相关论文: A (Slightly Less Brutal) Method for Numerically Ev…
Numerical solution of DGLAP $Q^2$ evolution equations is studied for polarized parton distributions by using a ``brute-force" method. NLO contributions to splitting functions are recently calculated,and they are included in our analysis.…
I report on a numerical program for the evolution of parton distributions. The program uses the Mellin-transform method with an optimized contour. Due to this optimized contour the program needs only a few evaluations of the integrand and…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
In this paper, the problem of the minimal description of the structure of a vector function f(x) over an $N$-dimensional interval is studied. Methods adaptively subdividing the original interval in smaller subintervals and evaluating f(x)…
Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
We investigate numerical solution of $Q^2$ evolution equations for structure functions in the nucleon and in nuclei. (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi and Mueller-Qiu evolution equations are solved in a brute-force method.…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
The latest structure function results, as presented at the ICHEP98 conference, are reviewed. A brief introduction to the formalism and the status of global analyses of parton distributions is given. The review focuses on three experimental…
In this paper, we propose a general approach for improving the efficiency of computing distribution functions. The idea is to truncate the domain of summation or integration.
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex…
Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…
We construct a dynamical model for the parton distributions in a nucleus by perturbative evolution of input distributions from a low starting scale. These input distributions are obtained by modifications of the corresponding free nucleon…
Structure functions are a measure of the partonic structure of hadrons, which is important for any process which involves colliding hadrons. They are a key ingredient for deriving partons distributions in nucleons. In recent years dramatic…
I recommend a few trivial changes to the routines that evaluate CTEQ parton distribution functions. These changes allow modern compilers to optimize the evaluation routines, while having no quantitative effect on the results. Computation…