Topological data analysis, including persistent homology, has undergone significant development in recent years. However, due to heterogenous nature of persistent homology features that do not have one-to-one correspondence across measurements, it is still difficult to build a coherent statistical inference procedure  . The paired data structure in persistent homology as birth and death events of topological features add further complexity to conducting inference. To address these current problems, we propose to analyze the birth and death events using lattice paths . The proposed lattice path method is implemented to characterize the topological features of the protein structures of corona viruses. This demonstrates new insights to building a coherent statistical inference procedure in persistent homology .
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, as birth and death in persistent diagrams, adds additional complexity to the development. 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 the topological characterization of the protein structures of COVID-19 viruse. We demonstrate that there are topological changes during the conformation change of spike proteins that are needed to initiate the infection of host cells .
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due to heterogenous nature of persistent homology features that do not have one-to-one correspondence across measurements, it is still difficult
one outstanding challenge is
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on persistent diagrams
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data structure in persistent homology
dependent data structure,
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events of topological features add further complexity to conducting inference. To address these current problems, we propose to analyze the birth and death events using lattice paths
in persistent diagrams, adds additional complexity to the development. 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
R
implemented to characterize the topological features
applied to the topological characterization
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corona viruses. This demonstrates new insights to building a coherent statistical inference procedure in persistent homology
COVID-19 viruse. We demonstrate that there are topological changes during the conformation change of spike proteins that are needed to initiate the infection of host cells