Related papers: Consistency of a needlet spectral estimator on the…
Basic aspects of the background of gravitational waves and its mathematical characterization are reviewed. The spectral energy density parameter $\Omega(f)$, commonly used as a quantifier of the background, is derived for an ensemble of…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
The acoustic radiation force exerted on a small sphere located at the focus of an ultrasonic beam is measured in a soft gel. It is proved to evolve quadratically with the local amplitude of the acoustic field. Strong oscillations of the…
In practice, the finite number of samples of the spherical radiation pattern or antenna gain are taken on the sphere for both the reconstruction of the antenna radiation pattern and the computation of mobile handset performance measures…
Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued…
The analysis of gravitational wave interferometer data requires estimates for the noise covariance matrix. For stationary noise, this amounts to estimating the power spectrum. Classical methods such as Welch averaging are used in many…
Accurate estimation of the sound field around a rigid sphere necessitates adequate sampling on the sphere, which may not always be possible. To overcome this challenge, this paper proposes a method for sound field estimation based on a…
Much attention has been given to the problem of estimating cosmological parameters from the $C_l$ measured by future experiments. Many of the approaches which are being used either invoke poorly controlled approximations or are…
This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similar and stationary properties, which includes the fractional Gaussian noise, under high frequency observations. In this…
Cosmic shear measurements rely on our ability to measure and correct the Point Spread Function (PSF) of the observations. This PSF is measured using stars in the field, which give a noisy measure at random points in the field. Using Wiener…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic…
We present a topological multiple testing scheme for detecting peaks on the sphere under isotropic Gaussian noise, where tests are performed at local maxima of the observed field filtered by the spherical needlet transform. Our setting is…
The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical…
We define a scalar measure of the local expansion rate based on how astronomers determine the Hubble constant. Our observable is the inverse conformal d'Alembertian acting on a unit ``standard candle.'' Because this quantity is an integral…
The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a…
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…