{"id":"https://openalex.org/W2010140892","doi":"https://doi.org/10.1155/2009/646975","title":"Cellular Neural Networks for NP-Hard Optimization","display_name":"Cellular Neural Networks for NP-Hard Optimization","publication_year":2009,"publication_date":"2009-01-18","ids":{"openalex":"https://openalex.org/W2010140892","doi":"https://doi.org/10.1155/2009/646975","mag":"2010140892"},"language":"en","primary_location":{"id":"doi:10.1155/2009/646975","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2009/646975","pdf_url":"https://asp-eurasipjournals.springeropen.com/counter/pdf/10.1155/2009/646975","source":{"id":"https://openalex.org/S35920007","display_name":"EURASIP Journal on Advances in Signal Processing","issn_l":"1687-6172","issn":["1687-6172","1687-6180"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Advances in Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://asp-eurasipjournals.springeropen.com/counter/pdf/10.1155/2009/646975","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038398506","display_name":"M\u00e1ria Ercsey-Ravasz","orcid":"https://orcid.org/0000-0003-4428-9953"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M\u00e1ria Ercsey-Ravasz","raw_affiliation_strings":["Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA","Department of Physics, University of Notre Dame, Notre Dame, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Physics, University of Notre Dame, Notre Dame, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110250070","display_name":"Tam\u00e1s Roska","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117195","display_name":"Institute for Computer Science and Control","ror":"https://ror.org/0249v7n71","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I31882830","display_name":"P\u00e1zm\u00e1ny P\u00e9ter Catholic University","ror":"https://ror.org/05v9kya57","country_code":"HU","type":"education","lineage":["https://openalex.org/I31882830"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Tam\u00e1s Roska","raw_affiliation_strings":["Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA-SZTAKI), 1111, Budapest, Hungary","Faculty of Information Technology, P\u00e9ter P\u00e1zmany Catholic University, 1083, Budapest, Hungary","Faculty of Information Technology, P\u00e9ter P\u00e1zmany Catholic University, Budapest, Hungary","Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA-SZTAKI), Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA-SZTAKI), 1111, Budapest, Hungary","institution_ids":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Faculty of Information Technology, P\u00e9ter P\u00e1zmany Catholic University, 1083, Budapest, Hungary","institution_ids":["https://openalex.org/I31882830"]},{"raw_affiliation_string":"Faculty of Information Technology, P\u00e9ter P\u00e1zmany Catholic University, Budapest, Hungary","institution_ids":["https://openalex.org/I31882830"]},{"raw_affiliation_string":"Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA-SZTAKI), Budapest, Hungary","institution_ids":["https://openalex.org/I4210117195","https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062113881","display_name":"Zolt\u00e1n N\u00e9da","orcid":"https://orcid.org/0000-0002-7319-5123"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n N\u00e9da","raw_affiliation_strings":["Faculty of Physics, Babe\u015f-Bolyai University, 400084, Cluj-Napoca, Romania","Faculty of Physics, Babe\u015f-Bolyai University, Cluj-Napoca, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Babe\u015f-Bolyai University, 400084, Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]},{"raw_affiliation_string":"Faculty of Physics, Babe\u015f-Bolyai University, Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038398506"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":{"value":1140,"currency":"GBP","value_usd":1398},"apc_paid":{"value":1140,"currency":"GBP","value_usd":1398},"fwci":1.4511,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82798953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2009","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9951000213623047,"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/computer-science","display_name":"Computer science","score":0.8153589963912964},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.7149606943130493},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.5218526124954224},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4824255406856537},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4710775911808014},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36865758895874023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32142072916030884},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3198435604572296}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8153589963912964},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.7149606943130493},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.5218526124954224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4824255406856537},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4710775911808014},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36865758895874023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32142072916030884},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3198435604572296}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2009/646975","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2009/646975","pdf_url":"https://asp-eurasipjournals.springeropen.com/counter/pdf/10.1155/2009/646975","source":{"id":"https://openalex.org/S35920007","display_name":"EURASIP