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

Shedding Light on the Galaxy Luminosity Function

From as early as the 1930s, astronomers have tried to quantify the statistical nature of the evolution and large-scale structure of galaxies by studying their luminosity distribution as a function of redshift - known as the galaxy luminosity function (LF). Accurately constructing the LF remains a popular and yet tricky pursuit in modern observational cosmology where the presence of observational selection effects due to e.g. detection thresholds in apparent magnitude, colour, surface brightness or some combination thereof can render any given galaxy survey incomplete and thus introduce bias into the LF. Over the last seventy years there have been numerous sophisticated statistical approaches devised to tackle these issues; all have advantages -- but not one is perfect. This review takes a broad historical look at the key statistical tools that have been developed over this period, discussing their relative merits and highlighting any significant extensions and modifications. In addition, the more generalised methods that have emerged within the last few years are examined. These methods propose a more rigorous statistical framework within which to determine the LF compared to some of the more traditional methods. I also look at how photometric redshift estimations are being incorporated into the LF methodology as well as considering the construction of bivariate LFs. Finally, I review the ongoing development of completeness estimators which test some of the fundamental assumptions going into LF estimators and can be powerful probes of any residual systematic effects inherent magnitude-redshift data.Comment: 95 pages, 23 figures, 3 tables. Now published in The Astronomy & Astrophysics Review. This version: bring in line with A&AR format requirements, also minor typo corrections made, additional citations and higher rez images adde

Leukocyte Telomere Length in Major Depression: Correlations with Chronicity, Inflammation and Oxidative Stress - Preliminary Findings

Depression is associated with an unusually high rate of aging-related illnesses and early mortality. One aspect of “accelerated aging” in depression may be shortened leukocyte telomeres. When telomeres critically shorten, as often occurs with repeated mitoses or in response to oxidation and inflammation, cells may die. Indeed, leukocyte telomere shortening predicts early mortality and medical illnesses in non-depressed populations. We sought to determine if leukocyte telomeres are shortened in Major Depressive Disorder (MDD), whether this is a function of lifetime depression exposure and whether this is related to putative mediators, oxidation and inflammation.Leukocyte telomere length was compared between 18 unmedicated MDD subjects and 17 controls and was correlated with lifetime depression chronicity and peripheral markers of oxidation (F2-isoprostane/Vitamin C ratio) and inflammation (IL-6). Analyses were controlled for age and sex.The depressed group, as a whole, did not differ from the controls in telomere length. However, telomere length was significantly inversely correlated with lifetime depression exposure, even after controlling for age (p<0.05). Average telomere length in the depressed subjects who were above the median of lifetime depression exposure (≥9.2 years' cumulative duration) was 281 base pairs shorter than that in controls (p<0.05), corresponding to approximately seven years of “accelerated cell aging.” Telomere length was inversely correlated with oxidative stress in the depressed subjects (p<0.01) and in the controls (p<0.05) and with inflammation in the depressed subjects (p<0.05).These preliminary data indicate that accelerated aging at the level of leukocyte telomeres is proportional to lifetime exposure to MDD. This might be related to cumulative exposure to oxidative stress and inflammation in MDD. This suggest that telomere shortening does not antedate depression and is not an intrinsic feature. Rather, telomere shortening may progress in proportion to lifetime depression exposure

Association of HLA-DRB1 amino acid residues with giant cell arteritis: genetic association study, meta-analysis and geo-epidemiological investigation

Introduction: Giant cell arteritis (GCA) is an autoimmune disease commonest in Northern Europe and Scandinavia. Previous studies report various associations with HLA-DRB1*04 and HLA-DRB1*01; HLA-DRB1 alleles show a gradient in population prevalence within Europe. Our aims were (1) to determine which amino acid residues within HLA-DRB1 best explained HLA-DRB1 allele susceptibility and protective effects in GCA, seen in UK data combined in meta-analysis with previously published data, and (2) to determine whether the incidence of GCA in different countries is associated with the population prevalence of the HLA-DRB1 alleles that we identified in our meta-analysis. Methods: GCA patients from the UK GCA Consortium were genotyped by using single-strand oligonucleotide polymerization, allele-specific polymerase chain reaction, and direct sequencing. Meta-analysis was used to compare and combine our results with published data, and public databases were used to identify amino acid residues that may explain observed susceptibility/protective effects. Finally, we determined the relationship of HLA-DRB1*04 population carrier frequency and latitude to GCA incidence reported in different countries. Results: In our UK data (225 cases and 1378 controls), HLA-DRB1*04 carriage was associated with GCA susceptibility (odds ratio (OR) = 2.69, P = 1.5×10 −11 ), but HLA-DRB1*01 was protective (adjusted OR = 0.55, P = 0.0046). In meta-analysis combined with 14 published studies (an additional 691 cases and 4038 controls), protective effects were seen from HLA-DR2, which comprises HLA-DRB1*15 and HLA-DRB1*16 (OR = 0.65, P = 8.2×10 −6 ) and possibly from HLA-DRB1*01 (OR = 0.73, P = 0.037). GCA incidence (n = 17 countries) was associated with population HLA-DRB1*04 allele frequency (P = 0.008; adjusted R 2 = 0.51 on univariable analysis, adjusted R 2 = 0.62 after also including latitude); latitude also made an independent contribution. Conclusions: We confirm that HLA-DRB1*04 is a GCA susceptibility allele. The susceptibility data are best explained by amino acid risk residues V, H, and H at positions 11, 13, and 33, contrary to previous suggestions of amino acids in the second hypervariable region. Worldwide, GCA incidence was independently associated both with population frequency of HLA-DRB1*04 and with latitude itself. We conclude that variation in population HLA-DRB1*04 frequency may partly explain variations in GCA incidence and that HLA-DRB1*04 may warrant investigation as a potential prognostic or predictive biomarker