{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T18:15:39Z","timestamp":1693419339552},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik, Leibniz-Institut im Forschungsverbund Berlin e.V."}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Geometric, robust-to-noise features of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply Fels\u2013Olver\u2019s moving-frame method (for geometric features) paired with the log-signature transform (for robust features) to construct a set of integral invariants under rigid motions for curves in <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^d$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> from the iterated-integrals signature. In particular, we show that one can algorithmically construct a set of invariants that characterize the equivalence class of the truncated iterated-integrals signature under orthogonal transformations, which yields a characterization of a curve in <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^d$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> under rigid motions (and tree-like extensions) and an explicit method to compare curves up to these transformations.\n<\/jats:p>","DOI":"10.1007\/s10208-022-09569-5","type":"journal-article","created":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T23:03:54Z","timestamp":1654124634000},"page":"1273-1333","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Moving-Frame Method for the Iterated-Integrals Signature: Orthogonal Invariants"],"prefix":"10.1007","volume":"23","author":[{"given":"Joscha","family":"Diehl","sequence":"first","affiliation":[]},{"given":"Rosa","family":"Prei\u00df","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Ruddy","sequence":"additional","affiliation":[]},{"given":"Nikolas","family":"Tapia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,1]]},"reference":[{"key":"9569_CR1","doi-asserted-by":"publisher","unstructured":"Boutin, M.: The pascal triangle of a discrete image: Definition, properties and application to shape analysis. Symmetry, Integrability and Geometry: Methods and Applications (2013). https:\/\/doi.org\/10.3842\/sigma.2013.031","DOI":"10.3842\/sigma.2013.031"},{"key":"9569_CR2","doi-asserted-by":"crossref","unstructured":"Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., Haker, S.: Differential and numerically invariant signatures curves applied to object recognition. Int. J. Computer vision 26, Paper 107,135 (1998)","DOI":"10.1023\/A:1007992709392"},{"key":"9569_CR3","volume-title":"La m\u00e9thode du rep\u00e8re mobile, la th\u00e9orie des groupes continus, et les espaces g\u00e9n\u00e9ralis\u00e9s, Expos\u00e9s de G\u00e9om\u00e9trie","author":"E Cartan","year":"1935","unstructured":"Cartan, E.: La m\u00e9thode du rep\u00e8re mobile, la th\u00e9orie des groupes continus, et les espaces g\u00e9n\u00e9ralis\u00e9s, Expos\u00e9s de G\u00e9om\u00e9trie, vol.\u00a05. Hermann, Paris (1935)"},{"key":"9569_CR4","unstructured":"Cartan, E.: La th\u00e9orie des groupes finis et continus et la g\u00e9om\u00e9trie diff\u00e9rentielle, trait\u00e9es par la m\u00e9thode du repere mobile. le\u00e7ons profess\u00e9es \u00e0 la sorbonne. tgfc (1951)"},{"key":"9569_CR5","doi-asserted-by":"publisher","unstructured":"Celledoni, E., Lystad, P.l.E., Tapia, N.: Signatures in shape analysis: an efficient approach to motion identification. In: Geometric science of information, Lecture Notes in Comput. Sci., vol. 11712, pp. 21\u201330. