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We study the 3-point functions of gauge-invariant scalar operators in four dimensional $\mathcal{N}=2$ superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…
We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
We consider conformal perturbation theory for $n$-point functions on the sphere in general 2D CFTs to first order in coupling constant. We regulate perturbation integrals using canonical hard disk excisions of size $\epsilon$ around the…
We address the correspondence-free alignment of two rotation sets on \(SO(3)\), a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis conventions. Our key idea is to…
abridged] A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of FFTs, which is…
Fringe projection profilometry has been increasingly sought and applied in dynamic three-dimensional (3D) shape measurement. In this work, a robust and high-efficiency 3D measurement based on Gray-code light is proposed. Unlike the…
The number of phase wraps in 2D wrapped phase map can be completely eliminated, or greatly reduced by frequency shifting. But the wraps usually cannot be optimally reduced using the conventional fast Fourier transform (FFT) because the…
Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a…
Recent studies shows that the orthogonal time frequency space (OTFS) waveform is a promising candidate for future communication. To meet users' potential demand for Integrated Sensing and Communication (ISAC) applications in 6G, the usage…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…
A binocular system developed by the author in terms of projective Fourier transform (PFT) of the conformal camera, which numerically integrates the head, eyes, and visual cortex, is used to process visual information during saccadic eye…
Point spread function (PSF) engineering has been pivotal in the remarkable progress made in high-resolution imaging in the last decades. However, the diversity in PSF structures attainable through existing engineering methods is limited.…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
We study four-point correlation functions of four generic half-BPS supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir of four-dimensional superconformal algebra to derive superconformal blocks which contribute…
Analyses of the galaxy N-Point Correlation Functions (NPCFs) have a large number of degrees of freedom, meaning one cannot directly estimate an invertible covariance matrix purely from mock catalogs, as has been the standard approach for…
The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms…