Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fixed design and measure the distance between functions by the mean squared error at the design points. While procedures based on exponential weights are known to solve the problem of model selection aggregation in expectation, they are, surprisingly, sub-optimal in deviation. We propose a new formulation called Q-aggregation that addresses this limitation; namely, its solution leads to sharp oracle inequalities that are optimal in a minimax sense. Moreover, based on the new formulation, we design greedy Q-aggregation procedures that produce sparse aggregation models achieving the optimal rate. The convergence and performance of these greedy procedures are illustrated and compared with other standard methods on simulated examples.

Polyureas were synthesized from diamines and carbon dioxide in the absence of any catalyst or solvent, analogous to the synthesis of urea from condensation of ammonia with carbon dioxide. The method used carbon dioxide as a carbonyl source to substitute highly toxic isocyanates for the synthesis of polyureas. FTIR and DFT calculations confirmed that strong bidentate hydrogen bonds were formed between urea motifs, and XRD patterns showed that the PUas were highly crystalline and formed a network structure through hydrogen bonds, which served as physical cross-links. The long chain PUas presented a microphase separated morphology as characterized by SAXS and showed a high melting temperature above 200 °C. The PUas showed high resistance to solvents and excellent thermal stability, which benefitted from their special network structures. The PUas synthesized by this method are a new kind of functional material and could serve some areas where their analogues with similar functional groups could not be applied.

Efficient and divergent one-pot synthesis of fully substituted 1H-pyrazoles and isoxazoles from cyclopropyl oximes based on reaction conditions selection is reported. Under Vilsmeier conditions (POCl3/DMF), substituted 1 H-pyrazoles were synthesized from 1-carbamoyl, 1-oximyl cyclopropanes via sequential ring-opening, chlorovinylation, and intramolecular aza-cyclization. In the presence of POCl3/CH2Cl2, substituted isoxazoles were obtained from the cyclopropyl oximes via ring-opening and intramolecular nucleophilic vinylic substitution (SNV) reactions.