Detection of gravitational waves using a network of detectors

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is essentially the magnitude of the network correlation vector constructed from the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended to address the problem of detection of such waves from other sources by some other types of detectors, e.g., bars or spheres, or even by networks of spatially well-separated detectors.Comment: 14 pages, RevTex, 1 postscript figure. Based on talk given at Workshop on Cosmology: Observations confront theories, IIT-Kharagpur, India (January 1999

Estimation of high-density activation maps during atrial fibrillation

The study of activation maps using multi-electrode arrays (MEA) can help to understand atrial fibrillation (AF) mechanisms. Activation mapping based on recorded unipolar electrograms (u-EGM) rely on the local activation time (LAT) detector, which has a limited robustness, accuracy, and generally requires manual post-edition. In general, LAT detection ignores spatiotemporal information about activation and conduction conveyed by the relation between signals of the MEA sensor. This work proposes an approach to construct activation maps by simultaneous analysis of u-EGMs from small clusters of MEA electrodes. The algorithm iteratively fits an activation pattern model to the acquired data. Accuracy was evaluated by comparing with audited maps created by expert electrophysiologists from a patient undergoing open-chest surgery during AF. The estimation error was -0.29 ± 6.01 ms (236 maps, 28369 LATs) with high correlation (¿ = 0.93). Therefore, activation maps can be decomposed into local activation patterns derived from fitting an activation model, resulting in smooth and comprehensive high-density activation maps

Role of surveillance biopsy frequency post intestine transplant: A tertiary care experience

Background: With only 81 intestine transplant (IT) in the U.S. in 2019, the literature on this type of solid organ transplant remains scarce. Frequent surveillance biopsy is required on the first month post IT due to high-risk of acute rejection, however, the frequency of surveillance biopsy 1-month post IT is often determined by the physician and the institutions\u27 preference. Aims: Report IT outcomes and clinical impact of surveillance biopsy at a single tertiary care center. Methods: This is a retrospective review of patients that underwent IT during the time-period between 08/2010 and 03/2020. Primary outcome was the correlation between increased protocol biopsies and mortality. Secondary outcomes included correlation between increased protocol biopsies and hospital re-admissions, length of hospital stay, and rate of biopsy proven rejection detection. Kaplan-Meier curves was used to perform the survival analysis at 6-month, 1-year, and 2-years post-transplant. Results: A total of 35 patients (mean age 47.6 ± 12.9 years, F 22 (63%) underwent IT for: ischemic bowel 11 (31%), Chron\u27s disease 9 (25%), neuroendocrine tumor 6 (17%), trauma 3 (9%) and \u27others\u27 6 (17%), of which 14 (40%) were part of multivisceral organ transplant. During the first-year posttransplant, the median number of biopsies was 12 (IQR 6-30), with evidence of definite acute graft rejection in 40%, 27%, and 41% at the 1-3, 3-6, and 6-12 post IT time intervals, respectively. During the duration of the study, the mortality rate was 18/35 (51%) at a median time of 37 (12-60) months post IT, and a total of 8/35 (23%) patients underwent enterectomy at a median time of 12 (8-36) months post IT (Table 1). In general, there was survival benefit for patients who had a total number of biopsies of ≥ 10 as compared to \u3c 10 biopsies at the time interval of 6-months post IT, (p=0.008) (Table 2). There was a non-significant trend with longer median length of hospital stay in patients with greater number of biopsies. Conclusion: Our results indicate evidence of survival benefit of increased protocol biopsies. Studies with larger sample sizes are required to validate our results

Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters

The paper deals with issues pertaining the detection of gravitational waves from coalescing binaries. We introduce the application of differential geometry to the problem of optimal detection of the `chirp signal'. We have also carried out extensive Monte Carlo simulations to understand the errors in the estimation of parameters of the binary system. We find that the errors are much more than those predicted by the covariance matrix even at a high SNR of 10-15. We also introduce the idea of using the instant of coalescence rather than the time of arrival to determine the direction to the source.Comment: 28 pages, REVTEX, 12 figures (bundled via uufiles command along with this paper) submitted to Phys. Rev.

On Estimation of the Post-Newtonian Parameters in the Gravitational-Wave Emission of a Coalescing Binary

The effect of the recently obtained 2nd post-Newtonian corrections on the accuracy of estimation of parameters of the gravitational-wave signal from a coalescing binary is investigated. It is shown that addition of this correction degrades considerably the accuracy of determination of individual masses of the members of the binary. However the chirp mass and the time parameter in the signal is still determined to a very good accuracy. The possibility of estimation of effects of other theories of gravity is investigated. The performance of the Newtonian filter is investigated and it is compared with performance of post-Newtonian search templates introduced recently. It is shown that both search templates can extract accurately useful information about the binary.Comment: 34 pages, 118Kb, LATEX format, submitted to Phys. Rev.

Performance of Newtonian filters in detecting gravitational waves from coalescing binaries

Coalescing binary systems are one of the most promising sources of gravitational waves. The technique of matched filtering used in the detection of gravitational waves from coalescing binaries relies on the construction of accurate templates. Until recently filters modelled on the quadrupole or the Newtonian approximation were deemed sufficient. Recently it was shown that post-Newtonian effects contribute to a secular growth in the phase difference between the actual signal and its corresponding Newtonian template. In this paper we investigate the possibility of compensating for the phase difference caused by the post-Newtonian terms by allowing for a shift in the Newtonian filter parameters. We find that Newtonian filters perform adequately for the purpose of detecting the presence of the signal for both the initial and the advanced LIGO detectors.Comment: Revtex 9 pages + 6 figures ( Can be obtained by "anonymous" ftp from 144.16.31.1 in dir /pub/rbs. Submitted to Physical Review D. IUCAA 1

Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars

We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.Comment: Submitted to the Astrophysical Journa