#### 833 Citations

Outer linear measure of connected sets via Steiner trees

- Mathematics
- 2019

We resurrect an old definition of the linear measure of a metric continuum in terms of Steiner trees, independently due to Menger (1930) and Choquet (1938). We generalise it to any metric space and… Expand

Series Refined Bounds on Kolmogorov Complexity for ω-Languages

- 2008

The paper investigates bounds on various notions of complexity for ω–languages. We understand the complexity of an ω–languages as the complexity of the most complex strings contained in it. There… Expand

Exact Constructive and Computable Dimensions

- Computer Science, Mathematics
- Theory of Computing Systems
- 2017

It is shown that the exact Hausdorff dimension of a set of infinite strings lower bounds the maximum complexity function of strings in this set, and a tight upper bound on the prefix complexity function for all strings in the set is obtained. Expand

Intrinsic dimension estimation: Advances and open problems

- Mathematics, Computer Science
- Inf. Sci.
- 2016

The aim of the paper is to review state-of-the-art of the methods of ID estimation, underlining the recent advances and the open problems. Expand

EEG-based subject-dependent emotion recognition algorithm using fractal dimension

- Computer Science
- 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
- 2014

A real-time Electroencephalogram (EEG)-based emotion recognition algorithm using Higuchi Fractal Dimension (FD) Spectrum is proposed and results show that using FD spectrum features it is possible to improve classification accuracy. Expand

Eigenvalues of measure theoretic Laplacians on Cantor-like sets

- Mathematics
- 2014

We study the eigenvalues of the Laplacian Δ µ . Here, µ is a singular measure
on a bounded interval with an irregular recursive structure, which include self-similar
measures as a special case. The… Expand

A note on moving average models for Gaussian random fields

- Mathematics
- 2013

The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matern covariance family and the Gaussian covariance falling… Expand

Foundations of measurement fractal theory for the fracture mechanics

- Physics
- 2012

A wide variety of natural objects can be described mathematically using fractal geometry as, for example, contours of clouds, coastlines , turbulence in fluids, fracture surfaces, or rugged surfaces… Expand

DETERMINISTIC FRACTALS BASED ON ARCHIMEDEAN SOLIDS

- Mathematics
- 2011

In the present work, the construction of fractals based on Archimedean solids was discussed. The methods of 3D fractals construction based on uniform polyhedra were pre- sented. It was shown that the… Expand

#### References

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