Related papers: More Uncertainty Principles for Metaplectic Time-F…
We derive a hierarchy of closures based on perturbations of well-known entropy-based closures; we therefore refer to them as perturbed entropy-based models. Our derivation reveals final equations containing an additional convective and…
Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…
We prove two forms of uncertainty principle for the Schr\"odinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) result for the imaginary harmonic oscillator.
Energy conversion in a physical system requires time-translation invariance breaking according to Noether's theorem. Closely associated with this symmetry-conservation relation, the frequencies of electromagnetic waves are found to be…
We approach uncertainty principles of Cowling-Price-Heis-\\enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in modulation spaces. The optimal…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
Invariant parameterization schemes for the eddy-vorticity flux in the barotropic vorticity equation on the beta-plane are constructed and then applied to turbulence modeling. This construction is realized by the exhaustive description of…
Consistent quantum formalism based on the localized basis of the Wannirer functions in Heisenberg and Schrodinger pictures to describe propagation of electromagnetic field in a three dimensional media including diffraction is presented. In…
In this paper, we study the frequency response of uncertain systems using Kharitonov stability theory on first order complex polynomial set. For an interval transfer function, we show that the minimal real part of the frequency response at…
Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
We introduce a deepfake video detection approach that exploits pixel-wise temporal inconsistencies, which traditional spatial frequency-based detectors often overlook. Traditional detectors represent temporal information merely by stacking…
This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
Uncertainty quantification is critical in scientific inverse problems to distinguish identifiable parameters from those that remain ambiguous given available measurements. The Conditional Diffusion Model-based Inverse Problem Solver (CDI)…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
This paper addresses the challenges of the Euler-Bernoulli beam theory regarding shortening and stretching assumptions. Certain boundary conditions, such as a cantilever with a horizontal spring attached to its end, result in beams that…
The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random,…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
The quaternion Fourier transform (QFT) satisfies some uncertainty principles similar to the Euclidean Fourier transform. In this paper, we establish Miyachi's theorem for this transform.