Norms of characters and lacunarity for compact Lie groups

This article gives upper and lower estimates for the p-norms of irreducible characters of compact Lie groups in terms of their dimension. These estimates are applied to give some new results on lacunary sets.     

The contraction of K to NM

By studying the contraction of K to $\text{N}\text{M}$ inside the Iwasawa decomposition of a semisimple Lie group of real rank 1, we realize the representations of $\text{NM}$ as limits of representations of K, obtaining in particular, limiting formulas for matrix entries.     

Two families of analytic γ-plots and their influence upon homogeneous nucleation kinetics

The equilibrium shapes corresponding to two different families of γ-plots are constructed. One γ-plot family comprises continuous variations from a sphere to an oblate ellipsoid. This set of γ-plots yields a sharp edge in the corresponding equilibrium shape when its aspect ratio is less than $\text{1}\text{√2}$. The other family consists of nephroids of revolution, varied in cross-sectional form from two slightly overlapping near-circles to an ellipse-like morphology. This family exhibits a facet at one boundary orientation in the equilibrium shape. For the analytical expression of the equilibrium shape, the ξ-vector formalism of Cahn and Hoffman is used and found to give results identical to those from the Euler-Lagrange method. The effects of the variations in equilibrium shape within the two families treated upon the principal parameters in the general equation for the time-dependent rate of nucleation are assessed in order to ascertain their relative influence on nucleation kinetics.     

Duration discrimination of steady and gliding tones: a new method for estimating sensitivity to rate of change

Thresholds for the detection of differences in duration were measured in a two-alternative, forced-choice task for four types of signals, all centered at 2000 Hz: (1) sinusoids fixed in frequency and level; (2) sinusoids of fixed frequency whose level was swept up or down by 5 or 10 dB; (3) sinusoids of fixed level whose frequency was swept up or down by 100 Hz; and (4) sinusoids whose level was swept up or down by 10 dB and whose frequency was swept up or down by 100 Hz. For types (2)-(4), the direction of the sweeps was fixed within a run. The duration of the standard was either fixed at 750 ms or was varied randomly from trial to trial by up to +/- 7% about 750 ms. The duration of the comparison signal was initially 100 ms greater than that of the standard and was varied adaptively to determine threshold. The pattern of results was similar for all four subjects tested. Duration-discrimination thresholds for the signals that were swept in level and/or frequency were lower than those for the fixed signal, typically by 15-20 ms. This indicates that subjects were sensitive to the rate of change of frequency and/or level and could use this as a cue for duration discrimination. The Weber fraction for rate of change was estimated to be about 0.05-0.06 and was similar for changes in level and in frequency.     

NMR determination of the conformation of a trimethylene interstrand cross-link in an oligodeoxynucleotide duplex containing a 5'-d(GpC) motif

Malondialdehyde interstrand cross-links in DNA show strong preference for 5'-d(CpG) sequences. The cross-links are unstable and a trimethylene cross-link has been used as a surrogate for structural studies. A previous structural study of the 5'-d(CpG) cross-link in the sequence 5'-d(AGGCGCCT), where G is the modified nucleotide, by NMR spectroscopy and molecular dynamics using a simulated annealing protocol showed the guanine residues and the tether lay approximately in a plane such that the trimethylene tether and probably the malondialdehyde tether, as well, could be accommodated without major disruptions of duplex structure [Dooley et al. J. Am Chem. Soc. 2001, 123, 1730-1739]. The trimethylene cross-link has now been studied in a GpC motif using the reverse sequence. The structure lacks the planarity seen with the 5'-d(CpG) sequence and is skewed about the trimethylene cross-link. Melting studies indicate that the trimethylene cross-link is thermodynamically less stable in the GpC motif than in the 5-d(CpG). Furthermore, lack of planarity of the GpC cross-link precludes making an isosteric replacement of the trimethylene tether by malondialdehyde. A similar argument can be used to explain the 5'-d(CpG) preference for interchain cross-linking by acrolein.     

Characterization of the copper-sulfur chromophores in nitrous oxide reductase by resonance raman spectroscopy: evidence for sulfur coordination in the catalytic cluster.

