Related papers: A Unified Poisson Summation Framework for Generali…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…
Localization microscopy often relies on detailed models of point spread functions. For applications such as deconvolution or PSF engineering, accurate models for light propagation in imaging systems with high numerical aperture are…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
We implement the Fourier shape parametrization within the point-coupling covariant density functional theory to construct the collective space, potential energy surface (PES), and mass tensor, which serve as inputs for the time-dependent…
We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds…
We introduce a fundamental lemma called the Poisson matching lemma, and apply it to prove one-shot achievability results for various settings, namely channels with state information at the encoder, lossy source coding with side information…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have…
We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation…
Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…
We present a hybrid numerical-quantum method for solving the Poisson equation under homogeneous Dirichlet boundary conditions, leveraging the Quantum Fourier Transform (QFT) to enhance computational efficiency and reduce time and space…
We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse…
Dimensionality reduction methods for count data are critical to a wide range of applications in medical informatics and other fields where model interpretability is paramount. For such data, hierarchical Poisson matrix factorization (HPF)…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian…
For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…