We present an algorithm for identifying the extreme rays of the conical hull of a finite set of vectors whose generated cone is pointed. This problem appears in diverse areas including stochastic programming, computational geometry, and non-parametric efficiency measurement. The standard approach consists of solving a linear program for every element of the set of vectors. The new algorithm differs in that it solves fewer and substantially smaller LPs. Extensive computational testing validates the algorithm and demonstrates that for a wide range of problems it is computationally superior to the standard approach.

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Combination of asenapine with valproic acid received regulatory approval for acute treatment of schizophrenia and maniac episodes of bipolar disorders. A simple LC–MS/MS method was developed and validated for simultaneous quantification of asenapine and valproic acid in human plasma. Internal standards were added to 300 μL of plasma sample prior to liquid–liquid extraction using methyl tertiary butyl ether (MTBE). Chromatographic separation was achieved on Phenomenex C18 column (50 mm×4.6 mm, 5 μm) in isocratic mode at 40 °C. The mobile phase used was 10 mM ammonium formate–acetonitrile (5:95, v/v) at a constant flow rate of 0.8 mL/min monitored on triple quadrupole mass spectrometer, operating in the multiple reaction monitoring (MRM) mode. The injection volume used for LC–MS/MS analysis was 15 μL and the run time was 2.5 min. These low run time and small injection volume suggest the high efficiency of the proposed method. The method was validated over the concentration range of 0.1–10.02 ng/mL and 10–20,000 ng/mL for asenapine and valproic acid respectively. The method recoveries of asenapine (81.33%), valproic acid (81.70%), gliclazide (78.45%) and benzoic acid (79.73) from spiked plasma samples were consistent and reproducible. The application of this method was demonstrated by a pharmacokinetic study in 8 healthy male volunteers with 5 mg asenapine and 250 mg valproic acid administration.

A sensitive and selective liquid chromatography-tandem mass spectrometry (LC-MS/MS) method was developed and validated for simultaneous determination of urapidil and aripiprazole in human plasma. A simple liquid-liquid extraction with ethyl acetate was used for the sample preparation. Chromatographic separation was achieved on a Phenomenex C18 (4.6 × 50 mm, 5 µm) column with 0.1% formic acid-acetonitrile (10:90, v/v) as the mobile phase with flow rate of 0.6 mL/min. The quantitation of the target compounds was determined in a positive ion multiple reaction monitoring mode. Calibration plots were linear over the range of 2.0-2503.95 ng/mL for urapidil and 1.0-500.19 ng/mL for aripiprazole. The lower limit of quantitation for urapidil and aripiprazole was 2.0 and 1.0 ng/mL, respectively. Mean recovery was in the range of 69.94-75.62% for both analytes and internal standards. Intra-day and inter-day precisions of the assay at three concentrations were 2.56-5.89% with accuracy of 92.31-97.83% for urapidil, and 3.14-6.84% with accuracy of 91.38-94.42% for aripiprazole. The method was successfully applied to human pharmacokinetic study of urapidil and aripiprazole in healthy human male volunteers.

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