{"id":"https://openalex.org/W795865546","doi":null,"title":"Nonlinear dynamics of pattern recognition and optimization","display_name":"Nonlinear dynamics of pattern recognition and optimization","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W795865546","mag":"795865546"},"language":"en","primary_location":{"id":"pmh:oai:dspace.lboro.ac.uk:2134/10694","doi":null,"is_oa":true,"landing_page_url":"https://dspace.lboro.ac.uk/2134/10694","pdf_url":"https://dspace.lboro.ac.uk/2134/10694","source":{"id":"https://openalex.org/S4306401023","display_name":"Loughborough University Institutional Repository (Loughborough University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143804889","host_organization_name":"Loughborough University","host_organization_lineage":["https://openalex.org/I143804889"],"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":"","raw_type":"Thesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.lboro.ac.uk/2134/10694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005646463","display_name":"Christopher J. Marsden","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christopher J. Marsden","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5005646463"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9955999851226807,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9955999851226807,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.0012000000569969416,"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"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.0008999999845400453,"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/velocity-field","display_name":"velocity field","score":0.5830000042915344},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"pattern recognition","score":0.6930000185966492},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"unsupervised learning","score":0.7829999923706055},{"id":"https://openalex.org/keywords/hopfield-neural-network","display_name":"Hopfield neural network","score":0.7549999952316284},{"id":"https://openalex.org/keywords/probabilistic-neural-network","display_name":"probabilistic neural network","score":0.9639999866485596},{"id":"https://openalex.org/keywords/density-estimation","display_name":"density estimation","score":0.5740000009536743},{"id":"https://openalex.org/keywords/strange-attractors","display_name":"chaotic attractors","score":0.6930000185966492},{"id":"https://openalex.org/keywords/global-optimization","display_name":"global optimization","score":0.8240000009536743},{"id":"https://openalex.org/keywords/phase-space-geometry","display_name":"phase space geometry","score":0.5690000057220459}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6443151235580444},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5815481543540955},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5643646121025085},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5550188422203064},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5301262736320496},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5181171298027039},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5036665797233582},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4768434762954712},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4654674530029297},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4345894753932953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28121742606163025},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15701323747634888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09400990605354309},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:dspace.lboro.ac.uk:2134/10694","doi":null,"is_oa":true,"landing_page_url":"https://dspace.lboro.ac.uk/2134/10694","pdf_url":"https://dspace.lboro.ac.uk/2134/10694","source":{"id":"https://openalex.org/S4306401023","display_name":"Loughborough University Institutional Repository (Loughborough University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143804889","host_organization_name":"Loughborough University","host_organization_lineage":["https://openalex.org/I143804889"],"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":"","raw_type":"Thesis"},{"id":"pmh:oai:figshare.com:article/9375779","doi":null,"is_oa":true,"landing_page_url":"https://figshare.com/articles/Nonlinear_dynamics_of_pattern_recognition_and_optimization/9375779","pdf_url":"https://figshare.com/articles/Nonlinear_dynamics_of_pattern_recognition_and_optimization/9375779","source":{"id":"https://openalex.org/S4306402585","display_name":"Loughborough University Research Repository (Loughborough University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143804889","host_organization_name":"Loughborough University","host_organization_lineage":["https://openalex.org/I143804889"],"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":"","raw_type":"Thesis"},{"id":"mag:795865546","doi":null,"is_oa":false,"landing_page_url":"https://repository.lboro.ac.uk/articles/Nonlinear_dynamics_of_pattern_recognition_and_optimization/9375779/files/16986905.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:dspace.lboro.ac.uk:2134/10694","doi":null,"is_oa":true,"landing_page_url":"https://dspace.lboro.ac.uk/2134/10694","pdf_url":"https://dspace.lboro.ac.uk/2134/10694","source":{"id":"https://openalex.org/S4306401023","display_name":"Loughborough University Institutional Repository (Loughborough University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143804889","host_organization_name":"Loughborough University","host_organization_lineage":["https://openalex.org/I143804889"],"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":"","raw_type":"Thesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W795865546.pdf","grobid_xml":"https://content.openalex.org/works/W795865546.