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math.AT2022
Sequents, barcodes, and homology
Saugata Basu, Negin Karisani, Laxmi Parida
We consider the problem of generating hypothesis from data based on ideas from logic. We introduce a notion of barcodes, which we call sequent barcodes, that mirrors the barcodes i…
math.AT2022
Computing the homology functor on semi-algebraic maps and diagrams
Saugata Basu, Negin Karisani
Developing an algorithm for computing the Betti numbers of semi-algebraic sets with singly exponential complexity has been a holy grail in algorithmic semi-algebraic geometry and o…
math.AT2022
Persistent homology of semi-algebraic sets
Saugata Basu, Negin Karisani
We give an algorithm with singly exponential complexity for computing the barcodes up to dimension (for any fixed ) of the filtration of a given semi-algebraic…