157 citations · 252 across the 26 of their papers we have counts for
7 papers · 1 filter
3d-printing Identification Spaces of the Square
Mikael Vejdemo-Johansson
We describe three identification spaces of the square, interesting choices of immersion into , and a process to construct 3d-printable models of their parametrization…
Certified Mapper: Repeated testing for acyclicity and obstructions to the nerve lemma
Mikael Vejdemo-Johansson, Alisa Leshchenko
The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma…
Sketches of a platypus: persistent homology and its algebraic foundations
Mikael Vejdemo-Johansson
The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The are…
Interleaved equivalence of categories of persistence modules
Mikael Vejdemo-Johansson
We demonstrate that an equivalence of categories using -interleavings as a fundamental component exists between the model of persistence modules as graded modules over…
Dualities in persistent (co)homology
Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their p…
Persistent Cohomology and Circular Coordinates
Vin de Silva, Mikael Vejdemo-Johansson
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low…
A partial -structure on the cohomology of
Mikael Vejdemo-Johansson
Suppose is a field of characteristic 2, and powers of 2. Then the -structure of the group cohomology algebras and are well known…