18,425 research outputs found
Prior-preconditioned conjugate gradient method for accelerated Gibbs sampling in "large & large " sparse Bayesian regression
In a modern observational study based on healthcare databases, the number of
observations and of predictors typically range in the order of ~
and of ~ . Despite the large sample size, data rarely provide
sufficient information to reliably estimate such a large number of parameters.
Sparse regression techniques provide potential solutions, one notable approach
being the Bayesian methods based on shrinkage priors. In the "large & large
" setting, however, posterior computation encounters a major bottleneck at
repeated sampling from a high-dimensional Gaussian distribution, whose
precision matrix is expensive to compute and factorize. In this article,
we present a novel algorithm to speed up this bottleneck based on the following
observation: we can cheaply generate a random vector such that the solution
to the linear system has the desired Gaussian distribution. We
can then solve the linear system by the conjugate gradient (CG) algorithm
through matrix-vector multiplications by , without ever explicitly
inverting . Rapid convergence of CG in this specific context is achieved
by the theory of prior-preconditioning we develop. We apply our algorithm to a
clinically relevant large-scale observational study with = 72,489 patients
and = 22,175 clinical covariates, designed to assess the relative risk of
adverse events from two alternative blood anti-coagulants. Our algorithm
demonstrates an order of magnitude speed-up in the posterior computation.Comment: 32 pages, 7 figures + Supplement (23 pages, 7 figures
Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals
We advocate a method to improve systematically the self-consistent harmonic
approximation (or the Gaussian approximation), which has been employed
extensively in condensed matter physics and statistical mechanics. We
demonstrate the {\em convergence} of the method in a model obtained from
dimensional reduction of SU() Yang-Mills theory in dimensions. Explicit
calculations have been carried out up to the 7th order in the large-N limit,
and we do observe a clear convergence to Monte Carlo results. For the convergence is already achieved at the 3rd order, which suggests that
the method is particularly useful for studying the IIB matrix model, a
conjectured nonperturbative definition of type IIB superstring theory.Comment: LaTeX, 4 pages, 5 figures; title slightly changed, explanations added
(16 pages, 14 figures), final version published in JHE
(2,0) Chern-Simons Supergravity Plus Matter Near the Boundary of AdS_3
We examine the boundary behaviour of the gauged N=(2,0) supergravity in D=3
coupled to an arbitrary number of scalar supermultiplets which parametrize a
Kahler manifold. In addition to the gravitational coupling constant, the model
depends on two parameters, namely the cosmological constant and the size of the
Kahler manifold. It is shown that regular and irregular boundary conditions can
be imposed on the matter fields depending on the size of the sigma model
manifold. It is also shown that the super AdS transformations in the bulk
produce the transformations of the N=(2,0) conformal supergravity and scalar
multiplets on the boundary, containing fields with nonvanishing Weyl weights
determined by the ratio of the sigma model and the gravitational coupling
constants. Various types of (2,0) superconformal multiplets are found on the
boundary and in one case the superconformal symmetry is shown to be realized in
an unconventional way.Comment: 28 pages, latex, references adde
Contact resistivity and current flow path at metal/graphene contact
The contact properties between metal and graphene were examined. The
electrical measurement on a multiprobe device with different contact areas
revealed that the current flow preferentially entered graphene at the edge of
the contact metal. The analysis using the cross-bridge Kelvin structure (CBK)
suggested that a transition from the edge conduction to area conduction
occurred for a contact length shorter than the transfer length of ~1 micron.
The contact resistivity for Ni was measured as ~5*10-6 Ohmcm2 using the CBK. A
simple calculation suggests that a contact resistivity less than 10-9 Ohmcm2 is
required for miniaturized graphene field effect transistors
Non-lattice simulation for supersymmetric gauge theories in one dimension
Lattice simulation of supersymmetric gauge theories is not straightforward.
In some cases the lack of manifest supersymmetry just necessitates cumbersome
fine-tuning, but in the worse cases the chiral and/or Majorana nature of
fermions makes it difficult to even formulate an appropriate lattice theory. We
propose to circumvent all these problems inherent in the lattice approach by
adopting a non-lattice approach in the case of one-dimensional supersymmetric
gauge theories, which are important in the string/M theory context.Comment: REVTeX4, 4 pages, 3 figure
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