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Register a new userOn the reduction of hypercubic lattice artifacts
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This note presents a comparative study of various options to reduce the errors coming from the discretization of a Quantum Field Theory in a lattice with hypercubic symmetry. We show that it is possible to perform an extrapolation towards the continuum which is able to eliminate systematically the artifacts which break the O(4) symmetry.
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The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI-MOM scheme a large part of these artifacts can be calculated and subtracted with the help of diagrammatic Lattice Perturbation Theory (LPT). Such calculations are typically restricted to 1-loop order, but one may overcome this limitation and calculate hypercubic corrections for any operator and action beyond the 1-loop order using Numerical Stochastic Perturbation Theory (NSPT). In this study, we explore the practicability of such an approach and consider, as a first test, the case of Wilson fermion bilinear operators in a quenched theory. Our results allow us to compare boosted and unboosted perturbative corrections up to the 3-loop order.
Lectures given at the Summer School on Modern perspectives in lattice QCD, Les Houches, August 3-28, 2009
The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. They are always present because simulations are done at lattice spacings $a$ and momenta $p$ with $ap$ not necessarily small. In this paper we try to suppress these artifacts by subtraction of one-loop contributions in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of $O(a^2)$.
Lattice artifacts in the 2d O(n) non-linear sigma-model are expected to be of the form O(a^2), and hence it was (when first observed) disturbing that some quantities in the O(3) model with various actions show parametrically stronger cutoff dependence, apparently O(a), up to very large correlation lengths. In a previous letter we described the solution to this puzzle. Based on the conventional framework of Symanziks effective action, we showed that there are logarithmic corrections to the O(a^2) artifacts which are especially large, (ln(a))^3, for n=3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3) and O(4) are also presented.
Convolutional Neural Networks (CNN) has been extensively studied for Hyperspectral Image Classification (HSIC) more specifically, 2D and 3D CNN models have proved highly efficient in exploiting the spatial and spectral information of Hyperspectral Images. However, 2D CNN only considers the spatial information and ignores the spectral information whereas 3D CNN jointly exploits spatial-spectral information at a high computational cost. Therefore, this work proposed a lightweight CNN (3D followed by 2D-CNN) model which significantly reduces the computational cost by distributing spatial-spectral feature extraction across a lighter model alongside a preprocessing that has been carried out to improve the classification results. Five benchmark Hyperspectral datasets (i.e., SalinasA, Salinas, Indian Pines, Pavia University, Pavia Center, and Botswana) are used for experimental evaluation. The experimental results show that the proposed pipeline outperformed in terms of generalization performance, statistical significance, and computational complexity, as compared to the state-of-the-art 2D/3D CNN models except commonly used computationally expensive design choices.
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