Total risk aversion,stochastic optimal control,and differential games

We present a connection between the theory of risk in the context of a stochastic optimal control problem and its relation to the theory of differential games. In particular, we define the notion of total risk aversion from the viewpoint of the upper value of a differential game. We prove that as the index of absolute risk aversion of a utility function in a stochastic control problem converges to infinity the (certainty equivalent) optimal payoff converges to the upper value of an associated deterministic differential game. The two main points of this paper are (1) a precise characterization oftotal risk aversion and (2) the construction of a stochastic optimal control problem intimately connected to a deterministic differential game.Partially supported by the Air Force Office of Scientific Research Grant No. AFOSR-86-0202.Partially supported by a grant from the National Science Foundation.     

Determination of absolute configurations from vibrational raman optical activity: (trans)-2,3-dimethylthiirane

Experimental and theoretical vibrational Raman optical activity (VROA) spectra of (2R,3R)-2,3-dimethylthiirane in the 200-1500 cm(-1) region are presented. The level of agreement obtained for the observed and predicted VROA signs suggests that the absolute configurations of chiral molecules can be determined confidently using VROA.     

Transition-metal complexes of a bifunctional tetradentate gallium alkoxide ligand

The mixed gallium transition-metal complexes [FeCl[Ga(2)((t)Bu)(4)(neol)(2)]] (1) and [M[Ga(2)((t)Bu)(4)(neol)(2)]], M = Co (2), Ni (3), Cu (4), have been prepared by the reaction of [Ga(2)((t)Bu)(4)(neol-H)(2)] (neol-H(2) = 2,2-dimethyl-propane-1,3-diol) with the appropriate metal halide and Proton Sponge. Compounds 1-4 have been characterized by NMR (3), UV/vis, and IR spectroscopy and magnetic susceptibility (solution and solid state), and their molecular structures have been confirmed by X-ray crystallography. The molecular structure of compounds 1-4 consists of a tetracyclic core formed from two four-membered and two six-membered rings. The central metal atom adopts a square pyramidal (1) or square planar (2-4) geometry. The magnetic susceptibilities for 1, 2, and 4 are as expected for strong ligand field environments. On the basis of spectroscopic and structural data, the [Ga(2)((t)Bu)(4)(neol)(2)](2-) ligand appears to be more flexible than other chelating ligands; this is proposed to be due to the flexibility in the O-Ga-O bond angle.     

Technical challenges in applying capillary electrophoresis-single strand conformation polymorphism for routine genetic analysis

Recent and future advances in population genetics will have a significant impact on health care practices and the economics of health care provision only if a spectrum of patient-tailored, effective methods of DNA screening for sequence alterations has been developed. Genetic screening by capillary electrophoresis-single strand conformation polymorphism (CE-SSCP), which is based upon the differences in electrophoretic mobilities of wild-type and mutant DNA species, offers an important complement to other presently available techniques such as Sanger sequencing and DNA hybridization arrays due to its simplicity, versatility, and low cost of analysis. A two-part review of CE-SSCP that discusses its advantages and limitations is presented. Emphasis is placed on technological aspects of CE-SSCP (including such rarely addressed issues as sample preparation protocols and the nature of the polymeric DNA separation matrix) as well as on the potential of CE-SSCP for routine genetic analysis. An attempt is made to organize and present the information in sufficient detail to allow the use of SSCP for routine genetic screening even by those inexperienced in CE. Some discussion of CE-based heteroduplex analysis (HA) is also presented.     

Cross Coupling of Substituted Anilines with Quinoline: Synthesis and Structural Characterization of HN(py)quin,PhN(py)quin,MesN(py)quin,and [PhN(py)(H-quin)]BF<Subscript>4</Subscript>

Abstract  

The molecular structure of (2,6-ⁱPr₂C₆H₃)N(quin)₂ (1) and both the methanol and toluene solvates of its copper complex [Cu{(2,6-ⁱPr₂C₆H₃)N(quin)₂}₂]BF₄, 2·MeOH and 2.2(C₆H₅Me), respectively, have been determined. The quinolyl rings in 1 adopt anti-syn (C_Ar–N–C–N_quin) conformation as a result of π–π stacking. The cation in 2·MeOH crystallizes on a C₂ axis, while the cation in 2·2(C₆H₅Me) is crystallographically independent. As a result of intramolecular π–π stacking there are significant changes within the coordination geometry about the copper centers between the two solvates, suggesting that the coordination around copper is supple. Crystal data: 1 group P2₁/c, a = 8.614(1), b = 16.137(3), c = 17.601(4) ?, β = 93.32(3)°, V = 2,442.5(9) ?³, Z = 4, R = 0.0544, wR ₂ = 0.1340. 2·MeOH group P3₂21, a = 13.254(1), b = 13.254(1), c = 27.214(5) ?, V = 4,140(1) ?³, Z = 3, R = 0.0392, wR ₂ = 0.0917. 2.2(C₆H₅Me) group P1, a = 11.677(2), b = 16.261(3), c = 17.077(3) ?, α = 93.63(3), β = 97.30(3), γ = 96.26(3)°, V = 3,187(1) ?³, Z = 4, R = 0.0526, wR ₂ = 0.1221.     

