5 papers
Topological simplification guided by forbidden regions
Jakub Leśkiewicz, Bartosz Furmanek, Michał Lipiński +1
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders c…
Apex Representatives
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Given a zigzag filtration, we want to find its barcode representatives, i.e., a compatible choice of bases for the homology groups that diagonalize the linear maps in the zigzag. T…
Persistent (Co)Homology in Matrix Multiplication Time
Dmitriy Morozov, Primoz Skraba
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found d…
Computing Betti tables and minimal presentations of zero-dimensional persistent homology
Yuan Luo, Dmitriy Morozov, Luis Scoccola
The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathem…
A Fast Algorithm for Computing Zigzag Representatives
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtr…