A new method for the estimation of the reverberation time from measured room impulse responses with application to Italian opera houses

The Schroeder's backward integration method is the most used method to extract the decay curve of an acoustic impulse response and to calculate the reverberation time from this curve. In the literature the limits and the possible improvements of this method are widely discussed. In this work a new method is proposed for the evaluation of the energy decay curve. The new method has been implemented in a Matlab toolbox. Its performance has been tested versus the most accredited literature method. The values of EDT and reverberation time extracted from the energy decay curves calculated with both methods have been compared in terms of the values themselves and in terms of their statistical representativeness. The main case study consists of nine Italian historical theatres in which acoustical measurements were performed. The comparison of the two extraction methods has also been applied to a critical case, i.e. the structural impulse responses of some building elements. The comparison underlines that both methods return a comparable value of the T30. Decreasing the range of evaluation, they reveal increasing differences; in particular, the main differences are in the first part of the decay, where the EDT is evaluated. This is a consequence of the fact that the new method returns a “locally" defined energy decay curve, whereas the Schroeder's method accumulates energy from the tail to the beginning of the impulse response. Another characteristic of the new method for the energy decay extraction curve is its independence on the background noise estimation. Finally, a statistical analysis is performed on the T30 and EDT values calculated from the impulse responses measurements in the Italian historical theatres. The aim of this evaluation is to know whether a subset of measurements could be considered representative for a complete characterization of these opera houses.

Estimation of Quasi-Rational DSGE Models

Small-scale dynamic stochastic general equilibrium have been treated as the benchmark of much of the monetary policy literature, given their ability to explain the impact of monetary policy on output, inflation and financial markets. One cause of the empirical failure of New Keynesian models is partially due to the Rational Expectations (RE) paradigm, which entails a tight structure on the dynamics of the system. Under this hypothesis, the agents are assumed to know the data genereting process. In this paper, we propose the econometric analysis of New Keynesian DSGE models under an alternative expectations generating paradigm, which can be regarded as an intermediate position between rational expectations and learning, nameley an adapted version of the "Quasi-Rational" Expectatations (QRE) hypothesis. Given the agents' statistical model, we build a pseudo-structural form from the baseline system of Euler equations, imposing that the length of the reduced form is the same as in the `best' statistical model.

The XENON1T experiment: Monte Carlo background estimation and sensitivity curves study

Despite the scientific achievement of the last decades in the astrophysical and cosmological fields, the majority of the Universe energy content is still unknown. A potential solution to the “missing mass problem” is the existence of dark matter in the form of WIMPs. Due to the very small cross section for WIMP-nuleon interactions, the number of expected events is very limited (about 1 ev/tonne/year), thus requiring detectors with large target mass and low background level. The aim of the XENON1T experiment, the first tonne-scale LXe based detector, is to be sensitive to WIMP-nucleon cross section as low as 10^-47 cm^2. To investigate the possibility of such a detector to reach its goal, Monte Carlo simulations are mandatory to estimate the background. To this aim, the GEANT4 toolkit has been used to implement the detector geometry and to simulate the decays from the various background sources: electromagnetic and nuclear. From the analysis of the simulations, the level of background has been found totally acceptable for the experiment purposes: about 1 background event in a 2 tonne-years exposure. Indeed, using the Maximum Gap method, the XENON1T sensitivity has been evaluated and the minimum for the WIMP-nucleon cross sections has been found at 1.87 x 10^-47 cm^2, at 90% CL, for a WIMP mass of 45 GeV/c^2. The results have been independently cross checked by using the Likelihood Ratio method that confirmed such results with an agreement within less than a factor two. Such a result is completely acceptable considering the intrinsic differences between the two statistical methods. Thus, in the PhD thesis it has been proven that the XENON1T detector will be able to reach the designed sensitivity, thus lowering the limits on the WIMP-nucleon cross section by about 2 orders of magnitude with respect to the current experiments.