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Molecular switches based on the 2H-1-benzopyran (chromene) scaffold have been widely developed for their desirable photochromic and mechanochromic properties. Extended π-conjugation is necessary to stabilize the ring-opened merocyanine dye at room temperature leading to efficient switching under ambient conditions. To this end, naphthopyrans represent a special class of benzo-annulated benzopyrans that have been studied extensively as both photoswitches and more recently as mechanophores, generating intensely colored merocyanine dyes upon exposure to ultraviolet light or mechanical force, respectively. Alternative annulation strategies with judicious heteroatom substitution have also been studied in the photochemistry literature, but the mechanochemistry of 2H-1-benzopyrans has yet to be explored. Here, we report the mechanochemical activation of an indole-fused 2H-1-benzopyran mechanophore that generates a yellow-colored merocyanine dye in polymers that is subsequently transformed to a purple-colored dye upon treatment with acid. Neutralization with base recovers the yellow-colored merocyanine isomer with trans exocyclic alkene geometry through an unusual acid-mediated alkene isomerization. This study expands the repertoire of mechanochromic mechanophores based on (hetero)annulated benzopyrans to enable multicolor chromomorphic behavior in response to both mechanical force and acid for applications in stimuli-responsive polymeric materials with complex switching properties. 

Abstract While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set—‘inferring the uncertainty of model parameters on the basis of observations’—has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. Extended Fiducial inference involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. Extended Fiducial inference also provides an innovative framework for semisupervised learning. 

This study was grounded in the spatial computational thinking model developed by the 3D Weather project funded by the NSF STEM+C program. The model reflects a discipline-based perspective towards computational thinking and captures the spatial nature of computational thinking in meteorology and the reliance of computational thinking on spatial thinking for geospatial analysis. The research was conducted among nineteen teachers attending the summer workshop offered by the project in its third project year to prepare them for teaching spatial computational thinking with IDV (Integrated Data Viewer, downloadable at https://www.unidata.ucar.edu/software/idv/) visualization of weather data. Quantitative survey data were collected measuring these teachers’ meteorology content knowledge, spatial computational thinking, self-efficacy for teaching spatial computational thinking, and epistemic cognition of teaching meteorology. The data were analyzed to examine the effects of the workshop in terms of these variables and the correlations among them were also explored. 

Large pretrained transformer models have revolutionized modern AI applications with their state-of-the-art performance in natural language processing (NLP). However, their substantial parameter count poses challenges for real-world deployment. To address this, researchers often reduce model size by pruning parameters based on their magnitude or sensitivity. Previous research has demonstrated the limitations of magnitude pruning, especially in the context of transfer learning for modern NLP tasks. In this paper, we introduce a new magnitude-based pruning algorithm called mixture Gaussian prior pruning (MGPP), which employs a mixture Gaussian prior for regularization. MGPP prunes non-expressive weights under the guidance of the mixture Gaussian prior, aiming to retain the model’s expressive capability. Extensive evaluations across various NLP tasks, including natural language understanding, question answering, and natural language generation, demonstrate the superiority of MGPP over existing pruning methods, particularly in high sparsity settings. Additionally, we provide a theoretical justification for the consistency of the sparse transformer, shedding light on the effectiveness of the proposed pruning method.