10,820 research outputs found
The classical double copy for Taub-NUT spacetime
The double copy is a much-studied relationship between gauge theory and
gravity amplitudes. Recently, this was generalised to an infinite family of
classical solutions to Einstein's equations, namely stationary Kerr-Schild
geometries. In this paper, we extend this to the Taub-NUT solution in gravity,
which has a double Kerr-Schild form. The single copy of this solution is a
dyon, whose electric and magnetic charges are related to the mass and NUT
charge in the gravity theory. Finally, we find hints that the classical double
copy extends to curved background geometries.Comment: 13 pages, no figures. Minor edits to match journal versio
Black holes and the double copy
Recently, a perturbative duality between gauge and gravity theories (the
double copy) has been discovered, that is believed to hold to all loop orders.
In this paper, we examine the relationship between classical solutions of
non-Abelian gauge theory and gravity. We propose a general class of gauge
theory solutions that double copy to gravity, namely those involving stationary
Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their
higher-dimensional equivalents) emerge as special cases. We also discuss plane
wave solutions. Furthermore, a recently examined double copy between the
self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a
momentum-space generalisation of the Kerr-Schild framework.Comment: 22 pages; typos corrected and references adde
Convex Optimization Methods for Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression
In this paper, we study convex optimization methods for computing the trace
norm regularized least squares estimate in multivariate linear regression. The
so-called factor estimation and selection (FES) method, recently proposed by
Yuan et al. [22], conducts parameter estimation and factor selection
simultaneously and have been shown to enjoy nice properties in both large and
finite samples. To compute the estimates, however, can be very challenging in
practice because of the high dimensionality and the trace norm constraint. In
this paper, we explore a variant of Nesterov's smooth method [20] and interior
point methods for computing the penalized least squares estimate. The
performance of these methods is then compared using a set of randomly generated
instances. We show that the variant of Nesterov's smooth method [20] generally
outperforms the interior point method implemented in SDPT3 version 4.0 (beta)
[19] substantially . Moreover, the former method is much more memory efficient.Comment: 27 page
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