{"id":"https://openalex.org/W2964268874","doi":"https://doi.org/10.1109/isit.2015.7282807","title":"Replica symmetric bound for restricted isometry constant","display_name":"Replica symmetric bound for restricted isometry constant","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W2964268874","doi":"https://doi.org/10.1109/isit.2015.7282807","mag":"2964268874"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2015.7282807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","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/A5001696601","display_name":"Ayaka Sakata","orcid":"https://orcid.org/0000-0003-1660-0222"},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]},{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ayaka Sakata","raw_affiliation_strings":["The Institute of Statistical Mathematics Tachikawa, Japan Theoretical Biology Laboratory, RIKEN, Wako, Japan"],"affiliations":[{"raw_affiliation_string":"The Institute of Statistical Mathematics Tachikawa, Japan Theoretical Biology Laboratory, RIKEN, Wako, Japan","institution_ids":["https://openalex.org/I4210134673","https://openalex.org/I4210110652"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002600110","display_name":"Yoshiyuki Kabashima","orcid":"https://orcid.org/0000-0002-2949-7108"},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]},{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshiyuki Kabashima","raw_affiliation_strings":["The Institute of Statistical Mathematics Tachikawa, Japan Theoretical Biology Laboratory, RIKEN, Wako, Japan"],"affiliations":[{"raw_affiliation_string":"The Institute of Statistical Mathematics Tachikawa, Japan Theoretical Biology Laboratory, RIKEN, Wako, Japan","institution_ids":["https://openalex.org/I4210134673","https://openalex.org/I4210110652"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001696601"],"corresponding_institution_ids":["https://openalex.org/I4210110652","https://openalex.org/I4210134673"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.31431159,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"72","issue":null,"first_page":"2006","last_page":"2010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9900000095367432,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/replica","display_name":"Replica","score":0.8779722452163696},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.705426037311554},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5857478380203247},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5423283576965332},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49768999218940735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4971957504749298},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.46764206886291504},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4517686367034912},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.4347708523273468},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.43318748474121094},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.42433929443359375},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4159046709537506},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4087563157081604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2673422694206238},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2281220555305481},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21685931086540222},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17994871735572815},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15062609314918518}],"concepts":[{"id":"https://openalex.org/C2775937380","wikidata":"https://www.wikidata.org/wiki/Q1232589","display_name":"Replica","level":2,"score":0.8779722452163696},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.705426037311554},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5857478380203247},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5423283576965332},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49768999218940735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4971957504749298},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46764206886291504},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4517686367034912},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.4347708523273468},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.43318748474121094},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.42433929443359375},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4159046709537506},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4087563157081604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2673422694206238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2281220555305481},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21685931086540222},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17994871735572815},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15062609314918518},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2015.7282807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1527520754","https://openalex.org/W1883653182","https://openalex.org/W1971565000","https://openalex.org/W1976249695","https://openalex.org/W2002664623","https://openalex.org/W2012961725","https://openalex.org/W2018429487","https://openalex.org/W2051039246","https://openalex.org/W2051607609","https://openalex.org/W2080815943","https://openalex.org/W2094503020","https://openalex.org/W2098602977","https://openalex.org/W2101675075","https://openalex.org/W2129131372","https://openalex.org/W2145096794","https://openalex.org/W2326812357","https://openalex.org/W3098889107","https://openalex.org/W3101006260","https://openalex.org/W4206502013","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W3013979739","https://openalex.org/W2655578171","https://openalex.org/W2577913821","https://openalex.org/W4296976839","https://openalex.org/W2460131733","https://openalex.org/W2953070151","https://openalex.org/W2372946558","https://openalex.org/W3126044086","https://openalex.org/W2743192809","https://openalex.org/W4236952075"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,35],"method":[3,42,96],"for":[4,26,50],"evaluating":[5],"restricted":[6],"isometry":[7],"constants":[8],"(RICs).":[9],"This":[10],"evaluation":[11],"is":[12,24,111],"reduced":[13],"to":[14,62,83,106],"the":[15,18,40,55,65,72,124,133],"identification":[16],"of":[17,20,31,67,102,123],"zero-points":[19],"entropy":[21],"density":[22],"which":[23,78],"defined":[25],"submatrices":[27],"that":[28,98,110,120],"are":[29],"composed":[30],"columns":[32],"selected":[33],"from":[34],"given":[36],"measurement":[37],"matrix.":[38],"Using":[39],"replica":[41,56,134],"developed":[43],"in":[44,114],"statistical":[45],"mechanics,":[46],"we":[47,70],"assess":[48],"RICs":[49],"Gaussian":[51],"random":[52],"matrices":[53],"under":[54],"symmetric":[57],"(RS)":[58],"assumption.":[59],"In":[60],"order":[61],"numerically":[63],"validate":[64],"adequacy":[66],"our":[68,99,121],"analysis,":[69],"employ":[71],"exchange":[73],"Monte":[74,91],"Carlo":[75,92],"(EMC)":[76],"method,":[77],"has":[79],"been":[80],"empirically":[81],"demonstrated":[82],"achieve":[84],"much":[85],"higher":[86],"numerical":[87],"accuracy":[88],"than":[89,113],"naive":[90],"methods.":[93],"The":[94],"EMC":[95],"suggests":[97],"theoretical":[100],"estimation":[101],"an":[103,107],"RIC":[104,125],"corresponds":[105],"upper":[108],"bound":[109],"tighter":[112],"preceding":[115],"studies.":[116],"Physical":[117],"consideration":[118],"indicates":[119],"assessment":[122],"could":[126],"be":[127],"improved":[128],"by":[129],"taking":[130],"into":[131],"account":[132],"symmetry":[135],"breaking.":[136]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}