{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:19:16Z","timestamp":1750220356416,"version":"3.41.0"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p>Transformation of a polynomial ODE system to a special quadratic form has been successfully used recently as a preprocessing step for model order reduction methods. However, to the best of our knowledge, there has been no practical algorithm for performing this step automatically with any optimality guarantees.<\/jats:p>\n          <jats:p>We present an algorithm that, given a system of polynomial ODEs, finds a transformation into a quadratic ODE system by introducing new variables which are monomials of the original variables. The algorithm is guaranteed to produce an optimal transformation of this form. The algorithm is implemented, and we demonstrate it on examples from the literature.<\/jats:p>","DOI":"10.1145\/3457341.3457350","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T22:07:02Z","timestamp":1615846022000},"page":"119-123","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal monomial quadratization for ODE systems"],"prefix":"10.1145","volume":"54","author":[{"given":"Andrey","family":"Bychkov","sequence":"first","affiliation":[{"name":"National Research University, Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gleb","family":"Pogudin","sequence":"additional","affiliation":[{"name":"LIX, CNRS, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404011430"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/trans2\/200\/09"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2011.2142184"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3272-5"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(85)90084-0"},{"key":"e_1_2_1_6_1","volume-title":"Balanced truncation model reduction for lifted nonlinear systems","author":"Kramer Boris","year":"2019","unstructured":"Boris Kramer and Karen E. Willcox . Balanced truncation model reduction for lifted nonlinear systems , 2019 . Boris Kramer and Karen E. Willcox. Balanced truncation model reduction for lifted nonlinear systems, 2019."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.2514\/1.J057791"},{"key":"e_1_2_1_8_1","first-page":"617","article-title":"Stochastic self-modulation of waves in nonequilibrium media","volume":"77","author":"Rabinovich Mikhail I.","year":"1979","unstructured":"Mikhail I. Rabinovich and Anatoly L. Fabrikant . Stochastic self-modulation of waves in nonequilibrium media . J. Exp. Theor. Phys , 77 : 617 -- 629 , 1979 . Mikhail I. Rabinovich and Anatoly L. Fabrikant. Stochastic self-modulation of waves in nonequilibrium media. J. Exp. Theor. Phys, 77:617--629, 1979.","journal-title":"J. Exp. Theor. Phys"},{"key":"e_1_2_1_9_1","volume-title":"Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation","author":"Ritschel Tobias K. S.","year":"2020","unstructured":"Tobias K. S. Ritschel , Frances Wei\u00df , Manuel Baumann , and Sara Grundel . Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation , 2020 . Tobias K. S. Ritschel, Frances Wei\u00df, Manuel Baumann, and Sara Grundel. Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation, 2020."},{"key":"e_1_2_1_10_1","volume-title":"Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Physical review letters, 94(4):048101","author":"Shilnikov Andrey","year":"2005","unstructured":"Andrey Shilnikov and Gennady Cymbalyuk . Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Physical review letters, 94(4):048101 , 2005 . Andrey Shilnikov and Gennady Cymbalyuk. Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Physical review letters, 94(4):048101, 2005."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3457341.3457350","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3457341.3457350","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:17:19Z","timestamp":1750191439000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3457341.3457350"}},"subtitle":["extended abstract"],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1145\/3457341.3457350"],"URL":"https:\/\/doi.org\/10.1145\/3457341.3457350","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2020,9]]},"assertion":[{"value":"2021-03-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}