{"id":"https://openalex.org/W4213125848","doi":"https://doi.org/10.3390/e24020290","title":"Entropy-Variance Curves of Binary Sequences Generated by Random Substitutions of Constant Length","display_name":"Entropy-Variance Curves of Binary Sequences Generated by Random Substitutions of Constant Length","publication_year":2022,"publication_date":"2022-02-18","ids":{"openalex":"https://openalex.org/W4213125848","doi":"https://doi.org/10.3390/e24020290","pmid":"https://pubmed.ncbi.nlm.nih.gov/35205584"},"language":"en","primary_location":{"id":"doi:10.3390/e24020290","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020290","pdf_url":"https://www.mdpi.com/1099-4300/24/2/290/pdf?version=1645176316","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/2/290/pdf?version=1645176316","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032215497","display_name":"Juan Carlos Nu\u00f1o","orcid":"https://orcid.org/0000-0003-4708-980X"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan Carlos Nu\u00f1o","raw_affiliation_strings":["Department of Applied Mathematics, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4708-980X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022501938","display_name":"Francisco J. Mu\u00f1oz","orcid":"https://orcid.org/0000-0002-0874-6275"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco J. Mu\u00f1oz","raw_affiliation_strings":["Department of Applied Mathematics, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0874-6275","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032215497"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0866,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40301898,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"2","first_page":"290","last_page":"290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.994700014591217,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.994700014591217,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9638000130653381,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12380","display_name":"Authorship Attribution and Profiling","score":0.9624000191688538,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7684864401817322},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.5972094535827637},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5454264283180237},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5068290829658508},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5003283023834229},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4966004490852356},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.47606366872787476},{"id":"https://openalex.org/keywords/maxima","display_name":"Maxima","score":0.4672432243824005},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4168550670146942},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.32304924726486206},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2798425257205963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1326378881931305}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684864401817322},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.5972094535827637},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5454264283180237},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5068290829658508},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5003283023834229},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4966004490852356},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.47606366872787476},{"id":"https://openalex.org/C91528185","wikidata":"https://www.wikidata.org/wiki/Q520952","display_name":"Maxima","level":3,"score":0.4672432243824005},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4168550670146942},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32304924726486206},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2798425257205963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1326378881931305},{"id":"https://openalex.org/C554144382","wikidata":"https://www.wikidata.org/wiki/Q213156","display_name":"Performance art","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},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"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/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e24020290","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020290","pdf_url":"https://www.mdpi.com/1099-4300/24/2/290/pdf?version=1645176316","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:35205584","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35205584","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:arXiv.org:2112.15563","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2112.15563","pdf_url":"https://arxiv.org/pdf/2112.15563","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:af53eb1807374c7695e1f75ad6e52634","is_oa":true,"landing_page_url":"https://doaj.org/article/af53eb1807374c7695e1f75ad6e52634","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 24, Iss 2, p 290 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/2/290/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24020290","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 24; Issue 2; Pages: 290","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8870815","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8870815","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"}],"best_oa_location":{"id":"doi:10.3390/e24020290","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020290","pdf_url":"https://www.mdpi.com/1099-4300/24/2/290/pdf?version=1645176316","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4213125848.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W48411592","https://openalex.org/W584208200","https://openalex.org/W1975527961","https://openalex.org/W2000226169","https://openalex.org/W2025967898","https://openalex.org/W2032121576","https://openalex.org/W2034426848","https://openalex.org/W2052115484","https://openalex.org/W2078206416","https://openalex.org/W2800860906","https://openalex.org/W2963399929","https://openalex.org/W4232040968","https://openalex.org/W4289236364","https://openalex.org/W4297780409","https://openalex.org/W4297888682"],"related_works":["https://openalex.org/W2384841017","https://openalex.org/W2063479817","https://openalex.org/W4301966802","https://openalex.org/W1583182756","https://openalex.org/W2330310849","https://openalex.org/W4210262656","https://openalex.org/W2778748440","https://openalex.org/W2018879631","https://openalex.org/W2950517741","https://openalex.org/W2116175468"],"abstract_inverted_index":{"We":[0,42,71,127],"study":[1],"some":[2],"properties":[3],"of":[4,11,26,50,58,68,84,91,105,110,131],"binary":[5],"sequences":[6,87,151],"generated":[7,86],"by":[8,44],"random":[9,37],"substitutions":[10,69],"constant":[12],"length.":[13,126],"Specifically,":[14],"assuming":[15],"the":[16,21,46,51,56,61,82,85,92,103,108,117,153],"alphabet":[17],"{0,1},":[18],"we":[19,115],"consider":[20],"following":[22],"asymmetric":[23],"substitution":[24,93,125],"rule":[25],"length":[27,94],"k:":[28],"0\u2192\u27e80,0,\u2026,0\u27e9":[29],"and":[30,79,81,101,124,159],"1\u2192\u27e8Y1,Y2,\u2026,Yk\u27e9,":[31],"where":[32,107],"Yi":[33],"is":[34],"a":[35,65,89],"Bernoulli":[36],"variable":[38,53],"with":[39,152],"parameter":[40],"p\u2208[0,1].":[41],"obtain":[43,116],"recurrence":[45],"discrete":[47],"probability":[48],"distribution":[49],"stochastic":[52],"that":[54],"counts":[55],"number":[57,66],"ones":[59],"in":[60],"sequence":[62],"formed":[63],"after":[64],"i":[67],"(iterations).":[70],"derive":[72],"its":[73],"first":[74],"two":[75,129,135],"statistical":[76],"moments,":[77],"mean":[78],"variance,":[80],"entropy":[83,155],"as":[88],"function":[90],"k":[95],"for":[96,121],"any":[97],"successive":[98],"iteration":[99,123],"i,":[100],"characterize":[102],"values":[104],"p":[106],"maxima":[109],"these":[111,134],"measures":[112],"occur.":[113],"Finally,":[114],"parametric":[118],"curves":[119],"entropy-variance":[120],"each":[122],"find":[128],"regimes":[130],"dependence":[132],"between":[133],"variables":[136],"that,":[137],"to":[138,149],"our":[139],"knowledge,":[140],"have":[141],"not":[142],"been":[143],"previously":[144],"described.":[145],"Besides,":[146],"it":[147],"allows":[148],"compare":[150],"same":[154],"but":[156],"different":[157],"variance":[158],"vice":[160],"versa.":[161]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
