Hexagonal Tilings: Tutte Uniqueness

We develop the necessary machinery in order to prove that hexagonal tilings are uniquely determined by their Tutte polynomial, showing as an example how to apply this technique to the toroidal hexagonal tiling.Comment: 12 figure

Hexagonal Tilings and Locally C6 Graphs

We give a complete classification of hexagonal tilings and locally C6 graphs, by showing that each of them has a natural embedding in the torus or in the Klein bottle. We also show that locally grid graphs are minors of hexagonal tilings (and by duality of locally C6 graphs) by contraction of a perfect matching and deletion of the resulting parallel edges, in a form suitable for the study of their Tutte uniqueness.Comment: 14 figure

Serendipitous discovery of a cluster of galaxies with a peculiar central galaxy

We report the serendipitous discovery of a cluster of galaxies at z=0.369. Thirty-eight candidate members were identified based on rough broad-band photometric redshifts, and three members were confirmed spectroscopically. The brightest cluster galaxy (BCG) is exceptionally blue, with B-V=0.12 and V-I=1.02. The surface-brightness profile of the BCG follows an r^(1/4)-law profile out to 3" in all three bands. The effective radius is significantly smaller in bluer bandpasses, resulting in a blue core and a color gradient opposite to the metallicity-induced color gradient observed in typical elliptical galaxies. Beyond 3" an extended envelope of emission in excess of the r^(1/4)-law profile is observed, the position angle of which coincides with the major axis of the galaxy cluster. The spectrum of the BCG contains strong Balmer absorption, a minimal 4000 A break, and a broad Mg II emission line, suggesting that the galaxy has undergone recent star formation and may harbor a central AGN. The presence of numerous nearby bright stars makes this cluster an interesting target for next-generation adaptive optics using natural guide stars.Comment: 21 pages, 8 figures, accepted for publication in the Astronomical Journa

The Origin of the Brightest Cluster Galaxies

Most clusters and groups of galaxies contain a giant elliptical galaxy in their centres which far outshines and outweighs normal ellipticals. The origin of these brightest cluster galaxies is intimately related to the collapse and formation of the cluster. Using an N-body simulation of a cluster of galaxies in a hierarchical cosmological model, we show that galaxy merging naturally produces a massive, central galaxy with surface brightness and velocity dispersion profiles similar to observed BCG's. To enhance the resolution of the simulation, 100 dark halos at $z=2$ are replaced with self-consistent disk+bulge+halo galaxy models following a Tully-Fisher relation using 100000 particles for the 20 largest galaxies and 10000 particles for the remaining ones. This technique allows us to analyze the stellar and dark matter components independently. The central galaxy forms through the merger of several massive galaxies along a filament early in the cluster's history. Galactic cannibalism of smaller galaxies through dynamical friction over a Hubble time only accounts for a small fraction of the accreted mass. The galaxy is a flattened, triaxial object whose long axis aligns with the primordial filament and the long axis of the cluster galaxy distribution agreeing with observed trends for galaxy-cluster alignment.Comment: Revised and accepted in ApJ, 25 pages, 10 figures, online version available at http://www.cita.utoronto.ca/~dubinski/bcg

An Incremental Learning Method to Support the Annotation of Workflows with Data-to-Data Relations

Workflow formalisations are often focused on the representation of a process with the primary objective to support execution. However, there are scenarios where what needs to be represented is the effect of the process on the data artefacts involved, for example when reasoning over the corresponding data policies. This can be achieved by annotating the workflow with the semantic relations that occur between these data artefacts. However, manually producing such annotations is difficult and time consuming. In this paper we introduce a method based on recommendations to support users in this task. Our approach is centred on an incremental rule association mining technique that allows to compensate the cold start problem due to the lack of a training set of annotated workflows. We discuss the implementation of a tool relying on this approach and how its application on an existing repository of workflows effectively enable the generation of such annotations

