The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

Fermi Large Area Telescope Constraints on the Gamma-ray Opacity of the Universe

The Extragalactic Background Light (EBL) includes photons with wavelengths from ultraviolet to infrared, which are effective at attenuating gamma rays with energy above ~10 GeV during propagation from sources at cosmological distances. This results in a redshift- and energy-dependent attenuation of the gamma-ray flux of extragalactic sources such as blazars and Gamma-Ray Bursts (GRBs). The Large Area Telescope onboard Fermi detects a sample of gamma-ray blazars with redshift up to z~3, and GRBs with redshift up to z~4.3. Using photons above 10 GeV collected by Fermi over more than one year of observations for these sources, we investigate the effect of gamma-ray flux attenuation by the EBL. We place upper limits on the gamma-ray opacity of the Universe at various energies and redshifts, and compare this with predictions from well-known EBL models. We find that an EBL intensity in the optical-ultraviolet wavelengths as great as predicted by the "baseline" model of Stecker et al. (2006) can be ruled out with high confidence.Comment: 42 pages, 12 figures, accepted version (24 Aug.2010) for publication in ApJ; Contact authors: A. Bouvier, A. Chen, S. Raino, S. Razzaque, A. Reimer, L.C. Reye

Mid-Infrared Laser Ablation of Stratum Corneum Enhances In Vitro Percutaneous Transport of Drugs

The precise removal of stratum corneum from cadaveric swine skin by a mid-infrared erbium: yttrium scandium gallium garnet laser (λ = 2.79 μm; 250 μsec pulse width) was assessed by electrical resistance measurements and documented by histology. The effects of stratum corneum removal by laser ablation and by adhesive tape-stripping on the in vitro penetration of 3H-hydrocortisone and 125I-γ-interferon were determined. Excised swine skin was irradiated with laser (1 J/cm2 31 mJ/pulse; 1 Hz; 2mm spot diameter). For skin penetration studies, laser pulses were delivered to discrete 2-mm areas to ablate up to 12.6% of the total 3-cm2 stratum corneum diffusional area. Franz in vitro skin penetration chambers were used to measure the cumulative 48-h penetration of 3H-hydrocortisone and 125I-γ-interferon in laser-treated and tape-stripped skin. Electrical resistance measurements and histologic studies demonstrated that 10-14 laser pulses at the above energy density were required to abolish skin resistance and selectively ablate stratum corneum without damage to adjacent dermal structures. Laser ablation of 12.6% of the surface area of stratum corneum produced a 2.8 and 2.1-times increase in permeability constant (kp) for 3H-hydrocortisone and 125I-λ-interferon, respectively. These studies demonstrate that a pulsed mid-infrared laser can reliably and precisely remove the stratum corneum, facilitating penetration of large molecules such as 125I-λ-interferon that cannot penetrate intact skin. This new technique may be useful for basic and clinical investigation of skin barrier properties

Highlights of Coastal Waves 1996

Highlights of Coastal Waves 199