论文标题
超图的持续同源性的稳定性
The stability of persistent homology of hypergraphs
论文作者
论文摘要
HyperGraph是涉及组相互作用的复杂网络的最通用模型。从亚历山大·格里戈尔（Alexander Grigor'yan），Yong Lin，Yuri Muranov和Shing-Tung Yau [18-22]，Stephane Bressan，Jingyan Li和本文的作者介绍了嵌入式超级读物同源性[6]，2019年在2019年介绍了蛋白质粘合性的24224，应用是关于超图的持续嵌入同源性的稳定性。在本文中，我们证明了持续嵌入的同源性的稳定性以及相关的简单复合物在超法上的过滤方面的持续同源性。我们将持续的同源方法应用于超图的形态，并证明了对过滤的扰动的稳定性。在某些条件下，我们证明了持久性贝蒂数字的恒定性在简单的Hypergraphs类型上。
Hypergraph is the most general model for complex networks involving group interactions. Taking the ideas of path homology from Alexander Grigor'yan, Yong Lin, Yuri Muranov and Shing-Tung Yau [18-22], Stephane Bressan, Jingyan Li and the authors of this article introduced embedded homology of hypergraphs [6] in 2019, which has leaded to successful applications in protein-ligand binding network [24, 25] in 2021. A fundamental question arising from practical applications is about the stability of the persistent embedded homology of hypergraphs. In this paper, we prove the stability of the persistent embedded homology as well as the persistent homology of the associated simplicial complex with respect to perturbations of the filtration on a hypergraph. We apply the persistent homology methods to morphisms of hypergraphs and prove the stability with respect to perturbations of the filtrations. We prove the constancy of the persistent Betti numbers under some conditions on the simple-homotopy types of hypergraphs.
