Lattice Paths for Persistent Diagrams with Application to COVID-19 Virus Spike Proteins
release_6samqlpqmncfhb5raaybcgxhvy
by
Moo K. Chung, Hernando Ombao
2021
Abstract
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, which are the births and deaths in persistent
diagrams, adds complexity to statistical inference. 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
study 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, a necessary step in infecting host
cells.
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