Lattice Paths for Persistent Diagrams
This provides a statistical inference method for persistent homology, specifically applied to analyze topological changes in COVID-19 spike proteins.
The authors tackled the challenge of statistical inference on persistent diagrams by introducing a lattice path representation and developing an exact inference procedure via combinatorial enumerations. They applied this method to COVID-19 spike proteins and demonstrated topological changes during conformational changes.
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.