We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ...ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
There has been much recent interest in studying anisotropies in the astrophysical gravitational-wave (GW) background, as these could provide us with interesting new information about galaxy ...clustering and large-scale structure. However, this information is obscured by shot noise, caused by the finite number of GW sources that contribute to the background at any given time. We develop a new method for estimating the angular spectrum of anisotropies, based on the principle of combining statistically-independent data segments. We show that this gives an unbiased estimate of the true, astrophysical spectrum, removing the offset due to shot noise power, and that in the limit of many data segments, it is the most efficient (i.e., lowest-variance) estimator possible.
We derive scaling laws for the signal-to-noise ratio of the optimal cross-correlation statistic, and show that the large power-law increase of the signal-to-noise ratio as a function of the ...observation time T that is usually assumed holds only at early times. After enough time has elapsed, pulsar timing arrays enter a new regime where the signal to noise only scales as . In addition, in this regime the quality of the pulsar timing data and the cadence become relatively unimportant. This occurs because the lowest frequencies of the pulsar timing residuals become gravitational-wave dominated. Pulsar timing arrays enter this regime more quickly than one might naively suspect. For T = 10 yr observations and typical stochastic background amplitudes, pulsars with residual root-mean-squares of less than about 1 μs are already in that regime. The best strategy to increase the detectability of the background in this regime is to increase the number of pulsars in the array. We also perform realistic simulations of the NANOGrav pulsar timing array, which through an aggressive pulsar survey campaign adds new millisecond pulsars regularly to its array, and show that a detection is possible within a decade, and could occur as early as 2016.
Sufficient statistics are combinations of data in terms of which the likelihood function can be rewritten without loss of information. Depending on the data volume reduction, the use of sufficient ...statistics as a preliminary step in a Bayesian analysis can lead to significant increases in efficiency when sampling from posterior distributions of model parameters. Here we show that the frequency integrand of the crosscorrelation statistic and its variance are approximate sufficient statistics for ground-based searches for stochastic gravitational-wave backgrounds. The sufficient statistics are approximate because one works in the weak-signal approximation and uses measured estimates of the autocorrelated power in each detector. We perform analytic and numerical calculations to show that, in this approximation, LIGO-Virgo's hybrid frequentist-Bayesian parameter estimation analysis is equivalent to a fully Bayesian analysis. This work closes a gap in the LIGO-Virgo literature and suggests directions for additional searches.
The discovery of new pharmaceutical drugs is one of the preeminent tasks-scientifically, economically, and socially-in biomedical research. Advances in informatics and computational biology have ...increased productivity at many stages of the drug discovery pipeline. Nevertheless, drug discovery has slowed, largely due to the reliance on small molecules as the primary source of novel hypotheses. Natural products (such as plant metabolites, animal toxins, and immunological components) comprise a vast and diverse source of bioactive compounds, some of which are supported by thousands of years of traditional medicine, and are largely disjoint from the set of small molecules used commonly for discovery. However, natural products possess unique characteristics that distinguish them from traditional small molecule drug candidates, requiring new methods and approaches for assessing their therapeutic potential. In this review, we investigate a number of state-of-the-art techniques in bioinformatics, cheminformatics, and knowledge engineering for data-driven drug discovery from natural products. We focus on methods that aim to bridge the gap between traditional small-molecule drug candidates and different classes of natural products. We also explore the current informatics knowledge gaps and other barriers that need to be overcome to fully leverage these compounds for drug discovery. Finally, we conclude with a "road map" of research priorities that seeks to realize this goal.
A major trend in biomedical research has been an ideological shift away from studying individual components of an organism or biological process in isolation, and towards how those components ...function collectively, forming the basis of the field now known as systems biology ...
We construct realistic sensitivity curves for pulsar timing array searches for gravitational waves, incorporating both red and white noise contributions to individual pulsar noise spectra, and the ...effect of fitting to a pulsar timing model. We demonstrate the method on both simulated pulsars and a realistic array consisting of a subset of NANOGrav pulsars used in recent analyses. A comparison between the results presented here and measured upper limit curves from actual analyses shows agreement to tens of percent. The resulting sensitivity curves can be used to assess the detectability of predicted gravitational-wave signals in the nanohertz frequency band in a coherent, flexible, and computationally efficient manner.
Abstract
Statistical anisotropy in the nanohertz-frequency gravitational wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a ...frequentist statistical framework that intrinsically restricts the GWB power to be positive, we establish scaling relations for multipole-dependent anisotropy decision thresholds that are a function of the noise properties, timing baselines, and cadences of the pulsars in a PTA. We verify that (i) a larger number of pulsars, and (ii) factors that lead to lower uncertainty on spatial cross-correlation measurements between pulsars, lead to a higher overall GWB signal-to-noise ratio, and lower anisotropy decision thresholds with which to reject the null hypothesis of isotropy. Using conservative simulations of realistic NANOGrav data sets, we predict that an anisotropic GWB with angular power
C
l
=1
> 0.3
C
l
=0
may be sufficient to produce tension with isotropy at the
p
= 3 × 10
−3
(∼3
σ
) level in near-future NANOGrav data with a 20 yr baseline. We present ready-to-use scaling relationships that can map these thresholds to any number of pulsars, configuration of pulsar noise properties, or sky coverage. We discuss how PTAs can improve the detection prospects for anisotropy, as well as how our methods can be adapted for more versatile searches.
Pulsar timing array (PTA) searches for a gravitational-wave background (GWB) typically include time-correlated "red" noise models intrinsic to each pulsar. Using a simple simulated PTA data set with ...an injected GWB signal we show that the details of the red noise models used, including the choice of amplitude priors and even which pulsars have red noise, have a striking impact on the GWB statistics, including both upper limits and estimates of the GWB amplitude. We find that the standard use of uniform priors on the red noise amplitude leads to 95% upper limits, as calculated from one-sided Bayesian credible intervals, that are less than the injected GWB amplitude 50% of the time. In addition, amplitude estimates of the GWB are systematically lower than the injected value by 10%-40%, depending on which models and priors are chosen for the intrinsic red noise. We tally the effects of model and prior choice and demonstrate how a "dropout" model, which allows flexible use of red noise models in a Bayesian approach, can improve GWB estimates throughout.
Romano and Creighton discuss the study on spectral shifts in general relativity by Narlikar, published in 1994. Narlikar provided a unified framework for interpreting spectral shifts in general ...relativity as Doppler shifts due to relative motion between a source and an observer. The key insight is to compare the four-velocity of the observer to that of the source obtained by parallel propagating the source four-velocity along the null geodesic of the photon connecting source and observer. The paper is well written, and we highly encourage others to read it. However, there are compensating sign errors in two equations in Sec. II, leading to a series of incorrect intermediate equations. The final expression for the spectral shift is unaffected, so the main conclusions of the paper are correct as is.
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