6,145 research outputs found
Flat space compressible fluid as holographic dual of black hole with curved horizon
We consider the fluid dual of -dimensional vacuum Einstein equation
either with or without a cosmological constant. The background solutions admit
black hole event horizons and the spatial sections of the horizons are
conformally flat. Therefore, a -dimensional flat Euclidean space
is contained in the conformal class of the spatial section of
the black hole horizon. A compressible, forced, stationary and viscous fluid
system can be constructed on the product (Newtonian) spacetime
as the lowest order fluctuation modes around
such black hole background. This construction provides the first example of
holographic duality which is beyond the class of bulk/boundary correspondence.Comment: 14 pages. V3: error corrections. To appear in JHE
Sparsifying the Fisher Linear Discriminant by Rotation
Many high dimensional classification techniques have been proposed in the
literature based on sparse linear discriminant analysis (LDA). To efficiently
use them, sparsity of linear classifiers is a prerequisite. However, this might
not be readily available in many applications, and rotations of data are
required to create the needed sparsity. In this paper, we propose a family of
rotations to create the required sparsity. The basic idea is to use the
principal components of the sample covariance matrix of the pooled samples and
its variants to rotate the data first and to then apply an existing high
dimensional classifier. This rotate-and-solve procedure can be combined with
any existing classifiers, and is robust against the sparsity level of the true
model. We show that these rotations do create the sparsity needed for high
dimensional classifications and provide theoretical understanding why such a
rotation works empirically. The effectiveness of the proposed method is
demonstrated by a number of simulated and real data examples, and the
improvements of our method over some popular high dimensional classification
rules are clearly shown.Comment: 30 pages and 9 figures. This paper has been accepted by Journal of
the Royal Statistical Society: Series B (Statistical Methodology). The first
two versions of this paper were uploaded to Bin Dong's web site under the
title "A Rotate-and-Solve Procedure for Classification" in 2013 May and 2014
January. This version may be slightly different from the published versio
Fluids and vortex from constrained fluctuations around C-metric black hole
By foliating the four-dimensional C-metric black hole spacetime, we consider
a kind of initial-value-like formulation of the vacuum Einstein's equation, the
holographic initial data is a double consisting of the induced metric and the
Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by
perturbing the initial data that generates the background spacetime, it is
shown that, in an appropriate limit, the fluctuation modes are governed by the
continuity equation and the compressible Navier-Stokes equation which describe
the momentum transport in non-relativistic viscous fluid on a flat Newtonian
space. It turns out that the flat space fluid behaves as a pure vortex and the
viscosity to entropy ratio is subjected to the black hole acceleration.Comment: 19 pages, LaTeX. v2: added a new reference. v3: major revisio
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