scholarly journals Algebraic stability of zigzag persistence modules

2018 ◽  
Vol 18 (6) ◽  
pp. 3133-3204 ◽  
Author(s):  
Magnus Botnan ◽  
Michael Lesnick
Keyword(s):  
Algebraic Stability ◽  
Persistence Modules ◽  
Zigzag Persistence

scholarly journals The reflection distance between zigzag persistence modules

2019 ◽  
Vol 3 (3) ◽  
pp. 185-219
Author(s):  
Alexander Elchesen ◽  
Facundo Mémoli
Keyword(s):  
Persistence Modules ◽  
Zigzag Persistence

scholarly journals On the Stability of Interval Decomposable Persistence Modules

2021 ◽  
Author(s):  
Håvard Bakke Bjerkevik
Keyword(s):  
Persistent Homology ◽  
Stability Theorem ◽  
Proof Technique ◽  
Algebraic Stability ◽  
Persistence Modules ◽  
Reeb Graphs ◽  
Central Result ◽  
The Stability

AbstractThe algebraic stability theorem for persistence modules is a central result in the theory of stability for persistent homology. We introduce a new proof technique which we use to prove a stability theorem for n-dimensional rectangle decomposable persistence modules up to a constant $$2n-1$$ 2 n - 1 that generalizes the algebraic stability theorem, and give an example showing that the bound cannot be improved for $$n=2$$ n = 2 . We then apply the technique to prove stability for block decomposable modules, from which novel results for zigzag modules and Reeb graphs follow. These results are improvements on weaker bounds in previous work, and the bounds we obtain are optimal.

scholarly journals Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules

2015 ◽  
Vol 22 (1) ◽  
pp. 227-296 ◽  
Author(s):  
Leonid Polterovich ◽  
Egor Shelukhin
Keyword(s):  
Hamiltonian Flows ◽  
Persistence Modules

scholarly journals Higher Interpolation and Extension for Persistence Modules

2017 ◽  
Vol 1 (1) ◽  
pp. 272-284 ◽  
Author(s):  
Peter Bubenik ◽  
Vin de Silva ◽  
Vidit Nanda
Keyword(s):  
Persistence Modules

Persistence Modules

2016 ◽  
pp. 15-29
Author(s):  
Frédéric Chazal ◽  
Vin de Silva ◽  
Marc Glisse ◽  
Steve Oudot
Keyword(s):  
Persistence Modules

scholarly journals Parametrized homology via zigzag persistence

2019 ◽  
Vol 19 (2) ◽  
pp. 657-700 ◽  
Author(s):  
Gunnar Carlsson ◽  
Vin de Silva ◽  
Sara Kališnik ◽  
Dmitriy Morozov
Keyword(s):  
Zigzag Persistence
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