Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Nonlinear Evolution of Cosmological Structures in Warm Dark Matter Models

The dark energy dominated warm dark matter (WDM) model is a promising alternative cosmological scenario. We explore large-scale structure formation in this paradigm. We do this in two different ways: with the halo model approach and with the help of an ensemble of high resolution N-body simulations. Combining these quasi-independent approaches, leads to a physical understanding of the important processes which shape the formation of structures. We take a detailed look at the halo mass function, the concentrations and the linear halo bias of WDM. In all cases we find interesting deviations with respect to CDM. In particular, the concentration-mass relation displays a turnover for group scale dark matter haloes, for the case of WDM particles with masses of the order ~0.25 keV. This may be interpreted as a hint for top-down structure formation on small scales. We implement our results into the halo model and find much better agreement with simulations. On small scales the WDM halo model now performs as well as its CDM counterpart.Comment: accepted for publication in MNRA

Rare coding variant analysis in a large cohort of Ashkenazi Jewish families with inflammatory bowel disease

Rare variants are thought to contribute to the genetics of inflammatory bowel disease (IBD), which is more common amongst the Ashkenazi Jewish (AJ) population. A family-based approach using exome sequencing of AJ individuals with IBD was employed with a view to identify novel rare genetic variants for this disease. Exome sequencing was performed on 960 Jewish individuals including 513 from 199 multiplex families with up to eight cases. Rare, damaging variants in loci prioritized by linkage analysis and those shared by multiple affected individuals within the same family were identified. Independent evidence of association of each variant with disease was assessed. A number of candidate variants were identified, including in genes involved in the immune system. The ability to achieve statistical significance in independent case/control replication data was limited by power and was only achieved for variants in the well-established Crohn's disease gene, NOD2. This work demonstrates the challenges of identifying disease-associated rare damaging variants from exome data, even amongst a favorable cohort of familial cases from a genetic isolate. Further research of the prioritized rare candidate variants is required to confirm their association with the disease

Measurement of the Depth of Maximum of Extensive Air Showers above 10^18 eV

We describe the measurement of the depth of maximum, Xmax, of the longitudinal development of air showers induced by cosmic rays. Almost four thousand events above 10^18 eV observed by the fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are selected for the analysis. The average shower maximum was found to evolve with energy at a rate of (106 +35/-21) g/cm^2/decade below 10^(18.24 +/- 0.05) eV and (24 +/- 3) g/cm^2/decade above this energy. The measured shower-to-shower fluctuations decrease from about 55 to 26 g/cm^2. The interpretation of these results in terms of the cosmic ray mass composition is briefly discussed.Comment: Accepted for publication by PR

The Pierre Auger Observatory III: Other Astrophysical Observations

Astrophysical observations of ultra-high-energy cosmic rays with the Pierre Auger ObservatoryComment: Contributions to the 32nd International Cosmic Ray Conference, Beijing, China, August 201

Operations of and Future Plans for the Pierre Auger Observatory

Technical reports on operations and features of the Pierre Auger Observatory, including ongoing and planned enhancements and the status of the future northern hemisphere portion of the Observatory. Contributions to the 31st International Cosmic Ray Conference, Lodz, Poland, July 2009.Comment: Contributions to the 31st ICRC, Lodz, Poland, July 200

Highlights from the Pierre Auger Observatory

The Pierre Auger Observatory is the world's largest cosmic ray observatory. Our current exposure reaches nearly 40,000 km$^2$ str and provides us with an unprecedented quality data set. The performance and stability of the detectors and their enhancements are described. Data analyses have led to a number of major breakthroughs. Among these we discuss the energy spectrum and the searches for large-scale anisotropies. We present analyses of our X$_{max}$ data and show how it can be interpreted in terms of mass composition. We also describe some new analyses that extract mass sensitive parameters from the 100% duty cycle SD data. A coherent interpretation of all these recent results opens new directions. The consequences regarding the cosmic ray composition and the properties of UHECR sources are briefly discussed.Comment: 9 pages, 12 figures, talk given at the 33rd International Cosmic Ray Conference, Rio de Janeiro 201

Anisotropy and chemical composition of ultra-high energy cosmic rays using arrival directions measured by the Pierre Auger Observatory

The Pierre Auger Collaboration has reported evidence for anisotropy in the distribution of arrival directions of the cosmic rays with energies $E>E_{th}=5.5\times 10^{19}$ eV. These show a correlation with the distribution of nearby extragalactic objects, including an apparent excess around the direction of Centaurus A. If the particles responsible for these excesses at $E>E_{th}$ are heavy nuclei with charge $Z$, the proton component of the sources should lead to excesses in the same regions at energies $E/Z$. We here report the lack of anisotropies in these directions at energies above $E_{th}/Z$ (for illustrative values of $Z=6,\ 13,\ 26$). If the anisotropies above $E_{th}$ are due to nuclei with charge $Z$, and under reasonable assumptions about the acceleration process, these observations imply stringent constraints on the allowed proton fraction at the lower energies