Related papers: The Brascamp-Lieb inequality and its influence on …
We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.
Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the…
In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…
For $1<p\le 2$, we establish sharp inequalities for the Fourier transform of the characteristic function of the $l^p$-unit ball $B_p\subset\mathbb{R}^2$. We show that $$ \sup_{\boldsymbol{\omega} \in \mathbb{R}^2} \|\boldsymbol{\omega}…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states of quantised radiation and their violation…
This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new…
This paper considers the Fourier transform over the slice of the Boolean hypercube. We prove a relationship between the Fourier coefficients of a function over the slice, and the Fourier coefficients of its restrictions. As an application,…
We address previous hypotheses about possible factors influencing the gender gap in attainment in physics. Specifically, previous studies claim that male advantage may arise from multiple-choice style questions, and that scaffolding may…
It is known that the local bound of a Bell inequality is sensitive to the knowledge of the external observer about the settings statistics. Here we ask how that sensitivity depends on the structure of that knowledge. It turns out that in…
Power laws in time and frequency appear in fields such as linear viscoelasticity and acoustics, viscous boundary layer problems, and dielectrics. This is consistent with fractional derivatives in the fundamental descriptions, since power…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…
In Official Statistics, interest for data integration has been increasingly growing, due to the need of extracting information from different sources. However, the effects of these procedures on the validity of the resulting statistical…
The interplay of flavour and collider physics is entering a new era with the start-up of the LHC. During the past few years rare B decays and in particular b -> s gamma transitions have been extensively used and provided exciting…
The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more important in high-energy astronomy. Many sophisticated tools are available for data…
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
We analyse the recent claim that a violation of a Bell's inequality has been observed in the $B$--meson system [A. Go, {\em Journal of Modern Optics} {\bf 51} (2004) 991]. The results of this experiment are a convincing proof of quantum…
Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation…