{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,6]],"date-time":"2025-07-06T12:21:22Z","timestamp":1751804482195,"version":"3.40.3"},"publisher-location":"Cham","reference-count":41,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030588137"},{"type":"electronic","value":"9783030588144"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-58814-4_11","type":"book-chapter","created":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T07:07:37Z","timestamp":1601622457000},"page":"145-162","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Large Scale Automatic Computations for Feynman Diagrams with up to Five Loops"],"prefix":"10.1007","author":[{"given":"E.","family":"de Doncker","sequence":"first","affiliation":[]},{"given":"F.","family":"Yuasa","sequence":"additional","affiliation":[]},{"given":"O.","family":"Olagbemi","sequence":"additional","affiliation":[]},{"given":"T.","family":"Ishikawa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,3]]},"reference":[{"key":"11_CR1","unstructured":"Adams, D.: The Hitchhiker\u2019s Guide to the Galaxy. Pocket Books, Simon & Shuster, Inc. (1981). ISBN 0-671-52721-5"},{"key":"11_CR2","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1145\/210232.210233","volume":"17","author":"J Berntsen","year":"1991","unstructured":"Berntsen, J., Espelid, T.O., Genz, A.: An adaptive algorithm for the approximate calculation of multiple integrals. ACM Trans. Math. Softw. 17, 437\u2013451 (1991)","journal-title":"ACM Trans. Math. Softw."},{"key":"11_CR3","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1145\/210232.210234","volume":"17","author":"J Berntsen","year":"1991","unstructured":"Berntsen, J., Espelid, T.O., Genz, A.: Algorithm 698: DCUHRE-an adaptive multidimensional integration routine for a vector of integrals. ACM Trans. Math. Softw. 17, 452\u2013456 (1991)","journal-title":"ACM Trans. Math. Softw."},{"key":"11_CR4","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.nuclphysb.2003.12.023","volume":"680","author":"T Binoth","year":"2004","unstructured":"Binoth, T., Heinrich, G.: Numerical evaluation of multi-loop integrals by sector decomposition. Nucl. Phys. B 680, 375 (2004). hep-ph\/0305234v1","journal-title":"Nucl. Phys. B"},{"key":"11_CR5","doi-asserted-by":"publisher","unstructured":"Borowka, S., Heinrich, G., Jahn, S., Jones, S.P., Kerner, M., Schlenk, J.: A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec. Comput. Phys. Commun. 240, 120\u2013137 (2019). Preprint: arXiv:1811.11720v1 [hep-ph]. https:\/\/arxiv.org\/abs\/1811.11720. https:\/\/doi.org\/10.1016\/j.cpc.2019.02.015","DOI":"10.1016\/j.cpc.2019.02.015"},{"key":"11_CR6","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1137\/0713071","volume":"13","author":"R Cranley","year":"1976","unstructured":"Cranley, R., Patterson, T.N.L.: Randomization of number theoretic methods for multiple integration. SIAM J. Numer. Anal. 13, 904\u2013914 (1976)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"11_CR7","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/0771-050X(76)90005-X","volume":"2","author":"L De Ridder","year":"1976","unstructured":"De Ridder, L., Van Dooren, P.: An adaptive algorithm for numerical integration over an n-dimensional cube. J. Comput. Appl. Math. 2(3), 207\u2013210 (1976)","journal-title":"J. Comput. Appl. Math."},{"key":"11_CR8","unstructured":"de Doncker, E., Almulihi, A., Yuasa, F.: High speed evaluation of loop integrals using lattice rules. J. Phys.: Conf. Series (JPCS) IOP Series 1085, 052005 (2018). http:\/\/iopscience.iop.org\/article\/10.1088\/1742-6596\/1085\/5\/052005"},{"key":"11_CR9","doi-asserted-by":"publisher","unstructured":"de Doncker, E., Almulihi, A., Yuasa, F.: Transformed lattice rules for Feynman loop integrals. J. Phys.: Conf. Series (JPCS) IOP Series 1136, 012002 (2018). https:\/\/doi.org\/10.1088\/1742-6596\/1136\/1\/012002","DOI":"10.1088\/1742-6596\/1136\/1\/012002"},{"key":"11_CR10","unstructured":"de Doncker, E., Genz, A., Gupta, A., Zanny, R.: Tools for distributed adaptive multivariate integration on NOW\u2019s: PARINT1.0 release. In: Supercomputing 1998 (1998)"},{"key":"11_CR11","series-title":"Mechanisms and Machine Science","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1007\/978-3-030-27053-7_62","volume-title":"Computational and Experimental Simulations in Engineering","author":"E de Doncker","year":"2020","unstructured":"de Doncker, E., Yuasa, F., Almulihi, A.: Efficient GPU integration for multi-loop Feynman diagrams with massless internal lines. In: Okada, H., Atluri, S.N. (eds.) ICCES 2019. MMS, vol. 75, pp. 737\u2013747. