74 citations · 74 across the 1 of their papers we have counts for
4 papers
The Depth Poset under Transpositions in the Filter
Herbert Edelsbrunner, Michał Lipiński, Marian Mrozek +2
The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing…
Conley-Morse persistence barcode: a homological signature of combinatorial bifurcations
Tamal K. Dey, Michał Lipiński, Manuel Soriano-Trigueros
Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations…
The poset of cancellations induced by gradient dynamics in a filtered Lefschetz complex
Herbert Edelsbrunner, Michał Lipiński, Marian Mrozek +1
Motivated by questions about simplification of topology, we take a discrete approach to the dependency of simplifying operations, using methods based on combinatorial gradient dyna…
A Survey of Vectorization Methods in Topological Data Analysis
Dashti Ali, Aras Asaad, Maria-Jose Jimenez +3
Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In th…