{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T21:06:28Z","timestamp":1770325588018,"version":"3.49.0"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Appl. and Comput. Topology"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s41468-020-00061-z","type":"journal-article","created":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T14:02:44Z","timestamp":1603548164000},"page":"1-53","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport"],"prefix":"10.1007","volume":"5","author":[{"given":"Vincent","family":"Divol","sequence":"first","affiliation":[]},{"given":"Th\u00e9o","family":"Lacombe","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,24]]},"reference":[{"issue":"8","key":"61_CR1","first-page":"1","volume":"18","author":"H Adams","year":"2017","unstructured":"Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., Chepushtanova, S., Hanson, E., Motta, F., Ziegelmeier, L.: Persistence images: a stable vector representation of persistent homology. J. Mach. Learn. Res. 18(8), 1\u201335 (2017)","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"61_CR2","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1137\/100805741","volume":"43","author":"M Agueh","year":"2011","unstructured":"Agueh, M., Carlier, G.: Barycenters in the Wasserstein space. SIAM J. Math. Anal. 43(2), 904\u2013924 (2011)","journal-title":"SIAM J. Math. Anal."},{"key":"61_CR3","volume-title":"Gradient Flows: In Metric Spaces and in the Space of Probability measures","author":"L Ambrosio","year":"2008","unstructured":"Ambrosio, L., Gigli, N., Savar\u00e9, G.: Gradient Flows: In Metric Spaces and in the Space of Probability measures. Springer, Berlin (2008)"},{"key":"61_CR4","volume-title":"Convergence of Probability Measures. Wiley Series in Probability and Statistics","author":"P Billingsley","year":"2013","unstructured":"Billingsley, P.: Convergence of Probability Measures. Wiley Series in Probability and Statistics. Wiley, New York (2013)"},{"issue":"4","key":"61_CR5","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10208-014-9201-4","volume":"14","author":"AJ Blumberg","year":"2014","unstructured":"Blumberg, A.J., Gal, I., Mandell, M.A., Pancia, M.: Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces. Found. Comput. Math. 14(4), 745\u2013789 (2014)","journal-title":"Found. Comput. Math."},{"issue":"4","key":"61_CR6","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1214\/16-AAP1232","volume":"27","author":"O Bobrowski","year":"2017","unstructured":"Bobrowski, O., Kahle, M., Skraba, P., et al.: Maximally persistent cycles in random geometric complexes. Ann. Appl. Probab. 27(4), 2032\u20132060 (2017)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"61_CR7","doi-asserted-by":"crossref","first-page":"262","DOI":"10.4064\/fm-20-1-262-176","volume":"20","author":"S Bochner","year":"1933","unstructured":"Bochner, S.: Integration von funktionen, deren werte die elemente eines vektorraumes sind. Fundam. Math. 20(1), 262\u2013276 (1933)","journal-title":"Fundam. Math."},{"key":"61_CR8","volume-title":"Measure Theory. No. v. 1 in Measure Theory","author":"V Bogachev","year":"2007","unstructured":"Bogachev, V.: Measure Theory. No. v. 1 in Measure Theory. Springer Berlin Heidelberg, Berlin (2007)"},{"key":"61_CR9","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.jsc.2016.03.009","volume":"78","author":"P Bubenik","year":"2017","unstructured":"Bubenik, P., D\u0142otko, P.: A persistence landscapes toolbox for topological statistics. J. Symb. Comput. 78, 91\u2013114 (2017)","journal-title":"J. Symb. Comput."},{"issue":"2","key":"61_CR10","doi-asserted-by":"crossref","first-page":"337","DOI":"10.4310\/HHA.2007.v9.n2.a12","volume":"9","author":"P Bubenik","year":"2007","unstructured":"Bubenik, P., Kim, P.T., et al.: A statistical approach to persistent homology. Homol. Homotopy Appl. 9(2), 337\u2013362 (2007)","journal-title":"Homol. Homotopy Appl."},{"key":"61_CR11","first-page":"1","volume":"2018","author":"P Bubenik","year":"2018","unstructured":"Bubenik, P., Vergili, T.: Topological spaces of persistence modules and their properties. J. Appl. Comput. Topol. 2018, 1\u201337 (2018)","journal-title":"J. Appl. Comput. Topol."