{"id":"https://openalex.org/W2910807695","doi":"https://doi.org/10.1155/2019/4096981","title":"Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies","display_name":"Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2910807695","doi":"https://doi.org/10.1155/2019/4096981","mag":"2910807695"},"language":"en","primary_location":{"id":"doi:10.1155/2019/4096981","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4096981","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4096981.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/4096981.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029401729","display_name":"Yujuan Han","orcid":"https://orcid.org/0000-0002-1395-4247"},"institutions":[{"id":"https://openalex.org/I96733725","display_name":"Shanghai Maritime University","ror":"https://ror.org/04z7qrj66","country_code":"CN","type":"education","lineage":["https://openalex.org/I96733725"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yujuan Han","raw_affiliation_strings":["College of Information Engineering, Shanghai Maritime University, Shanghai"],"raw_orcid":"https://orcid.org/0000-0002-1395-4247","affiliations":[{"raw_affiliation_string":"College of Information Engineering, Shanghai Maritime University, Shanghai","institution_ids":["https://openalex.org/I96733725"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030103251","display_name":"Wenlian Lu","orcid":"https://orcid.org/0000-0003-1880-6240"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210085920","display_name":"Shanghai Institute for Science of Science","ror":"https://ror.org/004srxn73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210085920"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenlian Lu","raw_affiliation_strings":["Research & Educational Center for the Control Engineering of Translational Precision Medicine (R-ECCE-TPM), Dalian University of Technology, Dalian","School of Mathematical Sciences, Institute of Science and Technology for Brain-Inspired Intelligence, Shanghai Center for Mathematical Sciences, The Laboratory of Mathematics for Nonlinear Science and the Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai","State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing"],"raw_orcid":"https://orcid.org/0000-0003-1880-6240","affiliations":[{"raw_affiliation_string":"Research & Educational Center for the Control Engineering of Translational Precision Medicine (R-ECCE-TPM), Dalian University of Technology, Dalian","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Mathematical Sciences, Institute of Science and Technology for Brain-Inspired Intelligence, Shanghai Center for Mathematical Sciences, The Laboratory of Mathematics for Nonlinear Science and the Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai","institution_ids":["https://openalex.org/I4210085920","https://openalex.org/I24943067"]},{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062509066","display_name":"Tianping Chen","orcid":"https://orcid.org/0000-0001-6117-6673"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianping Chen","raw_affiliation_strings":["School of Computer Sciences and Mathematical Sciences, Fudan University, Shanghai"],"raw_orcid":"https://orcid.org/0000-0001-6117-6673","affiliations":[{"raw_affiliation_string":"School of Computer Sciences and Mathematical Sciences, Fudan University, Shanghai","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015235110","display_name":"Changkai Sun","orcid":"https://orcid.org/0000-0002-5010-5009"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changkai Sun","raw_affiliation_strings":["State Key Laboratory of Fine Chemicals, Dalian R&D Center for Stem Cell and Tissue Engineering, Dalian University of Technology, Dalian","Research & Educational Center for the Control Engineering of Translational Precision Medicine (R-ECCE-TPM), Dalian University of Technology, Dalian"],"raw_orcid":"https://orcid.org/0000-0002-5010-5009","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Fine Chemicals, Dalian R&D Center for Stem Cell and Tissue Engineering, Dalian University of Technology, Dalian","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Research & Educational Center for the Control Engineering of Translational Precision Medicine (R-ECCE-TPM), Dalian University of Technology, Dalian","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030103251"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I24943067","https://openalex.org/I27357992","https://openalex.org/I4210085920","https://openalex.org/I4210156404"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.7435,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7318927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2019","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9994999766349792,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.8480890989303589},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7664874196052551},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5836942195892334},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.577172577381134},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5553002953529358},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5521640777587891},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5496014356613159},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5306847095489502},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.4940109848976135},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.48591843247413635},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.4406953752040863},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.4357050061225891},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4246731698513031},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33374321460723877},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3204064667224884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3163796067237854},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2551703453063965},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17187