论文标题
离散的莫尔斯理论，持续的同源性和forman-icci曲率
Discrete Morse Theory, Persistent Homology and Forman-Ricci Curvature
论文作者
论文摘要
使用Banchoff的离散摩尔斯理论，与Bloch的结果同时，基于后者的莫尔斯和莫尔斯理论之间的牢固联系，我们自己的先前算法基于后期，我们表明存在基于曲率的，有效的网络和超级核工程的曲率持久同源方案。我们还通过使用Bloch扩展Banchoff的工作来扩展提出的方法，以包括更多一般类型的网络。此外，我们显示了在组合环境中存在的缺陷与福尔曼的RICCI曲率之间的联系，从而解释了先前的经验结果，表明使用Forman的Morse理论获得的持久同源性结果与Forman的Ricci曲率在另一方面获得了非常强的相关性。
Using Banchoff's discrete Morse Theory, in tandem with Bloch's result on the strong connection between the former and Forman's Morse Theory, and our own previous algorithm based on the later, we show that there exists a curvature-based, efficient Persistent Homology scheme for networks and hypernetworks. We also broaden the proposed method to include more general types of networks, by using Bloch's extension of Banchoff's work. Moreover, we show the connection between defect and Forman's Ricci curvature that exists in the combinatorial setting, thus explaining previous empirical results showing very strong correlation between Persistent Homology results obtained using Forman's Morse Theory on the one hand, and Forman's Ricci curvature, on the other.
