Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

Cyclotetrabenzoin: Facile Synthesis of a Shape‐Persistent Molecular Square and Its Assembly into Hydrogen‐Bonded Nanotubes

Cyanide‐catalyzed benzoin condensation of terephthaldehyde produces a cyclic tetramer, which we propose to name cyclotetrabenzoin. Cyclotetrabenzoin is a square‐shaped macrocycle ornamented with four α‐hydroxyketone functionalities pointing away from the central cavity, the dimensions of which are 6.9×6.9 Å. In the solid state, these functional groups extensively hydrogen bond, resulting in a microporous three‐dimensional organic framework with one‐dimensional nanotube channels. This material exhibits permanent—albeit low‐porosity, with a Langmuir surface area of 52 m² g^?1. Cyclotetrabenzoin’s easy and inexpensive synthesis and purification may inspire the creation of other shape‐persistent macrocycles and porous molecular crystals by benzoin condensation.     

Formation of tryptanthrin compounds upon Oxone-induced dimerization of indole-3-carbaldehydes

Tryptanthrin is a natural product with numerous important pharmacological properties. Tryptanthrin and its analogs are commonly prepared by condensation of isatoic anhydride and isatin. In this Letter we investigate the formation of tryptanthrin derivatives upon Oxone-induced oxidative dimerization of indole-3-carbaldehydes.     

An fMRI study of magnitude comparison and exact addition in children

By contrast to the adult literature, in which a consistent parietofrontal network for number processing has been identified, the data from studies of number processing in children have been less consistent, probably due to differences in study design and control conditions. Number processing was examined using functional magnetic resonance imaging in 18 right-handed children (8–12 years) from the Cape Coloured community in Cape Town, South Africa, using Proximity Judgment and Exact Addition (EA) tasks. The findings were consistent with the hypothesis that, as in adults, the anterior horizontal intraparietal sulcus (HIPS) plays a major role in the representation and manipulation of quantity in children. The posterior medial frontal cortex, believed to be involved in performance monitoring in more complex arithmetic manipulations in adults, was extensively activated even for relatively simple symbolic number processing in the children. Other areas activated to a greater degree in the children included the left precentral sulcus, which may mediate number knowledge and, for EA, the head of the caudate nucleus, which is part of a fronto-subcortical circuit involved in the behavioral execution of sequences. Two regions that have been linked to number processing in adults — the angular gyrus and posterior superior parietal lobule — were not activated in the children. The data are consistent with the inference that although the functional specialization of the anterior HIPS may increase as symbolic number processing becomes increasingly automatic, this region and other elements of the parietofrontal network identified in adults are already reliably and robustly activated by middle childhood.     

Electrically driven oxygen separation through gadolinia-doped ceria using PrBaCo2O5?+?x and NdBaCo2O5?+?x electrodes

Oxygen gas can be electrochemically separated from ambient air with very high purity and compressed by using a solid-electrolyte ion-transport membrane. An electrolyte with high ionic conductivity such as gadolinium-doped ceria (CGO) and mixed conducting electrodes are used to construct the electrochemical cell. To achieve high oxygen flux, the electrodes must exhibit very fast electrode kinetics. Here, we report the performances of mixed conducting PrBaCo₂O_5 + x and NdBaCo₂O_5 + x electrodes in oxygen separation in a planar CGO electrolyte-supported cell. The properties of the electrode materials were evaluated using potentiostatic and potentiodynamic measurements and alternating current impedance spectroscopy. The oxygen flux was also measured using gas chromatography to confirm the absence of gas leaks. The electrodes demonstrated very low polarization resistances as a result of very high cathodic and anodic reaction rates at temperatures of 600–800 °C. High oxygen gas flow rates were observed on applying potentials up to 1 V with an almost linear relationship between the applied potential and the molar flow rate of oxygen gas.     

Characterization and optimization of heroin hapten-BSA conjugates: method development for the synthesis of reproducible hapten-based vaccines

A potential new treatment for drug addiction is immunization with vaccines that induce antibodies that can abrogate the addictive effects of the drug of abuse. One of the challenges in the development of a vaccine against drugs of abuse is the availability of an optimum procedure that gives reproducible and high yielding hapten-protein conjugates. In this study, a heroin/morphine surrogate hapten (MorHap) was coupled to bovine serum albumin (BSA) using maleimide-thiol chemistry. MorHap-BSA conjugates with 3, 5, 10, 15, 22, 28, and 34 haptens were obtained using different linker and hapten ratios. Using this optimized procedure, MorHap-BSA conjugates were synthesized with highly reproducible results and in high yields. The number of haptens attached to BSA was compared by 2,4,6-trinitrobenzenesulfonic acid (TNBS) assay, modified Ellman’s test and matrix assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS). Among the three methods, MALDI-TOF MS discriminated subtle differences in hapten density. The effect of hapten density on enzyme-linked immunosorbent assay (ELISA) performance was evaluated with seven MorHap-BSA conjugates of varying hapten densities, which were used as coating antigens. The highest antibody binding was obtained with MorHap-BSA conjugates containing 3–5 haptens. This is the first report that rigorously analyzes, optimizes and characterizes the conjugation of haptens to proteins that can be used for vaccines against drugs of abuse. The effect of hapten density on the ELISA detection of antibodies against haptens demonstrates the importance of careful characterization of the hapten density by the analytical techniques described.     

Sequential stochastic assignment under uncertainty: estimation and convergence

This paper generalizes the sequential stochastic assignment problem, involving the assignment of workers to sequentially arriving jobs, by introducing uncertainty into the job value distribution. Three estimators are presented that address various levels of uncertainty while simultaneously improving worker assignments. Specifically, each estimator is designed to utilize the unbiased and consistent properties of the sample mean to estimate the expected job value, while suppressing high variance effects during start-up. The key contribution is that closed-loop decision policies involving past job value observations can responsively adapt to changing environments and improve the overall reward resulting from pairing workers with jobs. Examples of applications that can benefit from these results include aviation passenger screening and the real estate market, as well as applications of the stochastic knapsack problem.     

The Molecular Composition of Soot

Soot (sometimes referred to as black carbon) is produced when hydrocarbon fuels are burned. Our hypothesis is that polynuclear aromatic hydrocarbon (PAH) molecules are the dominant component of soot, with individual PAH molecules forming ordered stacks that agglomerate into primary particles (PP). Here we show that the PAH composition of soot can be exactly determined and spatially resolved by low‐fluence laser desorption ionization, coupled with high‐resolution mass spectrometry imaging. This analysis revealed that PAHs of 239–838 Da, containing few oxygenated species, comprise the soot observed in an ethylene diffusion flame. As informed by chemical graph theory (CGT), the vast majority of species observed in the sampled particulate matter may be described as benzenoids, consisting of only fused 6‐membered rings. Within that limit, there is clear evidence for the presence of radical PAH in the particulate samples. Further, for benzenoid structures the observed empirical formulae limit the observed isomers to those which are nearly circular with high aromatic conjugation lengths for a given aromatic ring count. These results stand in contrast to recent reports that suggest higher aliphatic composition of primary particles.