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26980-7_3","DOI":"10.1007\/978-3-030-26980-7_3"},{"issue":"1","key":"9569_CR6","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1112\/plms\/s3-4.1.502","volume":"s3\u20134","author":"KT Chen","year":"1954","unstructured":"Chen, K.T.: Iterated integrals and exponential homomorphisms. Proceedings of the London Mathematical Society s3-4(1), 502\u2013512 (1954). https:\/\/doi.org\/10.1112\/plms\/s3-4.1.502","journal-title":"Proceedings of the London Mathematical Society"},{"issue":"1","key":"9569_CR7","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1112\/plms\/s3-4.1.502","volume":"s3\u20134","author":"KT Chen","year":"1954","unstructured":"Chen, K.T.: Iterated integrals and exponential homomorphisms. Proc. London Math. Soc. s3-4(1), 502\u2013512 (1954). https:\/\/doi.org\/10.1112\/plms\/s3-4.1.502","journal-title":"Proc. London Math. Soc."},{"key":"9569_CR8","doi-asserted-by":"publisher","unstructured":"Chen, K.T.: Integration of paths\u2014a faithful representation of paths by non-commutative formal power series. Trans. Amer. Math. Soc. 89, 395\u2013407 (1958). https:\/\/doi.org\/10.2307\/1993193","DOI":"10.2307\/1993193"},{"key":"9569_CR9","unstructured":"Chevyrev, I., Kormilitzin, A.: A primer on the signature method in machine learning (2016)"},{"issue":"4","key":"9569_CR10","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1007\/s13366-020-00493-9","volume":"61","author":"L Colmenarejo","year":"2020","unstructured":"Colmenarejo, L., Prei\u00df, R.: Signatures of paths transformed by polynomial maps. Beitr. Algebra Geom. 61(4), 695\u2013717 (2020). https:\/\/doi.org\/10.1007\/s13366-020-00493-9","journal-title":"Beitr. Algebra Geom."},{"key":"9569_CR11","doi-asserted-by":"crossref","unstructured":"Derksen, H., Kemper, G.: Computational invariant theory. Springer (2015)","DOI":"10.1007\/978-3-662-48422-7"},{"key":"9569_CR12","unstructured":"Diehl, J., Lyons, T., Prei\u00df, R., Reizenstein, J.: Areas of areas generate the shuffle algebra (2021)"},{"key":"9569_CR13","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s10440-018-00227-z","volume":"164","author":"J Diehl","year":"2019","unstructured":"Diehl, J., Reizenstein, J.: Invariants of Multidimensional Time Series Based on Their Iterated-Integral Signature. Acta Appl. Math. 164, 83\u2013122 (2019). https:\/\/doi.org\/10.1007\/s10440-018-00227-z","journal-title":"Acta Appl. Math."},{"issue":"2","key":"9569_CR14","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1023\/A:1005878210297","volume":"51","author":"M Fels","year":"1998","unstructured":"Fels, M., Olver, P.J.: Moving coframes: I. a practical algorithm. Acta Applicandae Mathematica 51(2), 161\u2013213 (1998)","journal-title":"Acta Applicandae Mathematica"},{"key":"9569_CR15","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1023\/A:1006195823000","volume":"55","author":"M Fels","year":"1999","unstructured":"Fels, M., Olver, P.J.: Moving Coframes. II. Regularization and Theoretical Foundations. Acta Appl. Math. 55, 127\u2013208 (1999)","journal-title":"Acta Appl. Math"},{"issue":"3","key":"9569_CR16","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1007\/s10440-008-9353-9","volume":"109","author":"S Feng","year":"2008","unstructured":"Feng, S., Kogan, I., Krim, H.: Classification of curves in 2d and 3d via affine integral signatures. Acta Applicandae Mathematicae 109(3), 903\u2013937 (2008). https:\/\/doi.org\/10.1007\/s10440-008-9353-9","journal-title":"Acta Applicandae Mathematicae"},{"key":"9569_CR17","doi-asserted-by":"publisher","first-page":"107148","DOI":"10.1016\/j.csda.2020.107148","volume":"157","author":"A Fermanian","year":"2021","unstructured":"Fermanian, A.: Embedding and learning with signatures. Computational Statistics & Data Analysis 157, 107148 (2021). https:\/\/doi.org\/10.1016\/j.csda.2020.107148","journal-title":"Computational Statistics & Data