Related papers: Numerical integration of subtraction terms
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincide with a discretisation point, and the jumps in the function…
We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate Taylor polynomial arithmetic and matrix…
Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature…
We include a resummation of large transverse momentum logarithms in the next-to-leading order (NLO) Balitsky-Kovchegov equation. The resummed evolution equation is shown to be stable, the evolution speed being significantly reduced by NLO…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
In this paper we discuss the definition, the construction and the implementation of \textit{generalised antenna functions} for final-state radiation up to Next-to-Next-to-Leading Order (NNLO) in QCD. Generalised antenna functions…
In a series of papers we have developed the method of iterated sector decomposition for the calculation of infrared divergent multi-loop integrals. Here we apply it to phase space integrals to calculate a contribution to the double real…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
We discuss recent progress in the calculation of integrated antenna functions for final-state radiation at N$^3$LO in QCD. Antenna functions are directly extracted from physical matrix elements for the decay of a colour-singlet state into…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
In this paper, we investigate the problem of mining numerical data in the framework of Formal Concept Analysis. The usual way is to use a scaling procedure --transforming numerical attributes into binary ones-- leading either to a loss of…
We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of…
In this presentation we review the current status in the automated evaluation of scattering amplitudes, with particular attention to the developments related with NLO calculations, which led to the construction of powerful multi-purpose…
We report on a new method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals.…
We present a new subtraction scheme for next-to-leading order QCD calculations, where the momentum mapping and the splitting functions have been derived in the context of an improved parton shower formulation. A main advantage of our scheme…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
We enumerate total cyclic orders on $\left\{1,\ldots,n\right\}$ where we prescribe the relative cyclic order of consecutive triples $(i,{i+1},{i+2})$, these integers being taken modulo $n$. In some cases, the problem reduces to the…
We extend the dipole formalism for massless and massive partons to random polarisations of the external partons. The dipole formalism was originally formulated for spin-summed matrix elements and later extended to individual helicity…