Results 1 to 10 of about 126 (85)
A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity [PDF]
Scientific ReportsWe 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 +3 more
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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
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FPT-Algorithms for computing Gromov-Hausdorff and interleaving distances between trees
Journal of Computational Geometry, 2022 The Gromov-Hausdorff distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the Gromov-Hausdorff distance
Elena Farahbakhsh Touli, Yusu Wang
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The Gromov-Hausdorff distance between ultrametric spaces: its structure and computation
Journal of Computational Geometry, 2023 $\DeclareMathOperator{\ugh}{u_\mathrm{GH}}\DeclareMathOperator{\dgh}{d_\mathrm{GH}}$The Gromov-Hausdorff distance ($d_\mathrm{GH}$) provides a natural way of quantifying the dissimilarity between two given metric spaces.
Facundo Mémoli +2 more
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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
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Nearly-doubling spaces of persistence diagrams
Journal of Computational Geometry, 2023 The space of persistence diagrams under bottleneck distance is known to have infinite doubling dimension. Because many metric search algorithms and data structures have bounds that depend on the dimension of the search space, the high dimensionality ...
Donald Sheehy, Siddharth Sheth
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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
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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 +4 more
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The continuous limit of large random planar maps [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We discuss scaling limits of random planar maps chosen uniformly over the set of all $2p$-angulations with $n$ faces. This leads to a limiting space called the Brownian map, which is viewed as a random compact metric space.
Jean-François Le Gall
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Chordal Hausdorff Convergence and Quasihyperbolic Distance
Analysis and Geometry in Metric Spaces, 2020 We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).
Herron David A. +2 more
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