20,261 research outputs found
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
The Bolocam Galactic Plane Survey: Survey Description and Data Reduction
We present the Bolocam Galactic Plane Survey (BGPS), a 1.1 mm continuum
survey at 33" effective resolution of 170 square degrees of the Galactic Plane
visible from the northern hemisphere. The survey is contiguous over the range
-10.5 < l < 90.5, |b| < 0.5 and encompasses 133 square degrees, including some
extended regions |b| < 1.5. In addition to the contiguous region, four targeted
regions in the outer Galaxy were observed: IC1396, a region towards the Perseus
Arm, W3/4/5, and Gem OB1. The BGPS has detected approximately 8400 clumps over
the entire area to a limiting non-uniform 1-sigma noise level in the range 11
to 53 mJy/beam in the inner Galaxy. The BGPS source catalog is presented in a
companion paper (Rosolowsky et al. 2010). This paper details the survey
observations and data reduction methods for the images. We discuss in detail
the determination of astrometric and flux density calibration uncertainties and
compare our results to the literature. Data processing algorithms that separate
astronomical signals from time-variable atmospheric fluctuations in the data
time-stream are presented. These algorithms reproduce the structure of the
astronomical sky over a limited range of angular scales and produce artifacts
in the vicinity of bright sources. Based on simulations, we find that extended
emission on scales larger than about 5.9' is nearly completely attenuated (>
90%) and the linear scale at which the attenuation reaches 50% is 3.8'.
Comparison with other millimeter-wave data sets implies a possible systematic
offset in flux calibration, for which no cause has been discovered. This
presentation serves as a companion and guide to the public data release through
NASA's Infrared Processing and Analysis Center (IPAC) Infrared Science Archive
(IRSA). New data releases will be provided through IPAC IRSA with any future
improvements in the reduction.Comment: Accepted for publication in Astrophysical Journal Supplemen
Reionization and Cosmology with 21 cm Fluctuations
Measurement of the spatial distribution of neutral hydrogen via the
redshifted 21 cm line promises to revolutionize our knowledge of the epoch of
reionization and the first galaxies, and may provide a powerful new tool for
observational cosmology from redshifts 1<z<4 . In this review we discuss recent
advances in our theoretical understanding of the epoch of reionization (EoR),
the application of 21 cm tomography to cosmology and measurements of the dark
energy equation of state after reionization, and the instrumentation and
observational techniques shared by 21 cm EoR and post reionization cosmology
machines. We place particular emphasis on the expected signal and observational
capabilities of first generation 21 cm fluctuation instruments.Comment: Invited review for Annual Review of Astronomy and Astrophysics (2010
volume
Learning and comparing functional connectomes across subjects
Functional connectomes capture brain interactions via synchronized
fluctuations in the functional magnetic resonance imaging signal. If measured
during rest, they map the intrinsic functional architecture of the brain. With
task-driven experiments they represent integration mechanisms between
specialized brain areas. Analyzing their variability across subjects and
conditions can reveal markers of brain pathologies and mechanisms underlying
cognition. Methods of estimating functional connectomes from the imaging signal
have undergone rapid developments and the literature is full of diverse
strategies for comparing them. This review aims to clarify links across
functional-connectivity methods as well as to expose different steps to perform
a group study of functional connectomes
High-dynamic-range extinction mapping of infrared dark clouds: Dependence of density variance with sonic Mach number in molecular clouds
Measuring the mass distribution of infrared dark clouds (IRDCs) over the wide
dynamic range of their column densities is a fundamental obstacle in
determining the initial conditions of high-mass star formation and star cluster
formation. We present a new technique to derive high-dynamic-range,
arcsecond-scale resolution column density data for IRDCs and demonstrate the
potential of such data in measuring the density variance - sonic Mach number
relation in molecular clouds. We combine near-infrared data from the
UKIDSS/Galactic Plane Survey with mid-infrared data from the Spitzer/GLIMPSE
survey to derive dust extinction maps for a sample of ten IRDCs. We then
examine the linewidths of the IRDCs using 13CO line emission data from the
FCRAO/Galactic Ring Survey and derive a column density - sonic Mach number
relation for them. For comparison, we also examine the relation in a sample of
nearby molecular clouds. The presented column density mapping technique
provides a very capable, temperature independent tool for mapping IRDCs over
the column density range equivalent to A_V=1-100 mag at a resolution of 2".
