1. The arithmetic topology of genetic alignments.
- Author
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Barrett, Christopher, Bura, Andrei, He, Qijun, Huang, Fenix, and Reidys, Christian
- Subjects
- *
ARITHMETIC , *GENETIC variation , *SEQUENCE alignment , *TOPOLOGY , *HAMMING distance , *GENETIC algorithms , *MATHEMATICAL complexes - Abstract
We propose a novel mathematical paradigm for the study of genetic variation in sequence alignments. This framework originates from extending the notion of pairwise relations, upon which current analysis is based on, to k-ary dissimilarity. This dissimilarity naturally leads to a generalization of simplicial complexes by endowing simplices with weights, compatible with the boundary operator. We introduce the notion of k-stances and dissimilarity complex, the former encapsulating arithmetic as well as topological structure expressing these k-ary relations. We study basic mathematical properties of dissimilarity complexes and show how this approach captures watershed moments of viral dynamics in the context of SARS-CoV-2 and H1N1 flu genomic data. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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