The changing of the guard: Molecular diversity and rapid evolution of β-defensins

Summary Defensins are small cationic peptides involved in innate immunity and are components of the first line of defence against invading pathogens. β-defensins are a subgroup of the defensin family that display a particular cysteine spacing and pattern of intramolecular bonding. These molecules are produced mostly by epithelia lining exposed surfaces and appear to have both antimicrobial and cell signalling functions. The unusually high degree of sequence variation in the mature peptide produced by the paralogous and in some cases orthologous genes implies extensive specialisation and species specific adaptation. Here we review recent functional data that are an important addition to our knowledge of the innate immune response and novel antibiotic design. We also consider the organisation and evolution of the genomic loci harbouring these genes where radical and rapid changes in β-defensin sequences have been shown to result from the interplay of both positive and negative selection. Consequently these genes provide some unusually clear glimpses of the processes of duplication and specialisation that have shaped the mammalian genome.     

Quantitative description of the T1 formation kinetics in an Al–Cu–Li alloy using differential scanning calorimetry,small-angle X-ray scattering and transmission electron microscopy

The object of the present study is to design a methodology to follow the kinetics of T₁ precipitation, in an AA2198 alloy, in terms of precipitate size, morphology (thickness, diameter) and volume fraction, during a two-temperature isothermal heat treatment. We used in situ small-angle X-ray scattering (SAXS) as a way to measure the evolution of the T₁ mean thickness and diameter during the heat treatment. Transmission electron microscopy (TEM) was then performed in order to calibrate these evolutions. Furthermore, we demonstrate that the volume fraction evolution can be described successfully using a simple analysis of the differential scanning calorimetry (DSC) thermograms. The latter was calibrated by selected observations in high angular annular dark field scanning transmission electron microscopy (HAADF-STEM). Microstructure evolution during DSC heating ramps was analysed using in situ SAXS: the T₁ phase transformation is found to consist in a two-step thickening process explained by two consecutive diffusion stages. The enthalpy of formation of the T₁ phase is deduced from the DSC measurements.     

Synthesis and catalytic properties of microemulsion-derived cerium oxide nanoparticles

The synthesis of cerium dioxide nanoparticles using an inverse microemulsion technique and precipitation method was investigated. Cerium hydroxide nanoparticles were synthesized by adding diluted ammonia to n-heptane–surfactant–cerium nitrate system. The micelle and particle size in the range of 5–12 nm were controlled by varying the molar water to surfactant ratio and analyzed by dynamic light scattering (DLS), small angle X-ray scattering (SAXS) and high-resolution transmission electron microscopy (HRTEM). Cerium hydroxide nanoparticles were isolated and subsequently treated at 100–600 °C to obtain nanoscale ceria. Crystallite sizes of cerium dioxide in the range of 6–16 nm were estimated by Scherrer analysis by X-ray diffraction (XRD) and HRTEM. The catalytic activity of particles annealed at 400 and 600 °C in soot combustion reactions was characterized by temperature-programmed oxidation (TPO) indicating a size-dependant activity. Crystallite sizes and catalytic stability of elevated ceria systems were tested in second combustion cycles.     

A TQFT Associated to the LMO Invariant of Three-Dimensional Manifolds

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup of the Mapping Class Group that contains the Torelli group. The N = 1 truncation is a TQFT for the Casson-Walker-Lescop invariant. The results of this article were obtained when the authors were at the Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA.     

Note on the Net Retention Volume in Chromatography with a Real Gas as a Carrier

The problem of the calculation and interpretation of the net retention volume with a real gas as carrier is revisited. The properties of the carrier are described by a first order virial equation of state. The net retention volume of a solute is related to the mean flow rate of the carrier, therefore determination of the mean flow rate of a real gas carrier is reviewed. It is shown that the mean flow rate cannot be calculated from the mean column pressure. With a real gas carrier the local capacity factor depends on the local pressure of the real gas. The basic relationship between the net retention volume and the function describing this pressure dependence is also reviewed. Precise formulae as well as practical approximations are presented for the calculation of the mean flow rate, of the mean column pressure, and of a representative pressure related to the mean capacity factor.     

Covariant Representations for Matrix-valued Transfer Operators

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on if the weight satisfies some low-pass condition.      

Immediate extensions of filtered rings

Summary A separated filtered ring has a maximally complete immediate extension. This is an analogue of Krull Theorem from valuation ring theory in the frame of filtered rings.

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Riassunto Un anello separato filtrato ha una immediata estensione massimale completa. Questo risultato è un analogo del teorema di Krull della teoria degli anelli di valutazione nell’ambito degli anelli filtrati.