4,161 research outputs found
Detection of gravitational waves from inspiraling compact binaries using a network of interferometric detectors
We formulate the data analysis problem for the detection of the Newtonian
waveform from an inspiraling compact-binary by a network of arbitrarily
oriented and arbitrarily distributed laser interferometric gravitational wave
detectors. We obtain for the first time the relation between the optimal
statistic and the magnitude of the network correlation vector, which is
constructed from the matched network-filter. This generalizes the calculation
reported in an earlier work (gr-qc/9906064), where the detectors are taken to
be coincident.Comment: 6 pages, RevTeX. Based on talk given at GWDAW-99, Rom
CanICA: Model-based extraction of reproducible group-level ICA patterns from fMRI time series
Spatial Independent Component Analysis (ICA) is an increasingly used
data-driven method to analyze functional Magnetic Resonance Imaging (fMRI)
data. To date, it has been used to extract meaningful patterns without prior
information. However, ICA is not robust to mild data variation and remains a
parameter-sensitive algorithm. The validity of the extracted patterns is hard
to establish, as well as the significance of differences between patterns
extracted from different groups of subjects. We start from a generative model
of the fMRI group data to introduce a probabilistic ICA pattern-extraction
algorithm, called CanICA (Canonical ICA). Thanks to an explicit noise model and
canonical correlation analysis, our method is auto-calibrated and identifies
the group-reproducible data subspace before performing ICA. We compare our
method to state-of-the-art multi-subject fMRI ICA methods and show that the
features extracted are more reproducible
An excess power statistic for detection of burst sources of gravitational radiation
We examine the properties of an excess power method to detect gravitational
waves in interferometric detector data. This method is designed to detect
short-duration (< 0.5 s) burst signals of unknown waveform, such as those from
supernovae or black hole mergers. If only the bursts' duration and frequency
band are known, the method is an optimal detection strategy in both Bayesian
and frequentist senses. It consists of summing the data power over the known
time interval and frequency band of the burst. If the detector noise is
stationary and Gaussian, this sum is distributed as a chi-squared (non-central
chi-squared) deviate in the absence (presence) of a signal. One can use these
distributions to compute frequentist detection thresholds for the measured
power. We derive the method from Bayesian analyses and show how to compute
Bayesian thresholds. More generically, when only upper and/or lower bounds on
the bursts duration and frequency band are known, one must search for excess
power in all concordant durations and bands. Two search schemes are presented
and their computational efficiencies are compared. We find that given
reasonable constraints on the effective duration and bandwidth of signals, the
excess power search can be performed on a single workstation. Furthermore, the
method can be almost as efficient as matched filtering when a large template
bank is required. Finally, we derive generalizations of the method to a network
of several interferometers under the assumption of Gaussian noise.Comment: 22 pages, 6 figure
Optimal detection of burst events in gravitational wave interferometric observatories
We consider the problem of detecting a burst signal of unknown shape. We
introduce a statistic which generalizes the excess power statistic proposed by
Flanagan and Hughes and extended by Anderson et al. The statistic we propose is
shown to be optimal for arbitrary noise spectral characteristic, under the two
hypotheses that the noise is Gaussian, and that the prior for the signal is
uniform. The statistic derivation is based on the assumption that a signal
affects only affects N samples in the data stream, but that no other
information is a priori available, and that the value of the signal at each
sample can be arbitrary. We show that the proposed statistic can be implemented
combining standard time-series analysis tools which can be efficiently
implemented, and the resulting computational cost is still compatible with an
on-line analysis of interferometric data. We generalize this version of an
excess power statistic to the multiple detector case, also including the effect
of correlated noise. We give full details about the implementation of the
algorithm, both for the single and the multiple detector case, and we discuss
exact and approximate forms, depending on the specific characteristics of the
noise and on the assumed length of the burst event. As a example, we show what
would be the sensitivity of the network of interferometers to a delta-function
burst.Comment: 21 pages, 5 figures in 3 groups. Submitted for publication to
Phys.Rev.D. A Mathematica notebook is available at
http://www.ligo.caltech.edu/~avicere/nda/burst/Burst.nb which allows to
reproduce the numerical results of the pape
Parameter-space metric of semicoherent searches for continuous gravitational waves
Continuous gravitational-wave (CW) signals such as emitted by spinning
neutron stars are an important target class for current detectors. However, the
enormous computational demand prohibits fully coherent broadband all-sky
searches for prior unknown CW sources over wide ranges of parameter space and
for yearlong observation times. More efficient hierarchical "semicoherent"
search strategies divide the data into segments much shorter than one year,
which are analyzed coherently; then detection statistics from different
segments are combined incoherently. To optimally perform the incoherent
combination, understanding of the underlying parameter-space structure is
requisite. This problem is addressed here by using new coordinates on the
parameter space, which yield the first analytical parameter-space metric for
the incoherent combination step. This semicoherent metric applies to broadband
all-sky surveys (also embedding directed searches at fixed sky position) for
isolated CW sources. Furthermore, the additional metric resolution attained
through the combination of segments is studied. From the search parameters (sky
position, frequency, and frequency derivatives), solely the metric resolution
in the frequency derivatives is found to significantly increase with the number
of segments.Comment: 14 pages, 5 figures (matching Phys.Rev.D version
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