In mathematics — specifically, in fractal geometry — the Assouad dimension is a definition of fractal dimension for subsets of a metric space. It was… (More)

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2017

2017

- Jonathan M. Fraser, Han Yu
- 2017

In a previous paper we introduced a new ‘dimension spectrum’, motivated by the Assouad dimension, designed to give precise… (More)

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2016

2016

- Matthias Hamann
- Combinatorica
- 2016

We construct spanning trees in locally finite hyperbolic graphs whose boundary has finite (Assouad) dimension that represent… (More)

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2014

2014

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension… (More)

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2014

2014

A fractal, as originally described by Mandelbrot, is a set with an irregular and fragmented shape. Many fractals that have been… (More)

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2011

2011

- John M. Mackay
- 2011

We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also… (More)

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2009

2009

- Samory Kpotufe
- COLT
- 2009

We present the first tree-based regressor whose convergence rate depends only on the intrinsic dimension of the data, namely its… (More)

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2009

2009

- Samory Kpotufe
- NIPS
- 2009

It was recently shown that certain nonparametric regressors can escape the curse of dimensionality when the intrinsic dimension… (More)

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2008

2008

- JEREMY T. TYSON
- 2008

We study global conformal Assouad dimension in the Heisenberg group H. For each α ∈ {0} ∪ [1, 2n+2], there is a bounded set in H… (More)

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2005

2005

- Scott W. Keith, T. Laakso
- 2005

Let α ≥ 1 and let (X, d, μ) be an α-homogeneous metric measure space with conformal Assouad dimension equal to α. Then there… (More)

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2001

2001

- JEREMY T. TYSON
- 2001

We study the relationship between the Assouad dimension and quasisymmetric mappings, showing that spaces of dimension strictly… (More)

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