Related papers: Logarithmic uncertainty principle for Clifford-wav…
Starting from the geometric calculus based on Clifford algebra, the idea that physical quantities are Clifford aggregates ("polyvectors") is explored. A generalized point particle action ("polyvector action") is proposed. It is shown that…
In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences,…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
The fundamental physical description of the Universe is based on two theories: Quantum Mechanics and General Relativity. Unified theory of Quantum Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG effects in…
We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
This paper describes the treatment of systematic uncertainties in a Likelihood formalism. RooUnfold, which includes most of the unfolding methods that are commonly used in particle physics, is used to compare a newly implemented method…
Within the mathematical analysis of deep convolutional neural networks, the wavelet scattering transform introduced by St\'ephane Mallat is a unique example of how the ideas of multiscale analysis can be combined with a cascade of modulus…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give…
Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position-momentum commutation relations. Some of these modified…
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…
Analogue gravity helps to find some gravitational systems which are similar to the evolution of perturbation in condensed matter systems. These analogies provide a very good tool for either side. In other words, some aspects of gravity…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
For a family of weight functions $h_\kappa$ that are invariant under a reflection group, the uncertainty principle on the unit sphere in the form of $$ \min_{1 \le i \le d} \int_{\mathbb{S}^{d-1}} (1- x_i) |f(x)|^2 h_\kappa^2(x) d\sigma…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Through the asymptotic expansion, the large-time behavior of the incompressible Navier-Stokes flow in $n$-dimensional whole space is drawn. In particular, the logarithmic evolution included in the flow velocity is the focus of attention.…
The coherence transformation is pivotal for quantum technologies, which cannot always be accomplished deterministically. We investigate the probabilistic coherence transformation under strictly incoherent operations. To this end, by virtue…
The spin-base invariant formalism of Dirac fermions in curved space maintains the essential symmetries of general covariance as well as similarity transformations of the Clifford algebra. We emphasize the advantages of the spin-base…