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W31001017","https://openalex.org/W562664693","https://openalex.org/W569610657","https://openalex.org/W1483766842","https://openalex.org/W1493856275","https://openalex.org/W1515909025","https://openalex.org/W1536929369","https://openalex.org/W1582366873","https://openalex.org/W1587522179","https://openalex.org/W1587859748","https://openalex.org/W1597286183","https://openalex.org/W1826987655","https://openalex.org/W1964053068","https://openalex.org/W1964168965","https://openalex.org/W1964703118","https://openalex.org/W1967755877","https://openalex.org/W1973886875","https://openalex.org/W1983617554","https://openalex.org/W1989097268","https://openalex.org/W1991408165","https://openalex.org/W1993681705","https://openalex.org/W1995341919","https://openalex.org/W2000420612","https://openalex.org/W2002445862","https://openalex.org/W2004417280","https://openalex.org/W2009375605","https://openalex.org/W2010526455","https://openalex.org/W2013085151","https://openalex.org/W2017277760","https://openalex.org/W2022107888","https://openalex.org/W2024060531","https://openalex.org/W2024800089","https://openalex.org/W2030341962","https://openalex.org/W2040870580","https://openalex.org/W2041341436","https://openalex.org/W2052272843","https://openalex.org/W2061191702","https://openalex.org/W2065450947","https://openalex.org/W2068150202","https://openalex.org/W2074869363","https://openalex.org/W2079606600","https://openalex.org/W2089876099","https://openalex.org/W2094631910","https://openalex.org/W2115581795","https://openalex.org/W2120282470","https://openalex.org/W2128084896","https://openalex.org/W2133671888","https://openalex.org/W2137337872","https://openalex.org/W2145482038","https://openalex.org/W2162887664","https://openalex.org/W2163288162","https://openalex.org/W2166050991","https://openalex.org/W2292343596","https://openalex.org/W2495796013","https://openalex.org/W2766736793","https://openalex.org/W2914656440","https://openalex.org/W2988716417","https://openalex.org/W3022436500","https://openalex.org/W4214891130"],"related_works":["https://openalex.org/W2316299746","https://openalex.org/W2771179472","https://openalex.org/W6926854571","https://openalex.org/W2890934472","https://openalex.org/W818949671","https://openalex.org/W3132105000","https://openalex.org/W1020201621","https://openalex.org/W2808439396","https://openalex.org/W3043244858","https://openalex.org/W4237485457"],"abstract_inverted_index":{"We":[0,25,121,231,329,340,360],"associate":[1],"learning":[2,56,301],"in":[3,18,194,276,318,347,356,392],"living":[4,299],"systems":[5,159,235,272,350],"with":[6,80],"the":[7,10,38,52,65,92,95,106,110,114,123,135,147,153,195,202,215,225,240,247,256,295,319,357,363,372,376,379],"shaping":[8,312],"of":[9,14,46,51,68,109,125,137,152,206,239,297,365,378],"velocity":[11,87],"vector":[12,40,88,96,132,257,334],"field":[13,97,133,258,335],"a":[15,31,49,85,237,310,332,348,387],"dynamical":[16,70],"system":[17,32,313],"response":[19],"to":[20,29,36,63,162,221,223,263,307],"external,":[21],"generally":[22],"random,":[23],"stimuli.":[24],"consider":[26,122],"various":[27,118],"approaches":[28],"implement":[30],"that":[33,169,342],"is":[34,75,134,267,305],"able":[35],"adapt":[37],"whole":[39],"field,":[41],"rather":[42],"than":[43],"just":[44],"parts":[45],"it":[47,304],"-":[48,127,250],"drawback":[50],"most":[53],"common":[54],"current":[55],"systems:":[57],"artificial":[58,163],"neural":[59,164,181,211,241],"networks.\\n\\nThis":[60],"leads":[61],"us":[62],"propose":[64],"mathematical":[66],"concept":[67,282],"self-shaping":[69,129,158,234],"systems.":[71,302],"To":[72],"begin,":[73],"there":[74],"an":[76,284,291],"empty":[77],"phase":[78,115,196,320],"space":[79,116,321],"no":[81],"attractors,":[82],"and":[83,99,103,187,189,254,261,278,300,367,375],"thus":[84],"zero":[86],"field.":[89],"Upon":[90],"receiving":[91],"random":[93,107],"stimulus,":[94],"deforms":[98],"eventually":[100],"becomes":[101],"smooth":[102],"deterministic,":[104],"despite":[105],"nature":[108],"applied":[111],"force,":[112],"while":[113],"develops":[117,145],"geometrical":[119],"objects.":[120,339],"simplest":[124],"these":[126],"gradient":[128,136],"systems,":[130],"whose":[131],"some":[138],"energy":[139],"function,":[140],"which":[141,351],"under":[142],"certain":[143],"conditions":[144,374],"into":[146],"multi-dimensional":[148],"probability":[149,203],"density":[150,204],"distribution":[151,205],"input.":[154],"\\n\\nWe":[155],"explain":[156],"how":[157,270,309,331,385],"are":[160],"relevant":[161],"networks.":[165],"Firstly,":[166],"we":[167,382],"show":[168,341],"they":[170,199],"can":[171,200],"potentially":[172],"perform":[173],"pattern":[174],"recognition":[175],"tasks":[176],"typically":[177],"implemented":[178,275],"by":[179,245],"Hopfield":[180],"networks,":[182,212],"but":[183,213],"without":[184,190,214],"any":[185],"supervision":[186],"on-line,":[188],"developing":[191],"spurious":[192],"minima":[193],"space.":[197],"Secondly,":[198],"reconstruct":[201],"input":[207],"signals,":[208],"like":[209],"probabilistic":[210],"need":[216],"for":[217,294],"new":[218,228,281],"training":[219],"patterns":[220],"have":[222,352],"enter":[224],"network":[226,242],"as":[227,236,323],"hardware":[229],"units.":[230],"therefore":[232],"regard":[233],"generalisation":[238],"concept,":[243],"achieved":[244],"abandoning":[246],"\"rigid":[248],"units":[249],"flexible":[251,260],"couplings''":[252],"paradigm":[253,293],"making":[255],"fully":[259],"amenable":[262],"external":[264],"force.":[265],"It":[266,287],"not":[268],"clear":[269],"such":[271,322,338,386],"could":[273,288,314,336,389],"be":[274,390],"hardware,":[277],"so":[279],"this":[280,343],"presents":[283],"engineering":[285],"challenge.":[286],"also":[289,361],"become":[290],"alternative":[292],"modelling":[296],"both":[298],"\\n\\nMathematically":[303],"interesting":[306],"find":[308],"self":[311],"develop":[315],"non-trivial":[316],"objects":[317],"periodic":[324],"orbits":[325],"or":[326],"chaotic":[327],"attractors.":[328],"investigate":[330],"delayed":[333],"form":[337],"method":[344,388],"produces":[345],"chaos":[346],"class":[349],"very":[353],"simple":[354],"dynamics":[355],"non-delayed":[358],"case.":[359],"demonstrate":[362],"coexistence":[364],"bounded":[366],"unbounded":[368],"solutions":[369],"dependent":[370],"on":[371],"initial":[373],"value":[377],"delay.":[380],"Finally,":[381],"speculate":[383],"about":[384],"used":[391],"global":[393],"optimization.":[394]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2016-06-24T00:00:00"}