Related papers: Uncertainty product for Vilenkin groups
Visualization and analysis of multivariate data and their uncertainty are top research challenges in data visualization. Constructing fiber surfaces is a popular technique for multivariate data visualization that generalizes the idea of…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
We introduce the concept of an imprecise Markov semigroup \(\mathbf Q\). It is a tool that allows us to represent ambiguity around both the transition probabilities and the invariant measure of a continuous-time Markov process via a…
The statistical behaviour of a product of independent, identically distributed random matrices in $\text{SL}(2,{\mathbb R})$ is encoded in the generalised Lyapunov exponent $\Lambda$; this is a function whose value at the complex number $2…
Classical mechanics unfolds within absolute time and Euclidean space, yet our knowledge of where events occur, when they occur, and how motion evolves is inherently uncertain. The special Galilean group provides a natural setting for…
We provide a unified and strengthened framework for the product form and the sum form variance-based uncertainty relations by constructing a unified uncertainty relation. In the unified framework, we deduce that the uncertainties of the…
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…
On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and…
The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…
We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
Quantifying predictive uncertainty of neural networks has recently attracted increasing attention. In this work, we focus on measuring uncertainty of graph neural networks (GNNs) for the task of node classification. Most existing GNNs model…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…
The non-relativistic quantum mechanics with the generalized uncertainty principle (GUP) is examined when the potential is one-dimensional $\delta-$function. It is shown that unlike usual quantum mechanics, the Schr\"{o}dinger and Feynman's…
The Generalized Uncertainty Principle (GUP) and Extended Uncertainty Principle (EUP) are modifications to the Heisenberg Uncertainly Principle (HUP), expected to apply as the energy approaches the Planck scale. Here we consider a possible…
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.
We consider the approximate properties of tight wavelet frames on Vilenkin group $G$. Let $\{G_n\}_{n\in \mathbb{Z} }$ be a main chain of subgroups, $X$ be a set of characters. We define a step function $\lambda({\chi})$ that is constant on…
We initiate the study of quadratic discrepancy for finite point sets on the Heisenberg group $\mathbb H^n$ with respect to upper Ahlfors regular probability measures. For a natural family of test sets given by left translations and…
We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…