58,220 research outputs found
Just Another Gibbs Additive Modeller: Interfacing JAGS and mgcv
The BUGS language offers a very flexible way of specifying complex
statistical models for the purposes of Gibbs sampling, while its JAGS variant
offers very convenient R integration via the rjags package. However, including
smoothers in JAGS models can involve some quite tedious coding, especially for
multivariate or adaptive smoothers. Further, if an additive smooth structure is
required then some care is needed, in order to centre smooths appropriately,
and to find appropriate starting values. R package mgcv implements a wide range
of smoothers, all in a manner appropriate for inclusion in JAGS code, and
automates centring and other smooth setup tasks. The purpose of this note is to
describe an interface between mgcv and JAGS, based around an R function,
`jagam', which takes a generalized additive model (GAM) as specified in mgcv
and automatically generates the JAGS model code and data required for inference
about the model via Gibbs sampling. Although the auto-generated JAGS code can
be run as is, the expectation is that the user would wish to modify it in order
to add complex stochastic model components readily specified in JAGS. A simple
interface is also provided for visualisation and further inference about the
estimated smooth components using standard mgcv functionality. The methods
described here will be un-necessarily inefficient if all that is required is
fully Bayesian inference about a standard GAM, rather than the full flexibility
of JAGS. In that case the BayesX package would be more efficient.Comment: Submitted to the Journal of Statistical Softwar
Moments of the Wigner Distribution and a Generalized Uncertainty Principle
The nonnegativity of the density operator of a state is faithfully coded in
its Wigner distribution, and this places constraints on the moments of the
Wigner distribution. These constraints are presented in a canonically invariant
form which is both concise and explicit. Since the conventional uncertainty
principle is such a constraint on the first and second moments, our result
constitutes a generalization of the same to all orders. Possible application in
quantum state reconstruction using optical homodyne tomography is noted.Comment: REVTex, no figures, 9 page
Hamilton's theory of turns revisited
We present a new approach to Hamilton's theory of turns for the groups
SO(3) and SU(2) which renders their properties, in particular their
composition law, nearly trivial and immediately evident upon inspection.
We show that the entire construction can be based on binary rotations rather
than mirror reflections.Comment: 7 pages, 4 figure
Tip streaming from drops flowing in a spiral microchannel
This fluid dynamics video shows drops of water being transported by a mean
flow of oil, in a microchannel shaped as a logarithmic spiral. The channel
shape means that the drops are submitted to an increasing shear and elongation
as they flow nearer to the center of the spiral. A critical point is reached at
which a long singular tail is observed behind the drops, indicating that the
drops are accelerating. This is called "Tip streaming".Comment: Abstract accompanying movie to the Gallery of Fluid Motion: APS-DFD
200
A BCS Condensate in NJL_3+1 ?
We present results from a lattice Monte Carlo study of the Nambu -
Jona-Lasinio model in 3+1 dimensions with a baryon chemical potential mu=/=0.
As mu is increased there is a transition from a chirally-broken phase to
relativistic quark matter, in which baryon number symmetry appears
spontaneously broken by a diquark condensate at the Fermi surface, implying a
superfluid ground state. Finite volume corrections to this relativistic BCS
scenario, however, are anomalously large.Comment: 5 pages, 3 figures, contribution to Strong and Electroweak Matter '02
(Heidelberg
Hamilton's Turns for the Lorentz Group
Hamilton in the course of his studies on quaternions came up with an elegant
geometric picture for the group SU(2). In this picture the group elements are
represented by ``turns'', which are equivalence classes of directed great
circle arcs on the unit sphere , in such a manner that the rule for
composition of group elements takes the form of the familiar parallelogram law
for the Euclidean translation group. It is only recently that this construction
has been generalized to the simplest noncompact group , the double cover of SO(2,1). The present work develops a theory of
turns for , the double and universal cover of SO(3,1) and ,
rendering a geometric representation in the spirit of Hamilton available for
all low dimensional semisimple Lie groups of interest in physics. The geometric
construction is illustrated through application to polar decomposition, and to
the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late
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