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Lipschitz Functions Have L p -Stable Persistence
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“There is also a stability result for the Wasserstein distances d p , with p finite, in the presence of a Lipschitz property for the functions, proved in Cohen-Steiner et al. (2010).”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Cohen-Steiner et al. (2010)
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Elements of Algebraic Topology
Munkres, J. R. (2018) · CRC Press eBooks · doi:10.1201/9780429493911 · Cited by 2,113
Topological Persistence and Simplification
Edelsbrunner, Letscher, & Zomorodian (2002) · Discrete & Computational Geometry · doi:10.1007/s00454-002-2885-2 · Cited by 1,779
Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591
ELEMENTS OF ALGEBRAIC TOPOLOGY
Kuratowski, K. (1972) · Elsevier eBooks · doi:10.1016/b978-0-08-016160-0.50028-2 · Cited by 1,290
Stability of Persistence Diagrams
Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. (2007) · Discrete & Computational Geometry · doi:10.1007/s00454-006-1276-5 · Cited by 1,280
Self-citationA High-Resolution Root Spatiotemporal Map Reveals Dominant Expression Patterns
Brady, S. M., Orlando, D. A., Lee, J., Wang, J. Y., Koch, J. D., Dinneny, J. R., Mace, D., Ohler, U., & Benfey, P. N. (2007) · Science · doi:10.1126/science.1146265 · Cited by 1,154
On the Translocation of Masses
Kantorovich, L. V. (2006) · Journal of Mathematical Sciences · doi:10.1007/s10958-006-0049-2 · Cited by 776
The Segmentation Clock: Converting Embryonic Time into Spatial Pattern
Pourquié, O. (2003) · Science · doi:10.1126/science.1085887 · Cited by 530
A Complex Oscillating Network of Signaling Genes Underlies the Mouse Segmentation Clock
Dequéant, M.-L., Glynn, E., Gaudenz, K., Wahl, M., Chen, J., Mushegian, A., & Pourquié, O. (2006) · Science · doi:10.1126/science.1133141 · Cited by 460
Benfey, P. N., & Scheres, B. (2000) · Current Biology · doi:10.1016/s0960-9822(00)00814-9 · Cited by 162
Research works printed but not linked: 2
- G. Monge, Mémoire sur la théorie des déblais et des remblais, in Histoire de l’Académie Royale des Sciences de Paris (1781), pp. 666–704.
- L.N. Wasserstein, Markov processes over denumerable products of spaces describing large systems of automata, Probl. Inf. Transm. 5, 47–52 (1969).
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Self-citation
Metadata
- Authors
- Cohen-Steiner, D., Edelsbrunner, H., Harer, J., & Mileyko, Y.
- Affiliations
- Duke University (US)
- Corresponding author
- Edelsbrunner, Herbert
- Venue
- Foundations of Computational Mathematics
- Published
- 2010-01-28
- Volume
- 10
- Issue
- 2
- Pages
- 127-139
- ISSN
- 1615-3375 (ISSN-L)
- 1615-3383
- OpenAlex
- W2122101130
- Cited by
- 284
- References
- 16
- Citations by year
- 2026: 19 · 2025: 20 · 2024: 26 · 2023: 32 · 2022: 26 · 2021: 35 · 2020: 25 · 2019: 12 · 2018: 16 · 2017: 13 · 2016: 11 · 2015: 12 · 2014: 14 · 2013: 7 · 2012: 9
- FWCI
- 7.22
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Foundations of Computational Mathematics (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- Lipschitz functions, persistence diagrams, Wasserstein distance, topological data analysis, systems biology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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