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

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

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

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

Angular sensitivity of blowfly photoreceptors: intracellular measurements and wave-optical predictions

The angular sensitivity of blowfly photoreceptors was measured in detail at wavelengths λ = 355, 494 and 588 nm. The measured curves often showed numerous sidebands, indicating the importance of diffraction by the facet lens. The shape of the angular sensitivity profile is dependent on wavelength. The main peak of the angular sensitivities at the shorter wavelengths was flattened. This phenomenon as well as the overall shape of the main peak can be quantitatively described by a wave-optical theory using realistic values for the optical parameters of the lens-photoreceptor system. At a constant response level of 6 mV (almost dark adapted), the visual acuity of the peripheral cells R1-6 is at longer wavelengths mainly diffraction limited, while at shorter wavelengths the visual acuity is limited by the waveguide properties of the rhabdomere. Closure of the pupil narrows the angular sensitivity profile at the shorter wavelengths. This effect can be fully described by assuming that the intracellular pupil progressively absorbs light from the higher order modes. In light-adapted cells R1-6 the visual acuity is mainly diffraction limited at all wavelengths.

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

Preliminary Results from Recent Measurements of the Antiprotonic Helium Hyperfine Structure

We report on preliminary results from a systematic study of the hyperfine (HF) structure of antiprotonic helium. This precise measurement which was commenced in 2006, has now been completed. Our initial analysis shows no apparent density or power dependence and therefore the results can be averaged. The statistical error of the observable M1 transitions is a factor of 60 smaller than that of three body quantum electrodynamic (QED) calculations, while their difference has been resolved to a precision comparable to theory (a factor of 10 better than our first measurement). This difference is sensitive to the antiproton magnetic moment and agreement between theory and experiment would lead to an increased precision of this parameter, thus providing a test of CPT invariance.Comment: 6 pages, 4 figure

Self-renewal of single mouse hematopoietic stem cells is reduced by JAK2V617F without compromising progenitor cell expansion

Recent descriptions of significant heterogeneity in normal stem cells and cancers have altered our understanding of tumorigenesis, emphasizing the need to understand how single stem cells are subverted to cause tumors. Human myeloproliferative neoplasms (MPNs) are thought to reflect transformation of a hematopoietic stem cell (HSC) and the majority harbor an acquired V617F mutation in the JAK2 tyrosine kinase, making them a paradigm for studying the early stages of tumor establishment and progression. The consequences of activating tyrosine kinase mutations for stem and progenitor cell behavior are unclear. In this article, we identify a distinct cellular mechanism operative in stem cells. By using conditional knock-in mice, we show that the HSC defect resulting from expression of heterozygous human JAK2V617F is both quantitative (reduced HSC numbers) and qualitative (lineage biases and reduced self-renewal per HSC). The defect is intrinsic to individual HSCs and their progeny are skewed toward proliferation and differentiation as evidenced by single cell and transplantation assays. Aged JAK2V617F show a more pronounced defect as assessed by transplantation, but mice that transform reacquire competitive self-renewal ability. Quantitative analysis of HSC-derived clones was used to model the fate choices of normal and JAK2-mutant HSCs and indicates that JAK2V617F reduces self-renewal of individual HSCs but leaves progenitor expansion intact. This conclusion is supported by paired daughter cell analyses, which indicate that JAK2-mutant HSCs more often give rise to two differentiated daughter cells. Together these data suggest that acquisition of JAK2V617F alone is insufficient for clonal expansion and disease progression and causes eventual HSC exhaustion. Moreover, our results show that clonal expansion of progenitor cells provides a window in which collaborating mutations can accumulate to drive disease progression. Characterizing the mechanism(s) of JAK2V617F subclinical clonal expansions and the transition to overt MPNs will illuminate the earliest stages of tumor establishment and subclone competition, fundamentally shifting the way we treat and manage cancers

Continuous-wave Raman laser pumped within a semiconductor disk laser cavity

A KGd(WO4)(2) Raman laser was pumped within the cavity of a cw diode-pumped InGaAs semiconductor disk laser (SDL). The Raman laser threshold was reached for 5: 6W of absorbed diode pump power, and output power up to 0.8W at 1143nm, with optical conversion efficiency of 7.5% with respect to the absorbed diode pump power, was demonstrated. Tuning the SDL resulted in tuning of the Raman laser output between 1133 and 1157nm