6,247 research outputs found
Robust Forecasting of Non-Stationary Time Series
This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable forecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series.Heteroscedasticity;Non-parametric regression;Prediction;Outliers;Robustness
About the morphology of dwarf spheroidal galaxies and their dark matter content
The morphological properties of the Carina, Sculptor and Fornax dwarfs are
investigated using new wide field data with a total area of 29 square degrees.
The stellar density maps are derived, hinting that Sculptor possesses tidal
tails indicating interaction with the Milky Way. Contrary to previous studies
we cannot find any sign of breaks in the density profiles for the Carina and
Fornax dwarfs. The possible existence of tidal tails in Sculptor and of King
limiting radii in Fornax and Carina are used to derive global M/L ratios,
without using kinematic data. By matching those M/L ratios to kinematically
derived values we are able to constrain the orbital parameters of the three
dwarfs. Fornax cannot have M/L smaller than 3 and must be close to its
perigalacticon now. The other extreme is Sculptor that needs to be on an orbit
with an eccentricity bigger than 0.5 to be able to form tidal tails despite its
kinematic M/L.Comment: 9 pages, 7 figures, accepted by A&
Vlasov simulation in multiple spatial dimensions
A long-standing challenge encountered in modeling plasma dynamics is
achieving practical Vlasov equation simulation in multiple spatial dimensions
over large length and time scales. While direct multi-dimension Vlasov
simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of
Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010,
http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown
promising results, in this paper we present an alternative, the Vlasov Multi
Dimensional (VMD) model, that is specifically designed to take advantage of
solution properties in regimes when plasma waves are confined to a narrow cone,
as may be the case for stimulated Raman scatter in large optic f# laser beams.
Perpendicular grid spacing large compared to a Debye length is then possible
without instability, enabling an order 10 decrease in required computational
resources compared to standard particle in cell (PIC) methods in 2D, with
another reduction of that order in 3D. Further advantage compared to PIC
methods accrues in regimes where particle noise is an issue. VMD and PIC
results in a 2D model of localized Langmuir waves are in qualitative agreement
An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images
Adaptive optics (AO) systems have significantly improved astronomical imaging
capabilities over the last decade, and are revolutionizing the kinds of science
possible with 4-5m class ground-based telescopes. A thorough understanding of
AO system performance at the telescope can enable new frontiers of science as
observations push AO systems to their performance limits. We look at recent
advances with wave front reconstruction (WFR) on the Advanced Electro-Optical
System (AEOS) 3.6 m telescope to show how progress made in improving WFR can be
measured directly in improved science images. We describe how a "waffle mode"
wave front error (which is not sensed by a Fried geometry Shack-Hartmann wave
front sensor) affects the AO point-spread function (PSF). We model details of
AEOS AO to simulate a PSF which matches the actual AO PSF in the I-band, and
show that while the older observed AEOS PSF contained several times more waffle
error than expected, improved WFR techniques noticeably improve AEOS AO
performance. We estimate the impact of these improved WFRs on H-band imaging at
AEOS, chosen based on the optimization of the Lyot Project near-infrared
coronagraph at this bandpass.Comment: 15 pages, 11 figures, 1 table; to appear in PASP, August 200
Robust Forecasting of Non-Stationary Time Series
This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable forecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series.
