The Helicobacter pylori Genome Project : insights into H. pylori population structure from analysis of a worldwide collection of complete genomes

Helicobacter pylori, a dominant member of the gastric microbiota, shares co-evolutionary history with humans. This has led to the development of genetically distinct H. pylori subpopulations associated with the geographic origin of the host and with differential gastric disease risk. Here, we provide insights into H. pylori population structure as a part of the Helicobacter pylori Genome Project (HpGP), a multi-disciplinary initiative aimed at elucidating H. pylori pathogenesis and identifying new therapeutic targets. We collected 1011 well-characterized clinical strains from 50 countries and generated high-quality genome sequences. We analysed core genome diversity and population structure of the HpGP dataset and 255 worldwide reference genomes to outline the ancestral contribution to Eurasian, African, and American populations. We found evidence of substantial contribution of population hpNorthAsia and subpopulation hspUral in Northern European H. pylori. The genomes of H. pylori isolated from northern and southern Indigenous Americans differed in that bacteria isolated in northern Indigenous communities were more similar to North Asian H. pylori while the southern had higher relatedness to hpEastAsia. Notably, we also found a highly clonal yet geographically dispersed North American subpopulation, which is negative for the cag pathogenicity island, and present in 7% of sequenced US genomes. We expect the HpGP dataset and the corresponding strains to become a major asset for H. pylori genomics

Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

We construct an a.e. approximately differentiable homeomorphism of a unit $n$-dimensional cube onto itself which is orientation preserving, has the Lusin property (N) and has the Jacobian determinant negative a.e. Moreover, the homeomorphism together with its inverse satisfy a rather general sub-Lipschitz condition, in particular it can be bi-H\"older continuous with an arbitrary exponent less than $1$