Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path representation for persistent diagrams. We then develop a new exact statistical inference procedure for lattice paths via combinatorial enumerations. The lattice path method is applied to the topological characterization of the protein structures of the COVID-19 virus. We demonstrate that there are topological changes during the conformational change of spike proteins.

翻译：近些年来,持久性同质学经历了重大发展,然而,一个尚未解决的挑战是如何在持久性图表上建立一致的统计推论程序。在本文中,我们首先为持久性图表提出一个新的拉特维丝路径代表。然后我们通过组合式计数,为拉特维丝路径制定一个新的精确统计推论程序。对于COVID-19病毒蛋白结构的地形定性,采用了拉特维丝路径方法。我们证明,在峰值蛋白质的直观变化中,存在着地形变化。