Related papers: Probability density functions of quantum mechanica…
Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal…
We investigate the behavior of spin-dependent parton distribution functions (PDFs) at large parton momentum fractions x in the context of global QCD analysis. We explore the constraints from existing deep-inelastic scattering data, and from…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…
Accurate uncertainty quantification of model predictions is a crucial problem in machine learning. Existing Bayesian methods, being highly iterative, are expensive to implement and often fail to accurately capture a model's true posterior…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a…
We present a theoretical framework to quantify statistical uncertainties in covariant density functional theory (CDFT) for both nuclear matter and finite nuclei, based on a relativistic point-coupling energy density functional (EDF). By…
The statistical approach is used to calculate the parton distribution functions (PDFs) of the nucleon. At first it is assumed that the partons are free particles and the light-front kinematic variables are employed to extract the Bjorken…
We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density…