Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes [PDF]
, 2015 We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the ...
Falconer, Kenneth, Mattila, Pertti
core +3 more sources
Statistical properties of topological Collet-Eckmann maps [PDF]
, 2006 We study geometric and statistical properties of complex rational maps satisfying the Topological Collet-Eckmann Condition. We show that every such a rational map possesses a unique conformal probability measure of minimal exponent, and that this measure
Przytycki, Feliks, Rivera-Letelier, Juan
core +3 more sources
The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
International Journal of Mathematics and Mathematical Sciences, 2002 We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have ...
Hongwen Guo, Dihe Hu
doaj +1 more source
Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences. [PDF]
PLoS ONE, 2015 Comparing DNA or protein sequences plays an important role in the functional analysis of genomes. Despite many methods available for sequences comparison, few methods retain the information content of sequences.
Kun Tian +5 more
doaj +1 more source
On the equality of Hausdorff measure and Hausdorff content [PDF]
, 2014 We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for any subset of a self-similar set corresponding to a nontrivial cylinder of ...
Farkas, Ábel, Fraser, Jonathan M.
core +1 more source
Dimensions and singular traces for spectral triples, with applications to fractals [PDF]
, 1992 Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit.
Guido, Daniele, Isola, Tommaso
core +3 more sources
An evaluation of performance measures for arterial brain vessel segmentation
BMC Medical Imaging, 2021 Background Arterial brain vessel segmentation allows utilising clinically relevant information contained within the cerebral vascular tree. Currently, however, no standardised performance measure is available to evaluate the quality of cerebral vessel ...
Orhun Utku Aydin +7 more
doaj +1 more source
Robust Geometry Estimation using the Generalized Voronoi Covariance Measure [PDF]
, 2015 The Voronoi Covariance Measure of a compact set K of R^d is a tensor-valued measure that encodes geometric information on K and which is known to be resilient to Hausdorff noise but sensitive to outliers. In this article, we generalize this notion to any
Cuel, Louis +3 more
core +3 more sources
Geometrical properties of the space of idempotent probability measures
Applied General Topology, 2021 Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''.
Kholsaid Fayzullayevich Kholturayev
doaj +1 more source
Some remarks on the Hausdorff measure of the Cantor set
SHS Web of Conferences, 2016 In this paper, the author further reveals some intrinsic properties of the Cantor set. By the properties, the author gives a new method for calculating the exact value of the Hausdorff measure of the Cantor set, and shows the facts that each covering ...
Wang Minghua
doaj +1 more source