6 papers
Computing Conley-Morse Persistence Barcode Efficiently by Updating Matrix Decompositions
Tamal K. Dey, Andrew Haas, Michał Lipiński
Recent advances in combinatorial dynamical systems that generalize the classic discrete Morse theory have prompted algorithmic studies of combinatorial vector fields. In this regar…
The poset of cancellations induced by gradient dynamics in a filtered Lefschetz complex
Herbert Edelsbrunner, MichaÅ LipiÅski, 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…
Conley-Morse persistence barcode: a homological signature of combinatorial bifurcations
Tamal K. Dey, MichaÅ LipiÅski, 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…
Topological simplification guided by forbidden regions
Jakub LeÅkiewicz, Bartosz Furmanek, MichaÅ LipiÅski +1
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders c…
The Depth Poset under Transpositions in the Filter
Herbert Edelsbrunner, MichaÅ LipiÅski, 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…
Computing a Connection Matrix and Persistence Efficiently from a Morse Decomposition
Tamal K. Dey, MichaÅ LipiÅski, Andrew Haas
Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is…