20 citations · 31 across the 10 of their papers we have counts for
6 papers · 1 filter
Stability and Approximations for Decorated Reeb Spaces
Justin Curry, Washington Mio, Tom Needham +2
Given a map from a topological space to a metric space , a decorated Reeb space consists of the Reeb space, together with an attribution function whose values re…
On Metrics for Analysis of Functional Data on Geometric Domains
Soheil Anbouhi, Washington Mio, Osman Berat Okutan
This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces,…
Universal Mappings and Analysis of Functional Data on Geometric Domains
Soheil Anbouhi, Washington Mio, Osman Berat Okutan
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Data…
Metric Graph Approximations of Geodesic Spaces
Facundo Memoli, Osman Berat Okutan, Qingsong Wang
We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitabl…
The Distortion of the Reeb Quotient Map on Riemannian Manifolds
Facundo Mémoli, Osman Berat Okutan
Given a metric space and a function , the Reeb construction gives metric a space together with a quotient map . Under suitable conditions…
Reeb Posets and Tree Approximations
Facundo Mémoli, Osman Berat Okutan
A well known result in the analysis of finite metric spaces due to Gromov says that given any there exists a \emph{tree metric} on such that $\|d_X-t_X\|_\infty…