随机场与复形的持久同调
Persistent Homology for Random Fields and Complexes
摘要：
我们讨论并回顾了应用代数拓扑学领域的最新进展，如持久同源性和条形码。特别是，我们讨论了这些是如何与了解更多关于流形学习随机点云数据，由随机顶点确定的单纯复形的代数结构，以及最详细的，随机场的漂移集的代数拓扑结构。
英文摘要：
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the algebraic topology of the excursion sets of random fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
