121 citations · 276 across the 10 of their papers we have counts for
10 papers
Interleaving and Gromov-Hausdorff distance
Peter Bubenik, Vin de Silva, Jonathan Scott
One of the central notions to emerge from the study of persistent homology is that of interleaving distance. It has found recent applications in symplectic and contact geometry, sh…
Theory of interleavings on categories with a flow
Vin de Silva, Elizabeth Munch, Anastasios Stefanou
The interleaving distance was originally defined in the field of Topological Data Analysis (TDA) by Chazal et al. as a metric on the class of persistence modules parametrized over…
Higher interpolation and extension for persistence modules
Peter Bubenik, Vin de Silva, Vidit Nanda
The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the sp…
Categorified Reeb Graphs
Vin de Silva, Elizabeth Munch, Amit Patel
The Reeb graph is a construction which originated in Morse theory to study a real valued function defined on a topological space. More recently, it has been used in various applica…
Metrics for generalized persistence modules
Peter Bubenik, Vin de Silva, Jonathan Scott
We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form…
The structure and stability of persistence modules
Frederic Chazal, Vin de Silva, Marc Glisse +1
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed…