Related papers: Technique for computing the PDFs and CDFs of non-n…
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…
The perturbative procedure of matching was proposed to connect parton quasi-distributions that are calculable in lattice QCD to the corresponding light-cone distributions which enter physical processes. Such a matching procedure has so far…
The L\'evy-Khintchine theorem is a classical result in Diophantine approximation that describes the asymptotic growth of the denominators of convergents in the continued fraction expansion of a typical real number. An effective version of…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
Parton distribution functions (PDFs) are an essential ingredient for theoretical predictions at colliders. Since their exact form is unknown, their handling and delivery for practical applications relies on approximate numerical methods. We…
In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…
Survival analysis holds a crucial role across diverse disciplines, such as economics, engineering and healthcare. It empowers researchers to analyze both time-invariant and time-varying data, encompassing phenomena like customer churn,…
We address the problem of uncertainty quantification for the deconvolution model \(Z = X + Y\), where \(X\) and \(Y\) are nonnegative random variables and the goal is to estimate the signal's distribution of \(X \sim F_0\) supported…
Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…
We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation…
Summarizing results from Joseph Mecke's last fragmentary manuscripts, the generating function and the Laplace transform for nonnegative random variables are considered. The concept of thickening of a random variable, as an inverse operation…
While it is a common knowledge that AC coefficients of Fourier-related transforms, like DCT-II of JPEG image compression, are from Laplace distribution, there was tested more general EPD (exponential power distribution) $\rho\sim…
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly…
In 1964 R.Gangolli published a L\'{e}vy-Khintchine type formula which characterised $K$ bi-invariant infinitely divisible probability measures on a symmetric space $G/K$. His main tool was Harish-Chandra's spherical functions which he used…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an…
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…
We present a lattice QCD calculation of the transversity isovector- and isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we determine…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
This paper focuses on representing the $L^{\infty}$-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to…