12 citations · 21 across the 6 of their papers we have counts for
6 papers
Bi-filtrations and persistence paths for 2-Morse functions
Ryan Budney, Tomasz Kaczynski
This paper studies the homotopy-type of bi-filtrations of compact manifolds induced as the pre-image of filtrations of the plane for generic smooth functions f : M --> R^2. The pri…
Linking combinatorial and classical dynamics: Conley index and Morse decompositions
Bogdan Batko, Tomasz Kaczynski, Marian Mrozek +1
We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F…
A New Matching Algorithm for Multidimensional Persistence
Madjid Allili, Tomasz Kaczynski, Claudia Landi +1
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended…
On differential systems with strongly indefinite variational structure
Cyril J. Batkam, Fabrice Colin, Tomasz Kaczynski
We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of st…
Reducing complexes in multidimensional persistent homology theory
Madjid Allili, Tomasz Kaczynski, Claudia Landi
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms co…
Comparison of Persistent Homologies for Vector Functions: from continuous to discrete and back
Niccolò Cavazza, Marc Ethier, Patrizio Frosini +2
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of t…