Extreme value properties of multivariate t copulas

The extremal dependence behavior of t copulas is examined and their extreme value limiting copulas, called the t-EV copulas, are derived explicitly using tail dependence functions. As two special cases, the Hüsler–Reiss and the Marshall–Olkin distributions emerge as limits of the t-EV copula as the degrees of freedom go to infinity and zero respectively. The t copula and its extremal variants attain a wide range in the set of bivariate tail dependence parameters. Supported by NSERC Discovery Grant.     

Cayley graphs as classifiers for data mining: The influence of asymmetries

The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids.     

Do trumpet players tune resonances of the vocal tract?

The acoustic impedance spectrum was measured in the mouths of seven trumpeters while they played normal notes and while they practiced "bending" the pitch below or above the normal value. The peaks in vocal tract impedance usually had magnitudes rather smaller than those of the bore of the trumpet. Over the range measured, none of the trumpeters showed systematic tuning of the resonances of the vocal tract. However, all players commented that the presence of the impedance head in the mouth prevented them from playing the very highest notes of which they were normally capable. It is therefore possible that these players might use either resonance tuning or perhaps very high impedance magnitudes for some notes beyond the measured range. The observed lack of tuning contrasts with measurements for the saxophone which, like the trumpet, has weak resonances in the third and fourth octaves. Saxophonists are only able to play the highest range by tuning resonances of the vocal tract, so that the series impedance has a very strong peak at a frequency near that of the desired note. This difference is explained by the greater control that the trumpet player has over the natural frequency of the vibrating valve.     

Electron–phonon coupling and vibrational modes contributing to linear electro‐optic effect of the efficient NLO chromophore 4‐(N,N‐dimethylamino)‐N‐methyl‐4′‐toluene sulfonate (DAST) from their vibrational spectra

The optimized geometry and structural features of the most prospective electro‐optic crystal 4‐(N,N‐dimethylamino)‐N‐methyl‐4′‐toluene sulfonate (DAST), and the vibrational spectral investigations have been comprehensively described with the near infrared Fourier transform (NIR FT) Raman and Fourier transform infrared (FT‐IR) spectra supported by the density functional theoretical (DFT) computations to elucidate the contribution of vibrational modes to the linear electro‐optic (LEO) effect. Mulliken population analysis and natural bond orbital (NBO) analysis have also been carried out to analyze the effects of intramolecular charge transfer (ICT), intramolecular hydrogen bonding and hyperconjugative interactions on the geometries. The influence of CT interaction between the phenyl ring and the dimethylamino group of the nonlinear optical (NLO) chromophore on the endocyclic and exocyclic angles, and the electronic effects such as hyperconjugation and back‐donation on the methyl hydrogen atoms have been examined. The concurrent intense activation of Raman and IR activities of the effective conjugation vibrational coordinate, which significantly contributes to the LEO effect resulting from the strong electron–phonon (e/ph) coupling, has been analyzed in detail. The effects of frontier orbitals, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), transition of electron density (ED) transfer and the influence of planarity in the stilbazolium ring on the first hyperpolarizability are also discussed. Copyright © 2008 John Wiley & Sons, Ltd.