Osman Berat Okutan

most citedThe Distortion of the Reeb Quotient Map on Riemannian Manifolds

2 citations · 2 across the 1 of their papers we have counts for

collaborators

4 papers

math.AT2021

Decorated Merge Trees for Persistent Topology

Justin Curry, Haibin Hang, Washington Mio +2

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both $π_{0}$ and $H_{n}$ information into a single data structure that disti…

math.AT2018

Quantitative Simplification of Filtered Simplicial Complexes

Facundo Mémoli, Osman Berat Okutan

We introduce a new invariant defined on the vertices of a given filtered simplicial complex, called codensity, which controls the impact of removing vertices on persistent homology…

math.MG2018★ 2 cited

The Distortion of the Reeb Quotient Map on Riemannian Manifolds

Facundo Mémoli, Osman Berat Okutan

Given a metric space $X$ and a function $f : X \to R$ , the Reeb construction gives metric a space $X_{f}$ together with a quotient map $X \to X_{f}$ . Under suitable conditions…

math.MG2018

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 $(X, d_{X})$ there exists a \emph{tree metric} $t_{X}$ on $X$ such that $\|d_X-t_X\|_\infty…