Cycles of length three and four in tournaments

Linial and Morgenstern conjectured that, among all $n$-vertex tournaments with $d\binom{n}{3}$ cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of equal size and one smaller part. We prove the conjecture for $d\ge 1/36$ by analyzing the possible spectrum of adjacency matrices of tournaments. We also demonstrate that the family of extremal examples is broader than expected and give its full description for $d\ge 1/16$

The MuPix Telescope: A Thin, high Rate Tracking Telescope

The MuPix Telescope is a particle tracking telescope, optimized for tracking low momentum particles and high rates. It is based on the novel High-Voltage Monolithic Active Pixel Sensors (HV-MAPS), designed for the Mu3e tracking detector. The telescope represents a first application of the HV-MAPS technology and also serves as test bed of the Mu3e readout chain. The telescope consists of up to eight layers of the newest prototypes, the MuPix7 sensors, which send data self-triggered via fast serial links to FPGAs, where the data is time-ordered and sent to the PC. A particle hit rate of 1 MHz per layer could be processed. Online tracking is performed with a subset of the incoming data. The general concept of the telescope, chip architecture, readout concept and online reconstruction are described. The performance of the sensor and of the telescope during test beam measurements are presented.Comment: Proceedings TWEPP 2016, 8 pages, 7 figure

The ALPS project: open source software for strongly correlated systems

We present the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). The software is available from our web server at http://alps.comp-phys.org.Comment: For full software and introductory turorials see http://alps.comp-phys.or

Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric