论文标题
通过瓶颈采样和同源
Sampling and homology via bottlenecks
论文作者
论文摘要
在本文中，我们提出了一种有效的算法，以产生光滑的紧凑型品种的密集样品。该过程部分基于该品种的计算$ \ textit {bottlenecks} $。使用几何信息，例如瓶颈和$ \ textit {local ress} $，我们还提供了所需的样品密度的界限，以确保可以从样本中恢复多种多样的同源性。算法的实现与Dufresne等人的数值实验以及与算法的计算比较一起提供。 al。
In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing $\textit{bottlenecks}$ of the variety. Using geometric information such as the bottlenecks and the $\textit{local reach}$ we also provide bounds on the density of the sample needed in order to guarantee that the homology of the variety can be recovered from the sample. An implementation of the algorithm is provided together with numerical experiments and a computational comparison to the algorithm by Dufresne et. al.
