Electron-Hadron Correlations in pp Collisions at \sqrt{s} = 2.76 TeV with the ALICE experiment

In this work we are studying the relative beauty to charm production in pp collisions at \sqrt{s} = 2.76 TeV, through correlations between electrons from heavy-flavour decay and charged hadrons, with the ALICE detector at the LHC. This study represents a baseline for the analysis in heavy-ion collisions where heavy flavour production is a powerful tool to study the Quark Gluon Plasma (QGP).Comment: Proceeding of the XII HADRON PHYSICS (2012, Bento Gon\c{c}alvez, Brazil) conference. 3 Pages, 4 Figure

Mathematical optimization for packing problems

During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques involved, concentrating on geometric packing problems such as the sphere-packing problem or the problem of packing regular tetrahedra in R^3.Comment: 17 pages, written for the SIAG/OPT Views-and-News, (v2) some updates and correction

Measurements of the correlation between electrons from heavy-flavour hadron decays and light hadrons with ALICE at the LHC

In relativistic heavy-ion physics two-particle correlations provide a very useful tool to investigate the Quark-Gluon Plasma (QGP). This observable is sensitive to several of the properties of the QGP such as resonances, interaction of partons with the medium and collective effects (e. g. elliptic flow). In the present work, the correlation function between electrons from heavy-flavour hadron decays and light hadrons was measured in pp and Pb-Pb collisions (central and semi-central). Furthermore, in pp collisions the relative beauty contribution to the total cross section of electrons from heavy-flavour decays was estimated by comparing the measured correlation with Monte-Carlo templates.Comment: Strangeness in Quark Matter 2013 conference proceedin

Measurements of electrons from heavy-flavour hadron decays in pp, p-Pb and Pb-Pb collisions with ALICE at the LHC

Heavy-flavour hadrons, i. e. hadrons carrying charm or beauty quarks, are a well-suited probe to study the Quark-Gluon Plasma (QGP) in relativistic heavy-ion collisions. For this reason, measurements of electrons from heavy-flavour hadron decays have been performed in pp, p-Pb and Pb-Pb collisions at the LHC with the ALICE detector. Results for the nuclear modification factors ($R_{\rm{pA}}$ and $R_{\rm{AA}}$) support a final-state energy loss of heavy quarks in central Pb-Pb collisions and, in semi-central collisions a positive elliptic flow coefficient $v_{2}$ of electrons from heavy-flavour hadron decays was observed. Furthermore, a double-ridge structure was observed in the measured two-particle angular correlation distribution, triggered by heavy-flavour decay electrons, in high-multiplicity p-Pb collisions relative to low-multiplicity p-Pb collisions and to pp collisions.Comment: Hard Probes 2013 conference proceedin

A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1

For $n \geq 2$ we construct a measurable subset of the unit ball in $\mathbb{R}^n$ that does not contain pairs of points at distance 1 and whose volume is greater than $(1/2)^n$ times the volume of the ball. This disproves a conjecture of Larman and Rogers from 1972.Comment: 3 pages, 1 figure; final version to appear in Mathematik

The positive semidefinite Grothendieck problem with rank constraint

Given a positive integer n and a positive semidefinite matrix A = (A_{ij}) of size m x m, the positive semidefinite Grothendieck problem with rank-n-constraint (SDP_n) is maximize \sum_{i=1}^m \sum_{j=1}^m A_{ij} x_i \cdot x_j, where x_1, ..., x_m \in S^{n-1}. In this paper we design a polynomial time approximation algorithm for SDP_n achieving an approximation ratio of \gamma(n) = \frac{2}{n}(\frac{\Gamma((n+1)/2)}{\Gamma(n/2)})^2 = 1 - \Theta(1/n). We show that under the assumption of the unique games conjecture the achieved approximation ratio is optimal: There is no polynomial time algorithm which approximates SDP_n with a ratio greater than \gamma(n). We improve the approximation ratio of the best known polynomial time algorithm for SDP_1 from 2/\pi to 2/(\pi\gamma(m)) = 2/\pi + \Theta(1/m), and we show a tighter approximation ratio for SDP_n when A is the Laplacian matrix of a graph with nonnegative edge weights.Comment: (v3) to appear in Proceedings of the 37th International Colloquium on Automata, Languages and Programming, 12 page

Grothendieck inequalities for semidefinite programs with rank constraint

Grothendieck inequalities are fundamental inequalities which are frequently used in many areas of mathematics and computer science. They can be interpreted as upper bounds for the integrality gap between two optimization problems: a difficult semidefinite program with rank-1 constraint and its easy semidefinite relaxation where the rank constrained is dropped. For instance, the integrality gap of the Goemans-Williamson approximation algorithm for MAX CUT can be seen as a Grothendieck inequality. In this paper we consider Grothendieck inequalities for ranks greater than 1 and we give two applications: approximating ground states in the n-vector model in statistical mechanics and XOR games in quantum information theory.Comment: 22 page