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

On some fundamental results about higher-rank graphs and their C*-algebras

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated to a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph {\Lambda} is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of infinite-path spaces when the k-graph is row finite with no sources. We conclude with a short direct proof of the characterisation, originally due to Robertson and Sims, of simplicity of the C*-algebra of a row-finite k-graph with no sources.Comment: 21 pages, two pictures prepared using TiK

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.

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

Specialized odorant receptors in social insects that detect cuticular hydrocarbon cues and candidate pheromones.

Eusocial insects use cuticular hydrocarbons as components of pheromones that mediate social behaviours, such as caste and nestmate recognition, and regulation of reproduction. In ants such as Harpegnathos saltator, the queen produces a pheromone which suppresses the development of workers' ovaries and if she is removed, workers can transition to a reproductive state known as gamergate. Here we functionally characterize a subfamily of odorant receptors (Ors) with a nine-exon gene structure that have undergone a massive expansion in ants and other eusocial insects. We deorphanize 22 representative members and find they can detect cuticular hydrocarbons from different ant castes, with one (HsOr263) that responds strongly to gamergate extract and a candidate queen pheromone component. After systematic testing with a diverse panel of hydrocarbons, we find that most Harpegnathos saltator Ors are narrowly tuned, suggesting that several receptors must contribute to detection and discrimination of different cuticular hydrocarbons important in mediating eusocial behaviour.Cuticular hydrocarbons (CHC) mediate the interactions between individuals in eusocial insects, but the sensory receptors for CHCs are unclear. Here the authors show that in ants such as H. saltator, the 9-exon subfamily of odorant receptors (HsOrs) responds to CHCs, and ectopic expression of HsOrs in Drosophila neurons imparts responsiveness to CHCs

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-repair ability of evolved self-assembling systems in cellular automata

Self-repairing systems are those that are able to reconfigure themselves following disruptions to bring them back into a defined normal state. In this paper we explore the self-repair ability of some cellular automata-like systems, which differ from classical cellular automata by the introduction of a local diffusion process inspired by chemical signalling processes in biological development. The update rules in these systems are evolved using genetic programming to self-assemble towards a target pattern. In particular, we demonstrate that once the update rules have been evolved for self-assembly, many of those update rules also provide a self-repair ability without any additional evolutionary process aimed specifically at self-repair

Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method

We use the effective-mass approximation and the density-functional theory with the local-density approximation for modeling two-dimensional nano-structures connected phase-coherently to two infinite leads. Using the non-equilibrium Green's function method the electron density and the current are calculated under a bias voltage. The problem of solving for the Green's functions numerically is formulated using the finite-element method (FEM). The Green's functions have non-reflecting open boundary conditions to take care of the infinite size of the system. We show how these boundary conditions are formulated in the FEM. The scheme is tested by calculating transmission probabilities for simple model potentials. The potential of the scheme is demonstrated by determining non-linear current-voltage behaviors of resonant tunneling structures.Comment: 13 pages,15 figure

Improved Study of the Antiprotonic Helium Hyperfine Structure

We report the initial results from a systematic study of the hyperfine (HF) structure of antiprotonic helium (n,l) = (37,~35) carried out at the Antiproton Decelerator (AD) at CERN. We performed a laser-microwave-laser resonance spectroscopy using a continuous wave (cw) pulse-amplified laser system and microwave cavity to measure the HF transition frequencies. Improvements in the spectral linewidth and stability of our laser system have increased the precision of these measurements by a factor of five and reduced the line width by a factor of three compared to our previous results. A comparison of the experimentally measured transition frequencies with three body QED calculations can be used to determine the antiproton spin magnetic moment, leading towards a test of CPT invariance.Comment: 14 pages 9 figure