The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

Multifunctional ToF-SIMS: combinatorial mapping of gradient energy substrates

We present a simple method for chemical modification of chlorosilane self-assembled monolayers (SAMs) on Si surfaces by exposure to a gradient of UV-ozone radiation to create stable substrates with a range of contact angles (θ_H2O≈5–95°) and surface energies on a single substrate. These gradient energy substrates are developed to potentially generate libraries for combinatorial studies of thin film phenomenology, where a systematic variation of interfacial surface energy represents one of the significant parameters along one axis. The graded oxidation process presents a systematic variation of surface chemical composition. We have utilized contact angle measurements and time-of-flight secondary ion mass spectrometry (ToF-SIMS) to investigate this variation for a series of ions, among which are SiCH₃⁺, SiOH⁺ and COOH⁻. We show that the macroscopic measurements of surface free energy/contact angle correlate with the detailed analysis of surface chemistry (as assessed by ToF-SIMS) on these test substrates.     

Construction of multiporphyrin arrays using ruthenium and rhodium coordination to phosphines

The synthesis of linear multiporphyrin arrays with mono- and bisphosphine-substituted porphyrins as ligand donors and ruthenium(II) or rhodium(III) porphyrins as ligand acceptors is described. With appropriate amounts of the building blocks mixed, linear dimeric and trimeric arrays have been synthesized and analyzed by (1)H NMR and (31)P NMR spectroscopy. The Ru/Rh acceptor porphyrins can be located either at the periphery or in the center of the array. Likewise, the monophosphine porphyrins can be positioned at the periphery, thus allowing a high degree of freedom in the overall composition of the arrays. This way, both donor and acceptor porphyrins can act as chain extenders or terminators. One of the trimeric complexes with two nickel and one ruthenium porphyrin has also been analyzed by X-ray crystallography. Attempts have also been made to synthesize higher order arrays by mixing appropriate amounts of the porphyrins; however, from the NMR data it cannot be concluded if monodisperse five, seven, or nine porphyrin arrays are present or if the solutions are composed of a statistical mixture of smaller and larger arrays.     

Synthetic erythropoietic proteins: tuning biological performance by site-specific polymer attachment

Chemical synthesis in combination with precision polymer modification allows the systematic exploration of the effect of protein properties, such as charge and hydrodynamic radius, on potency using defined, homogeneous conjugates. A series of polymer-modified synthetic erythropoiesis proteins were constructed that had a polypeptide chain similar to the amino acid sequence of human erythropoietin but differed significantly in the number and type of attached polymers. The analogs differed in charge from +5 to -26 at neutral pH and varied in molecular weight from 30 to 54 kDa. All were active in an in vitro cell proliferation assay. However, in vivo potency was found to be strongly dependent on overall charge and size. The trends observed in this study may serve as starting points for the construction of more potent synthetic EPO analogs in the future.     

The effect of reduction on rhenium(I) complexes with binaphthyridine and biquinoline ligands: a spectroscopic and computational study

A number of rhenium complexes with binaphthyridine and biquinoline ligands have been synthesized and studied. These are [Re(L)(CO)3Cl] where L = 3,3'-dimethylene-2,2'-bi-1,8-naphthyridine (dbn), 2,2'-bi-1,8-naphthyridine (bn), 3,3'-dimethylene-2,2'-biquinoline (dbq), and 3,3'-dimethyl-2,2'-biquinoline (diq). This series represents ligands in which the electronic properties and steric preferences are tuned. These complexes are modeled using density functional theory (DFT). An analysis of the resonance Raman spectra for these complexes, in concert with the vibrational assignments, reveals that the accepting molecular orbital (MO) in the metal-to-ligand charge transfer (MLCT) transition is the LUMO and causes bonding changes at the inter-ring section of the ligand. The electronic absorption spectroelectrochemistry for the reduced complexes of [Re(dbn)(CO)3Cl], [Re(dbq)(CO)3Cl], and [Re(diq)(CO)3Cl] suggest that the singly occupied MO is delocalized over the entire ligand structure despite the nonplanar nature of the diq ligand in [Re(diq)(CO)3Cl]. The IR spectroelectrochemistry for [Re(dbn)(CO)3Cl], [Re(dbq)(CO)3Cl], and [Re(bn)(CO)3Cl] reveal that reduction lowers the CO ligand vibrational frequencies to a similar extent in all three complexes. The substitution of naphthyridine for quinoline has little effect on the nature of the singly occupied MO. These data are supported by DFT calculations on the reduced complexes, which reveal that the ligands are flattened out by reduction: This may explain the similarity in the properties of the reduced complexes.     

