Wasserstein metric (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Wasserstein metric" in English language version.

refsWebsite

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18doi.org

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9worldcat.org

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5harvard.edu

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5semanticscholar.org

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4arxiv.org

69^th place

59^th place

4nih.gov

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2mlr.press

low place

1mathnet.ru

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1jstor.org

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1archives-ouvertes.fr

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1mfo.de

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1imperial.ac.uk

7,025^th place

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1ams.org

451^st place

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ams.org

Clement P, Desch W (2008). "An elementary proof of the triangle inequality for the Wasserstein metric". Proceedings of the American Mathematical Society. 136 (1): 333–339. doi:10.1090/S0002-9939-07-09020-X.

archives-ouvertes.fr

hal.archives-ouvertes.fr

Petitjean M (2002). "Chiral mixtures" (PDF). Journal of Mathematical Physics. 43 (8): 4147–4157. Bibcode:2002JMP....43.4147P. doi:10.1063/1.1484559. S2CID 85454709.

arxiv.org

Mukherjee S, Wethington D, Dey TK, Das J (March 2022). "Determining clinically relevant features in cytometry data using persistent homology". PLOS Computational Biology. 18 (3): e1009931. arXiv:2203.06263. Bibcode:2022PLSCB..18E9931M. doi:10.1371/journal.pcbi.1009931. PMC 9009779. PMID 35312683.
Ba, Demba; Dogra, Akshunna S.; Gambhir, Rikab; Tasissa, Abiy; Thaler, Jesse (2023-06-29). "SHAPER: can you hear the shape of a jet?". Journal of High Energy Physics. 2023 (6): 195. arXiv:2302.12266. Bibcode:2023JHEP...06..195B. doi:10.1007/JHEP06(2023)195. ISSN 1029-8479. S2CID 257205971.
Finlay, Chris; Jacobsen, Joern-Henrik; Nurbekyan, Levon; Oberman, Adam (2020-11-21). "How to Train Your Neural ODE: the World of Jacobian and Kinetic Regularization". International Conference on Machine Learning. PMLR: 3154–3164. arXiv:2002.02798.
Loeper G (July 2006). "Uniqueness of the solution to the Vlasov–Poisson system with bounded density". Journal de Mathématiques Pures et Appliquées. 86 (1): 68–79. arXiv:math/0504140. doi:10.1016/j.matpur.2006.01.005. ISSN 1292-8119. (See Theorem 2.9.)

