相关论文: Testing surface area with arbitrary accuracy
The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The…
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a…
We introduce a methodology to test models with spatial variations of the fine-structure constant $\alpha$, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
We prove area estimates for stable capillary $cmc$ (minimal) hypersurfaces $\Sigma$ with nonpositive Yamabe invariant that are properly immersed in a Riemannian $n$-dimensional manifold $M$ with scalar curvature $R^M$ and mean curvature of…
We give an explicit estimate of the area of a closed surface by the diameter and a lower bound of curvature. This is better than Calabi-Cao's estimate for a nonnegatively curved two-sphere.
Searches for spacetime variations of fundamental constants have entered an era of unprecedented precision. New, high quality quasar spectra require increasingly refined analytic methods. In this article, a continuation in a series to…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We present a solution of a question from S. Campi, P.…
This paper studies sample average approximation (SAA) in solving convex or strongly convex stochastic programming (SP) problems. In estimating SAA's sample efficiency, the state-of-the-art sample complexity bounds entail metric entropy…
A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…
Let X be a real algebraic surface. The comparison between the volume of real and complex loci of ample divisors D brings us to define the concordance, which is a number between 0 and 1. This number equals 1 when the Picard number is 1, and…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
In this paper, we show that the total area of two distinct surfaces with Gaussian curvature equal to 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least 4{\pi}. In other…
We show that a closed piecewise-linear hypersurface immersed in $R^n$ ($n\ge 3$) is the boundary of a convex body if and only if every point in the interior of each $(n-3)$-face has a neighborhood that lies on the boundary of some convex…
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the…
With the popularity of drone technologies, aerial photography has become prevalent in many daily scenarios such as environment monitoring, structure inspection, law enforcement etc. A central challenge in this domain is the efficient…
The quantization problem looks for best approximations of a probability measure on a given metric space by finitely many points, where the approximation error is measured with respect to the Wasserstein distance. On particular smooth…