The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
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)
Citations
Cites
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
Size theory as a topological tool for computer vision
Frosini, P., & Landi, C. (1999) · Cited by 137
Extending Persistence Using Poincaré and Lefschetz Duality
Cohen‐Steiner, D., Edelsbrunner, H., & Harer, J. (2009) · Foundations of Computational Mathematics · doi:10.1007/s10208-008-9038-9 · Cited by 124
Self-citationExtending Persistence Using Poincaré and Lefschetz Duality
Cohen‐Steiner, D., Edelsbrunner, H., & Harer, J. (2008) · Foundations of Computational Mathematics · doi:10.1007/s10208-008-9027-z · Cited by 124
Self-citationPersistence-sensitive simplification functions on 2-manifolds
Edelsbrunner, H., Morozov, D., & Pascucci, V. (2006) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/1137856.1137878 · Cited by 75
Self-citationComparison of Pattern Detection Methods in Microarray Time Series of the Segmentation Clock
Dequéant, M., Ahnert, S. E., Edelsbrunner, H., Fink, T., Glynn, E. F., Hattem, G. L., Kudlicki, A. S., Mileyko, Y., Morton, J., Mushegian, A. R., et al. (2008) · PLoS ONE · doi:10.1371/journal.pone.0002856 · Cited by 53
Self-citationPersistence-sensitive simplification of functions on 2-manlfolds
Edelsbrunner, H., Morozov, D., & Pascucci, V. (2006) · Cited by 18
Self-citation
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).
Cited by
Sorted by citations
Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302
Qi, Y., He, Y., Qi, X., Zhang, Y., & Yang, G. (2023) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv51070.2023.00558 · Cited by 656
Statistical topological data analysis using persistence landscapesPreprint
Bubenik, P. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1207.6437 · Cited by 628
MetaCycle: an integrated R package to evaluate periodicity in large scale data
Wu, G., Anafi, R. C., Hughes, M. E., Kornacker, K., & Hogenesch, J. B. (2016) · Bioinformatics · doi:10.1093/bioinformatics/btw405 · Cited by 560
A stable multi-scale kernel for topological machine learning
Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2015.7299106 · Cited by 305
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
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