Related papers: Determination of the Fine Structure Constant by $\…
A structural order parameter for disordered configurations is defined, based, not on local topologies, but on the degree of local restraint imposed on each atom. This restraint parameter provides a clear distinction between a strong liquid…
Let $\cal{P}$ be an affine invariant property of functions $\mathbb{F}_p^n \to [R]$ for fixed $p$ and $R$. We show that if $\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$…
The possibility of variation of the fundamental constants of nature has been a long-standing question, with important consequences for fundamental physics and cosmology. In particular, it has been shown that variations in the fine-structure…
In this paper, we observe a fixed number of unknown $2\pi$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high…
An algorithm for computing /pi(N) is presented.It is shown that using a symmetry of natural numbers we can easily compute /pi(N).This method relies on the fact that counting the number of odd composites not exceeding N suffices to calculate…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
From astrophysics there are indications that the finestructure constant $\alpha $ has changed during the past 10 billion years. Within grand unification one can deduce that also the QCD scale has changed. Tests for a time variation of this…
Current analyses of VLT/UVES quasar spectra disagree with the Keck/HIRES evidence for a varying fine-structure constant, alpha. To investigate this we introduce a simple method for calculating the minimum possible uncertainty on…
We give a derivation for the value of inf-sup constant for the bilinear form (p, div u). We prove that the value of inf-sup constant is equal to 1.0 in all cases and is independent of the size and shape of the domain. Numerical tests for…
We show why a dynamically varying fine structure constant does not impact on the Webb group's analysis as suggested by Bekenstein. We also provide a limit on the size of a possible correction to the Dirac Hamiltonian caused by a…
Recent measurements of a peak in the angular power spectrum of the cosmic microwave background appear to suggest that geometry of the universe is close to being flat. But if other accepted indicators of cosmological parameters are also…
Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on…
A phenomenological model is proposed to explain the recent observed cosmological variation of the fine structure constant as an effect of the quantum vacuum, assuming a flat universe with cosmological constant $\Lambda$ in the cases…
We compute a Monte Carlo approximation of {\pi} using importance sampling with shots coming out of a Mossberg 500 pump-action shotgun as the proposal distribution. An approximated value of 3.131 is obtained, corresponding to a 0.33% error…
Detecting or placing upper limits on spacetime variations of fundamental constants requires quantifying every potential source of uncertainty. We continue our previous study into the impact of continuum variations on measurements of the…
The low-energy $\pi\pi$ amplitude is computed explicitly to two-loop accuracy in the chiral expansion. It depends only on six independent (combinations of) low-energy constants which are not fixed by chiral symmetry. Four of these constants…