On the Gromov-Hausdorff distance between compact spaces
, 2023 This work provides an introduction to the Gromov-Hausdorff distance, discussing its original definition and its relationship with correspondences between spaces. We prove that the Gromov-Hausdorff distance serves as a metric for the set of isometry classes of compact metric spaces.
openaire +1 more source
Imaging-based representation and stratification of intra-tumor heterogeneity via tree-edit distance. [PDF]
Sci Rep, 2022 Cavinato L +5 more
europepmc +1 more source
Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
Let $G$ be a compact, connected metric graph and let $X\subseteq G$ be a subset. If $X$ is sufficiently dense in $G$, we show that the Gromov--Hausdorff distance matches the Hausdorff distance, namely $d_{GH}(G,X)=d_{H}(G,X)$. In a recent study, when the metric graph is the circle $G=S^1$ with circumference $2π$, the equality $d_{GH}(S^1,X)=d_{H}(S^1,X)
Adams, Henry +4 more
openaire +2 more sources
On manifolds with almost non-negative Ricci curvature and integrally-positive k th -scalar curvature. [PDF]
Math AnnCucinotta A, Mondino A.
europepmc +1 more source
Width Stability of Rotationally Symmetric Metrics. [PDF]
J Geom AnalStufflebeam H, Sweeney P.
europepmc +1 more source
Median geometry for spaces with measured walls and for groups. [PDF]
Math AnnChatterji I, Druţu C.
europepmc +1 more source
Lipschitz Stability of Travel Time Data. [PDF]
J Geom AnalIlmavirta J +4 more
europepmc +1 more source
Mathematically tractable models of random phylogenetic networks: an overview of some recent developments. [PDF]
Philos Trans R Soc Lond B Biol SciBienvenu F.
europepmc +1 more source
A Toponogov globalisation result for Lorentzian length spaces. [PDF]
Math AnnBeran T, Harvey J, Napper L, Rott F.
europepmc +1 more source
Topological data analysis of human brain networks through order statistics. [PDF]
PLoS One, 2023 Das S, Anand DV, Chung MK.
europepmc +1 more source