Efficient high-resolution refinement in cryo-EM with stochastic gradient descent

Electron cryomicroscopy (cryo-EM) is an imaging technique widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dimensional projections with unknown orientations. As the typical pipeline involves processing large amounts of data, efficient algorithms are crucial for fast and reliable results. The stochastic gradient descent (SGD) algorithm has been used to improve the speed of ab initio reconstruction, which results in a first, low-resolution estimation of the volume representing the molecule of interest, but has yet to be applied successfully in the high-resolution regime, where expectation-maximization algorithms achieve state-of-the-art results, at a high computational cost. In this article, we investigate the conditioning of the optimization problem and show that the large condition number prevents the successful application of gradient descent-based methods at high resolution. Our results include a theoretical analysis of the condition number of the optimization problem in a simplified setting where the individual projection directions are known, an algorithm based on computing a diagonal preconditioner using Hutchinson's diagonal estimator, and numerical experiments showing the improvement in the convergence speed when using the estimated preconditioner with SGD. The preconditioned SGD approach can potentially enable a simple and unified approach to ab initio reconstruction and high-resolution refinement with faster convergence speed and higher flexibility, and our results are a promising step in this direction.Comment: 22 pages, 7 figure

SENSOR ARRAY ABLE TO DETECT AND RECOGNISE CHEMICAL WARFARE AGENTS

In this paper we studied a device based on array of six different sensors with surface acoustic wave for detections and recognition of three chemical warfare agents (chloropicrin, soman and lewisite). The sensors are “delay line” type with a center frequency of 69.4 MHz. It presents an original algorithm to identify the nature and concentration of gas from a finite range of possible gases. Numerical program developed to implement this algorithm, provides to operators all the particulars of gas and an indicator of credibility of the results provided as a measure of the degree of disturbance of the signals received from sensors.SAW, chemical warfare agent, array of sensors, algorithm

Analysis of the Steinmetz compensation circuit with distorted waveforms through symmetrical component-based indicators

This paper deals with the use of a set of indicators defined within a symmetrical component-based framework to study the characteristics of the Steinmetz compensation circuit in the presence of waveform distortion. The Steinmetz circuit is applied to obtain balanced currents in a three-phase system supplying a single-phase load. The circuit is analyzed without and with harmonic distortion of the supply voltages. The compensation effect is represented by the classical unbalance factor and by the Total Phase Unbalance (TPU) indicator defined in the symmetrical component-based framework. Comparing the two indicators, it is shown that the classical unbalance factor is insufficient to represent the effect of voltage distortion and fails to detect the lack of total unbalance compensation occurring with distorted waveforms. Correct information is provided by calculating the TPU indicator. © 2009 IEEE

Linearly constrained evolutions of critical points and an application to cohesive fractures

We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material