相关论文: On the limits of spectral methods for frequency es…
Context: The technique of disentangling has been applied to numerous high-precision studies of spectroscopic binaries and multiple stars. Although, its possibilities have not yet been fully understood and exploited. Aims: Theoretical…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
A method is described for estimating effective scattering lengths via spectroscopy on a trapped pair of atoms. The method relies on the phenomena that the energy levels of two atoms in a harmonic trap are shifted by their collisional…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra when these are based on finite second-order statistics. The family of power spectra which is consistent with a given range of values for the…
In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a…
We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Measuring the centroid of a spectral line is a common problem in astronomy. Many methods have been devised to overcome limitations due to either noise in the spectra or asymmetric profiles, the most common of which are the intensity…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
Multi-object or integral field spectrographs are recognized techniques for achieving simultaneous spectroscopic observations of different or extended sky objects with a high multiplex factor. In this communication is described a…
In this work we study local oscillations in delay differential equations with a frequency domain methodology. The main result is a bifurcation equation from which the existence and expressions of local periodic solutions can be determined.…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
A fundamental principle of quantum theory, clearly manifested in the two-slit experiment, is that for any alternatives that cannot be distinguished by measurement physical predictions are obtained by summation of their amplitudes. In…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
The modern era in spectral line broadening began with the understanding that the slow(quasistatic) ion and fast(impact) electron perturbers could be treated separately. The problem remained of unifying these two theoretical limits. A scheme…
It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from $2m+1$ uniform temporal measurements. It is conjectured that a phase transition on the success of the…
We introduce and analyze the concept of space-spectrum uncertainty for certain commonly-used designs for spectrally programmable cameras. Our key finding states that, it is impossible to simultaneously capture high-resolution spatial images…