{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T00:43:19Z","timestamp":1767141799709,"version":"build-2238731810"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T00:00:00Z","timestamp":1737590400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T00:00:00Z","timestamp":1737590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["W1260-N35\/Vienna Graduate School on Computational Optimization (VGSCO)"],"award-info":[{"award-number":["W1260-N35\/Vienna Graduate School on Computational Optimization (VGSCO)"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V520251\/1 Project Reference 2445089"],"award-info":[{"award-number":["EP\/V520251\/1 Project Reference 2445089"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation\u2013linearization technique, the Shor relaxation, and the relaxation resulting from their combination. We establish several structural properties of these relaxations in relation to the corresponding relaxations of StQPs without any sparsity constraints, and pay particular attention to the rank-one feasible solutions retained by these relaxations. We then utilize these relations to establish several results about the quality of the lower bounds arising from different relaxations. We also present several conditions that ensure the exactness of each relaxation.<\/jats:p>","DOI":"10.1007\/s10957-024-02593-1","type":"journal-article","created":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T01:44:06Z","timestamp":1737596646000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints"],"prefix":"10.1007","volume":"204","author":[{"given":"Immanuel","family":"Bomze","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuzhou","family":"Qiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4141-3189","authenticated-orcid":false,"given":"E. Alper","family":"Y\u0131ld\u0131r\u0131m","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,23]]},"reference":[{"issue":"4","key":"2593_CR1","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1162\/rest_a_01258","volume":"106","author":"I Archakov","year":"2022","unstructured":"Archakov, I., Hansen, P.R.: A canonical representation of block matrices with applications to covariance and correlation matrices. Rev. Econ. Stat. 106(4), 1099\u20131113 (2022)","journal-title":"Rev. Econ. Stat."},{"issue":"4","key":"2593_CR2","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1023\/A:1008369322970","volume":"13","author":"IM Bomze","year":"1998","unstructured":"Bomze, I.M.: On standard quadratic optimization problems. J. Global Optim. 13(4), 369\u2013387 (1998)","journal-title":"J. Global Optim."},{"issue":"3","key":"2593_CR3","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1137\/S00361445003756","volume":"44","author":"IM Bomze","year":"2002","unstructured":"Bomze, I.M.: Regularity versus degeneracy in dynamics, games, and optimization: a unified approach to different aspects. SIAM Rev. 44(3), 394\u2013414 (2002)","journal-title":"SIAM Rev."},{"issue":"2","key":"2593_CR4","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1023\/A:1020209017701","volume":"24","author":"IM Bomze","year":"2002","unstructured":"Bomze, I.M., de Klerk, E.: Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. J. Global Optim. 24(2), 163\u2013185 (2002)","journal-title":"J. Global Optim."},{"issue":"2\u20133","key":"2593_CR5","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s10898-013-0126-2","volume":"59","author":"IM Bomze","year":"2014","unstructured":"Bomze, I.M., Gollowitzer, S., Y\u0131ld\u0131r\u0131m, E.A.: Rounding on the standard simplex: regular grids for global optimization. J. Global Optim. 59(2\u20133), 243\u2013258 (2014)","journal-title":"J. Global Optim."},{"issue":"1","key":"2593_CR6","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s10107-007-0138-0","volume":"115","author":"IM Bomze","year":"2008","unstructured":"Bomze, I.M., Locatelli, M., Tardella, F.: New and old bounds for standard quadratic optimization: dominance, equivalence and incomparability. Math. Program. 115(1), 31\u201364 (2008)","journal-title":"Math. Program."