In late December 2019, the novel coronavirus (Sars-Cov-2) and the resulting disease COVID-19 were first identified in Wuhan China. The disease slipped through containment measures, with the first known case in the United States being identified on January 20th, 2020. In this paper, we utilize survey data from the Inter-university Consortium for Political and Social Research and apply several statistical and machine learning models and techniques such as Decision Trees, Multinomial Logistic Regression, Naive Bayes, k-Nearest Neighbors, Support Vector Machines, Neural Networks, Random Forests, Gradient Tree Boosting, XGBoost, CatBoost, LightGBM, Synthetic Minority Oversampling, and Chi-Squared Test to analyze the impacts the COVID-19 pandemic has had on the mental health of frontline workers in the United States. Through the interpretation of the many models applied to the mental health survey data, we have concluded that the most important factor in predicting the mental health decline of a frontline worker is the healthcare role the individual is in (Nurse, Emergency Room Staff, Surgeon, etc.), followed by the amount of sleep the individual has had in the last week, the amount of COVID-19 related news an individual has consumed on average in a day, the age of the worker, and the usage of alcohol and cannabis.

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In large-scale optimization, when either forming or storing Hessian matrices are prohibitively expensive, quasi-Newton methods are often used in lieu of Newton's method because they only require first-order information to approximate the true Hessian. Multipoint symmetric secant (MSS) methods can be thought of as generalizations of quasi-Newton methods in that they attempt to impose additional requirements on their approximation of the Hessian. Given an initial Hessian approximation, MSS methods generate a sequence of matrices using rank-2 updates. For practical reasons, up to now, the initialization has been a constant multiple of the identity matrix. In this paper, we propose a new limited-memory MSS method that allows for dense initializations. Numerical results on the CUTEst test problems suggest that the MSS method using a dense initialization outperforms the standard initialization. Numerical results also suggest that this approach is competitive with a basic L-SR1 trust-region method. DedicationThis paper is dedicated to Oleg Burdakov who passed away June 1, 2021. S k = [s k−1 s k−2 . . . s 0 ] and Y k = [y k−1 y k−2 . . . y 0 ] .

The early diagnosis of lymph node metastasis in breast cancer is essential for enhancing treatment outcomes and overall prognosis. Unfortunately, pathologists often fail to identify small or subtle metastatic deposits, leading them to rely on cytokeratin stains for improved detection, although this approach is not without its flaws. To address the need for early detection, multiple-instance learning (MIL) has emerged as the preferred deep learning method for automatic tumor detection on whole slide images (WSIs). However, existing methods often fail to identify some small lesions due to insufficient attention to small regions. Attention-based multiple-instance learning (ABMIL)-based methods can be particularly problematic because they may focus too much on normal regions, leaving insufficient attention for small-tumor lesions. In this paper, we propose a new ABMIL-based model called normal representative keyset ABMIL (NRK-ABMIL), which addresseses this issue by adjusting the attention mechanism to give more attention to lesions. To accomplish this, the NRK-ABMIL creates an optimal keyset of normal patch embeddings called the normal representative keyset (NRK). The NRK roughly represents the underlying distribution of all normal patch embeddings and is used to modify the attention mechanism of the ABMIL. We evaluated NRK-ABMIL on the publicly available Camelyon16 and Camelyon17 datasets and found that it outperformed existing state-of-the-art methods in accurately identifying small tumor lesions that may spread over a few patches. Additionally, the NRK-ABMIL also performed exceptionally well in identifying medium/large tumor lesions.