Localized homology
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The projection pΣ: M(|Σ|,S) → |Σ| is a homotopy equivalence.
“It can be shown that p Σ is a homotopy equivalence (see [65]).”
From Topology and data (2009) · cites this paper as [65]
By using persistence, one can develop a systematic way of addressing questions of the source of features; the methodology is described in [65].
“By using persistence, one is able to develop a systematic way of addressing such questions.That methodology has been described in [65].”
From Topology and data (2009) · cites this paper as [65]
Persistent homology is able to bridge geometry and topology, leading to a new efficient approach for the simplification of biological structural complexity.
“Persistent homology22–25—a new branch of algebraic topology—is able to bridge geometry and topology, leading to a new efficient approach for the simplification of biological structural complexity26–31; however, it neglects critical chemical/biological information when it is directly applied to complex biomolecular structures.”
From A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation (2020) · cites this paper as [25]
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Gonzalez-Lorenzo, A. (2016) · doi:10.70675/a95fcb81ze808z4eafz9f6dz26764b15c6b2
Atom probe informed persistent homology analysis of precipitation topology and hardening
Zhu, S., & Zhou, T. (2026) · Materials & Design · doi:10.1016/j.matdes.2026.116278
Learning Topology-Aware Representations via Test-Time Adaptation for Anomaly Segmentation
Zia, A., Ali, U., Rehman, A., Ramzan, U., Han, K., Faheem, M., Qureshi, S., & Xiang, W. (2026) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2026.3710196
- Authors
- Zomorodian, A., & Carlsson, G.
- Affiliations
- Dartmouth College (US)
- Stanford University (US)
- Corresponding author
- Zomorodian, Afra
- ORCID
- Carlsson, Gunnar
- Venue
- Computational Geometry
- Publisher
- Elsevier BV
- Published
- 2008-11
- Volume
- 41
- Issue
- 3
- Pages
- 126-148
- ISSN
- 0925-7721 (ISSN-L)
- OpenAlex
- W2912929541
- Cited by
- 89
- References
- 35
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 2 · 2023: 4 · 2022: 2 · 2021: 4 · 2020: 7 · 2019: 7 · 2018: 5 · 2017: 4 · 2016: 6 · 2015: 8 · 2014: 6 · 2013: 4 · 2012: 3
- FWCI
- 9.68
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Computational Geometry (publishedVersion)
- Funders
- Defense Advanced Research Projects Agency (HR0011, HR0011-05-1-0007)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- tunnels, voids, topological data analysis, homology computation
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