Results 11 to 20 of about 7,327 (139)

Quantifying the Single-Cell Morphological Landscape of Cellular Transdifferentiation through Force Field Reconstruction. [PDF]

Adv Sci (Weinh)
This study reconstructs the driving force field of fibroblast‐to‐neuron transdifferentiation from sparse single‐cell images by decomposing it into flux and time‐dependent potential gradient, extending the landscape‐flux framework to non‐steady‐state systems.
Yu C, Liu C, Wang E, Wang J.
europepmc   +2 more sources

The Gromov–Hausdorff distance between spheres

Geometry & Topology, 2023
* We made some structural changes for better ...
Lim, Sunhyuk, Mémoli, Facundo, Smith, Zane   +2 more
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Hausdorff vs Gromov-Hausdorff distances

, 2023
Let $M$ be a closed Riemannian manifold and let $X\subseteq M$. If the sample $X$ is sufficiently dense relative to the curvature of $M$, then the Gromov-Hausdorff distance between $X$ and $M$ is bounded from below by half their Hausdorff distance, namely $d_{GH}(X,M) \ge \frac{1}{2} d_H(X,M)$.
Adams, Henry, Frick, Florian, Majhi, Sushovan, McBride, Nicholas   +3 more
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Vector Bundles and Gromov–Hausdorff Distance [PDF]

Journal of K-Theory, 2009
AbstractWe show how to make precise the vague idea that for compact metric spaces that are close together for Gromov–Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some
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The Dual Gromov-Hausdorff Propinquity [PDF]

, 2014
Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*-algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named ...
Alfsen, Bellissard, Blackadar, Burago, Connes, Connes, Connes, Dobrushin, Fell, Gromov, Gromov, Kadison, Kadison, Kantorovich, Kantorovich, Kerr, Kerr, Landsman, Latrémolière, Latrémolière, Latrémolière, Latrémolière, Li, Li, Li, Li, McShane, Morariu, Ozawa, Pedersen, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Rieffel, Seiberg, T'Hooft, Wasserstein, Wu, Wu   +45 more
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Some Properties of Gromov–Hausdorff Distances [PDF]

Discrete & Computational Geometry, 2012
Let \({\mathcal G}\) stand for the class of all compact metric spaces and let \(GH(.,.)\) be the Gromov-Hausdorff distance on it. In this paper, a modified Gromov-Hausdorff distance is introduced as \(\widehat{GH}(X,Y)= (1/2)\max\{\text{infdis}(X\to Y),\text{infdis}(Y\to X)\}\), \(X,Y\in {\mathcal G}\).
openaire   +3 more sources

Volume Comparison in the presence of a Gromov-Hausdorff ε−approximation II

Annals of the West University of Timisoara: Mathematics and Computer Science, 2018
Let (M, g) be any compact, connected, Riemannian manifold of dimension n. We use a transport of measures and the barycentre to construct a map from (M, g) onto a Hyperbolic manifold (ℍn/Λ, g0) (Λ is a torsionless subgroup of Isom(ℍn,g0)), in such a way ...
Sabatini Luca
doaj   +1 more source

Locally rich compact sets [PDF]

, 2015
We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any other ...
Chen, Changhao, Rossi, Eino
core   +1 more source

A quantitative obstruction to collapsing surfaces

Open Mathematics, 2019
We provide a quantitative obstruction to collapsing surfaces of genus at least 2 under a lower curvature bound and an upper diameter bound.
Katz Mikhail G.
doaj   +1 more source

Neck-pinching of C P 1 -structures in the PSL 2 C -character variety. [PDF]

J Topol
Abstract We characterize a certain neck‐pinching degeneration of (marked) CP1$\mathbb {C}{\rm P}^1$‐structures on a closed oriented surface S$S$ of genus at least two. In a more general setting, we take a path of CP1$\mathbb {C}{\rm P}^1$‐structures Ct(t⩾0)$C_t \nobreakspace (t \geqslant 0)$ on S$S$ that leaves every compact subset in its deformation ...
Baba S.
europepmc   +2 more sources