5 papers
Computing Connection Matrices via Persistence-like Reductions
Tamal K. Dey, Michał Lipiński, Marian Mrozek +1
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for…
Tracking Dynamical Features via Continuation and Persistence
Tamal K. Dey, Michał Lipiński, Marian Mrozek +1
Multivector fields and combinatorial dynamical systems have recently become a subject of interest due to their potential for use in computational methods. In this paper, we develop…
Persistence of Conley-Morse Graphs in Combinatorial Dynamical Systems
Tamal K. Dey, Marian Mrozek, Ryan Slechta
Multivector fields provide an avenue for studying continuous dynamical systems in a combinatorial framework. There are currently two approaches in the literature which use persiste…
Persistence of the Conley Index in Combinatorial Dynamical Systems
Tamal K. Dey, Marian Mrozek, Ryan Slechta
A combinatorial framework for dynamical systems provides an avenue for connecting classical dynamics with data-oriented, algorithmic methods. Combinatorial vector fields introduced…
Filtration Simplification for Persistent Homology via Edge Contraction
Tamal K. Dey, Ryan Slechta
Persistent homology is a popular data analysis technique that is used to capture the changing topology of a filtration associated with some simplicial complex . These topologica…