An extremal problem related to probability

Summary We consider a walk from a stateA ₁ to a stateA _n+1 in which the probability of remaining atA _i isp _i , and the probability of progressing fromA _i toA _i+1 is 1 –p _i . The probabilityW _nk of reachingA _n+1 fromA ₁ in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp ₁,,p _n . We determine the maximum value ofW _nk and the (unique) choice (p ₁,,p _n ) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

Activity of microemulsion-based nanoparticles at the human bio-nano interface: concentration-dependent effects on thrombosis and hemolysis in whole blood

Background: Although microemulsion-based nanoparticles (MEs) may be useful for drug delivery or scavenging, these benefits must be balanced against potential nanotoxicological effects in biological tissue (bio-nano interface). We investigated the actions of assembled MEs and their individual components at the bio-nano interface of thrombosis and hemolysis in human blood. Methods: Oil-in-water MEs were synthesized using ethylbutyrate, sodium caprylate, and pluronic F-68 (ME4) or F-127 (ME6) in 0.9% NaCl_w/v. The effects of MEs or components on thrombosis were determined using thrombo-elastography, platelet contractile force, clot elastic modulus, and platelet counting. For hemolysis, ME or components were incubated with erythrocytes, centrifuged, and washed for measurement of free hemoglobin by spectroscopy. Results and conclusions: The mean particle diameters (polydispersity index) for ME6 and ME4 were 23.6 ± 2.5 nm (0.362) and 14.0 ± 1.0 nm (0.008), respectively. MEs (0, 0.03, 0.3, 3 mM) markedly reduced the thromboelastograph maximal amplitude in a concentration-dependent manner (49.0 ± 4.2, 39.0 ± 5.6, 15.0 ± 8.7, 3.8 ± 1.3 mm, respectively), an effect highly correlated (r2 = 0.94) with similar changes caused by pluronic surfactants (48.7 ± 10.9, 30.7 ± 15.8, 20.0 ± 11.3, 2.0 ± 0.5) alone. Neither oil nor sodium caprylate alone affected the thromboelastograph. The clot contractile force was reduced by ME (27.3 ± 11.1–6.7 ± 3.4 kdynes/cm², P = 0.02, n = 5) whereas the platelet population not affected (175 ± 28–182 ± 23 10⁶/ml, P = 0.12, n = 6). This data suggests that MEs reduced platelet activity due to associated pluronic surfactants, but caused minimal changes in protein function necessary for coagulation. Although pharmacological concentrations of sodium caprylate caused hemolysis (EC₅₀ = 213 mM), MEs and pluronic surfactants did not disrupt erythrocytes. Knowledge of nanoparticle activity and potential associated nanotoxicity at this bio-nano interface enables rational ME design for in vivo applications.     

Discovery of structurally diverse natural product antagonists of chemokine receptor CXCR3

The chemokines (CXCL9, CXCL10 and CXCL11) and associated CXCR3 receptor are expressed during the inflammatory process from multiple sclerosis, atherosclerosis or organ transplantation resulting in the recruitment of lymphocytes leading to tissue damage. It is hypothesized that blocking of the ligand/CXCR3 receptor interaction has potential to provide opportunity for development of agents that would block tissue rejection. In this paper, four classes of natural product inhibitors (IC₅₀ ranging 0.1–41 M) have been described that block the CXCR3 receptor interaction of IP-10 ligand. These include a cyclic thiopeptide (duramycin), polyketide glycosides (roselipins), steroidal glycosides (hypoglausin A and dioscin) and a novel alkyl pyridinium alkaloid that were isolated by bioassay-guided fractionation of the organic extracts derived from actinomycete, fungal, plant and marine sources and discovered using ¹²⁵ I IP-10/CXCR3 binding assay. Duramycin was the most potent with an IC₅₀ of 0.1 M. Roselipins 2A, 2B and 1A showed IC₅₀ values of 14.6, 23.5, and 41 M, respectively. Diosgenin glycosides dioscin, hypoglaucin A and kallstroemin D exhibited IC₅₀ values of 2.1, 0.47 and 3 M, respectively. A novel cyclic 3-alkyl pyridinium salt isolated from a sponge displayed a binding IC₅₀ of 0.67 M.     

