An ordering of dependence for contingency tables

A majorization ordering is defined on matrices with the same row and column sums. This ordering is used as an ordering of dependence for contingency tables. Results are derived for maximal and minimal matrices with respect to the majorization ordering. This theory can be used to maximize and minimize Schur concave functions defined over matrices, when there are row and column sum constraints; in this paper, it is applied to the algorithm of Mehta and Patel (1983) for finding the P-value of Fisher's exact test.     

Index Reduction Formulas for Twisted Flag Varieties, II

This is a continuation of the determination begun in K-Theory 10 (1996), 517–596, of explicit index reduction formulas for function fields of twisted flag varieties of adjoint semisimple algebraic groups. We give index reduction formulas for the varieties associated to the classical simple groups of outer type A _n-1 and D _n, and the exceptional simple groups of type E ₆ and E ₇. We also give formulas for the varieties associated to transfers and direct products of algebraic groups. This allows one to compute recursively the index reduction formulas for the twisted flag varieties of any semi-simple algebraic group.     

Scale-invariant correlations in dynamic bacterial clusters

In Bacillus subtilis colonies, motile bacteria move collectively, spontaneously forming dynamic clusters. These bacterial clusters share similarities with other systems exhibiting polarized collective motion, such as bird flocks or fish schools. Here we study experimentally how velocity and orientation fluctuations within clusters are spatially correlated. For a range of cell density and cluster size, the correlation length is shown to be 30% of the spatial size of clusters, and the correlation functions collapse onto a master curve after rescaling the separation with correlation length. Our results demonstrate that correlations of velocity and orientation fluctuations are scale invariant in dynamic bacterial clusters.     

Activity of Compounds from Temperate Propolis against Trypanosoma brucei and Leishmania mexicana

Ethanolic extracts of samples of temperate zone propolis, four from the UK and one from Poland, were tested against three Trypanosoma brucei strains and displayed EC₅₀ values < 20 µg/mL. The extracts were fractionated, from which 12 compounds and one two-component mixture were isolated, and characterized by NMR and high-resolution mass spectrometry, as 3-acetoxypinobanksin, tectochrysin, kaempferol, pinocembrin, 4′-methoxykaempferol, galangin, chrysin, apigenin, pinostrobin, cinnamic acid, coumaric acid, cinnamyl ester/coumaric acid benzyl ester (mixture), 4′,7-dimethoxykaempferol, and naringenin 4′,7-dimethyl ether. The isolated compounds were tested against drug-sensitive and drug-resistant strains of T. brucei and Leishmania mexicana, with the highest activities ≤ 15 µM. The most active compounds against T. brucei were naringenin 4′,7 dimethyl ether and 4′methoxy kaempferol with activity of 15–20 µM against the three T. brucei strains. The most active compounds against L. mexicana were 4′,7-dimethoxykaempferol and the coumaric acid ester mixture, with EC₅₀ values of 12.9 ± 3.7 µM and 13.1 ± 1.0 µM. No loss of activity was found with the diamidine- and arsenical-resistant or phenanthridine-resistant T. brucei strains, or the miltefosine-resistant L. mexicana strain; no clear structure activity relationship was observed for the isolated compounds. Temperate propolis yields multiple compounds with anti-kinetoplastid activity.     

Second-order nonlinear optical properties of side-chain liquid crystalline polymers studied by second harmonic generation from thin films

The two independent elements of the second-order nonlinear optical susceptibility tensor of a range of contact poled, donor–acceptor substitued side-chain polymers are reported. The susceptibilities were measured by second harmonic generation from thin films, typically less than 0.5 μm thick, at a fundamental wavelength of 1064 nm. The largest value was χ = 2.64 pm/V which is three times greater than the χ value of KDP and was measured in a nitrobenzylidene side chain, polyhydroxystyrene polymer with an eleven unit alkyl chain spacer attaching the side group to the backbone. Typical susceptibility values obtained were χ～0.3 pm/V and X⁽²⁾₃₃～1 pm/V. The coherence lengths of the materials, which lay in the range 4–12 μm, were measured at 1064 nm by the maker fringe technique using thick, wedge-shaped samples.     

