De Bruijn cycles for covering codes

A de Bruijn covering code is a q‐ary string S so that every q‐ary string is at most R symbol changes from some n‐word appearing consecutively in S. We introduce these codes and prove that they can have size close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R = 11 and n = 13, followed by several open questions in this area. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Weak matching rules for quasicrystals

Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in perp-space are uniformly bounded. It is shown here that weak matching rules exist forN-fold symmetric tilings, whereN is any integer not divisible by four. The result suggests that, contrary to previous indications, quasicrystalline ground states are not confined to those symmetries for which the incommensurate ratios of wavevectors are quadratic irrationals. An explicit method of constructing weak matching rules forN-fold symmetric tilings in two dimensions is presented. It is shown that the generalization of the construction yields weak matching rules in the case of icosahedral symmetry as well.     

Synthesis of dityrosine cross-linked peptide dimers using the Miyaura-Suzuki reaction

[reaction: see text] Since peroxidase-catalyzed dityrosine formation is inefficient for peptides, we have developed alternative conditions for intermolecular dityrosine formation using the Miyaura-Suzuki reaction. A one-pot reaction is effective for cross-linking short peptides, but longer peptides inhibit the Suzuki step, mandating a traditional two-step procedure using potassium acetate for the Miyaura reaction and potassium carbonate for the Suzuki coupling. These palladium-based methods are complementary to the well-established peroxidase-catalyzed oxidative phenolic coupling of full-length proteins.     

Measurable supports,reducible spaces and the structure of the optimal σ-field in unbiased estimation

This paper generalizes a result bySapozhnikov relating the structure of the optimal -field in unbiased estimation to the reducibility of certain linear subspaces of estimators. For this purpose, the concept of a measurable support of (uncountably infinite) sets consisting of random variables is introduced, which could be of general interest. It turns out, that for a wide class of measure spaces, measurable supports of any subsets of measurable functions exist.     

OPTICAL AND THERMAL CHARACTERIZATION OF NATURAL (Sepia officinalis) MELANIN

Abstract The optical properties and the thermal diffusivity of natural cuttlefish ( Sepia officinalis ) melanin have been measured. The optical absorption and scattering properties of melanin particles were determined at 580 nm and 633 nm, using photometric and photothermal techniques. For the photometric studies, the absorption and the transport scattering coefficients were determined from the measurements of diffuse reflectance and transmittance. The scattering anisotropy was obtained from an additional measurement of the total attenuation coefficient and independently obtained by goniometry. For photothermal studies, pulsed photothermal radiometry was used to deduce the absorption and transport scattering coefficients via a model based on optical diffusion theory. Pulsed photothermal radiometry was also used to provide the thermal diffusivity of solid melanin pressed pellets.     

Formation of [b(n−1)+OH+H]+ ion structural analogs by solution-phase chemistry

Derivatization of a variety of peptides by a method known to enhance anhydride formation is demonstrated by mass spectrometry to yield ions that have elemental composition and fragmentation properties identical to [b(n-1) + OH + H]+ ions formed by gas-phase rearrangement and fragmentation. The [b(n-1) + OH + H]+ ions formed by gas-phase rearrangement and fragmentation and the solution-phase [b(n-1) + OH + H]+ ion structural analogs formed by derivatization chemistry show two different forms of dissociation using multiple-collision CAD in a quadrupole ion trap and unimolecular decomposition in a TOF-TOF; one group yields identical product ions as a truncated form of the peptide with a free C-terminal carboxylic acid and fragments at the same activation energy; the other group fragments differently from the truncated peptide, being more resistant to fragmentation than the truncated peptide and yielding primarily the [b(n-2) + OH + H]+ product ion. Nonergodic electron capture dissociation MS/MS suggests that any structural differences between the specific-fragmenting [b(n-1) + OH + H]+ ions and the truncated peptide is at the C-terminus of the peptide. The specific-fragmentation can be readily observed by MS(n) experiments to occur in an iterative fashion, suggesting that the C-terminal structure of the original [b(n-1) + OH + H]+ ion is maintained after subsequent rearrangement and fragmentation events in peptides which fragment specifically. A mechanism for the formation of specific-fragmenting and nonspecific-fragmenting [b(n-1) + OH + H]+ ions is proposed.