{"id":"https://openalex.org/W2125023618","doi":"https://doi.org/10.1109/isit.2009.5205495","title":"Entropy bounds for a Markov random subfield","display_name":"Entropy bounds for a Markov random subfield","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2125023618","doi":"https://doi.org/10.1109/isit.2009.5205495","mag":"2125023618"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5205495","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205495","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","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/A5038249161","display_name":"Matthew G. Reyes","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew G. Reyes","raw_affiliation_strings":["EECS Department, University of Michigan, Ann Arbor, MI, USA","EECS Dept., University of Michigan, Ann Arbor, 48109, USA"],"affiliations":[{"raw_affiliation_string":"EECS Department, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"EECS Dept., University of Michigan, Ann Arbor, 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053858700","display_name":"David L. Neuhoff","orcid":"https://orcid.org/0000-0002-0225-2303"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David L. Neuhoff","raw_affiliation_strings":["EECS Department, University of Michigan, Ann Arbor, MI, USA","EECS Dept., University of Michigan, Ann Arbor, 48109, USA"],"affiliations":[{"raw_affiliation_string":"EECS Department, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"EECS Dept., University of Michigan, Ann Arbor, 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038249161"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.2625,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.5952804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"309","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10222","display_name":"Genomics and Chromatin Dynamics","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10222","display_name":"Genomics and Chromatin Dynamics","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9772999882698059,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9732000231742859,"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/combinatorics","display_name":"Combinatorics","score":0.6777479648590088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.673102080821991},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.627446174621582},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4982583522796631},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.48615095019340515},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4819874167442322},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45867806673049927},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4515588879585266},{"id":"https://openalex.org/keywords/markov-random-field","display_name":"Markov random field","score":0.44763219356536865},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19998016953468323},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15602737665176392},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1094801127910614},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1086311936378479}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6777479648590088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.673102080821991},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.627446174621582},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4982583522796631},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.48615095019340515},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4819874167442322},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45867806673049927},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4515588879585266},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.44763219356536865},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19998016953468323},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15602737665176392},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1094801127910614},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1086311936378479},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"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:10.1109/isit.2009.5205495","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205495","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1530042113","https://openalex.org/W1573082642","https://openalex.org/W2009386142","https://openalex.org/W2020999234","https://openalex.org/W2097230740","https://openalex.org/W2099111195","https://openalex.org/W2102249220","https://openalex.org/W2120340025","https://openalex.org/W2135094946","https://openalex.org/W2160842254","https://openalex.org/W2160988325","https://openalex.org/W2332062191","https://openalex.org/W2478708596","https://openalex.org/W2582449852","https://openalex.org/W4231019034","https://openalex.org/W4293052541","https://openalex.org/W6678397451"],"related_works":["https://openalex.org/W1964872188","https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W2949367465","https://openalex.org/W2587048717","https://openalex.org/W4235203617","https://openalex.org/W2006359264","https://openalex.org/W3029201158","https://openalex.org/W4794847","https://openalex.org/W2056357792"],"abstract_inverted_index":{"Given":[0],"a":[1,11,18,34,112],"Markov":[2],"random":[3],"field":[4],"(MRF)":[5],"X":[6,28,47,125],"defined":[7,60],"by":[8,54,65,132],"potentials":[9,68],"on":[10,26,38,61,135,162,169],"graph":[12],"G":[13],"=":[14],"(V,E),":[15],"and":[16,111],"given":[17],"subset":[19],"U":[20,66,75],"\u00bf":[21],"V":[22],"of":[23,44,57,86,94,124,150,180],"the":[24,39,42,45,55,62,92,101,107,121,133,136,142,148,151,159,163,166,170,177,181],"sites":[25],"which":[27],"is":[29,51,97,129],"defined,":[30],"we":[31,81],"prove,":[32],"under":[33],"positive":[35],"correlation":[36],"constraint":[37],"MRF,":[40],"that":[41,91,120,156],"entropy":[43,56,93,123],"subfield":[46],"<sub":[48,126],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[49,127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">U</sub>":[50,128],"upper":[52,130],"bounded":[53,131],"an":[58,95],"MRF":[59,96,134],"subgraph":[63,138,172],"induced":[64,137,164,171],"with":[67,139],"taken":[69],"directly":[70],"from":[71,115,188],"those":[72],"assigned":[73],"to":[74,118,154,157],"in":[76,100],"G.":[77],"To":[78],"prove":[79],"this":[80],"use":[82,106,147],"exponential":[83,102,167,183],"family":[84],"representations":[85],"MRFs.":[87],"We":[88,104,145],"first":[89],"show":[90,119,155],"monotone":[98],"decreasing":[99],"parameters.":[103],"then":[105,146],"Maximum":[108],"Entropy":[109],"principle":[110],"well-known":[113],"result":[114,186],"information":[116],"geometry":[117],"marginal":[122,143,160],"moments":[140,161],"matching":[141],"distribution.":[144],"convexity":[149],"log-partition":[152],"function":[153],"match":[158],"subgraph,":[165],"coordinates":[168],"are":[173],"component-wise":[174],"greater":[175],"than":[176],"corresponding":[178],"parameter":[179],"original":[182],"characterization.":[184],"Our":[185],"follows":[187],"monotonicity.":[189]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}