Related papers: Using C++ to Calculate $\mathsf{SO(10)}$ Tensor Co…
In this thesis, we develop techniques for the analysis of SO(2N) invariant couplings which allows a full exhibition of the SU(N) invariant content of the spinor and tensor representations. The techniques utilize a so called Basic Theorem…
A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving $16_{\pm}$ semispinors of SO(10) chirality $\pm$…
Higgs multiplet in the vector-spinor representations of SO(10), i.e., the $144+\bar{144}$ multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry $SU(3)_C\times SU(2)_L\times…
We develop techniques for the analysis of SO(2N) invariant couplings which allow a full exhibition of the SU(N) invariant content of the spinor and tensor representations. The technique utilizes a basis consisting of a specific set of…
We present the program Top++ for the numerical evaluation of the total inclusive cross-section for producing top quark pairs at hadron colliders. The program calculates the cross-section in a) fixed order approach with exact next-to-next-to…
A review is given of a recently developed technique for the analysis of SO(2N) invariant couplings which allows a full exhibition of the SU(N) invariant content of couplings involving the SO(2N) semi-spinors $|\Psi_{\pm}>$ with chiralilty…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
Tensors (also commonly seen as multi-linear operators or as multi-dimensional arrays) are ubiquitous in scientific computing and in data science, and so are the software efforts for tensor operations. Particularly in recent years, we have…
We perform numerical fits of Grand Unified Models based on SO(10), using various combinations of 10-, 120- and 126-dimensional Higgs representations. Both the supersymmetric and non-supersymmetric versions are fitted, as well as both…
An analysis of the couplings of the 210 dimensional SO(10) vector multiplet to matter is given. Specifically we give an $SU(5)\times U(1)$ decomposition of the vector couplings $\bar{16}_{\pm}-16_{\pm}-210$, where $16_{\pm}$ is the…
We investigate Higgs Parity Unification-a realization of $SO(10)$ grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right…
We consider Grand Unified Theories based on $SO(10)$ which originate from $M$ theory on $G_2$ manifolds. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem involving an extra $\overline{{\bf…
We present the C++ library CppSs (C++ super-scalar), which provides efficient task-parallelism without the need for special compilers or other software. Any C++ compiler that supports C++11 is sufficient. CppSs features different…
An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++…
We present two precision tools for the simulation of Higgs-pair production via vector-boson fusion in the kappa framework for the parameterization of non-standard Higgs couplings. A new implementation of the process is developed in the…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
Tensor computations present significant performance challenges that impact a wide spectrum of applications ranging from machine learning, healthcare analytics, social network analysis, data mining to quantum chemistry and signal processing.…
The article presents and documents the Mathematica package SymBuild. This package implements the computation and manipulation of integrable symbols appearing in various calculations in high-energy scattering amplitudes. By using Gr\"obner…