Growth curves for algebras

This paper studies matrix representations of algebras (over a field) using countably-infinite matrices which are both row and column finite, and in which the bandwidth growth is controlled. The ideas lead naturally to a concept of "growth of an algebra", somewhat analogous to the growth associated with GK-dimension. They also lead in a similar way to a dimension function on general algebras, which we term bandwidth dimension. For each real number r ∈ [0,1], we construct an algebra having bandwidth dimension precisely r. Since the free algebra turns out to have bandwidth dimension 0, our new dimension promises to distinguish among algebras of infinite GK-dimension

Effects of pathogen priming on judgements of face and voice attractiveness and health [oral presentation]

It has been shown (e.g. Wells et al., 2011) that whilst individuals can use both face and voice quality to make judgements of perceived attractiveness and health, in face-voice compounds, face quality typically overshadows (dominates) the judgement. It has also been shown that priming about environmental pathogen load can have a significant effect on a range judgements and behaviours (e.g. Dunn & Chambers, 2011; Little et al., 2011). Here we report on two experiments (Exp. 1 & Exp. 2), in which we explored the effects of implicit pathogen priming on face/voice attractiveness ratings (Exp. 1) and voice health ratings (Exp. 2). In Exp. 1 we show that although average attractiveness ratings for component (face or voice) and compound (face-voice) targets do not significantly change, following priming, the amount of variance accounted for by the component voice ratings in relation to the compound face-voice ratings, significantly increased, thereby removing face overshadowing. In Exp. 2 we show that whilst priming significantly shifts voice health judgements, relative to baseline, there is also a significant difference between priming the past environment (time of target stimulus collection) or the present environment (time of rating). The difference was such that priming the past produced a significantly smaller shift in voice ratings than priming the present. The findings from both experiments demonstrate that personal preference changes when pathogen load is perceived to be high, and that temporal information mediates this influence. These findings are consistent with a behavioural immune system hypothesis (e.g. Schaller & Duncan 2007)

A Deep Search For Faint Galaxies Associated With Very Low-redshift C IV Absorbers: III. The Mass- and Environment-dependent Circumgalactic Medium

Using Hubble Space Telescope Cosmic Origins Spectrograph observations of 89 QSO sightlines through the Sloan Digital Sky Survey footprint, we study the relationships between C IV absorption systems and the properties of nearby galaxies as well as large-scale environment. To maintain sensitivity to very faint galaxies, we restrict our sample to 0.0015 < z < 0.015, which defines a complete galaxy survey to L > 0.01 L* or stellar mass log M_* > 8 Msun. We report two principal findings. First, for galaxies with impact parameter rho < 1 rvir, C IV detection strongly depends on the luminosity/stellar mass of the nearby galaxy. C IV is preferentially associated with galaxies with log M_* > 9.5 Msun; lower mass galaxies rarely exhibit significant C IV absorption (covering fraction f = 9 +12-6% for 11 galaxies with log M_* < 9.5 Msun). Second, C IV detection within the log M_* > 9.5 Msun population depends on environment. Using a fixed-aperture environmental density metric for galaxies with rho < 160 kpc at z < 0.055, we find that 57+/-12% (8/14) of galaxies in low-density regions (regions with fewer than seven L > 0.15 L* galaxies within 1.5 Mpc) have affiliated C IV absorption; however, none (0/7) of the galaxies in denser regions show C IV. Similarly, the C IV detection rate is lower for galaxies residing in groups with dark-matter halo masses of log Mhalo > 12.5 Msun. In contrast to C IV, H I is pervasive in the CGM without regard to mass or environment. These results indicate that C IV absorbers with log N(C IV) > 13.5 cm^-2 trace the halos of log M_* > 9.5 Msun galaxies but also reflect larger scale environmental conditions.Comment: 26 pages, 13 figures. ApJ, in pres

Non-equilibrium dynamics and floral trait interactions shape extant angiosperm diversity.

Why are some traits and trait combinations exceptionally common across the tree of life, whereas others are vanishingly rare? The distribution of trait diversity across a clade at any time depends on the ancestral state of the clade, the rate at which new phenotypes evolve, the differences in speciation and extinction rates across lineages, and whether an equilibrium has been reached. Here we examine the role of transition rates, differential diversification (speciation minus extinction) and non-equilibrium dynamics on the evolutionary history of angiosperms, a clade well known for the abundance of some trait combinations and the rarity of others. Our analysis reveals that three character states (corolla present, bilateral symmetry, reduced stamen number) act synergistically as a key innovation, doubling diversification rates for lineages in which this combination occurs. However, this combination is currently less common than predicted at equilibrium because the individual characters evolve infrequently. Simulations suggest that angiosperms will remain far from the equilibrium frequencies of character states well into the future. Such non-equilibrium dynamics may be common when major innovations evolve rarely, allowing lineages with ancestral forms to persist, and even outnumber those with diversification-enhancing states, for tens of millions of years

The Large, Oxygen-Rich Halos of Star-Forming Galaxies Are A Major Reservoir of Galactic Metals

The circumgalactic medium (CGM) is fed by galaxy outflows and accretion of intergalactic gas, but its mass, heavy element enrichment, and relation to galaxy properties are poorly constrained by observations. In a survey of the outskirts of 42 galaxies with the Cosmic Origins Spectrograph onboard the Hubble Space Telescope, we detected ubiquitous, large (150 kiloparsec) halos of ionized oxygen surrounding star-forming galaxies, but we find much less ionized oxygen around galaxies with little or no star formation. This ionized CGM contains a substantial mass of heavy elements and gas, perhaps far exceeding the reservoirs of gas in the galaxies themselves. It is a basic component of nearly all star-forming galaxies that is removed or transformed during the quenching of star formation and the transition to passive evolution.Comment: This paper is part of a set of three papers on circumgalactic gas observed with the Cosmic Origins Spectrograph on HST, to be published in Science, together with related papers by Tripp et al. and Lehner & Howk, in the November 18, 2011 edition. This version has not undergone final copyediting. Please see Science online for the final printed versio