Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low-rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For $n$ images of size $N$-by-$N$ pixels, we propose an algorithm for calculating this covariance estimator with computational complexity $\mathcal{O}(nN^4+\sqrt{\kappa}N^6 \log N)$, where the condition number $\kappa$ is empirically in the range $10$--$200$. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in 6D. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed non-consistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrices, we introduce a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.Comment: 52 pages, 11 figure

Adaptive dual-comb spectroscopy in the green region

Dual-comb spectroscopy is extended to the visible spectral range with a set-up based on two frequency-doubled femtosecond ytterbium-doped fiber lasers. The dense rovibronic spectrum of iodine around 19240 cm-1 is recorded within 12 ms at Doppler-limited resolution with a simple scheme that only uses free-running femtosecond lasers

MuMax: a new high-performance micromagnetic simulation tool

We present MuMax, a general-purpose micromagnetic simulation tool running on Graphical Processing Units (GPUs). MuMax is designed for high performance computations and specifically targets large simulations. In that case speedups of over a factor 100x can easily be obtained compared to the CPU-based OOMMF program developed at NIST. MuMax aims to be general and broadly applicable. It solves the classical Landau-Lifshitz equation taking into account the magnetostatic, exchange and anisotropy interactions, thermal effects and spin-transfer torque. Periodic boundary conditions can optionally be imposed. A spatial discretization using finite differences in 2 or 3 dimensions can be employed. MuMax is publicly available as open source software. It can thus be freely used and extended by community. Due to its high computational performance, MuMax should open up the possibility of running extensive simulations that would be nearly inaccessible with typical CPU-based simulators.Comment: To be published in JMM