Improving data quality for 3D electron diffraction (3D ED) by Gatan Image Filter and a new crystal tracking method

3D ED is an effective technique to determine the structures of submicron- or nano-sized crystals. In this paper, we implemented energy-filtered 3D ED using a Gatan Energy Filter (GIF) in both selected area electron diffraction mode and micro/nanoprobe mode. We explained the setup in detail, which improves the accessibility of energy-filtered 3D ED experiments as more electron microscopes are equipped with a GIF than an in-column filter. We also proposed a crystal tracking method in STEM mode using live HAADF image stream. This method enables us to collect energy-filtered 3D ED datasets in STEM mode with a larger tilt range without foregoing any frames. In order to compare the differences between energy-filtered 3D ED and normal 3D ED data, three crystalline samples have been studied in detail. We observed that the final R1 will improve 20% to 30% for energy-filtered datasets compared with unfiltered datasets and the structure became more reasonable. We also discussed the possible reasons that lead to the improvement

Benign Oscillation of Stochastic Gradient Descent with Large Learning Rates

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small $\ell_2$-norm and appear in each data point; (ii) strong features which have a larger $\ell_2$-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".Comment: 63 pages, 10 figure

Soil Liquid Limit and Plastic Limit Treating System Based on Analytic Method

AbstractAccording to two present China national standards, a software as Soil Liquid Limit and Plastic Limit Data Treating System, with analytic method, was developed using object-oriented visual programming tool. The analytic method used in the developed system was different to traditional method of treating soil liquid limit and plastic limit data. N-S algorithm flowchart demonstrated that switch statement and condition statement were taken as main algorithm and second level select nested structure was taken as main frame for the developed system. Three kinds of soil specimens were tested with liquid and plastic limit combined test and the test data was treated with graphic method, Excel software and Soil Liquid Limit and Plastic Limit Data Treating System. The comparative conclusion indicated that Soil Liquid Limit and Plastic Limit Data Treating System improved efficiency and accuracy evidently for treating soil liquid and plastic limit data and had advantages of easy operation and high reliability

Comparing the Usefulness of Distance, Monophyly and Character-Based DNA Barcoding Methods in Species Identification: A Case Study of Neogastropoda

DNA barcoding has recently been proposed as a promising tool for the rapid species identification in a wide range of animal taxa. Two broad methods (distance and monophyly-based methods) have been used. One method is based on degree of DNA sequence variation within and between species while another method requires the recovery of species as discrete clades (monophyly) on a phylogenetic tree. Nevertheless, some issues complicate the use of both methods. A recently applied new technique, the character-based DNA barcode method, however, characterizes species through a unique combination of diagnostic characters.Here we analyzed 108 COI and 102 16S rDNA sequences of 40 species of Neogastropoda from a wide phylogenetic range to assess the performance of distance, monophyly and character-based methods of DNA barcoding. The distance-based method for both COI and 16S rDNA genes performed poorly in terms of species identification. Obvious overlap between intraspecific and interspecific divergences for both genes was found. The “10× rule” threshold resulted in lumping about half of distinct species for both genes. The neighbour-joining phylogenetic tree of COI could distinguish all species studied. However, the 16S rDNA tree could not distinguish some closely related species. In contrast, the character-based barcode method for both genes successfully identified 100% of the neogastropod species included, and performed well in discriminating neogastropod genera.This present study demonstrates the effectiveness of the character-based barcoding method for species identification in different taxonomic levels, especially for discriminating the closely related species. While distance and monophyly-based methods commonly use COI as the ideal gene for barcoding, the character-based approach can perform well for species identification using relatively conserved gene markers (e.g., 16S rDNA in this study). Nevertheless, distance and monophyly-based methods, especially the monophyly-based method, can still be used to flag species

A Comparison of Structure Determination of Small Organic Molecules by 3D Electron Diffraction at Cryogenic and Room Temperature

3D electron diffraction (3D ED), also known as micro-crystal electron diffraction (MicroED), is a rapid, accurate, and robust method for structure determination of submicron-sized crystals. 3D ED has mainly been applied in material science until 2013, when MicroED was developed for studying macromolecular crystals. MicroED was considered as a cryo-electron microscopy method, as MicroED data collection is usually carried out in cryogenic conditions. As a result, some researchers may consider that 3D ED/MicroED data collection on crystals of small organic molecules can only be performed in cryogenic conditions. In this work, we determined the structure for sucrose and azobenzene tetracarboxylic acid (H4ABTC). The structure of H4ABTC is the first crystal structure ever reported for this molecule. We compared data quality and structure accuracy among datasets collected under cryogenic conditions and room temperature. With the improvement in data quality by data merging, it is possible to reveal hydrogen atom positions in small organic molecule structures under both temperature conditions. The experimental results showed that, if the sample is stable in the vacuum environment of a transmission electron microscope (TEM), the data quality of datasets collected under room temperature is at least as good as data collected under cryogenic conditions according to various indicators (resolution, I/σ(I), CC1/2 (%), R1, Rint, ADRA

A complicated quasicrystal approximant ∊16 predicted by the strong-reflections approach

The structure of the quasicrystal approximant ∊16 was predicted by the strong-reflections approach based on the known approximant ∊6

Structure determination of the zeolite IM-5 using electron crystallography

The structure of the complex zeolite IM-5 (Cmcm, a = 14.33(4) Å, b = 56.9(2) Å, c = 20.32(7) Å) was determined by combining selected area electron diffraction (SAED), 3D reconstruction of high resolution transmission electron microscopy (HRTEM) images from different zone axes and distance least squares (DLS) refinement. The unit cell parameters were determined from SAED. The space group was determined from extinctions in the SAED patterns and projection symmetries of HRTEM images. Using the structure factor amplitudes and phases of 144 independent reflections obtained from HRTEM images along the [100], [010] and [001] directions, a 3D electrostatic potential map was calculated by inverse Fourier transformation. From this 3D potential map, all 24 unique Si positions could be determined. Oxygen atoms were added between each Si-Si pair and further refined together with the Si positions by distance-least-squares. The final structure model deviates on average 0.16 Å for Si and 0.31 Å for O from the structure refined using X-ray powder diffraction data. This method is general and offers a new possibility for determining the structures of zeolites and other materials with complex structure