doi.org

Kantorovich LV (1939). "Mathematical Methods of Organizing and Planning Production". Management Science. 6 (4): 366–422. doi:10.1287/mnsc.6.4.366. JSTOR 2627082.
Olkin I, Pukelsheim F (October 1982). "The distance between two random vectors with given dispersion matrices". Linear Algebra and Its Applications. 48: 257–263. doi:10.1016/0024-3795(82)90112-4. ISSN 0024-3795.
S. S. Vallander, Theory of Probability and its Applications, 1974, Volume 18, Issue 4, Pages 784–786 DOI: https://doi.org/10.1137/1118101
Petitjean M (2002). "Chiral mixtures" (PDF). Journal of Mathematical Physics. 43 (8): 4147–4157. Bibcode:2002JMP....43.4147P. doi:10.1063/1.1484559. S2CID 85454709.
Petitjean M (2004). "From shape similarity to shape complementarity: toward a docking theory". Journal of Mathematical Chemistry. 35 (3): 147–158. doi:10.1023/B:JOMC.0000033252.59423.6b. S2CID 121320315.
Mukherjee S, Wethington D, Dey TK, Das J (March 2022). "Determining clinically relevant features in cytometry data using persistent homology". PLOS Computational Biology. 18 (3): e1009931. arXiv:2203.06263. Bibcode:2022PLSCB..18E9931M. doi:10.1371/journal.pcbi.1009931. PMC 9009779. PMID 35312683.
Frederick, Christina; Yang, Yunan (2022-05-06). "Seeing through rock with help from optimal transport". Snapshots of Modern Mathematics from Oberwolfach. doi:10.14760/SNAP-2022-004-EN.
Oizumi, Masafumi; Albantakis, Larissa; Tononi, Giulio (2014-05-08). "From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0". PLOS Computational Biology. 10 (5): e1003588. Bibcode:2014PLSCB..10E3588O. doi:10.1371/journal.pcbi.1003588. PMC 4014402. PMID 24811198.
Ba, Demba; Dogra, Akshunna S.; Gambhir, Rikab; Tasissa, Abiy; Thaler, Jesse (2023-06-29). "SHAPER: can you hear the shape of a jet?". Journal of High Energy Physics. 2023 (6): 195. arXiv:2302.12266. Bibcode:2023JHEP...06..195B. doi:10.1007/JHEP06(2023)195. ISSN 1029-8479. S2CID 257205971.
Clement P, Desch W (2008). "An elementary proof of the triangle inequality for the Wasserstein metric". Proceedings of the American Mathematical Society. 136 (1): 333–339. doi:10.1090/S0002-9939-07-09020-X.
Matoušek, Jiří; Gärtner, Bernd (2007), "Duality of Linear Programming", Understanding and Using Linear Programming, Universitext, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 81–104, doi:10.1007/978-3-540-30717-4_6, ISBN 978-3-540-30697-9, retrieved 2022-07-15
Benamou, Jean-David; Brenier, Yann (2000-01-01). "A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem". Numerische Mathematik. 84 (3): 375–393. doi:10.1007/s002110050002. ISSN 0945-3245. S2CID 1100384.
Peyre R (October 2018). "Comparison between W₂ distance and Ḣ⁻¹ norm, and localization of Wasserstein distance". ESAIM: Control, Optimisation and Calculus of Variations. 24 (4): 1489–1501. doi:10.1051/cocv/2017050. ISSN 1292-8119. (See Theorem 2.1.)
Loeper G (July 2006). "Uniqueness of the solution to the Vlasov–Poisson system with bounded density". Journal de Mathématiques Pures et Appliquées. 86 (1): 68–79. arXiv:math/0504140. doi:10.1016/j.matpur.2006.01.005. ISSN 1292-8119. (See Theorem 2.9.)
Peyre R (October 2018). "Comparison between W₂ distance and Ḣ⁻¹ norm, and localization of Wasserstein distance". ESAIM: Control, Optimisation and Calculus of Variations. 24 (4): 1489–1501. doi:10.1051/cocv/2017050. (See Theorem 2.5.)
Bogachev VI, Kolesnikov AV (October 2012). "The Monge–Kantorovich problem: achievements, connections, and perspectives". Russian Mathematical Surveys. 67 (5): 785–890. Bibcode:2012RuMaS..67..785B. doi:10.1070/RM2012v067n05ABEH004808. S2CID 121411457.
Givens, Clark R; Shortt, Rae Michael (1984). "A class of Wasserstein metrics for probability distributions". Michigan Mathematical Journal. 31 (2): 231–240. doi:10.1307/mmj/1029003026.

dx.doi.org

Matoušek, Jiří; Gärtner, Bernd (2007), "Duality of Linear Programming", Understanding and Using Linear Programming, Universitext, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 81–104, doi:10.1007/978-3-540-30717-4_6, ISBN 978-3-540-30697-9, retrieved 2022-07-15

