Archaeal ubiquity

In the seventeenth century, Antoine von Leeuwenhook used a simple microscope to discover that we live within a previously undetected microbial world containing an enormously diverse population of creatures. The late nineteenth and early twentieth century brought advances in microbial culture techniques and in biochemistry, uncovering the roles that microbes play in all aspects of our world, from causing disease to modulating geochemical cycles. In the last 25 years, molecular biology has revealed the complexity and pervasiveness of the microbial world and its importance for understanding the interactions that maintain living systems on the planet. The paper by Preston et al. (1) in this issue of the Proceedings provides a clear illustration of the power of these molecular techniques to describe new biological relationships and to pose important questions about the mechanisms that drive evolution. The analysis of ribosomal RNA gene sequences is one molecular approach that has radically altered our view of microbial diversity. Its application can be extended and expedited by the use of PCR. The confluence of these techniques has stimulated the rapid assembly of sequence information from homologues rRNA gene regions derived from virtually all classes of organisms. The data collected thus far support the scheme first presented by Woese et al. (2), which holds that the relationships among organisms can be summarized in the form of a universal phylogenetic tree comprised of one eukaryotic and two prokaryotic domains: the Eucarya, the Bacteria, and the Archaea (Fig. 1)

The ubiquity of conservative translations

We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal.Comment: 15 pages; to appear in Review of Symbolic Logi

Big Data, Digitization, and Social Change (Ubiquity Symposium)

The term “big data” is something of a misnomer. Every generation of computers since the 1950s has been confronted with problems where data was way too large for the memory and processing power available. This seemed like an inconvenience of the technology that would someday be resolved when the next generation of computers came along. So what is different about big data today? The revolution is happening at the convergence of two trends: the expansion of the internet into billions of computing devices, and the digitization of almost everything. The internet gives us access to vast amounts of data. Digitization creates digital representations for many things once thought to be beyond the reach of computing technology. The result is an explosion of innovation of network-based big data applications and the automation of cognitive tasks. This revolution is introducing what Brynjolfsson and McAfee call the “Second Machine Age.” This symposium will examine this revolution from a number of angles

The Ubiquity of the Rapid Neutron-Capture Process

To better characterize the abundance patterns produced by the r-process, we have derived new abundances or upper limits for the heavy elements zinc (Zn), yttrium (Y), lanthanum (La), europium (Eu), and lead (Pb). Our sample of 161 metal-poor stars includes new measurements from 88 high resolution and high signal-to-noise spectra obtained with the Tull Spectrograph on the 2.7m Smith Telescope at McDonald Observatory, and other abundances are adopted from the literature. We use models of the s-process in AGB stars to characterize the high Pb/Eu ratios produced in the s-process at low metallicity, and our new observations then allow us to identify a sample of stars with no detectable s-process material. In these stars, we find no significant increase in the Pb/Eu ratios with increasing metallicity. This suggests that s-process material was not widely dispersed until the overall Galactic metallicity grew considerably, perhaps even as high as [Fe/H]=-1.4. We identify a dispersion of at least 0.5 dex in [La/Eu] in metal-poor stars with [Eu/Fe]<+0.6 attributable to the r-process, suggesting that there is no unique "pure" r-process elemental ratio among pairs of rare earth elements. We confirm earlier detections of an anti-correlation between Y/Eu and Eu/Fe bookended by stars strongly enriched in the r-process (e.g., CS 22892-052) and those with deficiencies of the heavy elements (e.g., HD 122563). We can reproduce the range of Y/Eu ratios using simulations of high-entropy neutrino winds of core-collapse supernovae that include charged-particle and neutron-capture components of r-process nucleosynthesis. The heavy element abundance patterns in most metal-poor stars do not resemble that of CS 22892-052, but the presence of heavy elements such as Ba in nearly all metal-poor stars without s-process enrichment suggests that the r-process is a common phenomenon.Comment: Accepted for publication in the Astrophysical Journal. 25 pages, 13 figure

Describability via ubiquity and eutaxy in Diophantine approximation

We present a comprehensive framework for the study of the size and large intersection properties of sets of limsup type that arise naturally in Diophantine approximation and multifractal analysis. This setting encompasses the classical ubiquity techniques, as well as the mass and the large intersection transference principles, thereby leading to a thorough description of the properties in terms of Hausdorff measures and large intersection classes associated with general gauge functions. The sets issued from eutaxic sequences of points and optimal regular systems may naturally be described within this framework. The discussed applications include the classical homogeneous and inhomogeneous approximation, the approximation by algebraic numbers, the approximation by fractional parts, the study of uniform and Poisson random coverings, and the multifractal analysis of L{\'e}vy processes.Comment: 94 pages. Notes based on lectures given during the 2012 Program on Stochastics, Dimension and Dynamics at Morningside Center of Mathematics, the 2013 Arithmetic Geometry Year at Poncelet Laboratory, and the 2014 Spring School in Analysis held at Universite Blaise Pasca

Notions of Relative Ubiquity for Invariant Sets of Relational Structures

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is ubiquitous in the set of linear orderings on w

The Ubiquity and Dual Nature of Ultra Compact Dwarfs

We present the discovery of several Ultra Compact Dwarfs (UCDs) located in field/group environments. Examination of these objects, plus literature objects, confirms the existence of two distinct formation channels for UCDs. We find that the UCDs we have discovered around the group elliptical NGC3923 (and UCDs generally) have properties consistent with their being the most luminous members of the host galaxy's globular cluster (GC) system. We describe UCDs of this type as giant GCs (GGCs). In contrast, the UCD we have found associated with the isolated S0 NGC4546 is clearly the result of the stripping of a nucleated companion galaxy. The young age (~3.4 Gyr) of the UCD, the lack of a correspondingly young GC population, the apparently short dynamical friction decay timescale (~0.5 Gyr) of the UCD, and the presence of a counterrotating gas disc in the host galaxy (co-rotating with the UCD) together suggest that this UCD is the liberated nucleus remaining after the recent stripping of a companion by NGC4546. We suggest a general scheme that unifies the formation of GCs, UCDs, and galaxy nuclei. In this picture "normal" GCs are a composite population, composed of GCs formed in situ, GCs acquired from accreted galaxies, and a population of lower mass stripped dwarf nuclei masquerading as GCs. Above a "scaling onset mass" of 2x10^6 Msun (Mv ~ -10), UCDs emerge together with a mass-size relation and a likely mass-metallicity relation (the "blue tilt"). In the mass range up to 7x10^7 Msun (Mv ~ -13) UCDs comprise a composite population of GGCs and stripped nuclei. Above 7x10^7 Msun, UCDs must be almost exclusively stripped nuclei, as no sufficiently rich GC systems exist to populate such an extreme of the GCLF.Comment: 23 pages, 16 figures, accepted for publication in MNRA