Periodic 2-graphs arising from subshifts

Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz-Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whose $C^*$-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we call \emph{domino graphs}. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the $C^*$-algebras of domino graphs.Comment: 17 page

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Eye-Safe Solid-State Quasi-CW Raman Laser with Millisecond Pulse Duration

We demonstrate the first quasi-CW (ms-long pulses, pump duty cycle of 10%) end-diode pumped solid state laser generating eye-safe radiation via intracavity Raman conversion. The output power at the first Stokes wavelength (1524 nm) was 250 mW. A theoretical model was applied to analyze the laser system and provide routes for optimization. The possibility of true CW operation was discussed.Comment: Preprint accepted for publication in Optics Communications on Feb 6, 201

C*-algebras of labelled graphs II - Simplicity results

We prove simplicity and pure infiniteness results for a certain class of labelled graph $C^*$-algebras. We show, by example, that this class of unital labelled graph $C^*$-algebras is strictly larger than the class of unital graph $C^*$-algebras.Comment: 18 pages, 4 figure

FACTORS INFLUENCING THE STRESS-STRAIN BEHAVIOR OF CERAMIC MATERIALS.

The stress-strain behavior of ceramic materials is greatly influenced by microstructural features ranging from the presence of point defects in single crystals to the size and location of pores and nature of grain boundaries in polycrystals. Several factors may affect the behavior at anyone time, and the analysis of experimental data, particularly for polycrystals, is thus extremely difficult. This review examines the interpretation of mechanical behavior in materials having the rock salt structure, with particular emphasis on the role of impurities, the significance of grain boundary and/or intragranular porosity, and the problems associated with the intersection of slip bands. <br/

Twisted k-graph algebras associated to Bratteli diagrams

Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory and the gauge-invariant semifinite traces of the resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-R{\o}rdam-Sims.Comment: 28 pages, pictures prepared using tik

A family of 2-graphs arising from two-dimensional subshifts

Higher-rank graphs (or $k$-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz-Krieger $C^*$-algebras of Robertson and Steger. Here we consider a family of finite 2-graphs whose path spaces are dynamical systems of algebraic origin, as studied by Schmidt and others. We analyse the $C^*$-algebras of these 2-graphs, find criteria under which they are simple and purely infinite, and compute their $K$-theory. We find examples whose $C^*$-algebras satisfy the hypotheses of the classification theorem of Kirchberg and Phillips, but are not isomorphic to the $C^*$-algebras of ordinary directed graphs.Comment: 28 pages, 3 figures, 1 tabl

First observation of two hyperfine transitions in antiprotonic He-3

We report on the first experimental results for microwave spectroscopy of the hyperfine structure of antiprotonic He-3. Due to the helium nuclear spin, antiprotonic He-3 has a more complex hyperfine structure than antiprotonic He-4 which has already been studied before. Thus a comparison between theoretical calculations and the experimental results will provide a more stringent test of the three-body quantum electrodynamics (QED) theory. Two out of four super-super-hyperfine (SSHF) transition lines of the (n,L)=(36,34) state were observed. The measured frequencies of the individual transitions are 11.12559(14) GHz and 11.15839(18) GHz, less than 1 MHz higher than the current theoretical values, but still within their estimated errors. Although the experimental uncertainty for the difference of these frequencies is still very large as compared to that of theory, its measured value agrees with theoretical calculations. This difference is crucial to be determined because it is proportional to the magnetic moment of the antiproton.Comment: 8 pages, 6 figures, just published (online so far) in Physics Letters

ATRX has a critical and conserved role in mammalian sexual differentiation

BACKGROUND X-linked alpha thalassemia, mental retardation syndrome in humans is a rare recessive disorder caused by mutations in the ATRX gene. The disease is characterised by severe mental retardation, mild alpha-thalassemia, microcephaly, short stature, facial, skeletal, genital and gonadal abnormalities. RESULTS We examined the expression of ATRX and ATRY during early development and gonadogenesis in two distantly related mammals: the tammar wallaby (a marsupial) and the mouse (a eutherian). This is the first examination of ATRX and ATRY in the developing mammalian gonad and fetus. ATRX and ATRY were strongly expressed in the developing male and female gonad respectively, of both species. In testes, ATRY expression was detected in the Sertoli cells, germ cells and some interstitial cells. In the developing ovaries, ATRX was initially restricted to the germ cells, but was present in the granulosa cells of mature ovaries from the primary follicle stage onwards and in the corpus luteum. ATRX mRNA expression was also examined outside the gonad in both mouse and tammar wallaby whole embryos. ATRX was detected in the developing limbs, craniofacial elements, neural tissues, tail and phallus. These sites correspond with developmental deficiencies displayed by ATR-X patients. CONCLUSIONS There is a complex expression pattern throughout development in both mammals, consistent with many of the observed ATR-X syndrome phenotypes in humans. The distribution of ATRX mRNA and protein in the gonads was highly conserved between the tammar and the mouse. The expression profile within the germ cells and somatic cells strikingly overlaps with that of DMRT1, suggesting a possible link between these two genes in gonadal development. Taken together, these data suggest that ATRX has a critical and conserved role in normal development of the testis and ovary in both the somatic and germ cells, and that its broad roles in early mammalian development and gonadal function have remained unchanged for over 148 million years of mammalian evolution.This study was supported by a National Health and Medical Research Council R D Wright Fellowship to AJP the Australian Research Council Centre of Excellence in Kangaroo Genomics and a Federation Fellowship to MBR

Structural optimization of reversible dibromomaleimide peptide stapling

Methods to constrain peptides in a bioactive α‐helical conformation for inhibition of protein‐protein interactions represent an ongoing area of investigation in chemical biology. Recently, the first example of a reversible “stapling” methodology was described which exploits native cysteine or homocysteine residues spaced at the i and i + 4 positions in a peptide sequence together with the thiol selective reactivity of dibromomaleimides (a previous study). This manuscript reports on the optimization of the maleimide based constraint, focusing on the kinetics of macrocyclization and the extent to which helicity is promoted with different thiol containing amino acids. The study identified an optimal stapling combination of X1 = L‐Cys and X5 = L‐hCys in the context of the model peptide Ac‐X1AAAX5‐NH2, which should prove useful in implementing the dibromomaleimide stapling strategy in peptidomimetic ligand discovery programmes