Related papers: Multiply subtractive Kramers-Kroenig relations for…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…
Reliable atomic data have been computed for the spectral modeling of the nitrogen K lines, which may lead to useful astrophysical diagnostics. Data sets comprise valence and K-vacancy level energies, wavelengths, Einstein $A$-coefficients,…
The Kramers-Kronig (KK) algorithm, useful for retrieving the phase of a spectrum based on the known spectral amplitude, is applied to reconstruct the impulse response of a diffusive medium. It is demonstrated by a simulation of a 1D…
Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences…
We develop a quantitative mathematical theory that offers new perspectives on nonlinear harmonic generation in plasmonic structures arising from symmetry breaking. Focusing on second harmonic generation--the most fundamental process and the…
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…
The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an…
K-edge imaging is commonly used for viewing contrast pharmaceuticals in a variety of multi-energy x-ray imaging techniques, ranging from dual-energy and spectral computed tomography to fluoroscopy. When looking for the K-edge signal of a…
Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…
We present a comprehensive analysis of the the nonlinear optical Kerr effect in graphene. We directly solve the S-matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh- type crystal wave functions. We then convert to…
X-ray interaction with matter is an energy-dependent process that is contingent on the atomic structure of the constituent material elements. The most advanced models to capture this relationship currently rely on Monte Carlo (MC)…
We apply a recently developed technique utilizing machine learning for statistical analysis of computational nitrogen K-edge spectra of aqueous triglycine. This method, the emulator-based component analysis, identifies spectrally relevant…
A compact correlation-function expansion is developed for nth order optical susceptibilities in the frequency domain using the Keldysh-Schwinger loop. By not keeping track of the relative time ordering of bra and ket interactions at the two…
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of…
We study small data scattering of solutions to Nonlinear Klein-Gordon equations with suitable pure power nonlinearities, posed on $\mathbb{R}^d\times \mathcal{M}^k$ with $k\leq2$ and $d\geq1$ and $\mathcal{M}^k$ a compact Riemannian…
The principle of causality leads to linear Kramers-Kronig relations (KKR) that relate the real and imaginary parts of the complex modulus $G^{*}$ through integral transforms. Using the multiple integral generalization of the Boltzmann…
Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these…
This article extends the known restricted isometric projection of sparse datasets in Euclidean spaces $\mathbb{R}^N$ down into low-dimensional subspaces $\mathbb{R}^k, k \ll N,$ to the case of low-dimensional varieties $\mathcal{M} \subset…
We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its 'absorptive part', defined as a double…
Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric…