{"id":"https://openalex.org/W2043119815","doi":"https://doi.org/10.1109/tit.1987.1057324","title":"Some inequalities concerning random subsets of a set (Corresp.)","display_name":"Some inequalities concerning random subsets of a set (Corresp.)","publication_year":1987,"publication_date":"1987-07-01","ids":{"openalex":"https://openalex.org/W2043119815","doi":"https://doi.org/10.1109/tit.1987.1057324","mag":"2043119815"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1987.1057324","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1987.1057324","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5065344888","display_name":"F. K. Hwang","orcid":"https://orcid.org/0000-0003-3913-0198"},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F. Hwang","raw_affiliation_strings":["AT and T Bell Laboratories, Inc., Murray Hill, NJ, USA"],"affiliations":[{"raw_affiliation_string":"AT and T Bell Laboratories, Inc., Murray Hill, NJ, USA","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111774781","display_name":"L. A. Shepp","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Shepp","raw_affiliation_strings":["AT and T Bell Laboratories, Inc., Murray Hill, NJ, USA"],"affiliations":[{"raw_affiliation_string":"AT and T Bell Laboratories, Inc., Murray Hill, NJ, USA","institution_ids":["https://openalex.org/I1283103587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065344888"],"corresponding_institution_ids":["https://openalex.org/I1283103587"],"apc_list":null,"apc_paid":null,"fwci":1.0314,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74801519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"4","first_page":"596","last_page":"598"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9814000129699707,"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/T10142","display_name":"Formal Methods in Verification","score":0.9304999709129333,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/inequality","display_name":"Inequality","score":0.6616199612617493},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.625892162322998},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6178317666053772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5566766262054443},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5158533453941345},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4572036862373352},{"id":"https://openalex.org/keywords/conditional-probability","display_name":"Conditional probability","score":0.44015058875083923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37965887784957886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3760519027709961},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2319006621837616},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12995365262031555}],"concepts":[{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6616199612617493},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.625892162322998},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6178317666053772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5566766262054443},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5158533453941345},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4572036862373352},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.44015058875083923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37965887784957886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3760519027709961},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2319006621837616},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12995365262031555},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1987.1057324","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1987.1057324","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1980123206","https://openalex.org/W2130956934"],"related_works":["https://openalex.org/W3007838749","https://openalex.org/W2047131671","https://openalex.org/W2181432034","https://openalex.org/W4237951173","https://openalex.org/W2905264121","https://openalex.org/W4214479031","https://openalex.org/W4385826423","https://openalex.org/W4238658364","https://openalex.org/W2097696048","https://openalex.org/W1979149912"],"abstract_inverted_index":{"A":[0],"class":[1],"of":[2,13,24,30,67,70,87,89],"plausible":[3],"inequalities":[4,32],"between":[5],"conditional":[6,65],"probabilities":[7],"is":[8],"considered":[9],"involving":[10],"random":[11],"subsets":[12],"a":[14,25,71],"set":[15],"which":[16],"arise,":[17],"for":[18],"example,":[19],"in":[20],"studying":[21,63],"the":[22,31,40,64,68,85],"capacity":[23],"multiple":[26],"access":[27],"channel.":[28],"Some":[29,44],"are":[33,46,56],"true":[34,47],"and":[35],"can":[36],"be":[37],"proved":[38],"by":[39,77],"Fortuin-Kasteleyn-Ginibre":[41],"(FKG)":[42],"inequality.":[43],"others":[45,55],"but":[48],"seem":[49],"to":[50,62,74],"need":[51],"other":[52],"methods.":[53],"Still":[54],"false.":[57],"The":[58],"results":[59],"also":[60],"apply":[61],"probability":[66],"failure":[69,86],"device":[72],"designed":[73],"achieve":[75],"reliability":[76],"using":[78],"redundant":[79],"parts,":[80],"given":[81],"side":[82],"information":[83],"about":[84],"some":[88],"its":[90],"components.":[91]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
