Related papers: Dimensional Regularization in Quarkonium Calculati…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
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…
Quantizing images into discrete representations has been a fundamental problem in unified generative modeling. Predominant approaches learn the discrete representation either in a deterministic manner by selecting the best-matching token or…
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…
Second-order optimization methods, such as cubic regularized Newton methods, are known for their rapid convergence rates; nevertheless, they become impractical in high-dimensional problems due to their substantial memory requirements and…
In the paper, we calculate the fragmentation functions for $c \to \eta_c$ and $b \to \eta_b$ up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization…
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…
Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $\epsilon$-poles, allowing to define counter-terms with useful recursive…
This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing that with the correct discretization strategy, convergence -…
We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-p_T particles into fragmentation functions for hadronic initial states. We investigate the further…
Within an effective field theory framework we compute the most general structure of the one-loop corrections to the 4D gauge couplings in one- and two-dimensional orbifold compactifications with non-vanishing constant gauge background…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
Most previous calculations of the annihilation decay rates of heavy quarkonium were based on factorization assumptions that were unproven and, in some cases, even incorrect. The recent development of a general factorization formula for…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
We derive the in-medium gluon radiation spectrum off a quark within the path integral formalism at finite energies, including all next-to-eikonal corrections in the propagators of quarks and gluons. Results are computed for finite formation…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
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…