Related papers: Some recent developments in quantization of fracta…
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
We have devised a simple numerical technique to treat rugged data points that arise due to the insufficient gain setting error (or quantization error) of a digital instrument. This is a very wide spread problem that all experimentalists…
In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic…
Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
We provide a complete picture of the upper quantization dimension in terms of the R\'enyi dimension by proving that the upper quantization dimension $\bar{D}_{r}(\nu)$ of order $r>0$ for an arbitrary compactly supported Borel probability…
Fractal analysis has been shown to be useful in image processing for characterizing shape and gray-scale complexity. The fractal feature is a compact descriptor used to give a numerical measure of the degree of irregularity of the medical…
Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a…
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…
A simple method of calculating the Hausdorff-Besicovitch dimension of the Kronecker Product based fractals is presented together with a compact R script realizing it. The proposed new formula is based on traditionally used values of the…
After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…
Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure…
A summary of measurements of the fragmentation of charm quarks into a specific hadron is given. Measurements performed in photoproduction and deep inelastic scattering in $e^{\pm}p$, $pp$ and $e^+e^-$ collisions are compared, using…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…
In a recently published paper (J. of Modern Optics 50 (9) (2003) 1477-1486) a qualitative analysis of the moire effect observed by superposing two grids containing Cantor fractal structures was presented. It was shown that the moire effect…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
Recently it was proposed to use cavity-optomechanical systems to test for quantum gravity corrections to quantum canonical commutation relations [Nat. Phys. 8, 393-397 (2012)]. Improving the achievable precision of such devices represents a…