Stereoselective Synthesis of Diaminosuberic Acid Via a Chiral Alkynyl Oxazolidine

A novel, stereoselective synthesis of enantiomerically pure, N-protected diaminosuberic acid (6) is presented. The key step in the synthesis is the oxidative dimerization of the chiral alkynyl oxazolidine (2).     

Styrene-PEG (600) DMA Crosslinked Polymers for Absorption of Oil Derivatives

In this work, styrene (St) based crosslinked polymers were prepared for removal of oil derivatives from aqueous solutions. Polyethylene glycol (600) dimethacrylate (PEG (600) DMA) was used as crosslinker in synthesis of styrene based crosslinked polymers, for the first time. The polymers were characterized by FTIR, SEM, elemental analysis and solvent (toluene, chloroform and fuel-oil) absorption capacities. The effects of different reaction parameters like crosslinker type, diluents amount and the presence of pore forming agent on the absorption properties of polymers were investigated. The polymers synthesized by using PEG (600) DMA have higher solvent absorption capacity than that of synthesized by using conventional crosslinker. Furthermore, the polymers synthesized in the presence of good diluents have higher absorption capacities. The addition of pore forming agent into the reaction medium has also improved the absorption rate of polymers. The absorption capacity of polymers in different solvents is in order of chloroform > toluene > fuel-oil. It was seen that oil derivatives can be removed efficiently from water by the St-PEG (600) DMA polymers.     

Taylor dispersion monitored by electrospray mass spectrometry: a novel approach for studying diffusion in solution

This work describes a novel approach for monitoring analyte diffusion in solution that is based on electrospray ionization mass spectrometry (ESI-MS). A mass spectrometer at the end of a laminar flow tube is used to measure the Taylor dispersion of an initially sharp boundary between two solutions of different analyte concentration. This boundary is dispersed by the laminar flow profile in the tube. However, this effect is diminished by analyte diffusion that continuously changes the radial position, and hence the flow velocity of individual analyte molecules. The steepness of the resulting dispersion profile therefore increases with increasing diffusion coefficient of the analyte. A theoretical framework is developed to adapt the equations governing the dispersion process to the case of mass spectrometric detection. This novel technique is applied to determine the diffusion coefficients of choline and cytochrome c. The measured diffusion coefficients, (11.9 +/- 1.0) x 10(-10) m(2) s(-1) and (1.35 +/- 0.08) x 10(-10) m(2) s(-1), respectively, are in agreement with the results of control experiments where the Taylor dispersion of these two analytes was monitored optically. Due to the inherent selectivity and sensitivity of ESI-MS, it appears that the approach described in this work could become a valuable alternative to existing methods for studying diffusion processes, especially for experiments on multicomponent systems.     

Amplification of a cyclic mixed-metalloporphyrin tetramer from a dynamic combinatorial library through orthogonal metal coordination

A cyclic porphyrin tetramer, consisting of two bis-phosphine substituted zinc(II) porphyrin units and two Rh(III)TPP units, is selected and amplified virtually quantitatively from a dynamic combinatorial library using 4,4'-bipy as a scaffold and using orthogonal binding modes.     

A family of macrocyclic antibiotics with a mixed peptide-peptoid beta-hairpin backbone conformation

Macrocyclic peptidomimetics having a mixed peptide-peptoid backbone have been synthesized and shown to possess antibiotic activity against gram-positive and -negative bacteria with a low hemolytic activity against human erythrocytes; one is shown to adopt a regular beta-hairpin conformation by NMR in aqueous solution.