From the 1 of 10 linked papers with an AI index.
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Computing 1-Periodic Persistent Homology with Finite Windows
Adam Onus, Primoz Skraba
Let be a periodic cell complex endowed with a covering where is a finite quotient space of equivalence classes under translations acting on . We assume is…
Wasserstein Stability for Persistence Diagrams
Primoz Skraba, Katharine Turner
The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bot…
Persistent Local Systems of Periodic Spaces
Adam Onus, Primoz Skraba
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as…
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…
Möbius Homology
Amit Patel, Primoz Skraba
This paper introduces and develops Möbius homology, a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology…