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Constructive Dimension and Hausdorff Dimension: The Case of Exact Dimension

2011
The 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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Into the third dimension

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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Bounding the Global Dimension in Terms of the Dimension

Bulletin of the London Mathematical Society, 1985
Let k be a field. The author establishes the long suspected existence of a function f such that gl.dim(A)\(\leq f(n)\) for any n-dimensional k- algebra A of finite global dimension.
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Resistance dimension, random walk dimension and fractal dimension

Journal of Theoretical Probability, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Dimensions of meaning

Proceedings Supercomputing '92, 2003
The representation of documents and queries as vectors in a high-dimensional space is well-established in information retrieval. The author proposes that the semantics of words and contexts in a text be represented as vectors. The dimensions of the space are words and the initial vectors are determined by the words occurring close to the entity to be ...
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The fractal dimension of complex networks: A review

Information Fusion, 2021
Tao Wen, Kang Hao Cheong
exaly  

On the dimension of orders

The science reports of the Kanazawa University=金沢大学理科報告, 1955
Not ...
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On dimensions of dimension-bounded linear systems

Science China Information Sciences, 2020
Peixin Zhao   +3 more
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