| Tue, Jan 23, 2024
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Colloquium
3:30 PM
MSCS 514 | | Analyzing structure data using polynomial invariants
Pengyu Líu, University of California, Davis
| | | Abstract: Advancements in innovative technology such as high-throughput sequencing, cryogenic electron microscopy and artificial intelligence have enabled production of myriad structure data in life sciences. These data include molecular structures of nucleic acids and proteins, as well as phylogenetic trees of pathogens. Analyzing extensive structure data is challenging without proper representations, primarily due to structure polymorphism. Polynomial invariants, such as the Tutte polynomial for graphs and the Jones polynomial for knots, are essential mathematical objects in algebraic combinatorics and algebraic topology. They encode structural information and are compatible with modern data analytic tools. In this talk, we introduce a computationally efficient, interpretable and complete polynomial invariant for rooted and unrooted trees. We develop methods based on the polynomial invariant to study pathogen diversification and nucleic acid structures. With this approach, we reveal distinct diversification patterns of seasonal and tropical human influenza virus A H3N2, as well as a strong correlation between the nascent RNA secondary structure and R-loop formation. |
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