Related papers: Ultrafast Calculation of Diffuse Scattering from A…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
Volumetric crystal structure indexing and orientation mapping are key data processing steps for virtually any quantitative study of spatial correlations between the local chemistry and the microstructure of a material. For electron and…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…
The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…
Prompted by recent experimental developments, a theory of surface scattering of fast atoms at grazing incidence is developed. The theory gives rise to a quantum mechanical limit for ordered surfaces that describes coherent diffraction peaks…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing…
Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
We present a fast direct solver for the volume scattering problem of the Helmholtz equation. The algorithm is faster than existing methods. Moreover, discretization for our method is much simpler and more accurate than that for finite…
Simulations of scattering processes are essential in understanding the physics of our universe. Computing relevant scattering quantities from ab initio methods is extremely difficult on classical devices because of the substantial…
Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In…
In this article, a new method is discussed for the calibration and monitoring of photomultiplier tubes (PMTs). This method is based on a Discrete Fourier Transform (DFT) and it is fast and general so that it can be used in cases where an…
In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for instance, by acoustic or optical forces. Under the influence…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
We present an algorithm capable of detecting diffuse, dim sources of any size in an astronomical image. These sources often defeat traditional methods for source finding, which expand regions around points of high intensity. Extended…