6 papers
Discrete homology computations by reduction to zero differentials
Sterling Ebel, Chris Kapulkin, Nathan Kershaw
We develop a new algorithm for computing (persistent) discrete homology of graphs using reduction to zero differentials and active enumeration. This allows us to compute the fourth…
Stability of persistent path homology of path complexes
Chris Kapulkin, Kyle Koyanagi
We show stability of persistent path homology of path complexes. As a consequence, we deduce the stability of persistent path homology of hypergraphs and of sequence hypergraphs, a…
RedZeD: Computing persistent homology by Reduction to Zero Differentials
Chris Kapulkin, Nathan Kershaw
We introduce a new algorithm for computing persistent homology of Vietoris-Rips filtrations, which offers a considerable improvement both in terms of time and memory over the exist…
Towards fast computation of higher discrete homology
Jacob Ender, Chris Kapulkin
We develop a new algorithm for computing the second discrete homology group of a graph which is much faster when compared to existing algorithms. To do so, we identify five basic s…
Discrete homotopy hypothesis for n-types
Daniel Carranza, Chris Kapulkin
We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse…
Fast computation of the first discrete homology group
Jacob Ender, Chris Kapulkin
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significant…