Critical bond lengths and their role in spontaneous magnetostriction of R2Fe17CX (R=Y,Nd, Gd,Tb, Er)

High-energy high-flux synchrotron X-rays have been used to study the spontaneous magnetostriction of R₂Fe₁₇ (R=Y, Nd, Gd, Tb, Er) and their carbides in the temperature range 10–1100 K. Addition of interstitial carbon greatly increases both the Curie temperatures (T_C) and the spontaneous magnetostrain of the compounds, while reduces the anisotropy of the magnetostrain by expanding the distances between rare-earth and neighboring Fe sites. The increase of T_C with carbon is due to the increased spatial separation of the Fe hexagon layers. On the basal plane, the Fe hexagons are squeezed and the contribution of Fe sublattice to spontaneous magnetostriction is attenuated, while that of rare-earth sublattice is enhanced. The average bond magnetostrain around Fe sites are in linear relation with their hyperfine field intensities.     

Raman spectroscopy of 3‐(pent‐1‐enyl) methyl ether and selected deuterium‐labelled analogues

The Raman spectra of 3‐(pent‐1‐enyl) methyl ether (3‐methoxypent‐1‐ene) and four deuterium‐labelled analogues are reported and discussed. Correlations between specific structural features and the associated Raman bands are developed, with a view to enhancing the analytical application of Raman spectroscopy in investigating materials containing an alkenyl group. Particular attention is given to developing means of distinguishing the methyl group attached to the carbon skeleton from that of the methoxy group, to maximize the analytical utility of the signals associated with ν(sp² CH), ν(sp² CH₂) and ν(CC) stretching vibrations, and to interpreting in more detail certain δ(sp² CH) and δ(sp² CH₂) vibrations of the atoms of the double bond. These results establish a definitive spectroscopic protocol for differentiating a methoxy group from a methyl substituent attached directly to a carbon atom in unsaturated ethers. Copyright © 2007 John Wiley & Sons, Ltd.     

First measurement of the double spin asymmetry in (-->)e(-->)p-->e(prime)pi(+)n in the resonance region

The double spin asymmetry in the (-->)e(-->)p --> e(prime)pi(+)n reaction has been measured for the first time in the resonance region for four-momentum transfer Q2 = 0.35-1.5 GeV(2). Data were taken at Jefferson Lab with the CLAS detector using a 2.6 GeV polarized electron beam incident on a polarized solid NH3 target. Comparison with predictions of phenomenological models shows strong sensitivity to resonance contributions. Helicity-1/2 transitions are found to be dominant in the second and third resonance regions. The measured asymmetry is consistent with a faster rise with Q(2) of the helicity asymmetry A1 for the F(15)(1680) resonance than expected from the analysis of the unpolarized data.     

Spectral baseline ripple in hot-electron bolometer mixers due to local oscillator phase and amplitude instabilities

High resolution millimetre and submillimetre wave astronomical spectrometers using hot-electron bolometer mixers as detectors often show marked standing wave patterns in the spectral baseline. LO phase noise contributes through two mechanisms: the phase noise side-bands may be converted to amplitude noise in the source because of the power-frequency characteristic of the source, or they can be converted to in-band amplitude noise through the action of the quasi-optical discriminator formed by the mixer, beam-splitter and telescope structure. The baseline ripple components due to each of these mechanisms have different characteristic periods, and under some circumstances can dominate the spectrometer baseline. The ripple levels estimated using the theory agree well with those observed in practice. It is shown that with careful design systematic effects due to this cause can be reduced to a negligible level.     

Study of a carbon dioxide ring laser gyroscope

We have experimentally investigated a basic ring laser gyroscope (RLG) with carbon dioxide gain, and studied the prospects of developing a practical CO₂ RLG. Rotation sensing was demonstrated on a number of transitions in the 9.4 m and 10.4 m vibration-rotation bands. Gyro response is discussed with regard to lock-in, bias, homogeneous broadening effects, and high power operation. We show that such a system may offer important advantages over standard helium-neon RLGs, including reduced quantum limit and backscattering. The prospects and possible approaches for developing a practical high power CO₂ RLG are discussed, and a method of eliminating cross-saturation at high pressure is proposed and analyzed.