Related papers: Discretisation Errors in Landau Gauge on the Latti…
This paper considers the implicit Euler discretization of Levant's arbitrary order robust exact differentiator in presence of sampled measurements. Existing implicit discretizations of that differentiator are shown to exhibit either…
We numerically investigate the multicritical behavior of the three dimensional lattice system in which a SU(2) gauge field is coupled to two flavors of scalar fields transforming in the fundamental representation of the gauge group. In this…
In this paper we investigate the generalization error of gradient descent (GD) applied to an $\ell_2$-regularized OLS objective function in the linear model. Based on our analysis we develop new methodology for computationally tractable and…
The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore…
Complex contour deformations of the path integral have been demonstrated to significantly improve the signal-to-noise ratio of observables in previous studies of two-dimensional gauge theories with open boundary conditions. In this work,…
Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and…
Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this…
We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed…
The Gribov ambiguity problem is studied for compact lattice QED within the Lorentz gauge. In the Coulomb phase, Gribov copies are mainly caused by double Dirac sheets and zero-momentum modes of the gauge fields. Removing them by (non-)…
We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method. When the function is smooth…
Mislabeled data is a pervasive issue that undermines the performance of machine learning systems in real-world applications. An effective approach to mitigate this problem is to detect mislabeled instances and subject them to special…
We discuss the possibility to obtain a massive Landau gauge, based on the local composite operator (LCO) effective action framework combined with the Zimmerman reduction of couplings prescription. As a way to deal with the gauge ambiguity,…
Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear theoretical foundations. In particular, the consistency…
The development of improved algorithms for QCD on the lattice has enabled us to do calculations at small quark masses and get control over the chiral extrapolation. Also finer lattices have become possible, however, a severe slowing down…
In ab-initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. "Ab-initio" means a process performed without any good…
Gauge fixing in the non-perturbative domain of non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. To compare results from different methods it is necessary to resolve this ambiguity explicitly. Such a resolution is…
We construct symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450' chiral gauge theory, by leveraging bosonization and recently-proposed modifications of Villain-type lattice…
The present work aims at the application of finite element discretizations to a class of equilibrium problems involving moving constraints. Therefore, a Moreau--Yosida based regularization technique, controlled by a parameter, is discussed…
We construct an $O(a^2)$-improved overlap-Dirac operator by designing an improved overlap kernel, based on the Symanzik improvement program. Field rotation terms are also identified to improve off-shell amplitudes for both massless and…
We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of $O(a)$, including those proportional to the quark mass, leaving only errors of $O(a^2)$. The method exploits the…