{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T23:49:37Z","timestamp":1743032977280,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030799861"},{"type":"electronic","value":"9783030799878"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-79987-8_9","type":"book-chapter","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T23:05:05Z","timestamp":1625007905000},"page":"122-136","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Optimal Monomial Quadratization for ODE Systems"],"prefix":"10.1007","author":[{"given":"Andrey","family":"Bychkov","sequence":"first","affiliation":[]},{"given":"Gleb","family":"Pogudin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"issue":"2\u20133","key":"9_CR1","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10623-010-9364-1","volume":"55","author":"M Abreu","year":"2010","unstructured":"Abreu, M., Balbuena, C., Labbate, D.: Adjacency matrices of polarity graphs and of other C4-free graphs of large size. Des. Codes Crypt. 55(2\u20133), 221\u2013233 (2010). https:\/\/doi.org\/10.1007\/s10623-010-9364-1","journal-title":"Des. Codes Crypt."},{"key":"9_CR2","doi-asserted-by":"publisher","unstructured":"Alauddin, F.: Quadratization of ODEs: monomial vs. non-monomial. SIAM Undergraduate Res. Online 14 (2021). https:\/\/doi.org\/10.1137\/20s1360578","DOI":"10.1137\/20s1360578"},{"issue":"1","key":"9_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ipl.2014.07.008","volume":"115","author":"L Bulteau","year":"2015","unstructured":"Bulteau, L., Fertin, G., Rizzi, R., Vialette, S.: Some algorithmic results for [2]-sumset covers. Inf. Process. Lett. 115(1), 1\u20135 (2015). https:\/\/doi.org\/10.1016\/j.ipl.2014.07.008","journal-title":"Inf. Process. Lett."},{"key":"9_CR4","unstructured":"Carothers, D.C., Parker, G.E., Sochacki, J.S., Warne, P.G.: Some properties of solutions to polynomial systems of differential equations. Electron. J. Diff. Eqns. 2005(40), 1\u201317 (2005). http:\/\/emis.impa.br\/EMIS\/journals\/EJDE\/Volumes\/2005\/40\/carothers.pdf"},{"issue":"1","key":"9_CR5","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1002\/jgt.3190130107","volume":"13","author":"CRJ Clapham","year":"1989","unstructured":"Clapham, C.R.J., Flockhart, A., Sheehan, J.: Graphs without four-cycles. J. Graph Theor. 13(1), 29\u201347 (1989). https:\/\/doi.org\/10.1002\/jgt.3190130107","journal-title":"J. Graph Theor."},{"issue":"1\u20132","key":"9_CR6","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.jsv.2009.01.054","volume":"324","author":"B Cochelin","year":"2009","unstructured":"Cochelin, B., Vergez, C.: A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions. J. Sound Vib. 324(1\u20132), 243\u2013262 (2009). https:\/\/doi.org\/10.1016\/j.jsv.2009.01.054","journal-title":"J. Sound Vib."},{"key":"9_CR7","first-page":"215","volume":"1","author":"P Erd\u00f6s","year":"1966","unstructured":"Erd\u00f6s, P., R\u00e9nyi, A., S\u00f3s, V.: On a problem of graph theory. Studia Sci. Math. Hungar. 1, 215\u2013235 (1966)","journal-title":"Studia Sci. Math. Hungar."},{"key":"9_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1007\/978-3-642-02882-3_38","volume-title":"Computing and Combinatorics","author":"I Fagnot","year":"2009","unstructured":"Fagnot, I., Fertin, G., Vialette, S.: On finding small 2-generating sets. In: Ngo, H.Q. (ed.) COCOON 2009. LNCS, vol. 5609, pp. 378\u2013387. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-02882-3_38"},{"issue":"1","key":"9_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jctb.1996.0052","volume":"68","author":"Z F\u00fcredi","year":"1996","unstructured":"F\u00fcredi, Z.: On the number of edges of quadrilateral-free graphs. J. Comb. Theor. Ser. B 68(1), 1\u20136 (1996). https:\/\/doi.org\/10.1006\/jctb.1996.0052","journal-title":"J. Comb. Theor. Ser. B"},{"key":"9_CR10","unstructured":"Graham, R., Grotschel, M., Lov\u00e1sz, L.: Handbook of Combinatorics, vol. 2. North Holland (1995)"},{"issue":"9","key":"9_CR11","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1109\/TCAD.2011.2142184","volume":"30","author":"C Gu","year":"2011","unstructured":"Gu, C.: QLMOR: a projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 30(9), 1307\u20131320 (2011). https:\/\/doi.org\/10.1109\/TCAD.2011.2142184","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circuits Syst."