Related papers: Dedieu-Shub Measures
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
In this paper, a method of measuring the entropy is presented. Problems related to the entropy and the heat are also discussed.
Alternative approaches to Lebesgue integration are considered.
We discuss the problem of determining the dimension of self-similar sets and measures on $\mathbf{R}$. We focus on the developments of the last four years. At the end of the paper, we survey recent results about other aspects of…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
This is a survey article of the recent progresses on the metric behaviour of Ricci-flat K\"{a}hler-Einstein metrics along degenerations of Calabi-Yau manifolds.
We formulate a general statement of the problem of defining invariant measures with certain properties and suggest an ergodic method of perturbations for describing such measures.
This paper introduces the concept of symbolic sensor as an extension of the smart sensor one. Then, the links between the physical world and the symbolic one are introduced. The creation of symbols is proposed within the frame of the…
Motion capture systems, used across various domains, make body representations concrete through technical processes. We argue that the measurement of bodies and the validation of measurements for motion capture systems can be understood as…
We analyze the supports of weighted equilibrium measures in $\mathbb{C}^n$. We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight $w$. These examples…
We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural…
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…
To mimic the motion of biological swimmers in bodily fluids, a novel experimental system of micellar solubilization driven active droplets in a visco-elastic polymeric solution is presented. The visco-elastic nature of the medium,…
In this short paper I consider relation between measurements, numbers and p-adic mathematical physics. p-Adic numbers are not result of measurements, but nevertheless they play significant role in description of some systems and phenomena.…
I compare and discuss critically several measures of statistical significance in common use in astrophysics and in high energy physics. I also exhibit some relationships among them.
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
This note explains how the two measures used to define the $\mu$-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves…