Related papers: Uncertainty for convolutions of sets
Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…
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…
We prove a new version of the Uncertainty Principle of the form $\int |f|^2 \lesssim \int_{E^c} |f|^2 + \int_{\Sigma ^c}|\hat f|^2 $ where the sets $E$ and $\Sigma$ are $\epsilon$-thin in the following sense: $|E \cap D(x, \rho_1(x))| \le…
After a short introduction to the generalized uncertainty principle (GUP), we review some of the physical predictions of the GUP, and we focus in particular on the bounds that present experimental tests can put on the value of the…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results…
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
We propose a general framework for studying optimal issue of CAT bonds in the presence of uncertainty on the parameters. In particular, the intensity of arrival of natural disasters is inhomogeneous and may depend on unknown parameters.…
Though the sharp Heisenberg Uncertainty Principle has been extensively studied in the entire Euclidean spaces, the counterpart on the half spaces or more general orthants has been missing in the literature. We investigate the sharp…
Several results about the union-closed sets conjecture are presented.
This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…
In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and…
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…
This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…
We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr\"odinger equations with non-constant coefficients. We also…
In this paper, calculus of variation methods are generalized to find min-max optimal solution of uncertain dynamical systems with uncertain or certain cost. First, a new form of Euler-Lagrange conditions for uncertain systems is presented.…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…