Related papers: The Grasshopper Problem on the Sphere
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend…
This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
We investigate the snaking of localised patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, that are not…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter…
We review spherical and inhomogeneous analytic solutions of the field equations of Einstein and of scalar-tensor gravity, including Brans-Dicke theory, non-minimally (possibly conformally) coupled scalar fields, Horndeski, and beyond…
The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…
Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
Methodology is provided towards the solution of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean…
In the paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with…
In this work, we study a vector model of spontaneous spacetime-symmetry breaking coupled to gravity: the bumblebee model. The primary focus is on static spherically symmetric solutions. Complementing previous work on black hole solutions,…
Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which…