Analysis"},{"issue":"1","key":"9569_CR18","doi-asserted-by":"publisher","first-page":"209","DOI":"10.5802\/aif.3010","volume":"66","author":"L Foissy","year":"2016","unstructured":"Foissy, L., Patras, F., Thibon, J.Y.: Deformations of shuffles and quasi-shuffles. Ann. Inst. Fourier (Grenoble) 66(1), 209\u2013237 (2016)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"key":"9569_CR19","doi-asserted-by":"publisher","unstructured":"Friz, P.K., Hairer, M.: A Course on Rough Paths: With an Introduction to Regularity Structures, second edn. Universitext. Springer Nature Switzerland (2020). https:\/\/doi.org\/10.1007\/978-3-030-41556-3","DOI":"10.1007\/978-3-030-41556-3"},{"key":"9569_CR20","doi-asserted-by":"crossref","unstructured":"Friz, P.K., Victoir, N.B.: Multidimensional stochastic processes as rough paths: theory and applications, vol. 120. Cambridge University Press (2010)","DOI":"10.1017\/CBO9780511845079"},{"issue":"6","key":"9569_CR21","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1007\/s10208-018-9404-1","volume":"19","author":"P G\u00f6rlach","year":"2018","unstructured":"G\u00f6rlach, P., Hubert, E., Papadopoulo, T.: Rational invariants of even ternary forms under the orthogonal group. Foundations of Computational Mathematics 19(6), 1315\u20131361 (2018). https:\/\/doi.org\/10.1007\/s10208-018-9404-1","journal-title":"Foundations of Computational Mathematics"},{"key":"9569_CR22","doi-asserted-by":"crossref","unstructured":"Grim, A., Shakiban, C.: Applications of signature curves to characterize melanomas and moles. In: Applications of computer algebra, Springer Proc. Math. Stat., vol. 198, pp. 171\u2013189. Springer, Cham (2017)","DOI":"10.1007\/978-3-319-56932-1_11"},{"key":"9569_CR23","unstructured":"Harris, J.: Algebraic geometry: a first course, vol. 133. Springer Science & Business Media (2013)"},{"issue":"4","key":"9569_CR24","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/bf01208503","volume":"36","author":"D Hilbert","year":"1890","unstructured":"Hilbert, D.: Ueber die theorie der algebraischen formen. Mathematische Annalen 36(4), 473\u2013534 (1890). https:\/\/doi.org\/10.1007\/bf01208503","journal-title":"Mathematische Annalen"},{"issue":"2","key":"9569_CR25","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1007\/s10851-012-0358-7","volume":"45","author":"DJ Hoff","year":"2013","unstructured":"Hoff, D.J., Olver, P.J.: Extensions of invariant signatures for object recognition. J. Math. Imaging Vision 45(2), 176\u2013185 (2013). https:\/\/doi.org\/10.1007\/s10851-012-0358-7","journal-title":"J. Math. Imaging Vision"},{"issue":"1","key":"9569_CR26","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/s10851-013-0454-3","volume":"49","author":"DJ Hoff","year":"2014","unstructured":"Hoff, D.J., Olver, P.J.: Automatic solution of jigsaw puzzles. J. Math. Imaging Vision 49(1), 234\u2013250 (2014)","journal-title":"J. Math. Imaging Vision"},{"issue":"1\u20132","key":"9569_CR27","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.jsc.2006.03.005","volume":"42","author":"E Hubert","year":"2007","unstructured":"Hubert, E., Kogan, I.A.: Rational invariants of a group action. construction and rewriting. Journal of Symbolic Computation 42(1-2), 203\u2013217 (2007).","journal-title":"Journal of Symbolic Computation"},{"issue":"4","key":"9569_CR28","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s10208-006-0219-0","volume":"7","author":"E Hubert","year":"2007","unstructured":"Hubert, E., Kogan, I.A.: Smooth and algebraic invariants of a group action: local and global constructions. Found. Comput. Math. 7(4), 455\u2013493 (2007)","journal-title":"Found. Comput. Math."},{"key":"9569_CR29","doi-asserted-by":"crossref","unstructured":"Karlin, S., Shapley, L.S.: Geometry of moment spaces. 