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-27053-7_62"},{"key":"11_CR12","doi-asserted-by":"crossref","unstructured":"de Doncker, E., Yuasa, F., Almulihi, A., Nakasato, N., Daisaka, H., Ishikawa, T.: Numerical multi-loop integration on heterogeneous many-core processors. In: The Journal of Physics: Conference Series (JPCS), IOP Series (ACAT 2019) (2019, to appear)","DOI":"10.1088\/1742-6596\/1525\/1\/012002"},{"key":"11_CR13","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.cpc.2017.11.001","volume":"224","author":"E de Doncker","year":"2018","unstructured":"de Doncker, E., Yuasa, F., Kato, K., Ishikawa, T., Kapenga, J., Olagbemi, O.: Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals. Comput. Phys. Commun. 224, 164\u2013185 (2018). https:\/\/doi.org\/10.1016\/j.cpc.2017.11.001","journal-title":"Comput. Phys. Commun."},{"key":"11_CR14","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/0771-050X(80)90039-X","volume":"6","author":"A Genz","year":"1980","unstructured":"Genz, A., Malik, A.: An adaptive algorithm for numerical integration over an n-dimensional rectangular region. J. Comput. Appl. Math. 6, 295\u2013302 (1980)","journal-title":"J. Comput. Appl. Math."},{"key":"11_CR15","unstructured":"Goose - GRAPE9-MPx - for goose version 1.5.0: K & F Computing Research Co. (2014). (in Japanese)"},{"key":"11_CR16","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1016\/j.cpc.2007.03.006","volume":"176","author":"T Hahn","year":"2007","unstructured":"Hahn, T.: Cuba - a library for multidimensional numerical integration. Comput. Phys. Commun. 176, 712\u2013713 (2007). https:\/\/doi.org\/10.1016\/j.cpc.2007.03.006","journal-title":"Comput. Phys. Commun."},{"issue":"2\u20133","key":"11_CR17","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/S0010-4655(98)00173-8","volume":"118","author":"T Hahn","year":"1999","unstructured":"Hahn, T., P\u00e9rez-Victoria, M.: Automated one-loop calculations in four and D dimensions. Comput. Phys. Commun. 118(2\u20133), 153\u2013165 (1999). hep-ph\/9807565","journal-title":"Comput. Phys. Commun."},{"key":"11_CR18","unstructured":"\u2019t Hooft, G., Veltman, M.: Scalar one-loop integrals. Nucl. Phys. B 153, 365\u2013401 (1979)"},{"key":"11_CR19","doi-asserted-by":"crossref","unstructured":"Ishikawa, T., Nakazawa, N., Yasui, Y.: Numerical calculation of the full two-loop electroweak corrections to muon (g-2). Phys. Rev. D 99, 073004 (2019)","DOI":"10.1103\/PhysRevD.99.073004"},{"key":"11_CR20","first-page":"1207","volume":"124","author":"NM Korobov","year":"1959","unstructured":"Korobov, N.M.: The approximate computation of multiple integrals. Dokl. Akad. Nauk SSSR 124, 1207\u20131210 (1959). (Russian)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"11_CR21","unstructured":"Korobov, N.M.: Properties and calculation of optimal coefficients. Doklady Akademii Nauk SSSR 132, 1009\u20131012 (1960). Russ. Eng. trans. Soviet Math. Doklady 1, 696\u2013700"},{"key":"11_CR22","doi-asserted-by":"crossref","unstructured":"L\u2019Equyer, P., Munger, D.: Algorithm 958: lattice builder: a general software tool for constructing rank-1 lattice rules. ACM Trans. Math. Softw. 42(2), 15:1\u201315:30 (2016)","DOI":"10.1145\/2754929"},{"key":"11_CR23","unstructured":"MPI. http:\/\/www-unix.mcs.anl.gov\/mpi\/index.html"},{"key":"11_CR24","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/BF01659720","volume":"86","author":"H Niederreiter","year":"1978","unstructured":"Niederreiter, H.: Existence of good lattice points in the sense of hlawka. Monatshefte f\u00fcr Mathematik 86, 203\u2013219 (1978)","journal-title":"Monatshefte f\u00fcr Mathematik"},{"key":"11_CR25","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1090\/S0025-5718-06-01785-6","volume":"75","author":"D Nuyens","year":"2006","unstructured":"Nuyens, D., Cools, R.: Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces. Math. Comput. 75, 903\u2013920 (2006)","journal-title":"Math. Comput."},{"key":"11_CR26","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.jco.2005.07.002","volume":"22","author":"D Nuyens","year":"2006","unstructured":"Nuyens, D., Cools, R.: Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points. J. Complex. 22, 4\u201328 (2006)","journal-title":"J. Complex."},{"key":"11_CR27","doi-asserted-by":"crossref","unstructured":"Olagbemi, O.E.: Scalable algorithms and hybrid parallelization strategies for multivariate integration with ParAdapt and CUDA. Ph.D. thesis, Western Michigan University (2019)","DOI":"10.1109\/CSCI49370.2019.00093"},{"key":"11_CR28","unstructured":"Olagbemi, O.E., de Doncker, E.: Scalable algorithms for multivariate integration with ParAdapt and CUDA. In: Proceedings of 2019 International Conference on Computational Science and Computational Intelligence. IEEE Computer Society (2019). https:\/\/american-cse.org\/csci2019\/pdfs\/CSCI2019-14dQVW1stBtXVEInMQPd3t\/558400a481\/558400a481.pdf"},{"key":"11_CR29","unstructured":"PEZY Computing\/Exascaler Inc. http:\/\/www.exascaler.co.jp\/"},{"key":"11_CR30","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61786-7","volume-title":"QUADPACK. A Subroutine Package for Automatic Integration","author":"R Piessens","year":"1983","unstructured":"Piessens, R., de Doncker, E., \u00dcberhuber, C.W., Kahaner, D.K.: QUADPACK. A Subroutine Package for Automatic Integration. Springer Series in Computational Mathematics, vol. 1. Springer, Heidelberg (1983). https:\/\/doi.org\/10.1007\/978-3-642-61786-7"},{"key":"11_CR31","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1145\/321864.321870","volume":"22","author":"JR Rice","year":"1975","unstructured":"Rice, J.R.: A metalgorithm for adaptive quadrature. J. Assoc. Comput. Mach. 22, 61\u201382 (1975)","journal-title":"J. Assoc. Comput. Mach."