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A Dimension, Dimension Modules, and Markov Chains
Proceedings of the London Mathematical Society, 1983The author continues his joint work with \textit{W. Parry} [Ergodic Theory and Dyn. Syst. 1, 303-335 (1981; Zbl 0485.60063) and Bull. London Math. Soc. 14, 16-27 (1982; Zbl 0481.28015)] extending the theory of topological Markov chains to stochastic Markov chains by introducing a new notion of dimension and thus paralleling \textit{W.
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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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On the Relations and Differences Between Popper Dimension, Exclusion Dimension and VC-Dimension
2013A high-level relationPopper dimension—( Exclusion dimension—( VC dimension—( between Karl Popper’s ideas on “falsifiability of scientific theories” and the notion of “overfitting”Overfitting in statistical learning theory can be easily traced. However, it was pointed out that at the level of technical details the two concepts are significantly ...
Seldin, Yevgeny, Scholkopf, Bernhard
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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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On dimensions of dimension-bounded linear systems
Science China Information Sciences, 2020Peixin Zhao +3 more
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Fractal dimension and local intrinsic dimension
Physical Review A, 1989, Passamante, , Hediger, , Gollub
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