12,767 research outputs found
Rindler/Contracted-CFT Correspondence
Taking the flat-space limit (zero cosmological constant limit) of the
Rindler-AdS spacetime yields the Rindler metric. According to the proposal of
Flat/contracted-CFT correspondence, the flat-space limit on the bulk side of
asymptotically AdS spacetimes corresponds to the contraction of the conformal
field theory on the boundary. We use this proposal for the Rindler-AdS/CFT
correspondence and propose a dual theory for the Rindler spacetime, which is a
contracted conformal field theory (CCFT). We show that the two-dimensional CCFT
symmetries exactly predict the same two-point functions that one may find by
taking the flat-space limit of three-dimensional Rindler-AdS holographic
results. Using the Flat/CCFT proposal, we also calculate the three-dimensional
Rindler energy-momentum tensor. Since the near horizon geometry of non-extreme
black holes has a Rindler part, we note that it is plausible to find a dual
CCFT at the horizon of non-extreme black holes. By using our energy-momentum
tensor, we find the correct mass of non-rotating BTZ and show that the
Cardy-like formula for CCFT yields the Bekenstein-Hawking entropy of
non-extreme BTZ. Our current work is the first step towards describing the
entropy of non-extreme black holes in terms of CCFTs microstates which live on
the horizon.Comment: 18 pages, V2: typos corrected, published versio
Comparisons of Estimation Procedures for Nonlinear Multilevel Models
We introduce General Multilevel Models and discuss the estimation procedures that may be used to fit multilevel models. We apply the proposed procedures to three-level binary data generated in a simulation study. We compare the procedures by two criteria, Bias and efficiency. We find that the estimates of the fixed effects and variance components are substantially and significantly biased using Longford's Approximation and Goldstein's Generalized Least Squares approaches by two software packages VARCL and ML3. These estimates are not significantly biased and are very close to real values when we use Markov Chain Monte Carlo (MCMC) using Gibbs sampling or Nonparametric Maximum Likelihood (NPML) approach. The Gaussian Quadrature (GQ) approach, even with small number of mass points results in consistent estimates but computationally problematic. We conclude that the MCMC and the NPML approaches are the recommended procedures to fit multilevel models.
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