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We report a new method for the regiodivergent dearomative (3 + 2) reaction between 3-substituted indoles and oxyallyl cations. Access to both regioisomeric products is possible and is contingent on the presence or absence of a bromine atom on the substituted oxyallyl cation. In this way, we are able to prepare molecules that contain highly-hindered, stereodefined, vicinal, quaternary centers. Detailed computational studies employing energy decomposition analysis (EDA) at the DFT level establishes that regiochemical control arises from either reactant distortion energy or orbital mixing and dispersive forces, depending on the oxyallyl cation. Examination of the Natural Orbitals for Chemical Valence (NOCV) confirms that indole acts as the nucleophilic partner in the annulation reaction. 

We study the problem of classifier derandomization in machine learning: given a stochastic binary classifier f:X→[0,1], sample a deterministic classifier f̂ :X→{0,1} that approximates the output of f in aggregate over any data distribution. Recent work revealed how to efficiently derandomize a stochastic classifier with strong output approximation guarantees, but at the cost of individual fairness -- that is, if f treated similar inputs similarly, f̂ did not. In this paper, we initiate a systematic study of classifier derandomization with metric fairness guarantees. We show that the prior derandomization approach is almost maximally metric-unfair, and that a simple ``random threshold'' derandomization achieves optimal fairness preservation but with weaker output approximation. We then devise a derandomization procedure that provides an appealing tradeoff between these two: if f is α-metric fair according to a metric d with a locality-sensitive hash (LSH) family, then our derandomized f̂ is, with high probability, O(α)-metric fair and a close approximation of f. We also prove generic results applicable to all (fair and unfair) classifier derandomization procedures, including a bias-variance decomposition and reductions between various notions of metric fairness. 

The nucleophile-intercepted Beckmann fragmentation (NuBFr) has the potential to be broadly applicable to the synthesis of indoline alkaloid based natural products. However, the reaction has not been widely adopted, in part, because of limitations associated with the availability of appropriate promoter–Nu reagents. We have devised a stereospecific Ag(I)-promoted reaction for functionalizing NuBFr products to give novel compositions-of-matter that may be useful in synthesis and medicinal chemistry. With unhindered amine nucleophiles, structurally unique [2.2.2]-bicycloamidines are generated. We also disclose for the first time detailed density functional theory (DFT) studies which shed light on the mechanism of the NuBFr and Ag-promoted substitution reaction that supports an unusual aziridinium ion as a key intermediate.