657 research outputs found

    Periodicity in Rank 2 Graph Algebras

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    Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of \ca(\Fth). The periodic C*-algebras are characterized, and it is shown that \ca(\Fth) \simeq \rC(\bT) \otimes \fA where \fA is a simple C*-algebra.Comment: 27 page

    Wavelets and graph C∗C^*-algebras

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    Here we give an overview on the connection between wavelet theory and representation theory for graph C∗C^{\ast}-algebras, including the higher-rank graph C∗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

    Placental expression of pituitary hormones is an ancestral feature of therian mammals

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    <p>Abstract</p> <p>Background</p> <p>The placenta is essential for supplying nutrients and gases to the developing mammalian young before birth. While all mammals have a functional placenta, only in therian mammals (marsupials and eutherians) does the placenta closely appose or invade the uterine endometrium. The eutherian placenta secretes hormones that are structurally and functionally similar to pituitary growth hormone (GH), prolactin (PRL) and luteinizing hormone (LH). Marsupial and eutherian mammals diverged from a common ancestor approximately 125 to 148 million years ago and developed distinct reproductive strategies. As in eutherians, marsupials rely on a short-lived but functional placenta for embryogenesis.</p> <p>Results</p> <p>We characterized pituitary GH, GH-R, IGF-2, PRL and LHβ in a macropodid marsupial, the tammar wallaby, <it>Macropus eugenii</it>. These genes were expressed in the tammar placenta during the last third of gestation when most fetal growth occurs and active organogenesis is initiated. The mRNA of key growth genes GH, GH-R, IGF-2 and PRL were expressed during late pregnancy. We found significant up-regulation of GH, GH-R and IGF-2 after the start of the rapid growth phase of organogenesis which suggests that the placental growth hormones regulate the rapid phase of fetal growth.</p> <p>Conclusions</p> <p>This is the first demonstration of the existence of pituitary hormones in the marsupial placenta. Placental expression of these pituitary hormones has clearly been conserved in marsupials as in eutherian mammals, suggesting an ancestral origin of the evolution of placental expression and a critical function of these hormones in growth and development of all therian mammals.</p

    Relationship between the Molecular Structure and Switching Temperature in a Library of Spin-Crossover Molecular Materials

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    Structure–function relationships relating the spin-crossover (SCO) midpoint temperature (T1/2) in the solid state are surveyed for 43 members of the iron(II) dipyrazolylpyridine family of SCO compounds. The difference between T1/2 in the solid state and in solution [ΔT(latt)] is proposed as a measure of the lattice contribution to the transition temperature. Negative linear correlations between the SCO temperature and the magnitude of the rearrangement of the coordination sphere during SCO are evident among isostructural or near-isostructural subsets of compounds; that is, a larger change in the molecular structure during SCO stabilizes the high-spin state of a material. Improved correlations are often obtained when ΔT(latt), rather than the raw T1/2 value, is considered as the measure of the SCO temperature. Different lattice types show different tendencies to stabilize the high-spin or low-spin state of the molecules they contain, which correlates with the structural changes that most influence ΔT(latt) in each case. These relationships are mostly unaffected by the SCO cooperativity in the compounds or by the involvement of any crystallographic phase changes. One or two materials within each subset are outliers in some or all of these correlations, however, which, in some cases, can be attributed to small differences in their ligand geometry or unusual phase behavior during SCO. A reinvestigation of the structural chemistry of [Fe(3-bpp)2][NCS]2·nH2O [3-bpp = bis(1H-pyrazol-3-yl)pyridine; n = 0 or 2], undertaken as part of this study, is also presented

    Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations

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    The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory (DFT) in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics, and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALBs requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic

    Twisted k-graph algebras associated to Bratteli diagrams

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    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

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

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    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

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    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

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

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    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
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