Related papers: Computing with small quasigroups and loops
The aim of this paper is to provide an atlas of identity bases for varieties generated by small semigroups and groups. To help the working mathematician easily find information, we provide a companion website that runs in the background…
In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode and…
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…
Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…
Elaborating on the novel formulation of the loop-tree duality, we introduce the Mathematica package Lotty that automates the latter at multi-loop level. By studying the features of Lotty and recalling former studies, we discuss that the…
We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t \bar{t}$ production and $\gamma \gamma$ production in gluon fusion through a massive top-quark loop. All…
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for…
Structures that demonstrate nonclassicality are of foundational interest in quantum mechanics, and can also be seen as resources for numerous applications in quantum information processing - particularly in the Hilbert space of $N$ qubits.…
The open-source nonlinear solver Ipopt (https://projects.coin-or.org/Ipopt) is a widely-used software package for the solution of large-scale non-linear optimization problems. At its heart, it employs a third-party linear solver to solve a…
Developing intuition about quantum information theory problems is difficult, as is verifying or ruling-out of hypothesis. We present a Matlab package intended to provide the QIT community with a new and powerful tool-set for quantum…
We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. $6$-divisible Moufang loops with commuting inner…
Circuit cutting is a promising technique that leverages both quantum and classical computational resources, enabling the practical execution of large quantum circuits on noisy intermediate-scale quantum (NISQ) hardware. Recent approaches…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…
Gaussian processes (GPs) are a highly flexible, nonparametric statistical model that are commonly used to fit nonlinear relationships or account for correlation between observations. However, the computational load of fitting a Gaussian…
We briefly summarize the background of the HeLP-method for torsion units in group rings and present some functionality of a GAP-package implementing it.
There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…