On optimal probabilities in stochastic coordinate descent methods

We propose and analyze a new parallel coordinate descent method—NSync—in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen using an arbitrary probability law. This is the first method of this type. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities to the sets to optimize the bound. The complexity and practical performance of the method can outperform its uniform variant by an order of magnitude. Surprisingly, the strategy of updating a single randomly selected coordinate per iteration—with optimal probabilities—may require less iterations, both in theory and practice, than the strategy of updating all coordinates at every iteration.     

Application of Doehlert design in optimizing the determination of degraded products of nerve agents by ion-pair liquid chromatography electrospray ionization tandem mass spectrometry

A qualitative method was developed for the determination of degraded products of nerve agents by using ion-pair liquid chromatography electrospray ionization tandem mass spectrometry (IP-LC-ESI-MS(n)). Generally, alkylphosphonic acids (APAs) and O-alkyl alkylphosphonic acids (AAPAs) give deprotonated molecular ion [M-H](-) in negative mode. Interestingly, first time we obtained the molecular radical anion [M](.-) of phosphonic acids in negative mode by using tri-n-butyl amine as an ion-pairing agent. We interpreted this observation as an indication of electrochemical reduction of phosphonic acids in electrospray needle. Three variables such as sheath gas flow, electrospray needle voltage and pH of the mobile phase were investigated to enhance the molecular radical anion [M](.-) signal of each analyte. The Doehlert design was used to obtain the region in which the optimum value of such variables is simultaneously achieved. Limit of detection achieved was 0.5 microg mL(-1) for AAPAs and 10 microg mL(-1) for APAs. Excellent precision was observed with less than 8.61% RSD. Finally, the method was applied for the detection of ethyl methylphosphonic in aqueous extract of soil sample.     

In situ derivatization hollow fiber mediated liquid phase microextraction of alkylphosphonic acids from water

Alkylphosphonic acids (APAs), particularly the methyl-, ethyl-, isopropyl- and n-propyl-phosphonic acids are important markers of extremely toxic nerve agents. Hence, their detection and identification is of vital importance to verification of chemical weapons convention (CWC). Verification analysis of CWC requires development of fast, reliable, simple and reproducible sample preparation methods of water and soil samples. Present investigation is focused on the optimization of alkylation of APAs in water with subsequent extraction of alkylated acids by hollow fiber liquid phase microextraction (HF-LPME). This simple and sensitive sample preparation of APAs from water offered better recoveries in comparison to conventionally used extraction technique. Under optimized conditions, the APAs were detected at the concentration of 0.5-0.75 microg/mL with S/N ratio > or = 5, whereas the LODs for alkyl APAs (monobasic APAs) were achieved up to 0.1 microg/mL. The developed method was finally tested with water samples supplied in 19th official proficiency test conducted by the OPCW.     

Enrichment of low abundance proteins of Escherichia coli by hydroxyapatite chromatography.

Visualization of low-copy-number gene products is essential for the detection of novel drug targets by differential protein expression studies. We investigated the enrichment of low-abundance proteins of Escherichia coli by hydroxyapatite chromatography. The proteins of the various pools collected from a ceramic hydroxyapatite column were analyzed by two-dimensional electrophoresis and identified by matrix-assisted laser desorption ionization mass spectrometry. Approximately 800 spots corresponding to 296 different proteins were identified in the hydroxyapatite eluate. About 130 proteins that had not been detected in the two-dimensional gels of the total extract were identified. Hydroxyapatite chromatography enriched low-abundance but also major components of the E. coli protein extract. In particular, it enriched many low-molecular-mass proteins, such as cold-shock proteins. The proteins bound to the hydroxyapatite matrix belong to several classes, including enzymes with various catalytic activities, heat- and cold-shock proteins and many hypothetical and novel proteins with yet unknown functions. The results include a list of the proteins enriched by hydroxyapatite chromatography and a two-dimensional map of the enriched proteins. They may be useful in the design of protein purification pathways using master purification steps and in the search for novel drug targets.     

Determination of oversulfated chondroitin sulfate and dermatan sulfate impurities in heparin by capillary electrophoresis

Recently, oversulfated chondroitin sulfate (OSCS) present in certain lots of heparin was identified as the toxic contaminant responsible for severe side effects following intravenous heparin administration. The United States Pharmacopeia (USP) and European Pharmacopeia (Eur.Ph.) announced an immediate revision of their monographs for heparin sodium by adding two US Food and Drugs Administration-recommended tests for OSCS based on nuclear magnetic resonance and capillary electrophoresis (CE). However, the proposed CE method provides only partial separation of the OSCS contaminant from heparin, thereby hindering appropriate impurity profiling. Here we present an improved CE method that is especially useful for the reliable quantification of OSCS in heparin samples, but also allows determination of the common impurity dermatan sulfate (DS). Parameters such as type and concentration of background electrolyte, capillary temperature, sample concentration and injection volume were investigated and optimized. Enhancement of the OSCS–heparin separation was achieved by using high concentrations of Tris phosphate (pH 3.0) as background electrolyte. High currents and excessive Joule heating were prevented by employing fused-silica capillaries with an internal diameter of 25 μm. Good separations of OSCS, heparin and DS are obtained within 17 min. The method permits injection of relatively high heparin concentrations (up to 50 mg/ml) and large sample volumes (up to 5% of the capillary volume) allowing OSCS and DS determination in heparin down to the 0.05% and 0.5% (w/w) level, respectively. The CE method is shown to be repeatable and linear (R² > 0.99) for OSCS, heparin and DS. CE analyses of OSCS-contaminated heparin samples and different heparin standards further demonstrate the utility of the method.     

Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

Resolving intermediate solution structures during the formation of mesoporous SBA-15

The evolution of the solution microstructures during the formation of the hexagonal mesoporous material SBA-15 was studied by direct imaging and freeze-fracture replication cryo-TEM. A reaction mixture was sampled at different times after the addition of tetramethoxyorthosilane (TMOS) to an acidic solution of Pluronic P123 held at 50 degrees C. Solution microstructures were detected by direct imaging cryo-TEM in the time window of 6.5-40 min after the addition of the TMOS (t = 0). The micrographs revealed that the initial spheroidal micelles evolve into threadlike micelles, which become longer and straighter with time. Then bundles with the dimensions similar to those found in the final material appeared, although there was no sign of a hexagonal arrangement up to 40 min. Due to the appearance of a precipitate at 40 min the sample became too viscous, preventing clear observation of its content. To observe the structures present after 40 min, freeze-fracture replication was carried out as well. Such samples were collected also at 22 min and showed the presence of threadlike micelles in agreement with the direct imaging cryo-TEM micrographs. The 2 h samples showed some areas of hexagonal ordered structures, which become very clear at 2 h 50 min. The cryo-TEM measurements were carried out under the same reaction conditions used in earlier in situ EPR experiments, thus allowing us to correlate molecular level events with the microstructure shape evolutions. This showed that the elongation of the micelles is a consequence of a reduction of the polarity and the water content within the micelles due to silicate adsorption and polymerization. Similar experiments were carried out also on SBA-15 prepared with HCl and TMOS at 35 degrees C. The appearance of threadlike micelles, followed by clustering of the TLMs, was observed under these conditions as well, but the reaction rate was faster. This suggests that the observed mechanism for the formation of SBA-15 is general.