Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials †

Bell’s polynomials are used in many different fields of mathematics, ranging from number theory to operator theory. This paper shows a relevant application in probability theory aimed at computing the moments of generalized Gaussian distributions. To this end, a table containing the first values of the complete Bell’s polynomials is provided. Furthermore, a dedicated code for approximating the moments of the general distributions in terms of complete Bell’s polynomials is detailed. Several test cases concerning different nested functions are discussed.</p

On the eigenvalues of a kernel considered by A. M. Ostrowski

By using the inverse iteration method we improve approximation of the eigenvalues of a kernel connected with a problem considered by A.M. Ostrowski

Early Invasive Strategy for Unstable Angina: a New Meta-Analysis of Old Clinical Trials

Randomized controlled trials (RCTs) were conflicting to support whether unstable angina versus non-ST-elevation myocardial infarction (UA/NSTEMI) patients best undergo early invasive or a conservative revascularization strategy. RCTs with cardiac biomarkers, in MEDLINE, EMBASE, and Cochrane Central Register of Controlled Trials from 1975-2013 were reviewed considering all cause mortality, recurrent non-fatal myocardial infarction (MI) and their combination. Follow-up lasted from 6-24 months and the use of routine invasive strategy up to its end was associated with a significantly lower composite of all-cause mortality and recurrent non-fatal MI (Relative Risk [RR] 0.79; 95% confidence interval [CI], 0.70-0.90) in UA/NSTEMI. In NSTEMI, by the invasive strategy, there was no benefit (RR 1.19; 95%\u2009CI, 1.03-1.38). In the shorter time period, from randomization to discharge, a routine invasive strategy was associated with significantly higher odds of the combined end-point among UA/NSTEMI (RR 1.29; 95%\u2009CI, 1.05-1.58) and NSTEMI (RR 1.82; 95%\u2009CI, 1.34-2.48) patients. Therefore, in trials recruiting a large number of UA patients, by routine invasive strategy the largest benefit was seen, whereas in NSTEMI patients death and non-fatal MI were not lowered. Routine invasive treatment in UA patients is accordingly supported by the present study

All-sky search of NAUTILUS data

A search for periodic gravitational-wave signals from isolated neutron stars in the NAUTILUS detector data is presented. We have analyzed half a year of data over the frequency band $$Hz, the spindown range$$ Hz/s and over the entire sky. We have divided the data into 2 day stretches and we have analyzed each stretch coherently using matched filtering. We have imposed a low threshold for the optimal detection statistic to obtain a set of candidates that are further examined for coincidences among various data stretches. For some candidates we have also investigated the change of the signal-to-noise ratio when we increase the observation time from two to four days. Our analysis has not revealed any gravitational-wave signals. Therefore we have imposed upper limits on the dimensionless gravitational-wave amplitude over the parameter space that we have searched. Depending on frequency, our upper limit ranges from $3.4 \times 10^{-23}$ to $1.3 \times 10^{-22}$. We have attempted a statistical verification of the hypotheses leading to our conclusions. We estimate that our upper limit is accurate to within 18%.Comment: LaTeX, 12 page

Virgo calibration and reconstruction of the gravitational wave strain during VSR1

Virgo is a kilometer-length interferometer for gravitational waves detection located near Pisa. Its first science run, VSR1, occured from May to October 2007. The aims of the calibration are to measure the detector sensitivity and to reconstruct the time series of the gravitational wave strain h(t). The absolute length calibration is based on an original non-linear reconstruction of the differential arm length variations in free swinging Michelson configurations. It uses the laser wavelength as length standard. This method is used to calibrate the frequency dependent response of the Virgo mirror actuators and derive the detector in-loop response and sensitivity within ~5%. The principle of the strain reconstruction is highlighted and the h(t) systematic errors are estimated. A photon calibrator is used to check the sign of h(t). The reconstructed h(t) during VSR1 is valid from 10 Hz up to 10 kHz with systematic errors estimated to 6% in amplitude. The phase error is estimated to be 70 mrad below 1.9 kHz and 6 micro-seconds above.Comment: 8 pages, 8 figures, proceedings of Amaldi 8 conference, to be published in Journal of Physics Conference Series (JPCS). Second release: correct typo

A Cross-correlation method to search for gravitational wave bursts with AURIGA and Virgo

We present a method to search for transient GWs using a network of detectors with different spectral and directional sensitivities: the interferometer Virgo and the bar detector AURIGA. The data analysis method is based on the measurements of the correlated energy in the network by means of a weighted cross-correlation. To limit the computational load, this coherent analysis step is performed around time-frequency coincident triggers selected by an excess power event trigger generator tuned at low thresholds. The final selection of GW candidates is performed by a combined cut on the correlated energy and on the significance as measured by the event trigger generator. The method has been tested on one day of data of AURIGA and Virgo during September 2005. The outcomes are compared to the results of a stand-alone time-frequency coincidence search. We discuss the advantages and the limits of this approach, in view of a possible future joint search between AURIGA and one interferometric detector.Comment: 11 pages, 6 figures, submitted to CQG special issue for Amaldi 7 Proceeding

Calibration and sensitivity of the Virgo detector during its second science run

The Virgo detector is a kilometer-length interferometer for gravitational wave detection located near Pisa (Italy). During its second science run (VSR2) in 2009, six months of data were accumulated with a sensitivity close to its design. In this paper, the methods used to determine the parameters for sensitivity estimation and gravitational wave reconstruction are described. The main quantities to be calibrated are the frequency response of the mirror actuation and the sensing of the output power. Focus is also put on their absolute timing. The monitoring of the calibration data as well as the parameter estimation with independent techniques are discussed to provide an estimation of the calibration uncertainties. Finally, the estimation of the Virgo sensitivity in the frequency-domain is described and typical sensitivities measured during VSR2 are shown.Comment: 30 pages, 23 figures, 1 table. Published in Classical and Quantum Gravity (CQG), Corrigendum include

Scientific Objectives of Einstein Telescope

The advanced interferometer network will herald a new era in observational astronomy. There is a very strong science case to go beyond the advanced detector network and build detectors that operate in a frequency range from 1 Hz-10 kHz, with sensitivity a factor ten better in amplitude. Such detectors will be able to probe a range of topics in nuclear physics, astronomy, cosmology and fundamental physics, providing insights into many unsolved problems in these areas.Comment: 18 pages, 4 figures, Plenary talk given at Amaldi Meeting, July 201