79,668 research outputs found
Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
The Eisenhart-Duval lift allows embedding non-relativistic theories into a
Lorentzian geometrical setting. In this paper we study the lift from the point
of view of the Dirac equation and its hidden symmetries. We show that
dimensional reduction of the Dirac equation for the Eisenhart-Duval metric in
general gives rise to the non-relativistic Levy-Leblond equation in lower
dimension. We study in detail in which specific cases the lower dimensional
limit is given by the Dirac equation, with scalar and vector flux, and the
relation between lift, reduction and the hidden symmetries of the Dirac
equation. While there is a precise correspondence in the case of the lower
dimensional massive Dirac equation with no flux, we find that for generic
fluxes it is not possible to lift or reduce all solutions and hidden
symmetries. As a by-product of this analysis we construct new Lorentzian
metrics with special tensors by lifting Killing-Yano and Closed Conformal
Killing-Yano tensors and describe the general Conformal Killing-Yano tensor of
the Eisenhart-Duval lift metrics in terms of lower dimensional forms. Lastly,
we show how dimensionally reducing the higher dimensional operators of the
massless Dirac equation that are associated to shared hidden symmetries it is
possible to recover hidden symmetry operators for the Dirac equation with flux.Comment: 18 pages, no figures. Version 3: some typos corrected, some
discussions clarified, part of the abstract change
Spin-resolved optical conductivity of two-dimensional group-VIB transition-metal dichalcogenides
We present an ab-initio study of the spin-resolved optical conductivity of
two-dimensional (2D) group-VIB transition-metal dichalcogenides (TMDs). We
carry out fully-relativistic density-functional-theory calculations combined
with maximally localized Wannier functions to obtain band manifolds at
extremely high resolutions and focus on the photo-response of 2D TMDs to
circularly-polarized light in a wide frequency range. We present extensive
numerical results for monolayer TMDs involving molybdenum and tungsten combined
with sulphur and selenium. Our numerical approach allows us to locate with a
high degree of accuracy the positions of the points in the Brillouin zone that
are responsible for van Hove singularities in the optical response.
Surprisingly, some of the saddle points do not occur exactly along
high-symmetry directions in the Brillouin zone, although they happen to be in
their close proximity.Comment: 9 pages, 5 figure
On Regularization Parameter Estimation under Covariate Shift
This paper identifies a problem with the usual procedure for
L2-regularization parameter estimation in a domain adaptation setting. In such
a setting, there are differences between the distributions generating the
training data (source domain) and the test data (target domain). The usual
cross-validation procedure requires validation data, which can not be obtained
from the unlabeled target data. The problem is that if one decides to use
source validation data, the regularization parameter is underestimated. One
possible solution is to scale the source validation data through importance
weighting, but we show that this correction is not sufficient. We conclude the
paper with an empirical analysis of the effect of several importance weight
estimators on the estimation of the regularization parameter.Comment: 6 pages, 2 figures, 2 tables. Accepted to ICPR 201
A review of domain adaptation without target labels
Domain adaptation has become a prominent problem setting in machine learning
and related fields. This review asks the question: how can a classifier learn
from a source domain and generalize to a target domain? We present a
categorization of approaches, divided into, what we refer to as, sample-based,
feature-based and inference-based methods. Sample-based methods focus on
weighting individual observations during training based on their importance to
the target domain. Feature-based methods revolve around on mapping, projecting
and representing features such that a source classifier performs well on the
target domain and inference-based methods incorporate adaptation into the
parameter estimation procedure, for instance through constraints on the
optimization procedure. Additionally, we review a number of conditions that
allow for formulating bounds on the cross-domain generalization error. Our
categorization highlights recurring ideas and raises questions important to
further research.Comment: 20 pages, 5 figure
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