534,320 research outputs found
Characterization of Microlensing Planets with Moderately Wide Separations
In future high-cadence microlensing surveys, planets can be detected through
a new channel of an independent event produced by the planet itself. The two
populations of planets to be detected through this channel are wide-separation
planets and free-floating planets. Although they appear as similar short
time-scale events, the two populations of planets are widely different in
nature and thus distinguishing them is important. In this paper, we investigate
the lensing properties of events produced by planets with moderately wide
separations from host stars. We find that the lensing behavior of these events
is well described by the Chang-Refsdal lensing and the shear caused by the
primary not only produces a caustic but also makes the magnification contour
elongated along the primary-planet axis. The elongated magnification contour
implies that the light curves of these planetary events are generally
asymmetric and thus the asymmetry can be used to distinguish the events from
those produced by free-floating planets. The asymmetry can be noticed from the
overall shape of the light curve and thus can hardly be missed unlike the very
short-duration central perturbation caused by the caustic. In addition, the
asymmetry occurs regardless of the event magnification and thus the bound
nature of the planet can be identified for majority of these events. The close
approximation of the lensing light curve to that of the Chang-Refsdal lensing
implies that the analysis of the light curve yields only the information about
the projected separation between the host star and the planet.Comment: 4 pages, 2 figure
Pairs of Frequency-based Nonhomogeneous Dual Wavelet Frames in the Distribution Space
In this paper, we study nonhomogeneous wavelet systems which have close
relations to the fast wavelet transform and homogeneous wavelet systems. We
introduce and characterize a pair of frequency-based nonhomogeneous dual
wavelet frames in the distribution space; the proposed notion enables us to
completely separate the perfect reconstruction property of a wavelet system
from its stability property in function spaces. The results in this paper lead
to a natural explanation for the oblique extension principle, which has been
widely used to construct dual wavelet frames from refinable functions, without
any a priori condition on the generating wavelet functions and refinable
functions. A nonhomogeneous wavelet system, which is not necessarily derived
from refinable functions via a multiresolution analysis, not only has a natural
multiresolution-like structure that is closely linked to the fast wavelet
transform, but also plays a basic role in understanding many aspects of wavelet
theory. To illustrate the flexibility and generality of the approach in this
paper, we further extend our results to nonstationary wavelets with real
dilation factors and to nonstationary wavelet filter banks having the perfect
reconstruction property
Magnetic structure of our Galaxy: A review of observations
The magnetic structure in the Galactic disk, the Galactic center and the
Galactic halo can be delineated more clearly than ever before. In the Galactic
disk, the magnetic structure has been revealed by starlight polarization within
2 or 3 kpc of the Solar vicinity, by the distribution of the Zeeman splitting
of OH masers in two or three nearby spiral arms, and by pulsar dispersion
measures and rotation measures in nearly half of the disk. The polarized
thermal dust emission of clouds at infrared, mm and submm wavelengths and the
diffuse synchrotron emission are also related to the large-scale magnetic field
in the disk. The rotation measures of extragalactic radio sources at low
Galactic latitudes can be modeled by electron distributions and large-scale
magnetic fields. The statistical properties of the magnetized interstellar
medium at various scales have been studied using rotation measure data and
polarization data. In the Galactic center, the non-thermal filaments indicate
poloidal fields. There is no consensus on the field strength, maybe mG, maybe
tens of uG. The polarized dust emission and much enhanced rotation measures of
background radio sources are probably related to toroidal fields. In the
Galactic halo, the antisymmetric RM sky reveals large-scale toroidal fields
with reversed directions above and below the Galactic plane. Magnetic fields
from all parts of our Galaxy are connected to form a global field structure.
More observations are needed to explore the untouched regions and delineate how
fields in different parts are connected.Comment: 10+1 pages. Invited Review for IAU Symp.259: Cosmic Magnetic Fields:
From Planets, to Stars and Galaxies (Tenerife, Spain. Nov.3-7, 2009). K.G.
Strassmeier, A.G. Kosovichev & J.E. Beckman (eds.
High Dimensional Semiparametric Scale-Invariant Principal Component Analysis
We propose a new high dimensional semiparametric principal component analysis
(PCA) method, named Copula Component Analysis (COCA). The semiparametric model
assumes that, after unspecified marginally monotone transformations, the
distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA
in three aspects: (i) It is robust to modeling assumptions; (ii) It is robust
to outliers and data contamination; (iii) It is scale-invariant and yields more
interpretable results. We prove that the COCA estimators obtain fast estimation
rates and are feature selection consistent when the dimension is nearly
exponentially large relative to the sample size. Careful experiments confirm
that COCA outperforms sparse PCA on both synthetic and real-world datasets.Comment: Accepted in IEEE Transactions on Pattern Analysis and Machine
Intelligence (TPMAI
ECA: High Dimensional Elliptical Component Analysis in non-Gaussian Distributions
We present a robust alternative to principal component analysis (PCA) ---
called elliptical component analysis (ECA) --- for analyzing high dimensional,
elliptically distributed data. ECA estimates the eigenspace of the covariance
matrix of the elliptical data. To cope with heavy-tailed elliptical
distributions, a multivariate rank statistic is exploited. At the model-level,
we consider two settings: either that the leading eigenvectors of the
covariance matrix are non-sparse or that they are sparse. Methodologically, we
propose ECA procedures for both non-sparse and sparse settings. Theoretically,
we provide both non-asymptotic and asymptotic analyses quantifying the
theoretical performances of ECA. In the non-sparse setting, we show that ECA's
performance is highly related to the effective rank of the covariance matrix.
In the sparse setting, the results are twofold: (i) We show that the sparse ECA
estimator based on a combinatoric program attains the optimal rate of
convergence; (ii) Based on some recent developments in estimating sparse
leading eigenvectors, we show that a computationally efficient sparse ECA
estimator attains the optimal rate of convergence under a suboptimal scaling.Comment: to appear in JASA (T&M
Magnetic fields of our Galaxy on large and small scales
Magnetic fields have been observed on all scales in our Galaxy, from AU to
kpc. With pulsar dispersion measures and rotation measures, we can directly
measure the magnetic fields in a very large region of the Galactic disk. The
results show that the large-scale magnetic fields are aligned with the spiral
arms but reverse their directions many times from the inner-most arm (Norma) to
the outer arm (Perseus). The Zeeman splitting measurements of masers in HII
regions or star-formation regions not only show the structured fields inside
clouds, but also have a clear pattern in the global Galactic distribution of
all measured clouds which indicates the possible connection of the large-scale
and small-scale magnetic fields.Comment: 9 pages. Invited Talk at IAU Symp.242, 'Astrophysical Masers and
their Environments', Proceedings edited by J. M. Chapman & W. A. Baa
Sparse Median Graphs Estimation in a High Dimensional Semiparametric Model
In this manuscript a unified framework for conducting inference on complex
aggregated data in high dimensional settings is proposed. The data are assumed
to be a collection of multiple non-Gaussian realizations with underlying
undirected graphical structures. Utilizing the concept of median graphs in
summarizing the commonality across these graphical structures, a novel
semiparametric approach to modeling such complex aggregated data is provided
along with robust estimation of the median graph, which is assumed to be
sparse. The estimator is proved to be consistent in graph recovery and an upper
bound on the rate of convergence is given. Experiments on both synthetic and
real datasets are conducted to illustrate the empirical usefulness of the
proposed models and methods
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