Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud
arXiv:2112.03610 · doi:10.7566/JPSJ.91.091013
Abstract
This paper introduces persistent homology, which is a powerful tool to characterize the shape of data using the mathematical concept of topology. We explain the fundamental idea of persistent homology from scratch using some examples. We also review some applications of persistent homology to materials researches and software for persistent homology data analysis. HomCloud, one of persistent homology software, is especially featured in this paper.
References in corpus (14)
- A roadmap for the computation of persistent homology
- Hierarchical structures of amorphous solids characterized by persistent homology
- Clique topology reveals intrinsic geometric structure in neural correlations
- Ripser: efficient computation of Vietoris-Rips persistence barcodes
- Dualities in persistent (co)homology
- Dynamics and energy landscape in a tetrahedral network glass-former: Direct comparison with models of fragile liquids
- Generalized Persistence Diagrams for Persistence Modules over Posets
- Protein folding analysis using features obtained by persistent homology
- Persistence Homology Of Entangled Rings
- Molecular Insights into the Mechanical Properties of Polymer-Fullerene Bulk Heterojunctions for Organic Photovoltaic Applications
- Topology of Force Networks in Granular Media under Impact
- Impact-induced hardening in dense frictional suspensions
- Microscopic Description of Yielding in Glass Based on Persistent Homology
- Computing Persistent Homology with Various Coefficient Fields in a Single Pass
Cited by in corpus (10)
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- Topological Data Analysis of Ion Migration Mechanism
- Persistent homology analysis for dense QCD effective model with heavy quarks
- Revealing the Void-Size Distribution of Silica Glass using Persistent Homology
- Time series analysis using persistent homology of distance matrix
- Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics
- Geometric Bounds for Persistence
- Persistence is All You Need -- A Topological Lens on Microstructural Characterization