{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T03:24:14Z","timestamp":1779161054361,"version":"3.51.4"},"reference-count":160,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T00:00:00Z","timestamp":1559001600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T00:00:00Z","timestamp":1559001600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["400837"],"award-info":[{"award-number":["400837"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/I016945\/1"],"award-info":[{"award-number":["EP\/I016945\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N014189\/1"],"award-info":[{"award-number":["EP\/N014189\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["16-13261"],"award-info":[{"award-number":["16-13261"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1418261"],"award-info":[{"award-number":["1418261"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1045153"],"award-info":[{"award-number":["1045153"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000145","name":"Division of Information and Intelligent Systems","doi-asserted-by":"publisher","award":["1546331"],"award-info":[{"award-number":["1546331"]}],"id":[{"id":"10.13039\/100000145","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000145","name":"Division of Information and Intelligent Systems","doi-asserted-by":"publisher","award":["1320357"],"award-info":[{"award-number":["1320357"]}],"id":[{"id":"10.13039\/100000145","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s00454-019-00100-2","type":"journal-article","created":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T20:15:07Z","timestamp":1559074507000},"page":"150-211","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["The Geometry of Synchronization Problems and Learning Group Actions"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0436-689X","authenticated-orcid":false,"given":"Tingran","family":"Gao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacek","family":"Brodzki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sayan","family":"Mukherjee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,5,28]]},"reference":[{"issue":"4","key":"100_CR1","first-page":"72","volume":"34","author":"N Aigerman","year":"2015","unstructured":"Aigerman, N., Poranne, R., Lipman, Y.: Seamless surface mappings. ACM Trans. Graph. (TOG) 34(4), 72 (2015)","journal-title":"Seamless surface mappings. ACM Trans. Graph. (TOG)"},{"issue":"6","key":"100_CR2","doi-asserted-by":"publisher","first-page":"934","DOI":"10.1002\/cpa.21444","volume":"66","author":"R Al-Aifari","year":"2013","unstructured":"Al-Aifari, R., Daubechies, I., Lipman, Y.: Continuous procrustes distance between two surfaces. Commun. Pure Appl. Math. 66(6), 934\u2013964 (2013). https:\/\/doi.org\/10.1002\/cpa.21444","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"100_CR3","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1137\/S0097539792224474","volume":"24","author":"N Alon","year":"1995","unstructured":"Alon, N., Karp, R.M., Peleg, D., West, D.: A graph-theoretic game and its application to the k-server problem. SIAM J. Comput. 24(1), 78\u2013100 (1995)","journal-title":"SIAM J. Comput."},{"issue":"8","key":"100_CR4","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1109\/42.796283","volume":"18","author":"S Angenent","year":"1999","unstructured":"Angenent, S., Haker, S., Tannenbaum, A., Kikinis, R.: On the Laplace-Beltrami operator and brain surface flattening. IEEE Trans. Med. Imaging 18(8), 700\u2013711 (1999). https:\/\/doi.org\/10.1109\/42.796283","journal-title":"IEEE Trans. Med. Imaging"},{"key":"100_CR5","doi-asserted-by":"crossref","unstructured":"Anosov, D.V., Bolibruch, A.A.: The Riemann\u2013Hilbert problem. Aspects of Mathematics, vol. 22. Vieweg, Braunschweig (1994)","DOI":"10.1007\/978-3-322-92909-9"},{"key":"100_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492906210018","volume":"15","author":"DN Arnold","year":"2006","unstructured":"Arnold, D.N., Falk, R.S., Winther, R.: Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15, 1\u2013155 (2006)","journal-title":"Acta Numer."},{"key":"100_CR7","unstructured":"Atiyah, M.F., Bott, R.: The Yang\u2013Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 308(1505), 523\u2013615 (1983)"},{"key":"100_CR8","doi-asserted-by":"publisher","unstructured":"Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), pp. 1626\u20131633 (2011). https:\/\/doi.org\/10.1109\/ICCVW.2011.6130444","DOI":"10.1109\/ICCVW.2011.6130444"},{"key":"100_CR9","unstructured":"Bajaj, C., Gao, T., He, Z., Huang, Q., Liang, Z.: SMAC: simultaneous mapping and clustering using spectral decompositions. In: Proceedings of the 35th International Conference on Machine Learning, vol. 80, pp. 324\u2013333 (2018). http:\/\/proceedings.mlr.press\/v80\/bajaj18a.html"},{"key":"100_CR10","doi-asserted-by":"crossref","unstructured":"Bandeira, A.S., Charikar, M., Singer, A., Zhu, A.: Multireference alignment using semidefinite programming. In: Proceedings of the 5th Conference on Innovations in Theoretical Computer Science, pp. 459\u2013470. ACM, New York (2014)","DOI":"10.1145\/2554797.2554839"},{"key":"100_CR11","unstructured":"Bandeira, A.S., Chen, Y., Singer, A.: Non-unique Games over Compact Groups and Orientation Estimation in Cryo-EM (2015). arXiv:1505.03840"},{"key":"100_CR12","doi-asserted-by":"publisher","unstructured":"Bandeira, A.S., Kennedy, C., Singer, A.: Approximating the Little Grothendieck Problem over the Orthogonal and Unitary Groups. Mathematical Programming, pp. 1\u201343 (2016). https:\/\/doi.org\/10.1007\/s10107-016-0993-7","DOI":"10.1007\/s10107-016-0993-7"},{"issue":"4","key":"100_CR13","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1137\/120875338","volume":"34","author":"AS Bandeira","year":"2013","unstructured":"Bandeira, A.S., Singer, A., Spielman, D.A.: A cheeger inequality for the graph connection Laplacian. SIAM J. Matrix Anal. Appl. 34(4), 1611\u20131630 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"100_CR14","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1090\/conm\/453\/08795","volume":"453","author":"HJ Bandelt","year":"2008","unstructured":"Bandelt, H.J., Chepoi, V.: Metric graph theory and geometry: a survey. Contemp. Math. 453, 49\u201386 (2008)","journal-title":"Contemp. Math."},{"issue":"6","key":"100_CR15","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M Belkin","year":"2003","unstructured":"Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373\u20131396 (2003). https:\/\/doi.org\/10.1162\/089976603321780317","journal-title":"Neural Comput."