Synthesis,structure and characterization of [Mg7(μ3-OCH2CH2OMe)6(μ-OCH2CH2OMe)6][Al(n-Bu)4]2 – A cationic heptanuclear magnesium complex consisting of discrete cations and tetrabutylaluminate anions

Dibutylmagnesium (contaminated with Al(n-Bu)₃; n_Mg:n_Al ca. 1:0.2) was found to react with MeOCH₂CH₂OH followed by the addition of PhSCH(Me)Ph in the presence of 0.2 equiv n-butyllithium yielding [Mg₇(μ₃-OCH₂CH₂OMe)₆(μ-OCH₂CH₂OMe)₆][Al(n-Bu)₄]₂ (1) as the principal product (yield 40–45% referred to MeOCH₂CH₂OH). The single-crystal X-ray diffraction analysis revealed that the centrosymmetric cationic heptamagnesium complex is built up from seven edge-shared MgO₆ octahedra. The [Al(n-Bu)₄]⁻ anions adopt approximately a tetrahedral AlC₄ symmetry. ¹H, ¹³C and ²⁷Al NMR spectroscopic measurements showed that in THF solution the structures both of the heptamagnesium complex and the tetrabutylaluminate anion are preserved and that there are no cation–anion interactions reducing the symmetry. The ²⁷Al resonance (151.6 ppm) was found to be very sharp (w_1/2 = 5 Hz), the coupling constant ¹J(²⁷Al,¹³C) amounts to 72.3 Hz.     

Effect of sorbed methanol, current, and temperature on multicomponent transport in nafion-based direct methanol fuel cells

The CO2 in the cathode exhaust of a liquid feed direct methanol fuel cell (DMFC) has two sources: methanol diffuses through the membrane electrode assembly (MEA) to the cathode where it is catalytically oxidized to CO2; additionally, a portion of the CO2 produced at the anode diffuses through the MEA to the cathode. The potential-dependent CO2 exhaust from the cathode was monitored by online electrochemical mass spectrometry (ECMS) with air and with H2 at the cathode. The precise determination of the crossover rates of methanol and CO2, enabled by the subtractive normalization of the methanol/air to the methanol/H2 ECMS data, shows that methanol decreases the membrane viscosity and thus increases the diffusion coefficients of sorbed membrane components. The crossover of CO2 initially increases linearly with the Faradaic oxidation of methanol, reaches a temperature-dependent maximum, and then decreases. The membrane viscosity progressively increases as methanol is electrochemically depleted from the anode/electrolyte interface. The crossover maximum occurs when the current dependence of the diffusion coefficients and membrane CO2 solubility dominate over the Faradaic production of CO2. The plasticizing effect of methanol is corroborated by measurements of the rotational diffusion of TEMPONE (2,2,6,6-tetramethyl-4-piperidone N-oxide) spin probe by electron spin resonance spectroscopy. A linear inverse relationship between the methanol crossover rate and current density confirms the absence of methanol electro-osmotic drag at concentrations relevant to operating DMFCs. The purely diffusive transport of methanol is explained in terms of current proton solvation and methanol-water incomplete mixing theories.     

