Lattice Paths for Persistent Diagrams

Moo K. Chung, Hernando Ombao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


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.
Original languageEnglish (US)
Title of host publicationInterpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data
PublisherSpringer International Publishing
Number of pages10
ISBN (Print)9783030874438
StatePublished - Sep 21 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-10-05
Acknowledged KAUST grant number(s): CRG
Acknowledgements: The illustration of COVID-19 virus (Fig. 1 left) is provided by Alissa Eckert and Dan Higgins of Disease Control and Prevention (CDC), US. The proteins 6VXX and 6VYB are provided by Alexander Walls of University of Washington. The protein 6JX7 is provided by Tzu-Jing Yang of National Taiwan University. Figure 2-left is modified from an image in Wikipedia. This study is supported by NIH EB022856 and EB028753, NSF MDS-2010778, and CRG from KAUST.


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