{"id":"https://openalex.org/W2969117331","doi":"https://doi.org/10.1155/2019/5986562","title":"Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems","display_name":"Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2969117331","doi":"https://doi.org/10.1155/2019/5986562","mag":"2969117331"},"language":"en","primary_location":{"id":"doi:10.1155/2019/5986562","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5986562","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/5986562.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/2019/5986562.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051971369","display_name":"M. Lungaroni","orcid":"https://orcid.org/0000-0002-1500-363X"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Michele Lungaroni","raw_affiliation_strings":["Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043953788","display_name":"A. Murari","orcid":"https://orcid.org/0000-0002-3932-3865"},"institutions":[{"id":"https://openalex.org/I110120368","display_name":"National Agency for New Technologies, Energy and Sustainable Economic Development","ror":"https://ror.org/02an8es95","country_code":"IT","type":"government","lineage":["https://openalex.org/I110120368"]},{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Murari","raw_affiliation_strings":["Consorzio RFX (CNR, ENEA, INFN, Universita' di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, Italy","Consorzio RFX (CNR, ENEA, INFN, Universita' di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova"],"affiliations":[{"raw_affiliation_string":"Consorzio RFX (CNR, ENEA, INFN, Universita' di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, Italy","institution_ids":["https://openalex.org/I110120368","https://openalex.org/I138689650"]},{"raw_affiliation_string":"Consorzio RFX (CNR, ENEA, INFN, Universita' di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova","institution_ids":["https://openalex.org/I110120368","https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047626644","display_name":"E. Peluso","orcid":"https://orcid.org/0000-0002-6829-2180"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Emmanuele Peluso","raw_affiliation_strings":["Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007348092","display_name":"P. Gaudio","orcid":"https://orcid.org/0000-0003-0861-558X"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Pasqualino Gaudio","raw_affiliation_strings":["Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005343901","display_name":"M. Gelfusa","orcid":"https://orcid.org/0000-0001-5158-7292"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michela Gelfusa","raw_affiliation_strings":["Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Industrial Engineering, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome","institution_ids":["https://openalex.org/I116067653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5051971369"],"corresponding_institution_ids":["https://openalex.org/I116067653"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.6651,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65928471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9969000220298767,"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":0.9969000220298767,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoscedasticity","display_name":"Homoscedasticity","score":0.7423972487449646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5415809750556946},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5393826961517334},{"id":"https://openalex.org/keywords/normality","display_name":"Normality","score":0.5147483348846436},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4951988756656647},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.48848235607147217},{"id":"https://openalex.org/keywords/statistical-theory","display_name":"Statistical theory","score":0.4880320131778717},{"id":"https://openalex.org/keywords/statistical-power","display_name":"Statistical power","score":0.4337230920791626},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.42982736229896545},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4118686318397522},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41138288378715515},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4103330373764038},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3775632977485657},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.28209882974624634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27403175830841064}],"concepts":[{"id":"https://openalex.org/C104409967","wikidata":"https://www.wikidata.org/wiki/Q1054836","display_name":"Homoscedasticity","level":3,"score":0.7423972487449646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5415809750556946},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5393826961517334},{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.5147483348846436},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4951988756656647},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.48848235607147217},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.4880320131778717},{"id":"https://openalex.org/C96608239","wikidata":"https://www.wikidata.org/wiki/Q1199823","display_name":"Statistical power","level":2,"score":0.4337230920791626},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.42982736229896545},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4118686318397522},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41138288378715515},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4103330373764038},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3775632977485657},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.28209882974624634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27403175830841064},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/5986562","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5986562","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/5986562.