Graphical approaches for the control of generalised error rates

When simultaneously testing multiple hypotheses, the usual approach in the context of confirmatory clinical trials is to control the familywise error rate (FWER), which bounds the probability of making at least one false rejection. In many trial settings, these hypotheses will additionally have a hierarchical structure that reflects the relative importance and links between different clinical objectives. The graphical approach of Bretz et al. (2009) is a flexible and easily communicable way of controlling the FWER while respecting complex trial objectives and multiple structured hypotheses. However, the FWER can be a very stringent criterion that leads to procedures with low power, and may not be appropriate in exploratory trial settings. This motivates controlling generalised error rates, particularly when the number of hypotheses tested is no longer small. We consider the generalised familywise error rate (k-FWER), which is the probability of making k or more false rejections, as well as the tail probability of the false discovery proportion (FDP), which is the probability that the proportion of false rejections is greater than some threshold. We also consider asymptotic control of the false discovery rate (FDR), which is the expectation of the FDP. In this paper, we show how to control these generalised error rates when using the graphical approach and its extensions. We demonstrate the utility of the resulting graphical procedures on three clinical trial case studies.Biometrika Trust; Medical Research Council, Grant/Award Numbers: MC∖UU∖00002/6, MR/N028171/

MWL observations of VHE blazars in 2006

In 2006 the MAGIC telescope observed the well known very high energy (VHE, > 80 GeV) blazars Mrk 421 and Mrk 501 in the course of multi-wavelength campaigns, comprising measurements in the optical, X-ray and VHE regime. MAGIC performed additional snapshot observations on Mrk 421 around the MWL campaigns and detected the source each night with high significance, establishing once more flux variability on nightly scales for this object. For certain nights, the integral flux exceeded the one of Crab significantly, whereas the truly simultaneous observations have been conducted in a rather low flux state. The MAGIC observations contemporaneous to XMM-Newton revealed clear intra-night variability. No significant correlation between the spectral index and the flux could be found for the nine days of observations. The VHE observations of Mrk 501 have been conducted during one of the lowest flux states ever measured by MAGIC for this object. The VHE and optical light curves do not show significant variability, whereas the flux in X-rays increased by about 50 %. In this contribution, the results of the MAGIC observations will be presented in detail.Comment: Contribution to the 31st ICRC, Lodz, Poland, July 200

MARS, the MAGIC Analysis and Reconstruction Software

With the commissioning of the second MAGIC gamma-ray Cherenkov telescope situated close to MAGIC-I, the standard analysis package of the MAGIC collaboration, MARS, has been upgraded in order to perform the stereoscopic reconstruction of the detected atmospheric showers. MARS is a ROOT-based code written in C++, which includes all the necessary algorithms to transform the raw data recorded by the telescopes into information about the physics parameters of the observed targets. An overview of the methods for extracting the basic shower parameters is presented, together with a description of the tools used in the background discrimination and in the estimation of the gamma-ray source spectra.Comment: 4 pages, 0 figures, submitted to the 31st International Cosmic Ray Conference, {\L}odz 200

Self-Structuring of Granular Media under Internal Avalanches

We study the phenomenon of internal avalanching within the context of recently proposed ``Tetris'' lattice models for granular media. We define a recycling dynamics under which the system reaches a steady state which is self-structured, i.e. it shows a complex interplay between textured internal structures and critical avalanche behavior. Furthermore we develop a general mean-field theory for this class of systems and discuss possible scenarios for the breakdown of universality.Comment: 4 pages RevTex, 3 eps figures, revised version to appear in Phys. Rev. Let

Thermal resistivity of layered 4He films on ZYX graphite below 2 K

Thermal resistance and vapor pressure isotherms were taken near superfluid onset for ultra-thin helium films adsorbed on a ZYX graphite wafer between 1-2 K and 3-7 atomic layers. Our data are consistent with previous graphite onsets and are compatible with a current model of film droplet formation. Overlap of thermal resistance curves at 1.19 and 139 K is believed to be associated with discrete layering effects of 2D superfluid film properties.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23266/1/0000201.pd

Thermal resistivity of layered 4He films on ZYX graphite below 2 K

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23286/1/0000223.pd