11,056 research outputs found
Inference for variograms
The empirical variogram is a standard tool in the investigation and modelling of spatial
covariance. However, its properties can be difficult to identify and exploit in the
context of exploring the characteristics of individual datasets. This is particularly true
when seeking to move beyond description towards inferential statements about the
structure of the spatial covariance which may be present. A robust form of empirical
variogram based on a fourth-root transformation is used. This takes advantage of the
normal approximation which gives an excellent description of the variation exhibited
on this scale. Calculations of mean, variance and covariance of the binned empirical
variogram then allow useful computations such as confidence intervals to be added to
the underlying estimator. The comparison of variograms for different datasets provides
an illustration of this. The suitability of simplifying assumptions such as isotropy and
stationarity can then also be investigated through the construction of appropriate test
statistics and the distributional calculations required in the associated p-values can be
performed through quadratic form methods. Examples of the use of these methods in
assessing the form of spatial covariance present in datasets are shown, both through
hypothesis tests and in graphical form. A simulation study explores the properties of
the tests while pollution data on mosses in Galicia (North-West Spain) are used to
provide a real data illustration
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ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication
Alpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system that
has been developed at the University of Utah over the past 10 years. In addition to being
useful in modeling objects that are described by simple rotation and extrusion operations,
the real power of Alpha_l is demonstrated in the modeling of complex parts with sculptured
surfaces. For the past several years, a major research thrust has been to use Alpha_l to
semi-automatically generate process plan information and numerical control code to manufacture
mechanical parts directly from the models. A long term goal is to support an on-line
remote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereo
lithography machine has been added to the advanced manufacturing laboratory. The stereo
lithography process and other SFF techniques are of particular interest for supporting a
remote manufacturing facility in that these processes are inherently much safer than numerically
controlled machining. Special Alpha_l interfaces including a new slicing algorithm
are being developed for the SFF machine use. By generating a SFF part directly from
its NURBs description, Alpha_l should facilitate the manufacture of complex parts while
providing smoother surfaces.Mechanical Engineerin
Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape
We present a full pipeline for computing the medial axis transform of an
arbitrary 2D shape. The instability of the medial axis transform is overcome by
a pruning algorithm guided by a user-defined Hausdorff distance threshold. The
stable medial axis transform is then approximated by spline curves in 3D to
produce a smooth and compact representation. These spline curves are computed
by minimizing the approximation error between the input shape and the shape
represented by the medial axis transform. Our results on various 2D shapes
suggest that our method is practical and effective, and yields faithful and
compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing
Imprints of the quasar structure in time-delay light curves: Microlensing-aided reverberation mapping
Owing to the advent of large area photometric surveys, the possibility to use
broad band photometric data, instead of spectra, to measure the size of the
broad line region of active galactic nuclei, has raised a large interest. We
describe here a new method using time-delay lensed quasars where one or several
images are affected by microlensing due to stars in the lensing galaxy. Because
microlensing decreases (or increases) the flux of the continuum compared to the
broad line region, it changes the contrast between these two emission
components. We show that this effect can be used to effectively disentangle the
intrinsic variability of those two regions, offering the opportunity to perform
reverberation mapping based on single band photometric data. Based on simulated
light curves generated using a damped random walk model of quasar variability,
we show that measurement of the size of the broad line region can be achieved
using this method, provided one spectrum has been obtained independently during
the monitoring. This method is complementary to photometric reverberation
mapping and could also be extended to multi-band data. Because the effect
described above produces a variability pattern in difference light curves
between pairs of lensed images which is correlated with the time-lagged
continuum variability, it can potentially produce systematic errors in
measurement of time delays between pairs of lensed images. Simple simulations
indicate that time-delay measurement techniques which use a sufficiently
flexible model for the extrinsic variability are not affected by this effect
and produce accurate time delays.Comment: Accepted for publication in Astronomy and Astrophysic
Preliminary Results on HAT-P-4, TrES-3, XO-2, and GJ 436 from the NASA EPOXI Mission
EPOXI (EPOCh + DIXI) is a NASA Discovery Program Mission of Opportunity using
the Deep Impact flyby spacecraft. The EPOCh (Extrasolar Planet Observation and
Characterization) Science Investigation will gather photometric time series of
known transiting exoplanet systems from January through August 2008. Here we
describe the steps in the photometric extraction of the time series and present
preliminary results of the first four EPOCh targets.Comment: 4 pages, 2 figures. To appear in the Proceedings of the 253rd IAU
Symposium: "Transiting Planets", May 2008, Cambridge, M
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