{"id":"https://openalex.org/W1979197687","doi":"https://doi.org/10.1145/1967701.1967721","title":"Hybridization domain construction using curvature estimation","display_name":"Hybridization domain construction using curvature estimation","publication_year":2011,"publication_date":"2011-04-12","ids":{"openalex":"https://openalex.org/W1979197687","doi":"https://doi.org/10.1145/1967701.1967721","mag":"1979197687"},"language":"en","primary_location":{"id":"doi:10.1145/1967701.1967721","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1967701.1967721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th international conference on Hybrid systems: computation and control","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101717722","display_name":"Thao Dang","orcid":"https://orcid.org/0000-0002-7629-3853"},"institutions":[{"id":"https://openalex.org/I4210156361","display_name":"Verimag","ror":"https://ror.org/05afmzm11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210156361","https://openalex.org/I4210159245","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Thao Dang","raw_affiliation_strings":["CNRS/VERIMAG, Grenoble, France"],"affiliations":[{"raw_affiliation_string":"CNRS/VERIMAG, Grenoble, France","institution_ids":["https://openalex.org/I4210156361","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026602498","display_name":"Romain Testylier","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156361","display_name":"Verimag","ror":"https://ror.org/05afmzm11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210156361","https://openalex.org/I4210159245","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Romain Testylier","raw_affiliation_strings":["VERIMAG, Grenoble, France"],"affiliations":[{"raw_affiliation_string":"VERIMAG, Grenoble, France","institution_ids":["https://openalex.org/I4210156361"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101717722"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210156361"],"apc_list":null,"apc_paid":null,"fwci":1.9152,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85572225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"123","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5751417875289917},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.542560338973999},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5333207845687866},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5095920562744141},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5083288550376892},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4625204801559448},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.46188682317733765},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.4520428776741028},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41931331157684326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39547455310821533},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3432243764400482},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33970075845718384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21804368495941162},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13181522488594055},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.08906170725822449},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08873370289802551}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5751417875289917},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.542560338973999},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5333207845687866},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5095920562744141},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5083288550376892},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4625204801559448},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.46188682317733765},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.4520428776741028},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41931331157684326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39547455310821533},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3432243764400482},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33970075845718384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21804368495941162},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13181522488594055},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.08906170725822449},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08873370289802551},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1967701.1967721","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1967701.1967721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th international conference on Hybrid systems: computation and control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1489501223","https://openalex.org/W1499853177","https://openalex.org/W1510285870","https://openalex.org/W1511213320","https://openalex.org/W1532859487","https://openalex.org/W1561445488","https://openalex.org/W1569146343","https://openalex.org/W1569692898","https://openalex.org/W1586568018","https://openalex.org/W1598855039","https://openalex.org/W1606189410","https://openalex.org/W1606658314","https://openalex.org/W1975630497","https://openalex.org/W2023285936","https://openalex.org/W2131441094","https://openalex.org/W2147936671","https://openalex.org/W2150874139","https://openalex.org/W2154679417","https://openalex.org/W2157834152","https://openalex.org/W2158451642","https://openalex.org/W2296389869","https://openalex.org/W4252959020","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2140816194","https://openalex.org/W59754694","https://openalex.org/W2164153476","https://openalex.org/W2774442510","https://openalex.org/W4375851942","https://openalex.org/W2142388326","https://openalex.org/W1996190563","https://openalex.org/W2059046304","https://openalex.org/W2144878166","https://openalex.org/W2295922520"],"abstract_inverted_index":{"This":[0,175],"paper":[1,130],"is":[2,18,33,72,83],"concerned":[3],"with":[4,171],"the":[5,38,44,64,68,90,112,115,120,148,194,198],"reachability":[6,65],"computation":[7,66],"for":[8,106,152,166],"non-linear":[9,22,169],"systems":[10,170],"using":[11,50],"hybridization.":[12],"The":[13,29],"main":[14,139,195],"idea":[15],"of":[16,40,43,63,114,147,155,163,197],"hybridization":[17,108,184],"to":[19,74,125,181,192],"approximate":[20,69],"a":[21,26,46,58,76,94,104,153],"vector":[23,31],"field":[24,32],"by":[25,35],"piecewise-affine":[27,30],"one.":[28],"defined":[34],"building":[36],"around":[37],"set":[39],"current":[41],"states":[42],"system":[45],"simplicial":[47,77],"domain":[48,78,149],"and":[49,61,117,136],"linear":[51],"interpolation":[52,96],"over":[53],"its":[54,203],"vertices.":[55],"To":[56],"achieve":[57],"good":[59],"time-efficiency":[60],"accuracy":[62],"on":[67,80,89,111],"system,":[70],"it":[71],"important":[73],"find":[75],"which,":[79],"one":[81],"hand,":[82,92],"as":[84,86,200,202],"large":[85],"possible":[87],"and,":[88],"other":[91],"guarantees":[93],"small":[95],"error.":[97],"In":[98,128],"our":[99],"previous":[100],"work[8],":[101],"we":[102,131,142,159],"proposed":[103],"method":[105,121,151],"constructing":[107],"domains":[109],"based":[110],"curvature":[113,164],"dynamics":[116],"showed":[118],"how":[119],"can":[122,177],"be":[123,179],"applied":[124],"quadratic":[126,156],"systems.":[127,157],"this":[129,133],"pursue":[132],"work":[134],"further":[135],"present":[137],"two":[138],"results.":[140],"First,":[141],"prove":[143],"an":[144,161],"optimality":[145],"property":[146],"construction":[150],"class":[154],"Second,":[158],"propose":[160],"algorithm":[162,199],"estimation":[165,176],"more":[167],"general":[168],"non-constant":[172],"Hessian":[173],"matrices.":[174],"then":[178],"used":[180],"determine":[182],"efficient":[183],"domains.":[185],"We":[186],"also":[187],"describe":[188],"some":[189],"experimental":[190],"results":[191],"illustrate":[193],"ideas":[196],"well":[201],"performance.":[204]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
