Related papers: A Multiscale Butterfly Algorithm for Multidimensio…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Retrieving object phase from the optical fringe pattern is a critical task in quantitative phase imaging and often requires appropriate image preprocessing (background and noise minimization), especially when retrieving phase from the…
Modern Flash X-ray diffraction Imaging (FXI) acquires diffraction signals from single biomolecules at a high repetition rate from X-ray Free Electron Lasers (XFELs), easily obtaining millions of 2D diffraction patterns from a single…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Designing a robust controller for Modular Multilevel Converters (MMCs) is crucial to ensure stability and optimal dynamic performance under various operating conditions, including faulty and disturbed scenarios. The primary objective of…
Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation…
The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that…
We describe an adaptive multigrid algorithm for solving inverses of the domain-wall fermion operator. Our multigrid algorithm uses an adaptive projection of near-null vectors of the domain-wall operator onto coarser four-dimensional…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…
We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an…
Analysis and synthesis are key steps of the radio-interferometric imaging process, serving as a bridge between visibility and sky domains. They can be expressed as partial Fourier transforms involving a large number of non-uniform…
Bipartite networks are of great importance in many real-world applications. In bipartite networks, butterfly (i.e., a complete 2 x 2 biclique) is the smallest non-trivial cohesive structure and plays a key role. In this paper, we study the…
In even space-time dimensions the multi-loop Feynman integrals are integrals of rational function in projective space. By using an algorithm that extends the Griffiths--Dwork reduction for the case of projective hypersurfaces with…
Sharp L^2 estimates for oscillatory integral operators and Fourier integral operators associated with canonical relations having two-sided cusp or one-sided swallowtail singularities are obtained.
This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…
We address the problem of decomposing an image into albedo and shading. We propose the Fast Fourier Intrinsic Network, FFI-Net in short, that operates in the spectral domain, splitting the input into several spectral bands. Weights in…
This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a…