},{"key":"11_CR32","unstructured":"Ruijl, B., Herzog, F., Ueda, T., Vermaseren, J.A.M., Vogt, A.: The $${R}^*$$-operation and five loops calculations. In: 13th International Symposium on Radiative Corrections (2017)"},{"key":"11_CR33","doi-asserted-by":"publisher","unstructured":"Ruijl, B., Herzog, F., Ueda, T., Vermaseren, J.A.M., Vogt, A.: The $${R}^*$$-operation and combinatorial challenges at five loops. J. Phys.: Conf. Series (JPCS) IOP Series 1085, 052006 (2018). https:\/\/doi.org\/10.1088\/1742-6596\/1085\/5\/052006","DOI":"10.1088\/1742-6596\/1085\/5\/052006"},{"key":"11_CR34","unstructured":"Ruijl, B., Ueda, T., Vermaseren, J.A.M.: Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams. Technical report, 2017-019, Nikhef (2017). arXiv:1704.06650 [hep-ph]"},{"key":"11_CR35","volume-title":"CUDA by Example: An Introduction to General-Purpose GPU Programming","author":"J Sanders","year":"2010","unstructured":"Sanders, J., Kandrot, E.: CUDA by Example: An Introduction to General-Purpose GPU Programming. Pearson, London (2010)"},{"key":"11_CR36","first-page":"359","volume":"112","author":"A Sidi","year":"1993","unstructured":"Sidi, A.: A new variable transformation for numerical integration. Int. Ser. Numer. Math. 112, 359\u2013373 (1993)","journal-title":"Int. Ser. Numer. Math."},{"key":"11_CR37","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534723.001.0001","volume-title":"Lattice Methods for Multiple Integration","author":"I Sloan","year":"1994","unstructured":"Sloan, I., Joe, S.: Lattice Methods for Multiple Integration. Oxford University Press, Oxford (1994)"},{"issue":"3","key":"11_CR38","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s002110050244","volume":"75","author":"M Sugihara","year":"1997","unstructured":"Sugihara, M.: Optimality of the double exponential formula - functional analysis approach. Numer. Math. 75(3), 379\u2013395 (1997)","journal-title":"Numer. Math."},{"issue":"3","key":"11_CR39","doi-asserted-by":"publisher","first-page":"721","DOI":"10.2977\/prims\/1195192451","volume":"9","author":"H Takahasi","year":"1974","unstructured":"Takahasi, H., Mori, M.: Double exponential formulas for numerical integration. Publ. Res. Inst. Math. Sci. 9(3), 721\u2013741 (1974)","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"11_CR40","unstructured":"Torii, S., Ishikawa, H.: ZettaScaler: liquid immersion cooling manycore based supercomputer. Technical report, ExaScaler Inc., PEZY Computing K. K. (2017)"},{"key":"11_CR41","doi-asserted-by":"publisher","first-page":"91","DOI":"10.2307\/2002183","volume":"10","author":"P Wynn","year":"1956","unstructured":"Wynn, P.: On a device for computing the $$e_m(s_n)$$ transformation. Math. Tables Aids Comput. 10, 91\u201396 (1956)","journal-title":"Math. Tables Aids Comput."}],"container-title":["Lecture Notes in Computer Science","Computational Science and Its Applications \u2013 ICCSA 2020"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-58814-4_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T10:41:32Z","timestamp":1723718492000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-58814-4_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030588137","9783030588144"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-58814-4_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"3 October 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCSA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science and Its Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Cagliari","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 July 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 July 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccsa2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.iccsa.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Cyber chair 4","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1450","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"466","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"32","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"32% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.5","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Conference was held virtually due to COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}