Related papers: Spherical friezes
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…
This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of 3-dimensional sphere and some partial results are…
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of…
We study lattice points in d-dimensional spheres, and count their number in thin spherical segments. We found an upper bound depending only on the radius of the sphere and opening angle of the segment. To obtain this bound we slice the…
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…
We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a `slice' defined by minimizing the distance to a single generic `template' intersects the group orbit of every…
Fourier series of smooth, non-periodic functions on $[-1,1]$ are known to exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of overcoming these problems is by using a Fourier series on a larger domain, say $[-T,T]$…
The Fr\'echet distance is a popular metric for curves; however, its bottleneck character is a disadvantage in many applications. Here we introduce two variants of the Fr\'echet distance to cope with this problem and expand the work on…
For many shape analysis problems in computer vision and scientific imaging (e.g., computational anatomy, morphological cytometry), the ability to align two closed curves in the plane is crucial. In this paper, we concentrate on rigidly…
Let ${\cal T}$ be a triangulation of a set ${\cal P}$ of $n$ points in the plane, and let $e$ be an edge shared by two triangles in ${\cal T}$ such that the quadrilateral $Q$ formed by these two triangles is convex. A {\em flip} of $e$ is…
Optical interferometers may not require a phase-stable optical link between the stations if instead sources of quantum-mechanically entangled pairs could be provided to them, enabling long baselines. We developed a new variation of this…
We present here two new techniques to solve the one-dimensional random flight. The first one is an expansion in the number of collisions. The second one is the obtention of a Fourier series. This second technique can be applied to an…
This paper presents a new approach for dimension reduction of data observed in a sphere. Several dimension reduction techniques have recently developed for the analysis of non-Euclidean data. As a pioneer work, Hauberg (2016) attempted to…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
We investigate numerically different techniques to extract scattering amplitudes from the Euclidean Lattice {\phi}4 theory with two fields, having different masses. We present an exploratory study of the recently proposed method by Bruno…