Mechanism of carotenoid singlet excited state energy transfer in modified bacterial reaction centers

Ultrafast transient laser spectroscopy has been used to investigate carotenoid singlet excited state energy transfer in various Rhodobacter (Rb.) sphaeroides reaction centers (RCs) modified either genetically or chemically. The pathway and efficiency of energy transfer were examined as a function of the structures and energies of the donor and acceptor molecules. On the donor side, carotenoids with various extents of pi-electron conjugation were examined. RCs studied include those from the anaerobically grown wild-type strain containing the carotenoid spheroidene, which has 10 conjugated carbon-carbon double bonds; the GA strain containing neurosporene, which has nine conjugated double bonds; and aerobically grown wild-type cells, as well as aerobically grown H(M182)L mutant, both containing the carbonyl-containing carotenoid spheroidenone, which has 11 conjugated double bonds. By varying the structure of the carotenoid, we observed the effect of altering the energies of the carotenoid excited states on the rate of energy transfer. Both S(1)- and S(2)-mediated carotenoid-to-bacteriochlorophyll energy transfer processes were observed. The highest transfer efficiency, from both the S(1) and S(2) states, was observed using the carotenoid with the shortest chain. The S(1)-mediated carotenoid-to- bacteriochlorophyll energy transfer efficiencies were determined to be 96%, 84%, and 73% for neurosporene, spheroidene, and spheroidenone, respectively. The S(2)-mediated energy transfer efficiencies follow the same trend but could not be determined quantitatively because of limitations in the time resolution of the instrumentation. The dependence of the energy transfer rate on the energetics of the energy transfer acceptor was verified by performing measurements with RCs from the H(M182)L mutant. In this mutant, the bacteriochlorophyll (denoted B(B)) located between the carotenoid and the RC special pair (P) is replaced by a bacteriopheophytin (denoted phi(B)), where the Q(X) and Q(Y) bands of phi(B) are 1830 and 1290 cm(-1), respectively, higher in energy than those of B(B). These band shifts associated with phi(B) in the H(M182)L mutant significantly alter the spectral overlap between the carotenoid and phi(B), resulting in a significant decrease of the transfer efficiency from the carotenoid S(1) state to phi(B). This leaves energy transfer from the carotenoid S(2) state to phi(B) as the dominant channel. Largely because of this change in mechanism, the overall efficiency of energy transfer from the carotenoid to P decreases to less than 50% in this mutant. Because the spectral signature of phi(B) is different from that of B(A) in this mutant, we were able to demonstrate clearly that the carotenoid-to-P energy transfer is via phi(B). This finding supports the concept that, in wild-type RCs, the carotenoid-to-P energy transfer occurs through the cofactor located at the B(B) position.     

Polynuclear lanthanide complexes of a series of bridging ligands containing two tridentate N,N',O-donor units: structures and luminescence properties

A set of three potentially bridging ligands containing two tridentate chelating N,N',O-donor (pyrazole-pyridine-amide) donors separated by an o, m, or p-phenylene spacer has been prepared and their coordination chemistry with lanthanide(III) ions investigated. Ligand L(1) (p-phenylene spacer) forms complexes with a 2:3 M:L ratio according to the proportions used in the reaction mixture; the Ln(2)(L(1))(3) complexes contain two 9-coordinate Ln(III) centres with all three bridging ligands spanning both metal ions, and have a cylindrical (non-helical) 'mesocate' architecture. The 1:1 complexes display a range of structural types depending on the conditions used, including a cyclic Ln(4)(L(1))(4) tetranuclear helicate, a Ln(2)(L(1))(2) dinuclear mesocate, and an infinite one-dimensional coordination polymer in which metal ions and bridging ligands alternate along the sequence. ESMS studies indicate that the 1:1 complexes form a mixture of oligonuclear species {Ln(L(1))}(n) in solution (n up to 5) which are likely to be cyclic helicates. In contrast, ligands L(2) and L(3) (with o- and m-phenylene spacers, respectively) generally form dinuclear Ln(2)L(2) Ln(III) complexes in which the two ligands may be arranged in a helical or non-helical architecture about the two metal ions. These complexes also contain an additional exogenous bidentate bridging ligand, either acetate or formate, which has arisen from hydrolysis of solvent molecules promoted by the Lewis-acidity of the Ln(III) ions. Luminescence studies on some of the Nd(III) complexes showed that excitation into ligand-centred pi-pi* transitions result in the characteristic near-infrared luminescence from Nd(III) at 1060 nm.