The primal-dual method for approximation algorithms

In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to NP-hard problems in combinatorial optimization. Because of parallels with the primal-dual method commonly used in combinatorial optimization, we call it the primal-dual method for approximation algorithms. We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems. Received: June 19, 2000 / Accepted: February 7, 2001?Published online October 2, 2001     

Taveuniamides: new chlorinated toxins from a mixed assemblage of marine cyanobacteria

Brine shrimp toxicity guided fractionation of the extracts from two mixed Fijian collections of the cyanobacteria Lyngbya majuscula and Schizothrix sp. led to the isolation of eleven novel chlorinated lipids. All of these metabolites show an intriguing constellation of unsaturation (olefinic and acetylenic bonds) and chlorination at the two termini of a 15-carbon chain. The central carbon atom of the chain (C-8) is substituted in each case with an N-acetate function. Taveuniamides A-E have an adjacent carbomethoxy group at C-9 to form a protected β-amino acid while taveuniamides F-K have a methylene group at this position. A standard assortment of 2D NMR techniques in concert with mass spectrometry and other analytical techniques were used to define the structures of these novel metabolites. Taveuniamides F, G and K were the most potent brine shrimp toxins with LD₅₀s between 1.7-1.9 μg/mL.     

Multiple binding modes of the camptothecin family to DNA oligomers

The binding constants of camptothecin, topotecan and its lactone ring-opened carboxylate derivative to DNA octamers were measured by UV and NMR spectroscopy. The self-association of topotecan (TPT) was also measured. The carboxylate form of TPT binds in the same way as the lactone, but more weakly. Titration of TPT into d(GCGATCGC)2 shows a preferred location stacked onto the terminal G1 base. However, the intermolecular NOEs cannot be reconciled with a single conformation of the complex, and suggest a model of a limited number of conformations in fast exchange. MD calculations on four pairs of starting structures with TPT stacked onto the G1-C8 base pair in different orientations were therefore performed. The use of selected experimental "docking" restraints yielded ten MD trajectories covering a wide conformational space. From a combination of calculated free energies, NOEs and chemical shifts, some of the structures produced could be eliminated, and it is concluded that the data are consistent with two major families of conformations in fast exchange. One of these is the conformation found in a crystal of a TPT/DNA/topoisomerase I ternary complex [Proc. Natl. Acad. Sci. USA 2002, 99, 15 387-15 392].     

Continuous flow hydroformylation of alkenes in supercritical fluid-ionic liquid biphasic systems

A process for the hydroformylation of relatively low volatility alkenes (demonstrated for 1-dodecene) in a continuous flow system is described. The catalyst is dissolved in an ionic liquid while the substrate and gaseous reagents are transported into the reactor dissolved in supercritical CO(2), which simultaneously acts as a transport vector for aldehyde products. Decompression of the fluid mixture downstream yields products which are free of both reaction solvent and catalyst. The use of rhodium complexes of triaryl phosphites leads to ligand degradation through reaction of the ionic liquid with water and subsequent attack of the released HF on the phosphite. Sodium salts of sulfonated phosphines are insufficiently soluble in the ionic liquids to obtain acceptable rates, but replacing the sodium by a cation similar to that derived from the ionic liquid, allows good solubility and activity to be obtained. The nature of the ionic liquid is very important in achieving high rates, with 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amides giving the best activity if the alkyl chain is at least C(8). Catalyst turnover frequencies as high as 500 h(-1) have been observed, with the better rates at higher substrate flow rates. Rhodium leaching into the product stream can be as low as 0.012 ppm, except at low partial pressures of CO/H(2), when it is significantly higher. Oxygen impurities in the CO(2) feed can lead to oxidation of the phosphine giving higher rates, lower selectivities to the linear aldehyde, increased alkene isomerization and greater leaching of rhodium. However, it is found that under certain process conditions, the supercritical fluid-ionic liquid (SCF-IL) system can be operated continuously for several weeks without any visible sign of catalyst degradation. Comparisons with commercial hydroformylation processes are provided.     

The annealing behavior of implanted nitrogen in fcc stainless steel

Post-implantation annealing of N-implanted 304 stainless steel at 400 °C has been investigated by conversion electron Mössbauer spectroscopy, X-ray diffraction and Auger electron spectroscopy. After a 1 h anneal, the near complete dissolution of the as-implanted Fe₂N-like nitride phase results in a 9 at.% N fcc solid-solution phase. After the final anneal (64 h), N has diffused to a depth of about 2 m and remains in solid solution with an average content of 4 at.%. An average N diffusion coefficient at 400 °C is estimated to be 10^-12-10^-14 cm²/s, depending on anneal time, too small to explain the deep penetration observed in high-flux, high-dose N-implanted stainless steel. The present results provide additional evidence for beam controlled N migration where Cr plays an important role.