{"id":"https://openalex.org/W2967946008","doi":"https://doi.org/10.1137/19m1283495","title":"Invariant Synchrony Subspaces of Sets of Matrices","display_name":"Invariant Synchrony Subspaces of Sets of Matrices","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2967946008","doi":"https://doi.org/10.1137/19m1283495","mag":"2967946008"},"language":"en","primary_location":{"id":"doi:10.1137/19m1283495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1283495","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1908.05797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080317531","display_name":"John M. Neuberger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John M. Neuberger","raw_affiliation_strings":["Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Statistics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028732014","display_name":"N\u00e1ndor Sieben","orcid":"https://orcid.org/0000-0003-0937-7448"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N\u00e1ndor Sieben","raw_affiliation_strings":["Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060973053","display_name":"James W. Swift","orcid":"https://orcid.org/0000-0002-9433-9456"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James W. Swift","raw_affiliation_strings":["Mathematics and Statistics"],"raw_orcid":"https://orcid.org/0000-0002-9433-9456","affiliations":[{"raw_affiliation_string":"Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02684287,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2","first_page":"964","last_page":"993"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9904999732971191,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9904999732971191,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/linear-subspace","display_name":"Linear subspace","score":0.8973102569580078},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6875540018081665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6702135801315308},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.5561639666557312},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5283841490745544},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5276167392730713},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.4867424964904785},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47928160429000854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3384819030761719}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8973102569580078},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6875540018081665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6702135801315308},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.5561639666557312},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5283841490745544},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5276167392730713},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.4867424964904785},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47928160429000854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3384819030761719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1283495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1283495","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1908.05797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.05797","pdf_url":"https://arxiv.org/pdf/1908.05797","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2967946008","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1908.05797.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1908.05797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1908.05797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1908.05797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.05797","pdf_url":"https://arxiv.org/pdf/1908.05797","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2967946008.pdf","grobid_xml":"https://content.openalex.org/works/W2967946008.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W206333455","https://openalex.org/W1040425825","https://openalex.org/W1963649370","https://openalex.org/W1963868144","https://openalex.org/W1969617456","https://openalex.org/W1985952348","https://openalex.org/W1990032525","https://openalex.org/W1990600049","https://openalex.org/W2009092607","https://openalex.org/W2023167697","https://openalex.org/W2039350867","https://openalex.org/W2045425785","https://openalex.org/W2046830398","https://openalex.org/W2052427582","https://openalex.org/W2055378049","https://openalex.org/W2057550646","https://openalex.org/W2057864643","https://openalex.org/W2062745455","https://openalex.org/W2091329515","https://openalex.org/W2101420429","https://openalex.org/W2108909796","https://openalex.org/W2111085435","https://openalex.org/W2117734515","https://openalex.org/W2119077806","https://openalex.org/W2129270652","https://openalex.org/W2151138800","https://openalex.org/W2162350861","https://openalex.org/W2169632627","https://openalex.org/W2184384388","https://openalex.org/W2505116898","https://openalex.org/W2510701725","https://openalex.org/W2562769762","https://openalex.org/W2580464589","https://openalex.org/W2601563346","https://openalex.org/W2798974679","https://openalex.org/W2883089381","https://openalex.org/W2902388117","https://openalex.org/W2912352567","https://openalex.org/W2912810145","https://openalex.org/W2922262644","https://openalex.org/W2962814064","https://openalex.org/W2963076354","https://openalex.org/W3099323801","https://openalex.org/W3100746818","https://openalex.org/W3125246284"],"related_works":["https://openalex.org/W3042379885","https://openalex.org/W2047075885","https://openalex.org/W1577833613","https://openalex.org/W1560592371","https://openalex.org/W2296927943","https://openalex.org/W3098122028","https://openalex.org/W895236684","https://openalex.org/W2945522869","https://openalex.org/W3080542661","https://openalex.org/W2280335180","https://openalex.org/W2903899205","https://openalex.org/W2962841052","https://openalex.org/W3037432765","https://openalex.org/W2008470094","https://openalex.org/W1994184519","https://openalex.org/W3022988846","https://openalex.org/W3009121313","https://openalex.org/W1734854739","https://openalex.org/W1563154602","https://openalex.org/W2964291417"],"abstract_inverted_index":{"A":[0],"synchrony":[1,40,82,108],"subspace":[2],"of":[3,11,27,37,48,51,58,65,72,80,88,106,125],"$\\mathbb{R}^{n}$":[4],"is":[5,114],"defined":[6],"by":[7,31],"setting":[8],"certain":[9],"components":[10],"the":[12,49,77,89,97,104,123],"vectors":[13],"equal":[14],"according":[15],"to":[16,122],"an":[17],"equivalence":[18],"relation.":[19],"Synchrony":[20],"subspaces":[21,41,83],"invariant":[22,39,81,107],"under":[23],"a":[24,34,52],"given":[25],"set":[26],"square":[28],"matrices":[29],"ordered":[30],"inclusion":[32],"form":[33],"lattice.":[35],"Applications":[36],"these":[38],"include":[42],"equitable":[43,46],"and":[44,62,69,84,99,112],"almost":[45],"partitions":[47,64,71],"vertices":[50],"graph":[53,59],"used":[54],"in":[55,132],"many":[56,86],"areas":[57],"theory,":[60],"balanced":[61],"exo-balanced":[63],"coupled":[66],"cell":[67],"networks,":[68],"coset":[70],"Cayley":[73],"graphs.":[74],"We":[75,91],"study":[76],"basic":[78],"properties":[79],"provide":[85],"examples":[87],"applications.":[90],"also":[92],"present":[93],"what":[94],"we":[95],"call":[96],"split":[98],"cir":[100],"algorithm":[101,113],"for":[102,117,129],"finding":[103],"lattice":[105],"subspaces.":[109],"Our":[110],"theory":[111],"further":[115],"generalized":[116],"nonsquare":[118],"matrices.":[119],"This":[120],"leads":[121],"notion":[124],"tactical":[126],"decompositions":[127],"studied":[128],"its":[130],"application":[131],"design":[133],"theory.":[134]},"counts_by_year":[],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
