Related papers: Invertibility of Multi-Energy X-ray Transform
The development of medium-energy inelastic X-ray scattering (IXS) optics with meV and sub-meV resolution has attracted considerable efforts in recent years. Meanwhile, there are also concerns or debates about the fundamental and feasibility…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
The high-intensity version of multiwavelength anomalous diffraction (MAD) has a potential for solving the phase problem in femtosecond crystallography with x-ray free-electron lasers (XFELs). For MAD phasing, it is required to calculate or…
High-pressure induced structural transition from zircon-type phase into scheelite-type phase in YVO$_4$ is studied using ab initio calculations. Several structures with compressed volumes are evaluated, where for every considered volume the…
Magnetic Resonance Elastography (MRE) has become an essential tool in assessing the mechanical properties of soft tissues in-vivo, prompting significant progress in new inversion algorithms. This creates a need for a benchmarking framework…
X-ray absorption spectroscopy (XAS) is an explicit probe of the unoccupied electronic structure of materials and an invaluable tool for fingerprinting various electronic properties and phenomena. Computational methods capable of simulating…
The quantum Cram\'er-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a…
Inelastic scattering induces dephasing in mesoscopic systems. An analysis of previous models to simulate inelastic scattering in such systems is presented and also a relatively new model based on wave attenuation is introduced. The problem…
We present simple XSPEC models for fitting excess variance spectra of AGN. Using a simple Monte-Carlo approach, we simulate a range of spectra corresponding to physical parameters varying, then calculate the resulting variance spectra.…
In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities $p(x) \propto \exp{-E(x)}$ with an…
This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a…
We formulate the Quantum Inverse Scattering Method for the case of anyonic grading. This provides a general framework for constructing integrable models describing interacting hard-core anyons. Through this method we reconstruct the known…
Atomic three-grating Mach-Zehnder interferometry constitutes an important tool to probe fundamental aspects of the quantum theory. There is, however, a remarkable gap in the literature between the oversimplified models and robust numerical…
Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first, factor proportional to a power of the number of mesh…
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…
A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as…
X-ray spectroscopy is one of the most powerful tools to access structure and properties of matter in different states of aggregation as it allows to trace atomic and molecular energy levels in course of various physical and chemical…
For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs…
The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the…
Resonant inelastic x-ray scattering (RIXS) has become a powerful tool in the study of the electronic structure of condensed matter. Although the linewidths of many RIXS features are narrow, the experimental broadening can often hamper the…