An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages

Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a Flux Line in a Type-II superconductor with a bulk current $\vec J$. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the presence of transverse fluctuations are found not to influence the critical exponents that describe longitudinal correlations. For a manifold with $d=4-\epsilon$ internal dimensions, longitudinal fluctuations in an isotropic medium are described by a roughness exponent $\zeta_\parallel=\epsilon/3$ to all orders in $\epsilon$, and a dynamical exponent $z_\parallel=2-2\epsilon/9+O(\epsilon^2)$. Transverse fluctuations have a distinct and smaller roughness exponent $\zeta_\perp=\zeta_\parallel-d/2$ for an isotropic medium. Furthermore, their relaxation is much slower, characterized by a dynamical exponent $z_\perp=z_\parallel+1/\nu$, where $\nu=1/(2-\zeta_\parallel)$ is the correlation length exponent. The predicted exponents agree well with numerical results for a flux line in three dimensions. As in the case of interface depinning models, anisotropy leads to additional universality classes. A nonzero Hall angle, which has no analogue in the interface models, also affects the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0 manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail [email protected] in case of problem

On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes

The sensitivity of a search for sources of TeV neutrinos can be improved by grouping potential sources together into generic classes in a procedure that is known as source stacking. In this paper, we define catalogs of Active Galactic Nuclei (AGN) and use them to perform a source stacking analysis. The grouping of AGN into classes is done in two steps: first, AGN classes are defined, then, sources to be stacked are selected assuming that a potential neutrino flux is linearly correlated with the photon luminosity in a certain energy band (radio, IR, optical, keV, GeV, TeV). Lacking any secure detailed knowledge on neutrino production in AGN, this correlation is motivated by hadronic AGN models, as briefly reviewed in this paper. The source stacking search for neutrinos from generic AGN classes is illustrated using the data collected by the AMANDA-II high energy neutrino detector during the year 2000. No significant excess for any of the suggested groups was found.Comment: 43 pages, 12 figures, accepted by Astroparticle Physic

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

celosioides

Cryptantha celosioides (Eastwood) Paysoncock's-comb cryptantha;northern cryptantha;clustered cryptantha;tufted cryptantha;cock's-comb cat's-eye;butte candle;northern miner's candle;Sheldon's oreocaryacryptanthe fausse-célosieCryptantha celosioidesMt. Crandell: northeast ridgebare shale ridge6800 fee