},{"issue":"2","key":"61_CR12","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s00199-008-0415-z","volume":"42","author":"G Carlier","year":"2010","unstructured":"Carlier, G., Ekeland, I.: Matching for teams. Econ. Theor. 42(2), 397\u2013418 (2010)","journal-title":"Econ. Theor."},{"issue":"6","key":"61_CR13","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1051\/m2an\/2015033","volume":"49","author":"G Carlier","year":"2015","unstructured":"Carlier, G., Oberman, A., Oudet, E.: Numerical methods for matching for teams and Wasserstein barycenters. ESAIM Math. Model. Numer. Anal. 49(6), 1621\u20131642 (2015)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"61_CR14","unstructured":"Carri\u00e8re, M., Cuturi, M., Oudot, S.: Sliced Wasserstein kernel for persistence diagrams. In: 34th International Conference on Machine Learning (2017)"},{"issue":"5","key":"61_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/cgf.12692","volume":"34","author":"M Carri\u00e8re","year":"2015","unstructured":"Carri\u00e8re, M., Oudot, S.Y., Ovsjanikov, M.: Stable topological signatures for points on 3d shapes. Comput. Graph. Forum 34(5), 1\u201312 (2015). https:\/\/doi.org\/10.1111\/cgf.12692","journal-title":"Comput. Graph. Forum"},{"issue":"1","key":"61_CR16","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1002\/mana.200310050","volume":"254","author":"B Cascales","year":"2003","unstructured":"Cascales, B., Raja, M.: Measurable selectors for the metric projection. Math. Nachr. 254(1), 27\u201334 (2003)","journal-title":"Math. Nachr."},{"issue":"1","key":"61_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/07069938X","volume":"40","author":"T Champion","year":"2008","unstructured":"Champion, T., De Pascale, L., Juutinen, P.: The $$\\infty $$-Wasserstein distance: local solutions and existence of optimal transport maps. SIAM J. Math. Anal. 40(1), 1\u201320 (2008)","journal-title":"SIAM J. Math. Anal."},{"key":"61_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-42545-0","volume-title":"The Structure and Stability of Persistence Modules","author":"F Chazal","year":"2016","unstructured":"Chazal, F., De Silva, V., Glisse, M., Oudot, S.: The Structure and Stability of Persistence Modules. Springer, Berlin (2016)"},{"key":"61_CR19","unstructured":"Chazal, F., Fasy, B., Lecci, F., Michel, B., Rinaldo, A., Wasserman, L.: Subsampling methods for persistent homology. In: International Conference on Machine Learning, pp. 2143\u20132151 (2015)"},{"issue":"2","key":"61_CR20","doi-asserted-by":"publisher","first-page":"140","DOI":"10.20382\/jocg.v6i2a8","volume":"6","author":"F Chazal","year":"2015","unstructured":"Chazal, F., Fasy, B.T., Lecci, F., Rinaldo, A., Wasserman, L.A.: Stochastic convergence of persistence landscapes and silhouettes. JoCG 6(2), 140\u2013161 (2015). https:\/\/doi.org\/10.20382\/jocg.v6i2a8","journal-title":"JoCG"},{"key":"61_CR21","unstructured":"Chen, Y.C., Wang, D., Rinaldo, A., Wasserman, L.: Statistical analysis of persistence intensity functions (2015). arXiv preprint arXiv:1510.02502"},{"key":"61_CR22","unstructured":"Chizat, L., Peyr\u00e9, G., Schmitzer, B., Vialard, F.X.: Unbalanced optimal transport: geometry and kantorovich formulation (2015). arXiv preprint arXiv:1508.05216"},{"issue":"1","key":"61_CR23","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s00454-006-1276-5","volume":"37","author":"D Cohen-Steiner","year":"2007","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discrete Comput. Geom. 37(1), 103\u2013120 (2007)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"61_CR24","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10208-010-9060-6","volume":"10","author":"D Cohen-Steiner","year":"2010","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J., Mileyko, Y.: Lipschitz functions have Lp-stable persistence. Found. Comput. Math. 10(2), 127\u2013139 (2010)","journal-title":"Found. Comput. Math."