The LHC trigger and data acquisition systems will need significant modifications to operate at the HL-LHC. Due to the increased occupancy of each crossing, Level-1 trigger systems would experience degraded performance of the LHC algorithms presently
selecting up to 100 kHz of crossings from the LHC input rate of 40 MHz. The DAQ systems will experience larger event sizes due to greater occupancy and higher channel counts of new detectors. This paper summarizes findings and recommendations to upgrade the LHC experiments trigger and data acquisition systems for operation at the HL-HLC.
We discuss a procedure, which should be called Lenstras fix, for producing secure RSA moduli even when the random number generation is very poor.
Let $P$ be a set of $n$ points in the plane, each point moving along a given trajectory. A {em $k$-collinearity} is a pair $(L,t)$ of a line $L$ and a time $t$ such that $L$ contains at least $k$ points at time $t$, the points along $L$ do not all co
incide, and not all of them are collinear at all times. We show that, if the points move with constant velocity, then the number of 3-collinearities is at most $2binom{n}{3}$, and this bound is tight. There are $n$ points having $Omega(n^3/k^4 + n^2/k^2)$ distinct $k$-collinearities. Thus, the number of $k$-collinearities among $n$ points, for constant $k$, is $O(n^3)$, and this bound is asymptotically tight. In addition, there are $n$ points, moving in pairwise distinct directions with different speeds, such that no three points are ever collinear.
The Large Hadron Collider will commence operations in the latter half of 2008. The plans of the LHC experiments ALICE, ATLAS, CMS and LHCb are described. The scenario for progression of luminosity and the strategies of these 4 experiments to use the
initial data are detailed. There are significant measurements possible with integrated luminosities of 1, 10 and 100 pb^-1. These measurements will provide essential calibration and tests of the detectors, understanding of the Standard Model backgrounds and a first oportunity to look for new physics.
