Related papers: Calculation of multi-scale, multi-loop integrals u…
A new approach for the reduction of tensor integrals is described. The standard decomposition \`{a} la Davydychev is applied. Integrals with higher indices are then expressed in terms of scalar higher-dimensional integrals with generic…
A new simulation package, GSEIM, for solving a set of ordinary differential equations is presented. The organisation of the program is illustrated with the help of a block diagram. Various features of GSEIM are discussed. Two ways of…
We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the…
Machine Learning approaches like clustering methods deal with massive datasets that present an increasing challenge. We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method is based on…
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
In this paper, we present rIC3, an efficient bit-level hardware model checker primarily based on the IC3 algorithm. It boasts a highly efficient implementation and integrates several recently proposed optimizations, such as the specifically…
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show…
This work explores an unexpected application of Implicit Computational Complexity (ICC) to parallelize loops in imperative programs. Thanks to a lightweight dependency analysis, our algorithm allows splitting a loop into multiple loops that…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Modules and packages for the one-loop calculations at partonic level represent the first level of SANC output computer product. The next level represents Monte Carlo integrator mcsanc, realizing fully differential hadron level calculations…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
We calculate the three-loop Adler $D$-function of ${\cal N}=1$ SQCD regularized by higher covariant derivatives and find the subtraction scheme in which the exact NSVZ-like relation for this function that was recently proposed is valid.
We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis…
We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages,…