Matches in SemOpenAlex for { <https://semopenalex.org/work/W1964335664> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W1964335664 endingPage "5490" @default.
- W1964335664 startingPage "5485" @default.
- W1964335664 abstract "The certification, construction, and delineation of individual, infinite-length random sequences have been longstanding yet incompletely resolved problems. We address this topic via the study of normal numbers, which often have been viewed as reasonable proxies for randomness, given their limiting equidistribution of subblocks of all lengths. However, limitations arise within this perspective. First, we explicitly construct a normal number that satisfies the law of the iterated logarithm yet exhibits pairwise bias toward repeated values, rendering it inappropriate for any collection of random numbers. Accordingly, we deduce that the evaluation of higher-order block dynamics, even beyond limiting equidistribution and fluctuational typicality, is imperative in proper evaluation of sequential randomness. Second, we develop several criteria motivated by classical theorems for symmetric random walks, which lead to algorithms for generating normal numbers that satisfy a variety of attributes for the series of initial partial sums, including rates of sign changes, patterns of return times to 0, and the extent of fairness of the sequence. Such characteristics generally are unaddressed in most evaluations of randomness. More broadly, we can differentiate normal numbers both on the basis of multiple distinct qualitative attributes and quantitatively via a spectrum of rates within each attribute. Furthermore, we exhibit a toolkit of techniques to construct normal sequences that realize diverse a priori specifications, including profound biases. Overall, we elucidate the vast diversity within the category of normal sequences." @default.
- W1964335664 created "2016-06-24" @default.
- W1964335664 creator A5015945699 @default.
- W1964335664 creator A5087494381 @default.
- W1964335664 date "2014-03-31" @default.
- W1964335664 modified "2023-09-24" @default.
- W1964335664 title "Higher-order dangers and precisely constructed taxa in models of randomness" @default.
- W1964335664 cites W1504894794 @default.
- W1964335664 cites W1547322272 @default.
- W1964335664 cites W1574049752 @default.
- W1964335664 cites W1599469804 @default.
- W1964335664 cites W1971085446 @default.
- W1964335664 cites W1985224565 @default.
- W1964335664 cites W1986692269 @default.
- W1964335664 cites W2007453203 @default.
- W1964335664 cites W2012395266 @default.
- W1964335664 cites W2028490525 @default.
- W1964335664 cites W2032627084 @default.
- W1964335664 cites W2046624281 @default.
- W1964335664 cites W2067580807 @default.
- W1964335664 cites W2077204677 @default.
- W1964335664 cites W2082647537 @default.
- W1964335664 cites W2085544694 @default.
- W1964335664 cites W2087456401 @default.
- W1964335664 cites W2089818247 @default.
- W1964335664 cites W2145880011 @default.
- W1964335664 cites W2318068524 @default.
- W1964335664 doi "https://doi.org/10.1073/pnas.1402621111" @default.
- W1964335664 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/3992646" @default.
- W1964335664 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/24706776" @default.
- W1964335664 hasPublicationYear "2014" @default.
- W1964335664 type Work @default.
- W1964335664 sameAs 1964335664 @default.
- W1964335664 citedByCount "3" @default.
- W1964335664 countsByYear W19643356642018 @default.
- W1964335664 countsByYear W19643356642023 @default.
- W1964335664 crossrefType "journal-article" @default.
- W1964335664 hasAuthorship W1964335664A5015945699 @default.
- W1964335664 hasAuthorship W1964335664A5087494381 @default.
- W1964335664 hasBestOaLocation W19643356641 @default.
- W1964335664 hasConcept C105795698 @default.
- W1964335664 hasConcept C111472728 @default.
- W1964335664 hasConcept C11413529 @default.
- W1964335664 hasConcept C125112378 @default.
- W1964335664 hasConcept C138885662 @default.
- W1964335664 hasConcept C184898388 @default.
- W1964335664 hasConcept C2778112365 @default.
- W1964335664 hasConcept C33923547 @default.
- W1964335664 hasConcept C41008148 @default.
- W1964335664 hasConcept C54355233 @default.
- W1964335664 hasConcept C75553542 @default.
- W1964335664 hasConcept C80444323 @default.
- W1964335664 hasConcept C86803240 @default.
- W1964335664 hasConceptScore W1964335664C105795698 @default.
- W1964335664 hasConceptScore W1964335664C111472728 @default.
- W1964335664 hasConceptScore W1964335664C11413529 @default.
- W1964335664 hasConceptScore W1964335664C125112378 @default.
- W1964335664 hasConceptScore W1964335664C138885662 @default.
- W1964335664 hasConceptScore W1964335664C184898388 @default.
- W1964335664 hasConceptScore W1964335664C2778112365 @default.
- W1964335664 hasConceptScore W1964335664C33923547 @default.
- W1964335664 hasConceptScore W1964335664C41008148 @default.
- W1964335664 hasConceptScore W1964335664C54355233 @default.
- W1964335664 hasConceptScore W1964335664C75553542 @default.
- W1964335664 hasConceptScore W1964335664C80444323 @default.
- W1964335664 hasConceptScore W1964335664C86803240 @default.
- W1964335664 hasIssue "15" @default.
- W1964335664 hasLocation W19643356641 @default.
- W1964335664 hasLocation W19643356642 @default.
- W1964335664 hasLocation W19643356643 @default.
- W1964335664 hasLocation W19643356644 @default.
- W1964335664 hasOpenAccess W1964335664 @default.
- W1964335664 hasPrimaryLocation W19643356641 @default.
- W1964335664 hasRelatedWork W1244529000 @default.
- W1964335664 hasRelatedWork W1975748160 @default.
- W1964335664 hasRelatedWork W1998950781 @default.
- W1964335664 hasRelatedWork W2387908448 @default.
- W1964335664 hasRelatedWork W2549839751 @default.
- W1964335664 hasRelatedWork W2952827053 @default.
- W1964335664 hasRelatedWork W2963252158 @default.
- W1964335664 hasRelatedWork W2993498308 @default.
- W1964335664 hasRelatedWork W3033828522 @default.
- W1964335664 hasRelatedWork W3033954861 @default.
- W1964335664 hasVolume "111" @default.
- W1964335664 isParatext "false" @default.
- W1964335664 isRetracted "false" @default.
- W1964335664 magId "1964335664" @default.
- W1964335664 workType "article" @default.