Related papers: Statistical Estimation of Mean Lorentzian Line Wid…
We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby…
The Voigt profile - a convolution of a Gaussian and a Lorentzian - accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting such to experimental spectra yields both the Lorentzian natural…
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…
We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest.…
Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the…
Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high-angle diffraction in reciprocal space. In electron microscopy, correlation in the…
A simple approximation scheme to describe the width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides…
We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in…
We develop a formulation of the Baade-Wesselink method which uses the Fourier coefficients of the observables. We derive an explicit, analytic expression to determine the mean radius from each Fourier order. The simplicity of this method…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
We study the filtering and smoothing problem for continuous-time linear Gaussian systems. While classical approaches such as the Kalman-Bucy filter and the Rauch-Tung-Striebel (RTS) smoother provide recursive formulas for the conditional…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
The fundamental multidimensional line spectral estimation problem is addressed utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) algorithm, multidimensional VALSE (MDVALSE) is…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1 < q < 3, the q-functions pass from the usual Gaussian form,…
Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration…
The aim of this paper is to associate a measure for certain sets of paths in the Euclidean plane $\mathbb{R}^2$ with fixed starting and ending points. Then, working on parameterized surfaces with a specific Riemannian metric, we define and…
While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian…
Two-dimensional coherent spectroscopy (2DCS) provides simultaneous measurement of homogeneous and inhomogeneous linewidths through quantitative lineshape analysis. However, conventional lineshape analysis methods assume Gaussian…