Globular Clusters in Dense Clusters of Galaxies

Deep imaging data from the Keck II telescope are employed to study the globular cluster (GC) populations in the cores of six rich Abell clusters. The sample includes A754, A1644, A2124, A2147, A2151, and A2152, and spans the redshift range z = 0.035-0.066. The clusters also range in morphology from spiral-rich, irregular systems to centrally concentrated cD clusters rich in early-type galaxies. Globular cluster specific frequencies S_N and luminosity function dispersions are measured for a total of 9 galaxies in six central fields. The measured values of S_N for the six brightest cluster galaxies (BCGs) are all higher than typical values for giant ellipticals, in accord with the known S_N-density correlations. The three non-BCGs analyzed also have elevated values of S_N, confirming that central location is a primary factor. The number of GCs per unit mass for these fields are consistent with those found in an earlier sample, giving further evidence that GC number scales with mass and that the S_N variations are due to a deficit of halo light, i.e., S_N reflects mass-to-light ratio. The discussion builds on an earlier suggestion that the GCs (both metal rich and metal poor) around the central cluster galaxies were assembled at early times, and that star formation halted prematurely in the central galaxies at the epoch of cluster collapse. This is consistent with recent simulations of BCG/cluster formation. The subsequent addition of luminous material through cluster dynamical evolution can cause S_N to decrease, and we may be seeing the first evidence of this. Finally, the GC luminosity function measurements are used to constrain the relative distances of the three clusters that make up the Hercules supercluster.Comment: Uses emulateapj.sty (included); 17 pages with 9 included PostScript figures. Figures 1-6 are separate GIF images (so 15 figures total) available from http://astro.caltech.edu/~jpb/clusters -- the full PostScript version of the paper (20 pages; 2.2 Mb compressed) incorporating Figures 1-6 can also be grabbed from this URL. Accepted for publication in A

The Dependence of Galaxy Shape on Luminosity and Surface Brightness Profile

For a sample of 96,951 galaxies from the Sloan Digital Sky Survey Data Release 3, we study the distribution of apparent axis ratios as a function of r-band absolute magnitude and surface brightness profile type. We use the parameter fracDeV to quantify the profile type (fracDeV = 1 for a de Vaucouleurs profile; fracDeV = 0 for an exponential profile). When the apparent axis ratio q_{am} is estimated from the moments of the light distribution, the roundest galaxies are very bright (M_r \sim -23) de Vaucouleurs galaxies and the flattest are modestly bright (M_r \sim -18) exponential galaxies. When the apparent axis ratio q_{25} is estimated from the axis ratio of the 25 mag/arcsec^2 isophote, we find that de Vaucouleurs galaxies are flatter than exponential galaxies of the same absolute magnitude. For a given surface brightness profile type, very bright galaxies are rounder, on average, than fainter galaxies. We deconvolve the distributions of apparent axis ratios to find the distribution of the intrinsic short-to-long axis ratio gamma, assuming constant triaxiality T. For all profile types and luminosities, the distribution of apparent axis ratios is inconsistent with a population of oblate spheroids, but is usually consistent with a population of prolate spheroids. Bright galaxies with a de Vaucouleurs profile (M_r < -21.84, fracDeV > 0.9) have a distribution of q_{am} that is consistent with triaxiality in the range 0.4 < T < 0.8, with mean intrinsic axis ratio 0.66 < gamma < 0.69. The fainter de Vaucouleurs galaxies are best fit with prolate spheroids (T = 1) with mean axis ratio gamma = 0.51.Comment: 32 pages, 12 figures, to appear in Ap

Effectiveness of the Lapidus plate system in foot surgery: A PRISMA compliant systematic review

Lapidus arthrodesis is an established standard procedure to correct various foot surgery problems and hallux limitus, hypermobility of the first ray, hallux abductus valgus, and symptomatic lesser metatarsal. After decades, many fixation methods in the orthopaedic surgery industry have been developed for decreasing complications and improving this technique. The aim of this PRISMA compliant systematic review is to analyse the effectiveness of several lapidus plate systems in foot surgery. We have carried out the first systematic review of the relevant published literature so as to systematically evaluate the scientific knowledge available now on this association, assigning predefined eligibility criteria. Fourteen studies were selected which had an overall of 738 cases. The first tarsal metatarsal joint and hallux valgus were treated by the application of different types of Lapidus plate system. The optimal level of the fixation in these procedures is related with the type and system insertion place of the plate with or without screw in each specific foot disease. There is an insufficient number of studies about the effectiveness of the different types of Lapidus plate system in foot surgery, and there is a need to increase outcomes knowledge on the level of the fixation, sort of the system, and insert place in foot surgery

Singular perturbations in the quadratic family with multiple poles

Agraïments: The first author is partially supported by the European Community through the project 035651-1-2-CODY.We consider the quadratic family of complex maps given by qc(z) = z2 + c where c is the center of a hyperbolic component in the Mandelbrot set. Then, we introduce a singular perturbation on the corresponding bounded superattracting cycle by adding one pole to each point in the cycle. When c = −1 the Julia set of q−1 is the well known basilica and the perturbed map is given by fλ(z) = z2 − 1 + λ/(z d0 (z + 1)d1) where d0, d1 ≥ 1 are integers, and λ is a complex parameter such that (...) is very small. We focus on the topological characteristics of the Julia and Fatou sets of fλ that arise when the parameter λ becomes nonzero. We give sufficient conditions on the order of the poles so that for small λ the Julia sets consist of the union of homeomorphic copies of the unperturbed Julia set, countably many Cantor sets of concentric closed curves, and Cantor sets of point components that accumulate on them