},{"issue":"1\u20133","key":"100_CR16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1023\/B:MACH.0000033120.25363.1e","volume":"56","author":"M Belkin","year":"2004","unstructured":"Belkin, M., Niyogi, P.: Semi-supervised learning on Riemannian manifolds. Mach. Learn. 56(1\u20133), 209\u2013239 (2004)","journal-title":"Mach. Learn."},{"issue":"4","key":"100_CR17","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/15427951.2010.557277","volume":"6","author":"J Blitzstein","year":"2010","unstructured":"Blitzstein, J., Diaconis, P.: A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Internet Math. 6(4), 489\u2013522 (2010)","journal-title":"Internet Math."},{"key":"100_CR18","volume-title":"Discrete Differential Geometry","author":"AI Bobenko","year":"2008","unstructured":"Bobenko, A.I., Sullivan, J.M., Schr\u00f6der, P., Ziegler, G.: Discrete Differential Geometry. Springer, Heidelberg (2008)"},{"issue":"2","key":"100_CR19","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1070\/RM1990v045n02ABEH002350","volume":"45","author":"AA Bolibrukh","year":"1990","unstructured":"Bolibrukh, A.A.: The Riemann-Hilbert problem. Russ. Math. Surv. 45(2), 11\u201358 (1990)","journal-title":"Russ. Math. Surv."},{"key":"100_CR20","doi-asserted-by":"crossref","unstructured":"Bott, R., Tu, L.W.: Differential Forms in Algebraic Topology. Graduate Texts in Mathematics, vol. 82. Springer, New York (1982)","DOI":"10.1007\/978-1-4757-3951-0"},{"issue":"1","key":"100_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imaiai\/iat006","volume":"3","author":"N Boumal","year":"2014","unstructured":"Boumal, N., Singer, A., Absil, P.A., Blondel, V.D.: Cram\u00e9r-Rao bounds for synchronization of rotations. Inf. Inference 3(1), 1\u201339 (2014)","journal-title":"Inf. Inference"},{"issue":"6","key":"100_CR22","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.jhevol.2008.08.002","volume":"55","author":"DM Boyer","year":"2008","unstructured":"Boyer, D.M.: Relief index of second mandibular molars is a correlate of diet among prosimian primates and other euarchontan mammals. J. Hum. Evol. 55(6), 1118\u20131137 (2008)","journal-title":"J. Hum. Evol."},{"key":"100_CR23","doi-asserted-by":"publisher","unstructured":"Boyer, D.M., Lipman, Y., St. Clair, E., Puente, J., Patel, B.A., Funkhouser, T., Jernvall, J., Daubechies, I.: Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Proc. Natl. Acad. Sci. U.S.A. 108(45), 18,221\u201318,226 (2011). https:\/\/doi.org\/10.1073\/pnas.1112822108","DOI":"10.1073\/pnas.1112822108"},{"issue":"1","key":"100_CR24","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1002\/ar.23084","volume":"298","author":"DM Boyer","year":"2015","unstructured":"Boyer, D.M., Puente, J., Gladman, J.T., Glynn, C., Mukherjee, S., Yapuncich, G.S., Daubechies, I.: A new fully automated approach for aligning and comparing shapes. Anat. Rec. 298(1), 249\u2013276 (2015)","journal-title":"Anat. Rec."},{"key":"100_CR25","unstructured":"Br\u00f6cker, T., tom Dieck, T.: Representations of Compact Lie Groups. Graduate Texts in Mathematics. Springer, Heidelberg (2003)"},{"key":"100_CR26","volume-title":"Numerical Geometry of Non-Rigid Shapes","author":"AM Bronstein","year":"2008","unstructured":"Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes. Springer, New York (2008)"},{"key":"100_CR27","doi-asserted-by":"crossref","unstructured":"Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1704\u20131711. IEEE (2010)","DOI":"10.1109\/CVPR.2010.5539838"},{"key":"100_CR28","doi-asserted-by":"crossref","unstructured":"Brown, R.: Groupoids and van Kampen\u2019s Theorem. Proc. Lond. Math. Soc. (3) 17, pp. 385\u2013401. Citeseer (1967)","DOI":"10.1112\/plms\/s3-17.3.385"},{"key":"100_CR29","doi-asserted-by":"crossref","unstructured":"Brown, R., Higgins, P., Sivera, R.: Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids. EMS Series of Lectures in Mathematics. European Mathematical Society, Zurich (2011)","DOI":"10.4171\/083"},{"key":"100_CR30","volume-title":"Loop Spaces, Characteristic Classes and Geometric Quantization","author":"JL Brylinski","year":"2007","unstructured":"Brylinski, J.L.: Loop Spaces, Characteristic Classes and Geometric Quantization, vol. 107. Springer, New York (2007)"},{"issue":"2","key":"100_CR31","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1002\/ajpa.21489","volume":"145","author":"JM Bunn","year":"2011","unstructured":"Bunn, J.M., Boyer, D.M., Lipman, Y., St Clair, E.M., Jernvall, J., Daubechies, I.: Comparing Dirichlet normal surface energy of tooth crowns, a new technique of molar shape quantification for dietary inference, with previous methods in isolation and in combination. Am. J. Phys. Anthropol. 145(2), 247\u2013261 (2011)","journal-title":"Am. J. Phys. Anthropol."},{"issue":"3","key":"100_CR32","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1287\/moor.1110.0500","volume":"36","author":"O Candogan","year":"2011","unstructured":"Candogan, O., Menache, I., Ozdaglar, A., Parrilo, P.A.: Flows and decompositions of games: harmonic and potential games. Math. Oper. Res. 36(3), 474\u2013503 (2011). https:\/\/doi.org\/10.1287\/moor.1110.0500","journal-title":"Math. Oper. Res."},{"issue":"02","key":"100_CR33","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1142\/S0218654305000761","volume":"11","author":"G Carlsson","year":"2005","unstructured":"Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.J.: Persistence barcodes for shapes. Int. J. Shape Model. 11(02), 149\u2013187 (2005)","journal-title":"Int. J. Shape Model."},{"issue":"1","key":"100_CR34","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1137\/130935458","volume":"25","author":"KN Chaudhury","year":"2015","unstructured":"Chaudhury, K.N., Khoo, Y., Singer, A.: Global registration of multiple point clouds using semidefinite programming. SIAM J. Optim. 25(1), 468\u2013501 (2015)","journal-title":"SIAM J. Optim."},{"key":"100_CR35","doi-asserted-by":"crossref","unstructured":"Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. In: Problems in Analysis (Papers dedicated to Salomon Bochner, 1969), pp. 195\u2013199. Princeton University Press, Princeton (1970)","DOI":"10.1515\/9781400869312-013"},{"key":"100_CR36","unstructured":"Chen, Y., Guibas, L., Huang, Q.: Near-optimal joint object matching via convex relaxation. In: Jebara, T., Xing, E.P. (eds.) Proceedings of the 31st International Conference on Machine Learning (ICML-14) (JMLR Workshop and Conference Proceedings ), pp. 100\u2013108 (2014)"},{"key":"100_CR37","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1137\/1111041","volume":"11","author":"NN Chentsov","year":"1966","unstructured":"Chentsov, N.N.: A systematic theory of exponential families of probability distributions. Theor. Probab. Appl. 11, 425\u2013425 (1966)","journal-title":"Theor. Probab. Appl."