{"title":"Lattice Paths for Persistent Diagrams.","authors":"Moo K Chung, Hernando Ombao","doi":"10.1007/978-3-030-87444-5_8","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":73499,"journal":{"name":"Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data : 4th International Workshop, iMIMIC 2021, and 1st International Workshop, TDA4MedicalData 2021, He...","volume":"12929 ","pages":"77-86"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8730383/pdf/nihms-1763408.pdf","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data : 4th International Workshop, iMIMIC 2021, and 1st International Workshop, TDA4MedicalData 2021, He...","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/978-3-030-87444-5_8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
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.
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