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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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Bounding the Global Dimension in Terms of the Dimension
Bulletin of the London Mathematical Society, 1985Let 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, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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 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, 2021Tao Wen, Kang Hao Cheong
exaly
On dimensions of dimension-bounded linear systems
Science China Information Sciences, 2020Peixin Zhao +3 more
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Dimension by dimension dynamic sine cosine algorithm for global optimization problems
Applied Soft Computing Journal, 2021Jingsen Liu
exaly

