Results 1 to 10 of about 7,363 (139)

Branching Geodesics of the Gromov-Hausdorff Distance

Analysis and Geometry in Metric Spaces, 2022
In this paper, we first evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metric spaces equipped with the Gromov ...
Ishiki Yoshito
doaj   +4 more sources

A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity [PDF]

Scientific Reports
We introduce a cohomology-based Gromov–Hausdorff ultrametric method to analyze 1-dimensional and higher-dimensional (co)homology groups, focusing on loops, voids, and higher-dimensional cavity structures in simplicial complexes, to address typical ...
JunJie Wee, Xue Gong, Wilderich Tuschmann, Kelin Xia   +3 more
doaj   +2 more sources

Some Properties of Gromov–Hausdorff Distances [PDF]

Discrete and 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 \(\widehat{GH}(X,Y)= (1/2)\max\{\text{infdis}(X\to Y),\text{infdis}(Y\to X)\}\), \(X,Y\in {\mathcal G}\).
Facundo Memoli
exaly   +4 more sources

Quantized Gromov–Hausdorff distance

Journal of Functional Analysis, 2006
A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel's Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We
exaly   +3 more sources

Geometry of non-Archimedean Gromov-Hausdorff distance [PDF]

P-Adic Numbers, Ultrametric Analysis, and Applications, 2009
49 ...
exaly   +4 more sources

Approximating Gromov-Hausdorff distance in Euclidean space

Computational Geometry: Theory and Applications
The Gromov-Hausdorff distance $(d_{GH})$ proves to be a useful distance measure between shapes. In order to approximate $d_{GH}$ for compact subsets $X,Y\subset\mathbb{R}^d$, we look into its relationship with $d_{H,iso}$, the infimum Hausdorff distance under Euclidean isometries.
Sushovan Majhi, Jeffrey Scott Vitter, Carola Wenk   +2 more
exaly   +3 more sources

Structural stability for scalar reaction-diffusion equations

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we prove the structural stability for a family of scalar reaction-diffusion equations. Our arguments consist of using invariant manifold theorem to reduce the problem to a finite dimension and then, we use the structural stability of Morse–
Jihoon Lee, Leonardo Pires
doaj   +1 more source

Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets

Axioms, 2023
The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the
Wenjuan Ren, Zhanpeng Yang, Xipeng Li
doaj   +1 more source

The Gromov–Hausdorff distance between spheres

Geometry & Topology, 2023
* We made some structural changes for better ...
Lim, Sunhyuk, Mémoli, Facundo, Smith, Zane   +2 more
openaire   +2 more sources

Exact topological inference of the resting-state brain networks in twins [PDF]

Network Neuroscience, 2019
A cycle in a brain network is a subset of a connected component with redundant additional connections. If there are many cycles in a connected component, the connected component is more densely connected.
Moo K. Chung, Hyekyoung Lee, Alex DiChristofano, Hernando Ombao, Victor Solo   +4 more
doaj   +1 more source