Matches in SemOpenAlex for { <https://semopenalex.org/work/W2118923545> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W2118923545 startingPage "520" @default.
- W2118923545 abstract "Some quite recent results from the area of Deterministic Chaos have considerable significance for practitioners of Information Theory. In 1959 Kolmogorov observed that Shannon’s probabilistic theory of information could be applied to symbolic encodings of the phase-space descriptions of physical non-linear dynamical systems so that one might characterise a process in terms of its Kolmogorov-Sinai entropy. Pesin’s theorem in 1977, proved that for certain deterministic non-linear dynamical systems exhibiting chaotic behaviour, the Kolmogorov-Sinai entropy h KS is given by the sum of the positive Lyapunov exponents for the process, i.e. h KS = ∑ i λ + i [3]. For a number of simple non-linear processes the Lyapunov exponents may be computed very precisely. Thus a non-linear dynamical systems may be viewed as an information source whose corresponding source entropy is accurately known. The existence of simple ‘calibrated’ sources such as the logistic map (ẋ = f(x) = rx(1−x)), [3] provides a means for precisely evaluating the performance of compression schemes, but also information measures such as the grammar based measures described in [1][4]. In respect of [1][2], the authors have computed the average T-entropy from sample encodings of the symbolic dynamics for the logistic map, and compared these values directly with the corresponding known Lyapunov exponents. As the Figure below shows, the average T-entropy for strings of 10 bits long closely agree with the positive Lyapunov exponents for the one dimensional dynamical system. The values are plotted here as a function of the system parameter r at increments of 0.0001 . The difference between the T-entropy and Lyapunov exponents averages about 1% RMS of full scale over the whole range, r ∈ [0, ln(2)]. Such agreement may be interpreted as strong evidence of the link between this grammar based information measure for finite strings and the probabilistic entropy measure of Shannon for information sources. That the process imbues individual finite sample strings with its corresponding information characteristics, echoes the our quotation from Kolmogorov. Clearly the T-entropy reflects the fine structure of chaotic attractors. Thus Deterministic Information Theory [2] appears to offer a new approach for evaluating the limits of compression for individual finite strings, while Deterministic Chaos Theory results further allow one to select precisely calibrated information sources to be used to assess the performance of specific compression algorithms." @default.
- W2118923545 created "2016-06-24" @default.
- W2118923545 creator A5075702311 @default.
- W2118923545 creator A5087116261 @default.
- W2118923545 date "2001-03-27" @default.
- W2118923545 modified "2023-09-24" @default.
- W2118923545 title "Deterministic Chaos and Information Theory" @default.
- W2118923545 cites W1836205513 @default.
- W2118923545 cites W2043263351 @default.
- W2118923545 cites W2050082536 @default.
- W2118923545 doi "https://doi.org/10.1109/dcc.2001.10034" @default.
- W2118923545 hasPublicationYear "2001" @default.
- W2118923545 type Work @default.
- W2118923545 sameAs 2118923545 @default.
- W2118923545 citedByCount "5" @default.
- W2118923545 countsByYear W21189235452012 @default.
- W2118923545 countsByYear W21189235452014 @default.
- W2118923545 countsByYear W21189235452016 @default.
- W2118923545 crossrefType "proceedings-article" @default.
- W2118923545 hasAuthorship W2118923545A5075702311 @default.
- W2118923545 hasAuthorship W2118923545A5087116261 @default.
- W2118923545 hasConcept C105795698 @default.
- W2118923545 hasConcept C106301342 @default.
- W2118923545 hasConcept C118615104 @default.
- W2118923545 hasConcept C121332964 @default.
- W2118923545 hasConcept C121864883 @default.
- W2118923545 hasConcept C154945302 @default.
- W2118923545 hasConcept C16101541 @default.
- W2118923545 hasConcept C191544260 @default.
- W2118923545 hasConcept C202444582 @default.
- W2118923545 hasConcept C205330730 @default.
- W2118923545 hasConcept C2777052490 @default.
- W2118923545 hasConcept C28826006 @default.
- W2118923545 hasConcept C33923547 @default.
- W2118923545 hasConcept C41008148 @default.
- W2118923545 hasConcept C49937458 @default.
- W2118923545 hasConcept C52622258 @default.
- W2118923545 hasConcept C62520636 @default.
- W2118923545 hasConcept C79379906 @default.
- W2118923545 hasConceptScore W2118923545C105795698 @default.
- W2118923545 hasConceptScore W2118923545C106301342 @default.
- W2118923545 hasConceptScore W2118923545C118615104 @default.
- W2118923545 hasConceptScore W2118923545C121332964 @default.
- W2118923545 hasConceptScore W2118923545C121864883 @default.
- W2118923545 hasConceptScore W2118923545C154945302 @default.
- W2118923545 hasConceptScore W2118923545C16101541 @default.
- W2118923545 hasConceptScore W2118923545C191544260 @default.
- W2118923545 hasConceptScore W2118923545C202444582 @default.
- W2118923545 hasConceptScore W2118923545C205330730 @default.
- W2118923545 hasConceptScore W2118923545C2777052490 @default.
- W2118923545 hasConceptScore W2118923545C28826006 @default.
- W2118923545 hasConceptScore W2118923545C33923547 @default.
- W2118923545 hasConceptScore W2118923545C41008148 @default.
- W2118923545 hasConceptScore W2118923545C49937458 @default.
- W2118923545 hasConceptScore W2118923545C52622258 @default.
- W2118923545 hasConceptScore W2118923545C62520636 @default.
- W2118923545 hasConceptScore W2118923545C79379906 @default.
- W2118923545 hasLocation W21189235451 @default.
- W2118923545 hasOpenAccess W2118923545 @default.
- W2118923545 hasPrimaryLocation W21189235451 @default.
- W2118923545 hasRelatedWork W117438875 @default.
- W2118923545 hasRelatedWork W117881727 @default.
- W2118923545 hasRelatedWork W1524780944 @default.
- W2118923545 hasRelatedWork W1543179125 @default.
- W2118923545 hasRelatedWork W1610965566 @default.
- W2118923545 hasRelatedWork W1965924984 @default.
- W2118923545 hasRelatedWork W1966013935 @default.
- W2118923545 hasRelatedWork W1973422686 @default.
- W2118923545 hasRelatedWork W2001178064 @default.
- W2118923545 hasRelatedWork W2007694269 @default.
- W2118923545 hasRelatedWork W2049293757 @default.
- W2118923545 hasRelatedWork W2101042300 @default.
- W2118923545 hasRelatedWork W2215617304 @default.
- W2118923545 hasRelatedWork W2347964653 @default.
- W2118923545 hasRelatedWork W2555602451 @default.
- W2118923545 hasRelatedWork W2612336801 @default.
- W2118923545 hasRelatedWork W27264036 @default.
- W2118923545 hasRelatedWork W2944684612 @default.
- W2118923545 hasRelatedWork W96086835 @default.
- W2118923545 hasRelatedWork W986229 @default.
- W2118923545 isParatext "false" @default.
- W2118923545 isRetracted "false" @default.
- W2118923545 magId "2118923545" @default.
- W2118923545 workType "article" @default.