32 citations · 33 across the 7 of their papers we have counts for
4 papers · 1 filter
Morse Theoretic Templates for High Dimensional Homology Computation
Shaun Harker, Konstantin Mischaikow, Kelly Spendlove
We introduce the notion of a template for discrete Morse theory. Templates provide a memory efficient approach to the computation of homological invariants (e.g., homology, persist…
Persistent homology with non-contractible preimages
Konstantin Mischaikow, Charles Weibel
For a fixed , we analyze the space of all sequences , approximating a continuous function on the circle, with a given persistence diagram , and show that t…
Contractibility of a persistence map preimage
Jacek Cyranka, Konstantin Mischaikow, Charles Weibel
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that e…
A Comparison Framework for Interleaved Persistence Modules
Shaun Harker, Miroslav Kramar, Rachel Levanger +1
We present a generalization of the induced matching theorem and use it to prove a generalization of the algebraic stability theorem for -indexed pointwise finite-dimens…