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We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an…
An empirical model has been developed to reproduce the drift of the spectrum recorded by EIS on board Hinode using instrumental temperatures and relative motion of the spacecraft. The EIS spectrum shows an artificial drift in wavelength…
Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…
This research thesis presents a novel higher-order spectral element method (SEM) formulated in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex anisotropic media. In this study, we consider a…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
We performed STM-ENDOR experiments where the intensity of one of the hyperfine components detected in ESR-STM is recorded while an rf power is irradiated into the tunneling junction and its frequency is swept. When the latter frequency is…
Reliable quantitative analysis in scanning (transmission) electron microscopy (S(T)EM) is often hindered by image drift during long-duration spectral mapping for elemental analysis or for various material functions. We here present…
Based on luminosity contributions, we develop a spectroscopic modelling method to derive atmospheric parameters of component stars in binary systems. The method is designed for those spectra of binaries which show double-lined features due…
Multidimensional coherent optical spectroscopy is one of the most powerful tools for investigating complex quantum mechanical systems. While it was conceived decades ago in magnetic resonance spectroscopy using micro- and radio-waves, it…
Single-molecule F\"orster resonance energy transfer (smFRET) is increasingly being used to determine distances, structures, and dynamics of biomolecules in vitro and in vivo. However, generalized protocols and FRET standards ensuring both…
Electronic transitions involving core-level orbitals offer a localized, atomic-site and element specific peek window into statistical systems such as molecular liquids. Although formally understood, the complex relation between structure…
The noise of a device under test (DUT) is measured simultaneously with two instruments, each of which contributes its own background. The average cross power spectral density converges to the DUT power spectral density. This method enables…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…
Precision measurements of the beam pattern response are needed to predict the response of a radio telescope. Mapping the beam of a low frequency radio array presents a unique challenge and science cases such as the observation of the 21\,cm…
This work formally investigates the differential evolution indicators as a tool for ultrasonic tracking of elastic transformation and fracturing in randomly heterogeneous solids. Within the framework of periodic sensing, it is assumed that…
Sequential monitoring of images has broad applications across various domains, including climate science, ecosystem monitoring, medical diagnostics, and so forth. In many such applications, images acquired over time exhibit gradual changes,…
We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
Nuclear Magnetic Resonance (NMR) spectroscopy is a central characterization method for molecular structure elucidation, yet interpreting NMR spectra to deduce molecular structures remains challenging due to the complexity of spectral data…