Related papers: Regularization Schemes and Higher Order Correction…
Renormalization scheme uncertainties in the next-next-to-leading order QCD predictions are discussed. To obtain an estimate of these uncertainties it is proposed to compare predictions in all schemes that do not have unnaturally large…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
A next-to-leading order calculation for single top production including spin-dependent observables requires efficient techniques for the calculation of the relevant loop amplitudes. We discuss the adaption of dimensional regularization, the…
In this letter we discuss a regularization scheme for the integration of generic on-shell forms. The basic idea is to extend the three-particle amplitudes to the space of unphysical helicities keeping the dimension of the related coupling…
Deep Reinforcement Learning (Deep RL) has been receiving increasingly more attention thanks to its encouraging performance on a variety of control tasks. Yet, conventional regularization techniques in training neural networks (e.g., $L_2$…
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
The complete set of Feynman rules for the rational part R of QCD corrections in the MSSM are calculated at the one-loop level, which can be very useful in the next-to-leading order calculations in supersymmetric models. Our results are…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…
In this review article we report on the newest developments in precision calculations in supersymmetric theories. An important issue related to this topic is the construction of a regularization scheme preserving simultaneously gauge…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
The state-of-the-art in current two-loop QCD amplitude calculations is at five-particle scattering. Computing two-loop six-particle processes requires knowledge of the corresponding one-loop amplitudes to higher orders in the dimensional…
Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative…
We consider variants of dimensional regularization, including the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED), and present the gluon and quark form factors in the FDH scheme at next-to-next-to-leading order. We…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
We discuss how to apply regularization by dimensional reduction for computing hadronic cross sections at next-to-leading order. We analyze the infrared singularity structure, demonstrate that there are no problems with factorization, and…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
In the field of machine learning there is a growing interest towards more robust and generalizable algorithms. This is for example important to bridge the gap between the environment in which the training data was collected and the…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…