Homotopy Theoretic Models of Type Theory

We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it. On the other hand, those conditions are easy to check and provide a wide class of models some of which are listed in the paper.Comment: Corrected version of the published articl

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.Comment: 19 pages, 22 figure

Probing the energy bands of a Bose-Einstein condensate in an optical lattice

We simulate three experimental methods which could be realized in the laboratory to probe the band excitation energies and the momentum distribution of a Bose-Einstein condensate inside an optical lattice. The values of the excitation energies obtained in these different methods agree within the accuracy of the simulation. The meaning of the results in terms of density and phase deformations is tested by studying the relaxation of a phase-modulated condensate towards the ground state.Comment: 5 pages, 5 figure

The gut microbiota in multiple sclerosis varies with disease activity

BACKGROUND: Multiple sclerosis is a chronic immune-mediated disease of the brain and spinal cord resulting in physical and cognitive impairment in young adults. It is hypothesized that a disrupted bacterial and viral gut microbiota is a part of the pathogenesis mediating disease impact through an altered gut microbiota-brain axis. The aim of this study is to explore the characteristics of gut microbiota in multiple sclerosis and to associate it with disease variables, as the etiology of the disease remains only partially known. METHODS: Here, in a case-control setting involving 148 Danish cases with multiple sclerosis and 148 matched healthy control subjects, we performed shotgun sequencing of fecal microbial DNA and associated bacterial and viral microbiota findings with plasma cytokines, blood cell gene expression profiles, and disease activity. RESULTS: We found 61 bacterial species that were differentially abundant when comparing all multiple sclerosis cases with healthy controls, among which 31 species were enriched in cases. A cluster of inflammation markers composed of blood leukocytes, CRP, and blood cell gene expression of IL17A and IL6 was positively associated with a cluster of multiple sclerosis-related species. Bacterial species that were more abundant in cases with disease-active treatment-naïve multiple sclerosis were positively linked to a group of plasma cytokines including IL-22, IL-17A, IFN-β, IL-33, and TNF-α. The bacterial species richness of treatment-naïve multiple sclerosis cases was associated with number of relapses over a follow-up period of 2 years. However, in non-disease-active cases, we identified two bacterial species, Faecalibacterium prausnitzii and Gordonibacter urolithinfaciens, whose absolute abundance was enriched. These bacteria are known to produce anti-inflammatory metabolites including butyrate and urolithin. In addition, cases with multiple sclerosis had a higher viral species diversity and a higher abundance of Caudovirales bacteriophages. CONCLUSIONS: Considerable aberrations are present in the gut microbiota of patients with multiple sclerosis that are directly associated with blood biomarkers of inflammation, and in treatment-naïve cases bacterial richness is positively associated with disease activity. Yet, the finding of two symbiotic bacterial species in non-disease-active cases that produce favorable immune-modulating compounds provides a rationale for testing these bacteria as adjunct therapeutics in future clinical trials

The Influence of Age and Sex on Genetic Associations with Adult Body Size and Shape : A Large-Scale Genome-Wide Interaction Study

Genome-wide association studies (GWAS) have identified more than 100 genetic variants contributing to BMI, a measure of body size, or waist-to-hip ratio (adjusted for BMI, WHRadjBMI), a measure of body shape. Body size and shape change as people grow older and these changes differ substantially between men and women. To systematically screen for age-and/or sex-specific effects of genetic variants on BMI and WHRadjBMI, we performed meta-analyses of 114 studies (up to 320,485 individuals of European descent) with genome-wide chip and/or Metabochip data by the Genetic Investigation of Anthropometric Traits (GIANT) Consortium. Each study tested the association of up to similar to 2.8M SNPs with BMI and WHRadjBMI in four strata (men 50y, women 50y) and summary statistics were combined in stratum-specific meta-analyses. We then screened for variants that showed age-specific effects (G x AGE), sex-specific effects (G x SEX) or age-specific effects that differed between men and women (G x AGE x SEX). For BMI, we identified 15 loci (11 previously established for main effects, four novel) that showed significant (FDR= 50y). No sex-dependent effects were identified for BMI. For WHRadjBMI, we identified 44 loci (27 previously established for main effects, 17 novel) with sex-specific effects, of which 28 showed larger effects in women than in men, five showed larger effects in men than in women, and 11 showed opposite effects between sexes. No age-dependent effects were identified for WHRadjBMI. This is the first genome-wide interaction meta-analysis to report convincing evidence of age-dependent genetic effects on BMI. In addition, we confirm the sex-specificity of genetic effects on WHRadjBMI. These results may providefurther insights into the biology that underlies weight change with age or the sexually dimorphism of body shape.Peer reviewe