2,598 research outputs found
Gravitational wave radiometry: Mapping a stochastic gravitational wave background
The problem of the detection and mapping of a stochastic gravitational wave
background (SGWB), either of cosmological or astrophysical origin, bears a
strong semblance to the analysis of CMB anisotropy and polarization. The basic
statistic we use is the cross-correlation between the data from a pair of
detectors. In order to `point' the pair of detectors at different locations one
must suitably delay the signal by the amount it takes for the gravitational
waves (GW) to travel to both detectors corresponding to a source direction.
Then the raw (observed) sky map of the SGWB is the signal convolved with a beam
response function that varies with location in the sky. We first present a
thorough analytic understanding of the structure of the beam response function
using an analytic approach employing the stationary phase approximation. The
true sky map is obtained by numerically deconvolving the beam function in the
integral (convolution) equation. We adopt the maximum likelihood framework to
estimate the true sky map that has been successfully used in the broadly
similar, well-studied CMB map making problem. We numerically implement and
demonstrate the method on simulated (unpolarized) SGWB for the radiometer
consisting of the LIGO pair of detectors at Hanford and Livingston. We include
`realistic' additive Gaussian noise in each data stream based on the LIGO-I
noise power spectral density. The extension of the method to multiple baselines
and polarized GWB is outlined. In the near future the network of GW detectors,
including the Advanced LIGO and Virgo detectors that will be sensitive to
sources within a thousand times larger spatial volume, could provide promising
data sets for GW radiometry.Comment: 24 pages, 19 figures, pdflatex. Matched version published in Phys.
Rev. D - minor change
Slepian functions and their use in signal estimation and spectral analysis
It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden,
Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla
Scalar and vector Slepian functions, spherical signal estimation and spectral analysis
It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and, particularly for applications in the
geosciences, for scalar and vectorial signals defined on the surface of a unit
sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics,
edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be
published by Springer Verlag. This is a slightly modified but expanded
version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the
Handbook, when it was called: Slepian functions and their use in signal
estimation and spectral analysi
Cosmology at Low Frequencies: The 21 cm Transition and the High-Redshift Universe
Observations of the high-redshift Universe with the 21 cm hyperfine line of
neutral hydrogen promise to open an entirely new window onto the early phases
of cosmic structure formation. Here we review the physics of the 21 cm
transition, focusing on processes relevant at high redshifts, and describe the
insights to be gained from such observations. These include measuring the
matter power spectrum at z~50, observing the formation of the cosmic web and
the first luminous sources, and mapping the reionization of the intergalactic
medium. The epoch of reionization is of particular interest, because large HII
regions will seed substantial fluctuations in the 21 cm background. We also
discuss the experimental challenges involved in detecting this signal, with an
emphasis on the Galactic and extragalactic foregrounds. These increase rapidly
toward low frequencies and are especially severe for the highest redshift
applications. Assuming that these difficulties can be overcome, the redshifted
21 cm line will offer unique insight into the high-redshift Universe,
complementing other probes but providing the only direct, three-dimensional
view of structure formation from z~200 to z~6.Comment: extended review accepted by Physics Reports, 207 pages, 44 figures
(some low resolution); version with high resolution figures available at
http://pantheon.yale.edu/~srf28/21cm/index.htm; minor changes to match
published versio
Isolated ionospheric disturbances as deduced from global GPS network
International audienceWe investigate an unusual class of medium-scale traveling ionospheric disturbances of the nonwave type, isolated ionospheric disturbances (IIDs) that manifest themselves in total electron content (TEC) variations in the form of single aperiodic negative TEC disturbances of a duration of about 10min (the total electron content spikes, TECS). The data were obtained using the technology of global detection of ionospheric disturbances using measurements of TEC variations from a global network of receivers of the GPS. For the first time, we present the TECS morphology for 170 days in 1998?2001. The total number of TEC series, with a duration of each series of about 2.3h (2h18m), exceeded 850000. It was found that TECS are observed in no more than 1?2% of the total number of TEC series mainly in the nighttime in the spring and autumn periods. The TECS amplitude exceeds the mean value of the "background" TEC variation amplitude by a factor of 5?10 as a minimum. TECS represent a local phenomenon with a typical radius of spatial correlation not larger than 500km. The IID-induced TEC variations are similar in their amplitude, form and duration to the TEC response to shock-acoustic waves (SAW) generated during rocket launchings and earthquakes. However, the IID propagation velocity is less than the SAW velocity (800?1000m/s) and are most likely to correspond to the velocity of background medium-scale acoustic-gravity waves, on the order of 100?200m/s. Key words. Ionosphere (ionospheric irregularities, instruments and techniques) - Radio science (ionospheric propagation
Deep Point Correlation Design
Designing point patterns with desired properties can require substantial
effort, both in hand-crafting coding and mathematical derivation. Retaining
these properties in multiple dimensions or for a substantial number of points
can be challenging and computationally expensive. Tackling those two issues,
we suggest to automatically generate scalable point patterns from design
goals using deep learning. We phrase pattern generation as a deep composition of weighted distance-based unstructured filters. Deep point pattern
design means to optimize over the space of all such compositions according to
a user-provided point correlation loss, a small program which measures a pattern’s fidelity in respect to its spatial or spectral statistics, linear or non-linear
(e. g., radial) projections, or any arbitrary combination thereof. Our analysis
shows that we can emulate a large set of existing patterns (blue, green, step,
projective, stair, etc.-noise), generalize them to countless new combinations
in a systematic way and leverage existing error estimation formulations to
generate novel point patterns for a user-provided class of integrand functions.
Our point patterns scale favorably to multiple dimensions and numbers of
points: we demonstrate nearly 10 k points in 10-D produced in one second
on one GPU. All the resources (source code and the pre-trained networks)
can be found at https://sampling.mpi-inf.mpg.de/deepsampling.html
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