Related papers: Modern techniques of multiloop calculations
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
We propose a method for computing numerically integrals defined via $i \epsilon$ deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce…
We discuss some aspects of the theory of subelliptic estimates.
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
This is an introductory article to the theory of multiple gaps.
This note reports on an independent implementation of calculating one-loop amplitudes semi-numerically using generalized unitarity techniques. The algorithm implemented in form of a C++ code closely follows the method by Ellis, Giele,…
We apply recently proposed regional predictive control approaches to several examples to evaluate their efficiency. We present numerical results as well as hardware-in-the-loop (HIL) results.
The aim of this work is to give an introduction to the theoretical background and computational complexity of Markov chain Monte Carlo methods. Most of the mathematical results related to the convergence are not found in most of the…
Work in progress concerning alternative formalizations of arithmetic.
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
We present a completely numerical method of calculating one-loop amplitudes. Our approach is built upon two different existing methods: the contour deformation and the extrapolation methods. Taking the best features of each of them, we…
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
The search for signals of new physics at the forthcoming LHC experiments involves the analysis of final states characterised by a high number of hadronic jets or identified particles. Precise theoretical predictions for these processes…
This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.
We give a more detailed description of the new system of Pl\"ucker-like equations from [4], discuss how it relates to the usual Pl\"ucker equations, and correct a mistake in that article.
In the investigation carried out, the superconducting nanotube paraconductivity calculation algorithm is defined more precisely.
We present new versions of the Mathematica package FeynCalc and the FeynHelpers add-on that represent an important contribution to the collection of public codes for semi-automatic evaluation of multiloop Feynman diagrams. FeynHelpers…
Over the last ten years, we have seen a significant increase in industrial data, tremendous improvement in computational power, and major theoretical advances in machine learning. This opens up an opportunity to use modern machine learning…