12. American Mathematical Soc. (1953)","DOI":"10.1090\/memo\/0012"},{"key":"9569_CR30","doi-asserted-by":"crossref","unstructured":"Kawski, M.: Chronological calculus in systems and control theory. Mathematics of Complexity and Dynamical Systems p.\u00a088 (2011)","DOI":"10.1007\/978-1-4614-1806-1_7"},{"issue":"2","key":"9569_CR31","doi-asserted-by":"publisher","first-page":"266","DOI":"10.4153\/CJM-2003-013-2","volume":"55","author":"IA Kogan","year":"2003","unstructured":"Kogan, I.A.: Two algorithms for a moving frame construction. Canadian Journal of Mathematics 55(2), 266\u2013291 (2003)","journal-title":"Canadian Journal of Mathematics"},{"issue":"1","key":"9569_CR32","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1137\/19m1242859","volume":"4","author":"IA Kogan","year":"2020","unstructured":"Kogan, I.A., Ruddy, M., Vinzant, C.: Differential signatures of algebraic curves. SIAM Journal on Applied Algebra and Geometry 4(1), 185\u2013226 (2020). https:\/\/doi.org\/10.1137\/19m1242859","journal-title":"SIAM Journal on Applied Algebra and Geometry"},{"key":"9569_CR33","unstructured":"Lee, D., Ghrist, R.: Path signatures on lie groups (2020)"},{"issue":"369","key":"9569_CR34","doi-asserted-by":"publisher","first-page":"346","DOI":"10.2307\/3612914","volume":"49","author":"DE Littlewood","year":"1965","unstructured":"Littlewood, D.E., Gurevich, G.B., Radok, J.R.M., Spencer, A.J.M.: Foundation of the theory of algebraic invariants. The Mathematical Gazette 49(369), 346 (1965). https:\/\/doi.org\/10.2307\/3612914","journal-title":"The Mathematical Gazette"},{"issue":"2","key":"9569_CR35","doi-asserted-by":"publisher","first-page":"215","DOI":"10.4171\/RMI\/240","volume":"14","author":"TJ Lyons","year":"1998","unstructured":"Lyons, T.J.: Differential equations driven by rough signals. Revista Matem\u00e1tica Iberoamericana 14(2), 215\u2013310 (1998)","journal-title":"Revista Matem\u00e1tica Iberoamericana"},{"key":"9569_CR36","doi-asserted-by":"crossref","unstructured":"Lyons, T.J., Yam, P.S.: On gauss\u2013green theorem and boundaries of a class of h\u00f6lder domains. Journal de math\u00e9matiques pures et appliqu\u00e9es 85(1), 38\u201353 (2006)","DOI":"10.1016\/j.matpur.2005.10.005"},{"key":"9569_CR37","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/S1570-7954(07)05007-3","volume":"5","author":"D Manchon","year":"2008","unstructured":"Manchon, D.: Hopf algebras in renormalisation. Handbook of algebra 5, 365\u2013427 (2008)","journal-title":"Handbook of algebra"},{"key":"9569_CR38","doi-asserted-by":"publisher","unstructured":"Manchon, D.: Hopf algebras in renormalisation. In: Handbook of algebra. Vol. 5, Handb. Algebr., vol.\u00a05, pp. 365\u2013427. Elsevier\/North-Holland, Amsterdam (2008). https:\/\/doi.org\/10.1016\/S1570-7954(07)05007-3","DOI":"10.1016\/S1570-7954(07)05007-3"},{"issue":"3","key":"9569_CR39","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1016\/j.bbe.2017.04.004","volume":"37","author":"J Morales","year":"2017","unstructured":"Morales, J., Akopian, D.: Physical activity recognition by smartphones, a survey. Biocybernetics and Biomedical Engineering 37(3), 388\u2013400 (2017)","journal-title":"Biocybernetics and Biomedical Engineering"},{"issue":"3","key":"9569_CR40","doi-asserted-by":"publisher","first-page":"766","DOI":"10.2307\/2372927","volume":"81","author":"M Nagata","year":"1959","unstructured":"Nagata, M.: On the 14-th problem of hilbert. American Journal of Mathematics 81(3), 766 (1959). https:\/\/doi.org\/10.2307\/2372927","journal-title":"American Journal of Mathematics"},{"key":"9569_CR41","doi-asserted-by":"publisher","unstructured":"Olver, P.J.: Classical