},{"key":"61_CR25","unstructured":"Cuturi, M.: Sinkhorn distances: Lightspeed computation of optimal transport. In: Advances in Neural Information Processing Systems, pp. 2292\u20132300 (2013)"},{"issue":"2","key":"61_CR26","doi-asserted-by":"publisher","first-page":"127","DOI":"10.20382\/jocg.v10i2a7","volume":"10","author":"V Divol","year":"2019","unstructured":"Divol, V., Chazal, F.: The density of expected persistence diagrams and its kernel based estimation. JoCG 10(2), 127\u2013153 (2019). https:\/\/doi.org\/10.20382\/jocg.v10i2a7","journal-title":"JoCG"},{"issue":"3","key":"61_CR27","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s41468-019-00032-z","volume":"3","author":"V Divol","year":"2019","unstructured":"Divol, V., Polonik, W.: On the choice of weight functions for linear representations of persistence diagrams. J. Appl. Comput. Topol. 3(3), 249\u2013283 (2019)","journal-title":"J. Appl. Comput. Topol."},{"key":"61_CR28","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., Harer, J.: Computational topology: an introduction. American Mathematical Soc, (2010)","DOI":"10.1090\/mbk\/069"},{"issue":"2","key":"61_CR29","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/s00205-008-0212-7","volume":"195","author":"A Figalli","year":"2010","unstructured":"Figalli, A.: The optimal partial transport problem. Arch. Ration. Mech. Anal. 195(2), 533\u2013560 (2010)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"2","key":"61_CR30","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.matpur.2009.11.005","volume":"94","author":"A Figalli","year":"2010","unstructured":"Figalli, A., Gigli, N.: A new transportation distance between non-negative measures, with applications to gradients flows with dirichlet boundary conditions. J. Math. Pures Appl. 94(2), 107\u2013130 (2010)","journal-title":"J. Math. Pures Appl."},{"key":"61_CR31","unstructured":"Flamary, R., Courty, N.: POT python optimal transport library (2017). https:\/\/github.com\/rflamary\/POT"},{"key":"61_CR32","volume-title":"Real Analysis: Modern Techniques and Their Applications. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts","author":"G Folland","year":"2013","unstructured":"Folland, G.: Real Analysis: Modern Techniques and Their Applications. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley, New York (2013)"},{"key":"61_CR33","unstructured":"Genevay, A., Peyre, G., Cuturi, M.: Learning generative models with sinkhorn divergences. In: International Conference on Artificial Intelligence and Statistics, pp. 1608\u20131617 (2018)"},{"key":"61_CR34","unstructured":"Goel, A., Trinh, K.D., Tsunoda, K.: Asymptotic behavior of Betti numbers of random geometric complexes (2018). arXiv preprint arXiv:1805.05032"},{"key":"61_CR35","volume-title":"Combinatorial Theory","author":"M Hall","year":"1986","unstructured":"Hall, M.: Combinatorial Theory, 2nd edn. Wiley, New York (1986)","edition":"2"},{"key":"61_CR36","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1520877113","author":"Y Hiraoka","year":"2016","unstructured":"Hiraoka, Y., Nakamura, T., Hirata, A., Escolar, E.G., Matsue, K., Nishiura, Y.: Hierarchical structures of amorphous solids characterized by persistent homology. Proc. Natl. Acad. Sci. (2016). https:\/\/doi.org\/10.1073\/pnas.1520877113","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"5","key":"61_CR37","doi-asserted-by":"crossref","first-page":"2740","DOI":"10.1214\/17-AAP1371","volume":"28","author":"Y Hiraoka","year":"2018","unstructured":"Hiraoka, Y., Shirai, T., Trinh, K.D., et al.: Limit theorems for persistence diagrams. Ann. Appl. Probab. 28(5), 2740\u20132780 (2018)","journal-title":"Ann. Appl. Probab."},{"issue":"126","key":"61_CR38","first-page":"1","volume":"20","author":"CD Hofer","year":"2019","unstructured":"Hofer, C.D., Kwitt, R., Niethammer, M.: Learning representations of persistence barcodes. J. Mach. Learn. Res. 20(126), 1\u201345 (2019)","journal-title":"J. Mach. Learn. Res."},{"key":"61_CR39","doi-asserted-by":"crossref","DOI":"10.1515\/9783112525609","volume-title":"Random Measures","author":"O Kallenberg","year":"1983","unstructured":"Kallenberg, O.: Random Measures. Elsevier, Amsterdam (1983)"},{"key":"61_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4190-4","volume-title":"Classical Descriptive Set Theory. Graduate Texts in Mathematics","author":"A Kechris","year":"1995","unstructured":"Kechris, A.: Classical Descriptive Set Theory. Graduate Texts in Mathematics. Springer, Berlin (1995)"},{"issue":"1","key":"61_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3064175","volume":"22","author":"M Kerber","year":"2017","unstructured":"Kerber, M., Morozov, D., Nigmetov, A.: Geometry helps to compare persistence diagrams. J. Exp. Algorithmics 22(1), 1\u20134 (2017)","journal-title":"J. Exp. Algorithmics"},{"issue":"11\/12","key":"61_CR42","first-page":"1117","volume":"21","author":"S Kondratyev","year":"2016","unstructured":"Kondratyev, S., Monsaingeon, L., Vorotnikov, D., et al.: A new optimal transport distance on the space of finite Radon measures. Adv. Differ. Equ. 21(11\/12), 1117\u20131164 (2016)","journal-title":"Adv. Differ. Equ."