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The absolute stereochemistry of the α-amino and α-hydroxyphosphonates is determined using a chiroptical sensor. 

An effective catalyst has been developed for the three-component reaction of aldehydes, anilines and phosphites in an asymmetric catalytic Kabachnik–Fields reaction to give α-aminophosphonates. A catalyst was sought that would give high asymmetric inductions for aromatic and, and more particularly, for aliphatic aldehydes since there has not previously been an effective catalyst developed for this class of aldehydes. The optimal catalyst is prepared from three equivalents of the 7,7′-di- t -butylVANOL ligand, one equivalent of N -methylimidazole and one equivalent of zirconium tetraisopropoxide. This catalyst was most efficient in the presence of 10 mol% benzoic acid. Optimal conditions for aryl aldehydes required the use of 3,5-diisopropyl-2-hydroxyaniline and gave the aryl α-aminophosphonates in up to 96% yield and 98% ee over 11 different aryl aldehydes. The best aniline for aliphatic aldehydes was found to be 3- t -butyl-2-hydroxyaniline and gave the corresponding phosphonates in up to 83% yield and 97% ee over 18 examples. The asymmetric inductions for aliphatic aldehydes were comparable with those for aromatic aldehydes with a mean induction of 90% ee for the former and 91% ee for the latter. The best method for the liberation of the free amine from the aniline substituted α-aminophosphonates involved oxidation with N -iodosuccinimide. 

Sparse learning models are popular in many application areas. Objective functions in sparse learning models are usually non-smooth, which makes it difficult to solve them numerically. We develop a fast and convergent two-step iteration scheme for solving a class of non-differentiable optimization models motivated from sparse learning. To overcome the difficulty of the non-differentiability of the models, we first present characterizations of their solutions as fixed-points of mappings involving the proximity operators of the functions appearing in the objective functions. We then introduce a two-step fixed-point algorithm to compute the solutions. We establish convergence results of the proposed two-step iteration scheme and compare it with the alternating direction method of multipliers (ADMM). In particular, we derive specific two-step iteration algorithms for three models in machine learning: l1-SVM classification, l1-SVM regression, and the SVM classification with the group LASSO regularizer. Numerical experiments with some synthetic datasets and some benchmark datasets show that the proposed algorithm outperforms ADMM and the linear programming method in computational time and memory storage costs.