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:art.torvergata.it:2108/232547","is_oa":true,"landing_page_url":"http://hdl.handle.net/2108/232547","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:ffc8644b8a264af684aa6b7cb4c99830","is_oa":true,"landing_page_url":"https://doaj.org/article/ffc8644b8a264af684aa6b7cb4c99830","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/5986562","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5986562","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/5986562.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2969117331.pdf","grobid_xml":"https://content.openalex.org/works/W2969117331.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W330725924","https://openalex.org/W782004971","https://openalex.org/W1541491296","https://openalex.org/W1564436890","https://openalex.org/W1619787994","https://openalex.org/W1999082188","https://openalex.org/W2011017151","https://openalex.org/W2026482919","https://openalex.org/W2027615005","https://openalex.org/W2108161450","https://openalex.org/W2113635440","https://openalex.org/W2133599080","https://openalex.org/W2144981148","https://openalex.org/W2200602655","https://openalex.org/W2260934868","https://openalex.org/W4205806204","https://openalex.org/W4238291432","https://openalex.org/W4246307643","https://openalex.org/W4250006366","https://openalex.org/W4300940930"],"related_works":["https://openalex.org/W2071289071","https://openalex.org/W2491949033","https://openalex.org/W2896694371","https://openalex.org/W2202323525","https://openalex.org/W2045925085","https://openalex.org/W2380849986","https://openalex.org/W2966735239","https://openalex.org/W3198676628","https://openalex.org/W2072022037","https://openalex.org/W2915863966"],"abstract_inverted_index":{"In":[0,57],"the":[1,4,35,42,95,107,114,169,192,206,209,214,235,245,253,257,264],"last":[2],"years":[3],"reputation":[5],"of":[6,19,28,39,106,116,138,142,150,188,198,201,208,217,222,238,275],"medical,":[7],"economic,":[8],"and":[9,22,37,73,181,224,229],"scientific":[10],"expertise":[11],"has":[12,31,63],"been":[13,85],"strongly":[14],"damaged":[15],"by":[16,135,251],"a":[17,128,199,268],"series":[18,200],"false":[20],"predictions":[21],"contradictory":[23],"studies.":[24],"The":[25,119,196],"lax":[26],"application":[27],"statistical":[29,51,82,162,218,277],"principles":[30],"certainly":[32],"contributed":[33],"to":[34,226],"uncertainty":[36],"loss":[38],"confidence":[40],"in":[41,50,152,185,212,240,248,256,271],"sciences.":[43],"Various":[44],"assumptions,":[45],"generally":[46],"held":[47],"as":[48],"valid":[49],"treatments,":[52],"have":[53,84],"proved":[54],"their":[55],"limits.":[56],"particular,":[58],"since":[59],"some":[60],"time":[61],"it":[62,155],"emerged":[64],"quite":[65],"clearly":[66],"that":[67,263],"even":[68,237],"slightly":[69],"departures":[70],"from":[71,127,220],"normality":[72],"homoscedasticity":[74],"can":[75,88,121,164,279],"affect":[76],"significantly":[77],"classic":[78],"significance":[79],"tests.":[80],"Robust":[81],"methods":[83,254],"developed,":[86],"which":[87,272],"provide":[89],"much":[90],"more":[91,179,183],"reliable":[92],"estimates.":[93],"On":[94],"other":[96],"hand,":[97],"they":[98],"do":[99],"not":[100,123],"address":[101],"an":[102],"additional":[103,148],"problem":[104],"typical":[105],"natural":[108],"sciences,":[109],"whose":[110],"data":[111,120],"are":[112],"often":[113],"output":[115],"delicate":[117],"measurements.":[118],"therefore":[122],"only":[124],"be":[125,133,165,280],"sampled":[126],"nonnormal":[129],"pdf":[130],"but":[131],"also":[132,273],"affected":[134],"significant":[136],"levels":[137],"Gaussian":[139,173,189],"additive":[140],"noise":[141,187,274],"various":[143],"amplitude.":[144],"To":[145],"tackle":[146],"this":[147,153],"source":[149],"uncertainty,":[151],"paper":[154],"is":[156,177,234,260],"shown":[157],"how":[158],"already":[159],"developed":[160],"robust":[161],"tools":[163],"usefully":[166],"complemented":[167],"with":[168],"Geodesic":[170],"Distance":[171],"on":[172],"Manifolds.":[174],"This":[175],"metric":[176],"conceptually":[178],"appropriate":[180],"practically":[182],"effective,":[184],"handling":[186],"distribution,":[190],"than":[191],"traditional":[193],"Euclidean":[194],"distance.":[195],"results":[197],"systematic":[202],"numerical":[203],"tests":[204],"show":[205],"advantages":[207],"proposed":[210,255,265],"approach":[211,266],"all":[213],"main":[215],"aspects":[216],"inference,":[219],"measures":[221],"location":[223],"scale":[225],"size":[227],"effects":[228],"hypothesis":[230],"testing.":[231],"Particularly":[232],"relevant":[233],"reduction":[236],"35%":[239],"Type":[241],"II":[242],"errors,":[243],"proving":[244],"important":[246],"improvement":[247],"power":[249],"obtained":[250],"applying":[252],"paper.":[258],"It":[259],"worth":[261],"emphasizing":[262],"provides":[267],"general":[269],"framework,":[270],"different":[276],"distributions":[278],"dealt":[281],"with.":[282]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}