Topological data analysis, including persistent homology, has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. The paired dependent data structure, as birth and death in persistent diagrams, adds additional complexity to the development. In this paper, we present a new lattice path representation for persistent diagrams. A new exact statistical inference procedure is developed for lattice paths via combinatorial enumerations. The proposed lattice path method is applied to the topological characterization of the protein structures of COVID-19 viruse. We demonstrate that there are topological changes during the conformation change of spike proteins that are needed to initiate the infection of host cells.

翻译：近年来,包括持久性同系物在内的地形学数据分析有了重大发展,然而,一个突出的挑战是如何在持久性图表上建立一致的统计推断程序。相配的依附数据结构,作为持久性图表中的出生和死亡,增加了发展的复杂性。在本文中,我们为持久性图表提出了一个新的拉特式路径图。通过组合式查点,为拉特式路径制定了一个新的精确统计推断程序。提议的拉特式路径方法适用于COVID-19病毒蛋白结构的表层定性。我们证明,在引发宿主细胞感染所需的峰值蛋白质的相容变化过程中,存在着表面变化。