{"id":"https://openalex.org/W2067640675","doi":"https://doi.org/10.2168/lmcs-8(1:23)2012","title":"The rapid points of a complex oscillation","display_name":"The rapid points of a complex oscillation","publication_year":2012,"publication_date":"2012-03-09","ids":{"openalex":"https://openalex.org/W2067640675","doi":"https://doi.org/10.2168/lmcs-8(1:23)2012","mag":"2067640675"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-8(1:23)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:23)2012","pdf_url":"https://lmcs.episciences.org/1188/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/1188/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038375053","display_name":"Paul Potgieter","orcid":"https://orcid.org/0000-0002-0145-0455"},"institutions":[{"id":"https://openalex.org/I165390105","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49","country_code":"ZA","type":"education","lineage":["https://openalex.org/I165390105"]},{"id":"https://openalex.org/I4210166250","display_name":"Universidade de Santo Amaro","ror":"https://ror.org/05nvmzs58","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210166250"]}],"countries":["BR","ZA"],"is_corresponding":true,"raw_author_name":"Paul Potgieter","raw_affiliation_strings":["UNISA"],"affiliations":[{"raw_affiliation_string":"UNISA","institution_ids":["https://openalex.org/I165390105","https://openalex.org/I4210166250"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038375053"],"corresponding_institution_ids":["https://openalex.org/I165390105","https://openalex.org/I4210166250"],"apc_list":null,"apc_paid":null,"fwci":1.6768,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8163036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"Volume 8, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9980000257492065,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.8957971334457397},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.802976667881012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6493834257125854},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6010443568229675},{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.5184985399246216},{"id":"https://openalex.org/keywords/packing-dimension","display_name":"Packing dimension","score":0.4293642044067383},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.4169635772705078},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41205018758773804},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4111427664756775},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3524128794670105},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33834415674209595},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.2270628809928894},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.2204558551311493},{"id":"https://openalex.org/keywords/minkowski\u2013bouligand-dimension","display_name":"Minkowski\u2013Bouligand dimension","score":0.19725048542022705},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13397133350372314},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12816163897514343},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0712534487247467}],"concepts":[{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.8957971334457397},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.802976667881012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6493834257125854},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6010443568229675},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.5184985399246216},{"id":"https://openalex.org/C80661125","wikidata":"https://www.wikidata.org/wiki/Q5404299","display_name":"Packing dimension","level":5,"score":0.4293642044067383},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.4169635772705078},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41205018758773804},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4111427664756775},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3524128794670105},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33834415674209595},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.2270628809928894},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.2204558551311493},{"id":"https://openalex.org/C101597101","wikidata":"https://www.wikidata.org/wiki/Q2555655","display_name":"Minkowski\u2013Bouligand dimension","level":4,"score":0.19725048542022705},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13397133350372314},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12816163897514343},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0712534487247467},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2168/lmcs-8(1:23)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:23)2012","pdf_url":"https://lmcs.episciences.org/1188/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1202.3855","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1202.3855","pdf_url":"https://arxiv.org/pdf/1202.3855","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:CiteSeerX.psu:10.1.1.752.3043","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.752.3043","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1202.3855.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:af39d2e75a6b457e839e3c3e8edd042c","is_oa":true,"landing_page_url":"https://doaj.org/article/af39d2e75a6b457e839e3c3e8edd042c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 8, Issue 1 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-8(1:23)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(1:23)2012","pdf_url":"https://lmcs.episciences.org/1188/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2067640675.pdf","grobid_xml":"https://content.openalex.org/works/W2067640675.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W652869183","https://openalex.org/W1494933974","https://openalex.org/W1600856650","https://openalex.org/W1964724368","https://openalex.org/W1997344521","https://openalex.org/W2039021986","https://openalex.org/W2040372652","https://openalex.org/W2056268316","https://openalex.org/W2060280752","https://openalex.org/W2064975723","https://openalex.org/W2169990656","https://openalex.org/W2751862591","https://openalex.org/W4300353561","https://openalex.org/W4390545247"],"related_works":["https://openalex.org/W2354845264","https://openalex.org/W2045810234","https://openalex.org/W2157707209","https://openalex.org/W2962871033","https://openalex.org/W2016287320","https://openalex.org/W2082930779","https://openalex.org/W4288096853","https://openalex.org/W2500320410","https://openalex.org/W3105605836","https://openalex.org/W3098745549"],"abstract_inverted_index":{"By":[0],"considering":[1],"a":[2,11],"counting-type":[3],"argument":[4],"on":[5,20],"Brownian":[6,30,52],"sample":[7],"paths,":[8],"we":[9,39],"prove":[10],"result":[12],"similar":[13],"to":[14,45],"that":[15,55],"of":[16,25,29,33,36],"Orey":[17],"and":[18],"Taylor":[19],"the":[21,26,34,37,43,60],"exact":[22],"Hausdorff":[23],"dimension":[24],"rapid":[27,57],"points":[28,58],"motion.":[31],"Because":[32],"nature":[35],"proof":[38],"can":[40],"then":[41],"apply":[42],"concepts":[44],"so-called":[46],"complex":[47],"oscillations":[48],"(or":[49],"'algorithmically":[50],"random":[51],"motion'),":[53],"showing":[54],"their":[56],"have":[59],"same":[61],"dimension.":[62]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