},{"key":"100_CR38","doi-asserted-by":"crossref","unstructured":"Chung, F.R.: Spectral Graph Theory No. 92. CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence (1997)","DOI":"10.1090\/cbms\/092"},{"key":"100_CR39","first-page":"378","volume":"2","author":"FR Chung","year":"2007","unstructured":"Chung, F.R.: Four proofs for the Cheeger inequality and graph partition algorithms. Proc. ICCM 2, 378 (2007)","journal-title":"Proc. ICCM"},{"issue":"11","key":"100_CR40","doi-asserted-by":"publisher","first-page":"6313","DOI":"10.1073\/pnas.0937490100","volume":"100","author":"FR Chung","year":"2003","unstructured":"Chung, F.R., Lu, L., Vu, V.: Spectra of random graphs with given expected degrees. Proc. Natl. Acad. Sci. U.S.A. 100(11), 6313\u20136318 (2003). https:\/\/doi.org\/10.1073\/pnas.0937490100","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"100_CR41","doi-asserted-by":"publisher","unstructured":"Coifman, R.R., Lafon, S.: Diffusion maps. Appl. Comput. Harmon. Anal. 21(1), 5\u201330 (2006). https:\/\/doi.org\/10.1016\/j.acha.2006.04.006. Special Issue: Diffusion Maps and Wavelets","DOI":"10.1016\/j.acha.2006.04.006"},{"issue":"21","key":"100_CR42","doi-asserted-by":"publisher","first-page":"7426","DOI":"10.1073\/pnas.0500334102","volume":"102","author":"RR Coifman","year":"2005","unstructured":"Coifman, R.R., Lafon, S., Lee, A.B., Maggioni, M., Nadler, B., Warner, F., Zucker, S.W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc. Natl. Acad. Sci. U.S.A. 102(21), 7426\u20137431 (2005). https:\/\/doi.org\/10.1073\/pnas.0500334102","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"issue":"21","key":"100_CR43","doi-asserted-by":"publisher","first-page":"7432","DOI":"10.1073\/pnas.0500896102","volume":"102","author":"RR Coifman","year":"2005","unstructured":"Coifman, R.R., Lafon, S., Lee, A.B., Maggioni, M., Nadler, B., Warner, F., Zucker, S.W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods. Proc. Natl. Acad. Sci. U.S.A. 102(21), 7432\u20137437 (2005). https:\/\/doi.org\/10.1073\/pnas.0500896102","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"100_CR44","doi-asserted-by":"crossref","unstructured":"Coja-Oghlan, A., Lanka, A.: The spectral gap of random graphs with given expected degrees. International Colloquium on Automata. Languages, and Programming, pp. 15\u201326. Springer, Heidelberg (2006)","DOI":"10.1007\/11786986_3"},{"issue":"1","key":"100_CR45","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/BF02698807","volume":"62","author":"A Connes","year":"1985","unstructured":"Connes, A.: Noncommutative differential geometry. Inst. Hautes \u00c9tudes Sci. Publ. Math. 62(1), 41\u2013144 (1985). https:\/\/doi.org\/10.1007\/BF02698807","journal-title":"Inst. Hautes \u00c9tudes Sci. Publ. Math."},{"key":"100_CR46","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/978-3-0346-0425-3_3","volume-title":"Visions in Mathematics","author":"A Connes","year":"2000","unstructured":"Connes, A.: Noncommutative geometry. In: Alon, N., et al. (eds.) Visions in Mathematics, pp. 481\u2013559. Birkhauser, Basel (2000)"},{"key":"100_CR47","doi-asserted-by":"crossref","first-page":"361","DOI":"10.4310\/jdg\/1214442469","volume":"28","author":"K Corlette","year":"1988","unstructured":"Corlette, K.: Flat G-bundles with canonical metrics. J. Differ. Geom. 28, 361\u2013382 (1988)","journal-title":"J. Differ. Geom."},{"key":"100_CR48","volume-title":"Mathematical Methods of Statistics","author":"H Cram\u00e9r","year":"1946","unstructured":"Cram\u00e9r, H.: Mathematical Methods of Statistics. Princeton University Press, Princeton (1946)"},{"key":"100_CR49","doi-asserted-by":"publisher","unstructured":"Crane, K., de\u00a0Goes, F., Desbrun, M., Schr\u00f6der, P.: Digital geometry processing with discrete exterior calculus. In: ACM SIGGRAPH 2013 Courses, SIGGRAPH\u201913, pp. 7:1\u20137:126. ACM, New York (2013). https:\/\/doi.org\/10.1145\/2504435.2504442","DOI":"10.1145\/2504435.2504442"},{"issue":"1","key":"100_CR50","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/TNSE.2016.2523761","volume":"3","author":"M Cucuringu","year":"2016","unstructured":"Cucuringu, M.: Sync-Rank: robust ranking, constrained ranking and rank aggregation via eigenvector and SDP synchronization. IEEE Trans. Netw. Sci. Eng. 3(1), 58\u201379 (2016)","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"issue":"3","key":"100_CR51","first-page":"19","volume":"8","author":"M Cucuringu","year":"2012","unstructured":"Cucuringu, M., Lipman, Y., Singer, A.: Sensor network localization by eigenvector synchronization over the Euclidean group. ACM Trans. Sensor Netw. (TOSN) 8(3), 19 (2012)","journal-title":"ACM Trans. Sensor Netw. (TOSN)"},{"key":"100_CR52","doi-asserted-by":"crossref","unstructured":"Deligne, P.: \u00c9quations Diff\u00e9rentielles \u00e0 Points Singuliers R\u00e9guliers. Lecture Notes in Mathematics, vol. 163. Springer, Berlin (1970)","DOI":"10.1007\/BFb0061194"},{"key":"100_CR53","unstructured":"Desbrun, M., Hirani, A.N., Leok, M., Marsden, J.E.: Discrete Exterior Calculus (2005). arXiv:math\/0508341"},{"key":"100_CR54","doi-asserted-by":"crossref","first-page":"5591","DOI":"10.1073\/pnas.1031596100","volume":"100","author":"DL Donoho","year":"2003","unstructured":"Donoho, D.L., Grimes, C.: Hessian eigenmaps: new locally linear embedding techniques for high-dimensional data. Proc. Natl. Acad. Sci. U.S.A. 100, 5591\u20135596 (2003)","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"100_CR55","volume-title":"Statistical Shape Analysis","author":"IL Dryden","year":"1998","unstructured":"Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis, vol. 4. Wiley, New York (1998)"},{"issue":"3","key":"100_CR56","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0040-9383(76)90038-0","volume":"15","author":"JL Dupont","year":"1976","unstructured":"Dupont, J.L.: Simplicial de Rham cohomology and characteristic classes of flat bundles. Topology 15(3), 233\u2013245 (1976)","journal-title":"Topology"},{"key":"100_CR57","volume-title":"Computational Topology: An Introduction","author":"H Edelsbrunner","year":"2010","unstructured":"Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. American Mathematical Society, Providence (2010)"},{"issue":"1","key":"100_CR58","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1214\/14-AOS1275","volume":"44","author":"N El Karoui","year":"2016","unstructured":"El Karoui, N., Wu, H.