{"id":"https://openalex.org/W3202884773","doi":"https://doi.org/10.3390/e23101295","title":"Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences","display_name":"Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences","publication_year":2021,"publication_date":"2021-09-30","ids":{"openalex":"https://openalex.org/W3202884773","doi":"https://doi.org/10.3390/e23101295","mag":"3202884773","pmid":"https://pubmed.ncbi.nlm.nih.gov/34682019"},"language":"en","primary_location":{"id":"doi:10.3390/e23101295","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23101295","pdf_url":"https://www.mdpi.com/1099-4300/23/10/1295/pdf?version=1634187177","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/10/1295/pdf?version=1634187177","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015351071","display_name":"Akio Tsuneda","orcid":"https://orcid.org/0000-0002-6531-2043"},"institutions":[{"id":"https://openalex.org/I96036126","display_name":"Kumamoto University","ror":"https://ror.org/02cgss904","country_code":"JP","type":"education","lineage":["https://openalex.org/I96036126"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Akio Tsuneda","raw_affiliation_strings":["Division of Informatics and Energy, Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan"],"raw_orcid":"https://orcid.org/0000-0002-6531-2043","affiliations":[{"raw_affiliation_string":"Division of Informatics and Energy, Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan","institution_ids":["https://openalex.org/I96036126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015351071"],"corresponding_institution_ids":["https://openalex.org/I96036126"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.1813,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.46856617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"23","issue":"10","first_page":"1295","last_page":"1295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9567000269889832,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9465000033378601,"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/binary-number","display_name":"Binary number","score":0.7457637786865234},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7192971706390381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6315967440605164},{"id":"https://openalex.org/keywords/pseudorandom-binary-sequence","display_name":"Pseudorandom binary sequence","score":0.6102511286735535},{"id":"https://openalex.org/keywords/complementary-sequences","display_name":"Complementary sequences","score":0.5529029965400696},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5437813997268677},{"id":"https://openalex.org/keywords/correlation-function","display_name":"Correlation function (quantum field theory)","score":0.5295765399932861},{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.5162386894226074},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49267274141311646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46799322962760925},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3757149875164032},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30001986026763916},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15736550092697144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13676360249519348},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13617241382598877},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12095504999160767},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11667338013648987}],"concepts":[{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7457637786865234},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7192971706390381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6315967440605164},{"id":"https://openalex.org/C128040838","wikidata":"https://www.wikidata.org/wiki/Q1810628","display_name":"Pseudorandom binary sequence","level":3,"score":0.6102511286735535},{"id":"https://openalex.org/C32795469","wikidata":"https://www.wikidata.org/wiki/Q5156430","display_name":"Complementary sequences","level":2,"score":0.5529029965400696},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5437813997268677},{"id":"https://openalex.org/C53622274","wikidata":"https://www.wikidata.org/wiki/Q2496679","display_name":"Correlation function (quantum field theory)","level":3,"score":0.5295765399932861},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5162386894226074},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49267274141311646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46799322962760925},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3757149875164032},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30001986026763916},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15736550092697144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13676360249519348},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13617241382598877},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12095504999160767},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11667338013648987},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23101295","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23101295","pdf_url":"https://www.mdpi.com/1099-4300/23/10/1295/pdf?version=1634187177","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:34682019","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34682019","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:8535036","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8535036","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:4ce80e9b274341688dc872cb560d8ce6","is_oa":true,"landing_page_url":"https://doaj.org/article/4ce80e9b274341688dc872cb560d8ce6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 10, p 1295 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/10/1295/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23101295","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 23; Issue 10; Pages: 1295","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23101295","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23101295","pdf_url":"https://www.mdpi.com/1099-4300/23/10/1295/pdf?version=1634187177","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3667028330","display_name":"Fundamental Study on Random Techniques Using Chaos Theory","funder_award_id":"19K12158","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3202884773.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1913313886","https://openalex.org/W1968971721","https://openalex.org/W2017584411","https://openalex.org/W2043782855","https://openalex.org/W2081024858","https://openalex.org/W2083724486","https://openalex.org/W2101353425","https://openalex.org/W2102875151","https://openalex.org/W2117095095","https://openalex.org/W2165130379","https://openalex.org/W2482944896","https://openalex.org/W2725458275","https://openalex.org/W2904214469","https://openalex.org/W2905420870","https://openalex.org/W3099556301","https://openalex.org/W4247385211"],"related_works":["https://openalex.org/W2006887475","https://openalex.org/W2331845658","https://openalex.org/W3194090512","https://openalex.org/W3116549321","https://openalex.org/W2055371868","https://openalex.org/W2138245574","https://openalex.org/W2383713013","https://openalex.org/W2367415877","https://openalex.org/W2355024443","https://openalex.org/W4205273415"],"abstract_inverted_index":{"This":[0,63],"paper":[1],"discusses":[2],"the":[3,24,56,60,66,70,78,82,115,123,144,147,156,163],"auto-correlation":[4,26,47,57,67,79,117,137],"functions":[5,58,80],"of":[6,28,59,69,81,136,146,155,165,175],"m-bit":[7,30,71,94,131,149],"random":[8,95],"numbers":[9],"obtained":[10,32],"from":[11],"m":[12,34],"chaotic":[13,99,108],"binary":[14,35,61,84,100,158],"sequences":[15,36,72,96,101,132,150,159],"generated":[16,93,105,148],"by":[17,33,51,77,106],"one-dimensional":[18,107],"nonlinear":[19],"maps.":[20,109],"First,":[21],"we":[22,92,128,140],"provide":[23],"theoretical":[25,125],"function":[27,48],"an":[29],"sequence":[31],"that":[37,65,114,143],"are":[38,119,151,160],"assumed":[39],"to":[40,43,122,171],"be":[41,74],"uncorrelated":[42],"each":[44],"other.":[45],"The":[46,110],"is":[49,169],"expressed":[50],"a":[52,90,134],"simple":[53],"form":[54],"using":[55,89,97],"sequences.":[62,85],"implies":[64],"properties":[68],"can":[73,129],"easily":[75],"controlled":[76],"original":[83,157],"In":[86],"numerical":[87,111,116],"experiments":[88,112],"computer,":[91],"some":[98],"with":[102,133],"prescribed":[103],"auto-correlations":[104],"show":[113,142],"values":[118],"almost":[120],"equal":[121,170],"corresponding":[124],"ones,":[126],"and":[127,173],"generate":[130],"variety":[135],"properties.":[138],"Furthermore,":[139],"also":[141],"distributions":[145],"uniform":[152],"if":[153],"all":[154],"balanced":[161],"(i.e.,":[162],"probability":[164],"1":[166],"(or":[167],"0)":[168],"1/2)":[172],"independent":[174],"one":[176],"another.":[177]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2021-10-11T00:00:00"}