Related papers: The Ghost Measures of Affine Regular Sequences
Detecting any evolution of dimensionless in the ratios of physical quantities, such as the fine structure constant, would prove that the Weak Equivalence Principle is violated and lead to a paradigm shift in physics. High resolution…
In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than…
In astronomy, the problem of black holes is arguably second in importance only to the problem of cosmology. A current frontier in black hole research is the measurement of spin. During the past three years, the spins of several stellar-mass…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
Classical ghost imaging is a computational imaging technique that employs patterned illumination. It is very similar in concept to the single-pixel camera in that an image may be reconstructed from a set of measurements even though all…
We study the \emph{upper regularity dimension} which describes the extremal local scaling behaviour of a measure and effectively quantifies the notion of \emph{doubling}. We conduct a thorough study of the upper regularity dimension,…
This paper introduces a $K$-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented…
In this article we study a renormalization scheme with which we find all semi-regular continued fractions of a number in a natural way. We define two maps, T_slow and T_fast: these maps are defined for (x,y) in [0,1], where x is the number…
Computational ghost imaging relies on the decomposition of an image into patterns that are summed together with weights that measure the overlap of each pattern with the scene being imaged. These tasks rely on a computer. Here we…
We conduct the multifractal analysis of self-affine measures for "almost all" family of affine maps. Besides partially extending Falconer's formula of $L^q$-spectrum outside the range $1< q\leq 2$, the multifractal formalism is also…
This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random…
The main goal of this paper is to study topological and measure-theoretic properties of an intriguing family of strange planar attractors. Building towards these results, we first show that any generic Lebesgue measure preserving map $f$…
Frequency correlations are a versatile and powerful tool which can be exploited to perform spectral analysis of objects whose direct measurement might be unfeasible. This is achieved through a so-called ghost spectrometer, that can be…
The twisted Gaussian Schell Model describes a family of partially coherent beams that present several interesting characteristics, and as such have attracted attention in classical and quantum optics. Recent techniques have been…
The anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody…
We analytically study the linear propagation of arbitrarily shaped light-pulses through an absorbing medium with a narrow transparency-window or through a resonant amplifying medium. We point out that, under certain general conditions, the…
An independent random cascade measure is specified by a random generator, a vector of dimension c with non-negative components. The dimension c is called the branching cascade parameter. It is shown under certain restrictions that, if this…
We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the…
The primary object of this paper is to prove the conjecture of the authors from a previous paper, explaining how to recover the weak dimension of a ring from its derived category. In the process, we develop a theory of weak dimension, which…
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…