-T.: Graph connection Laplacian methods can be made robust to noise. Ann. Stat. 44(1), 346\u2013372 (2016). https:\/\/doi.org\/10.1214\/14-AOS1275","journal-title":"Ann. Stat."},{"issue":"3","key":"100_CR59","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0040-9383(88)90014-6","volume":"27","author":"H Esnault","year":"1988","unstructured":"Esnault, H.: Characteristic classes of flat bundles. Topology 27(3), 323\u2013352 (1988)","journal-title":"Topology"},{"issue":"7123","key":"100_CR60","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1038\/nature05433","volume":"445","author":"AR Evans","year":"2007","unstructured":"Evans, A.R., Wilson, G.P., Fortelius, M., Jernvall, J.: High-level similarity of dentitions in carnivorans and rodents. Nature 445(7123), 78\u201381 (2007)","journal-title":"Nature"},{"key":"100_CR61","unstructured":"Fanuel, M., Ala\u00edz, C.M., Suykens, J.A.K.: Magnetic Eigenmaps for Community Detection in Directed Networks (2016). arXiv:1606.07359"},{"key":"100_CR62","unstructured":"Fanuel, M., Suykens, J.A.K.: Deformed Laplacians and spectral ranking in directed networks (2015). arXiv:1511.00492"},{"issue":"1","key":"100_CR63","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0022-4049(90)90075-S","volume":"69","author":"Y F\u00e9lix","year":"1990","unstructured":"F\u00e9lix, Y., Lavendhomme, R.: On de Rham\u2019s theorem in synthetic differential geometry. J. Pure and Appl. Algebra 69(1), 21\u201331 (1990)","journal-title":"J. Pure and Appl. Algebra"},{"key":"100_CR64","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1098\/rsta.1922.0009","volume":"222","author":"RA Fisher","year":"1922","unstructured":"Fisher, R.A.: On the mathematical foundations of theoretical statistics. Philos. Trans. R. Soc. Lond. A 222, 309\u2013368 (1922)","journal-title":"Philos. Trans. R. Soc. Lond. A"},{"key":"100_CR65","unstructured":"Gao, T.: Hypoelliptic Diffusion Maps and Their Applications in Automated Geometric Morphometrics. Ph.D. Thesis, Duke University (2015)"},{"key":"100_CR66","unstructured":"Gao, T.: The diffusion geometry of fibre bundles: horizontal diffusion maps. submitted (2016) arXiv:1602.02330"},{"issue":"1","key":"100_CR67","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1137\/18M1203481","volume":"1","author":"T Gao","year":"2019","unstructured":"Gao, T., Kovalsky, S.Z., Boyer, D.M., Daubechies, I.: Gaussian process landmarking for three-dimensional geometric morphometrics. SIAM J. Math. Data Sci. 1(1), 237\u2013267 (2019). https:\/\/doi.org\/10.1137\/18M1203481","journal-title":"SIAM J. Math. Data Sci."},{"issue":"1","key":"100_CR68","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1137\/18M1184035","volume":"1","author":"T Gao","year":"2019","unstructured":"Gao, T., Kovalsky, S.Z., Daubechies, I.: Gaussian process landmarking on manifolds. SIAM J. Math. Data Sci. 1(1), 208\u2013236 (2019). https:\/\/doi.org\/10.1137\/18M1184035","journal-title":"SIAM J. Math. Data Sci."},{"issue":"4","key":"100_CR69","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1002\/ar.23700","volume":"301","author":"T Gao","year":"2018","unstructured":"Gao, T., Yapuncich, G.S., Daubechies, I., Mukherjee, S., Boyer, D.M.: Development and assessment of fully automated and globally transitive geometric morphometric methods, with application to a biological comparative dataset with high interspecific variation. Anat. Rec. 301(4), 636\u2013658 (2018). https:\/\/doi.org\/10.1002\/ar.23700","journal-title":"Anat. Rec."},{"key":"100_CR70","doi-asserted-by":"crossref","unstructured":"Garc\u00eda-Raboso, A., Rayan, S.: Introduction to nonabelian hodge theory. Calabi-Yau Varieties: Arithmetic. Geometry and Physics, pp. 131\u2013171. Springer, Cham (2015)","DOI":"10.1007\/978-1-4939-2830-9_5"},{"issue":"1","key":"100_CR71","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1090\/S0273-0979-1982-14974-6","volume":"6","author":"WM Goldman","year":"1982","unstructured":"Goldman, W.M.: Characteristic classes and representations of discrete subgroups of lie groups. Bull. Am. Math. Soc. 6(1), 91\u201394 (1982)","journal-title":"Bull. Am. Math. Soc."},{"key":"100_CR72","doi-asserted-by":"crossref","unstructured":"Goldman, W.M.: Mapping class group dynamics on surface group representations. Problems on Mapping Class Groups and Related Topics. Proceedings of the Symposium on Pure Mathematics, vol. 74, pp. 189\u2013214. American Mathematical Society, Providence (2006)","DOI":"10.1090\/pspum\/074\/2264541"},{"issue":"1","key":"100_CR73","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/ajpa.22934","volume":"160","author":"PN Gonzalez","year":"2016","unstructured":"Gonzalez, P.N., Barbeito-Andr\u00e9s, J., D\u2019Addona, L.A., Bernal, V., Perez, S.I.: Technical Note: performance of semi- and fully automated approaches for registration of 3D surface coordinates in geometric morphometric studies. Am. J. Phys. Anthropol. 160(1), 169\u2013178 (2016)","journal-title":"Am. J. Phys. Anthropol."},{"issue":"1","key":"100_CR74","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF02291478","volume":"40","author":"JC Gower","year":"1975","unstructured":"Gower, J.C.: Generalized procrustes analysis. Psychometrika 40(1), 33\u201351 (1975). https:\/\/doi.org\/10.1007\/BF02291478","journal-title":"Psychometrika"},{"key":"100_CR75","doi-asserted-by":"crossref","unstructured":"Gower, J.C., Dijksterhuis, G.B.: Procrustes Problems. Oxford Statistical Science Series, vol. 3. Oxford University Press, Oxford (2004)","DOI":"10.1093\/acprof:oso\/9780198510581.001.0001"},{"key":"100_CR76","unstructured":"Haefliger, A.: Complexes of Groups and Orbihedra. Group Theory From a Geometrical Viewpoint. In: Proceedings of a Workshop, Held at the International Centre for Theoretical Physics in Trieste, Italy, 26 March-6 April 1990, pp. 504\u2013540. World Scientific, Singapore (1991)"},{"issue":"1\u20132","key":"100_CR77","doi-asserted-by":"crossref","first-page":"275","DOI":"10.5802\/aif.1292","volume":"42","author":"A Haefliger","year":"1992","unstructured":"Haefliger, A.: Extension of complexes of groups. Ann. Inst. Fourier Grenobl\u00e9 42(1\u20132), 275\u2013311 (1992)","journal-title":"Ann. Inst. Fourier Grenobl\u00e9"},{"issue":"3","key":"100_CR78","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s11263-012-0601-0","volume":"103","author":"R Hartley","year":"2013","unstructured":"Hartley, R., Trumpf, J., Dai, Y., Li, H.: Rotation averaging. Int. J. Comput. Vis. 103(3), 267\u2013305 (2013). https:\/\/doi.org\/10.1007\/s11263-012-0601-0","journal-title":"Int. J. Comput. Vis."