Related papers: The Grasshopper Problem on the Sphere
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that…
In this paper, we provide $R$-estimators of the location of a rotationally symmetric distribution on the unit sphere of $\R^k$. In order to do so we first prove the local asymptotic normality property of a sequence of rotationally symmetric…
We define spherical Heron triangles (spherical triangles with "rational" side-lengths and angles) and parametrize them via rational points of certain families of elliptic curves. We show that the congruent number problem has infinitely many…
A new efficient approach to the analysis of nonlinear higher-spin equations, that treats democratically auxiliary spinor variables $Z_A$ and integration homotopy parameters in the non-linear vertices of the higher-spin theory, is developed.…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…
We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance…
In this work, we investigate the construction of spherically symmetric solutions within the framework of modified teleparallel gravity, focusing in particular on $f({\cal T})$ theory, where ${\cal T}$ represents the torsion scalar.…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
Given a Riemannian manifold $M$ and an $L^2$-normalized Laplacian eigenfunction $\psi$ on $M$ with eigenvalue $\lambda^2$, a general problem in analysis is to understand how the mass of $\psi$ distributes around $M$. There are different…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
We consider the numerical approximation of variational problems with orthotropic growth, that is those where the integrand depends strongly on the coordinate directions with possibly different growth in each direction. Under realistic…
Spherically embedded spatial data are spatially indexed observations whose values naturally reside on or can be equivalently mapped to the unit sphere. Such data are increasingly ubiquitous in fields ranging from geochemistry to demography.…
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
We study the problem of learning mixtures of linear classifiers under Gaussian covariates. Given sample access to a mixture of $r$ distributions on $\mathbb{R}^n$ of the form $(\mathbf{x},y_{\ell})$, $\ell\in [r]$, where…
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this…
A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of…