Assessing the diagnostic power of variables measured with a detection limit

The phenomenon of the limit of detection (LoD) often happens in many practical situations because of technique and instrument limitations. In the literature, some reports show that, in general, to apply conventional methods to evaluate the diagnostic power of variables while ignoring LoD could be seriously biased. Although the area under the receiver operating characteristic (ROC) curve can be estimated consistently if the distribution of variables are known. In practical situation, such information is usually not available. On the other hand, it has been proved that the area under ROC curve of a variable with a LoD and no distribution assumptions is usually biased no matter what kinds of replacement strategies are used. However, there is a lack of similar studies on the partial area under ROC curve (pAUC), and because this measure is usually preferred in practice, it is of interest to examine whether the estimate of pAUC of a variable measured with a LoD behaves the same. In this study, we found that for some LoD scenarios, and even without distribution assumption, consistent estimate of pAUC can be constructed. When the consistent estimate of pAUC cannot be obtained, the bias can be ineffectual in practical situations, and the proposed estimator can be a good approximation of pAUC. Numerical studies using simulated data sets and real data examples are reported.     

Synthesis of Polysubstituted Symmetrical BODIPYs via Fischer Carbene Complexes: Theoretical,Photophysical and Electrochemical Evaluation

A series of new symmetrical highly substituted BODIPYs 6 a – l was synthesized through a prefunctionalization approach in 35 %–89 % yields from the pyrrole core. This strategy allowed modulation of the substituents at the different positions based on the choice of Fischer's alkynyl carbenes, oxazolones and aldehydes used as precursors. The substituent variation at positions 2, 6, 3 and 5 had the greatest effect on the modulation of their photophysical properties such as absorption (λ_abs) and emission (λ_em) wavelengths, extinction coefficient (ϵ), quantum yields (ϕ), Stokes shifts (Δν), fluorescence decay, radiative (k_rad) and non-radiative (k_nr) constants and the CIE 1931 coordinates. Theoretical calculations allowed to corroborate the effect of the substituents of meso-position on the modification of the dihedral angles. Cyclic voltammetry studies revealed that the BODIPY series presents similar redox potential behavior, being electrochemically active even in successive cycles, which suggests that transport by diffusion is the dominant process.     

Ten-membered rings as key interaction motifs in folding of desmuramyl di-, tri-, and tetrapeptides

Structural Chemistry - Muropeptides are fragments of polymeric peptidoglycan, unique constituent of bacterial cell walls, acting as immunostimulators (adjuvants). The smallest biologically active...     

Completions of symplectic reflection algebras

In this paper, we study the structure of completions of symplectic reflection algebras. Our results provide a reduction to smaller algebras. We apply this reduction to the study of two-sided ideals and Harish–Chandra bimodules.     

The conformation of epinephrine in polar solvents: an NMR study

Structural Chemistry - Epinephrine (Epi) is a physiologically important catecholamine. Molecular conformation of Epi controls the interactions with other molecules and its biological effects. There...