},{"key":"2593_CR7","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-1-4757-2600-8_6","volume-title":"Developments in Global Optimization","author":"IM Bomze","year":"1997","unstructured":"Bomze, I.M., Pelillo, M., Giacomini, R.: Evolutionary approach to the maximum clique problem: empirical evidence on a larger scale. In: Bomze, I.M., Csendes, T., Horst, R., Pardalos, P.M. (eds.) Developments in Global Optimization, pp. 95\u2013108. Springer, Boston (1997)"},{"key":"2593_CR8","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/s10589-022-00440-5","volume":"84","author":"IM Bomze","year":"2023","unstructured":"Bomze, I.M., Peng, B.: Conic formulation of QPCCs applied to truly sparse QPs. Comput. Optim. Appl. 84, 703\u2013735 (2023)","journal-title":"Comput. Optim. Appl."},{"key":"2593_CR9","unstructured":"Bomze, I.M., Peng, B., Qiu, Y., Y\u0131ld\u0131r\u0131m, E.A.: Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization. Mathematical Programming Computation, to appear (2025). arxiv:2406.01239"},{"issue":"3","key":"2593_CR10","doi-asserted-by":"publisher","first-page":"2211","DOI":"10.1137\/18M1206953","volume":"29","author":"IM Bomze","year":"2019","unstructured":"Bomze, I.M., Rinaldi, F., Rota-Bul\u00f2, S.: First-order methods for the impatient: support identification in finite time with convergent Frank-Wolfe variants. SIAM J. Optim. 29(3), 2211\u20132226 (2019)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2593_CR11","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1287\/moor.2017.0877","volume":"43","author":"IM Bomze","year":"2018","unstructured":"Bomze, I.M., Schachinger, W., Ullrich, R.: The complexity of simple models: a study of worst and typical hard cases for the standard quadratic optimization problem. Math. Oper. Res. 43(2), 651\u2013674 (2018)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"2593_CR12","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1137\/070711815","volume":"20","author":"S Bundfuss","year":"2009","unstructured":"Bundfuss, S., D\u00fcr, M.: An adaptive linear approximation algorithm for copositive programs. SIAM J. Optim. 20(1), 30\u201353 (2009)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"2593_CR13","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s10107-008-0223-z","volume":"120","author":"S Burer","year":"2009","unstructured":"Burer, S.: On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Program. 120(2), 479\u2013495 (2009)","journal-title":"Math. Program."},{"issue":"3","key":"2593_CR14","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1287\/moor.2014.0692","volume":"40","author":"X Chen","year":"2015","unstructured":"Chen, X., Peng, J.: New analysis on sparse solutions to random standard quadratic optimization problems and extensions. Math. Oper. Res. 40(3), 725\u2013738 (2015)","journal-title":"Math. Oper. Res."},{"key":"2593_CR15","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s10107-012-0519-x","volume":"141","author":"X Chen","year":"2013","unstructured":"Chen, X., Peng, J., Zhang, S.: Sparse solutions to random standard quadratic optimization problems. Math. Program. 141, 273\u2013293 (2013)","journal-title":"Math. Program."},{"issue":"5","key":"2593_CR16","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1093\/rfs\/hhm075","volume":"22","author":"V DeMiguel","year":"2009","unstructured":"DeMiguel, V., Garlappi, L., Uppal, R.: Optimal versus naive diversification: How inefficient is the 1\/n portfolio strategy? Review of Financ. Stud. 22(5), 1915\u20131953 (2009)","journal-title":"Review of Financ. Stud."},{"issue":"1","key":"2593_CR17","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1017\/S0305004100036185","volume":"58","author":"PH Diananda","year":"1962","unstructured":"Diananda, P.H.: On non-negative forms in real variables some or all of which are non-negative. Math. Proc. Camb. Philos. Soc. 58(1), 17\u201325 (1962)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"542","key":"2593_CR18","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1080\/01621459.2022.2133718","volume":"118","author":"JH Du","year":"2022","unstructured":"Du, J.H., Guo, Y., Wang, X.: High-dimensional portfolio selection with cardinality constraints. J. Am. Stat. Assoc. 118(542), 779\u2013791 (2022)","journal-title":"J. Am. Stat. Assoc."},{"issue":"4","key":"2593_CR19","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1137\/S1052623401383248","volume":"12","author":"E de Klerk","year":"2002","unstructured":"de Klerk, E., Pasechnik, D.V.: Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12(4), 875\u2013892 (2002)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"2593_CR20","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1287\/opre.2013.1170","volume":"61","author":"J Gao","year":"2013","unstructured":"Gao, J., Li, D.: Optimal cardinality constrained portfolio selection. Oper. Res. 61(3), 745\u2013761 (2013)","journal-title":"Oper. Res."