harvard.edu

ui.adsabs.harvard.edu

Petitjean M (2002). "Chiral mixtures" (PDF). Journal of Mathematical Physics. 43 (8): 4147–4157. Bibcode:2002JMP....43.4147P. doi:10.1063/1.1484559. S2CID 85454709.
Mukherjee S, Wethington D, Dey TK, Das J (March 2022). "Determining clinically relevant features in cytometry data using persistent homology". PLOS Computational Biology. 18 (3): e1009931. arXiv:2203.06263. Bibcode:2022PLSCB..18E9931M. doi:10.1371/journal.pcbi.1009931. PMC 9009779. PMID 35312683.
Oizumi, Masafumi; Albantakis, Larissa; Tononi, Giulio (2014-05-08). "From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0". PLOS Computational Biology. 10 (5): e1003588. Bibcode:2014PLSCB..10E3588O. doi:10.1371/journal.pcbi.1003588. PMC 4014402. PMID 24811198.
Ba, Demba; Dogra, Akshunna S.; Gambhir, Rikab; Tasissa, Abiy; Thaler, Jesse (2023-06-29). "SHAPER: can you hear the shape of a jet?". Journal of High Energy Physics. 2023 (6): 195. arXiv:2302.12266. Bibcode:2023JHEP...06..195B. doi:10.1007/JHEP06(2023)195. ISSN 1029-8479. S2CID 257205971.
Bogachev VI, Kolesnikov AV (October 2012). "The Monge–Kantorovich problem: achievements, connections, and perspectives". Russian Mathematical Surveys. 67 (5): 785–890. Bibcode:2012RuMaS..67..785B. doi:10.1070/RM2012v067n05ABEH004808. S2CID 121411457.

imperial.ac.uk

"Awards, fellowships and the shape of physics: News from the College | Imperial News | Imperial College London". Imperial News. 2023-03-29. Retrieved 2023-10-31.

jstor.org

Kantorovich LV (1939). "Mathematical Methods of Organizing and Planning Production". Management Science. 6 (4): 366–422. doi:10.1287/mnsc.6.4.366. JSTOR 2627082.

mathnet.ru

Vaserstein LN (1969). "Markov processes over denumerable products of spaces, describing large systems of automata" (PDF). Problemy Peredači Informacii. 5 (3): 64–72.

mfo.de

publications.mfo.de

Frederick, Christina; Yang, Yunan (2022-05-06). "Seeing through rock with help from optimal transport". Snapshots of Modern Mathematics from Oberwolfach. doi:10.14760/SNAP-2022-004-EN.

mlr.press

proceedings.mlr.press

Arjovsky M, Chintala S, Bottou L (July 2017). "Wasserstein Generative Adversarial Networks". International Conference on Machine Learning 214-223: 214–223.
Finlay, Chris; Jacobsen, Joern-Henrik; Nurbekyan, Levon; Oberman, Adam (2020-11-21). "How to Train Your Neural ODE: the World of Jacobian and Kinetic Regularization". International Conference on Machine Learning. PMLR: 3154–3164. arXiv:2002.02798.

nih.gov

ncbi.nlm.nih.gov

Mukherjee S, Wethington D, Dey TK, Das J (March 2022). "Determining clinically relevant features in cytometry data using persistent homology". PLOS Computational Biology. 18 (3): e1009931. arXiv:2203.06263. Bibcode:2022PLSCB..18E9931M. doi:10.1371/journal.pcbi.1009931. PMC 9009779. PMID 35312683.
Oizumi, Masafumi; Albantakis, Larissa; Tononi, Giulio (2014-05-08). "From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0". PLOS Computational Biology. 10 (5): e1003588. Bibcode:2014PLSCB..10E3588O. doi:10.1371/journal.pcbi.1003588. PMC 4014402. PMID 24811198.

pubmed.ncbi.nlm.nih.gov

Mukherjee S, Wethington D, Dey TK, Das J (March 2022). "Determining clinically relevant features in cytometry data using persistent homology". PLOS Computational Biology. 18 (3): e1009931. arXiv:2203.06263. Bibcode:2022PLSCB..18E9931M. doi:10.1371/journal.pcbi.1009931. PMC 9009779. PMID 35312683.
Oizumi, Masafumi; Albantakis, Larissa; Tononi, Giulio (2014-05-08). "From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0". PLOS Computational Biology. 10 (5): e1003588. Bibcode:2014PLSCB..10E3588O. doi:10.1371/journal.pcbi.1003588. PMC 4014402. PMID 24811198.

