Time-frequency analysis on the adeles over the rationals

We show that the construction of Gabor frames in $L^{2}(\mathbb{R})$ with generators in $\mathbf{S}_{0}(\mathbb{R})$ and with respect to time-frequency shifts from a rectangular lattice $\alpha\mathbb{Z}\times\beta\mathbb{Z}$ is equivalent to the construction of certain Gabor frames for $L^{2}$ over the adeles over the rationals and the group $\mathbb{R}\times\mathbb{Q}_{p}$. Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on $\mathbb{R}\times\mathbb{Q}_{p}$ with the construction of certain Heisenberg modules.Comment: minor revisions, added more references, added a Balian-Low type result in the form of Proposition 4.

On the Usefulness of Modulation Spaces in Deformation Quantization

We discuss the relevance to deformation quantization of Feichtinger's modulation spaces, especially of the weighted Sjoestrand classes. These function spaces are good classes of symbols of pseudo-differential operators (observables). They have a widespread use in time-frequency analysis and related topics, but are not very well-known in physics. It turns out that they are particularly well adapted to the study of the Moyal star-product and of the star-exponential.Comment: Submitte

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Evolutionary tradeoffs in cellular composition across diverse bacteria

One of the most important classic and contemporary interests in biology is the connection between cellular composition and physiological function. Decades of research have allowed us to understand the detailed relationship between various cellular components and processes for individual species, and have uncovered common functionality across diverse species. However, there still remains the need for frameworks that can mechanistically predict the tradeoffs between cellular functions and elucidate and interpret average trends across species. Here we provide a comprehensive analysis of how cellular composition changes across the diversity of bacteria as connected with physiological function and metabolism, spanning five orders of magnitude in body size. We present an analysis of the trends with cell volume that covers shifts in genomic, protein, cellular envelope, RNA and ribosomal content. We show that trends in protein content are more complex than a simple proportionality with the overall genome size, and that the number of ribosomes is simply explained by cross-species shifts in biosynthesis requirements. Furthermore, we show that the largest and smallest bacteria are limited by physical space requirements. At the lower end of size, cell volume is dominated by DNA and protein content—the requirement for which predicts a lower limit on cell size that is in good agreement with the smallest observed bacteria. At the upper end of bacterial size, we have identified a point at which the number of ribosomes required for biosynthesis exceeds available cell volume. Between these limits we are able to discuss systematic and dramatic shifts in cellular composition. Much of our analysis is connected with the basic energetics of cells where we show that the scaling of metabolic rate is surprisingly superlinear with all cellular components

Retroelement-guided protein diversification abounds in vast lineages of Bacteria and Archaea

Major radiations of enigmatic Bacteria and Archaea with large inventories of uncharacterized proteins are a striking feature of the Tree of Life1-5. The processes that led to functional diversity in these lineages, which may contribute to a host-dependent lifestyle, are poorly understood. Here, we show that diversity-generating retroelements (DGRs), which guide site-specific protein hypervariability6-8, are prominent features of genomically reduced organisms from the bacterial candidate phyla radiation (CPR) and as yet uncultivated phyla belonging to the DPANN (Diapherotrites, Parvarchaeota, Aenigmarchaeota, Nanoarchaeota and Nanohaloarchaea) archaeal superphylum. From reconstructed genomes we have defined monophyletic bacterial and archaeal DGR lineages that expand the known DGR range by 120% and reveal a history of horizontal retroelement transfer. Retroelement-guided diversification is further shown to be active in current CPR and DPANN populations, with an assortment of protein targets potentially involved in attachment, defence and regulation. Based on observations of DGR abundance, function and evolutionary history, we find that targeted protein diversification is a pronounced trait of CPR and DPANN phyla compared to other bacterial and archaeal phyla. This diversification mechanism may provide CPR and DPANN organisms with a versatile tool that could be used for adaptation to a dynamic, host-dependent existence

Microbial metagenomes from three aquifers in the Fennoscandian shield terrestrial deep biosphere reveal metabolic partitioning among populations

Microorganisms in the terrestrial deep biosphere host up to 20% of the earth's biomass and are suggested to be sustained by the gases hydrogen and carbon dioxide. A metagenome analysis of three deep subsurface water types of contrasting age (from &lt;20 to several thousand years) and depth (171 to 448 m) revealed phylogenetically distinct microbial community subsets that either passed or were retained by a 0.22 mu m filter. Such cells of &lt;0.22 mu m would have been overlooked in previous studies relying on membrane capture. Metagenomes from the three water types were used for reconstruction of 69 distinct microbial genomes, each with &gt;86% coverage. The populations were dominated by Proteobacteria, Candidate divisions, unclassified archaea and unclassified bacteria. The estimated genome sizes of the &lt;0.22 mu m populations were generally smaller than their phylogenetically closest relatives, suggesting that small dimensions along with a reduced genome size may be adaptations to oligotrophy. Shallow 'modern marine' water showed community members with a predominantly heterotrophic lifestyle. In contrast, the deeper, 'old saline' water adhered more closely to the current paradigm of a hydrogen-driven deep biosphere. The data were finally used to create a combined metabolic model of the deep terrestrial biosphere microbial community.Supplementary information available for this article at http://www.nature.com/ismej/journal/v10/n5/suppinfo/ismej2015185s1.html</p