10,031,316 research outputs found

    Securing level 3 in mathematics

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    SBML Level 3 Package Proposal: Flux

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    This document describes an easy to implement package for storing information related 
to flux balance analysis of SBML Level 3 models (the FBA package). In addition, 
we provide an example of how this package may be implemented and used as a SBML
Level 2 annotation

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

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    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

    Artinian level algebras of codimension 3

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    In this paper, we continue the study of which hh-vectors =˝(1,3,...,hd1,hd,hd+1)\H=(1,3,..., h_{d-1}, h_d, h_{d+1}) can be the Hilbert function of a level algebra by investigating Artinian level algebras of codimension 3 with the condition β2,d+2(Ilex)=β1,d+1(Ilex)\beta_{2,d+2}(I^{\rm lex})=\beta_{1,d+1}(I^{\rm lex}), where IlexI^{\rm lex} is the lex-segment ideal associated with an ideal II. Our approach is to adopt an homological method called {\it Cancellation Principle}: the minimal free resolution of II is obtained from that of IlexI^{\rm lex} by canceling some adjacent terms of the same shift. We prove that when β1,d+2(Ilex)=β2,d+2(Ilex)\beta_{1,d+2}(I^{\rm lex})=\beta_{2,d+2}(I^{\rm lex}), R/IR/I can be an Artinian level kk-algebra only if either hd1<hd<hd+1h_{d-1}<h_d<h_{d+1} or hd1=hd=hd+1=d+1h_{d-1}=h_d=h_{d+1}=d+1 holds. We also apply our results to show that for =˝(1,3,...,hd1,hd,hd+1)\H=(1,3,..., h_{d-1}, h_d, h_{d+1}), the Hilbert function of an Artinian algebra of codimension 3 with the condition hd1=hd<hd+1h_{d-1}=h_d<h_{d+1}, (a) if hd3d+2h_d\leq 3d+2, then hh-vector \H cannot be level, and (b) if hd3d+3h_d\geq 3d+3, then there is a level algebra with Hilbert function \H for some value of hd+1h_{d+1}.Comment: 15 page

    Extended project : challenging level 3 students

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    Consultation on the extended project: level 3

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    Early Years Educator (Level 3): qualifications criteria

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