18 citations · 18 across the 3 of their papers we have counts for
4 papers · 1 filter
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 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…
Lefschetz Complexes as Finite Topological Spaces
Jacek Kubica, Marian Mrozek
We consider a fixed basis of a finitely generated free chain complex as a finite topological space and we present a sufficient condition for the singular homology of this space to…
Fundamental Group Algorithm for low dimensional tessellated CW complexes
P. Brendel, G. Ellis, M. Juda +1
We present a detailed description of a fundamental group algorithm based on Forman's combinatorial version of Morse theory. We use this algorithm in a classification problem of pri…