Related papers: Reconstructing parton distribution function based …
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem. In this study, we present and evaluate the efficiency of a selection…
We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower…
Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to…
Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides $\langle x \rangle$, face severe challenges from…
We present a new method, based on Gaussian process regression, for reconstructing the continuous $x$-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the unphysical…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state…
We apply a classical mathematical problem, the moment problem, with its related mathematical achievements, to the study of the parton distribution function (PDF) in hadron physics, and propose a strategy to sieve the moments of the PDF by…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
We present a nonperturbative determination of the pion valence parton distribution function (PDF) moment ratios $\left\langle x^{n-1} \right\rangle / \left\langle x \right\rangle$ up to $n=6$, using the gradient flow in lattice QCD. As a…
We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem…
We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework…
We present a new method to calculate moments of parton distribution functions of any order with lattice QCD computations. This method leverages the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution functions. We perform a systematic analysis using three lattice ensembles at two…
In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue measure. We propose a non-linear exponential transform of…