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As critical race theorists would remind us, those most impacted have the greatest insight to create change. This paper applies a critical race theory framework to explore the leadership experiences of two African American and one Latinx American mathematics teacher educator and how they address issues of race, racism, and (in)justice in teacher professional development. Data analysis from semi-structured interviews, publicly available webinars and podcasts, and other published materials from the educators (eg. articles and books) reveal how they engaged teachers to attend to issues of race and racism by challenging persistent masternarratives about mathematics and mathematics ability; centering on counternarratives on the cultural identities and mathematical understanding of students of Color, and engaging in community-based pedagogies to promote coalitional resistance. 

A mechanochemistry based approach is proposed to detect and map stress history during dynamic processes. Spiropyran (SP), a force sensitive molecular probe, was incorporated as a crosslinker into multiple network elastomers (MNE). When these mechanochromic MNEs are loaded, SP undergoes a well-known force-activated reaction to merocyanine (MC) changing its absorption in the visible range (visible blue color). This SP to MC transition is not reversible within the time frame of the experiment and the color change reports the concentration of activated molecules. During subsequent loading–unloading cycles the MC undergoes a fast and reversible isomerization resulting in a slight shift of absorption spectrum and results in a second color change (blue to purple color corresponding to the loading–unloading cycles). Quantification of the color changes by using chromaticity shows that the exact color observed upon unloading is characteristic not only of the current stress (reported by the shift in color due to MC isomerization), but of the maximum stress that the material has seen during the loading cycle (reported by the shift in color due to the change in MC concentration). We show that these two color changes can be separated unambiguously and we use them to map the stress history in the loading and unloading process occurring as a crack opens up and propagates, breaking the material. Color maps on fractured samples are compared with finite element simulations and the agreement is excellent. 

Data selection methods, such as active learning and core-set selection, are useful tools for machine learning on large datasets. However, they can be prohibitively expensive to apply in deep learning because they depend on feature representations that need to be learned. In this work, we show that we can greatly improve the computational efficiency by using a small proxy model to perform data selection (e.g., selecting data points to label for active learning). By removing hidden layers from the target model, using smaller architectures, and training for fewer epochs, we create proxies that are an order of magnitude faster to train. Although these small proxy models have higher error rates, we find that they empirically provide useful signals for data selection. We evaluate this “selection via proxy” (SVP) approach on several data selection tasks across five datasets: CIFAR10, CIFAR100, ImageNet, Amazon Review Polarity, and Amazon Review Full. For active learning, applying SVP can give an order of magnitude improvement in data selection runtime (i.e., the time it takes to repeatedly train and select points) without significantly increasing the final error (often within 0.1%). For core-set selection on CIFAR10, proxies that are over 10 faster to train than their larger, more accurate targets can remove up to 50% of the data without harming the final accuracy of the target, leading to a 1:6 end-to-end training time improvement.