Related papers: Analytical reconstruction of isotropic turbulence …

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 Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…

Let ${\mathfrak{G}}\subset\mathbb{R}^{3}$ with $vol(\mathfrak{G})\sim L^{3}$. Let ${\mathscr{T}}(x)$ be a Gaussian random field $\forall~x\in\mathfrak{G}$ with expectation $\mathbf{E}[{\mathscr{T}}(x)]=0$ and correlation…

We study the k-space fluctuations of the waveaction about its mean spectrum in the turbulence of dispersive waves. We use a minimal model based on the Random Phase Approximation (RPA) and derive evolution equations for the arbitrary-order…

Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a…

This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…

Noise pollution caused by inflow turbulence is a major problem in many applications, such as propellers and fans. Leading edge noise models, e.g., Amiet's model, are widely applied to predict the noise produced by these applications. This…

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…

Using a qubit to probe non-Gaussian noise environments is theoretically studied in the context of classical random telegraph processes. Protocols for control pulses are developed to effectively scan higher noise correlations, offering…

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…

Atmospheric turbulence causes significant image degradation due to pixel displacement (tilt) and blur, particularly in long-range imaging applications. In this paper, we propose a novel framework for atmospheric turbulence mitigation,…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…

Optical beams propagating through atmospheric turbulence undergo spatiotemporal intensity fluctuations that deviate significantly from an ideal Gaussian profile. In this work, we present a unified theoretical and experimental framework for…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…

Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography.…

We consider a special type of Restricted Boltzmann machine (RBM), namely a Gaussian-spherical RBM where the visible units have Gaussian priors while the vector of hidden variables is constrained to stay on an ${\mathbbm L}_2$ sphere. The…

The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…

This paper is concerned with the modeling errors appeared in the numerical methods of inverse medium scattering problems (IMSP). Optimization based iterative methods are wildly employed to solve IMSP, which are computationally intensive due…