{"id":"https://openalex.org/W3018058094","doi":"https://doi.org/10.1109/lsp.2020.2990086","title":"Diffusion LMS With Communication Delays: Stability and Performance Analysis","display_name":"Diffusion LMS With Communication Delays: Stability and Performance Analysis","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3018058094","doi":"https://doi.org/10.1109/lsp.2020.2990086","mag":"3018058094"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2020.2990086","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2020.2990086","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.08881","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Fei Hua","orcid":"https://orcid.org/0000-0003-0195-0422"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I4210119200","display_name":"Institut de Recherche sur le Cancer et le Vieillissement de Nice","ror":"https://ror.org/01td3kv81","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I201841394","https://openalex.org/I4210096427","https://openalex.org/I4210119200"]},{"id":"https://openalex.org/I4210126779","display_name":"Observatoire de la C\u00f4te d\u2019Azur","ror":"https://ror.org/039fj2469","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210126779"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Fei Hua","raw_affiliation_strings":["School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an, China","Universit\u00e9 C\u00f4te d\u2019Azur, OCA, CNRS, 06108 Nice, France"],"raw_orcid":"https://orcid.org/0000-0003-0195-0422","affiliations":[{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d\u2019Azur, OCA, CNRS, 06108 Nice, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210119200","https://openalex.org/I4210126779"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Roula Nassif","orcid":"https://orcid.org/0000-0001-9663-8559"},"institutions":[{"id":"https://openalex.org/I98635879","display_name":"American University of Beirut","ror":"https://ror.org/04pznsd21","country_code":"LB","type":"education","lineage":["https://openalex.org/I98635879"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Roula Nassif","raw_affiliation_strings":["American University of Beirut, Beirut, Lebanon"],"raw_orcid":"https://orcid.org/0000-0001-9663-8559","affiliations":[{"raw_affiliation_string":"American University of Beirut, Beirut, Lebanon","institution_ids":["https://openalex.org/I98635879"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Cedric Richard","orcid":"https://orcid.org/0000-0003-2890-141X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210119200","display_name":"Institut de Recherche sur le Cancer et le Vieillissement de Nice","ror":"https://ror.org/01td3kv81","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I201841394","https://openalex.org/I4210096427","https://openalex.org/I4210119200"]},{"id":"https://openalex.org/I4210126779","display_name":"Observatoire de la C\u00f4te d\u2019Azur","ror":"https://ror.org/039fj2469","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210126779"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cedric Richard","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d\u2019Azur, OCA, CNRS, 06108 Nice, France"],"raw_orcid":"https://orcid.org/0000-0003-2890-141X","affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d\u2019Azur, OCA, CNRS, 06108 Nice, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210119200","https://openalex.org/I4210126779"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Haiyan Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiyan Wang","raw_affiliation_strings":["School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi\u2019an, China","School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ali H. Sayed","orcid":"https://orcid.org/0000-0002-5125-5519"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ali H. Sayed","raw_affiliation_strings":["School of Engineering, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-5125-5519","affiliations":[{"raw_affiliation_string":"School of Engineering, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8556,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.90943219,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":null,"first_page":"730","last_page":"734"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.002400000113993883,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.0020000000949949026,"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/stability","display_name":"Stability (learning theory)","score":0.7728999853134155},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6686000227928162},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6661999821662903},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.5724999904632568},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4271000027656555},{"id":"https://openalex.org/keywords/transient-analysis","display_name":"Transient analysis","score":0.4194999933242798},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.41290000081062317},{"id":"https://openalex.org/keywords/least-mean-squares-filter","display_name":"Least mean squares filter","score":0.40400001406669617}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7728999853134155},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6686000227928162},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6661999821662903},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.5724999904632568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5544000267982483},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4271000027656555},{"id":"https://openalex.org/C2989121073","wikidata":"https://www.wikidata.org/wiki/Q1309019","display_name":"Transient analysis","level":3,"score":0.4194999933242798},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.41290000081062317},{"id":"https://openalex.org/C32617633","wikidata":"https://www.wikidata.org/wiki/Q1426666","display_name":"Least