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  1. We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest-neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin-glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L × L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X - and Z -basis spin-glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin-glass order parameters jump discontinuously. 
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  2. Mello-Thoms, Claudia R. ; Taylor-Phillips, Sian (Ed.)
    There is increasing interest in using deep learning and computer vision to help guide clinical decisions, such as whether to order a biopsy based on a mammogram. Existing networks are typically black box, unable to explain how they make their predictions. We present an interpretable deep-learning network which explains its predictions in terms of BI-RADS features mass shape and mass margin. Our model predicts mass margin and mass shape, then uses the logits from those interpretable models to predict malignancy, also using an interpretable model. The interpretable mass margin model explains its predictions using a prototypical parts model. The interpretable mass shape model predicts segmentations, fits an ellipse, then determines shape based on the goodness of fit and eccentricity of the fitted ellipse. While including mass shape logits in the malignancy prediction model did not improve performance, we present this technique as part of a framework for better clinician-AI communication. 
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