21,110 research outputs found
Estimating sufficient reductions of the predictors in abundant high-dimensional regressions
We study the asymptotic behavior of a class of methods for sufficient
dimension reduction in high-dimension regressions, as the sample size and
number of predictors grow in various alignments. It is demonstrated that these
methods are consistent in a variety of settings, particularly in abundant
regressions where most predictors contribute some information on the response,
and oracle rates are possible. Simulation results are presented to support the
theoretical conclusion.Comment: Published in at http://dx.doi.org/10.1214/11-AOS962 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A random wave model for the Aharonov-Bohm effect
We study an ensemble of random waves subject to the Aharonov-Bohm effect. The
introduction of a point with a magnetic flux of arbitrary strength into a
random wave ensemble gives a family of wavefunctions whose distribution of
vortices (complex zeros) are responsible for the topological phase associated
with the Aharonov-Bohm effect. Analytical expressions are found for the vortex
number and topological charge densities as functions of distance from the flux
point. Comparison is made with the distribution of vortices in the isotropic
random wave model. The results indicate that as the flux approaches
half-integer values, a vortex with the same sign as the fractional part of the
flux is attracted to the flux point, merging with it at half-integer flux.
Other features of the Aharonov-Bohm vortex distribution are also explored.Comment: 16 pages, 5 figure
XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically
integrating initial value problems that range from a single ordinary
differential equation up to systems of coupled stochastic partial differential
equations. The equations are described in a high-level XML-based script, and
the package generates low-level optionally parallelised C++ code for the
efficient solution of those equations. It combines the advantages of high-level
simulations, namely fast and low-error development, with the speed, portability
and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS
package, and features support for a much wider problem space while also
producing faster code.Comment: 9 pages, 5 figure
Multivariate Design of Experiments for Engineering Dimensional Analysis
We consider the design of dimensional analysis experiments when there is more
than a single response. We first give a brief overview of dimensional analysis
experiments and the dimensional analysis (DA) procedure. The validity of the DA
method for univariate responses was established by the Buckingham -Theorem
in the early 20th century. We extend the theorem to the multivariate case,
develop basic criteria for multivariate design of DA and give guidelines for
design construction. Finally, we illustrate the construction of designs for DA
experiments for an example involving the design of a heat exchanger
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