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The catalytic uses of metal carbenes for addition, insertion, and cycloaddition reactions are dependent on their carbene precursor. The limited methods available for the preparation of diazo esters, which are the most common carbene precursors, restricts their ability to impart structural diversity in metal carbene reactions. Here we report a new methodology for the preparation of diverse vinyldiazoacetate esters and their effective uses in highly enantiocontrolled cyclopropanation, N-H bond insertion, O-H bond insertion, and [3+2] cycloaddition reactions. 1,2,3-Triazine 1-oxides with a sp3-C-H bond at the 5-position undergo base catalyzed Dimroth-type rearrangement to form multiply substituted oximidovinyldiazoacetates in high yields at or below room temperature, and these diverse vinyldiazo compounds undergo catalytic metal carbene transformations to produce oximidovinylcyclopropanes, α-oximidovinyl-α-amino acids and α-hydroxy acids, as well as tricyclic indole derivatives in high yields and enantioselectivities. The new access to vinyldiazo compounds has applicability to a vast array of metal carbene transformations. 

Abstract Measuring observables to constrain models using maximum-likelihood estimation is fundamental to many physics experiments. Wilks' theorem provides a simple way to construct confidence intervals on model parameters, but it only applies under certain conditions. These conditions, such as nested hypotheses and unbounded parameters, are often violated in neutrino oscillation measurements and other experimental scenarios. Monte Carlo methods can address these issues, albeit at increased computational cost. In the presence of nuisance parameters, however, the best way to implement a Monte Carlo method is ambiguous. This paper documents the method selected by the NOvA experiment, the profile construction. It presents the toy studies that informed the choice of method, details of its implementation, and tests performed to validate it. It also includes some practical considerations which may be of use to others choosing to use the profile construction.