Moment-based metrics for molecules computable from cryogenic electron microscopy images.

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam's method, relies on the moments of the two-dimensional (2D) images. Inspired by Kam's method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3D alignment.

Fast principal component analysis for cryo-electron microscopy images.

Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions.

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms.

The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints.

FAST EXPANSION INTO HARMONICS ON THE DISK: A STEERABLE BASIS WITH FAST RADIAL CONVOLUTIONS.

We present a fast and numerically accurate method for expanding digitized images representing functions on [-1, 1] supported on the disk in the harmonics (Dirichlet Laplacian eigenfunctions) on the disk. Our method, which we refer to as the Fast Disk Harmonics Transform (FDHT), runs in operations. This basis is also known as the Fourier-Bessel basis, and it has several computational advantages: it is orthogonal, ordered by frequency, and steerable in the sense that images expanded in the basis can be rotated by applying a diagonal transform to the coefficients.

Anomalous Chained Turbulence in Actively Driven Flows on Spheres.

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in nonplanar geometries.

Distinct Migration and Contact Dynamics of Resting and IL-2-Activated Human Natural Killer Cells.

Natural killer (NK) cells serve as one of the first lines of defense against viral infections and transformed cells. NK cell cytotoxicity is not dependent on antigen presentation by target cells, but is dependent on integration of activating and inhibitory signals triggered by receptor-ligand interactions formed at a tight intercellular contact between the NK and target cell, i.e.