{"id":"https://openalex.org/W2586490810","doi":"https://doi.org/10.1142/s0218127417500146","title":"Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations","display_name":"Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2586490810","doi":"https://doi.org/10.1142/s0218127417500146","mag":"2586490810"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417500146","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500146","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1702.02533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111952299","display_name":"Sylvain Contassot\u2010Vivier","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210150455","display_name":"Teer Coatings (United Kingdom)","ror":"https://ror.org/04vfyfx73","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210150455"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"Sylvain Contassot-Vivier","raw_affiliation_strings":["LORIA, Universit\u00e9 de Lorraine, Nancy, France","SIMulating and Building IOT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LORIA, Universit\u00e9 de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838"]},{"raw_affiliation_string":"SIMulating and Building IOT","institution_ids":["https://openalex.org/I4210150455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045365430","display_name":"Jean-Fran\u00e7ois Couchot","orcid":"https://orcid.org/0000-0001-6437-5598"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2802759292","display_name":"Franche-Comt\u00e9 \u00c9lectronique M\u00e9canique Thermique et Optique - Sciences et Technologies","ror":"https://ror.org/004fmxv66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802759292","https://openalex.org/I37553959","https://openalex.org/I4210095849","https://openalex.org/I4405256580","https://openalex.org/I53262699"]},{"id":"https://openalex.org/I4210118524","display_name":"Universit\u00e9 Bourgogne Franche-Comt\u00e9","ror":"https://ror.org/02dn7x778","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210118524"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Fran\u00e7ois Couchot","raw_affiliation_strings":["FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comt\u00e9 (UBFC), France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comt\u00e9 (UBFC), France","institution_ids":["https://openalex.org/I2802759292","https://openalex.org/I4210118524","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033093688","display_name":"Christophe Guyeux","orcid":"https://orcid.org/0000-0003-0195-4378"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2802759292","display_name":"Franche-Comt\u00e9 \u00c9lectronique M\u00e9canique Thermique et Optique - Sciences et Technologies","ror":"https://ror.org/004fmxv66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802759292","https://openalex.org/I37553959","https://openalex.org/I4210095849","https://openalex.org/I4405256580","https://openalex.org/I53262699"]},{"id":"https://openalex.org/I4210118524","display_name":"Universit\u00e9 Bourgogne Franche-Comt\u00e9","ror":"https://ror.org/02dn7x778","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210118524"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Guyeux","raw_affiliation_strings":["FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comt\u00e9 (UBFC), France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comt\u00e9 (UBFC), France","institution_ids":["https://openalex.org/I2802759292","https://openalex.org/I4210118524","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081683705","display_name":"Pierre\u2010Cyrille H\u00e9am","orcid":"https://orcid.org/0000-0002-1125-1767"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2802759292","display_name":"Franche-Comt\u00e9 \u00c9lectronique M\u00e9canique Thermique et Optique - Sciences et Technologies","ror":"https://ror.org/004fmxv66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802759292","https://openalex.org/I37553959","https://openalex.org/I4210095849","https://openalex.org/I4405256580","https://openalex.org/I53262699"]},{"id":"https://openalex.org/I4210118524","display_name":"Universit\u00e9 Bourgogne Franche-Comt\u00e9","ror":"https://ror.org/02dn7x778","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210118524"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre-Cyrille Heam","raw_affiliation_strings":["FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comt\u00e9 (UBFC), France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FEMTO-ST Institute, CNRS, Univ. Bourgogne Franche-Comt\u00e9 (UBFC), France","institution_ids":["https://openalex.org/I2802759292","https://openalex.org/I4210118524","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9237,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.83449742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"01","first_page":"1750014","last_page":"1750014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":1.0,"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":1.0,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9962999820709229,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9865999817848206,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.940564751625061},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.8630770444869995},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5931713581085205},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48538410663604736},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4853438436985016},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4781951904296875},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46263498067855835},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.454093873500824},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.44988399744033813},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4338022768497467},{"id":"https://openalex.org/keywords/random-number-generation","display_name":"Random number