Decoding crystallography from high-resolution electron imaging and diffraction datasets with deep learning.

While machine learning has been making enormous strides in many technical areas, it is still massively underused in transmission electron microscopy. To address this, a convolutional neural network model was developed for reliable classification of crystal structures from small numbers of electron images and diffraction patterns with no preferred orientation. Diffraction data containing 571,340 individual crystals divided among seven families, 32 genera, and 230 space groups were used to train the network. Despite the highly imbalanced dataset, the network narrows down the space groups to the top two with over 70% confidence in the worst case and up to 95% in the common cases. As examples, we benchmarked against alloys to two-dimensional materials to cross-validate our deep-learning model against high-resolution transmission electron images and diffraction patterns. We present this result both as a research tool and deep-learning application for diffraction analysis.

The Viking viewer for connectomics: scalable multi-user annotation and summarization of large volume data sets.

Modern microscope automation permits the collection of vast amounts of continuous anatomical imagery in both two and three dimensions. These large data sets present significant challenges for data storage, access, viewing, annotation and analysis. The cost and overhead of collecting and storing the data can be extremely high. Large data sets quickly exceed an individual's capability for timely analysis and present challenges in efficiently applying transforms, if needed. Finally annotated anatomical data sets can represent a significant investment of resources and should be easily accessible to the scientific community. The Viking application was our solution created to view and annotate a 16.5 TB ultrastructural retinal connectome volume and we demonstrate its utility in reconstructing neural networks for a distinctive retinal amacrine cell class. Viking has several key features. (1) It works over the internet using HTTP and supports many concurrent users limited only by hardware. (2) It supports a multi-user, collaborative annotation strategy. (3) It cleanly demarcates viewing and analysis from data collection and hosting. (4) It is capable of applying transformations in real-time. (5) It has an easily extensible user interface, allowing addition of specialized modules without rewriting the viewer.

Improving the stability of algebraic curves for applications.

An algebraic curve is defined as the zero set of a polynomial in two variables. Algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics. The main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data. Usually, arguments against using algebraic curves involve references to mathematicians Wilkinson (and Runge). The first goal of this article is to understand the stability issue of algebraic curve fitting. Then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed, and its properties are investigated. The fitting algorithm is of sufficient stability for very fast position-invariant shape recognition, position estimation, and shape tracking, based on invariants and new representations. Among appropriate applications are shape-based indexing into image databases.