb{E}[F_G]$, of such an embedding which is equivalent to studying its average…
Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning. These discretized operators usually depend on bandwidth parameters whose tuning remains a…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
We prove that the Riemannian metric on a compact manifold of dimension $n\geq 3$ with smooth boundary can be uniquely determined, up to an isometry fixing the boundary, by the Dirichlet-to-Neumann map associated to the Laplace-Beltrami…
Eigendecomposition of the Laplace-Beltrami operator is instrumental for a variety of applications from physics to data science. We develop a numerical method of computation of the eigenvalues and eigenfunctions of the Laplace-Beltrami…
This paper studies a distributed stochastic optimization problem over random networks with imperfect communications subject to a global constraint, which is the intersection of local constraint sets assigned to agents. The global cost…
In this paper, we study a class of eigenvalue problems involving both local as well as nonlocal operators, precisely the classical Laplace operator and the fractional Laplace operator in the presence of mixed boundary conditions, that is…
This paper deals with the error estimate in problems of periodic homogenization. The methods used are those of the periodic unfolding. We give the upper bound of the distance between the unfolded gradient of a function belonging to…
In this work is considered an elliptic problem, referred to as the Ventcel problem, involvinga second order term on the domain boundary (the Laplace-Beltrami operator). A variationalformulation of the Ventcel problem is studied, leading to…
Let $n\geq 2$ and $r\in \{1, \cdots, n-1\}$ be integers, $M$ be a compact smooth K\''ahler manifold of complex dimension $n$, $E$ be a holomorphic vector bundle with complex rank $r$ and equipped with an hermitian metric $h_E$, and $L$ be…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
We study the additive eigenvalues on changing domains, along with the associated vanishing discount problems. We consider the convergence of the vanishing discount problem on changing domains for a general scaling type $\Omega_\lambda =…
We undertake a critical evaluation of recent observational information on $\Omega_m$ and $\Omega_\Lambda$ in order to identify possible sources of systematic errors and effects of simplified statistical analyses. We combine observations for…
We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic…
We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent…
We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex periodic exponentials and spherical harmonics, respectively,…