Related papers: Dimensional Reduction and Hadronic Processes

We discuss a modification of the next-to-next-to-leading order (NNLO) subtraction scheme based on the residue-improved sector decomposition that reduces the number of double-real emission sectors from five to four. In particular, a sector…

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…

This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…

We investigate the regularization-scheme dependence of scattering amplitudes in massless QCD and find that the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED) are consistent at least up to NNLO in the perturbative…

An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…

We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…

We establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix. For this sake, we define the notion of normality of a $p$-adic operator, and give several criteria for the normality. We…

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

We describe how the nested soft-collinear subtraction scheme [1] can be used to compute the next-to-next-to-leading order (NNLO) QCD corrections to the production of an arbitrary number of gluonic jets in hadron collisions. We show that the…

Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout…

This paper investigates a class of Lagrangian control systems with $n$ degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds.…

The possibility is discussed that existence of renormalon singularities is not the internal property of the specific field theory but depends on the renormalization scheme.

Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalise to systems with higher codimension discontinuities. These higher…

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…

We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. With this…

One obstacle that so far prevents the introduction of machine learning models primarily in critical areas is the lack of explainability. In this work, a practicable approach of gaining explainability of deep artificial neural networks (NN)…

We use renormalization as a tool to extract universal features of the NN interaction in quark and soliton nucleon models, having the same long distance behaviour but different short distance components. While fine tuning conditions in the…

We study the Lorentz and Dirac algebra, including antisymmetric $\epsilon$ tensors and the $\gamma_5$ matrix, in implicit gauge-invariant regularization/renormalization methods defined in fixed integer dimensions. They include constrained…

In the usual procedure for toroidal Kaluza-Klein reduction, all the higher-dimensional fields are taken to be independent of the coordinates on the internal space. It has recently been observed that a generalisation of this procedure is…

A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth…