Lattice Paths for Persistent Diagrams

Type
Conference Paper

Authors
Chung, Moo K.
Ombao, Hernando

KAUST Department
Biostatistics Group
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Statistics Program

KAUST Grant Number
CRG

Preprint Posting Date
2021-05-01

Online Publication Date
2021-09-21

Print Publication Date
2021

Date
2021-09-21

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.

Citation
Chung, M. K., & Ombao, H. (2021). Lattice Paths for Persistent Diagrams. Lecture Notes in Computer Science, 77–86. doi:10.1007/978-3-030-87444-5_8

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.

Publisher
Springer International Publishing

Conference/Event Name
4th International Workshop on Interpretability of Machine Intelligence in Medical Image Computing, iMIMIC 2020 and 1st International Workshop on Topological Data Analysis and Its Applications for Medical Data, TDA4MedicalData 2021 held in conjunction with 24th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2021

DOI
10.1007/978-3-030-87444-5_8

arXiv
2105.00351

Additional Links
https://link.springer.com/10.1007/978-3-030-87444-5_8

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