Generalised supersymmetry and p-brane actions

We investigate the most general N=1 graded extension of the Poincare algebra, and find the corresponding supersymmetry transformations and the associated superspaces. We find that the supersymmetry for which {Q,Q} = P is not special, and in fact must be treated democratically with a whole class of supersymmetries. We show that there are two distinct types of grading, and a new class of general spinors is defined. The associated superspaces are shown to be either of the usual type, or flat with no torsion. p-branes are discussed in these general superspaces and twelve dimensions emerges as maximal. New types of brane are discovered which could explain many features of the standard p-brane theories.Comment: 29 pages, LaTex, no figures. Errors in degrees of freedom counting corrected, leading to altered brane sca

Human leukocyte antigens and genetic susceptibility to lymphoma

Familial aggregation, coupled with ethnic variation in incidence, suggests that inherited susceptibility plays a role in the development of lymphoma, and the search for genetic risk factors has highlighted the contribution of the human leukocyte antigen (HLA) complex. In a landmark study published almost 50 years ago, Hodgkin lymphoma (HL) was the first disease to be associated with HLA variation. It is now clear that Epstein-Barr virus (EBV)-positive and -negative HL are strongly associated with specific HLA polymorphisms but these differ by EBV status of the tumours. HLA class I alleles are consistently associated with EBV-positive HL while a polymorphism in HLA class II is the strongest predictor of risk of EBV-negative HL. Recent investigations, particularly genome-wide association studies (GWAS), have also revealed associations between HLA and common types of non-Hodgkin lymphoma (NHL). Follicular lymphoma is strongly associated with two distinct haplotypes in HLA class II whereas diffuse large B-cell lymphoma is most strongly associated with HLA-B*08. Although chronic lymphocytic leukaemia is associated with variation in HLA class II, the strongest signals in GWAS are from non-HLA polymorphisms, suggesting that inherited susceptibility is explained by co-inheritance of multiple low risk variants. Associations between B-cell derived lymphoma and HLA variation suggest that antigen presentation, or lack of, plays an important role in disease pathogenesis but the precise mechanisms have yet to be elucidated

Etale homotopy types of moduli stacks of algebraic curves with symmetries

Using the machinery of etale homotopy theory a' la Artin-Mazur we determine the etale homotopy types of moduli stacks over \bar{\Q} parametrizing families of algebraic curves of genus g greater than 1 endowed with an action of a finite group G of automorphisms, which comes with a fixed embedding in the mapping class group, such that in the associated complex analytic situation the action of G is precisely the differentiable action induced by this specified embedding of G in the mapping class group.Comment: 27 page

Relationship between Hubble type and spectroscopic class in local galaxies

We compare the Hubble type and the spectroscopic class of the galaxies with spectra in SDSS/DR7. As it is long known, elliptical galaxies tend to be red whereas spiral galaxies tend to be blue, however, this relationship presents a large scatter, which we measure and quantify in detail. We compare the Automatic Spectroscopic K-means based classification (ASK) with most of the commonly used morphological classifications. All of them provide consistent results. Given a spectral class, the morphological type wavers with a standard deviation between 2 and 3 T types, and the same large dispersion characterizes the variability of spectral classes fixed the morphological type. The distributions of Hubble types given an ASK class are very skewed -- they present long tails that go to the late morphological types for the red galaxies, and to the early morphological types for the blue spectroscopic classes. The scatter is not produced by problems in the classification, and it remains when particular subsets are considered. A considerable fraction of the red galaxies are spirals (40--60 %), but they never present very late Hubble types (Sd or later). Even though red spectra are not associated with ellipticals, most ellipticals do have red spectra: 97 % of the ellipticals in the morphological catalog by Nair & Abraham, used here for reference, belong to ASK 0, 2 or 3. It contains only a 3 % of blue ellipticals. The galaxies in the green valley class (ASK~5) are mostly spirals, and the AGN class (ASK 6) presents a large scatter of Hubble types from E to Sd. From redshift 0.25 to now the galaxies redden from ASK 2 to ASK 0, as expected from the passive evolution of their stellar populations. Two of the ASK classes (1 and 4) gather edge-on spirals, a property of interest in studies requiring knowing the intrinsic shape of a galaxy (e.g., weak lensing calibration).Comment: Accepted for publication in ApJ. 16 pages. 12 Figs. 2 summary table

On a Nielsen-Thurston classification theory for cluster modular groups

We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping class group of a surface.Comment: 33 pages, 9 figures. To appear in Annales de l'Institut Fourie