Invariant Theory. Cambridge University Press (1999). https:\/\/doi.org\/10.1017\/cbo9780511623660","DOI":"10.1017\/cbo9780511623660"},{"issue":"1","key":"9569_CR42","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10208001001","volume":"1","author":"PJ Olver","year":"2001","unstructured":"Olver, P.J.: Joint invariant signatures. Foundations of Computational Mathematics 1(1), 3\u201368 (2001). https:\/\/doi.org\/10.1007\/s10208001001","journal-title":"Foundations of Computational Mathematics"},{"key":"9569_CR43","unstructured":"Olver, P.J.: Lectures on Moving Frames (2018)"},{"issue":"4","key":"9569_CR44","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1007\/PL00005432","volume":"87","author":"B Owren","year":"2001","unstructured":"Owren, B., Marthinsen, A.: Integration methods based on canonical coordinates of the second kind. Numerische Mathematik 87(4), 763\u2013790 (2001)","journal-title":"Numerische Mathematik"},{"key":"9569_CR45","unstructured":"Perrin, D.: Factorizations of free monoids. In: M.\u00a0Lothaire (ed.) Combinatorics on Words, 2nd edn. Cambridge University Press (2011)"},{"key":"9569_CR46","doi-asserted-by":"crossref","unstructured":"Popov, V.L., Vinberg, E.B.: Invariant theory. In: Algebraic geometry IV, pp. 123\u2013278. Springer (1994)","DOI":"10.1007\/978-3-662-03073-8_2"},{"issue":"2","key":"9569_CR47","doi-asserted-by":"publisher","first-page":"210","DOI":"10.2307\/1970243","volume":"68","author":"R Ree","year":"1958","unstructured":"Ree, R.: Lie elements and an algebra associated with shuffles. Ann. Math. (2) 68(2), 210\u2013220 (1958). https:\/\/doi.org\/10.2307\/1970243","journal-title":"Ann. Math. (2)"},{"key":"9569_CR48","unstructured":"Rudin, W., et\u00a0al.: Principles of mathematical analysis, vol.\u00a03. McGraw-hill New York (1964)"},{"key":"9569_CR49","unstructured":"Salvi, C.: Rough paths, kernels, differential equations and an algebra of functions on streams. Ph.D. thesis, University of Oxford (2021)"},{"key":"9569_CR50","unstructured":"Sturmfels, B.: Algorithms in invariant theory. Springer Science & Business Media (2008)"},{"issue":"2","key":"9569_CR51","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1017\/s0956792519000020","volume":"31","author":"SL Tuznik","year":"2019","unstructured":"Tuznik, S.L., Olver, P.J., Tannenbaum, A.: Equi-affine differential invariants for invariant feature point detection. European Journal of Applied Mathematics 31(2), 277\u2013296 (2019). https:\/\/doi.org\/10.1017\/s0956792519000020","journal-title":"European Journal of Applied Mathematics"},{"key":"9569_CR52","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.culher.2018.03.001","volume":"33","author":"Y Zhang","year":"2018","unstructured":"Zhang, Y., Li, K., Chen, X., Zhang, S., Geng, G.: A multi feature fusion method for reassembly of 3d cultural heritage artifacts. Journal of Cultural Heritage 33, 191\u2013200 (2018)","journal-title":"Journal of Cultural Heritage"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-022-09569-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10208-022-09569-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-022-09569-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T22:02:31Z","timestamp":1693346551000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10208-022-09569-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,1]]},"references-count":52,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["9569"],"URL":"https:\/\/doi.org\/10.1007\/s10208-022-09569-5","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,1]]},"assertion":[{"value":"7 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 June 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}