{"id":"https://openalex.org/W2072533954","doi":"https://doi.org/10.1021/ci0300036","title":"Improved Estimation of the Ranking Probabilities in Partial Orders Using Random Linear Extensions by Approximation of the Mutual Ranking Probability","display_name":"Improved Estimation of the Ranking Probabilities in Partial Orders Using Random Linear Extensions by Approximation of the Mutual Ranking Probability","publication_year":2003,"publication_date":"2003-08-23","ids":{"openalex":"https://openalex.org/W2072533954","doi":"https://doi.org/10.1021/ci0300036","mag":"2072533954","pmid":"https://pubmed.ncbi.nlm.nih.gov/14502480"},"language":"en","primary_location":{"id":"doi:10.1021/ci0300036","is_oa":false,"landing_page_url":"https://doi.org/10.1021/ci0300036","pdf_url":null,"source":{"id":"https://openalex.org/S171559003","display_name":"Journal of Chemical Information and Computer Sciences","issn_l":"0095-2338","issn":["0095-2338","1520-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320006","host_organization_name":"American Chemical Society","host_organization_lineage":["https://openalex.org/P4310320006"],"host_organization_lineage_names":["American Chemical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Chemical Information and Computer Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5007907749","display_name":"Dorte Lerche","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I35570632","display_name":"\u00d8rsted (Denmark)","ror":"https://ror.org/02as34v38","country_code":"DK","type":"company","lineage":["https://openalex.org/I35570632"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Dorte Lerche","raw_affiliation_strings":["Institute of Chemistry, H.C. \u00d8rsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark, Department for Policy Analysis, National Environmental Research Institute, P.O. Box 358, DK-4000 Roskilde, Denmark, and Institute of Freshwater Ecology and Inland Fisheries, Mueggelseedamm 310, D-12587 Berlin-Friedrichshagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Chemistry, H.C. \u00d8rsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark, Department for Policy Analysis, National Environmental Research Institute, P.O. Box 358, DK-4000 Roskilde, Denmark, and Institute of Freshwater Ecology and Inland Fisheries, Mueggelseedamm 310, D-12587 Berlin-Friedrichshagen, Germany","institution_ids":["https://openalex.org/I35570632","https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101780317","display_name":"Peter Borgen S\u00f8rensen","orcid":"https://orcid.org/0000-0003-1338-7198"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I35570632","display_name":"\u00d8rsted (Denmark)","ror":"https://ror.org/02as34v38","country_code":"DK","type":"company","lineage":["https://openalex.org/I35570632"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Peter B. S\u00f8rensen","raw_affiliation_strings":["Institute of Chemistry, H.C. \u00d8rsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark, Department for Policy Analysis, National Environmental Research Institute, P.O. Box 358, DK-4000 Roskilde, Denmark, and Institute of Freshwater Ecology and Inland Fisheries, Mueggelseedamm 310, D-12587 Berlin-Friedrichshagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Chemistry, H.C. \u00d8rsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark, Department for Policy Analysis, National Environmental Research Institute, P.O. Box 358, DK-4000 Roskilde, Denmark, and Institute of Freshwater Ecology and Inland Fisheries, Mueggelseedamm 310, D-12587 Berlin-Friedrichshagen, Germany","institution_ids":["https://openalex.org/I35570632","https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069958083","display_name":"Rainer Br\u00fcggemann","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I35570632","display_name":"\u00d8rsted (Denmark)","ror":"https://ror.org/02as34v38","country_code":"DK","type":"company","lineage":["https://openalex.org/I35570632"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Rainer Br\u00fcggemann","raw_affiliation_strings":["Institute of Chemistry, H.C. \u00d8rsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark, Department for Policy Analysis, National Environmental Research Institute, P.O. Box 358, DK-4000 Roskilde, Denmark, and Institute of Freshwater Ecology and Inland Fisheries, Mueggelseedamm 310, D-12587 Berlin-Friedrichshagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Chemistry, H.C. \u00d8rsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark, Department for Policy Analysis, National Environmental Research Institute, P.O. Box 358, DK-4000 Roskilde, Denmark, and Institute of Freshwater Ecology and Inland Fisheries, Mueggelseedamm 310, D-12587 Berlin-Friedrichshagen, Germany","institution_ids":["https://openalex.org/I35570632","https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8261,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.92639627,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"43","issue":"5","first_page":"1471","last_page":"1480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13297","display_name":"History and advancements in chemistry","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13297","display_name":"History and advancements in chemistry","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10973","display_name":"Radioactive element chemistry and processing","score":0.9724000096321106,"subfield":{"id":"https://openalex.org/subfields/1604","display_name":"Inorganic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12527","display_name":"Chemistry and Stereochemistry Studies","score":0.9689000248908997,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hasse-diagram","display_name":"Hasse