semanticscholar.org

api.semanticscholar.org

Petitjean M (2002). "Chiral mixtures" (PDF). Journal of Mathematical Physics. 43 (8): 4147–4157. Bibcode:2002JMP....43.4147P. doi:10.1063/1.1484559. S2CID 85454709.
Petitjean M (2004). "From shape similarity to shape complementarity: toward a docking theory". Journal of Mathematical Chemistry. 35 (3): 147–158. doi:10.1023/B:JOMC.0000033252.59423.6b. S2CID 121320315.
Ba, Demba; Dogra, Akshunna S.; Gambhir, Rikab; Tasissa, Abiy; Thaler, Jesse (2023-06-29). "SHAPER: can you hear the shape of a jet?". Journal of High Energy Physics. 2023 (6): 195. arXiv:2302.12266. Bibcode:2023JHEP...06..195B. doi:10.1007/JHEP06(2023)195. ISSN 1029-8479. S2CID 257205971.
Benamou, Jean-David; Brenier, Yann (2000-01-01). "A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem". Numerische Mathematik. 84 (3): 375–393. doi:10.1007/s002110050002. ISSN 0945-3245. S2CID 1100384.
Bogachev VI, Kolesnikov AV (October 2012). "The Monge–Kantorovich problem: achievements, connections, and perspectives". Russian Mathematical Surveys. 67 (5): 785–890. Bibcode:2012RuMaS..67..785B. doi:10.1070/RM2012v067n05ABEH004808. S2CID 121411457.

worldcat.org

search.worldcat.org

Olkin I, Pukelsheim F (October 1982). "The distance between two random vectors with given dispersion matrices". Linear Algebra and Its Applications. 48: 257–263. doi:10.1016/0024-3795(82)90112-4. ISSN 0024-3795.
Ba, Demba; Dogra, Akshunna S.; Gambhir, Rikab; Tasissa, Abiy; Thaler, Jesse (2023-06-29). "SHAPER: can you hear the shape of a jet?". Journal of High Energy Physics. 2023 (6): 195. arXiv:2302.12266. Bibcode:2023JHEP...06..195B. doi:10.1007/JHEP06(2023)195. ISSN 1029-8479. S2CID 257205971.
Villani, Cédric (2003). "Chapter 1: The Kantorovich Duality". Topics in optimal transportation. Providence, RI: American Mathematical Society. ISBN 0-8218-3312-X. OCLC 51477002.
Villani, Cédric (2003). "1.1.3. The shipper's problem.". Topics in optimal transportation. Providence, RI: American Mathematical Society. ISBN 0-8218-3312-X. OCLC 51477002.
Benamou, Jean-David; Brenier, Yann (2000-01-01). "A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem". Numerische Mathematik. 84 (3): 375–393. doi:10.1007/s002110050002. ISSN 0945-3245. S2CID 1100384.
Peyre R (October 2018). "Comparison between W₂ distance and Ḣ⁻¹ norm, and localization of Wasserstein distance". ESAIM: Control, Optimisation and Calculus of Variations. 24 (4): 1489–1501. doi:10.1051/cocv/2017050. ISSN 1292-8119. (See Theorem 2.1.)
Loeper G (July 2006). "Uniqueness of the solution to the Vlasov–Poisson system with bounded density". Journal de Mathématiques Pures et Appliquées. 86 (1): 68–79. arXiv:math/0504140. doi:10.1016/j.matpur.2006.01.005. ISSN 1292-8119. (See Theorem 2.9.)

worldcat.org

Villani, Cédric (2003). "Chapter 1: The Kantorovich Duality". Topics in optimal transportation. Providence, RI: American Mathematical Society. ISBN 0-8218-3312-X. OCLC 51477002.
Villani, Cédric (2003). "1.1.3. The shipper's problem.". Topics in optimal transportation. Providence, RI: American Mathematical Society. ISBN 0-8218-3312-X. OCLC 51477002.