},{"issue":"3","key":"100_CR79","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1112\/plms\/s3-55.1.59","volume":"55","author":"NJ Hitchin","year":"1987","unstructured":"Hitchin, N.J.: The self-duality equations on a Riemann surface. Proc. Lond. Math. Soc. 55(3), 59\u2013126 (1987)","journal-title":"Proc. Lond. Math. Soc."},{"issue":"2","key":"100_CR80","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF02161419","volume":"131","author":"NJ Hitchin","year":"1990","unstructured":"Hitchin, N.J.: Flat connections and geometric quantization. Commun. Math. Phys. 131(2), 347\u2013380 (1990)","journal-title":"Commun. Math. Phys."},{"key":"100_CR81","unstructured":"Hoffman, C., Kahle, M., Paquette, E.: Spectral Gaps of Random Graphs and Applications to Random Topology. arXiv preprint arXiv:1201.0425 (2012)"},{"key":"100_CR82","unstructured":"Huang, Q., Guibas, L.: Consistent shape maps via semidefinite programming. computer graphics Forum. In: Proceedings of Eurographics Symposium on Geometry Processing (SGP) 32(5), 177\u2013186 (2013)"},{"issue":"4","key":"100_CR83","first-page":"36","volume":"33","author":"Q Huang","year":"2014","unstructured":"Huang, Q., Wang, F., Guibas, L.: Functional map networks for analyzing and exploring large shape collections. ACM Trans. Graph. (TOG) 33(4), 36 (2014)","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"100_CR84","doi-asserted-by":"crossref","unstructured":"Huang, Q., Zhang, G., Gao, L., Hu, S., Bustcher, A., Guibas, L.: An optimization approach for extracting and encoding consistent maps in a shape collection. ACM Trans. Graph. 31, 125:1\u2013125:11 (2012)","DOI":"10.1145\/2366145.2366186"},{"issue":"1","key":"100_CR85","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s10107-010-0419-x","volume":"127","author":"X Jiang","year":"2011","unstructured":"Jiang, X., Lim, L.H., Yao, Y., Ye, Y.: Statistical ranking and combinatorial Hodge theory. Math. Progr. 127(1), 203\u2013244 (2011)","journal-title":"Math. Progr."},{"issue":"5","key":"100_CR86","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/MCSE.2012.91","volume":"15","author":"JL Johnson","year":"2013","unstructured":"Johnson, J.L., Goldring, T.: Discrete Hodge theory on graphs: a tutorial. Comput. Sci. Eng. 15(5), 42\u201355 (2013)","journal-title":"Comput. Sci. Eng."},{"issue":"4","key":"100_CR87","doi-asserted-by":"crossref","first-page":"857","DOI":"10.2307\/2373408","volume":"89","author":"FW Kamber","year":"1967","unstructured":"Kamber, F.W., Tondeur, P.: Flat bundles and characteristic classes of group-representations. Am. J. Math. 89(4), 857\u2013886 (1967)","journal-title":"Am. J. Math."},{"key":"100_CR88","doi-asserted-by":"crossref","unstructured":"Kashiwara, M.: Faisceaux Constructibles et Syst\u00e8mes Holonomes d\u2019\u00e9quations aux D\u00e9riv\u00e9es Partielles Lin\u00e9aires \u00e0 Points Singuliers R\u00e9guliers. S\u00e9minaire \u00c9quations aux d\u00e9riv\u00e9es partielles (Polytechnique) pp. 1\u20136 (1979)","DOI":"10.5802\/jedp.214"},{"issue":"2","key":"100_CR89","doi-asserted-by":"crossref","first-page":"319","DOI":"10.2977\/prims\/1195181610","volume":"20","author":"M Kashiwara","year":"1984","unstructured":"Kashiwara, M.: The Riemann-Hilbert problem for holonomic systems. Publ. Res. Inst. Math. Sci. 20(2), 319\u2013365 (1984)","journal-title":"Publ. Res. Inst. Math. Sci."},{"issue":"5","key":"100_CR90","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1214\/10-AOP596","volume":"39","author":"R Kenyon","year":"2011","unstructured":"Kenyon, R.: Spanning forests and the vector bundle Laplacian. Ann. Probab. 39(5), 1983\u20132017 (2011)","journal-title":"Ann. Probab."},{"issue":"5","key":"100_CR91","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1111\/cgf.12701","volume":"34","author":"I Kezurer","year":"2015","unstructured":"Kezurer, I., Kovalsky, S.Z., Basri, R., Lipman, Y.: Tight relaxation of quadratic matching. Comput. Graph. Forum 34(5), 115\u2013128 (2015). https:\/\/doi.org\/10.1111\/cgf.12701","journal-title":"Comput. Graph. Forum"},{"issue":"03","key":"100_CR92","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1017\/S0004972700005426","volume":"25","author":"A Kock","year":"1982","unstructured":"Kock, A.: Differential forms with values in groups. Bull. Aust. Math. Soc. 25(03), 357\u2013386 (1982)","journal-title":"Bull. Aust. Math. Soc."},{"key":"100_CR93","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511550812","volume-title":"Synthetic Differential Geometry","author":"A Kock","year":"2006","unstructured":"Kock, A.: Synthetic Differential Geometry, vol. 333. Cambridge University Press, Cambridge (2006)"},{"key":"100_CR94","doi-asserted-by":"crossref","unstructured":"Koehl, P., Hass, J.: Landmark-free geometric methods in biological shape analysis. J. R. Soc. Interface 12(113), 20150,795 (2015)","DOI":"10.1098\/rsif.2015.0795"},{"key":"100_CR95","doi-asserted-by":"crossref","unstructured":"Kokkinos, I., Bronstein, M.M., Litman, R., Bronstein, A.M.: Intrinsic shape context descriptors for deformable shapes. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 159\u2013166. IEEE (2012)","DOI":"10.1109\/CVPR.2012.6247671"},{"issue":"4","key":"100_CR96","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1145\/2601097.2601142","volume":"33","author":"SZ Kovalsky","year":"2014","unstructured":"Kovalsky, S.Z., Aigerman, N., Basri, R., Lipman, Y.: Controlling singular values with semidefinite programming. ACM Trans. Graph. 33(4), 69\u201371 (2014)","journal-title":"ACM Trans. Graph."},{"key":"100_CR97","doi-asserted-by":"publisher","unstructured":"Kyng, R., Lee, Y.T., Peng, R., Sachdeva, S., Spielman, D.A.: Sparsified Cholesky and multigrid solvers for connection Laplacians. In: Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, pp. 842\u2013850. ACM, New York (2016). https:\/\/doi.org\/10.1145\/2897518.2897640","DOI":"10.1145\/2897518.2897640"},{"key":"100_CR98","doi-asserted-by":"crossref","unstructured":"Labourie, F.: Lectures on Representations of Surface Groups. Zurich Lectures in Advanced Mathematics. European Mathematical Society (2013)","DOI":"10.4171\/127"},{"key":"100_CR99","unstructured":"Lai, R., Zhao, H.: Multi-Scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace\u2013Beltrami Eigenmap. arXiv preprint arXiv:1406.3758 (2014)"},{"key":"100_CR100","doi-asserted-by":"crossref","unstructured":"Lee, J.M.: Introduction to Smooth Manifolds. Graduate Texts in Mathematics, vol. 218. Springer, New York (2003)","DOI":"10.1007\/978-0-387-21752-9"},{"key":"100_CR101","unstructured":"Lim, L.H.: Hodge Laplacians on Graphs. arXiv preprint arXiv:1507.05379 (2015)"},{"issue":"3","key":"100_CR102","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1016\/j.aim.2011.01.020","volume":"227","author":"Y Lipman","year":"2011","unstructured":"Lipman, Y., Daubechies, I.: Conformal Wasserstein distances: comparing surfaces in polynomial time. Adv. Math. 227(3), 1047\u20131077 (2011). https:\/\/doi.org\/10.1016\/j.aim.2011.01.020","journal-title":"Adv. Math."