712 research outputs found
A Bayesian approach to the estimation of maps between riemannian manifolds
Let \Theta be a smooth compact oriented manifold without boundary, embedded
in a euclidean space and let \gamma be a smooth map \Theta into a riemannian
manifold \Lambda. An unknown state \theta \in \Theta is observed via
X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white
Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of
the map \gamma we derive a second-order asymptotic expansion for the related
Bayesian risk. The calculation involves the geometry of the underlying spaces
\Theta and \Lambda, in particular, the integration-by-parts formula. Using this
result, a second-order minimax estimator of \gamma is found based on the modern
theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s
31, 41, 4
Viewpoints: A high-performance high-dimensional exploratory data analysis tool
Scientific data sets continue to increase in both size and complexity. In the
past, dedicated graphics systems at supercomputing centers were required to
visualize large data sets, but as the price of commodity graphics hardware has
dropped and its capability has increased, it is now possible, in principle, to
view large complex data sets on a single workstation. To do this in practice,
an investigator will need software that is written to take advantage of the
relevant graphics hardware. The Viewpoints visualization package described
herein is an example of such software. Viewpoints is an interactive tool for
exploratory visual analysis of large, high-dimensional (multivariate) data. It
leverages the capabilities of modern graphics boards (GPUs) to run on a single
workstation or laptop. Viewpoints is minimalist: it attempts to do a small set
of useful things very well (or at least very quickly) in comparison with
similar packages today. Its basic feature set includes linked scatter plots
with brushing, dynamic histograms, normalization and outlier detection/removal.
Viewpoints was originally designed for astrophysicists, but it has since been
used in a variety of fields that range from astronomy, quantum chemistry, fluid
dynamics, machine learning, bioinformatics, and finance to information
technology server log mining. In this article, we describe the Viewpoints
package and show examples of its usage.Comment: 18 pages, 3 figures, PASP in press, this version corresponds more
closely to that to be publishe
Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk
When a parameter of interest is nondifferentiable in the probability, the
existing theory of semiparametric efficient estimation is not applicable, as it
does not have an influence function. Song (2014) recently developed a local
asymptotic minimax estimation theory for a parameter that is a
nondifferentiable transform of a regular parameter, where the nondifferentiable
transform is a composite map of a continuous piecewise linear map with a single
kink point and a translation-scale equivariant map. The contribution of this
paper is two fold. First, this paper extends the local asymptotic minimax
theory to nondifferentiable transforms that are a composite map of a Lipschitz
continuous map having a finite set of nondifferentiability points and a
translation-scale equivariant map. Second, this paper investigates the
discontinuity of the local asymptotic minimax risk in the true probability and
shows that the proposed estimator remains to be optimal even when the risk is
locally robustified not only over the scores at the true probability, but also
over the true probability itself. However, the local robustification does not
resolve the issue of discontinuity in the local asymptotic minimax risk
Quality quantification model of basic raw materials
Basic raw materials belong to the key input sources in the production of pig iron. The properties of basic raw materials can be evaluated using a variety of criteria. The essential ones include the physical and chemical properties. Current competitive pressures, however, force the producers of iron more and more often to include cost and logistic criteria into the decision-making process. In this area, however, they are facing a problem of how to convert a variety of vastly different parameters into one evaluation indicator in order to compare the available raw materials. This article deals with the analysis of a model created to evaluate the basic raw materials, which was designed as part of the research
Theories for multiple resonances
Two microscopic theories for multiple resonances in nuclei are compared,
n-particle-hole RPA and quantized Time-Dependent Hartree-Fock (TDHF). The
Lipkin-Meshkov-Glick model is used as test case. We find that quantized TDHF is
superior in many respects, except for very small systems.Comment: 14 Pages, 3 figures available upon request
Anatomy of nuclear shape transition in the relativistic mean field theory
A detailed microscopic study of the temperature dependence of the shapes of
some rare-earth nuclei is made in the relativistic mean field theory. Analyses
of the thermal evolution of the single-particle orbitals and their occupancies
leading to the collapse of the deformation are presented. The role of the
non-linear field on the shape transition in different nuclei is also
investigated; in its absence the shape transition is found to be sharper.Comment: REVTEX file (13pages), 12 figures, Phys. Rev. C(in press),
\documentstyle[aps,preprint]{revtex
Mesoscopic fluctuations of the ground state spin of a small metal particle
We study the statistical distribution of the ground state spin for an
ensemble of small metallic grains, using a random-matrix toy model. Using the
Hartree Fock approximation, we find that already for interaction strengths well
below the Stoner criterion there is an appreciable probability that the ground
state has a finite, nonzero spin. Possible relations to experiments are
discussed.Comment: 4 pages, RevTeX; 1 figure included with eps
Small damping approach in Fermi-liquid theory
The validity of small damping approximation (SDA) for the quasi-classical
description of the averaged properties of nuclei at high temperatures is
studied within the framework of collisional kinetic theory. The isoscalar
collective quadrupole vibrations in hot nuclei are considered. We show that the
extension of the SDA, by accounting for the damping of the distribution
function in the collision integral reduces the rate of variation
with temperature of the Fermi surface distortion effects. The damping of the
in the collision integral increases significantly the collisional
width of the giant quadrupole resonance (GQR) for small enough values of the
relaxation time. The temperature dependence of the eigenenergy of the GQR
becomes much more weaker than in the corresponding SDA case.Comment: 11 pages, 3 figure
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