{"id":"https://openalex.org/W1489501223","doi":"https://doi.org/10.1007/3-540-46430-1_27","title":"Level Set Methods for Computation in Hybrid Systems","display_name":"Level Set Methods for Computation in Hybrid Systems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1489501223","doi":"https://doi.org/10.1007/3-540-46430-1_27","mag":"1489501223"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-46430-1_27","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-46430-1_27","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5086488324","display_name":"Ian M. Mitchell","orcid":"https://orcid.org/0000-0001-7053-441X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ian Mitchell","raw_affiliation_strings":["Scientific Computing and Computational Mathematics Program, Gates 2B, Stanford University, Stanford, CA, 94305"],"affiliations":[{"raw_affiliation_string":"Scientific Computing and Computational Mathematics Program, Gates 2B, Stanford University, Stanford, CA, 94305","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045155646","display_name":"Claire J. Tomlin","orcid":"https://orcid.org/0000-0003-3192-3185"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]},{"id":"https://openalex.org/I13805885","display_name":"Vaughn College of Aeronautics and Technology","ror":"https://ror.org/056e22e24","country_code":"US","type":"education","lineage":["https://openalex.org/I13805885"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Claire J. Tomlin","raw_affiliation_strings":["Department of Aeronautics and Astronautics, 250 Durand, Stanford University, Stanford, CA, 94305"],"affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics, 250 Durand, Stanford University, Stanford, CA, 94305","institution_ids":["https://openalex.org/I13805885","https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086488324"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":16.1519,"has_fulltext":false,"cited_by_count":232,"citation_normalized_percentile":{"value":0.9951156,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"310","last_page":"323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987999796867371,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.980388879776001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7622573375701904},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6865116357803345},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.617536723613739},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.6086390018463135},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.5951398611068726},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5904955863952637},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49224916100502014},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.45998615026474},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.41910967230796814},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39584943652153015},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3756411671638489},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3305169939994812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1962117850780487},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0757451057434082}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.980388879776001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7622573375701904},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6865116357803345},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.617536723613739},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6086390018463135},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.5951398611068726},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5904955863952637},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49224916100502014},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.45998615026474},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.41910967230796814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39584943652153015},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3756411671638489},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3305169939994812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1962117850780487},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0757451057434082},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-46430-1_27","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-46430-1_27","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W9012611","https://openalex.org/W1238092070","https://openalex.org/W1487586009","https://openalex.org/W1495543552","https://openalex.org/W1498285565","https://openalex.org/W1522448884","https://openalex.org/W1523071932","https://openalex.org/W1533617471","https://openalex.org/W1534714322","https://openalex.org/W1562722544","https://openalex.org/W1607870502","https://openalex.org/W1726255445","https://openalex.org/W1874725288","https://openalex.org/W1900127520","https://openalex.org/W1991113069","https://openalex.org/W1995691455","https://openalex.org/W2057462050","https://openalex.org/W2101508170","https://openalex.org/W2110065373","https://openalex.org/W2117374887","https://openalex.org/W2130519480","https://openalex.org/W2136545402","https://openalex.org/W2144965436","https://openalex.org/W2162196264","https://openalex.org/W2749408143","https://openalex.org/W2911432472","https://openalex.org/W2913760422","https://openalex.org/W4210875302","https://openalex.org/W4239369248","https://openalex.org/W4241127195"],"related_works":["https://openalex.org/W2357387646","https://openalex.org/W856973001","https://openalex.org/W2047831585","https://openalex.org/W4253760428","https://openalex.org/W3208672221","https://openalex.org/W2952920810","https://openalex.org/W4293477811","https://openalex.org/W2017676950","https://openalex.org/W78063724","https://openalex.org/W197679583"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":13}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}