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Providing drug products for pediatric patients is a challenging problem for the pharmaceutical industry. Children often require flexible low-dose medication with features like taste-masking and ease of swallowing. In recent years, mini-tablets have emerged as an attractive dosing solution that can meet these requirements. They are small form oral dosages around 2-4 mm in diameter that can be dispensed individually or in combination. Conventionally, they are made using methods like direct compression and hot melt extrusion. This study introduces a new technique to make mini-tablets: drop-on-demand 3D printing. Here the active ingredient is suspended in a liquid excipient, the formulation is printed as droplets and each drop is solidified to yield a mini-tablet. An optimal solvent bath that can uniformly capture mini-tablets is designed and dosages of Atorvastatin (active ingredient) are produced as a test case. Quality of these dosages is determined by measuring their content uniformity. 

We consider the high-dimensional linear regression model and assume that a fraction of the responses are contaminated by an adversary with complete knowledge of the data and the underlying distribution. We are interested in the situation when the dense additive noise can be heavy-tailed but the predictors have sub-Gaussian distribution. We establish minimax lower bounds that depend on the the fraction of the contaminated data and the tails of the additive noise. Moreover, we design a modification of the square root Slope estimator with several desirable features: (a) it is provably robust to adversarial contamination, with the performance guarantees that take the form of sub-Gaussian deviation inequalities and match the lower error bounds up to log-factors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the noise, and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze the performance of the proposed estimator, we prove several properties of matrices with sub-Gaussian rows that could be of independent interest. 

Neonicotinoids (NNs) are commonly found throughout the environment on surfaces such as seeds, soil, vegetation, and blowing dust particles. However, there is a paucity of data on the kinetics and oxidation products formed on contact with the atmosphere which limits understanding of their potentially far-reaching impacts. In this study, in situ attenuated total reflectance (ATR) FTIR spectroscopy was used to investigate the OH oxidation of thin films of three solid NNs, imidacloprid (IMD), dinotefuran (DNF) and clothianidin (CLD) at 295 ± 3 K. The experimentally measured reaction probabilities based on initial rates of NN loss are (1.6 ± 0.8) × 10 −2 for IMD, (1.5 ± 0.6) × 10 −2 for DNF and (0.9 ± 0.2) × 10 −2 for CLD (±1 σ ), suggesting initial NN lifetimes with respect to OH of 10–17 days. The kinetics were interpreted using a multiphase kinetics model, KM-SUB, which showed that the OH uptake and reaction occurred primarily in the surface layer. Products identified by mass spectrometry included carbonyl-, alcohol- and olefin-containing species formed via hydrogen abstraction from aliphatic C–H groups. Additionally, carbonyl-containing desnitro and urea derivative products were observed from secondary reactions of the initially formed photodegradation products. Reaction with OH will contribute to NN loss both during the day as well as at night when there are non-photolytic sources of this radical. Thus, OH reactions with both the parent neonicotinoid and its photodegradation products should be considered in assessing their environmental impacts. 

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random distribution of the Bayesian optimization outputs, quantification of this uncertainty is rarely studied in the literature. In this work, we propose a novel approach to assess the output uncertainty of Bayesian optimization algorithms, which proceeds by constructing confidence regions of the maximum point (or value) of the objective function. These regions can be computed efficiently, and their confidence levels are guaranteed by the uniform error bounds for sequential Gaussian process regression newly developed in the present work. Our theory provides a unified uncertainty quantification framework for all existing sequential sampling policies and stopping criteria.