相关论文: Symmetry-adapted Wannier functions in the maximal …
We investigate the localization properties of independent electrons in a periodic background, possibly including a periodic magnetic field, as e.g. in Chern insulators and in Quantum Hall systems. Since, generically, the spectrum of the…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both…
Wannier tight-binding models are effective models constructed from first-principles calculations. As such, they bridge a gap between the accuracy of first-principles calculations and the computational simplicity of effective models. In this…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
In this paper, we study the localization phenomena in a slender cylinder composed of an incompressible hyperelastic material subjected to axial tension. We aim to construct the analytical solutions based on a three-dimensional setting and…
A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…
Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend a choice of unitary transform known as a gauge…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…
Ab initio determination of model Hamiltonian parameters for strongly correlated materials is a key issue in applying many-particle theoretical tools to real narrow-band materials. We propose a self-contained calculation scheme to construct,…
Wannier functions of the one dimensional Schroedinger equation with elliptic one gap potentials are explicitly constructed. Properties of these functions are analytically and numerically investigated. In particular we derive an expression…
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…
It has been widely recognized that the 0/1 loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to…
We present a formulation of the density-functional theory + Hubbard model (DFT+U) method that is self-consistent over the choice of Hubbard projectors used to define the correlated subspaces. In order to overcome the arbitrariness in this…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
We consider an arbitrary square integrable function $F$ on the phase space and look for the Wigner function closest to it with respect to the $L^2$ norm. It is well known that the minimizing solution is the Wigner function of any…
We introduce a localized version of the nudging data assimilation algorithm for the periodic 2D Navier-Stokes equations in which observations are confined (i.e., localized) to a window that moves across the entire domain along a…
We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…