},{"issue":"281","key":"100_CR103","first-page":"331","volume":"82","author":"Y Lipman","year":"2013","unstructured":"Lipman, Y., Puente, J., Daubechies, I.: Conformal Wasserstein distance: II. Computational aspects and extensions. Math. Comput. 82(281), 331\u2013381 (2013)","journal-title":"Computational aspects and extensions. Math. Comput."},{"key":"100_CR104","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1090\/S0002-9947-1976-0402774-3","volume":"217","author":"HS Lue","year":"1976","unstructured":"Lue, H.S.: Characteristic classes for the deformation of flat connections. Trans. Am. Math. Soc. 217, 379\u2013393 (1976)","journal-title":"Trans. Am. Math. Soc."},{"key":"100_CR105","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511569357","volume-title":"An Introduction to Noncommutative Differential Geometry and Its Physical Applications","author":"J Madore","year":"1999","unstructured":"Madore, J.: An Introduction to Noncommutative Differential Geometry and Its Physical Applications, vol. 257. Cambridge University Press, Cambridge (1999)"},{"key":"100_CR106","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.geomphys.2013.02.004","volume":"69","author":"S Majid","year":"2013","unstructured":"Majid, S.: Noncommutative Riemannian geometry on graphs. J. Geom. Phys. 69, 74\u201393 (2013)","journal-title":"J. Geom. Phys."},{"key":"100_CR107","first-page":"49","volume":"2","author":"PC Malhanobis","year":"1936","unstructured":"Malhanobis, P.C.: On the generalized distance in statistics. Proc. Natl. Inst. Sci. India 2, 49\u201355 (1936)","journal-title":"Proc. Natl. Inst. Sci. India"},{"issue":"4","key":"100_CR108","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1145\/2897824.2925913","volume":"35","author":"H Maron","year":"2016","unstructured":"Maron, H., Dym, N., Kezurer, I., Kovalsky, S., Lipman, Y.: Point registration via efficient convex relaxation. ACM Trans. Graph. (TOG) 35(4), 73 (2016)","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"100_CR109","doi-asserted-by":"crossref","unstructured":"Martinec, D., Pajdla, T.: Robust rotation and translation estimation in multiview reconstruction. In: 2007 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1\u20138. IEEE (2007)","DOI":"10.1109\/CVPR.2007.383115"},{"key":"100_CR110","doi-asserted-by":"crossref","unstructured":"Mebkhout, Z.: Sur le Probleme de Hilbert-Riemann. Complex Analysis. Microlocal Calculus and Relativistic Quantum Theory, pp. 90\u2013110. Springer, Berlin (1980)","DOI":"10.1007\/3-540-09996-4_31"},{"issue":"1","key":"100_CR111","first-page":"63","volume":"51","author":"Z Mebkhout","year":"1984","unstructured":"Mebkhout, Z.: Une Autre \u00c9quivalence de cat\u00e9gories. Compos. Math. 51(1), 63\u201388 (1984)","journal-title":"Compos. Math."},{"key":"100_CR112","volume-title":"Topics in Differential Geometry","author":"PW Michor","year":"2008","unstructured":"Michor, P.W.: Topics in Differential Geometry, vol. 93. American Mathematical Society, Providence (2008)"},{"issue":"1","key":"100_CR113","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF02564579","volume":"32","author":"J Milnor","year":"1958","unstructured":"Milnor, J.: On the existence of a connection with curvature zero. Comment. Math. Helv. 32(1), 215\u2013223 (1958)","journal-title":"Comment. Math. Helv."},{"key":"100_CR114","doi-asserted-by":"crossref","unstructured":"Milnor, J., Stasheff, J.D.: Characteristic classes. In: Annals of Mathematics Studies, vol. 76. Princeton University Press, Princeton (1974)","DOI":"10.1515\/9781400881826"},{"key":"100_CR115","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/199","volume-title":"Geometry of Characteristic Classes","author":"S Morita","year":"2001","unstructured":"Morita, S.: Geometry of Characteristic Classes, vol. 199. American Mathematical Society, Providence (2001)"},{"issue":"2","key":"100_CR116","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/rsa.20645","volume":"49","author":"S Mukherjee","year":"2016","unstructured":"Mukherjee, S., Steenbergen, J.: Random walks on simplicial complexes and harmonics. Random Struct. Algorithms 49(2), 379\u2013405 (2016)","journal-title":"Random Struct. Algorithms"},{"key":"100_CR117","doi-asserted-by":"crossref","unstructured":"Naor, A., Regev, O., Vidick, T.: Efficient rounding for the noncommutative Grothendieck inequality. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of computing, pp. 71\u201380. ACM, New York (2013)","DOI":"10.1145\/2488608.2488618"},{"issue":"5","key":"100_CR118","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1111\/j.1467-8659.2011.02022.x","volume":"30","author":"A Nguyen","year":"2011","unstructured":"Nguyen, A., Ben-Chen, M., Welnicka, K., Ye, Y., Guibas, L.: An optimization approach to improving collections of shape maps. Comput. Graph. Forum 30(5), 1481\u20131491 (2011)","journal-title":"Comput. Graph. Forum"},{"key":"100_CR119","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s10914-016-9326-0","volume":"23","author":"JD Pampush","year":"2016","unstructured":"Pampush, J.D., Winchester, J.M., Morse, P.E., Vining, A.Q., Boyer, D.M., Kay, R.F.: Introducing molaR: a new R package for quantitative topographic analysis of teeth (and other topographic surfaces). J. Mamm. Evol. 23, 397\u2013412 (2016)","journal-title":"J. Mamm. Evol."},{"issue":"2","key":"100_CR120","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1002\/rsa.20657","volume":"50","author":"O Parzanchevski","year":"2016","unstructured":"Parzanchevski, O., Rosenthal, R.: Simplicial complexes: spectrum, homology and random walks. Random Struct. Algorithms 50(2), 225\u2013261 (2016)","journal-title":"Random Struct. Algorithms"},{"issue":"2","key":"100_CR121","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s00493-014-3002-x","volume":"36","author":"O Parzanchevski","year":"2015","unstructured":"Parzanchevski, O., Rosenthal, R., Tessler, R.J.: Isoperimetric inequalities in simplicial complexes. Combinatorica 36(2), 195\u2013227 (2015)","journal-title":"Combinatorica"},{"issue":"1","key":"100_CR122","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/10586458.1993.10504266","volume":"2","author":"U Pinkall","year":"1993","unstructured":"Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2(1), 15\u201336 (1993)","journal-title":"Exp. Math."