{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:41:52Z","timestamp":1740109312759,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T00:00:00Z","timestamp":1592611200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T00:00:00Z","timestamp":1592611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["338077"],"award-info":[{"award-number":["338077"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Suomen Akatemia","doi-asserted-by":"publisher","award":["276031","282938","283262","283437"],"award-info":[{"award-number":["276031","282938","283262","283437"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Algorithmica"],"published-print":{"date-parts":[[2020,11]]},"abstract":"Abstract<\/jats:title>We derandomize Valiant\u2019s (J ACM 62, Article 13, 2015) subquadratic-time algorithm for finding outlier correlations in binary data. This demonstrates that it is possible to perform a deterministic subquadratic-time similarity join of high dimensionality. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiant\u2019s randomized algorithm, but the precise constants we save over quadratic scaling are more modest. Our main technical tool for derandomization is an explicit family of correlation amplifiers<\/jats:italic> built via a family of zigzag-product expanders by Reingold et al. (Ann Math 155(1):157\u2013187, 2002). We say that a function $$f:\\{-1,1\\}^d\\rightarrow \\{-1,1\\}^D$$<\/jats:tex-math>\n\nf<\/mml:mi>\n:<\/mml:mo>\n\n\n{<\/mml:mo>\n-<\/mml:mo>\n1<\/mml:mn>\n,<\/mml:mo>\n1<\/mml:mn>\n}<\/mml:mo>\n<\/mml:mrow>\nd<\/mml:mi>\n<\/mml:msup>\n\u2192<\/mml:mo>\n\n\n{<\/mml:mo>\n-<\/mml:mo>\n1<\/mml:mn>\n,<\/mml:mo>\n1<\/mml:mn>\n}<\/mml:mo>\n<\/mml:mrow>\nD<\/mml:mi>\n<\/mml:msup>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> is a correlation amplifier<\/jats:italic> with threshold $$0\\le \\tau \\le 1$$<\/jats:tex-math>\n\n0<\/mml:mn>\n\u2264<\/mml:mo>\n\u03c4<\/mml:mi>\n\u2264<\/mml:mo>\n1<\/mml:mn>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>, error $$\\gamma \\ge 1$$<\/jats:tex-math>\n\n\u03b3<\/mml:mi>\n\u2265<\/mml:mo>\n1<\/mml:mn>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and strength p<\/jats:italic> an even positive integer if for all pairs of vectors $$x,y\\in \\{-1,1\\}^d$$<\/jats:tex-math>\n\nx<\/mml:mi>\n,<\/mml:mo>\ny<\/mml:mi>\n\u2208<\/mml:mo>\n\n\n{<\/mml:mo>\n-<\/mml:mo>\n1<\/mml:mn>\n,<\/mml:mo>\n1<\/mml:mn>\n}<\/mml:mo>\n<\/mml:mrow>\nd<\/mml:mi>\n<\/mml:msup>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> it holds that (i) $$|\\langle x,y\\rangle |<\\tau d$$<\/jats:tex-math>\n\n|<\/mml:mo>\n\u27e8<\/mml:mo>\nx<\/mml:mi>\n,<\/mml:mo>\ny<\/mml:mi>\n\u27e9<\/mml:mo>\n|<\/mml:mo>\n<<\/mml:mo>\n\u03c4<\/mml:mi>\nd<\/mml:mi>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> implies $$|\\langle f(x),f(y)\\rangle |\\le (\\tau \\gamma )^pD$$<\/jats:tex-math>\n\n\n|<\/mml:mo>\n\n\u27e8<\/mml:mo>\nf<\/mml:mi>\n\n(<\/mml:mo>\nx<\/mml:mi>\n)<\/mml:mo>\n<\/mml:mrow>\n,<\/mml:mo>\nf<\/mml:mi>\n\n(<\/mml:mo>\ny<\/mml:mi>\n)<\/mml:mo>\n<\/mml:mrow>\n\u27e9<\/mml:mo>\n<\/mml:mrow>\n|<\/mml:mo>\n<\/mml:mrow>\n\u2264<\/mml:mo>\n\n\n(<\/mml:mo>\n\u03c4<\/mml:mi>\n\u03b3<\/mml:mi>\n)<\/mml:mo>\n<\/mml:mrow>\np<\/mml:mi>\n<\/mml:msup>\nD<\/mml:mi>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>; and (ii) $$|\\langle x,y\\rangle |\\ge \\tau d$$<\/jats:tex-math>\n\n|<\/mml:mo>\n\u27e8<\/mml:mo>\nx<\/mml:mi>\n,<\/mml:mo>\ny<\/mml:mi>\n\u27e9<\/mml:mo>\n|<\/mml:mo>\n\u2265<\/mml:mo>\n\u03c4<\/mml:mi>\nd<\/mml:mi>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> implies $$\\left (\\frac{\\langle x,y\\rangle }{\\gamma d}\\right )^pD \\le \\langle f(x),f(y)\\rangle \\le \\left (\\frac{\\gamma \\langle x,y\\rangle }{d}\\right )^pD$$<\/jats:tex-math>\n\n\n\n\n\n\u27e8<\/mml:mo>\nx<\/mml:mi>\n,<\/mml:mo>\ny<\/mml:mi>\n\u27e9<\/mml:mo>\n<\/mml:mrow>\n\n\u03b3<\/mml:mi>\nd<\/mml:mi>\n<\/mml:mrow>\n<\/mml:mfrac>\n<\/mml:mfenced>\np<\/mml:mi>\n<\/mml:msup>\nD<\/mml:mi>\n\u2264<\/mml:mo>\n\n\u27e8<\/mml:mo>\nf<\/mml:mi>\n\n(<\/mml:mo>\nx<\/mml:mi>\n)<\/mml:mo>\n<\/mml:mrow>\n,<\/mml:mo>\nf<\/mml:mi>\n\n(<\/mml:mo>\ny<\/mml:mi>\n)<\/mml:mo>\n<\/mml:mrow>\n\u27e9<\/mml:mo>\n<\/mml:mrow>\n\u2264<\/mml:mo>\n\n\n\n\n\u03b3<\/mml:mi>\n\u27e8<\/mml:mo>\nx<\/mml:mi>\n,<\/mml:mo>\ny<\/mml:mi>\n\u27e9<\/mml:mo>\n<\/mml:mrow>\nd<\/mml:mi>\n<\/mml:mfrac>\n<\/mml:mfenced>\np<\/mml:mi>\n<\/mml:msup>\nD<\/mml:mi>\n<\/mml:mrow>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00453-020-00727-1","type":"journal-article","created":{"date-parts":[[2020,6,20]],"date-time":"2020-06-20T05:02:24Z","timestamp":1592629344000},"page":"3306-3337","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time"],"prefix":"10.1007","volume":"82","author":[{"given":"Matti","family":"Karppa","sequence":"first","affiliation":[]},{"given":"Petteri","family":"Kaski","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4859-1463","authenticated-orcid":false,"given":"Jukka","family":"Kohonen","sequence":"additional","affiliation":[]},{"given":"Padraig","family":"\u00d3 Cath\u00e1in","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,20]]},"reference":[{"key":"727_CR1","doi-asserted-by":"crossref","unstructured":"Ahle, T.D., Pagh, R., Razenshteyn, I., Silvestri, F.: On the complexity of inner product similarity join. arXiv:1510.02824 (2015)","DOI":"10.1145\/2902251.2902285"},{"key":"727_CR2","doi-asserted-by":"crossref","unstructured":"Alman, J., Chan, T.M., Williams, R.: Polynomial representations of threshold functions and algorithmic applications. arXiv:1608.04355 (2016)","DOI":"10.1109\/FOCS.2016.57"},{"key":"727_CR3","doi-asserted-by":"crossref","unstructured":"Alman, J., Williams, R.: Probabilistic polynomials and Hamming nearest neighbors. In: Proceedings of the 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 136\u2013150. IEEE Computer Society, Los Alamitos, CA, USA (2015)","DOI":"10.1109\/FOCS.2015.18"},{"issue":"1\u20133","key":"727_CR4","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/S0012-365X(03)00227-9","volume":"273","author":"N Alon","year":"2003","unstructured":"Alon, N.: Problems and results in extremal combinatorics\u2014I. Discrete Math. 273(1\u20133), 31\u201353 (2003)","journal-title":"Discrete Math."},{"key":"727_CR5","doi-asserted-by":"crossref","unstructured":"Andoni, A., Indyk, P., Nguyen, H.L., Razenshteyn, I.: Beyond locality-sensitive hashing. In: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1018\u20131028. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2014)","DOI":"10.1137\/1.9781611973402.76"},{"key":"727_CR6","doi-asserted-by":"crossref","unstructured":"Andoni, A., Laarhoven, T., Razenshteyn, I.P., Waingarten, E.: Optimal hashing-based time-space trade-offs for approximate near neighbors. arXiv:1608.03580 (2016)","DOI":"10.1137\/1.9781611974782.4"},{"key":"727_CR7","doi-asserted-by":"crossref","unstructured":"Andoni, A., Razenshteyn, I.: Optimal data-dependent hashing for approximate near neighbors. In: Proceedings of the 47th ACM Annual Symposium on the Theory of Computing (STOC), pp. 793\u2013801. Association for Computing Machinery, New York, NY, USA (2015)","DOI":"10.1145\/2746539.2746553"},{"issue":"4","key":"727_CR8","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1145\/792538.792543","volume":"50","author":"A Blum","year":"2003","unstructured":"Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506\u2013519 (2003)","journal-title":"J. ACM"},{"issue":"3","key":"727_CR9","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1137\/120871626","volume":"42","author":"LE Celis","year":"2013","unstructured":"Celis, L.E., Reingold, O., Segev, G., Wieder, U.: Balls and bins: smaller hash families and faster evaluation. SIAM J. Comput. 42(3), 1030\u20131050 (2013)","journal-title":"SIAM J. Comput."},{"key":"727_CR10","first-page":"1246","volume-title":"Proceeding of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","author":"TM Chan","year":"2016","unstructured":"Chan, T.M., Williams, R.: Deterministic APSP, orthogonal vectors, and more: quickly derandomizing Razborov\u2013Smolensky. In: Krauthgamer, R. (ed.) Proceeding of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1246\u20131255. Society for Industrial and Applied Mathematics, Arlington, VA, USA (2016)"},{"issue":"8","key":"727_CR11","doi-asserted-by":"publisher","first-page":"4166","DOI":"10.1109\/TIT.2010.2050814","volume":"56","author":"M Dubiner","year":"2010","unstructured":"Dubiner, M.: Bucketing coding and information theory for the statistical high-dimensional nearest-neighbor problem. IEEE Trans. Inf. Theory 56(8), 4166\u20134179 (2010)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"727_CR12","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1137\/070684914","volume":"39","author":"V Feldman","year":"2009","unstructured":"Feldman, V., Gopalan, P., Khot, S., Ponnuswami, A.K.: On agnostic learning of parities, monomials, and halfspaces. SIAM J. Comput. 39(2), 606\u2013645 (2009)","journal-title":"SIAM J. Comput."},{"key":"727_CR13","unstructured":"Gionis, A., Indyk, P., Motwani, R.: Similarity search in high dimensions via hashing. In: Atkinson, M.P., Orlowska, M.E., Valduriez, P., Zdonik, S.B., Brodie, M.L. (eds.) Proceedings of the 25th International Conference on Very Large Data Bases (VLDB\u201999), pp. 518\u2013529. Morgan Kaufmann, Edinburgh, Scotland, UK (1999)"},{"key":"727_CR14","doi-asserted-by":"crossref","unstructured":"Gopalan, P., Kane, D., Meka, R.: Pseudorandomness via the Discrete Fourier Transform. In: Proceedings of the IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 903\u2013922. IEEE Computer Society, Berkeley, CA, USA (2015)","DOI":"10.1109\/FOCS.2015.60"},{"issue":"3","key":"727_CR15","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1137\/110854990","volume":"42","author":"P Gopalan","year":"2013","unstructured":"Gopalan, P., Meka, R., Reingold, O., Zuckerman, D.: Pseudorandom generators for combinatorial shapes. SIAM J. Comput. 42(3), 1051\u20131076 (2013)","journal-title":"SIAM J. Comput."},{"key":"727_CR16","doi-asserted-by":"crossref","unstructured":"Grigorescu, E., Reyzin, L., Vempala, S.: On noise-tolerant learning of sparse parities and related problems. In: Proceedings of the 22nd International Conference on Algorithmic Learning Theory (ALT), pp. 413\u2013424. Springer, Berlin (2011)","DOI":"10.1007\/978-3-642-24412-4_32"},{"key":"727_CR17","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1080\/01621459.1963.10500830","volume":"58","author":"W Hoeffding","year":"1963","unstructured":"Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58, 13\u201330 (1963)","journal-title":"J. Am. Stat. Assoc."