Related papers: Frontiers of sphere recognition in practice
We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in $\mathbb{R}^d$, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is…
The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current…
The need for more transparent face recognition (FR), along with other visual-based decision-making systems has recently attracted more attention in research, society, and industry. The reasons why two face images are matched or not matched…
Given topological spaces X and Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y . We consider a computational version, where X, Y are given as finite simplicial complexes, and the…
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except $4$-dimensional cases: in these cases standard spheres are characterized. Canonical…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
Let U denote the Urysohn sphere and consider U as a metric structure in the empty continuous signature. We prove that every definable function from U^n to U is either a projection function or else has relatively compact range. As a…
We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge 4$.
In this paper we prescribe a fourth order conformal invariant 9the Paneitz Curvature) on five and six spheres. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem,…
The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial…
We introduce and analyze the concept of space-spectrum uncertainty for certain commonly-used designs for spectrally programmable cameras. Our key finding states that, it is impossible to simultaneously capture high-resolution spatial images…
We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representation formula. As a result, it follows that cuspidal cross…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
We show that nonlinear optimization techniques can successfully be applied to realize and to inscribe matroid polytopes and simplicial spheres. Thus we obtain a complete classification of neighborly polytopes of dimension $4$, $6$ and $7$…
An expression for the functional determinant on a sphere for a massive (scalar) field derived by Denef, Hartnoll and Sachdev using quasinormal modes is shown to exist already in the literature together with the multiplicative anomaly…
We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
We characterize atypical values at infinity of a real polynomial function of three variables by a certain sum of indices of the gradient vector field of the function restricted to a sphere with a sufficiently large radius. This is an…
The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…