},{"key":"100_CR123","unstructured":"Puente, J.: Distances and Algorithms to Compare Sets of Shapes for Automated Biological Morphometrics. Ph.D. thesis, Princeton University Press, Princeton (2013)"},{"key":"100_CR124","doi-asserted-by":"crossref","unstructured":"Rangarajan, A., Chui, H., Bookstein, F.L.: The softassign procrustes matching algorithm. In: Information Processing in Medical Imaging, pp. 29\u201342. Springer, New York (1997)","DOI":"10.1007\/3-540-63046-5_3"},{"key":"100_CR125","first-page":"81","volume":"37","author":"CR Rao","year":"1945","unstructured":"Rao, C.R.: Information and accuracy obtainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81\u201391 (1945)","journal-title":"Bull. Calcutta Math. Soc."},{"key":"100_CR126","doi-asserted-by":"crossref","unstructured":"Raviv, D., Bronstein, M.M., Bronstein, A.M., Kimmel, R.: Volumetric heat kernel signatures. In: Proceedings of the ACM Workshop on 3D Object Retrieval, pp. 39\u201344. ACM, New York (2010)","DOI":"10.1145\/1877808.1877817"},{"key":"100_CR127","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"ST Roweis","year":"2000","unstructured":"Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323\u20132326 (2000)","journal-title":"Science"},{"issue":"8","key":"100_CR128","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1109\/34.868688","volume":"22","author":"J Shi","year":"2000","unstructured":"Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888\u2013905 (2000)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"3","key":"100_CR129","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1137\/120863642","volume":"5","author":"Y Shkolnisky","year":"2012","unstructured":"Shkolnisky, Y., Singer, A.: Viewing direction estimation in Cryo-EM using synchronization. SIAM J. Imaging Sci. 5(3), 1088\u20131110 (2012)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"100_CR130","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02699491","volume":"75","author":"CT Simpson","year":"1992","unstructured":"Simpson, C.T.: Higgs bundles and local systems. Publ. Math. l\u2019IH\u00c9S 75(1), 5\u201395 (1992)","journal-title":"Publ. Math. l\u2019IH\u00c9S"},{"issue":"1","key":"100_CR131","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/BF02698887","volume":"79","author":"CT Simpson","year":"1994","unstructured":"Simpson, C.T.: Moduli of representations of the fundamental group of a smooth projective variety I. Publ. Math. l\u2019IH\u00c9S 79(1), 47\u2013129 (1994)","journal-title":"Publ. Math. l\u2019IH\u00c9S"},{"issue":"1","key":"100_CR132","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/BF02698895","volume":"80","author":"CT Simpson","year":"1994","unstructured":"Simpson, C.T.: Moduli of representations of the fundamental group of a smooth projective variety. II. Publ. Math. Inst. Hautes Sci. 80(1), 5\u201379 (1994). https:\/\/doi.org\/10.1007\/BF02698895","journal-title":"II. Publ. Math. Inst. Hautes Sci."},{"issue":"1","key":"100_CR133","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.acha.2010.02.001","volume":"30","author":"A Singer","year":"2011","unstructured":"Singer, A.: Angular synchronization by eigenvectors and semidefinite programming. Appl. Comput. Harm. Anal. 30(1), 20\u201336 (2011). https:\/\/doi.org\/10.1016\/j.acha.2010.02.001","journal-title":"Appl. Comput. Harm. Anal."},{"issue":"1","key":"100_CR134","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.acha.2010.10.001","volume":"31","author":"A Singer","year":"2011","unstructured":"Singer, A.: Ht, Wu: Orientability and diffusion maps. Appl. Computat. Harmon. Anal. 31(1), 44\u201358 (2011). https:\/\/doi.org\/10.1016\/j.acha.2010.10.001","journal-title":"Appl. Computat. Harmon. Anal."},{"issue":"8","key":"100_CR135","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1002\/cpa.21395","volume":"65","author":"A Singer","year":"2012","unstructured":"Singer, A.: Ht, Wu: Vector diffusion maps and the connection Laplacian. Commun. Pure Appl. Math. 65(8), 1067\u20131144 (2012). https:\/\/doi.org\/10.1002\/cpa.21395","journal-title":"Commun. Pure Appl. Math."},{"key":"100_CR136","unstructured":"Singer, A., Wu, H.-T.: Spectral Convergence of the Connection Laplacian from Random Samples. arXiv preprint arXiv:1306.1587 (2013)"},{"issue":"2","key":"100_CR137","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1137\/090778390","volume":"4","author":"A Singer","year":"2011","unstructured":"Singer, A., Zhao, Z., Shkolnisky, Y., Hadani, R.: Viewing angle classification of cryo-electron microscopy images using eigenvectors. SIAM J. Imaging Sci. 4(2), 723\u2013759 (2011)","journal-title":"SIAM J. Imaging Sci."},{"issue":"5","key":"100_CR138","doi-asserted-by":"publisher","first-page":"1617","DOI":"10.1111\/j.1467-8659.2012.03167.x","volume":"31","author":"J Solomon","year":"2012","unstructured":"Solomon, J., Nguyen, A., Butscher, A., Ben-Chen, M., Guibas, L.: Soft maps between surfaces. Comput. Graph. Forum 31(5), 1617\u20131626 (2012). https:\/\/doi.org\/10.1111\/j.1467-8659.2012.03167.x","journal-title":"Comput. Graph. Forum"},{"key":"100_CR139","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.aam.2014.01.002","volume":"56","author":"J Steenbergen","year":"2014","unstructured":"Steenbergen, J., Klivans, C., Mukherjee, S.: A Cheeger-type inequality on simplicial complexes. Adv. Appl. Math. 56, 56\u201377 (2014)","journal-title":"Adv. Appl. Math."},{"key":"100_CR140","doi-asserted-by":"crossref","unstructured":"Steenrod, N.E.: The Topology of Fibre Bundles. Princeton Mathematical Series, vol. 14. Princeton University Press, Princeton (1951)","DOI":"10.1515\/9781400883875"},{"key":"100_CR141","doi-asserted-by":"crossref","unstructured":"Su, Z., Zeng, W., Shi, R., Wang, Y., Sun, J., Gu, X.: Area preserving brain mapping. