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We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education., Comment: 181 pages, 8 figures, 280 tables

Pathology is practiced by visual inspection of histochemically stained tissue slides. While the hematoxylin and eosin (H&E) stain is most commonly used, special stains can provide additional contrast to different tissue components. Here, we demonstrate the utility of supervised learning-based computational stain transformation from H&E to special stains (Masson’s Trichrome, periodic acid-Schiff and Jones silver stain) using kidney needle core biopsy tissue sections. Based on the evaluation by three renal pathologists, followed by adjudication by a fourth pathologist, we show that the generation of virtual special stains from existing H&E images improves the diagnosis of several non-neoplastic kidney diseases, sampled from 58 unique subjects (P = 0.0095). A second study found that the quality of the computationally generated special stains was statistically equivalent to those which were histochemically stained. This stain-to-stain transformation framework can improve preliminary diagnoses when additional special stains are needed, also providing significant savings in time and cost., Performing multiple histological stains on a biopsy can be costly and time consuming. Here the authors present a method for the digital transformation of H&E stained tissue into special stains (e.g., PAS, Masson’s Trichrome and Jones silver stain), and demonstrate that it improves diagnoses over the use of H&E only.

Treatment halts recurrence of Clostridium difficile bacteria, but a commercial pill is still far off.

Living near livestock farms and manure-treated fields associated with higher rates of antibiotic-resistant infection.

Geologists, engineers and social scientists are poised to swoop in before reconstruction gets under way.