Preparation,characterisation and modification of carbon‐based monolithic rods for chromatographic applications

A range of porous carbon‐based monolithic (PCM) rods with flow‐through pore sizes of 1, 2, 5 and 10 μm, were produced using a silica particle template method. The rods were characterised using SEM and energy‐dispersive X‐ray spectroscopy, BET surface area and porous structure analysis, dilatometry and thermal gravimetry. SEM evaluation of the carbon monolithic structures revealed an interconnected rigid bimodal porous structure and energy‐dispersive X‐ray spectroscopy analysis verified the quantitative removal of the embedded silica beads. The specific surface areas of the 1, 2, 5 and 10 μm rods were 178, 154, 84 and 125 m²/g after pyrolysis and silica removal, respectively. Shrinkage of the monolithic rods during pyrolysis is proportional to the particle size of the silica used and ranged from 9 to 12%. Mercury porosimetry showed a narrow distribution of pore sizes, with an average of ～700 nm for the 1 μm carbon monolith. The suitability of bare and surface oxidised PCM rods for the use as a stationary phase for reversed and normal phase LC was explored. The additional modification of PCM rods with gold micro‐particles followed by 6‐mercaptohexanoic acid was performed and ion‐exchange properties were evaluated.     

Free-solution electrophoresis of DNA modified with drag-tags at both ends

In end-labeled free-solution electrophoresis (ELFSE), DNA molecules are labeled with a frictional modifier or "drag-tag", allowing their size-based electrophoretic separation in free solution. Among the interesting observations from early work with dsDNA using streptavidin as a drag-tag was that the drag induced by including a streptavidin label at both ends was significantly more than double that from a single streptavidin (Heller, C. et al.., J. Chromatogr. A 1998, 806, 113-121). This finding was assumed to be in error, and subsequent work focused on experiments in which only a single drag-tag is appended to one end of the DNA molecule. Recent theoretical work (McCormick, L. C., Slater, G. W., Electrophoresis 2005, 26, 1659-1667) has examined the contribution of end-effects to the free-solution electrophoretic mobility of charged-uncharged polymer conjugates, reopening the question of enhanced drag from placing a drag-tag at both ends. In this study, this effect is investigated experimentally, using custom-synthesized ssDNA oligonucleotides allowing the attachment of drag-tags to one or both ends, as well as dsDNA PCR products generated with primers appropriate for the attachment of drag-tags at one or both ends. A range of sizes of drag-tags are used, including synthetic polypeptoid drag-tags as well as genetically engineered protein polymer drag-tags. The enhanced drag arising from labeling both ends has been confirmed, with 6-9% additional drag for the ssDNA and 10-23% additional drag for the dsDNA arising from labeling both ends than would be expected from simply doubling the size of the drag-tag at one end. The experimental results for ssDNA labeled at both ends are compared to the predictions of the recent theory of end-effects, with reasonably good quantitative agreement. These experimental findings demonstrate the feasibility of enhancing ELFSE separations by labeling both ends of the DNA molecule, leading to greater resolving power and a wider range of applications for this technique.     

An optimized microchip electrophoresis system for mutation detection by tandem SSCP and heteroduplex analysis for p53 gene exons 5-9

With the complete sequencing of the human genome, there is a growing need for rapid, highly sensitive genetic mutation detection methods suitable for clinical implementation. DNA-based diagnostics such as single-strand conformational polymorphism (SSCP) and heteroduplex analysis (HA) are commonly used in research laboratories to screen for mutations, but the slab gel electrophoresis (SGE) format is ill-suited for routine clinical use. The translation of these assays from SGE to microfluidic chips offers significant speed, cost, and sensitivity advantages; however, numerous parameters must be optimized to provide highly sensitive mutation detection. Here we present a methodical study of system parameters including polymer matrix, wall coating, analysis temperature, and electric field strengths on the effectiveness of mutation detection by tandem SSCP/HA for DNA samples from exons 5-9 of the p53 gene. The effects of polymer matrix concentration and average molar mass were studied for linear polyacrylamide (LPA) solutions. We determined that a matrix of 8% w/v 600 kDa LPA provides the most reliable SSCP/HA mutation detection on chips. The inclusion of a small amount of the dynamic wall-coating polymer poly-N-hydroxyethylacrylamide in the matrix substantially improves the resolution of SSCP conformers and extends the coating lifetime. We investigated electrophoresis temperatures between 17 and 35 degrees C and found that the lowest temperature accessible on our chip electrophoresis system gives the best condition for high sensitivity of the tandem SSCP/HA method, especially for the SSCP conformers. Finally, the use of electrical fields between 350 and 450 V/cm provided rapid separations (<10 min) with well-resolved DNA peaks for both SSCP and HA.     

Single wall carbon nanotube amplification: en route to a type-specific growth mechanism

With the desire to mass produce any specific n,m type of single wall carbon nanotube (SWNT) from a small sample of the same material, we disclose here the preliminary work directed toward that goal. The ultimate protocol would involve taking a single n,m-type nanotube sample, cutting the nanotubes in that sample into many short nanotubes, using each of those short nanotubes as a template for growing much longer nanotubes of the same type, and then repeating the process. The result would be an amplification of the original tube type: a parent SWNT serving as the prolific progenitor of future identical SWNT types. As a proof-of-concept, we use here a short SWNT seed as a template for vapor liquid solid (VLS) amplification growth of an individual long SWNT. The original short SWNT seed was a polymer-wrapped SWNT, end-carboxylated, and further tethered with Fe salts at its ends. The Fe salts were to act as the growth catalysts upon subsequent reductive activation. Deposition of the short SWNT-Fe tipped species upon an oxide surface was followed by heating in air to consume the polymer wrappers, then reducing the Fe salts to Fe(0) under a H2-rich atmosphere. During this heating, the Fe(0) can etch back into the short SWNT so that the short SWNT acts as a template for new growth to a long SWNT that occurs upon introduction of C2H4 as a carbon source. Analysis indicated that the templated VLS-grown long SWNT had the same diameter and surface orientation as the original short SWNT seed, although amplifying the original n,m type remains to be proven. This study could pave the way for an amplified growth process of SWNTs en route to any n,m tube type synthesis from a starting sample of pure nanotubes.