Nitrous oxide reductase (N(2)OR) from Pseudomonas stutzeri, a dimeric enzyme with a canonical metal ion content of at least six Cu ions per subunit, contains two types of multinuclear copper sites: Cu(A) and Cu(Z). An electron-transfer role for the dinuclear Cu(A) site is indicated based on its similarity to the Cu(A) site in cytochrome c oxidase (CcO), a dicysteinate-bridged, mixed-valence cluster. The Cu(Z) site is the catalytic site, which had long been thought to have novel spectroscopic properties. However, the low-energy electronic transitions and resonance Raman features attributable to Cu(Z) have been difficult to reconcile with a lack of conserved cysteine residues in standard alignments of N(2)OR sequences, other than those associated with the Cu(A) site. Recent evidence indicates that nitrous oxide reductase contains acid-labile sulfide and that this sulfide is a constituent of the Cu(Z) site (Rasmussen, T.; Berks, B. C.; Sanders-Loehr, J.; Dooley, D. M.; Zumft, W. G.; Thomson, A. J. Biochemistry 2000, 39, 12753-12756). We have used resonance Raman (RR) spectroscopy to selectively probe the Cu(A) and Cu(Z) sites of N(2)OR in three oxidation states (oxidized, semireduced, and reduced) as well as Cu(A)-only and Cu(Z)-only variants. The Cu(A) (mixed-valence, also designated as A(mv)) RR spectrum exhibits 10 vibrational modes between 220 and 410 cm(-1), with >1-cm(-1) (34)S isotope shifts that sum to -16.6 cm(-1). Many of these modes are also sensitive to (65)Cu and (15)N(His) and, thus, can be assigned to coupling of the Cu-S stretch, nu(Cu-S), with cysteine and histidine vibrations of the Cu(2)Cys(2)His(2) core. The RR spectrum of the Cu(Z) site (Z(ox)) reveals a novel Cu-sulfur chromophore with four S isotope-sensitive modes at 293, 347, 352, and 408 cm(-1), with a total (34)S shift of -19.9 cm(-)(1). The magnitude of the S isotope shifts and wide spread of perturbed frequencies are similar to those observed in Cu(A) and therefore suggest a sulfur-bridged cluster in Z(ox). The Z(ox) site has its nu(Cu-S)-containing modes at higher energy and exhibits less mixing with ligand deformations, compared to Cu(A). Reduction by dithionite produces a mixed-valence Cu(Z) site (Z(mv)) with six S isotope-sensitive RR modes between 282 and 382 cm(-1) and a total (34)S-shift of -16.9 cm(-1). The observation of a nearly identical RR spectrum in the C622D variant of N(2)OR, which lacks one of the conserved Cu(A) Cys residues, establishes that Cu-S vibrations observed in this variant arise from the Z(mv) site. Furthermore, none of the features assigned to Cu(Z) are detected in a second variant that contains only Cu(A). Therefore the resonance Raman spectra reported here provide compelling evidence for a unique Cu-S cluster in the catalytic site of nitrous oxide reductase.     

RNA-templated semiconductor nanocrystals

The use of a biomolecular RNA template for the synthesis of CdS semiconductor nanocrystals is described. Transfer RNA, with a well-defined three-dimensional structure, is used as a scaffold and ligand system in the aqueous synthesis of CdS. We have found that nanocrystal structures can be modulated by the structure of the templating tRNA. When possessing a folded three-dimensional structure, tRNA-templated synthesis yields a single product. If the same tRNA is rendered unstructured through the introduction of destabilizing mutations, a range of products are observed. The results reported indicate that biomolecules can be used to systematically engineer the structures and properties of semiconductor-based materials, and that the synergy between the dimensions of nanostructures and biomolecules provides a means to tune the properties of materials with nanoscale precision.     

Nonsingular dynamical systems,Bratteli diagrams and Markov odometers

We prove that any ergodic non-singular transformation is orbit equivalent to a Markov odometer which is uniquely ergodic.     

Absolute pitch correlates with high performance on interval naming tasks

Absolute pitch, the rare ability to identify or produce a musical tone without a reference tone, has been shown to be advantageous in some musical tasks; however, its relevance in musical contexts primarily involving relative pitch has been questioned. To explore this issue, 36 trained musicians-18 absolute pitch possessors and 18 non-possessors with equivalent age of onset and duration of musical training-were tested on interval naming tasks requiring only relative pitch. The intervals to be named were either ascending or descending with separation ranging from 1 to 12 semitones and equally involved all 12 pitch classes. Three different conditions were employed; these used brief sine waves, piano tones, and piano tones preceded by a V7-I chord cadence so as to establish a tonal context. The possession of absolute pitch was strongly correlated with enhanced performance on all these tests of relative pitch. Furthermore, no evidence was found that this absolute pitch avantage depended on key, interval size, or musical context.