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We describe theoretical backgrounds for a computer program that recognizes all closed orientable 3-manifolds up to complexity 8. The program can treat also not necessarily closed 3-manifolds of bigger complexities, but here some…
The Spectral Airglow Temperature Imager is an instrument, specially designed for investigation of the wave processes in the Mesosphere-Lower Thermosphere. In order to determine the kinematic parameters of a wave, the values of a physical…
We present a new Mathematica package that provides a platform to perform multi-loop computations. ANATAR integrates several existing tools designed for higher-order computations. In particular, it uses QGRAF to generate Feynman diagrams and…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…
FormCalc is a Mathematica package for the automatic computation of tree-level and one-loop Feynman amplitudes. It accepts diagrams generated by FeynArts, simplifies them, and generates a complete Fortran code for their numerical evaluation.…
Recently, we proposed a new approach using a punctured Elliptic curve in the CHY framework in order to compute one-loop scattering amplitudes. In this note, we further develop this approach by introducing a set of connectors, which become…
Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
PENLAB is an open source software package for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these. It is written entirely in MATLAB. PENLAB is a young brother of our code PENNON \cite{pennon}…
We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
We present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory. It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. Our…
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
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…
We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
In this chapter we are concerned with external auditory representations of programs, also known as program auralization. As program auralization systems tend to use musical representations they are necessarily affected by artistic and…
An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with…
A detailed analysis to the [1,2] Pad\'e approximation to the $\pi\pi$ scattering 2--loop amplitudes in chiral perturbation theory is made.