{"id":"https://openalex.org/W1972838891","doi":"https://doi.org/10.1109/itw.2013.6691331","title":"Bounding the entropic region via information geometry","display_name":"Bounding the entropic region via information geometry","publication_year":2013,"publication_date":"2013-09-01","ids":{"openalex":"https://openalex.org/W1972838891","doi":"https://doi.org/10.1109/itw.2013.6691331","mag":"1972838891"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2013.6691331","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2013.6691331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-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/A5026897397","display_name":"Yunshu Liu","orcid":"https://orcid.org/0000-0002-1415-3601"},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yunshu Liu","raw_affiliation_strings":["Dept. of ECE, Drexel University, Philadelphia, PA, USA","Dept. of ECE, Drexel University, Philadelphia, PA, 19104, USA"],"affiliations":[{"raw_affiliation_string":"Dept. of ECE, Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Dept. of ECE, Drexel University, Philadelphia, PA, 19104, USA","institution_ids":["https://openalex.org/I72816309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060945955","display_name":"John MacLaren Walsh","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John MacLaren Walsh","raw_affiliation_strings":["Dept. of ECE, Drexel University, Philadelphia, PA, USA","Dept. of ECE, Drexel University, Philadelphia, PA, 19104, USA"],"affiliations":[{"raw_affiliation_string":"Dept. of ECE, Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Dept. of ECE, Drexel University, Philadelphia, PA, 19104, USA","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026897397"],"corresponding_institution_ids":["https://openalex.org/I72816309"],"apc_list":null,"apc_paid":null,"fwci":0.9977,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75049852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"191","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9821000099182129,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9785000085830688,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8256781101226807},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.8087725043296814},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6585712432861328},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6500388979911804},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6230483055114746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5352298617362976},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4867865741252899},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4276151955127716},{"id":"https://openalex.org/keywords/affine-geometry","display_name":"Affine geometry","score":0.4239533543586731},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4203953146934509},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33400899171829224},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.242939293384552},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1650078296661377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13712745904922485}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8256781101226807},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.8087725043296814},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6585712432861328},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6500388979911804},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6230483055114746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5352298617362976},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4867865741252899},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4276151955127716},{"id":"https://openalex.org/C23684344","wikidata":"https://www.wikidata.org/wiki/Q382520","display_name":"Affine geometry","level":4,"score":0.4239533543586731},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4203953146934509},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33400899171829224},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.242939293384552},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1650078296661377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13712745904922485},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw.2013.6691331","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2013.6691331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6499999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W81860024","https://openalex.org/W108696806","https://openalex.org/W1573082642","https://openalex.org/W1588284605","https://openalex.org/W1672833098","https://openalex.org/W1965124840","https://openalex.org/W2057878779","https://openalex.org/W2062154999","https://openalex.org/W2082979238","https://openalex.org/W2086387649","https://openalex.org/W2095127695","https://openalex.org/W2102789782","https://openalex.org/W2104389845","https://openalex.org/W2113940092","https://openalex.org/W2114325434","https://openalex.org/W2122093339","https://openalex.org/W2132219316","https://openalex.org/W2138753678","https://openalex.org/W2140678653","https://openalex.org/W2143203964","https://openalex.org/W2147681281","https://openalex.org/W2158227403","https://openalex.org/W2161024633","https://openalex.org/W2164554299","https://openalex.org/W2170184107","https://openalex.org/W2313526252","https://openalex.org/W4247719530","https://openalex.org/W6634556549","https://openalex.org/W6675728212"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W3150707192","https://openalex.org/W2913689990","https://openalex.org/W4245686311","https://openalex.org/W2955697456","https://openalex.org/W3103229299","https://openalex.org/W1972838891","https://openalex.org/W2091838250","https://openalex.org/W2535497761","https://openalex.org/W3171516916"],"abstract_inverted_index":{"This":[0,47],"paper":[1],"suggests":[2],"that":[3,29],"information":[4,26,51,96,120],"geometry":[5,27,121],"may":[6],"form":[7],"a":[8,61,93,100,108],"natural":[9],"framework":[10],"to":[11,91],"deal":[12],"with":[13,32,42,77],"the":[14,18,39,55,78,81,117,124,127],"unknown":[15],"part":[16,79],"of":[17,20,25,45,54,67,80,126],"boundary":[19,125],"entropic":[21,82,128],"region.":[22,129],"An":[23],"application":[24],"shows":[28],"distributions":[30,68],"associated":[31],"Shannon":[33],"facets":[34],"can":[35],"be":[36],"associated,":[37],"in":[38,99],"right":[40],"coordinates,":[41],"affine":[43,95],"collections":[44],"distributions.":[46],"observation":[48],"allows":[49],"an":[50],"geometric":[52,97],"reinterpretation":[53],"Shannon-type":[56],"inequalities":[57],"as":[58],"arising":[59],"from":[60],"Pythagorean":[62],"style":[63],"relationship.":[64],"The":[65],"set":[66],"which":[69,84],"violate":[70],"Ingleton's":[71],"inequality,":[72],"and":[73,107,122],"hence":[74],"are":[75],"linked":[76],"region":[83],"is":[85,88],"yet":[86],"undetermined,":[87],"shown":[89],"also":[90],"have":[92],"surprising":[94],"structure":[98],"special":[101],"case":[102],"involving":[103],"four":[104],"random":[105],"variables":[106],"certain":[109],"support.":[110],"These":[111],"facts":[112],"provide":[113],"strong":[114],"evidence":[115],"for":[116],"link":[118],"between":[119],"characterizing":[123]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}