相关论文: On the limits of spectral methods for frequency es…
While optical and quantum efficiency are on the rise, and spectrographs becoming massively multiplexed, measuring spectral energy distributions of astronomical sources with accuracy remains a challenge. In addition to atmospheric…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
Multiple codes are available to derive atmospheric parameters and individual chemical abundances from high-resolution spectra of AFGKM stars. Almost all spectroscopists have their own preferences regarding which code and method to use. But…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
When backgrounds are not well enough controlled to measure the value of some physical parameter, one may still obtain an upper limit on the parameter. A single experiment may have several detectors, each of which can alone be used to derive…
An algorithm for calculating the spectral intensity of radiation due to the coherent addition of many particles with arbitrary trajectories is described. Direct numerical integration of the Lienard-Wiechert potentials, in the far-field, for…
The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode…
This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…
This article introduces a novel approach to the classification of categorical time series under the supervised learning paradigm. To construct meaningful features for categorical time series classification, we consider two relevant…
In some applications of frequency estimation, it is challenging to sample at as high as the Nyquist rate due to hardware limitations. An effective solution is to use multiple sub-Nyquist channels with coprime undersampling ratios to jointly…
It is the purpose of the paper to describe the virtues of time-frequency methods for signal processing applications, having astronomical time series in mind. Different methods are considered and their potential usefulness respectively…
Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some…