{"id":"https://openalex.org/W2738308924","doi":"https://doi.org/10.1515/mcma-2017-0112","title":"Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies","display_name":"Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies","publication_year":2017,"publication_date":"2017-07-20","ids":{"openalex":"https://openalex.org/W2738308924","doi":"https://doi.org/10.1515/mcma-2017-0112","mag":"2738308924"},"language":"en","primary_location":{"id":"doi:10.1515/mcma-2017-0112","is_oa":false,"landing_page_url":"https://doi.org/10.1515/mcma-2017-0112","pdf_url":null,"source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Monte Carlo Methods and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103482716","display_name":"Mircea Grigoriu","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mircea Grigoriu","raw_affiliation_strings":["School of Civil & Environmental Engineering , Cornell University , Ithaca , NY 14853-3501 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil & Environmental Engineering , Cornell University , Ithaca , NY 14853-3501 , USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103482716"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":0.3662,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.55619867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"23","issue":"3","first_page":"165","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.983299970626831,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.7347617745399475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6283187866210938},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.6181493997573853},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5267250537872314},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46626338362693787},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43588557839393616},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3441450595855713},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3242446184158325},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17878305912017822},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14906635880470276}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7347617745399475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6283187866210938},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.6181493997573853},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5267250537872314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46626338362693787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43588557839393616},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3441450595855713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3242446184158325},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17878305912017822},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14906635880470276},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/mcma-2017-0112","is_oa":false,"landing_page_url":"https://doi.org/10.1515/mcma-2017-0112","pdf_url":null,"source":{"id":"https://openalex.org/S142132501","display_name":"Monte Carlo Methods and Applications","issn_l":"0929-9629","issn":["0929-9629","1569-3961"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Monte Carlo Methods and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2416734728","display_name":null,"funder_award_id":"CMMI-1639669","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2917587613","display_name":null,"funder_award_id":"CMMI-1265511","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W641104018","https://openalex.org/W1971313725","https://openalex.org/W1977808362","https://openalex.org/W1984478718","https://openalex.org/W1990476418","https://openalex.org/W1998267166","https://openalex.org/W2006982184","https://openalex.org/W2016352053","https://openalex.org/W2019291207","https://openalex.org/W2019757719","https://openalex.org/W2038030613","https://openalex.org/W2058362163","https://openalex.org/W2062993069","https://openalex.org/W2065646801","https://openalex.org/W2067761373","https://openalex.org/W2072399658","https://openalex.org/W2079321251","https://openalex.org/W2079572314","https://openalex.org/W2080813767","https://openalex.org/W2080908214","https://openalex.org/W3105113255","https://openalex.org/W3138984420","https://openalex.org/W4206950497","https://openalex.org/W4233367026","https://openalex.org/W4250749378","https://openalex.org/W4255034261"],"related_works":["https://openalex.org/W2357256365","https://openalex.org/W2348502264","https://openalex.org/W2365486383","https://openalex.org/W2362059367","https://openalex.org/W2901443725","https://openalex.org/W2350084742","https://openalex.org/W2393870460","https://openalex.org/W2357988862","https://openalex.org/W2005266888","https://openalex.org/W2240255144"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"algorithm":[2,15,138,156],"is":[3,16],"developed":[4],"for":[5,50,139],"generating":[6,140],"samples":[7,141],"of":[8,22,54,64,92,97,116,121,142,151],"vector-valued":[9,23,143],"Gaussian":[10,144],"processes":[11],"and":[12,34,157],"fields.":[13],"The":[14,128],"based":[17],"on":[18],"Karhunen\u2013Lo\u00e8ve":[19],"(KL)":[20],"representations":[21,53],"random":[24],"functions":[25,96],"<m:math":[26,43,57,65,80,98,122],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mi>Z</m:mi><m:mo>\u2062</m:mo><m:mrow><m:mo":[27,66,99,123],"stretchy=\"false\">(</m:mo><m:mi>x</m:mi><m:mo":[28,60,67,100,124],"stretchy=\"false\">)</m:mo></m:mrow></m:mrow></m:math>":[29,68,101,125],"{Z(x)}":[30,69,102,126],"with":[31],"finite":[32],"variances":[33],"their":[35],"construction":[36],"involves":[37],"two":[38],"steps.":[39],"First,":[40],"truncation":[41,78],"levels":[42,79],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mo":[44,58,81],"stretchy=\"false\">{</m:mo><m:msub><m:mi>m</m:mi><m:mi>i</m:mi></m:msub><m:mo":[45,82],"stretchy=\"false\">}</m:mo></m:mrow></m:math>":[46,62,83],"{\\{m_{i}\\}}":[47,84],"are":[48,85,110,130],"selected":[49],"the":[51,55,77,90,114,117,149,152],"KL":[52],"components":[56],"stretchy=\"false\">{</m:mo><m:mrow><m:msub><m:mi>Z</m:mi><m:mi>i</m:mi></m:msub><m:mo>\u2062</m:mo><m:mrow><m:mo":[59],"stretchy=\"false\">)</m:mo></m:mrow></m:mrow><m:mo":[61],"{\\{Z_{i}(x)\\}}":[63],"such":[70],"that":[71],"they":[72],"meet":[73],"imposed":[74],"accuracies.":[75],"Second,":[76],"accepted":[86],"or":[87,104],"increased":[88],"if":[89],"accuracies":[91],"resulting":[93],"cross":[94],"correlation":[95],"satisfy":[103],"violate":[105],"preset":[106],"constraints.":[107],"Theoretical":[108],"arguments":[109],"used":[111],"to":[112,132],"prove":[113],"validity":[115],"proposed":[118,153],"KL-based":[119],"models":[120,129],".":[127],"applied":[131],"develop":[133],"an":[134],"efficient":[135],"Monte":[136,154],"Carlo":[137,155],"functions.":[145],"Numerical":[146],"examples":[147],"illustrate":[148],"implementation":[150],"demonstrate":[158],"its":[159],"performance.":[160]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}