相关论文: Consistency Relations for an Implicit n-dimensiona…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are…

The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…

Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…

We generalise the $\eta$ regularisation scheme in order to develop a framework for systematically studying regularisation of loops in quantum field theory. This allows us to "solve" a set of gauge consistency conditions for families of…

The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional spacetime and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales,…

Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which…

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…

A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and…

In the field of machine learning there is a growing interest towards more robust and generalizable algorithms. This is for example important to bridge the gap between the environment in which the training data was collected and the…

It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and…

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…

In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in…

Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

We examine the subtleties of regularization schemes in four-dimensional space ($4S$), related in particular to the introduction of the $\gamma_5$ matrix. To illustrate we use a "Bumblebee" model featuring dynamically induced Lorentz…

We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link…

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial…