Deductive synthesis of recursive plans in linear logic

Linear logic has previously been shown to be suitable for describing and deductively solving planning problems involving conjunction and disjunction. We introduce a recursively defined datatype and a corresponding induction rule, thereby allowing recursive plans to be synthesised. In order to make explicit the relationship between proofs and plans, we enhance the linear logic deduction rules to handle plans as a form of proof term

The Sloan Lens ACS Survey. IX. Colors, Lensing and Stellar Masses of Early-type Galaxies

We present the current photometric dataset for the Sloan Lens ACS (SLACS) Survey, including HST photometry from ACS, WFPC2, and NICMOS. These data have enabled the confirmation of an additional 15 grade `A' (certain) lens systems, bringing the number of SLACS grade `A' lenses to 85; including 13 grade `B' (likely) systems, SLACS has identified nearly 100 lenses and lens candidates. Approximately 80% of the grade `A' systems have elliptical morphologies while ~10% show spiral structure; the remaining lenses have lenticular morphologies. Spectroscopic redshifts for the lens and source are available for every system, making SLACS the largest homogeneous dataset of galaxy-scale lenses to date. We have developed a novel Bayesian stellar population analysis code to determine robust stellar masses with accurate error estimates. We apply this code to deep, high-resolution HST imaging and determine stellar masses with typical statistical errors of 0.1 dex; we find that these stellar masses are unbiased compared to estimates obtained using SDSS photometry, provided that informative priors are used. The stellar masses range from 10^10.5 to 10^11.8 M$_\odot$ and the typical stellar mass fraction within the Einstein radius is 0.4, assuming a Chabrier IMF. The ensemble properties of the SLACS lens galaxies, e.g. stellar masses and projected ellipticities, appear to be indistinguishable from other SDSS galaxies with similar stellar velocity dispersions. This further supports that SLACS lenses are representative of the overall population of massive early-type galaxies with M* >~ 10^11 M$_\odot$, and are therefore an ideal dataset to investigate the kpc-scale distribution of luminous and dark matter in galaxies out to z ~ 0.5.Comment: 20 pages, 18 figures, 5 tables, published in Ap

Luminous Satellites of Early-Type Galaxies I: Spatial Distribution

We study the spatial distribution of faint satellites of intermediate redshift (0.1<z<0.8), early-type galaxies, selected from the GOODS fields. We combine high resolution HST images and state-of-the-art host subtraction techniques to detect satellites of unprecedented faintness and proximity to intermediate redshift host galaxies (up to 5.5 magnitudes fainter and as close as 0."5/2.5 kpc to the host centers). We model the spatial distribution of objects near the hosts as a combination of an isotropic, homogenous background/foreground population and a satellite population with a power law radial profile and an elliptical angular distribution. We detect a significant population of satellites, Ns =1.7 (+0.9,-0.8) that is comparable to the number of Milky Way satellites with similar host-satellite contrast.The average projected radial profile of the satellite distribution is isothermal, gamma_p= -1.0(+0.3,-0.4), which is consistent with the observed central mass density profile of massive early-type galaxies. Furthermore, the satellite distribution is highly anisotropic (isotropy is ruled out at a >99.99% confidence level). Defining phi to be the offset between the major axis of the satellite spatial distribution and the major axis of the host light profile, we find a maximum posterior probability of phi = 0 and |phi| less than 42 degrees at the 68% confidence level. The alignment of the satellite distribution with the light of the host is consistent with simulations, assuming that light traces mass for the host galaxy as observed for lens galaxies. The anisotropy of the satellite population enhances its ability to produce the flux ratio anomalies observed in gravitationally lensed quasars.Comment: 21 pages, 16 figures, Accepted for publication in Ap

Observational Evidence for the Co-evolution of Galaxy Mergers, Quasars, and the Blue/Red Galaxy Transition

We compile a number of observations to estimate the time-averaged rate of formation or buildup of red sequence galaxies, as a function of mass and redshift. Comparing this with the mass functions of mergers and quasar hosts, and independently comparing their clustering properties as a function of redshift, we find that these populations trace the same mass distribution, with similar evolution, at redshifts 0<z<~1.5. Knowing one of the quasar, merger, or elliptical mass/luminosity functions, it is possible to predict the others. Allowing for greater model dependence, we compare the rate of early-type buildup with the implied merger and quasar triggering rates as a function of mass and redshift and find agreement. Over this redshift range, observed merger fractions can account for the entire bright quasar luminosity function and buildup of the red sequence at all but the highest masses at low redshift (>~10^11 M_solar at z<~0.3) where 'dry' mergers appear to dominate. This supports a necessary prediction of theories where mergers between gas-rich galaxies produce ellipticals with an associated phase of quasar activity, after which the remnant becomes red. These populations trace a similar characteristic transition mass, possibly reflecting the mass above which the elliptical population is mostly (>~50%) assembled at a given redshift, which increases with redshift over the observed range in a manner consistent with suggestions that cosmic downsizing may apply to red galaxy assembly as well as star formation. These mass distributions as a function of redshift do not uniformly trace the all/red/blue galaxy population, ruling out models in which quasar activity is generically associated with star formation or is long lived in 'old' systems.Comment: 24 pages, 17 figures. Accepted to ApJ. Substantially revised and expanded to match published versio

Siderophores as an iron source for picocyanobacteria in deep chlorophyll maximum layers of the oligotrophic ocean

Prochlorococcus and Synechococcus are the most abundant photosynthesizing organisms in the oceans. Gene content variation among picocyanobacterial populations in separate ocean basins often mirrors the selective pressures imposed by the region's distinct biogeochemistry. By pairing genomic datasets with trace metal concentrations from across the global ocean, we show that the genomic capacity for siderophore-mediated iron uptake is widespread in Synechococcus and low-light adapted Prochlorococcus populations from deep chlorophyll maximum layers of iron-depleted regions of the oligotrophic Pacific and S. Atlantic oceans: Prochlorococcus siderophore consumers were absent in the N. Atlantic ocean (higher new iron flux) but constituted up to half of all Prochlorococcus genomes from metagenomes in the N. Pacific (lower new iron flux). Picocyanobacterial siderophore consumers, like many other bacteria with this trait, also lack siderophore biosynthesis genes indicating that they scavenge exogenous siderophores from seawater. Statistical modeling suggests that the capacity for siderophore uptake is endemic to remote ocean regions where atmospheric iron fluxes are the smallest, especially at deep chlorophyll maximum and primary nitrite maximum layers. We argue that abundant siderophore consumers at these two common oceanographic features could be a symptom of wider community iron stress, consistent with prior hypotheses. Our results provide a clear example of iron as a selective force driving the evolution of marine picocyanobacteria

Patterns of Diatom Diversity Correlate With Dissolved Trace Metal Concentrations and Longitudinal Position in the Notheast Pacific Coastal Offshore Transition Zone

Diatoms are important primary producers in the northeast Pacific Ocean, with their productivity closely linked to pulses of trace elements in the western high nitrate, low chlorophyll (HNLC) region of the oceanographic time series transect \u27Line P.\u27 Recently, the coastal-HNLC transition zone of the Line P transect was identified as a hotspot of phytoplankton productivity, potentially controlled by a combination of trace element and macronutrient concentrations. Here we describe diatom community composition in the eastern Line P transect, including the coastal- HNLC transition zone, with a method using high-throughput sequencing of diatom 18S gene amplicons. We identified significant correlations between shifting diatom community composition and longitude combined with concentrations of dissolved copper and 2 other dissolved trace metals (dissolved Fe [dFe] and/or dissolved zinc) and/or a physical factor (salinity or density). None of these variables on its own was significantly correlated with shifts in community composition, and 3 of the factors (dFe, salinity, and density) correlated with one another. Longitude could incorporate multiple factors that may influence diatom communities, including distance from shore, proximity of sampling stations, and an integration of previous pulses of macro- and micro-nutrients. We also evaluated in situ Fe limitation of the diatom Thalassiosira oceanica using a quantitative reverse-transcription polymerase chain reaction method, and found biological evidence of Fe stress in samples from the coastal-HNLC transition zone. Combined, our results support a prior hypothesis that dissolved trace metals as well as longitudinal distance may be important to diatom diversity in the coastal-HNLC transition zone of the Line P transect

Graphical Reasoning in Compact Closed Categories for Quantum Computation

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.Comment: 21 pages, 9 figures. This is the journal version of the paper published at AIS

A Compact Early-type Galaxy at z = 0.6 Under a Magnifying Lens: Evidence For Inside-out Growth

We use Keck laser guide star adaptive optics imaging and exploit the magnifying effects of strong gravitational lensing (the effective resolution is FWHM ~ 200 pc) to investigate the sub-kpc scale of an intermediate-redshift (z = 0.63) massive early-type galaxy being lensed by a foreground early-type galaxy; we dub this class of strong gravitational lens systems EELs, e.g., early-type/early-type lenses. We find that the background source is massive (M* = 10^{10.9} M_sun) and compact (r_e = 1.1 kpc), and a two-component fit is required to model accurately the surface brightness distribution, including an extended low-surface-brightness component. This extended component may arise from the evolution of higher-redshift `red nuggets' or may already be in place at z ~ 2 but is unobservable due to cosmological surface brightness dimming.Comment: 5 pages, 4 figures; accepted to MNRA