On Franklin’s relativistic rotational transformation and its modification

Unlike the Lorentz transformation which replaces the Galilean transformation among inertial frames at high relative velocities, there seems to be no such a consensus in the case of coordinate transformation between inertial frames and uniformly rotating ones. There have been some attempts to generalize the Galilean rotational transformation to high rotational velocities. Here we introduce a modified version of one of these transformations proposed by Philip Franklin in 1922. The modified version is shown to resolve some of the drawbacks of the Franklin transformation, specially with respect to the corresponding spacetime metric in the rotating frame. This new transformation introduces non-inertial eccentric observers on a uniformly rotating disk and the corresponding metric in the rotating frame is shown to be consistent with the one obtained through Galilean rotational transformation for points close to the rotation axis. Employing the threading formulation of spacetime decomposition, spatial distances and time intervals in the spacetime metric of a rotating observer's frame are also discussed.Comment: 30 pages, 2 figures, replaced with the published versio

A genomic catalog of Earth’s microbiomes

The reconstruction of bacterial and archaeal genomes from shotgun metagenomes has enabled insights into the ecology and evolution of environmental and host-associated microbiomes. Here we applied this approach to >10,000 metagenomes collected from diverse habitats covering all of Earth’s continents and oceans, including metagenomes from human and animal hosts, engineered environments, and natural and agricultural soils, to capture extant microbial, metabolic and functional potential. This comprehensive catalog includes 52,515 metagenome-assembled genomes representing 12,556 novel candidate species-level operational taxonomic units spanning 135 phyla. The catalog expands the known phylogenetic diversity of bacteria and archaea by 44% and is broadly available for streamlined comparative analyses, interactive exploration, metabolic modeling and bulk download. We demonstrate the utility of this collection for understanding secondary-metabolite biosynthetic potential and for resolving thousands of new host linkages to uncultivated viruses. This resource underscores the value of genome-centric approaches for revealing genomic properties of uncultivated microorganisms that affect ecosystem processes