Note on the Irreducible Triangulations of the Klein Bottle

We give the complete list of the 29 irreducible triangulations of the Klein bottle. We show how the construction of Lawrencenko and Negami, which listed only 25 such irreducible triangulations, can be modified at two points to produce the 4 additional irreducible triangulations of the Klein bottle.Comment: 10 pages, 8 figures, submitted to Journal of Combinatorial Theory, Series B. Section 3 expande

Irreducible Triangulations are Small

A triangulation of a surface is \emph{irreducible} if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus $g\geq1$ has at most $13g-4$ vertices. The best previous bound was $171g-72$.Comment: v2: Referees' comments incorporate

Introducing TAXI: a Transportable Array for eXtremely large area Instrumentation studies

A common challenge in many experiments in high-energy astroparticle physics is the need for sparse instrumentation in areas of 100 km2 and above, often in remote and harsh environments. All these arrays have similar requirements for read-out and communication, power generation and distribution, and synchronization. Within the TAXI project we are developing a transportable, modular four-station test-array that allows us to study different approaches to solve the aforementioned problems in the laboratory and in the field. Well-defined interfaces will provide easy interchange of the components to be tested and easy transport and setup will allow in-situ testing at different sites. Every station consists of three well-understood 1 m2 scintillation detectors with nanosecond time resolution, which provide an air shower trigger. An additional sensor, currently a radio antenna for air shower detection in the 100 MHz band, is connected for testing and calibration purposes. We introduce the TAXI project and report the status and performance of the first TAXI station deployed at the Zeuthen site of DESY.Comment: 4 pages, 3 figures, presented at ARENA 2014, Annapolis, MD, June 201