Search

We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green’s function for the scalar wave equation …

Singularity swap quadrature (SSQ) is an effective method for the evaluation at nearby targets of potentials due to densities on curves in three dimensions. While highly accurate in …

We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in …

The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection …

The remarkable cohesion and coordination observed in moving animal groups and their collective responsiveness to threats are thought to be mediated by scale-free correlations, where changes in …

We present an automatic, high-order accurate, and adaptive Brillouin zone integration algorithm for the calculation of the optical conductivity with a non-zero but small broadening factor …

Fast Ewald summation is the most widely used approach for computing long-range Coulomb interactions in molecular dynamics (MD) simulations. While the asymptotic scaling is nearly optimal, its …

A direct solver is introduced for solving overdetermined linear systems involving nonuniform discrete Fourier transform matrices. Such matrices can be transformed into a Cauchy-like form that has …

Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy …

We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes …

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 …

We present a high-order boundary integral equation (BIE) method for the frequency-domain acoustic scattering of a point source by a singly-periodic, infinite, corrugated boundary. We …

We introduce an efficient numerical method for second-order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions …

We present nifty-ls, a software package for fast and accurate evaluation of the Lomb–Scargle periodogram. nifty-ls leverages the fact that Lomb–Scargle can be computed …

The efficiency of Hamiltonian Monte Carlo (HMC) can suffer when sampling a distribution with a wide range of length scales, because the small step sizes needed for stability …

The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical …

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on …

We present efficient methods for Brillouin zone integration with a non-zero but possibly very small broadening factor η, focusing on cases in which downfolded Hamiltonians can be …

Cryo-electron microscopy (cryo-EM) has recently become a leading method for obtaining high-resolution structures of biological macromolecules. However, cryo-EM is limited to biomolecular samples with …

Cryo-electron microscopy (cryo-EM) has recently become a leading method for obtaining high-resolution structures of biological macromolecules. However, cryo-EM is limited to biomolecular samples with …

We present an efficient method for propagating the time-dependent Kohn–Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials …

Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close …

We introduce a numerical method for the solution of the time-dependent Schrödinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We …

Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude …

Linear systems involving contiguous submatrices of the discrete Fourier transform (DFT)matrix arise in many applications, such as Fourier extension, superresolution, and coherent diffraction imaging. We show that …

mathematical illustrations by Alex H. Barnett: In Discriminating Data, Wendy Hui Kyong Chun reveals how polarization is a goal—not an error—within big data and machine learning …

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature …

Nonuniform fast Fourier transforms dominate the computational cost in many applications including image reconstruction and signal processing. We thus present a general-purpose GPU-based CUDA library for …

In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted …

The most popular algorithm for the nonuniform fast Fourier transform (NUFFT) uses the dilation of a kernel \(phi\) to spread (or interpolate) between given nonuniform points and a …

We present a fast algorithm for computing the diffracted field from arbitrary binary (sharp-edged) planar apertures and occulters in the scalar Fresnel approximation, for up to moderately …

With rheology applications in mind, we present a fast solver for the time-dependent effective viscosity of an infinite lattice containing one or more neutrally buoyant smooth rigid …

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples …

The method of Helsing and co-workers evaluates Laplace and related layer potentials generated by a panel (composite) quadrature on a curve, efficiently and with high-order accuracy …

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient …

Spike sorting is a crucial step in electrophysiological studies of neuronal activity. While many spike sorting packages are available, there is little consensus about which are most accurate …

We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nyström …

An important component of many image alignment methods is the calculation of inner products (correlations) between an image of \(ntimes n\) pixels and another image translated by some …

We study the stability properties of explicit marching schemes for second-kind Volterra integral equations that arise when solving boundary value problems for the heat equation by means …

The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations …

The brain is a massive neuronal network, organized into anatomically distributed sub-circuits, with functionally relevant activity occurring at timescales ranging from milliseconds to years. Current methods to …

The brain is a massive neuronal network, organized into anatomically distributed sub-circuits, with functionally relevant activity occurring at timescales ranging from milliseconds to years. Current methods to …

For smooth bounded domains in ℝn, we prove upper and lower L2 bounds on the boundary data of Neumann eigenfunctions, and we prove quasiorthogonality of this boundary data …

We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic …

Understanding the detailed dynamics of neuronal networks will require the simultaneous measurement of spike trains from hundreds of neurons (or more). Currently, approaches to extracting spike times and …

Determining the three-dimensional (3D) structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has …