相关论文: Ambiguities in Pauli-Villars regularization

Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…

A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…

The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless…

We consider the homogenization of a semilinear elliptic equation where the coefficients of the second-order differential operator may be discontinuous. We establish the existence and uniqueness of the fine-scale solution, followed by an a…

In inverse problems, the use of an $\ell_{12}$ analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased…

The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the…

A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms…

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…

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The…

Consider reconstructing a signal $x$ by minimizing a weighted sum of a convex differentiable negative log-likelihood (NLL) (data-fidelity) term and a convex regularization term that imposes a convex-set constraint on $x$ and enforces its…

We revisit the regularity theory for uniformly elliptic equations.

We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…

We establish partial regularity for vector-valued solutions to inhomogeneous elliptic systems in divergence form where the coefficients are possibly discontinuous with respect to $x$. More precisely, we assume a VMO-condition with respect…

The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also…

New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…

A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…

One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…