Early Search for Supersymmetry at ATLAS

The search for physics beyond the Standard Model (BSM) is one of the most important goals for the general purpose detector ATLAS at the Large Hadron Collider at CERN. Supersymmetry search strategies based on generic event signatures of high jet multiplicity and large missing transverse momentum, optionally including leptons in the final state with R-parity conservation are discussed in this document. We review the results for above SUSY search strategies with first data up to 305 $nb^{-1}$ of integrated luminosity collected by ATLAS during 2010 at a centre-of-mass energy of 7 TeV.Comment: 6 pages, to appear in the Proceedings of Kruge 2010 Workshop on Discovery Physics at the LHC, South Africa, 5-10 Dec 2010, available on the CERN document server under the number ATL-PHYS-PROC-2011-01

ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm

Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such features is the utilization of parabolic scaling. One prominent example is the shearlet system. Our objective in this paper is three-fold: We firstly develop a digital shearlet theory which is rationally designed in the sense that it is the digitization of the existing shearlet theory for continuous data. This implicates that shearlet theory provides a unified treatment of both the continuum and digital realm. Secondly, we analyze the utilization of pseudo-polar grids and the pseudo-polar Fourier transform for digital implementations of parabolic scaling algorithms. We derive an isometric pseudo-polar Fourier transform by careful weighting of the pseudo-polar grid, allowing exploitation of its adjoint for the inverse transform. This leads to a digital implementation of the shearlet transform; an accompanying Matlab toolbox called ShearLab is provided. And, thirdly, we introduce various quantitative measures for digital parabolic scaling algorithms in general, allowing one to tune parameters and objectively improve the implementation as well as compare different directional transform implementations. The usefulness of such measures is exemplarily demonstrated for the digital shearlet transform.Comment: submitted to SIAM J. Multiscale Model. Simu