Sampling Quantum Nonlocal Correlations with High Probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).

The Lateral Trigger Probability function for the Ultra-High Energy Cosmic Ray showers detected by the Pierre Auger Observatory

In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an Extensive Air Shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 10(17) and 10(19) eV and zenith angles up to 65 degrees. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte Carlo results showing how LTP functions from data are in good agreement with simulations.

Epidermal Growth Factor Impairs Palatal Shelf Adhesion and Fusion in the T gf-β3 Null Mutant

The cleft palate presented by transforming growth factor-β3 (Tgf-β3 ) null mutant mice is caused by altered palatal shelf adhesion, cell proliferation, epithelial-to-mesenchymal transformation and cell death. The expression of epidermal growth factor (EGF), transforming growth factor-β1 ( Tgf-β1 ) and muscle segment homeobox-1 (Msx-1) is modified in the palates of these knockout mice, and the cell proliferation defect is caused by the change in EGF expression. In this study, we aimed to determine whether this change in EGF expression has any effect on the other mechanisms altered in Tgf-β 3 knockout mouse palates. We tested the effect of inhibiting EGF activity in vitro in the knockout palates via the addition of Tyrphostin AG 1478. We also investigated possible interactions between EGF, Tgf-β 1 and Msx-1 in Tgf-β 3 null mouse palate cultures. The results show that the inhibition of EGF activity in Tgf-β 3 null mouse palate cultures improves palatal shelf adhesion and fusion, with a particular effect on cell death, and restores the normal distribution pattern of Msx-1 in the palatal esenchyme. Inhibition of TGF-β 1 does not affect either EGF or Msx-1 expression.