Related papers: Computing radiative corrections in four dimensions
We employ the density matrix renormalization group (DMRG) and the wave function factorization method for the numerical solution of large scale nuclear structure problems. The DMRG exhibits an improved convergence for problems with realistic…
Controlling the false discovery rate (FDR) is a popular approach to multiple testing, variable selection, and related problems of simultaneous inference. In many contemporary applications, models are not specified by discrete variables,…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization…
We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly…
We describe the calculation of the one-loop corrections to $H \to \gamma \gamma$ and $g g \to H$ within the four-dimensional unsubtraction/loop-tree duality (FDU/LTD) approach. The fact that these corrections are both IR and UV finite is…
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the…
The naive perturbation expansion for many-fermion systems is infrared divergent. One can remove these divergences by introducing counterterms. To do this without changing the model, one has to solve an inversion equation. We call this…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we present a new method, the inserter regularization method,…
In several preceding studies, the explicitly covariant formulation of light front dynamics was developed and applied to many observables. In the present study we show how in this approach the renormalization procedure for the first…
In this paper I argue that infinities in the classical computation theory such as the unsolvability of the Halting Problem can be addressed in the same way as Feynman divergences in Quantum Field Theory, and that meaningful versions of…
We present an alternative procedure for defining infra-red counterterms within dimensional regularisation for use in the $R^*$ procedure. The counterterms are given by simple closed expressions, and lead to the standard MSbar UV…
This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
The regularization and renormalization of the radiative mass-type quadrupole moment of inspiralling compact binaries (without spins) is investigated at the fourth post-Newtonian (4PN) approximation of general relativity. As clear from the…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
This paper presents a novel factorization-based, low-rank regularization method for solving multidimensional deconvolution problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented…