Related papers: Status reports from the GRACE Group
Based on the OPP technique and the HELAC framework, HELAC-1LOOP is a program that is capable of numerically evaluating QCD virtual corrections to scattering amplitudes. A detailed presentation of the algorithm is given, along with…
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on…
In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e.,…
Numerical relativity simulations of merging black holes provide the most accurate description of the binary dynamics and the emitted gravitational wave signal. However, practical considerations such as imperfect initial data and initial…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
Mathematica package LiteRed is described. It performs the heuristic search of the symbolic IBP reduction rules for loop integrals. It implements also several convenient tools for the search of the symmetry relations, construction of the…
We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer…
One-loop counterterms are computed in the first order formalism for the Einstein-Hilbert action with a minimally coupled scalar field using the background field method and the heat kernel technique. The {\em off-shell} divergent piece in…
We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to judge when computational errors are irrelevant and estimate the…
We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several…
With the advent of a new generation of telescopes (INTEGRAL, Fermi, H.E.S.S., MAGIC, VERITAS, MILAGRO) and the prospects of planned observatories such as CTA or HAWC, gamma-ray astronomy is becoming an integral part of modern astrophysical…
SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint…
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…
We propose a novel multivariate Monte Carlo method as an efficient and flexible approach to analyzing extended X-ray sources with the Reflection Grating Spectrometer (RGS) on XMM Newton. A multi-dimensional interpolation method is used to…
As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…
We present a new approach to Reggeization of gauge amplitudes based on the universal properties of their infrared singularities. Using the "dipole formula", a compact ansatz for all infrared singularities of massless amplitudes, we study…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…