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This is for a highlight of the application-oriented numerical computation and optimization-a celebration of 60 years of the IJCM publication. On a usual rainy day in early May 1964, the first issue of the International Journal of Computer Mathematics (IJCM) was published in London, Great Britain. Apparently, mathematicians around the world felt and were excited by the morningtide and shock waves from digital computations, after the success of modern computer hardware configuration and software structures. The twilight of the digital new age inspired the pioneers, and this also led to the birth of the IJCM, even before the invention of the word numerical analysis. The first volume of the IJCM consisted of 4 issues, 314 pages of 16 peer-reviewed research papers, and 4 book reviews. 

In most synthetic self-assembly processes the size of the final structure grows unbound and is only limited by the number of accessible microscopic building blocks. In comparison, biological assemblies can autonomously regulate their size and shape. One mechanism for such self-regulation is based on the chirality of microscopic units. Chirality induces a twisted geometry of building blocks that is incompatible with long-ranged crystalline packing, thereby stopping the assembly’s growth at a given stage. Chiral self-regulating self-assemblies, based on thermodynamic equilibration rather than kinetic trapping, remain an elusive target that has attracted considerable attention. So far studies of chiral self-assembly processes have focused on non-responsive systems, whose equilibrium points are not easily shifted in situ, which limits their versatility and applicability. Here, we demonstrate stimuli-responsive self-regulating self-assembly. This assembly is composed of chiral and magnetically alignable nanorods, where the effective chirality is modulable by balancing chirality-induced twisting with magnet-induced untwisting alignment. Changing the magnetic field intensity, controls the strength of self-regulation, leading to assemblies whose sizes and shapes are rationally controlled. The described size/shape control mechanism is tunable, reversible, robust, and widely applicable, opening up new possibilities for generating biomimetics structures with desirable functions and properties. 

The space hurricane is a newly discovered large-scale three-dimensional magnetic vortex structure that spans the polar ionosphere and magnetosphere. It has been suggested to open a fast energy transport channel for the solar wind to invade Earth’s magnetosphere under northward interplanetary magnetic field (IMF) conditions. It is, therefore, an important phenomenon to understand the solar wind–magnetosphere–ionosphere coupling process under northward IMF conditions. In this study, we report the three-dimensional ionospheric plasma properties of a space hurricane event in the Northern Hemisphere observed by multiple instruments. Based on the convection velocity observations from ground-based radars and polar satellites, we confirm that the major modulation to the polar cap convection called a space hurricane rotates clockwise at the altitude of the ionosphere. Ground-based incoherent scatter radar and polar satellite observations reveal four features associated with the space hurricane: 1) strong plasma flow shears and being embedded in a clockwise lobe convection cell; 2) a major addition to the total energy deposition in the ionosphere–thermosphere system by Joule heating; 3) downward ionospheric electron transport; and 4) multiple ion-temperature enhancements in the sunward velocity region, likely from the spiral arms of the space hurricane. These results present, first, the impact of space hurricane on the low-altitude ionosphere and provide additional insights on the magnetospheric impact on structuring in the polar ionosphere. 

This study reported the application of an interactive Open Education Resource, namely, an open virtual experiment simulator education tool (OVESET), in teaching the kinetics of atom transfer radical polymerization (ATRP) in a polymer science classroom. The OVESET ATRP kinetic simulator aims at improving students’ inductive reasoning skills. Students were encouraged to perform virtual experiments to systematically examine the influence of each parameter, e.g., type of polymerization and concentrations of reagents, and to observe and make logical explanations of the general trends behind each series of experiments. The tool was designed to maximize accessibility and flexibility through open licensing. The simulator runs under the Jupyter Notebook environment, which is free to use, modify, and redistribute; therefore, instructors can adapt the simulator based on their teaching contexts. The simulator can be applied in a classroom setting without requiring any software installation and can be used across different operating systems. Assessment of the implementation demonstrated that students’ learning outcomes and STEM and polymer science identity were improved. Students also rated the tool as useful in increasing their understanding and inductive reasoning. The quick and in-place response of the notebook makes it ideal for both in-class demonstrations and after-class practices. The tool is freely available at https://bit.ly/ATRP-Simulator. 

Mixup is a data augmentation technique that relies on training using random convex combinations of data points and their labels. In recent years, Mixup has become a standard primitive used in the training of state-of-the-art image classification models due to its demonstrated benefits over empirical risk minimization with regards to generalization and robustness. In this work, we try to explain some of this success from a feature learning perspective. We focus our attention on classification problems in which each class may have multiple associated features (or views) that can be used to predict the class correctly. Our main theoretical results demonstrate that, for a non-trivial class of data distributions with two features per class, training a 2-layer convolutional network using empirical risk minimization can lead to learning only one feature for almost all classes while training with a specific instantiation of Mixup succeeds in learning both features for every class. We also show empirically that these theoretical insights extend to the practical settings of image benchmarks modified to have additional synthetic features. 

Recently, researchers observed that gradient descent for deep neural networks operates in an “edge-of-stability” (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) is often larger than stability threshold 2/\eta (where \eta is the step size). Despite this, the loss oscillates and converges in the long run, and the sharpness at the end is just slightly below 2/\eta . While many other well-understood nonconvex objectives such as matrix factorization or two-layer networks can also converge despite large sharpness, there is often a larger gap between sharpness of the endpoint and 2/\eta . In this paper, we study EoS phenomenon by constructing a simple function that has the same behavior. We give rigorous analysis for its training dynamics in a large local region and explain why the fnal converging point has sharpness close to 2/\eta . Globally we observe that the training dynamics for our example have an interesting bifurcating behavior, which was also observed in the training of neural nets.