mean squares filter","level":3,"score":0.40400001406669617},{"id":"https://openalex.org/C52970973","wikidata":"https://www.wikidata.org/wiki/Q2497134","display_name":"Adaptive system","level":2,"score":0.3862999975681305},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35659998655319214},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.32249999046325684},{"id":"https://openalex.org/C3020028006","wikidata":"https://www.wikidata.org/wiki/Q9158","display_name":"Electronic mail","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C143141573","wikidata":"https://www.wikidata.org/wiki/Q7450971","display_name":"Sense (electronics)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C85761212","wikidata":"https://www.wikidata.org/wiki/Q1974593","display_name":"Transient response","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C192126672","wikidata":"https://www.wikidata.org/wiki/Q1068715","display_name":"Telecommunications network","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C2986587452","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical analysis","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2556999921798706},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.25029999017715454}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/lsp.2020.2990086","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2020.2990086","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.08881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.08881","pdf_url":"https://arxiv.org/pdf/2004.08881","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":"pmh:oai:HAL:hal-03347250v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03347250","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2020, 27, pp.730 - 734. ⟨10.1109/lsp.2020.2990086⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:infoscience.epfl.ch:278174","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/169506","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.08881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.08881","pdf_url":"https://arxiv.org/pdf/2004.08881","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":[{"id":"https://openalex.org/G2113015678","display_name":"3IA C\u00f4te d'Azur","funder_award_id":"ANR-19-P3IA-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2262987027","display_name":null,"funder_award_id":"61671386","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4602883951","display_name":null,"funder_award_id":"205121-184999","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7302324134","display_name":"Distributed adaptation and learning over graph signals","funder_award_id":"ANR-19-CE48-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8051732561","display_name":null,"funder_award_id":"61901385","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8183348528","display_name":"\u4e92\u8865\u7801\u952e\u63a7\u9ad8\u901f\u6c34\u58f0\u6269\u9891\u901a\u4fe1\u65b0\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61771396","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W338925043","https://openalex.org/W1988795359","https://openalex.org/W2024307985","https://openalex.org/W2042664989","https://openalex.org/W2046767029","https://openalex.org/W2075677880","https://openalex.org/W2076428552","https://openalex.org/W2089855386","https://openalex.org/W2107396783","https://openalex.org/W2111857756","https://openalex.org/W2121820607","https://openalex.org/W2129906637","https://openalex.org/W2141788746","https://openalex.org/W2154834860","https://openalex.org/W2155723880","https://openalex.org/W2160643434","https://openalex.org/W2161305486","https://openalex.org/W2169167445","https://openalex.org/W2342863306","https://openalex.org/W2402585016","https://openalex.org/W2605994693","https://openalex.org/W2789890080","https://openalex.org/W2962833434","https://openalex.org/W2962907301","https://openalex.org/W2963395095","https://openalex.org/W2963544917","https://openalex.org/W2963866791","https://openalex.org/W2964165783","https://openalex.org/W2964240094","https://openalex.org/W3021272668","https://openalex.org/W4238850922","https://openalex.org/W4239240501","https://openalex.org/W6674727558","https://openalex.org/W6684139056"],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,20,31,37,45,48,64,68,72,90,103,108,117],"problem":[3],"of":[4,71,89,107],"distributed":[5],"estimation":[6],"over":[7],"adaptive":[8],"networks":[9],"where":[10,25],"communication":[11,32],"delays":[12,46,98],"exist":[13],"between":[14],"nodes.":[15],"In":[16],"particular,":[17],"we":[18,57],"investigate":[19],"diffusion":[21,73,95,109],"Least-Mean-Square":[22],"(LMS)":[23],"strategy":[24],"delayed":[26,76],"intermediate":[27],"estimates":[28],"(due":[29],"to":[30],"channels)":[33],"are":[34,86],"employed":[35],"during":[36],"combination":[38],"step.":[39],"One":[40,88],"important":[41],"question":[42],"is:":[43],"Do":[44],"affect":[47],"stability":[49],"condition":[50,106],"and":[51,66,81],"performance?":[52],"To":[53],"answer":[54],"this":[55],"question,":[56],"conduct":[58],"a":[59],"detailed":[60],"performance":[61],"analysis":[62],"in":[63,67],"mean":[65],"mean-square-error":[69],"sense":[70],"LMS":[74,96,110],"with":[75,97],"estimates.":[77],"Stability":[78],"conditions,":[79],"transient":[80],"steady-state":[82],"mean-square-deviation":[83],"(MSD)":[84],"expressions":[85],"provided.":[87],"main":[91],"findings":[92],"is":[93],"that":[94],"can":[99],"still":[100],"converge":[101],"under":[102],"same":[104],"step-sizes":[105],"without":[111],"delays.":[112],"Finally,":[113],"simulation":[114],"results":[115],"illustrate":[116],"theoretical":[118],"findings.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2020-05-01T00:00:00"}