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We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing…
We introduce the physical factorisation scheme, which is necessary to describe observables which are `not completely inclusive'. We derive the formulae for NLO DGLAP evolution in this scheme, and also for the `rotation' of the conventional…
Reliable uncertainty estimates are an important tool for helping autonomous agents or human decision makers understand and leverage predictive models. However, existing approaches to estimating uncertainty largely ignore the possibility of…
The goal of this study is to find a prescription for defining parton distributions (PDFs) which are most appropriate for use in those codes where only LO matrix elements (MEs) are used, as in many Monte Carlo generators. We describe a…
Deviations from scale invariance resulting from small perturbations of a general two dimensional conformal field theory are studied. They are expressed in terms of beta functions for renormalization of general couplings under local change…
Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is…
From benign overfitting in overparameterized models to rich power-law scalings in performance, simple ridge regression displays surprising behaviors sometimes thought to be limited to deep neural networks. This balance of phenomenological…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two…
The results on polarized parton densities (PDFs) obtained using different methods of QCD analysis of the present polarized DIS data are discussed. Their dependence on the method used in the analysis, accounting or not for the kinematic and…
We review recent progress towards a determination of a set of polarized parton distributions from a global set of deep-inelastic scattering data based on the NNPDF methodology, in analogy with the unpolarized case. This method is designed…
We revise the relation between Parton Distribution Functions (PDFs) and matrix elements computable from lattice QCD, focusing on the quasi-Parton Distribution Functions (qPDFs) approach. We exploit the relation between PDFs and qPDFs in the…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
We present the first NNPDF full set of Parton Distribution Functions from a comprehensive DIS analysis. This approach, combining a Monte Carlo sampling of the probability measure in the space of PDFs with the use of neural networks as…
We present a new prescription to account for heavy quark mass effects in the determination of parton distribution functions (PDFs) based on the FONLL scheme. Our prescription makes explicit use of the freedom to choose the number of active…
Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…
The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no…
We discuss the determination of the parton substructure of hadrons by casting it as a peculiar form of pattern recognition problem in which the pattern is a probability distribution, and we present the way this problem has been tackled and…