相关论文: Uncertainty product for Vilenkin groups

Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso,…

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…

In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…

We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two…

In this paper we prove sharp weighted Hardy-type inequalities on Carnot groups with the homogeneous norm $N=u^{1/(2-Q)}$ associated to Folland's fundamental solution $u$ for the sub-Laplacian $\Delta_{\mathbb{G}}$. We also prove uncertainty…

Heisenberg uncertainty principle describes a basic restriction on observer's ability of precisely predicting the measurement for a pair of non-commuting observables, and virtually is at the core of quantum mechanics. We herein aim to study…

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 explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…

Let $G$ be a countable discrete group with an orthogonal representation $\alpha$ on a real Hilbert space $H$. We prove $L_p$ Poincar\'e inequalities for the group measure space $L_\infty(\Omega_H,\gamma)\rtimes G$, where both the group…

In this work we find that not only the Heisenberg-like uncertainty products and the R\'enyi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the $D$-dimensional hydrogenic and oscillator-like…

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse…

In this paper, we invoke a generalized uncertainty principle (GUP) in the symmetry-reduced cosmological Hamiltonian for a universe driven by a quintessence scalar field with potential. Our study focuses on semi-classical regime. In…

Photoplethysmography (PPG) signals encode information about relative changes in blood volume that can be used to assess various aspects of cardiac health non-invasively, e.g.\ to detect atrial fibrillation (AF) or predict blood pressure…

In this note, an alternative approach to establish observability for semigroups based on their smoothing properties is presented. The results discussed here are closely related to those recently obtained in [arXiv:2112.01788], but the…

A method is suggested to decompose the statistical and systematic uncertainties from the residues between the calculation of a theoretical model and the observed data. The residues and the parameters of the model can be obtained through the…

We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schr\"{o}dinger-type uncertainty relations are provided. These new lower…

In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…

Stable states (particles), ghosts and unstables states (particles) are discussed with respect to the time representations involved, their unitary groups and the induced Hilbert spaces. Unstable particles with their decay channels are…

In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…