9,129 research outputs found
Understanding differences in regional poverty rates
An examination of the huge variation in U.S. regional poverty rates, showing that although demographic, policy, and cost-of-living factors all play a role, economic differences are key.Income ; Regional economics
Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation
Nonparametric Bayesian approaches to clustering, information retrieval,
language modeling and object recognition have recently shown great promise as a
new paradigm for unsupervised data analysis. Most contributions have focused on
the Dirichlet process mixture models or extensions thereof for which efficient
Gibbs samplers exist. In this paper we explore Gibbs samplers for infinite
complexity mixture models in the stick breaking representation. The advantage
of this representation is improved modeling flexibility. For instance, one can
design the prior distribution over cluster sizes or couple multiple infinite
mixture models (e.g. over time) at the level of their parameters (i.e. the
dependent Dirichlet process model). However, Gibbs samplers for infinite
mixture models (as recently introduced in the statistics literature) seem to
mix poorly over cluster labels. Among others issues, this can have the adverse
effect that labels for the same cluster in coupled mixture models are mixed up.
We introduce additional moves in these samplers to improve mixing over cluster
labels and to bring clusters into correspondence. An application to modeling of
storm trajectories is used to illustrate these ideas.Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty
in Artificial Intelligence (UAI2006
Polarization singularities from unfolding an optical vortex through a birefringent crystal
Optical vortices (nodal lines and phase singularities) are the generic singularities of scalar optics but are unstable in vector optics. We investigate experimentally and theoretically the unfolding of a uniformly polarized optical vortex beam on propagation through a birefringent crystal and characterize the output field in terms of polarization singularities (C lines and points of circular polarization; L surfaces and lines of linear polarization). The field is described both in the 2-dimensional transverse plane, and in three dimensions, where the third is abstract, representing an optical path length propagated through the crystal. Many phenomena of singular optics, such as topological charge conservation and singularity reconnections, occur naturally in the description
Polarization singularities from unfolding an optical vortex through a birefringent crystal
Optical vortices (nodal lines and phase singularities) are the generic singularities of scalar optics but are unstable in vector optics. We investigate experimentally and theoretically the unfolding of a uniformly polarized optical vortex beam on propagation through a birefringent crystal and characterize the output field in terms of polarization singularities (C lines and points of circular polarization; L surfaces and lines of linear polarization). The field is described both in the 2-dimensional transverse plane, and in three dimensions, where the third is abstract, representing an optical path length propagated through the crystal. Many phenomena of singular optics, such as topological charge conservation and singularity reconnections, occur naturally in the description
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