64,232 research outputs found
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations
The effects of different parametrizations on the convergence of Bayesian
computational algorithms for hierarchical models are well explored. Techniques
such as centering, noncentering and partial noncentering can be used to
accelerate convergence in MCMC and EM algorithms but are still not well studied
for variational Bayes (VB) methods. As a fast deterministic approach to
posterior approximation, VB is attracting increasing interest due to its
suitability for large high-dimensional data. Use of different parametrizations
for VB has not only computational but also statistical implications, as
different parametrizations are associated with different factorized posterior
approximations. We examine the use of partially noncentered parametrizations in
VB for generalized linear mixed models (GLMMs). Our paper makes four
contributions. First, we show how to implement an algorithm called nonconjugate
variational message passing for GLMMs. Second, we show that the partially
noncentered parametrization can adapt to the quantity of information in the
data and determine a parametrization close to optimal. Third, we show that
partial noncentering can accelerate convergence and produce more accurate
posterior approximations than centering or noncentering. Finally, we
demonstrate how the variational lower bound, produced as part of the
computation, can be useful for model selection.Comment: Published in at http://dx.doi.org/10.1214/13-STS418 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
We study the low-energy limit of a compactification of N=4 U(n) super
Yang-Mills theory on with boundary conditions modified by an S-duality
and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the
compactification of this 2+1D theory by identifying a dual weakly coupled
type-IIA background. The Hilbert space of normalizable ground states is
finite-dimensional and appears to exhibit a rich structure of sectors. We
identify most of them with Hilbert spaces of Chern-Simons theory (with
appropriate gauge groups and levels). We also discuss a realization of a
related twisted compactification in terms of the (2,0)-theory, where the recent
solution by Gaiotto and Witten of the boundary conditions describing D3-branes
ending on a (p,q) 5-brane plays a crucial role.Comment: 104 pages, 5 figures. Revisions to subsection (6.6) and other minor
corrections included in version
Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling
We study the short-range correlation strength of three dimensional spin half
dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction
is modeled by the contact pseudopotential. In the high temperature limit, we
derive the expression for the second order virial expansion of the
thermodynamic potential via the ladder diagrams. We further evaluate the second
order virial expansion in the limit that the spin-orbit coupling constants are
small, and find that the correlation strength between the fermions increases as
the forth power of the spin-orbit coupling constants. At zero temperature, we
consider the cases in which there are symmetric spin-orbit couplings in two or
three directions. In such cases, there is always a two-body bound state of zero
net momentum. In the limit that the average interparticle distance is much
larger than the dimension of the two-body bound state, the system primarily
consists of condensed bosonic molecules that fermions pair to form; we find
that the correlation strength also becomes bigger compared to that in the
absence of spin-orbit coupling. Our results indicate that generic spin-orbit
coupling enhances the short-range correlations of the Fermi gases. Measurement
of such enhancement by photoassociation experiment is also discussed.Comment: 7 pages, 4 figure
Astrochemical confirmation of the rapid evolution of massive YSOs and explanation for the inferred ages of hot cores
Aims. To understand the roles of infall and protostellar evolution on the
envelopes of massive young stellar objects (YSOs).
Methods. The chemical evolution of gas and dust is traced, including infall
and realistic source evolution. The temperatures are determined
self-consistently. Both ad/desorption of ices using recent laboratory
temperature-programmed-desorption measurements are included.
Results. The observed water abundance jump near 100 K is reproduced by an
evaporation front which moves outward as the luminosity increases. Ion-molecule
reactions produce water below 100 K. The age of the source is constrained to t
\~ 8 +/- 4 x 10^4 yrs since YSO formation. It is shown that the chemical
age-dating of hot cores at ~ few x 10^3 - 10^4 yr and the disappearance of hot
cores on a timescale of ~ 10^5 yr is a natural consequence of infall in a
dynamic envelope and protostellar evolution. Dynamical structures of ~ 350AU
such as disks should contain most of the complex second generation species. The
assumed order of desorption kinetics does not affect these results.Comment: Accepted by A&A Letters; 4 pages, 5 figure
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