217,582 research outputs found

    Abelian varieties over finite fields as basic Abelian varieties

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    Simple mass formulas on Shimura varieties of PEL-type

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    Kottwitz-Rapoport strata in the Siegel moduli spaces

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    Why Study Noise due to Two Level Systems: A Suggestion for Experimentalists

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    Noise is often considered to be a nuisance. Here we argue that it can be a useful probe of fluctuating two level systems in glasses. It can be used to: (1) shed light on whether the fluctuations are correlated or independent events; (2) determine if there is a low temperature glass or phase transition among interacting two level systems, and if the hierarchical or droplet model can be used to describe the glassy phase; and (3) find the lower bound of the two level system relaxation rate without going to ultralow temperatures. Finally we point out that understanding noise due to two level systems is important for technological applications such as quantum qubits that use Josephson junctions.Comment: 15 pages, 4 figures, Latex, to be published in J. Low Temp. Phys. issue in honor of S. Hunklinge

    Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties

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    Critical behavior of quasi-two-dimensional semiconducting ferromagnet CrGeTe3_3

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    The critical properties of the single-crystalline semiconducting ferromagnet CrGeTe3_3 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β=0.200±0.003\beta = 0.200\pm0.003 with critical temperature Tc=62.65±0.07T_c = 62.65\pm0.07 K and γ=1.28±0.03\gamma = 1.28\pm0.03 with Tc=62.75±0.06T_c = 62.75\pm0.06 K are obtained by the Kouvel-Fisher method whereas δ=7.96±0.01\delta = 7.96\pm0.01 is obtained by the critical isotherm analysis at Tc=62.7T_c = 62.7 K. These critical exponents obey the Widom scaling relation δ=1+γ/β\delta = 1+\gamma/\beta, indicating self-consistency of the obtained values. With these critical exponents the isotherm M(H)M(H) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m=f±(h)m = f_\pm(h), where mm and hh are renormalized magnetization and field, respectively. The determined exponents match well with those calculated from the results of renormalization group approach for a two-dimensional Ising system coupled with long-range interaction between spins decaying as J(r)r(d+σ)J(r)\approx r^{-(d+\sigma)} with σ=1.52\sigma=1.52

    A partially collapsed Gibbs sampler for Bayesian quantile regression

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    We introduce a set of new Gibbs sampler for Bayesian analysis of quantile re-gression model. The new algorithm, which partially collapsing an ordinary Gibbs sampler, is called Partially Collapsed Gibbs (PCG) sampler. Although the Metropolis-Hastings algorithm has been employed in Bayesian quantile regression, including median regression, PCG has superior convergence properties to an ordinary Gibbs sampler. Moreover, Our PCG sampler algorithm, which is based on a theoretic derivation of an asymmetric Laplace as scale mixtures of normal distributions, requires less computation than the ordinary Gibbs sampler and can significantly reduce the computation involved in approximating the Bayes Factor and marginal likelihood. Like the ordinary Gibbs sampler, the PCG sample can also be used to calculate any associated marginal and predictive distributions. The quantile regression PCG sampler is illustrated by analysing simulated data and the data of length of stay in hospital. The latter provides new insight into hospital perfor-mance. C-code along with an R interface for our algorithms is publicly available on request from the first author. JEL classification: C11, C14, C21, C31, C52, C53
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