},{"key":"61_CR43","doi-asserted-by":"publisher","first-page":"042207","DOI":"10.1103\/PhysRevE.87.042207","volume":"87","author":"M Kramar","year":"2013","unstructured":"Kramar, M., Goullet, A., Kondic, L., Mischaikow, K.: Persistence of force networks in compressed granular media. Phys. Rev. E 87, 042207 (2013). https:\/\/doi.org\/10.1103\/PhysRevE.87.042207","journal-title":"Phys. Rev. E"},{"issue":"1","key":"61_CR44","first-page":"6947","volume":"18","author":"G Kusano","year":"2017","unstructured":"Kusano, G., Fukumizu, K., Hiraoka, Y.: Kernel method for persistence diagrams via kernel embedding and weight factor. J. Mach. Learn. Res. 18(1), 6947\u20136987 (2017)","journal-title":"J. Mach. Learn. Res."},{"key":"61_CR45","unstructured":"Kusano, G., Hiraoka, Y., Fukumizu, K.: Persistence weighted gaussian kernel for topological data analysis. In: International Conference on Machine Learning, pp. 2004\u20132013 (2016)"},{"key":"61_CR46","unstructured":"Kwitt, R., Huber, S., Niethammer, M., Lin, W., Bauer, U.: Statistical topological data analysis - a kernel perspective. In: Advances in neural information processing systems, pp. 3070\u20133078 (2015)"},{"key":"61_CR47","unstructured":"Lacombe, T., Cuturi, M., Oudot, S.: Large scale computation of means and clusters for persistence diagrams using optimal transport. In: Advances in Neural Information Processing Systems (2018)"},{"key":"61_CR48","doi-asserted-by":"crossref","unstructured":"Le\u00a0Gouic, T., Loubes, J.M.: Existence and consistency of Wasserstein barycenters. Probability Theory and Related Fields 1\u201317 (2016)","DOI":"10.1007\/s00440-016-0727-z"},{"key":"61_CR49","doi-asserted-by":"crossref","unstructured":"Li, C., Ovsjanikov, M., Chazal, F.: Persistence-based structural recognition. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2014)","DOI":"10.1109\/CVPR.2014.257"},{"issue":"12","key":"61_CR50","doi-asserted-by":"crossref","first-page":"124007","DOI":"10.1088\/0266-5611\/27\/12\/124007","volume":"27","author":"Y Mileyko","year":"2011","unstructured":"Mileyko, Y., Mukherjee, S., Harer, J.: Probability measures on the space of persistence diagrams. Inverse Prob. 27(12), 124007 (2011)","journal-title":"Inverse Prob."},{"issue":"4","key":"61_CR51","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s11040-011-9097-z","volume":"14","author":"L Nielsen","year":"2011","unstructured":"Nielsen, L.: Weak convergence and Banach space-valued functions: improving the stability theory of feynman\u2019s operational calculi. Math. Phys. Anal. Geom. 14(4), 279\u2013294 (2011)","journal-title":"Math. Phys. Anal. Geom."},{"key":"61_CR52","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/209","volume-title":"Persistence Theory: From Quiver Representations to Data Analysis","author":"SY Oudot","year":"2015","unstructured":"Oudot, S.Y.: Persistence Theory: From Quiver Representations to Data Analysis, vol. 209. American Mathematical Society, Providence (2015)"},{"issue":"1","key":"61_CR53","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/0047-259X(74)90005-0","volume":"4","author":"MD Perlman","year":"1974","unstructured":"Perlman, M.D.: Jensen\u2019s inequality for a convex vector-valued function on an infinite-dimensional space. J. Multivar. Anal. 4(1), 52\u201365 (1974)","journal-title":"J. Multivar. Anal."},{"key":"61_CR54","unstructured":"Peyr\u00e9, G., Cuturi, M.: Computational optimal transport. 