Journal on Advances in Signal Processing","issn_l":"1687-6172","issn":["1687-6172","1687-6180"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Advances in Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0802.1150","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0802.1150","pdf_url":"https://arxiv.org/pdf/0802.1150","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"pmh:oai:doaj.org/article:0d8dcab9ec414fa0b8042cdffa35fb49","is_oa":false,"landing_page_url":"https://doaj.org/article/0d8dcab9ec414fa0b8042cdffa35fb49","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EURASIP Journal on Advances in Signal Processing, Vol 2009 (2009)","raw_type":"article"},{"id":"pmh:oai:eprints.sztaki.hu:5875","is_oa":false,"landing_page_url":"http://eprints.sztaki.hu/5875/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401907","display_name":"SZTAKI Publication Repository (Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I7597260","host_organization_name":"Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I7597260"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ISI Article"}],"best_oa_location":{"id":"doi:10.1155/2009/646975","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2009/646975","pdf_url":"https://asp-eurasipjournals.springeropen.com/counter/pdf/10.1155/2009/646975","source":{"id":"https://openalex.org/S35920007","display_name":"EURASIP Journal on Advances in Signal Processing","issn_l":"1687-6172","issn":["1687-6172","1687-6180"],"is_oa":true,"is_in_doaj":true,"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Advances in Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.5899999737739563}],"awards":[{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320334927","display_name":"Consiliul National al Cercetarii Stiintifice","ror":"https://ror.org/035rrps97"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2010140892.pdf","grobid_xml":"https://content.openalex.org/works/W2010140892.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1527520754","https://openalex.org/W1535832430","https://openalex.org/W1570173134","https://openalex.org/W1908449472","https://openalex.org/W1967084746","https://openalex.org/W2013520638","https://openalex.org/W2022820481","https://openalex.org/W2024060531","https://openalex.org/W2030405774","https://openalex.org/W2057127289","https://openalex.org/W2066039621","https://openalex.org/W2086333739","https://openalex.org/W2106548008","https://openalex.org/W2117148079","https://openalex.org/W2124214878","https://openalex.org/W2128099001","https://openalex.org/W2128480563","https://openalex.org/W2130416988","https://openalex.org/W2136913207","https://openalex.org/W2151162785","https://openalex.org/W2160121923","https://openalex.org/W2167267517","https://openalex.org/W2167295983","https://openalex.org/W2169938874","https://openalex.org/W2326812357"],"related_works":["https://openalex.org/W2067147118","https://openalex.org/W2392013129","https://openalex.org/W2025427163","https://openalex.org/W2113777112","https://openalex.org/W2884994975","https://openalex.org/W2357727223","https://openalex.org/W2119109137","https://openalex.org/W2117878353","https://openalex.org/W2153172467","https://openalex.org/W2787670184"],"abstract_inverted_index":{"A":[0],"cellular":[1],"neural/nonlinear":[2],"network":[3],"(CNN)":[4],"is":[5,26],"used":[6],"for":[7],"NP-hard":[8],"optimization.":[9],"We":[10],"prove":[11],"that":[12,44],"a":[13,31,51,61],"CNN":[14,101],"in":[15,141],"which":[16],"the":[17,27,38,55,74,85,93,97,120,130],"parameters":[18,122],"of":[19,30,40,54,119,129],"all":[20],"cells":[21],"can":[22,70],"be":[23,71,104],"separately":[24],"controlled":[25],"analog":[28],"correspondent":[29],"two-dimensional":[32],"Ising-type":[33],"(Edwards-Anderson)":[34],"spin-glass":[35,56],"system.":[36],"Using":[37],"properties":[39],"CNN,":[41],"we":[42,132],"show":[43],"one":[45],"single":[46],"operation":[47],"(template)":[48],"always":[49],"yields":[50],"local":[52,117],"minimum":[53],"energy":[57],"function.":[58],"This":[59],"way,":[60],"very":[62],"fast":[63],"optimization":[64],"method,":[65],"similar":[66],"to":[67],"simulated":[68,94],"annealing,":[69],"built.":[72],"Estimating":[73],"simulation":[75],"time":[76,86],"needed":[77,87],"on":[78,88,127],"CNN-based":[79],"computers,":[80],"and":[81],"comparing":[82],"it":[83],"with":[84],"normal":[89],"digital":[90,107],"computers":[91,102,108],"using":[92],"annealing":[95],"algorithm,":[96],"results":[98],"are":[99],"astonishing.":[100],"could":[103,136],"faster":[105],"than":[106],"already":[109,124],"at":[110],"10":[111,113],"\u00d7":[112],"lattice":[114],"sizes.":[115],"The":[116],"control":[118],"template":[121],"was":[123],"partially":[125],"realized":[126],"some":[128],"hardwares,":[131],"think":[133],"this":[134,142],"study":[135],"further":[137],"motivate":[138],"their":[139],"development":[140],"direction.":[143]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}