},{"issue":"4","key":"727_CR18","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1090\/S0273-0979-06-01126-8","volume":"43","author":"S Hoory","year":"2006","unstructured":"Hoory, S., Linial, N., Wigderson, A.: Expander graphs and their applications. Bull. Am. Math. Soc. 43(4), 439\u2013561 (2006)","journal-title":"Bull. Am. Math. Soc."},{"issue":"2","key":"727_CR19","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1006\/jcss.2000.1727","volume":"62","author":"R Impagliazzo","year":"2001","unstructured":"Impagliazzo, R., Paturi, R.: On the complexity of $$k$$-SAT. J. Comput. Syst. Sci. 62(2), 367\u2013375 (2001)","journal-title":"J. Comput. Syst. Sci."},{"key":"727_CR20","doi-asserted-by":"crossref","unstructured":"Indyk, P., Motwani, R.: Approximate nearest neighbors: Towards removing the curse of dimensionality. In: Proceedings of the 30th Annual ACM Symposium on the Theory of Computing (STOC), pp. 604\u2013613. Association for Computing Machinery, New York, NY, USA (1998)","DOI":"10.1145\/276698.276876"},{"key":"727_CR21","doi-asserted-by":"crossref","unstructured":"Kane, D.M., Meka, R., Nelson, J.: Almost optimal explicit Johnson-Lindenstrauss families. In: Proceeding of the 14th International Workshop on Approximation, Randomization, and Combinatorial Optimization, RANDOM and 15th International Workshop on Algorithms and Techniques, APPROX, pp. 628\u2013639. Princeton, NJ, USA (2011)","DOI":"10.1007\/978-3-642-22935-0_53"},{"key":"727_CR22","doi-asserted-by":"crossref","unstructured":"Kapralov, M.: Smooth tradeoffs between insert and query complexity in nearest neighbor search. In: Proceedings of the 34th ACM Symposium on Principles of Database Systems (PODS), pp. 329\u2013342. Association for Computing Machinery, New York, NY, USA (2015)","DOI":"10.1145\/2745754.2745761"},{"key":"727_CR23","doi-asserted-by":"crossref","unstructured":"Karppa, M., Kaski, P., Kohonen, J.: A faster subquadratic algorithm for finding outlier correlations. In: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms, (SODA), pp. 1288\u20131305. Society for Industrial and Applied Mathematics, Arlington, VA, USA (2016)","DOI":"10.1137\/1.9781611974331.ch90"},{"key":"727_CR24","doi-asserted-by":"crossref","unstructured":"Kothari, P.K., Meka, R.: Almost optimal pseudorandom generators for spherical caps. In: Proceedings of the 47th Annual ACM Symposium on Theory of Computing (STOC), pp. 247\u2013256. Portland, OR, USA (2015)","DOI":"10.1145\/2746539.2746611"},{"key":"727_CR25","doi-asserted-by":"crossref","unstructured":"Le Gall, F.: Faster algorithms for rectangular matrix multiplication. In: Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 514\u2013523. IEEE Computer Society, Los Alamitos, CA, USA (2012)","DOI":"10.1109\/FOCS.2012.80"},{"key":"727_CR26","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/BF02126799","volume":"8","author":"A Lubotzky","year":"1988","unstructured":"Lubotzky, A., Phillips, R., Sarnak, P.: Ramanujan graphs. Combinatorica 8, 261\u2013277 (1988)","journal-title":"Combinatorica"},{"key":"727_CR27","doi-asserted-by":"crossref","unstructured":"May, A., Ozerov, I.: On computing nearest neighbors with applications to decoding of binary linear codes. In: Proceedings of the EUROCRYPT 2015\u201434th Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 203\u2013228. Springer, Berlin (2015)","DOI":"10.1007\/978-3-662-46800-5_9"},{"issue":"3","key":"727_CR28","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1016\/j.jcss.2004.04.002","volume":"69","author":"E Mossel","year":"2004","unstructured":"Mossel, E., O\u2019Donnell, R., Servedio, R.A.: Learning functions of $$k$$ relevant variables. J. Comput. Syst. Sci. 69(3), 421\u2013434 (2004)","journal-title":"J. Comput. Syst. Sci."