25 citations · 33 across the 8 of their papers we have counts for
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math.AT2022★ 2 cited
Projected distances for multi-parameter persistence modules
Nicolas Berkouk, Francois Petit
Relying on sheaf theory, we introduce the notions of projected barcodes and projected distances for multi-parameter persistence modules. Projected barcodes are defined as derived p…
math.AT2020★ 1 cited
Thickening of the diagonal and interleaving distance
Francois Petit, Pierre Schapira
Given a topological space , a thickening kernel is a monoidal presheaf on with values in the monoidal category of derived kernels on . A bi-thickenin…
math.AT2019★ 25 cited
Ephemeral persistence modules and distance comparison
Nicolas Berkouk, Francois Petit
We provide a definition of ephemeral multi-persistent modules and prove that the quotient of persistent modules by the ephemeral ones is equivalent to the category of -sheaves.…