A New Strategy for Deep Wide-Field High Resolution Optical Imaging
We propose a new strategy for obtaining enhanced resolution (FWHM = 0.12
arcsec) deep optical images over a wide field of view. As is well known, this
type of image quality can be obtained in principle simply by fast guiding on a
small (D = 1.5m) telescope at a good site, but only for target objects which
lie within a limited angular distance of a suitably bright guide star. For high
altitude turbulence this 'isokinetic angle' is approximately 1 arcminute. With
a 1 degree field say one would need to track and correct the motions of
thousands of isokinetic patches, yet there are typically too few sufficiently
bright guide stars to provide the necessary guiding information. Our proposed
solution to these problems has two novel features. The first is to use
orthogonal transfer charge-coupled device (OTCCD) technology to effectively
implement a wide field 'rubber focal plane' detector composed of an array of
cells which can be guided independently. The second is to combine measured
motions of a set of guide stars made with an array of telescopes to provide the
extra information needed to fully determine the deflection field. We discuss
the performance, feasibility and design constraints on a system which would
provide the collecting area equivalent to a single 9m telescope, a 1 degree
square field and 0.12 arcsec FWHM image quality.Comment: 46 pages, 22 figures, submitted to PASP, a version with higher
resolution images and other supplementary material can be found at
http://www.ifa.hawaii.edu/~kaiser/wfhr
A New Shear Estimator for Weak Lensing Observations
We present a new shear estimator for weak lensing observations which properly
accounts for the effects of a realistic point spread function (PSF). Images of
faint galaxies are subject to gravitational shearing followed by smearing with
the instrumental and/or atmospheric PSF. We construct a `finite resolution
shear operator' which when applied to an observed image has the same effect as
a gravitational shear applied prior to smearing. This operator allows one to
calibrate essentially any shear estimator. We then specialize to the case of
weighted second moment shear estimators. We compute the shear polarizability
which gives the response of an individual galaxy's polarization to a
gravitational shear. We then compute the response of the population of
galaxies, and thereby construct an optimal weighting scheme for combining shear
estimates from galaxies of various shapes, luminosities and sizes. We define a
figure of merit --- an inverse shear variance per unit solid angle --- which
characterizes the quality of image data for shear measurement. The new method
is tested with simulated image data. We discuss the correction for anisotropy
of the PSF and propose a new technique involving measuring shapes from images
which have been convolved with a re-circularizing PSF. We draw attention to a
hitherto ignored noise related bias and show how this can be analyzed and
corrected for. The analysis here draws heavily on the properties of real PSF's
and we include as an appendix a brief review, highlighting those aspects which
are relevant for weak lensing.Comment: 39 pages, 9 figure
Methods and Algorithms for Robust Filtering
We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Improvements can be achieved by using robust regression methods, which work even in real time because of increased computational power and faster algorithms. Extending recent work we present filters for robust online signal extraction and discuss their merits for preserving trends, abrupt shifts and extremes and for the removal of spikes
The effect of atmospheric turbulence on entangled orbital angular momentum states
We analyze the effect of atmospheric Kolmogorov turbulence on entangled
orbital angular momentum states generated by parametric down-conversion. We
calculate joint and signal photon detection probabilities and obtain
numerically their dependence on the mode-width-to-Fried-parameter ratio. We
demonstrate that entangled photons are less robust to the effects of Kolmogorov
turbulence compared to single photons. In contrast, signal photons are more
robust than single photons in the lowest-order mode. We also obtain numerically
a scaling relation between the value of the mode-width-to-Fried-parameter ratio
for which the joint detection probabilities is a maximum and the momentum
mismatch between signal and idler photons after propagation through the medium.Comment: To appear in New Journal of Physic
Speckle Statistics in Adaptively Corrected Images
(abridged) Imaging observations are generally affected by a fluctuating
background of speckles, a particular problem when detecting faint stellar
companions at small angular separations. Knowing the distribution of the
speckle intensities at a given location in the image plane is important for
understanding the noise limits of companion detection. The speckle noise limit
in a long-exposure image is characterized by the intensity variance and the
speckle lifetime. In this paper we address the former quantity through the
distribution function of speckle intensity. Previous theoretical work has
predicted a form for this distribution function at a single location in the
image plane. We developed a fast readout mode to take short exposures of
stellar images corrected by adaptive optics at the ground-based UCO/Lick
Observatory, with integration times of 5 ms and a time between successive
frames of 14.5 ms ( m). These observations temporally
oversample and spatially Nyquist sample the observed speckle patterns. We show,
for various locations in the image plane, the observed distribution of speckle
intensities is consistent with the predicted form. Additionally, we demonstrate
a method by which and can be mapped over the image plane. As the
quantity is proportional to the PSF of the telescope free of random
atmospheric aberrations, this method can be used for PSF calibration and
reconstruction.Comment: 7 pages, 4 figures, ApJ accepte
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