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Rhenium-catalyzed stereoselective transposition of allylic alcohols is reported. In the presence of 1 mol% of Re 2 O 7 , ( E )- or ( Z )-δ-hydroxymethyl- anti -homoallylic alcohols were converted into the acetals of 2-methyl-1,3- syn -diols with excellent diastereoselectivities. 1,3- syn -Diol acetals can also be synthesized from ( E )-δ-hydroxymethyl- syn -homoallylic alcohols. 

We report herein a Cu‐catalyzed regio‐, diastereo‐ and enantioselective acylboration of 1,3‐butadienylboronate with acyl fluorides. Under the developed conditions, the reactions provide (Z)‐β,γ‐unsaturated ketones bearing an α‐tertiary stereocenter with highZ‐selectivity and excellent enantioselectivities. While direct access to highly enantioenrichedE‐isomers was not successful, we showed that such molecules can be synthesized with excellentE‐selectivity and optical purities via Pd‐catalyzed alkene isomerization from the correspondingZ‐isomers. The orthogonal chemical reactivities of the functional groups embedded in the ketone products allow for diverse chemoselective transformations, which provides a valuable platform for further derivatization.

 

We report herein a Cu‐catalyzed regio‐, diastereo‐ and enantioselective acylboration of 1,3‐butadienylboronate with acyl fluorides. Under the developed conditions, the reactions provide (Z)‐β,γ‐unsaturated ketones bearing an α‐tertiary stereocenter with highZ‐selectivity and excellent enantioselectivities. While direct access to highly enantioenrichedE‐isomers was not successful, we showed that such molecules can be synthesized with excellentE‐selectivity and optical purities via Pd‐catalyzed alkene isomerization from the correspondingZ‐isomers. The orthogonal chemical reactivities of the functional groups embedded in the ketone products allow for diverse chemoselective transformations, which provides a valuable platform for further derivatization.

 

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.