{"id":"https://openalex.org/W3022518276","doi":"https://doi.org/10.1137/19m1296537","title":"A Model for Optimal Human Navigation with Stochastic Effects","display_name":"A Model for Optimal Human Navigation with Stochastic Effects","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3022518276","doi":"https://doi.org/10.1137/19m1296537","mag":"3022518276"},"language":"en","primary_location":{"id":"doi:10.1137/19m1296537","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296537","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2005.03615","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064882746","display_name":"Christian Parkinson","orcid":"https://orcid.org/0000-0003-1532-5409"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christian Parkinson","raw_affiliation_strings":["University of California-Los Angeles"],"affiliations":[{"raw_affiliation_string":"University of California-Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015516611","display_name":"D. J. Arnold","orcid":"https://orcid.org/0000-0002-1096-938X"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Arnold","raw_affiliation_strings":["University of California, Los Angeles (UCLA)"],"affiliations":[{"raw_affiliation_string":"University of California, Los Angeles (UCLA)","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea Bertozzi","raw_affiliation_strings":["University of California Los Angeles (UCLA)"],"affiliations":[{"raw_affiliation_string":"University of California Los Angeles (UCLA)","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002037883","display_name":"Stanley Osher","orcid":"https://orcid.org/0000-0002-7900-4658"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stanley Osher","raw_affiliation_strings":["University of California Los Angeles (UCLA)"],"affiliations":[{"raw_affiliation_string":"University of California Los Angeles (UCLA)","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064882746"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":0.0981,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.37868891,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"80","issue":"4","first_page":"1862","last_page":"1881"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11500","display_name":"Evacuation and Crowd Dynamics","score":0.9599000215530396,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"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/T11622","display_name":"Maritime Navigation and Safety","score":0.9024999737739563,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/terrain","display_name":"Terrain","score":0.7052779793739319},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5958901643753052},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5835920572280884},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5622626543045044},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.5536162853240967},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5323441624641418},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5162417888641357},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5137597322463989},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4860401749610901},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.4431278109550476},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.4325394630432129},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41803622245788574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.366365909576416},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07651829719543457},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.07100170850753784}],"concepts":[{"id":"https://openalex.org/C161840515","wikidata":"https://www.wikidata.org/wiki/Q186131","display_name":"Terrain","level":2,"score":0.7052779793739319},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5958901643753052},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5835920572280884},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5622626543045044},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.5536162853240967},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5323441624641418},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5162417888641357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5137597322463989},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4860401749610901},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.4431278109550476},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.4325394630432129},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41803622245788574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.366365909576416},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07651829719543457},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.07100170850753784},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/19m1296537","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296537","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2005.03615","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.03615","pdf_url":"https://arxiv.org/pdf/2005.03615","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":"","raw_type":"text"},{"id":"mag:3022518276","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2005.03615","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:escholarship.org/ark:/13030/qt91k373xd","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/91k373xd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON