Canopies generalize vines and vineyards by tracking simplex pairs in filtered chain complexes instead of persistence diagram points, with proofs of homeomorphism and applications to multiplicity and monodromy.
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PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
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Canopies: A Generalization of Vines and Vineyards for Parameterized Persistence
Canopies generalize vines and vineyards by tracking simplex pairs in filtered chain complexes instead of persistence diagram points, with proofs of homeomorphism and applications to multiplicity and monodromy.