},{"key":"2593_CR21","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s10107-020-01611-0","volume":"193","author":"YG G\u00f6kmen","year":"2022","unstructured":"G\u00f6kmen, Y.G., Y\u0131ld\u0131r\u0131m, E.A.: On standard quadratic programs with exact and inexact doubly nonnegative relaxations. Math. Program. 193, 365\u2013403 (2022)","journal-title":"Math. Program."},{"key":"2593_CR22","volume-title":"The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection","author":"J Hofbauer","year":"1988","unstructured":"Hofbauer, J., Sigmund, K.: The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection. Cambridge University Press, Cambridge (1988)"},{"key":"2593_CR23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139173179","volume-title":"Evolutionary Games and Population Dynamics","author":"J Hofbauer","year":"1998","unstructured":"Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)"},{"key":"2593_CR24","volume-title":"Resource Allocation Problems: Algorithmic Approaches","author":"T Ibaraki","year":"1988","unstructured":"Ibaraki, T., Katoh, N.: Resource Allocation Problems: Algorithmic Approaches. MIT Press, Boston (1988)"},{"issue":"2","key":"2593_CR25","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/S0022-0000(03)00006-0","volume":"66","author":"H Kellerer","year":"2003","unstructured":"Kellerer, H., Mansini, R., Pferschy, U., Speranza, M.G.: An efficient fully polynomial approximation scheme for the subset-sum problem. J. Comput. Syst. Sci. 66(2), 349\u2013370 (2003)","journal-title":"J. Comput. Syst. Sci."},{"key":"2593_CR26","doi-asserted-by":"publisher","first-page":"113","DOI":"10.2307\/3214150","volume":"25","author":"J Kingman","year":"1988","unstructured":"Kingman, J.: Typical polymorphisms maintained by selection at a single locus. J. Appl. Probab. 25, 113\u2013125 (1988)","journal-title":"J. Appl. Probab."},{"key":"2593_CR27","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1017\/S0305004100035635","volume":"57","author":"JFC Kingman","year":"1961","unstructured":"Kingman, J.F.C.: A mathematical problem in population genetics. Proc. Camb. Philos. Soc. 57, 574\u2013582 (1961)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"2593_CR28","doi-asserted-by":"crossref","unstructured":"Kontogiannis, S., Spirakis, P.: Counting stable strategies in random evolutionary games. In: X.\u00a0Deng, D.\u00a0Du (eds.) Proceedings of the 16th annual international symposium on algorithms and computation (ISAAC 2005), LNCS, vol. 3827, pp. 839\u2013848. Springer, Heidelberg (2006)","DOI":"10.1007\/11602613_84"},{"issue":"8\u201310","key":"2593_CR29","doi-asserted-by":"publisher","first-page":"933","DOI":"10.1016\/j.tcs.2008.12.056","volume":"410","author":"SC Kontogiannis","year":"2009","unstructured":"Kontogiannis, S.C., Spirakis, P.G.: On the support size of stable strategies in random games. Theoret. Comput. Sci. 410(8\u201310), 933\u2013942 (2009)","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"2593_CR30","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1007\/s00453-008-9227-6","volume":"57","author":"SC Kontogiannis","year":"2010","unstructured":"Kontogiannis, S.C., Spirakis, P.G.: Well supported approximate equilibria in bimatrix games. Algorithmica 57(2), 653\u2013667 (2010)","journal-title":"Algorithmica"},{"issue":"1","key":"2593_CR31","first-page":"77","volume":"7","author":"H Markowitz","year":"1952","unstructured":"Markowitz, H.: Portfolio selection. J. Finance 7(1), 77\u201391 (1952)","journal-title":"J. Finance"},{"key":"2593_CR32","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1098\/rsta.1994.0063","volume":"347","author":"H Markowitz","year":"1994","unstructured":"Markowitz, H.: The general mean-variance portfolio selection problem. Philos. Trans. R. Soc. Lond. Ser. A: Phys. Eng. Sci. 347, 543\u2013549 (1994)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A: Phys. Eng. Sci."},{"issue":"2","key":"2593_CR33","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1111\/itor.12541","volume":"26","author":"L Mencarelli","year":"2019","unstructured":"Mencarelli, L., D\u2019Ambrosio, C.: Complex portfolio selection via convex mixed-integer quadratic programming: a survey. Int. Trans. Oper. Res. 26(2), 389\u2013414 (2019)","journal-title":"Int. Trans. Oper. Res."