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Mathematical Structures in Computer Science, 2005
Following Lutz's approach to effective (constructive) dimension, we define a notion of dimension for individual sequences based on Schnorr's concept(s) of randomness. In contrast to computable randomness and Schnorr randomness, the dimension concepts defined via computable martingales and Schnorr tests coincide.
Rodney G. Downey +2 more
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Following Lutz's approach to effective (constructive) dimension, we define a notion of dimension for individual sequences based on Schnorr's concept(s) of randomness. In contrast to computable randomness and Schnorr randomness, the dimension concepts defined via computable martingales and Schnorr tests coincide.
Rodney G. Downey +2 more
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2010 IEEE International Symposium on Information Theory, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yihong Wu 0001, Sergio Verdú
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yihong Wu 0001, Sergio Verdú
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An overview of dimensions and dimensions badge
Library Hi Tech News, 2022Purpose Research assessment has long been important for directing research funding, rationalizing research organizations and enhancing productivity, including concentrating on specialized subjects. But due to a lack of data, research assessment procedures centered on simple indicators that solely included publications and their citation counts.
Vineet Jamwal, Harish Kumar
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New dimension in multifractals: The exponential dimension
Physical Review A, 1989We propose a new dimension, the exponential dimension, to take proper account of the harmonic lengths that vary inversely to the stage of refinement in the multifractal measure. The need for this dimension arises due to the infinite singularity index which is otherwise obtained with these lengths.
, Gupte, , Amritkar
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SIAM Journal on Discrete Mathematics, 1997
Summary: The hull [\textit{E. F. Assmus jun.} and \textit{J. D. Key}, Discrete Math. 83, 161-187 (1990; Zbl 0707.51012); Designs and their codes, Cambridge Tracts in Mathematics 103, Cambridge University Press, p. 43 (1992; Zbl 0762.05001)] of a linear code is defined to be its intersection with its dual.
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Summary: The hull [\textit{E. F. Assmus jun.} and \textit{J. D. Key}, Discrete Math. 83, 161-187 (1990; Zbl 0707.51012); Designs and their codes, Cambridge Tracts in Mathematics 103, Cambridge University Press, p. 43 (1992; Zbl 0762.05001)] of a linear code is defined to be its intersection with its dual.
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Constructive Dimension and Hausdorff Dimension: The Case of Exact Dimension
2011The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko's result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov ...
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Nature Methods, 2012
Three-dimensional visualizations are effective for spatial data but rarely for other data types.
Nils, Gehlenborg, Bang, Wong
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Three-dimensional visualizations are effective for spatial data but rarely for other data types.
Nils, Gehlenborg, Bang, Wong
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