651991844177},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06894713640213013}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8480890989303589},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7664874196052551},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5836942195892334},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.577172577381134},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5553002953529358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5521640777587891},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5496014356613159},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5306847095489502},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.4940109848976135},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.48591843247413635},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.4406953752040863},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.4357050061225891},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4246731698513031},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33374321460723877},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3204064667224884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3163796067237854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2551703453063965},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17187651991844177},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06894713640213013},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/4096981","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4096981","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4096981.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:4096981","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/4096981.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:f7d04bebbc594d8090e4e6997ddf1b2d","is_oa":false,"landing_page_url":"https://doaj.org/article/f7d04bebbc594d8090e4e6997ddf1b2d","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":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/4096981","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4096981","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4096981.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1753660729","display_name":"\u590d\u6742\u8026\u5408\u52a8\u6001\u7f51\u7edc\u7cfb\u7edf\u7684\u8026\u5408\u673a\u5236\u4e0e\u534f\u8c03\u884c\u4e3a\u63a7\u5236","funder_award_id":"61673119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2341053655","display_name":null,"funder_award_id":"91630314","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5277577257","display_name":"\u89e6\u53d1\u66f4\u65b0\u673a\u5236\u4e0b\u590d\u6742\u8026\u5408\u7cfb\u7edf\u7684\u62d3\u6251\u63a7\u5236\u7b97\u6cd5\u7684\u8bbe\u8ba1\u4e0e\u5206\u6790","funder_award_id":"61703271","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2910807695.pdf","grobid_xml":"https://content.openalex.org/works/W2910807695.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W84676611","https://openalex.org/W391578156","https://openalex.org/W1964647857","https://openalex.org/W1993300865","https://openalex.org/W1998059521","https://openalex.org/W2041833126","https://openalex.org/W2061264075","https://openalex.org/W2067056511","https://openalex.org/W2071121304","https://openalex.org/W2075489015","https://openalex.org/W2076041173","https://openalex.org/W2077508593","https://openalex.org/W2091412518","https://openalex.org/W2099175737","https://openalex.org/W2113127719","https://openalex.org/W2125668987","https://openalex.org/W2137340504","https://openalex.org/W2146890818","https://openalex.org/W2160643434","https://openalex.org/W2165744313","https://openalex.org/W2341325336","https://openalex.org/W2518104650","https://openalex.org/W2552971530","https://openalex.org/W2592775921","https://openalex.org/W2735914266","https://openalex.org/W2964136144","https://openalex.org/W3100384848","https://openalex.org/W4247555059"],"related_works":["https://openalex.org/W2363199028","https://openalex.org/W2033567934","https://openalex.org/W2782194400","https://openalex.org/W2365236566","https://openalex.org/W4206573252","https://openalex.org/W2023776467","https://openalex.org/W2987887460","https://openalex.org/W3196251681","https://openalex.org/W2230758337","https://openalex.org/W2011214451"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"how":[3],"to":[4,9,41,55,95,101,135,141,165],"choose":[5],"pinned":[6,105,147],"node":[7,65,106,148],"set":[8],"maximize":[10],"the":[11,30,51,59,62,72,81,87,91,103,109,117,124,131,136,143,146],"convergence":[12],"rate":[13],"of":[14,22,32,46,58,64,90,111,128,130,145],"multiagent":[15,69],"systems":[16,70],"under":[17],"digraph":[18],"topologies":[19],"in":[20,44,66],"cases":[21],"sufficiently":[23,33,112],"small":[24,34],"and":[25],"large":[26,113],"pinning":[27,35,67,114],"strength.":[28],"In":[29,108],"case":[31,110],"strength,":[36,115],"perturbation":[37],"methods":[38],"are":[39,153,158,163],"employed":[40],"derive":[42],"formulas":[43],"terms":[45],"asymptotics":[47],"that":[48,50,152],"indicate":[49],"left":[52,88],"eigenvector":[53],"corresponding":[54,94,134],"eigenvalue":[56,96],"zero":[57,97],"Laplacian":[60,92,132],"measures":[61],"importance":[63],"control":[68],"if":[71],"underlying":[73],"network":[74,82],"has":[75],"a":[76,120],"spanning":[77,85],"tree,":[78],"whereas":[79],"for":[80,155],"with":[83],"no":[84],"trees,":[86],"eigenvectors":[89],"matrix":[93],"can":[98],"be":[99],"used":[100,140],"select":[102],"optimal":[104],"set.":[107,149],"by":[116],"similar":[118],"method,":[119],"metric":[121],"based":[122],"on":[123],"smallest":[125],"real":[126],"part":[127],"eigenvalues":[129],"submatrix":[133],"unpinned":[137],"nodes":[138],"is":[139],"measure":[142],"stabilizability":[144],"Different":[150],"algorithms":[151],"applicable":[154],"different":[156],"scenarios":[157],"develped.":[159],"Several":[160],"numerical":[161],"simulations":[162],"given":[164],"verify":[166],"theoretical":[167],"results.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}