Using the data provided by the technique, we present the first direct
measurement of the relationship between the column density dispersion,
\sigma_{N/}, and sonic Mach number, M_s, in molecular clouds. We detect
correlation between the variables with about 3-sigma confidence. We derive the
relation \sigma_{N/} = (0.047 \pm 0.016) Ms, which is suggestive of the
correlation coefficient between the volume density and sonic Mach number,
\sigma_{\rho/} = (0.20^{+0.37}_{-0.22}) Ms, in which the quoted
uncertainties indicate the 3-sigma range. When coupled with the results of
recent numerical works, the existence of the correlation supports the picture
of weak correlation between the magnetic field strength and density in
molecular clouds (i.e., B ~ \rho^{0.5}).Comment: Accepted for publication in A&A. 29 pages. Download the version with
full-resolution figures from
http://www.mpia-hd.mpg.de/homes/jtkainul/NexusI/PaperII_arxiv.pdf.g
Structure and Fragmentation of a high line-mass filament: Nessie
An increasing number of hundred-parsec scale, high line-mass filaments have
been detected in the Galaxy. Their evolutionary path, including fragmentation
towards star formation, is virtually unknown. We characterize the fragmentation
within the Nessie filament, covering size-scales between 0.1-100 pc. We
also connect the small-scale fragments to the star-forming potential of the
cloud. We combine near-infrared data from the VVV survey with mid-infrared
GLIMPSE data to derive a high-resolution dust extinction map and apply a
wavelet decomposition technique on it to analyze the fragmentation
characteristics of the cloud, which are compared with predictions from
fragmentation models. We compare the detected objects to those identified in
10 times coarser resolution from ATLASGAL data. We present a
high-resolution extinction map of Nessie. We estimate the mean line-mass of
Nessie to be 627 M/pc and the distance to be 3.5 kpc. We
find that Nessie shows fragmentation at multiple size scales. The
nearest-neighbour separations of the fragments at all scales are within a
factor of 2 of the Jeans' length at that scale. However, the relationship
between the mean densities of the fragments and their separations is
significantly shallower than expected for Jeans' fragmentation. The
relationship is similar to the one predicted for a filament that exhibits a
Larson-like scaling between size-scale and velocity dispersion; such a scaling
may result from turbulent support. Based on the number of YSOs in Nessie, we
estimate that the star formation rate is 371 M/Myr; similar
values result if using the number of dense cores, or the amount of dense gas,
as the proxy of star formation. The star formation efficiency is 0.017. These
numbers indicate that Nessie's star-forming content is comparable to the Solar
neighborhood giant molecular clouds like Orion A
What determines the density structure of molecular clouds? A case study of Orion B with <i>Herschel</i>
A key parameter to the description of all star formation processes is the density structure of the gas. In this Letter, we make use of probability distribution functions (PDFs) of Herschel column density maps of Orion B, Aquila, and Polaris, obtained with the Herschel Gould Belt survey (HGBS). We aim to understand which physical processes influence the PDF shape, and with which signatures. The PDFs of Orion B (Aquila) show a lognormal distribution for low column densities until AV ~ 3 (6), and a power-law tail for high column densities, consistent with a ρα r-2 profile for the equivalent spherical density distribution. The PDF of Orion B is broadened by external compression due to the nearby OB stellar aggregates. The PDF of a quiescent subregion of the non-star-forming Polaris cloud is nearly lognormal, indicating that supersonic turbulence governs the density distribution. But we also observe a deviation from the lognormal shape at AV > 1 for a subregion in Polaris that includes a prominent filament. We conclude that (1) the point where the PDF deviates from the lognormal form does not trace a universal AV -threshold for star formation, (2) statistical density fluctuations, intermittency, and magnetic fields can cause excess from the lognormal PDF at an early cloud formation stage, (3) core formation and/or global collapse of filaments and a non-isothermal gas distribution lead to a power-law tail, and (4) external compression broadens the column density PDF, consistent with numerical simulations
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