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2235\u20132242 (2013)","DOI":"10.1109\/CVPR.2013.290"},{"issue":"5","key":"100_CR142","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1111\/j.1467-8659.2009.01515.x","volume":"28","author":"J Sun","year":"2009","unstructured":"Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28(5), 1383\u20131392 (2009)","journal-title":"Comput. Graph. Forum"},{"key":"100_CR143","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780199605880.001.0001","volume-title":"Differential Geometry: Bundles, Connections, Metrics and Curvature","author":"C Taubes","year":"2011","unstructured":"Taubes, C.: Differential Geometry: Bundles, Connections, Metrics and Curvature, vol. 23. Oxford University Press, Oxford (2011)"},{"key":"100_CR144","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum, J.B., de Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319\u20132323 (2000)","journal-title":"Science"},{"key":"100_CR145","doi-asserted-by":"crossref","unstructured":"Tu, L.W.: Hodge Theory and the Local Torelli Problem. Memoirs of the American Mathematical Society, vol. 43(279). American Mathematical Society, Providence (1983)","DOI":"10.1090\/memo\/0279"},{"key":"100_CR146","volume-title":"Global Alignment of Multiple 3-D Scans using Eigenvector Synchronization (bachelor thesis)","author":"T Tzveneva","year":"2011","unstructured":"Tzveneva, T., Singer, A., Rusinkiewicz, S.: Global Alignment of Multiple 3-D Scans using Eigenvector Synchronization (bachelor thesis). Technical Report, Princeton University Press, Princeton, Tech. Rep. (2011)"},{"key":"100_CR147","unstructured":"van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. J. Mach. Learn. Res. 9(Nov), 2579\u20132605 (2008)"},{"issue":"2\u20133","key":"100_CR148","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01169581","volume":"42","author":"E Vassiliou","year":"1983","unstructured":"Vassiliou, E.: Flat bundles and holonomy homomorphisms. Manuscr. Math. 42(2\u20133), 161\u2013170 (1983)","journal-title":"Manuscr. Math."},{"key":"100_CR149","volume-title":"Topics in Optimal Transportation","author":"C Villani","year":"2003","unstructured":"Villani, C.: Topics in Optimal Transportation. Graduate Studies in Mathematics. American Mathematical Society, Providence (2003)"},{"key":"100_CR150","volume-title":"Optimal Transport: Old and New","author":"C Villani","year":"2008","unstructured":"Villani, C.: Optimal Transport: Old and New, 2009th edn. Grundlehren der Mathematischen Wissenschaften. Springer, Berlin (2008)","edition":"2009"},{"issue":"14","key":"100_CR151","doi-asserted-by":"crossref","first-page":"5041","DOI":"10.1002\/ece3.3058","volume":"7","author":"NS Vitek","year":"2017","unstructured":"Vitek, N.S., Manz, C.L., Gao, T., Bloch, J.I., Strait, S.G., Boyer, D.M.: Semi-supervised determination of pseudocryptic morphotypes using observer-free characterizations of anatomical alignment and shape. Ecol. Evol. 7(14), 5041\u20135055 (2017)","journal-title":"Ecol. Evol."},{"issue":"4","key":"100_CR152","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","volume":"17","author":"U Von Luxburg","year":"2007","unstructured":"Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395\u2013416 (2007)","journal-title":"Stat. Comput."},{"key":"100_CR153","doi-asserted-by":"crossref","unstructured":"Wang, F., Huang, Q., Guibas, L.: Image co-segmentation via consistent functional maps. In: 2013 IEEE International Conference on Computer Vision (ICCV), pp. 849\u2013856. IEEE (2013)","DOI":"10.1109\/ICCV.2013.110"},{"issue":"2","key":"100_CR154","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1093\/imaiai\/iat005","volume":"2","author":"L Wang","year":"2013","unstructured":"Wang, L., Singer, A.: Exact and stable recovery of rotations for robust synchronization. Inf. Inference 2(2), 145\u2013193 (2013). https:\/\/doi.org\/10.1093\/imaiai\/iat005","journal-title":"Inf. Inference"},{"key":"100_CR155","doi-asserted-by":"crossref","unstructured":"Weinstein, A.: The symplectic structure on moduli space. In: The Floer Memorial Volume, pp. 627\u2013635. Birkh\u00e4user, Basel (1995)","DOI":"10.1007\/978-3-0348-9217-9_27"},{"key":"100_CR156","doi-asserted-by":"crossref","unstructured":"Wells, R.O.: Differential Analysis on Complex Manifolds. Graduate Texts in Mathematics, vol. 65. Springer, Berlin (2007)","DOI":"10.1007\/978-0-387-73892-5_3"},{"key":"100_CR157","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1142\/9789814401364_0010","volume":"23","author":"EZ Xia","year":"2012","unstructured":"Xia, E.Z.: Abelian and non-abelian cohomology. Geometry, Topology and Dynamics of Character Varieties 23, 309\u2013349 (2012)","journal-title":"Geometry, Topology and Dynamics of Character Varieties"},{"issue":"1","key":"100_CR158","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1137\/16M1070220","volume":"1","author":"K Ye","year":"2017","unstructured":"Ye, K., Lim, L.H.: Cohomology of cryo-electron microscopy. SIAM J. Appl. Algebra Geom. 1(1), 507\u2013535 (2017). https:\/\/doi.org\/10.1137\/16M1070220","journal-title":"SIAM J. Appl. Algebra Geom."},{"issue":"12","key":"100_CR159","doi-asserted-by":"publisher","first-page":"2838","DOI":"10.1109\/TVCG.2013.135","volume":"19","author":"X Zhao","year":"2013","unstructured":"Zhao, X., Su, Z., Gu, X., Kaufman, A., Sun, J., Gao, J., Luo, F.: Area-preservation mapping using optimal mass transport. IEEE Trans. Vis. Comput. Graph. 19(12), 2838\u20132847 (2013). https:\/\/doi.org\/10.1109\/TVCG.2013.135","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"100_CR160","doi-asserted-by":"publisher","unstructured":"Zhu, L., Haker, S., Tannenbaum, A.: Area-preserving mappings for the visualization of medical structures. In: Ellis, R., Peters, T. (eds.) Medical Image Computing and Computer-Assisted Intervention (MICCAI 2003). Lecture Notes in Computer Science, vol. 2879, pp. 277\u2013284. Springer, Berlin (2003). https:\/\/doi.org\/10.1007\/978-3-540-39903-2_35","DOI":"10.1007\/978-3-540-39903-2_35"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00100-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-019-00100-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00100-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,18]],"date-time":"2022-09-18T19:39:11Z","timestamp":1663529951000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-019-00100-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,28]]},"references-count":160,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["100"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00100-2","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,28]]},"assertion":[{"value":"16 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 April 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 May 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}