4 citations · 6 across the 5 of their papers we have counts for
6 papers
Fast free resolutions of bifiltered chain complexes
Ulrich Bauer, Tamal K. Dey, Michael Kerber +2
In a -critical bifiltration, every simplex enters along a staircase with at most steps. Examples with include degree-Rips bifiltrations and models of the multicover bi…
Computing Projective Implicit Representations from Poset Towers
Tamal K. Dey, Florian Russold
A family of simplicial complexes connected by simplicial maps and indexed by a finite poset is called a poset tower. Poset towers subsume multi-parameter filtrations, zigzag fi…
Representing two-parameter persistence modules via graphcodes
Michael Kerber, Florian Russold
Graphcodes were recently introduced as a technique to employ two-parameter persistence modules in machine learning tasks (Kerber and Russold, NeurIPS 2024). We show in this work th…
Graphcode: Learning from multiparameter persistent homology using graph neural networks
Michael Kerber, Florian Russold
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes hand…
Efficient Algorithms for Complexes of Persistence Modules with Applications
Tamal K. Dey, Florian Russold, Shreyas N. Samaga
We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We…
Persistent sheaf cohomology
Florian Russold
We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topologica…