Possible tau appearance experiment with atmospheric neutrinos

We suggest an experimental measurement that could detect the appearance of the tau neutrinos in muon to tau neutrino oscillations of atmospheric neutrinos by measuring the energy spectra of neutrino induced showers. Tau neutrinos deposit a large fraction of their energy in showers generated in CC interactions and the subsequent tau--lepton decay. The appearance of tau neutrinos will enhance the spectrum of neutrino induced showers in energy ranges corresponding to the neutrino oscillation parameters. A shower rate lower than the `no oscillation' prediction is an indication for oscillations into sterile neutrinos.Comment: RevTeX, four pages with 4 postscript figure

The Period map for quantum cohomology of P2\mathbb{P}^2

We invert the period map defined by the second structure connection of quantum cohomology of $\mathbb{P}^2$. For small quantum cohomology the inverse is given explicitly in terms of the Eisenstein series $E_4$ and $E_6$, while for big quantum cohomology the inverse is determined perturbatively as a Taylor series expansion whose coefficients are quasi-modular forms.Comment: 58 pages. Typos fixed. The previous version was extended in the following way: we proved the Laplace transform version of the $\Gamma$-conjecture for $\mathbb{P}^2$, worked out the structure of a Schwarz triangular map, and added an appendix explaining the relation to vertex algebras and W-constraints. Version accepted in Adv. in Mat