},{"issue":"4","key":"9_CR12","doi-asserted-by":"publisher","first-page":"2827","DOI":"10.1007\/s11071-019-04989-5","volume":"98","author":"L Guillot","year":"2019","unstructured":"Guillot, L., Cochelin, B., Vergez, C.: A Taylor series-based continuation method for solutions of dynamical systems. Nonlinear Dyn. 98(4), 2827\u20132845 (2019). https:\/\/doi.org\/10.1007\/s11071-019-04989-5","journal-title":"Nonlinear Dyn."},{"key":"9_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/978-3-030-60327-4_7","volume-title":"Computational Methods in Systems Biology","author":"M Hemery","year":"2020","unstructured":"Hemery, M., Fages, F., Soliman, S.: On the complexity of quadratization for polynomial differential equations. In: Abate, A., Petrov, T., Wolf, V. (eds.) CMSB 2020. LNCS, vol. 12314, pp. 120\u2013140. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-60327-4_7"},{"issue":"4","key":"9_CR14","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1016\/j.jsv.2012.09.033","volume":"332","author":"S Karkar","year":"2013","unstructured":"Karkar, S., Cochelin, B., Vergez, C.: A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions: the case of non-polynomial nonlinearities. J. Sound Vib. 332(4), 968\u2013977 (2013). https:\/\/doi.org\/10.1016\/j.jsv.2012.09.033","journal-title":"J. Sound Vib."},{"key":"9_CR15","unstructured":"Kramer, B., Willcox, K.E.: Balanced truncation model reduction for lifted nonlinear systems (2019). https:\/\/arxiv.org\/abs\/1907.12084"},{"issue":"6","key":"9_CR16","doi-asserted-by":"publisher","first-page":"2297","DOI":"10.2514\/1.J057791","volume":"57","author":"B Kramer","year":"2019","unstructured":"Kramer, B., Willcox, K.E.: Nonlinear model order reduction via lifting transformations and proper orthogonal decomposition. AIAA J. 57(6), 2297\u20132307 (2019). https:\/\/doi.org\/10.2514\/1.J057791","journal-title":"AIAA J."},{"key":"9_CR17","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.disopt.2016.01.005","volume":"19","author":"DR Morrison","year":"2016","unstructured":"Morrison, D.R., Jacobson, S.H., Sauppe, J.J., Sewell, E.C.: Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning. Discret. Optim. 19, 79\u2013102 (2016). https:\/\/doi.org\/10.1016\/j.disopt.2016.01.005","journal-title":"Discret. Optim."},{"key":"9_CR18","unstructured":"OEIS Foundation Inc.: The on-line encyclopedia of integer sequences. http:\/\/oeis.org"},{"key":"9_CR19","first-page":"617","volume":"77","author":"MI Rabinovich","year":"1979","unstructured":"Rabinovich, M.I., Fabrikant, A.L.: Stochastic self-modulation of waves in nonequilibrium media. J. Exp. Theor. Phys. 77, 617\u2013629 (1979)","journal-title":"J. Exp. Theor. Phys."},{"key":"9_CR20","doi-asserted-by":"publisher","unstructured":"Ritschel, T.K., Wei\u00df, F., Baumann, M., Grundel, S.: Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation. at-Automatisierungstechnik 68(12), 1022\u20131034 (2020). https:\/\/doi.org\/10.1515\/auto-2020-0070","DOI":"10.1515\/auto-2020-0070"}],"container-title":["Lecture Notes in Computer Science","Combinatorial Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-79987-8_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T23:10:51Z","timestamp":1625008251000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-79987-8_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030799861","9783030799878"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-79987-8_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"30 June 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IWOCA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Combinatorial Algorithms","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ottawa, ON","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 July 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 July 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"32","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iwoca2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/iwoca2021.eecs.uottawa.ca\/","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":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"107","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":"38","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":"0","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":"36% - 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":"3.1","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":"9.1","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":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The workshop was held virtually.","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)"}}]}}