Related papers: Self-similar sets and measures on the line
Quantization dimension has been computed for many invariant measures of dynamically defined fractals having well separated cylinders, that is, in the cases when the so-called Open Set Condition (OSC) holds. To attack the same problem in…
Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $\RR^d$. In particular, we classify all periodic…
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…
In this article, we show that Fourier eigenmeasures supported on spheres with radii given by a locally finite sequence, which we call $k$-spherical measures, correspond to Fourier series exhibiting a modular-type transformation behaviour…
We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
We use contraction method in probabilistic metric spaces to prove existence and uniqueness of selfsimilar random fractal measures.
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
We introduce and study the \emph{Fourier spectrum} which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for both sets and measures. We establish some fundamental theory…
Time series are ubiquitous, and a measure to assess their similarity is a core part of many computational systems. In particular, the similarity measure is the most essential ingredient of time series clustering and classification systems.…
We study the decay of $\mu(B(x,r)\cap C)/\mu(B(x,r))$ as $r\downarrow 0$ for different kinds of measures $\mu$ on $\R^n$ and various cones $C$ around $x$. As an application, we provide sufficient conditions implying that the local…
Similarity measures play a central role in various data science application domains for a wide assortment of tasks. This guide describes a comprehensive set of prevalent similarity measures to serve both non-experts and professional.…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so…
We prove that a self similar measure is absolutely continuous providing that it satisfies a condition depending on its Garsia entropy, contraction ratio, and the separation between different points in approximations of the self similar…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
We survey a new area of parameter-free similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a…
We exhibit an asymmetry phenomenon for uniqueness sets in $\ell^q$. Specifically, we construct sets that do not support measures with $\ell^q$-summable Fourier coefficients, yet simultaneously support measures whose positive frequencies…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
Locally finite self-similar graphs with bounded geometry and without bounded geometry as well as non-locally finite self-similar graphs are characterized by the structure of their cell graphs. Geometric properties concerning the volume…