Related papers: Continuous Donoho-Elad Spark Uncertainty Principle

We consider a class of production-inventory problems with box uncertainty sets from the seminal work of Ben-Tal et al. (2004) on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule…

Since their introduction by Erd\H{o}s in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding…

One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian…

The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…

The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result…

Simultaneous localization and mapping (SLAM) plays a vital role in mapping unknown spaces and aiding autonomous navigation. Virtually all state-of-the-art solutions today for 2D SLAM are designed for dense and accurate sensors such as laser…

There has been a growing interest in deep learning-based prognostic and health management (PHM) for building end-to-end maintenance decision support systems, especially due to the rapid development of autonomous systems. However, the low…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic…

The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty…

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…

We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

The structured singular value $\mu$ was introduced independently by Doyle and Safanov as a tool for analyzing robustness of system stability and performance in the presence of structured uncertainty in the system parameters. While the…

We extend Strichartz's uncertainty principle [18] from the setting of the Sobolov space W 1,2 (R) to more general Besov spaces B 1/p p,1 (R). The main result gives an estimate from below of the trace of a function from the Besov space on a…

Quantum gravity models predict a minimal measurable length which gives rise to a modification in the uncertainty principle. One of the simplest manifestations of these generalised uncertainty principles is the linear quadratic generalised…

The classical support uncertainty principle states that the signal and its discrete Fourier transform (DFT) cannot be localized simultaneously in an arbitrary small area in the time and the frequency domain. The product of the number of…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

In this paper we consider solving \emph{noisy} under-determined systems of linear equations with sparse solutions. A noiseless equivalent attracted enormous attention in recent years, above all, due to work of…

Motivated from Deutsch entropic uncertainty principle and several product uncertainty principles, we derive an uncertainty principle for the product of entropies using functions.