Lattice Paths for Persistent Diagrams

TL;DR

This paper introduces a lattice path representation for persistent diagrams and develops an exact statistical inference method, applying it to analyze topological changes in COVID-19 protein structures.

Contribution

It presents a novel lattice path approach for persistent diagrams and a new statistical inference procedure based on combinatorial enumeration.

Findings

Identifies topological changes during spike protein conformational shifts

Provides a new mathematical framework for persistent diagram analysis

Demonstrates application to COVID-19 protein structures

Abstract

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.