Supercharacters,symmetric functions in noncommuting variables,and related Hopf algebras

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.     

Intermolecular energy transfer across nanocrystalline semiconductor surfaces

The yields and dynamics for energy transfer from the metal-to-ligand charge-transfer excited states of Ru(deeb)(bpy)(2)(PF(6))(2), Ru(2+), and Os(deeb)(bpy)(2)(PF(6))(2), Os(2+), where deeb is 4,4'-(CH(3)CH(2)CO(2))(2)-2,2'-bipyridine, anchored to mesoporous nanocrystalline (anatase) TiO(2) thin films were quantified. Lateral energy transfer from Ru(2+)* to Os(2+) was observed, and the yields were measured as a function of the relative surface coverage and the external solvent environment (CH(3)CN, THF, CCl(4), and hexanes). Excited-state decay of Ru(2+)*/TiO(2) was well described by a parallel first- and second-order kinetic model, whereas Os(2+)*/TiO(2) decayed with first-order kinetics within experimental error. The first-order component was assigned to the radiative and nonradiative decay pathways (tau = 1 micros for Ru(2+)*/TiO(2) and tau = 50 ns for Os(2+)*/TiO(2)). The second-order component was attributed to intermolecular energy transfer followed by triplet-triplet annihilation. An analytical model was derived that allowed determination of the fraction of excited-states that follow the two pathways. The fraction of Ru(2+)*/TiO(2) that decayed through the second-order pathway increased with surface coverage and excitation intensity. Monte Carlo simulations were performed to estimate the Ru(2+)* --> Ru(2+) intermolecular energy transfer rate constant of (30 ns)(-1).     

Spectre et homologie des variétés hyperboliques complexes de congruenceSpectrum and homology of congruence complex hyperbolic manifolds

In the first part of this Note, we show that the first non-zero eigenvalue of the Laplace operator on 1-forms of a standard congruence arithmetic complex hyperbolic n-manifold is always $\text{?}\text{10n?11}\text{25}$. The following parts of this Note concern homological applications of this result. We prove, in particular, that if Sh⁰H?Sh⁰G are two Shimura varieties of type U(n?1,1) and U(n,1), the natural map H_2n?3(Sh⁰H)→H_2n?3(Sh⁰G) is injective, first step of a “Lefschetz theorem” for Shimura varieties. To cite this article: N. Bergeron, L. Clozel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 995–998.     

Identification of EZH2 and EZH1 Small Molecule Inhibitors with Selective Impact on Diffuse Large B Cell Lymphoma Cell Growth

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Constrained optimization in cartesian coordinates

Modifications are made to a previously published algorithm for constrained optimization in Cartesian coordinates (J. Comp. Chem., 13 , 240, 1992) to incorporate both fixed and dummy atoms. Standard distance and angle constraints can now be specified with respect to dummy atoms, greatly extending the range of constraints that can be handled. Fixed atoms can be eliminated from the optimization space and so there is no need to calculate their gradients resulting in potentially significant savings of CPU time in ab initio computations. Several examples illustrate the range and versatility of the modified algorithm. © John Wiley & Sons, Inc.     

Interfacial microgels formed by oppositely charged polyelectrolytes and surfactants. 1. Influence of polyelectrolyte molecular weight

The synergistic adsorption and complexation of polystyrene sulfonate, PSS (a highly charged anionic polyelectrolyte), and dodecyltrimethylammonium bromide, C12TAB (a cationic surfactant), at the air-water interface can lead to interfacial gels that strongly influence foam-film drainage and stability. The formation and characteristics of these gels have been studied as a function of PSS molecular weight by combining surface tension, ellipsometry, and foam-film drainage experiments. Simultaneously the solution electromotive force has been measured to track the polymer-surfactant interactions in the bulk solution. It has been found that there is a critical molecular weight for surface gelation as well as for bulk precipitation and aggregation. Furthermore, we show that for the lowest molecular weights, PSS adsorbs with C12TAB in compact layers at the air-water interface. In particular, for mixtures of C12TAB with the monomer compound of the PSS repeat unit (e.g. Mw = 208), interfacial complexation is found to be similar to that of catanionic mixtures (mixtures of surfactants of opposite charge).     

Trans-limonene dioxide,a promising bio-based epoxy monomer

Vast quantities of the natural terpene (R)-limonene can be collected from food waste. Epoxidation of its two double bonds provides limonene dioxide (LDO), a difunctional epoxy monomer. However, LDO is a mixture of four isomers, two of which (trans-LDO) are actually difunctional while the others (cis-LDO) have one epoxide group which is significantly less reactive, as revealed by Fourier transformed infrared spectroscopic analysis of formulations cross-linked with polyethylene imine. These results are also confirmed when preparing epoxy formulations using respectively cis or trans isomers. From DFT calculations, the reactivity of each epoxide group of LDO has been assessed in model reactions with primary and secondary amines, in the presence of amine or alcohol hydrogen-bond donors. The kinetics of cross-linking has also been probed by differential scanning calorimetry. As measured by dynamic mechanical analysis, the resulting epoxy resins based on trans isomers have a storage modulus of ca 1GPa at room temperature and a glass transition temperature (T_g) of 70°C. These results demonstrate that trans LDO is a promising bio-based epoxy monomer, which could be used as an alternative to petroleum-based epoxy monomers.     

Exploiting domain knowledge for improved quantitative high-throughput screening curve fitting

Least-squares fitting of the Hill equation to quantitative high-throughput screening (qHTS) assays results in frequent unsatisfactory fits. We learn and exploit prior knowledge to improve the Hill fitting in a nonlinear regression method called domain knowledge fitter (DK-fitter). This paper formulates and solves DK-fitter for 44 public qHTS data sets. This new Hill parameter estimation technique is validated using three unbiased approaches, including a novel method that involves generating simulated samples. This paper fosters the extraction of higher quality information from screens for improved potency evaluation.     

Spatially inhomogeneous enhancement of fluorescence by a monolayer of silver nanoparticles

Near-field scanning optical microscopy (NSOM) was applied to study the effect of a two-dimensional array of silver nanoparticles on the spatial distribution and magnitude of fluorescence signal enhancement for a monolayer of Rhodamine 6G (Rh6G). Twenty polyelectrolyte monolayers were deposited between the nanoparticles and the dye by a layer-by-layer deposition technique resulting in a 15-20 nm separation cushion, necessary to minimize the fluorescence signal quenching. The fluorescence signal in NSOM images was found to be distributed inhomogeneously as small (100-200 nm in diameter) fluorescent clusters with typically 5-30 times higher fluorescence intensities than a sample without nanoparticles. The position and relative intensity of the clusters was found to be dependent on the excitation wavelength, suggesting that the enhancement originates from the nanoparticle surface plasmon resonance.