Related papers: Dimensional regularization vs methods in fixed dim…

It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.

Given a holomorphic regularisation procedure (e.g. Riesz or dimensional regularisation) on classical symbols, we define renormalised multiple integrals of radial classical symbols with linear constraints. To do so, we first prove the…

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…

Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to…

We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…

The necessity of renormalization arises from the infinite integrals which are caused by the discrepancy between the orders of differential and integral operators in the four dimensional QFTs. Therefore in view of the fact that finiteness…

After proving a multi-dimensional extension of Zalcman's renormalization lemma and considering maximality problems about dimensions, we find renormalizing polynomial families for iterated elementary mappings, extending this result to some…

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing…

In the present paper we propose generalizations of the regularity and counting lemmas for multidimensional matrices under a finite alphabet. Firstly, we prove a variant of a multidimensional regularity lemma with the help of a translation…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

We perform a brief review on Dirac's procedure applied to the well known Einstein's linearized gravity in $N > 2$ dimensions. Considering it as a gauge theory and therefore the manifestation of second class constraints in analogy with the…

In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general…

We show how to use dimensional regularization to determine, within the Arnowitt-Deser-Misner canonical formalism, the reduced Hamiltonian describing the dynamics of two gravitationally interacting point masses. Implementing, at the third…

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…

In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting,…

A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…

In this work, the general form of $2\times2$ Dirac matrices for 2+1 dimension is found. In order to find this general representation, all relations among the elements of the matrices and matrices themselves are found,and the generalized…

Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…

We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a regularization effect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small…

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…