A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level.

We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates 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 dataset of questions from Massachusetts Institute of Technology (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 pretrained 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 automatically solves university-level mathematics course questions at a human level and explains and generates university-level mathematics course questions at scale, a milestone for higher education.

Isolated Medial Cuneiform Fractures: A Systematic Search and Qualitative Analysis of Case Studies.

BACKGROUND: Isolated medial cuneiform fracture is a rare but diagnostically challenging condition. Diagnostic delay in these cases may lead to delays in ideal treatment approaches and prolonged symptoms. An understanding of clinical presentation is needed to expedite diagnosis, facilitate decision making, and guide treatment approach. METHODS: Case studies/series were searched in four databases until September 2019. Included studies had participants with a history of traumatic closed medial cuneiform fracture. Studies were excluded if the medial cuneiform fractures were open fractures, associated with multitrauma, or associated with dislocation/Lisfranc injury. Three blinded reviewers assessed the methodological quality of the studies, and a qualitative synthesis was performed. RESULTS: Ten studies comprising 15 patients were identified. Mean ± SD patient age was 38.0 ± 12.8 years, with 86.7% of reported participants being men. The overall methodological quality was moderate to high, and reporting of the patient selection criteria was poor overall. The most commonly reported clinical symptoms were localized tenderness (60.0%) and edema (53.3%). Direct blow was the most common inciting trauma (46.2%), followed by axial load (30.8%) and avulsion injuries (23.1%). Baseline radiographs were occult in 72.7% of patients; magnetic resonance imaging and computed tomography were the most common diagnostic modalities. Mean ± SD diagnostic delay was 64.7 ± 89.6 days. Conservative management was pursued in 54.5% of patients, with reported resolution of symptoms in 3 to 6 months. Surgical intervention occurred in 45.5% of patients and resulted in functional restoration in 3 to 6 months in all but one patient. CONCLUSIONS: Initial radiographs for isolated medial cuneiform fractures are frequently occult. Due to expedience and relatively low cost, radiographs are still a viable first-line imaging modality. If clinical concern remains, magnetic resonance imaging may be pursued to minimize diagnostic delay. Conservative management is a viable treatment method, with expected return to full function in 3 to 6 months.

Controlling Interactions between Quantum Emitters Using Atom Arrays.

We investigate the potential for two-dimensional atom arrays to modify the radiation and interaction of individual quantum emitters. Specifically, we demonstrate that control over the emission linewidths, resonant frequency shifts, and local driving field enhancement in impurity atoms is possible due to strong dipole-dipole interactions within ordered, subwavelength atom array configurations. We demonstrate that these effects can be used to dramatically enhance coherent dipole-dipole interactions between distant impurity atoms within an atom array. Possible experimental realizations and potential applications are discussed.

Radiographically Occult Medial Cuneiform Impaction Fracture.

A 25-year-old woman reported to the emergency department with right medial midfoot pain after kicking a wall. Radiographs were noncontributory and the patient was diagnosed with a metatarsal contusion. Persistent pain post injury led her to seek a direct-access physical therapy evaluation. Following examination, the physical therapist requested magnetic resonance imaging, which confirmed a medial cuneiform fracture. J Orthop Sports Phys Ther 2019;49(9):675. doi:10.2519/jospt.2019.8778.

Microbial safety and quality of fresh herbs from Los Angeles, Orange County and Seattle farmers' markets.

BACKGROUND: Farmers' markets have been growing in popularity in the United States, but the microbial quality and safety of the food sold at these markets is currently unknown. The purpose of this study was to assess the microbial safety and quality of fresh basil, parsley and cilantro sold at farmers' markets in the Los Angeles, Orange County and greater Seattle areas. RESULTS: A total of 133 samples (52 basil, 41 cilantro and 40 parsley) were collected from 13 different farmers' markets and tested for Salmonella and generic Escherichia coli. One sample (parsley) was confirmed positive for Salmonella and 24.1% of samples were positive for generic E. coli, with a range of 0.70-3.15 log CFU g(-1) . Among the herbs tested, basil showed the highest percentage of samples with generic E. coli (26.9%), followed by cilantro (24.4%) and then parsley (20.0%). For 12% of samples, the levels of generic E. coli exceeded guidelines established by the Public Health Laboratory Service for microbiological quality of ready-to-eat foods. CONCLUSION: Overall, this study indicates the presence of Salmonella and generic E. coli in fresh herbs sold at farmers' markets; however, additional studies are needed to determine the sources and extent of contamination.