Asymptotics in the random assignment problem

Summary We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.Research supported by NSF Grant MCS90-01710     

Finite-time implications of relaxation times for stochastically monotone processes

Summary For a continuous-time finite state Markov process with stationary distribution , it is well-known thatP ⁱ (X ^t =j)- ^j isO(e ^-t ) ast, for a certain . For a stochastically monotone process for which the reversed process is also stochastically monotone, one can obtain bounds valid for allt. Precisely, exp(-t). The proof exploits duality for stochastically monotone processes.Research supported by National Science Foundation Grant MCS 84-03239     

A general strategy for the diastereoselective synthesis of 2,6-diaryl-3,7-dioxabicyclo[3.3.0]octane lignans

A strategy for the stereoselective synthesis of all the possible diastereoisomers of the 2,6-diaryl-3,7-dioxabicyclo[3.3.0]octane (furofuran) lignans from a single dihydrofuran precursor is described. The key steps involve a diastereocontrolled templated cationic cyclization followed by stereoselective reduction of the resulting methyl glycoside.     

Asymptotics for Euclidean minimal spanning trees on random points

Summary Asymptotic results for the Euclidean minimal spanning tree onn random vertices inR ^d can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in allR ^d. In particular we prove a conjecture of Robert Bland: the sum of thed'th powers of the edge-lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofR ^d tends to a constant asn.Whether the limit forest is in fact a single tree is a hard open problem, relating to continuum percolation.Research supported by N.S.F. Grants MCS87-11426 and MCS 90-01710Research supported in part by N.S.F. Grant DMS88-12868, A.F.O.S.R. Grant 89-0301, ARO Grant DAAL03-89-G-0092 and NSA Grant MDA-904-H-2034     

Analysis of polyfluoroalkyl substances and bisphenol A in dried blood spots by liquid chromatography tandem mass spectrometry

Dried blood spots (DBS), collected as part of the newborn screening program (NSP) in the USA, is a valuable resource for studies on environmental chemical exposures and associated health outcomes in newborns. Nevertheless, determination of concentrations of environmental chemicals in DBS requires assays with great sensitivity, as the typical volume of blood available on a DBS with 16-mm diameter disc is approximately 50 μL. In this study, we developed a liquid–liquid extraction and high-performance liquid chromatography/tandem mass spectrometry method for the detection of perfluorooctanesulfonate (PFOS), perfluorooctanoate (PFOA), and bisphenol A (BPA) in DBS. The method was validated for accuracy, precision, and sensitivity, by spiking of target chemicals at different levels on Whatman 903 filter cards, which is used in the collection of DBS by the NSP. Contamination arising from collection, storage, and handling of DBS is an important issue to be considered in the analysis of trace levels of environmental chemicals in DBS. For the evaluation of the magnitude of background contamination, field blanks were prepared from unspotted portions of DBS filter cards collected by the NSP. The method was applied for the measurement of PFOS, PFOA, and BPA in 192 DBS specimens provided by NSP of New York State. PFOS and PFOA were detected in 100 % of the specimens analyzed. The concentrations of PFOS and PFOA measured in DBS were similar to those reported earlier in the whole blood samples of newborns. BPA was also found in 86 % of the specimens at concentrations ranging from 0.2 to 36 ng/mL (excluding two outliers). Further studies are needed to evaluate the sources of BPA exposures and health outcomes in newborns.     

Polyphenolics with Strong Antioxidant Activity from Acacia nilotica Ameliorate Some Biochemical Signs of Arsenic-Induced Neurotoxicity and Oxidative Stress in Mice

Neurotoxicity is a serious health problem of patients chronically exposed to arsenic. There is no specific treatment of this problem. Oxidative stress has been implicated in the pathological process of neurotoxicity. Polyphenolics have proven antioxidant activity, thereby offering protection against oxidative stress. In this study, we have isolated the polyphenolics from Acacia nilotica and investigated its effect against arsenic-induced neurotoxicity and oxidative stress in mice. Acacia nilotica polyphenolics prepared from column chromatography of the crude methanol extract using diaion resin contained a phenolic content of 452.185 ± 7.879 mg gallic acid equivalent/gm of sample and flavonoid content of 200.075 ± 0.755 mg catechin equivalent/gm of sample. The polyphenolics exhibited potent antioxidant activity with respect to free radical scavenging ability, total antioxidant activity and inhibition of lipid peroxidation. Administration of arsenic in mice showed a reduction of acetylcholinesterase activity in the brain which was counteracted by Acacia nilotica polyphenolics. Similarly, elevation of lipid peroxidation and depletion of glutathione in the brain of mice was effectively restored to normal level by Acacia nilotica polyphenolics. Gallic acid methyl ester, catechin and catechin-7-gallate were identified in the polyphenolics as the major active compounds. These results suggest that Acacia nilotica polyphenolics due to its strong antioxidant potential might be effective in the management of arsenic induced neurotoxicity.     

The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results

We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have been studied in physics as simple exemplars of systems exhibiting slow relaxation. In our East model the natural conjecture is that the relaxation time (p), that is 1/(spectral gap), satisfies log (p) as p0. We prove this up to a factor of 2. The upper bound uses the Poincaré comparison argument applied to a wave (long-range) comparison process, which we analyze by probabilistic techniques. Such comparison arguments go back to Holley (1984, 1985). The lower bound, which atypically is not easy, involves construction and analysis of a certain coalescing random jumps process.     

Some optical studies with the air-acetylene flame

The application of Schlieren and shadow techniques for the study of flame processes is discussed in relation to analytically useful premixed flames. The information obtained, particularly with shadowgraphs, may be correlated with the measured signals and signal noise in atomic-absorption and flame-emission spectrometry.     

The dihydrofuran template approach to furofuran synthesis

Flash vacuum pyrrolysis of vinyl epoxides provides cis-dihydrofuran carboxylic esters in good yields and diastereoselectivities, which, on base-promoted epimerisation afford the complementary trans series. The compounds provide a viable template for a Lewis acid promoted cyclisation to provide the 2,6-diaryl-3,7-dioxabicyclo[3.3.0]octane core found in the furofuran series of natural lignans. This strategy is stereodivergent and can be controlled to provide the exo-exo, exo-endo or endo-endo stereochemistries. The approach has been exemplified in syntheses of the sesamyl furofurans (+/-)-epiasarinin and (+/-)-asarinin.     

Using XPS to determine solute solubility in room temperature ionic liquids

X-Ray Photoelectron Spectroscopy (XPS) was used to quantify the amount of bromide ions present in two samples of [C(4)mpyrr]Br dissolved in the room temperature ionic liquid (RTIL) [C(4)mpyrr][N(Tf)2]. One sample was of a known concentration (0.436 Br atom%); the other was a saturated solution. The results obtained from quantitative XPS analysis indicated that the saturated sample had a concentration, or solubility, of 0.90 Br atom% (746 mM) at 298 K, which was then independently confirmed by potential-step chronoamperometry of the same solution.