Comparing the degrees of enumerability and the closed Medvedev degrees

We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees

Big issues for small feet : developmental, biomechanical and clinical narratives on children's footwear

The effects of footwear on the development of children's feet has been debated for many years and recent work from the developmental and biomechanical literature has challenged long-held views about footwear and the impact on foot development. This narrative review draws upon existing studies from developmental, biomechanical and clinical literature to explore the effects of footwear on the development of the foot. The emerging findings from this support the need for progress in [children's] footwear science and advance understanding of the interaction between the foot and shoe. Ensuring clear and credible messages inform practice requires a progressive evidence base but this remains big issue in children's footwear research

A Polymorphism in the HLA-DPB1 Gene Is Associated with Susceptibility to Multiple Sclerosis

We conducted an association study across the human leukocyte antigen (HLA) complex to identify loci associated with multiple sclerosis (MS). Comparing 1927 SNPs in 1618 MS cases and 3413 controls of European ancestry, we identified seven SNPs that were independently associated with MS conditional on the others (each ). All associations were significant in an independent replication cohort of 2212 cases and 2251 controls () and were highly significant in the combined dataset (). The associated SNPs included proxies for HLA-DRB1*15:01 and HLA-DRB1*03:01, and SNPs in moderate linkage disequilibrium (LD) with HLA-A*02:01, HLA-DRB1*04:01 and HLA-DRB1*13:03. We also found a strong association with rs9277535 in the class II gene HLA-DPB1 (discovery set , replication set , combined ). HLA-DPB1 is located centromeric of the more commonly typed class II genes HLA-DRB1, -DQA1 and -DQB1. It is separated from these genes by a recombination hotspot, and the association is not affected by conditioning on genotypes at DRB1, DQA1 and DQB1. Hence rs9277535 represents an independent MS-susceptibility locus of genome-wide significance. It is correlated with the HLA-DPB1*03:01 allele, which has been implicated previously in MS in smaller studies. Further genotyping in large datasets is required to confirm and resolve this association