2017\u201386 (2017)"},{"key":"61_CR55","doi-asserted-by":"crossref","unstructured":"Reininghaus, J., Huber, S., Bauer, U., Kwitt, R.: A stable multi-scale kernel for topological machine learning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4741\u20134748 (2015)","DOI":"10.1109\/CVPR.2015.7299106"},{"key":"61_CR56","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-20828-2","volume-title":"Optimal Transport for Applied Mathematicians","author":"F Santambrogio","year":"2015","unstructured":"Santambrogio, F.: Optimal Transport for Applied Mathematicians. Birk\u00e4user, New York (2015)"},{"issue":"1","key":"61_CR57","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s13373-017-0101-1","volume":"7","author":"F Santambrogio","year":"2017","unstructured":"Santambrogio, F.: Euclidean, metric, and Wasserstein gradient flows: an overview. Bull. Math. Sci. 7(1), 87\u2013154 (2017)","journal-title":"Bull. Math. Sci."},{"key":"61_CR58","volume-title":"Combinatorial Optimization: Polyhedra and Efficiency","author":"A Schrijver","year":"2003","unstructured":"Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency, vol. 24. Springer, Berlin (2003)"},{"key":"61_CR59","unstructured":"Schweinhart, B.: Weighted persistent homology sums of random \u010cech complexes (2018). arXiv preprint arXiv:1807.07054"},{"key":"61_CR60","doi-asserted-by":"crossref","unstructured":"Som, A., Thopalli, K., Natesan\u00a0Ramamurthy, K., Venkataraman, V., Shukla, A., Turaga, P.: Perturbation robust representations of topological persistence diagrams. In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 617\u2013635 (2018)","DOI":"10.1007\/978-3-030-01234-2_38"},{"issue":"6","key":"61_CR61","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.4153\/CJM-2014-044-6","volume":"67","author":"NG Trillos","year":"2015","unstructured":"Trillos, N.G., Slep\u010dev, D.: On the rate of convergence of empirical measures in $$\\infty $$-transportation distance. Can. J. Math. 67(6), 1358\u20131383 (2015)","journal-title":"Can. J. Math."},{"key":"61_CR62","unstructured":"Turner, K.: Means and medians of sets of persistence diagrams (2013). arXiv preprint arXiv:1307.8300"},{"issue":"1","key":"61_CR63","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s00454-014-9604-7","volume":"52","author":"K Turner","year":"2014","unstructured":"Turner, K., Mileyko, Y., Mukherjee, S., Harer, J.: Fr\u00e9chet means for distributions of persistence diagrams. Discrete Comput. Geom. 52(1), 44\u201370 (2014)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"61_CR64","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1093\/imaiai\/iau011","volume":"3","author":"K Turner","year":"2014","unstructured":"Turner, K., Mukherjee, S., Boyer, D.M.: Persistent homology transform for modeling shapes and surfaces. Inf. Inference J. IMA 3(4), 310\u2013344 (2014). https:\/\/doi.org\/10.1093\/imaiai\/iau011","journal-title":"Inf. Inference J. IMA"},{"key":"61_CR65","first-page":"228","volume":"12","author":"Y Umeda","year":"2017","unstructured":"Umeda, Y.: Time series classification via topological data analysis. Inf. Media Technol. 12, 228\u2013239 (2017)","journal-title":"Inf. Media Technol."},{"key":"61_CR66","volume-title":"Topics in Optimal Transportation","author":"C Villani","year":"2003","unstructured":"Villani, C.: Topics in Optimal Transportation, vol. 58. American Mathematical Society, Providence (2003)"},{"key":"61_CR67","volume-title":"Optimal Transport: Old and New","author":"C Villani","year":"2008","unstructured":"Villani, C.: Optimal Transport: Old and New, vol. 338. Springer, Berlin (2008)"}],"container-title":["Journal of Applied and Computational Topology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41468-020-00061-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41468-020-00061-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41468-020-00061-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T15:40:05Z","timestamp":1669304405000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41468-020-00061-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,24]]},"references-count":67,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["61"],"URL":"https:\/\/doi.org\/10.1007\/s41468-020-00061-z","relation":{},"ISSN":["2367-1726","2367-1734"],"issn-type":[{"value":"2367-1726","type":"print"},{"value":"2367-1734","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,24]]},"assertion":[{"value":"5 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 October 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"On behalf of all authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}