{"id":"https://openalex.org/W2798585023","doi":"https://doi.org/10.1109/tcsi.2018.2868277","title":"Circuit Theory in Projective Space and Homogeneous Circuit Models","display_name":"Circuit Theory in Projective Space and Homogeneous Circuit Models","publication_year":2018,"publication_date":"2018-10-05","ids":{"openalex":"https://openalex.org/W2798585023","doi":"https://doi.org/10.1109/tcsi.2018.2868277","mag":"2798585023"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2018.2868277","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2018.2868277","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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/1804.09643","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055431715","display_name":"Ricardo Riaza","orcid":"https://orcid.org/0000-0003-0868-4446"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Ricardo Riaza","raw_affiliation_strings":["Information Processing and Telecommunications Center, ETSI Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain","[Information Processing and Telecommunications Center, ETSI Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain]"],"raw_orcid":"https://orcid.org/0000-0003-0868-4446","affiliations":[{"raw_affiliation_string":"Information Processing and Telecommunications Center, ETSI Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"[Information Processing and Telecommunications Center, ETSI Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain]","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055431715"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07579925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"66","issue":"2","first_page":"463","last_page":"476"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944000244140625,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944000244140625,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9944000244140625,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5838661789894104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5398336052894592},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5009605884552002},{"id":"https://openalex.org/keywords/equivalent-circuit","display_name":"Equivalent circuit","score":0.4904281795024872},{"id":"https://openalex.org/keywords/nodal-analysis","display_name":"Nodal analysis","score":0.46900391578674316},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.46094781160354614},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4476173520088196},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.44071537256240845},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.4210923910140991},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34077972173690796},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33367919921875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.326238751411438},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2739299237728119},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.1618087887763977},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11859121918678284},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.11143302917480469}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5838661789894104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5398336052894592},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5009605884552002},{"id":"https://openalex.org/C23572009","wikidata":"https://www.wikidata.org/wiki/Q964981","display_name":"Equivalent circuit","level":3,"score":0.4904281795024872},{"id":"https://openalex.org/C105473148","wikidata":"https://www.wikidata.org/wiki/Q1203451","display_name":"Nodal analysis","level":2,"score":0.46900391578674316},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.46094781160354614},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4476173520088196},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.44071537256240845},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.4210923910140991},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34077972173690796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33367919921875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.326238751411438},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2739299237728119},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.1618087887763977},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11859121918678284},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.11143302917480469},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tcsi.2018.2868277","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2018.2868277","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1804.09643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.09643","pdf_url":"https://arxiv.org/pdf/1804.09643","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:2798585023","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.09643.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.1804.09643","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.09643","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:1804.09643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.09643","pdf_url":"https://arxiv.org/pdf/1804.09643","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W620608122","https://openalex.org/W629758729","https://openalex.org/W1542938076","https://openalex.org/W1608680948","https://openalex.org/W1881659028","https://openalex.org/W1966657789","https://openalex.org/W2000791724","https://openalex.org/W2004308928","https://openalex.org/W2035493017","https://openalex.org/W2076978869","https://openalex.org/W2156294472","https://openalex.org/W2226921407","https://openalex.org/W2242990183","https://openalex.org/W2478324200","https://openalex.org/W4235970972","https://openalex.org/W4237496336","https://openalex.org/W4297833479"],"related_works":["https://openalex.org/W2962917080","https://openalex.org/W2069715170","https://openalex.org/W2188188051","https://openalex.org/W2181796914","https://openalex.org/W2090918333","https://openalex.org/W2058493568","https://openalex.org/W2498201234","https://openalex.org/W1973846863","https://openalex.org/W2040309571","https://openalex.org/W1972481868","https://openalex.org/W1973931807","https://openalex.org/W2606403834","https://openalex.org/W2082151847","https://openalex.org/W2047129940","https://openalex.org/W2089464813","https://openalex.org/W2082053247","https://openalex.org/W2044264392","https://openalex.org/W2102564298","https://openalex.org/W2118337051","https://openalex.org/W2465936981"],"abstract_inverted_index":{"This":[0,81],"paper":[1],"presents":[2],"a":[3,19,25,51,58,86,190],"general":[4,88,191],"framework":[5],"for":[6,57,85,189,232],"linear":[7,99],"circuit":[8,34,93,150],"analysis":[9],"based":[10],"on":[11,78,115],"elementary":[12],"aspects":[13],"of":[14,28,74,91,147,159,193,198,211],"projective":[15],"geometry.":[16],"We":[17,239],"use":[18],"flexible":[20],"approach":[21,219],"in":[22,50,66,196,204,250],"which":[23,53,106,164],"no":[24],"priori":[26],"assignment":[27,40],"an":[29,39,156],"electrical":[30],"nature":[31],"to":[32,71,102,243],"the":[33,55,79,83,116,122,136,149,152,199,215,251,257],"branches":[35],"is":[36,41,155],"necessary.":[37],"Such":[38],"eventually":[42],"done":[43],"just":[44],"by":[45,95,227],"setting":[46],"certain":[47,113,233],"model":[48],"parameters,":[49],"way":[52,84],"avoids":[54],"need":[56],"distinction":[59],"between":[60],"voltage":[61],"and":[62,133,142,166,176,203,247],"current":[63],"sources":[64,246],"and,":[65],"addition,":[67],"makes":[68],"it":[69],"possible":[70],"get":[72],"rid":[73],"voltageor":[75],"current-control":[76],"assumptions":[77],"impedances.":[80],"paves":[82],"completely":[87],"m-dimensional":[89,157],"reduction":[90,120],"any":[92],"defined":[94],"m":[96],"twoterminal,":[97],"uncoupled":[98],"elements,":[100],"contrary":[101],"most":[103],"classical":[104,225],"methods":[105,226],"at":[107],"one":[108],"step":[109],"or":[110],"another":[111],"impose":[112],"restrictions":[114],"allowed":[117],"devices.":[118],"The":[119],"has":[121],"form":[123],"(316)":[124],"u":[125,154],"=":[126,172,178],"(":[127],"A":[128,132],"P)":[129],"s.":[130],"Here,":[131],"B":[134],"capture":[135],"graph":[137],"topology,":[138],"whereas":[139],"P,":[140],"Q,":[141],"s":[143],"comprise":[144],"homogeneous":[145,229,237,252],"descriptions":[146,230],"all":[148],"elements;":[151],"unknown":[153],"vector":[158],"(say)":[160],"\u201cseed\u201d":[161],"variables":[162],"from":[163],"currents":[165],"voltages":[167],"are":[168,184],"obtained":[169],"as":[170],"i":[171],"Pu":[173],"-":[174],"Qs":[175],"v":[177],"Qu":[179],"+":[180],"Ps.":[181],"Computational":[182],"implementations":[183],"straightforward.":[185],"These":[186],"models":[187],"allow":[188],"characterization":[192],"non-degenerate":[194],"configurations":[195],"terms":[197],"multihomogeneous":[200],"Kirchhoff":[201],"polynomial,":[202],"this":[205],"direction,":[206],"we":[207],"present":[208],"some":[209],"results":[210],"independent":[212],"interest":[213],"involving":[214],"matrix-tree":[216],"theorem.":[217],"Our":[218],"can":[220],"be":[221],"easily":[222],"combined":[223],"with":[224],"using":[228],"only":[231],"branches,":[234],"yielding":[235],"partially":[236],"models.":[238],"also":[240],"indicate":[241],"how":[242],"accommodate":[244],"controlled":[245],"coupled":[248],"devices":[249],"framework.":[253],"Several":[254],"examples":[255],"illustrate":[256],"results.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}