Related papers: Experimental study of energy-minimizing point conf…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Given $N$ geodesic caps on the unit sphere in $\mathbb{R}^d$, and whose total normalized surface area sums to one, what is the maximal surface area their union can cover? In this work, we provide an asymptotically sharp upper bound for an…
A new concept, the spherical TPC, presents unique advantages when low energy neutrinos are to be detected. Some of the applications are: a) observation of the e oscillation when emitted by a tritium source (<E e > = 14 keV) in a 10 m radius…
Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a…
Spherical coverings on the S2 sphere and their algebraic numbers are given for the putatively optimal global solutions for some n-congruent spherical caps with minimal radius to completely cover the S2 sphere. A few locally optimal…
Clues to the shape of our Universe can be found by searching the CMB for matching circles of temperature patterns. A full sky search of the CMB, mapped extremely accurately by NASA's WMAP satellite, returned no detection of such matching…
We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotopy class of mappings of the 2-sphere which represents the…
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…
The Tammes problem is to find the arrangement of N points on a unit sphere which maximizes the minimum distance between any two points. This problem is presently solved for several values of N, namely for N=3,4,6,12 by L. Fejes Toth (1943);…
Within the two-center shell model parameterization we have defined the optimal shape which fissioning nuclei attain just before the scission and calculated the total deformation energy (liquid drop part plus the shell correction) as…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
How much energy does a quantum computer consume? Are they more efficient than their classical counterparts? In this work, we make a step towards answering these questions. We define the energy efficiency of a quantum computer as the ratio…
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is optimal with respect to a large class of potential functions…
We consider the critical points (equilibria) of a planar potential generated by $n$ Newtonian point masses augmented with a quadratic term (such as arises from a centrifugal effect). Particular cases of this problem have been considered…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
In this study we address existing deficiencies in the literature on applications of Particle Swarm Optimization to generate optimal designs. We present the results of a large computer study in which we bench-mark both efficiency and…
We demonstrate a method for exact determination of the quadratic curve of minimal energy and minimal curvature variation through three non-colinear points in the plane, including methods to determine the tangent vector and curvature at any…
The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite…
This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the…