The LHCb Vertex Locator performance and Vertex Locator upgrade

LHCb is an experiment dedicated to the study of new physics in the decays of beauty and charm hadrons at the Large Hadron Collider (LHC) at CERN. The Vertex Locator (VELO) is the silicon detector surrounding the LHCb interaction point. The detector operates in a severe and highly non-uniform radiation environment. The small pitch and analogue readout result in a best single hit precision of 4 $\rm \mu$m. The upgrade of the LHCb experiment, planned for 2018, will transform the entire readout to a trigger-less system operating at 40 MHz event rate. The vertex detector will have to cope with radiation levels up to 10$^{16}$ 1 MeV$\rm n_{eq}/cm^2$, more than an order of magnitude higher than those expected at the current experiment. A solution is under development with a pixel detector, based on the Timepix/Medipix family of chips with 55 x 55 $\rm \mu m$ pixels. In addition a micro-strip solution is also under development, with finer pitch, higher granularity and lower mass than the current detector. The current status of the VELO will be described together with recent testbeam results.Comment: Proceedings for the "*14th International Workshop on Radiation Imaging Detector IWORID 2012*

A remark on approximation with polynomials and greedy bases

We investigate properties of the $m$-th error of approximation by polynomials with constant coefficients $\mathcal{D}_{m}(x)$ and with modulus-constant coefficients $\mathcal{D}_{m}^{\ast}(x)$ introduced by Bern\'a and Blasco (2016) to study greedy bases in Banach spaces. We characterize when $\liminf_{m}{\mathcal{D}_{m}(x)}$ and $\liminf_{m}{\mathcal{D}_{m}^*(x)}$ are equivalent to $\| x\|$ in terms of the democracy and superdemocracy functions, and provide sufficient conditions ensuring that $\lim_{m}{\mathcal{D}_{m}^*(x)} = \lim_{m}{\mathcal{D}_{m}(x)} = \| x\|$, extending previous very particular results

Video Prioritization for Unequal Error Protection

We analyze the effect of packet losses in video sequences and propose a lightweight Unequal Error Protection strategy which, by choosing which packet is discarded, reduces strongly the Mean Square Error of the received sequenc