diagram","score":0.8935364484786987},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.865054726600647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7477717399597168},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46539151668548584},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4623594880104065},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4536168575286865},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.44807010889053345},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3870297074317932},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3220614790916443},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2995782494544983},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.2720848023891449},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19644790887832642},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12818658351898193}],"concepts":[{"id":"https://openalex.org/C140002607","wikidata":"https://www.wikidata.org/wiki/Q901446","display_name":"Hasse diagram","level":3,"score":0.8935364484786987},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.865054726600647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7477717399597168},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46539151668548584},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4623594880104065},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4536168575286865},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.44807010889053345},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3870297074317932},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3220614790916443},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2995782494544983},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.2720848023891449},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19644790887832642},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12818658351898193},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1021/ci0300036","is_oa":false,"landing_page_url":"https://doi.org/10.1021/ci0300036","pdf_url":null,"source":{"id":"https://openalex.org/S171559003","display_name":"Journal of Chemical Information and Computer Sciences","issn_l":"0095-2338","issn":["0095-2338","1520-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320006","host_organization_name":"American Chemical Society","host_organization_lineage":["https://openalex.org/P4310320006"],"host_organization_lineage_names":["American Chemical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Chemical Information and Computer Sciences","raw_type":"journal-article"},{"id":"pmid:14502480","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/14502480","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of chemical information and computer sciences","raw_type":null},{"id":"pmh:oai:pure.atira.dk:publications/adccd370-7e9d-11dd-a5a8-000ea68e967b","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/adccd370-7e9d-11dd-a5a8-000ea68e967b","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lerche, D B, S\u00f8rensen, P B & Br\u00fcggemann, R 2003, 'Improved Estimation of the Ranking Probabilities in Partial Orders Using Random Linear Extensions by Approximation of the Mutual Ranking Probability', Journal of Chemical Information and Modeling, vol. 43, no. 5, pp. 1471-1480.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.6499999761581421,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1997962112","https://openalex.org/W2019488197","https://openalex.org/W2057810670","https://openalex.org/W2086114113","https://openalex.org/W2089365195","https://openalex.org/W2093397547","https://openalex.org/W2102688498","https://openalex.org/W2186170183","https://openalex.org/W4206992701","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W2385052507","https://openalex.org/W2383039218","https://openalex.org/W2807533020","https://openalex.org/W1166792502","https://openalex.org/W2022031171","https://openalex.org/W2031947348","https://openalex.org/W1995271960","https://openalex.org/W3094620933","https://openalex.org/W1967769373","https://openalex.org/W3111153127"],"abstract_inverted_index":{"The":[0],"application":[1],"of":[2,18,25,32,59,70,103,115,122,133,160],"partial":[3,135],"order":[4,54],"theory":[5],"and":[6,155],"Hasse":[7,26],"diagram":[8,27],"technique":[9,28],"in":[10,22,149],"environmental":[11],"science":[12],"is":[13,29,50,73,76,98],"getting":[14],"increasing":[15],"attention.":[16],"One":[17],"the":[19,23,30,41,46,53,67,104,110,116,120,123,141,166,170],"latest":[20],"developments":[21],"field":[24],"use":[31],"random":[33],"linear":[34,71],"extensions":[35,72],"to":[36,153],"estimate":[37],"ranking":[38,47,106,118,124],"probabilities.":[39],"In":[40,94,165],"original":[42],"algorithm":[43],"for":[44],"estimating":[45],"probability":[48,79,107,119],"it":[49,97],"assumed":[51],"that":[52,80],"between":[55],"two":[56],"incomparable":[57],"pair":[58],"objects":[60],"can":[61,89,108,162],"be":[62,84,90,163],"chosen":[63,139],"randomly.":[64],"However,":[65],"if":[66,100],"total":[68],"set":[69,132],"considered":[74],"there":[75],"a":[77,130,156],"specific":[78],"one":[81],"object":[82],"will":[83],"larger":[85],"than":[86],"another,":[87],"which":[88],"far":[91],"from":[92,151],"50%.":[93],"this":[95],"study":[96],"investigated":[99],"an":[101,113],"approximation":[102,114],"mutual":[105,117],"improve":[109],"algorithm.":[111],"Applying":[112],"estimation":[121],"probabilities":[125],"are":[126],"significantly":[127],"improved.":[128],"Using":[129],"test":[131],"39":[134],"orders":[136],"with":[137],"randomly":[138],"values":[140],"relative":[142,158,171],"mean":[143],"root":[144],"square":[145],"difference":[146],"(MRSD)":[147],"decrease":[148],"average":[150],"7.9%":[152],"2.2%":[154],"maximum":[157],"improvement":[159],"90%":[161],"found.":[164],"most":[167],"successful":[168],"case":[169],"MRSD":[172],"goes":[173],"as":[174,176],"low":[175],"0.77%.":[177]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}