Related papers: The Fourier Spectral Characterization for the Corr…
We discuss the analytic presentations of the high-order correlation functions in the N-slit diffraction with thermal light in a recent paper [Phys. Rev. Lett. 109, 233603 (2012)]. Our analysis shows that the superresolving fringes in the…
Functional Spectral Imaging (FSI) models image formation as the recovery of tissue surrogates such as density and stiffness from spectral perturbations of a self-adjoint elliptic operator. Rather than relying on reflectivity or relaxation…
Despite their impressive performance in classification tasks, neural networks are known to be vulnerable to adversarial attacks, subtle perturbations of the input data designed to deceive the model. In this work, we investigate the…
Response functions of quantum systems, such as electron Green's functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and…
We calculate the spectral functions of model systems describing 5f-compounds adopting Cluster Perturbation Theory. The method allows for an accurate treatment of the short-range correlations. The calculated excitation spectra exhibit…
The analysis of Fourier-transformed scanning-tunneling-microscopy (STM) images with subatomic resolution is a common tool for studying properties of quasiparticle excitations in strongly correlated materials. While Fourier amplitudes are…
Memory hard functions (MHFs) are an important cryptographic primitive that are used to design egalitarian proofs of work and in the construction of moderately expensive key-derivation functions resistant to brute-force attacks. Broadly…
Hydrogen bonding is an important non-covalent interaction that plays a major role in molecular self-organization and supramolecular structures. It can be described accurately with ab initio quantum chemical wave function methods, which…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
Despite the success of convolutional neural networks (CNNs) in many computer vision and image analysis tasks, they remain vulnerable against so-called adversarial attacks: Small, crafted perturbations in the input images can lead to false…
We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…
We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\bx)$ and a density…
Computing Fourier transforms of k-sparse signals, where only k of N frequencies are non-zero, is fundamental in compressed sensing, radar, and medical imaging. While the Fast Fourier Transform (FFT) evaluates all N frequencies in $O(N \log…
To reach the next frontier in multimode nonlinear optics, it is crucial to better understand the classical and quantum phenomena of systems with many interacting degrees of freedom -- both how they emerge and how they can be tailored to…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images…
As a fundamental building block for quantum computation and communication protocols, the correct verification of the two-photon interference (TPI) contrast between two independent quantum light sources is of utmost importance. Here, we…
Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the…
In this thesis we analyse three aspects of Conformal Field Theories (CFTs). First, we consider correlation functions of descendant states in two-dimensional CFTs. We discuss a recursive formula to calculate them and provide a computer…
Steady-state density functional theory, called i-DFT, is employed to compute spectral and transmission properties of general interacting nanoscale regions coupled to electronic reservoirs. Exchange-correlation functionals are constructed…