Related papers: GLoop: A Monte Carlo program to construct higher-l…

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…

A Monte Carlo program is presented for the computation of the most general cross section for two-photon production in e+e- collisions at fixed two-photon invariant mass W. Functions implemented for the five gamma* gamma* structure functions…

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…

In this note I illustrate the program MINT, a FORTRAN program for Monte Carlo adaptive integration and generation of unweighted distributions.

We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…

Monte Carlo simulation using the standard single-spin flip algorithm often fails to sample over the entire configuration space at low temperatures for frustrated spin systems. A typical example is a class of spin-ice type Ising models. In…

We propose Orthogonal Monte Carlo Dropout, a mechanism that enforces strict orthogonality when combining sparse semantic vectors without extra time complexity. Low-Rank Adaptation (LoRA), a popular fine-tuning method for large models,…

In lattice QCD the calculation of disconnected quark loops from the trace of the inverse quark matrix has large noise variance. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials on a…

We introduce mlOSP, a computational template for Machine Learning for Optimal Stopping Problems. The template is implemented in the R statistical environment and publicly available via a GitHub repository. mlOSP presents a unified numerical…

Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…

We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.

Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is…

We simulate TIP3P water using a constrained Monte Carlo algorithm to generate electrostatic interactions eliminating the need to sum over long ranged Coulomb interactions. We study discretization errors when interpolating charges using…

These lectures given to graduate students in high energy physics, provide an introduction to Monte Carlo methods. After an overview of classical numerical quadrature rules, Monte Carlo integration together with variance-reducing techniques…

This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…

The aim of XLOOPS is to calculate one-particle irreducible Feynman diagrams with one or two closed loops for arbitrary processes in the Standard model of particles and related theories. Up to now this aim is realized for all one-loop…

This is a companion to our lectures GAP and loops, to be delivered at the Workshops Loops 2007, Prague, Czech Republic. In the lectures we introduce the GAP package LOOPS, describe its capabilities, and explain in detail how to use it. In…

The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…

FiniteFlow is a public framework for defining and executing numerical algorithms over finite fields and reconstructing multivariate rational functions. The framework allows to build complex algorithms by combining basic building blocks into…

Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The…