Related papers: Determination of the Fine Structure Constant by $\…
Conformal prediction is a simple and powerful tool that can quantify uncertainty without any distributional assumptions. Many existing methods only address the average coverage guarantee, which is not ideal compared to the stronger…
We present a new form of the Machin-like formula for $\pi$ that can be generated by using iteration. This form of the Machin-like formula may be promising for computation of the constant $\pi$ due to rapidly increasing integers at each step…
Given a random variable $X$ and considered a family of its possible distortions, we define two new measures of distance between $X$ and each its distortion. For these distance measures, which are extensions of the Gini's mean difference,…
Endeavours of the unification of the four fundamental interactions have resulted in a development of theories having cosmological solutions in which low-energy limits of fundamental physical constants vary with time. The validity of such…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
In this paper, we present a fixed point method for high-precision computation of number $\pi$ based on the sine function. Let $P\in \mathbb{N}$. We define the function: \[ S\left(x\right) =x+\sum_{k=1}^{P}\left(\prod_{\ell=1}^{k-1}\frac…
We propose In-like Pr10+ as a candidate for the development of a high-accuracy optical clock with high sensitivity to a time variation of the fine-structure constant, (\dot alpha}/alpha, as well as favorable experimental systematics. We…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
The local a priori estimate for the finite element approximation is essential for underlying the local and parallel technique. It is well known that the constant coefficients in the inequality is independent of the mesh size. But it is not…
As a fundamental concept in information theory, mutual information ($MI$) has been commonly applied to quantify association between random vectors. Most existing nonparametric estimators of $MI$ have unstable statistical performance since…
Effective condition monitoring in complex systems requires identifying change points (CPs) in the frequency domain, as the structural changes often arise across multiple frequencies. This paper extends recent advancements in statistically…
Elastic constants are central material properties, frequently reported in experimental and theoretical studies. While their computation is straightforward in the absence of thermal fluctuations, finite--temperature methods often suffer from…
It has been proposed that the radio-frequency electric-dipole (E1) transition between two nearly degenerate opposite-parity states in atomic dysprosium should be highly sensitive to possible temporal variation of the fine structure constant…
We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on $^{87}$Sr,…
We derive strong observational limits on any possible large-scale spatial variation in the values of physical 'constants' whose space-time evolution is driven by a scalar field. The limits are imposed by the isotropy of the microwave…
Ab initio calculations of the spin wave stiffness constant $D$ for elemental Fe and Ni performed by different groups in the past have led to values with a considerable spread of 50-100 %. We present results for the stiffness constant $D$ of…
In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed…
The aim of this paper is to present a method for identifying the structure of a rule in a fuzzy model. For this purpose, an ATMS shall be used (Zurita 1994). An algorithm obtaining the identification of the structure will be suggested…
The use of the fundamental constants for the definition of the most important measurement units of the International System, was considered a good solution to found it on more solid bases. From further analysis, this solution was found…
For decades, improved theory and experiment of the $n=2$ $^3$P fine structure of helium have allowed for increasingly-precise tests of quantum electrodynamics, determinations of the fine-structure constant $\alpha$, and limitations on…