Level-3 Calorimetric Resolution available for the Level-1 and Level-2 CDF Triggers

As the Tevatron luminosity increases sophisticated selections are required to be efficient in selecting rare events among a very huge background. To cope with this problem, CDF has pushed the offline calorimeter algorithm reconstruction resolution up to Level 2 and, when possible, even up to Level 1, increasing efficiency and, at the same time, keeping under control the rates. The CDF Run II Level 2 calorimeter trigger is implemented in hardware and is based on a simple algorithm that was used in Run I. This system has worked well for Run II at low luminosity. As the Tevatron instantaneous luminosity increases, the limitation due to this simple algorithm starts to become clear: some of the most important jet and MET (Missing ET) related triggers have large growth terms in cross section at higher luminosity. In this paper, we present an upgrade of the Level 2 Calorimeter system which makes the calorimeter trigger tower information available directly to a CPU allowing more sophisticated algorithms to be implemented in software. Both Level 2 jets and MET can be made nearly equivalent to offline quality, thus significantly improving the performance and flexibility of the jet and MET related triggers. However in order to fully take advantage of the new L2 triggering capabilities having at Level 1 the same L2 MET resolution is necessary. The new Level-1 MET resolution is calculated by dedicated hardware. This paper describes the design, the hardware and software implementation and the performance of the upgraded calorimeter trigger system both at Level 2 and Level 1.Comment: 5 pages, 5 figures,34th International Conference on High Energy Physics, Philadelphia, 200

Siegel modular forms of genus 2 and level 2

We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular forms.Comment: 46 pages. To appear in International Journal of Mathematic

Many 2-level polytopes from matroids

The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-level matroids generalize series-parallel graphs, which have been already successfully analyzed from the enumerative perspective. We bring to light some structural properties of 2-level matroids and exploit them for enumerative purposes. Moreover, the counting results are used to show that the number of combinatorially non-equivalent (n-1)-dimensional 2-level polytopes is bounded from below by $c \cdot n^{-5/2} \cdot \rho^{-n}$, where $c\approx 0.03791727$ and $\rho^{-1} \approx 4.88052854$.Comment: revised version, 19 pages, 7 figure