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math.AT2019
Intrinsic Topological Transforms via the Distance Kernel Embedding
Clément Maria, Steve Oudot, Elchanan Solomon
Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measure…
math.AT2018
Inverse Problems in Topological Persistence
Steve Oudot, Elchanan Solomon
In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. th…
math.AT2018
Stability of Extended Functional Persistence in Dimensions Zero and One
Elchanan Solomon
The stability result, as stated, is incorrect. In particular, the 1-dimensional extended persistence diagrams of a finely-triangulated simplicial complex X equipped with a continuo…