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math.AC2026
Localized Persistent Commutative Algebra
Kaiyue He, Faisal Suwayyid, Guo-Wei Wei
We develop a localized persistent theory of commutative algebra for Stanley-Reisner rings, based on local cohomology supported at a coordinate prime rather than at the maximal idea…
math.AC2025
Persistent commutative algebra on graphs and hypergraphs
Faisal Suwayyid, Guo-Wei Wei
We introduce a persistent commutative algebra for studying the algebraic and combinatorial evolution of edge ideals of graphs and hypergraphs under filtration. Building on the Pers…
math.AC2025
GBNL: Graded Betti Number Learning of Complex Biological Data
Mushal Zia, Faisal Suwayyid, Guo-Wei Wei
While persistent homology is widely used for data shape analysis, persistent commutative algebra (PCA) has seen limited adoption in machine learning and data science. Unlike persis…