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math.AT2026
Real Tree Vineyards have Vines
Michael Hull, Thomas Payne, Thomas Weighill
We show that every vineyard can be decomposed into vines, that is, every path in the space of persistence diagrams can be decomposed into a sequence of paths in $\mat…
math.AT2026
Topological optimization with birth and death cochains
Thomas Weighill, Ling Zhou
We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike bir…