We present a supervised machine learning approach to the inversion of Fredholm integrals of the first kind as they arise, for example, in the analytic continuation problem of quantum many-body physics. The approach provides a natural regularization for the ill-conditioned inverse of the Fredholm kernel, as well as an efficient and stable treatment of constraints. The key observation is that the stability of the forward problem permits the construction of a large database of outputs for physically meaningful inputs. Applying machine learning to this database generates a regression function of controlled complexity, which returns approximate solutions for previously unseen inputs; the approximate solutions are then projected onto the subspace of functions satisfying relevant constraints. Under standard error metrics the method performs as well or better than the Maximum Entropy method for low input noise and is substantially more robust to increased input noise. We suggest that the methodology will be similarly effective for other problems involving a formally ill-conditioned inversion of an integral operator, provided that the forward problem can be efficiently solved.

Restricting in-person interactions is an important technique for limiting the spread of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). Although early research found strong associations between cell phone mobility and infection spread during the initial outbreaks in the United States, it is unclear whether this relationship persists across locations and time. We propose an interpretable statistical model to identify spatiotemporal variation in the association between mobility and infection rates. Using 1 year of US county-level data, we found that sharp drops in mobility often coincided with declining infection rates in the most populous counties in spring 2020. However, the association varied considerably in other locations and across time. Our findings are sensitive to model flexibility, as more restrictive models average over local effects and mask much of the spatiotemporal variation. We conclude that mobility does not appear to be a reliable leading indicator of infection rates, which may have important policy implications.

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Mucoepidermoid carcinoma is a relatively common neoplasm of the major and minor salivary glands that can secondarily involve skin. In the vicinity of the ear lobe, mimicry of a benign cyst, both clinically and histopathologically is a diagnostic pitfall to avoid. The clinical manifestations, diagnostic histopathology, and clinical course of mucoepidermoid carcinoma of the parotid gland presenting as a clinically benign periauricular cystic nodule in four patients ranging in age from 11 to 63 years, are analyzed in the present report. Illustrating the challenge of accurate diagnosis, three of the four cases were initially misinterpreted on biopsy as benign cystic lesions. Multiple biopsies displayed foamy histiocytes around mucinous extravasations into dermis that mimicked ruptured epithelial cysts in two cases before malignancy was ascertained. This series demonstrates the need to include parotid tumor in the differential diagnosis of odd periauricular cyst-like expansions and adenosquamous proliferations. Mucoepidermoid carcinoma in particular can explain indolent, infra-auricular 'mucinous cysts'. Familiarity with this syndrome should arouse suspicion of parotid carcinoma when a 'cyst' or nodule is located near the earlobe. Delay in diagnosis results in larger surgical procedures than are otherwise necessary.

Accurate measurement of daily infection incidence is crucial to epidemic response. However, delays in symptom onset, testing, and reporting obscure the dynamics of transmission, necessitating methods to remove the effects of stochastic delays from observed data. Existing estimators can be sensitive to model misspecification and censored observations; many analysts have instead used methods that exhibit strong bias. We develop an estimator with a regularization scheme to cope with stochastic delays, which we term the robust incidence deconvolution estimator. We compare the method to existing estimators in a simulation study, measuring accuracy in a variety of experimental conditions. We then use the method to study COVID-19 records in the United States, highlighting its stability in the face of misspecification and right censoring. To implement the robust incidence deconvolution estimator, we release incidental, a ready-to-use R implementation of our estimator that can aid ongoing efforts to monitor the COVID-19 pandemic.