Ordinary Percolation with Discontinuous Transitions

Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a nontrivial critical point. There, the usual order parameter, describing the probability of any node to be part of the largest cluster, jumps instantly to a finite value. Here, we provide a simple example of this transition in form of a small-world network consisting of a one-dimensional lattice combined with a hierarchy of long-range bonds that reveals many features of the transition in a mathematically rigorous manner.Comment: RevTex, 5 pages, 4 eps-figs, and Mathematica Notebook as Supplement included. Final version, with several corrections and improvements. For related work, see http://www.physics.emory.edu/faculty/boettcher

On Fano schemes of complete intersections

We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete intersection is irregular of dimension at least 2, and for the Fano surfaces we deduce formulas for their holomorphic Euler characteristic.Comment: Added lacking references, corrected acknowledgments, minor editorial change

Measurement of J/ψ production in association with a W ± boson with pp data at 8 TeV

A measurement of the production of a prompt J/ψ meson in association with a W± boson with W± → μν and J/ψ → μ+μ− is presented for J/ψ transverse momenta in the range 8.5–150 GeV and rapidity |yJ/ψ| < 2.1 using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton-proton centre-of-mass energy of s = 8 TeV and correspond to an integrated luminosity of 20.3 fb−1. The ratio of the prompt J/ψ plus W± cross-section to the inclusive W± cross-section is presented as a differential measurement as a function of J/ψ transverse momenta and compared with theoretical predictions using different double-parton-scattering cross-sections. [Figure not available: see fulltext.]