Related papers: Dipole Splitting Algorithm -- A practical algorith…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
We propose and analyze an adaptive step-size variant of the Davis-Yin three operator splitting. This method can solve optimization problems composed by a sum of a smooth term for which we have access to its gradient and an arbitrary number…
We compute the next-to-leading order (NLO) QCD corrections to the $1 \to 2$ splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze…
A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary…
In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
We report on the implementation of a coherent dipole shower algorithm along with an automated implementation for dipole subtraction and for performing POWHEG- and MC@NLO-type matching to next-to-leading order (NLO) calculations. Both…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent…
We define the collinear factorization scheme, which absorbs only the collinear physics into the parton distribution functions. In order to isolate the collinear physics, we introduce a procedure to combine real and virtual corrections,…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection,…
We present a new parton level Monte Carlo program for the calculation of jet cross sections in Deep Inelastic Scattering based on Born and next-to-leading order matrix elements. Using a class of invariant jet definition schemes, the program…
Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…
Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
The phase space slicing method of two cutoffs for next-to-leading-order Monte-Carlo style QCD corrections has been applied to many physics processes. The method is intuitive, simple to implement, and relies on a minimum of process dependent…
Sequences set is a mathematical model used in many applications. As the number of the sequences becomes larger, single sequence set model is not appropriate for the rapidly increasing problem sizes. For example, more and more text…
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
We present the extension of two general algorithms for the treatment of infrared singularities arising in electroweak corrections to decay processes at next-to-leading order: the dipole subtraction formalism and the one-cutoff slicing…