generation","score":0.4300629496574402},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4214669466018677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3601887822151184},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19417405128479004},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1656380593776703},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15860441327095032},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09896218776702881},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09062358736991882},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08202692866325378},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07323348522186279}],"concepts":[{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.940564751625061},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.8630770444869995},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5931713581085205},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48538410663604736},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4853438436985016},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4781951904296875},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46263498067855835},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.454093873500824},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.44988399744033813},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4338022768497467},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.4300629496574402},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4214669466018677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3601887822151184},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19417405128479004},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1656380593776703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15860441327095032},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09896218776702881},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09062358736991882},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08202692866325378},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07323348522186279},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218127417500146","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500146","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1702.02533","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.02533","pdf_url":"https://arxiv.org/pdf/1702.02533","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:HAL:hal-01640515v1","is_oa":false,"landing_page_url":"https://hal.inria.fr/hal-01640515","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0218-1274","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-02300025v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02300025","pdf_url":null,"source":{"id":"https://openalex.org/S4406922276","display_name":"INRIA a CCSD electronic archive server","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0218-1274","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-03003541v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-03003541","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International journal of bifurcation and chaos in applied sciences and engineering , 2017, 27 (01), pp.1750014. ⟨10.1142/S0218127417500146⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1702.02533","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.02533","pdf_url":"https://arxiv.org/pdf/1702.02533","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"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W96532434","https://openalex.org/W1963898916","https://openalex.org/W1979684610","https://openalex.org/W1998538686","https://openalex.org/W2000826481","https://openalex.org/W2081024858","https://openalex.org/W2095595785","https://openalex.org/W2102875151","https://openalex.org/W2110387808","https://openalex.org/W2126403241","https://openalex.org/W2295821770","https://openalex.org/W2335364920","https://openalex.org/W2399357094","https://openalex.org/W2471517265","https://openalex.org/W2763534418","https://openalex.org/W2899702797","https://openalex.org/W2951328979","https://openalex.org/W3041796517","https://openalex.org/W3138265894","https://openalex.org/W3198310217","https://openalex.org/W4239398473"],"related_works":["https://openalex.org/W2772380824","https://openalex.org/W2104480405","https://openalex.org/W2062045810","https://openalex.org/W1534576401","https://openalex.org/W2988803943","https://openalex.org/W3124991594","https://openalex.org/W2775374936","https://openalex.org/W3111658143","https://openalex.org/W2987824994","https://openalex.org/W2626887348"],"abstract_inverted_index":{"Designing":[0],"a":[1,7,64,72,85,99,104,115,166],"pseudorandom":[2],"number":[3],"generator":[4],"(PRNG)":[5],"is":[6,42,140,149,169],"difficult":[8,123],"and":[9,151],"complex":[10],"task.":[11],"Many":[12],"recent":[13],"works":[14],"have":[15,92,130],"considered":[16],"chaotic":[17,49,73,82,116,134],"functions":[18,50,62],"as":[19,111],"the":[20,25,28,55,90,94,112,122,127,137,145,158,162,176,180],"basis":[21,113],"of":[22,27,36,54,61,89,96,114,136,144,157,161],"built":[23],"PRNGs:":[24],"quality":[26],"output":[29],"would":[30],"indeed":[31],"be":[32,77],"an":[33],"obvious":[34],"consequence":[35],"some":[37,81,88],"chaos":[38],"properties.":[39],"However,":[40],"there":[41],"no":[43],"direct":[44],"reasoning":[45],"that":[46,175],"goes":[47],"from":[48],"to":[51,70,164],"uniform":[52,167],"distribution":[53,168],"output.":[56],"Moreover,":[57],"embedding":[58],"such":[59],"kind":[60],"into":[63,98],"PRNG":[65,139],"does":[66],"not":[67],"necessarily":[68],"allow":[69],"get":[71],"output,":[74],"which":[75],"could":[76],"required":[78],"for":[79],"simulating":[80],"behaviors.":[83],"In":[84,118],"previous":[86,128],"work,":[87],"authors":[91],"proposed":[93],"idea":[95],"walking":[97],"[Formula:":[100],"see":[101],"text]-cube":[102],"where":[103],"balanced":[105,146],"Hamiltonian":[106,147],"cycle":[107,148],"has":[108],"been":[109,131],"removed":[110],"PRNG.":[117],"this":[119],"article,":[120],"all":[121],"issues":[124],"observed":[125],"in":[126],"work":[129],"tackled.":[132],"The":[133,142],"behavior":[135],"whole":[138],"proven.":[141],"construction":[143],"theoretically":[150],"practically":[152],"solved.":[153],"An":[154],"upper":[155],"bound":[156],"expected":[159],"length":[160],"walk":[163],"obtain":[165],"calculated.":[170],"Finally":[171],"practical":[172],"experiments":[173],"show":[174],"generators":[177],"successfully":[178],"pass":[179],"classical":[181],"statistical":[182],"tests.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}