},{"key":"2593_CR34","doi-asserted-by":"publisher","first-page":"533","DOI":"10.4153\/CJM-1965-053-6","volume":"17","author":"TS Motzkin","year":"1965","unstructured":"Motzkin, T.S., Straus, E.G.: Maxima for graphs and a new proof of a theorem of Tur\u00e1n. Can. J. Math. 17, 533\u2013540 (1965)","journal-title":"Can. J. Math."},{"key":"2593_CR35","volume-title":"Polyhedral properties of RLT relaxations of nonconvex quadratic programs and their implications on exact relaxations","author":"Y Qiu","year":"2024","unstructured":"Qiu, Y., Y\u0131ld\u0131r\u0131m, E.A.: Polyhedral properties of RLT relaxations of nonconvex quadratic programs and their implications on exact relaxations. Math, Program (2024)"},{"key":"2593_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/978-3-642-14980-1_26","volume-title":"Structural, Syntactic, and Statistical Pattern Recognition, SSPR &SPR 2010","author":"S Rota Bul\u00f2","year":"2010","unstructured":"Rota Bul\u00f2, S., Pelillo, M., Bomze, I.M.: Fast population game dynamics for dominant sets and other quadratic optimization problems. In: Hancock, E., Wilson, R., Windeatt, T., Ulusoy, I., Escolano, F. (eds.) Structural, Syntactic, and Statistical Pattern Recognition, SSPR &SPR 2010. Lecture Notes in Computer Science, vol. 6218, pp. 275\u2013285. Springer, Heidelberg (2010)"},{"key":"2593_CR37","volume-title":"Population Games and Evolutionary Dynamics","author":"WH Sandholm","year":"2010","unstructured":"Sandholm, W.H.: Population Games and Evolutionary Dynamics. MIT Press, Cambridge (2010)"},{"issue":"13","key":"2593_CR38","doi-asserted-by":"publisher","first-page":"2439","DOI":"10.1016\/j.dam.2007.09.020","volume":"156","author":"A Scozzari","year":"2008","unstructured":"Scozzari, A., Tardella, F.: A clique algorithm for standard quadratic programming. Discret. Appl. Math. 156(13), 2439\u20132448 (2008)","journal-title":"Discret. Appl. Math."},{"key":"2593_CR39","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4388-3","volume-title":"A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems","author":"HD Sherali","year":"1999","unstructured":"Sherali, H.D., Adams, W.P.: A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Springer, Boston (1999)"},{"issue":"1","key":"2593_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01100203","volume":"7","author":"HD Sherali","year":"1995","unstructured":"Sherali, H.D., Tun\u00e7bilek, C.H.: A reformulation-convexification approach for solving nonconvex quadratic programming problems. J. Global Optim. 7(1), 1\u201331 (1995)","journal-title":"J. Global Optim."},{"key":"2593_CR41","volume-title":"Evolutionary Game Theory","author":"JW Weibull","year":"1995","unstructured":"Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1995)"},{"issue":"1","key":"2593_CR42","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1080\/10556788.2010.540014","volume":"27","author":"EA Y\u0131ld\u0131r\u0131m","year":"2012","unstructured":"Y\u0131ld\u0131r\u0131m, E.A.: On the accuracy of uniform polyhedral approximations of the copositive cone. Optim. Methods Softw. 27(1), 155\u2013173 (2012)","journal-title":"Optim. Methods Softw."}],"updated-by":[{"DOI":"10.1007\/s10957-025-02670-z","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T00:00:00Z","timestamp":1746403200000}}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02593-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-024-02593-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02593-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T14:02:52Z","timestamp":1746540172000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-024-02593-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,23]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["2593"],"URL":"https:\/\/doi.org\/10.1007\/s10957-024-02593-1","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,23]]},"assertion":[{"value":"28 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2025","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The missing hyperlinks to equations has been included and the typos in proof of Lemma 3.4, the Matrix Q of Remark 4.1 and reference 9 has been corrected.","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2025","order":7,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":8,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":9,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s10957-025-02670-z","URL":"https:\/\/doi.org\/10.1007\/s10957-025-02670-z","order":10,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"38"}}