APPLIED MATHEMATICS, vol 80, iss 4","raw_type":"article"},{"id":"doi:10.48550/arxiv.2005.03615","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.03615","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2005.03615","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.03615","pdf_url":"https://arxiv.org/pdf/2005.03615","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":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6800000071525574}],"awards":[{"id":"https://openalex.org/G5948696453","display_name":null,"funder_award_id":"DMS-1737770","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7666184963","display_name":null,"funder_award_id":"HM0210-14-1-0003","funder_id":"https://openalex.org/F4320332165","funder_display_name":"National Geospatial-Intelligence Agency"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332165","display_name":"National Geospatial-Intelligence Agency","ror":"https://ror.org/02k4pxv54"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3022518276.pdf","grobid_xml":"https://content.openalex.org/works/W3022518276.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W125396517","https://openalex.org/W142873887","https://openalex.org/W153353184","https://openalex.org/W239524345","https://openalex.org/W1092373588","https://openalex.org/W1130790355","https://openalex.org/W1690983060","https://openalex.org/W1751205362","https://openalex.org/W1970900018","https://openalex.org/W1971331422","https://openalex.org/W1975904651","https://openalex.org/W1987169966","https://openalex.org/W1991113069","https://openalex.org/W2003009438","https://openalex.org/W2008709032","https://openalex.org/W2024693023","https://openalex.org/W2042553152","https://openalex.org/W2045849310","https://openalex.org/W2055341194","https://openalex.org/W2061537700","https://openalex.org/W2090501324","https://openalex.org/W2094668823","https://openalex.org/W2098432798","https://openalex.org/W2113162852","https://openalex.org/W2115827349","https://openalex.org/W2132003031","https://openalex.org/W2132457975","https://openalex.org/W2139132599","https://openalex.org/W2148586584","https://openalex.org/W2151959308","https://openalex.org/W2161129003","https://openalex.org/W2169528473","https://openalex.org/W2267184893","https://openalex.org/W2313274380","https://openalex.org/W2343616166","https://openalex.org/W2498807917","https://openalex.org/W2548262140","https://openalex.org/W2561843528","https://openalex.org/W2608377476","https://openalex.org/W2749408143","https://openalex.org/W2771197443","https://openalex.org/W2791784110","https://openalex.org/W2794332241","https://openalex.org/W2887284695","https://openalex.org/W2963298741","https://openalex.org/W2963806607"],"related_works":["https://openalex.org/W2794332241","https://openalex.org/W2057987580","https://openalex.org/W45777778","https://openalex.org/W3027033463","https://openalex.org/W2217930275","https://openalex.org/W2076378565","https://openalex.org/W3027201825","https://openalex.org/W2159471525","https://openalex.org/W3121818018","https://openalex.org/W2954291171","https://openalex.org/W1963731672","https://openalex.org/W1883131750","https://openalex.org/W1991104163","https://openalex.org/W2049403211","https://openalex.org/W2902564581","https://openalex.org/W2160276057","https://openalex.org/W2039720176","https://openalex.org/W3122268216","https://openalex.org/W3013762108","https://openalex.org/W2792763958"],"abstract_inverted_index":{"We":[0,76,96],"present":[1],"a":[2,16,21,45,57,71],"method":[3],"for":[4,26,63,92],"optimal":[5,103,116,150,156],"path":[6,104,151],"planning":[7],"of":[8,35,47,51,85,101,125,133],"human":[9,27,41],"walking":[10,42],"paths":[11,117],"in":[12,65,80,109,143],"mountainous":[13],"terrain":[14],"using":[15],"control":[17],"theoretic":[18],"formulation":[19],"and":[20,40,68,83,88,127],"Hamilton--Jacobi--Bellman":[22,72],"equation.":[23],"Previous":[24],"models":[25],"navigation":[28],"were":[29],"entirely":[30],"deterministic,":[31],"assuming":[32],"perfect":[33],"knowledge":[34],"the":[36,48,52,66,78,81,94,110,115,120,131,134,141,144,149,154],"ambient":[37],"elevation":[38],"data":[39],"velocity":[43],"as":[44,130],"function":[46],"local":[49],"slope":[50],"terrain.":[53],"Our":[54],"model":[55,79,121],"includes":[56,70],"stochastic":[58,86],"component":[59],"which":[60],"can":[61],"account":[62],"uncertainty":[64,108,126,135],"problem":[67],"thus":[69,140],"equation":[73,145],"with":[74],"viscosity.":[75],"discuss":[77,97],"presence":[82],"absence":[84],"effects":[87],"suggest":[89],"numerical":[90],"methods":[91],"simulating":[93],"model.":[95],"two":[98],"different":[99,123],"notions":[100],"an":[102],"when":[105],"there":[106],"is":[107],"problem.":[111],"Finally,":[112],"we":[113],"compare":[114],"suggested":[118],"by":[119],"at":[122],"levels":[124],"observe":[128],"that":[129],"size":[132],"tends":[136,146,152],"to":[137,147],"zero":[138],"(and":[139],"viscosity":[142],"zero),":[148],"toward":[153],"deterministic":[155],"path.":[157]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}