Related papers: Continuous Donoho-Elad Spark Uncertainty Principle
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
Solutions to the interval observation problem for delayed impulsive and switched systems with $L_1$-performance are provided. The approach is based on first obtaining stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis…
Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. For linear models, it is…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
Most rational systems can be described in terms of orthonormal basis functions. This paper considers the reconstruction of a sparse coefficient vector for a rational transfer function under a pair of orthonormal rational function bases and…
Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole physics near the well-known Planck scale. The…
The generalized uncertainty principle of string theory is derived in the framework of Quantum Geometry by taking into account the existence of an upper limit on the acceleration of massive particles.
This paper focuses on studying the Donoho-Stark's type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, Clifford wavelet transform and their properties is conducted. Next,…
We give a pedagogical introduction to the generalized uncertainty principle (GUP), by showing how it naturally emerges when the action of gravity is taken into account in measurement processes. We review some physical predictions of the…
Dependency on the preparation of state for the Heisenberg uncertainty principle can be removed with the help of entropy uncertainty principle. The shortness of the uncertainty principle (UP) can be overcome with the help of the concept of…
We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing…
The emergence of the generalized uncertainty principle and the existence of a non-zero minimal length are intertwined. On the other hand, the Heisenberg uncertainty principle forms the core of the EPR paradox. Subsequently, here, the…
We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\Delta x$ or a geodesic ball of radius $R$.…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
An Extended Uncertainty Principle inspired Schwarzschild metric that allows for large scale modifications to gravitation is presented. At a new fundamental length scale $\Ls$, the usual black hole characteristics (horizon radius, ISCO, and…
Under Wigdersons' framework and by sorting out the technical points in the recent works of Tang (J. Fourier Anal. Appl. 31 (2025)) and Dias-Luef-Prata (J. Math. Pures Appl. (9) 198 (2025)), we prove an abstract uncertainty principle for…
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…
We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…
The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…
Perturbation theory is developed to analyze the impact of noise on data and has been an essential part of numerical analysis. Recently, it has played an important role in designing and analyzing matrix algorithms. One of the most useful…