},{"issue":"4","key":"727_CR29","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1137\/050646858","volume":"21","author":"R Motwani","year":"2007","unstructured":"Motwani, R., Naor, A., Panigrahy, R.: Lower bounds on locality sensitive hashing. SIAM J. Discrete Math. 21(4), 930\u2013935 (2007)","journal-title":"SIAM J. Discrete Math."},{"key":"727_CR30","doi-asserted-by":"crossref","unstructured":"O\u2019Donnell, R., Yi, W., Zhou, Y.: Optimal lower bounds for locality-sensitive hashing (except when q is tiny). ACM Trans. Comput. Theory 6(1), Article 5 (2014)","DOI":"10.1145\/2578221"},{"key":"727_CR31","doi-asserted-by":"crossref","unstructured":"Pagh, R.: Locality-sensitive hashing without false negatives. In: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1\u20139. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2016)","DOI":"10.1137\/1.9781611974331.ch1"},{"key":"727_CR32","doi-asserted-by":"crossref","unstructured":"Paturi, R., Rajasekaran, S., Reif, J.H.: The light bulb problem. In: Proceedings of the 2nd Annual Workshop on Computational Learning Theory (COLT), pp. 261\u2013268. Association for Computing Machinery, New York, NY, USA (1989)","DOI":"10.1016\/B978-0-08-094829-4.50021-0"},{"key":"727_CR33","doi-asserted-by":"crossref","unstructured":"Pham, N., Pagh, R.: Scalability and total recall with fast Covering LSH. arXiv:1602.02620 (2016)","DOI":"10.1145\/2983323.2983742"},{"issue":"1","key":"727_CR34","doi-asserted-by":"publisher","first-page":"157","DOI":"10.2307\/3062153","volume":"155","author":"O Reingold","year":"2002","unstructured":"Reingold, O., Vadhan, S., Wigderson, A.: Entropy waves, the zig-zag graph product, and new constant-degree expanders. Ann. Math. 155(1), 157\u2013187 (2002)","journal-title":"Ann. Math."},{"key":"727_CR35","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1090\/S0025-5718-1990-0993933-0","volume":"54","author":"V Shoup","year":"1990","unstructured":"Shoup, V.: New algorithms for finding irreducible polynomials over finite fields. Math. Comput. 54, 435\u2013447 (1990)","journal-title":"Math. Comput."},{"key":"727_CR36","doi-asserted-by":"crossref","unstructured":"Valiant, G.: Finding correlations in subquadratic time, with applications to learning parities and the closest pair problem. J. ACM 62(2), Article 13 (2015)","DOI":"10.1145\/2728167"},{"key":"727_CR37","unstructured":"Valiant, L.G.: Functionality in neural nets. In: Proceedings of the 1st Annual Workshop on Computational Learning Theory (COLT), pp. 28\u201339. Association for Computing Machinery, New York, NY, USA (1988)"}],"container-title":["Algorithmica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-020-00727-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00453-020-00727-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-020-00727-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,19]],"date-time":"2021-06-19T23:25:07Z","timestamp":1624145107000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00453-020-00727-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,20]]},"references-count":37,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["727"],"URL":"https:\/\/doi.org\/10.1007\/s00453-020-00727-1","relation":{},"ISSN":["0178-4617","1432-0541"],"issn-type":[{"type":"print","value":"0178-4617"},{"type":"electronic","value":"1432-0541"}],"subject":[],"published":{"date-parts":[[2020,6,20]]},"assertion":[{"value":"1 December 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}