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In this paper, we give estimators of the frequency, amplitude and phase of a noisy sinusoidal signal with time-varying amplitude by using the algebraic parametric techniques introduced by Fliess and Sira-Ramirez. We apply a similar strategy to estimate these parameters by using modulating functions method. The convergence of the noise error part due to a large class of noises is studied to show the robustness and the stability of these methods. We also show that the estimators obtained by modulating functions method are robust to large sampling period and to non zero-mean noises.
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Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits; in this paper, we extend this method so that it can deal with the realistic noise effect. The validity of the proposed noise model is supported by an experimental demonstration on an IBM Q device, which accordingly enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.
We propose an observation-driven time-varying SVAR model where, in agreement with the Lucas Critique, structural shocks drive both the evolution of the macro variables and the dynamics of the VAR parameters. Contrary to existing approaches where parameters follow a stochastic process with random and exogenous shocks, our observation-driven specification allows the evolution of the parameters to be driven by realized past structural shocks, thus opening the possibility to gauge the impact of observed shocks and hypothetical policy interventions on the future evolution of the economic system.
Several differentiating algorithms of the noisy signals are considered. The proposed wavelet based technique is compared with others based on the Fourier transform and the finite differences. The accuracy of the calculations for different algorithms is estimated for two model examples.
A search for a time-varying $bar{ u}_{e}$ signal was performed with 621 days of data acquired by the Daya Bay Reactor Neutrino Experiment over 704 calendar days. The time spectrum of the measured $overline{ u}_e$ flux normalized to its prediction was analyzed with a Lomb-Scargle periodogram, which yielded no significant signal for periods ranging from 2 hours to nearly 2 years. The normalized time spectrum was also fit for a sidereal modulation under the Standard Model extension (SME) framework to search for Lorentz and CPT violation (LV-CPTV). Limits were obtained for all six flavor pairs $bar{e}bar{mu}$, $bar{e}bar{tau}$, $bar{mu}bar{tau}$, $bar{e}bar{e},bar{mu}bar{mu}$ and $bar{tau}bar{tau}$ by fitting them one at a time, constituting the first experimental constraints on the latter three. Daya Bays high statistics and unique layout of multiple directions from three pairs of reactors to three experimental halls allowed the simultaneous constraint of individual SME LV-CPTV coefficients without assuming others contribute negligibly, a first for a neutrino experiment.
Are geometrical summaries of the CMB and LSS sufficient for estimating cosmological parameters? And how does our choice of a dark energy model impact the current constraints on standard cosmological parameters? We address these questions in the context of the widely used CPL parametrization of a time varying equation of state w in a cosmology allowing spatial curvature. We study examples of different behavior allowed in a CPL parametrization in a phase diagram, and relate these to effects on the observables. We examine parameter constraints in such a cosmology by combining WMAP5, SDSS, SNe, HST data sets by comparing the power spectra. We carefully quantify the differences of these constraints to those obtained by using geometrical summaries for the same data sets. We find that (a) using summary parameters instead of the full data sets give parameter constraints that are similar, but with discernible differences, (b) due to degeneracies, the constraints on the standard parameters broaden significantly for the same data sets. In particular, we find that in the context of CPL dark energy, (i) a Harrison-Zeldovich spectrum cannot be ruled out at $2sigma$ levels with our current data sets. and (ii) the SNe IA, HST, and WMAP 5 data are not sufficient to constrain spatial curvature; we additionally require the SDSS DR4 data to achieve this.
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