Dynamics of Three Agent Games

We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the probabilities that the team with the highest, middle or lowest accumulated score wins. We study the full family of solutions in the regime, where the number of agents and competitions is large, which can be regarded as a hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six qualitatively different asymptotic score distributions and we also provide a qualitative understanding of these results. We checked our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement. The three agent game can be regarded as a social model where a player can be favored or disfavored for advancement, based on his/her accumulated score. It is also possible to decide the outcome of a three agent game through a mini tournament of two-a gent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent-games. We discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to write down the corresponding score evolution equations for $n$-agent games

Deep Luminosity Functions and Colour-Magnitude Relations for Cluster Galaxies at 0.2 < z < 0.6

We derive deep $I$ band luminosity functions and colour-magnitude diagrams from HST imaging for eleven $0.2<z<0.6$ clusters observed at various stages of merging, and a comparison sample of five more relaxed clusters at similar redshifts. The characteristic magnitude $M^*$ evolves passively out to $z=0.6$, while the faint end slope of the luminosity function is $\alpha \sim -1$ at all redshifts. Cluster galaxies must have been completely assembled down to $M_I \sim -18$ out to $z=0.6$. We observe tight colour-magnitude relations over a luminosity range of up to 8 magnitudes, consistent with the passive evolution of ancient stellar populations. This is found in all clusters, irrespective of their dynamical status (involved in a collision or not, or even within subclusters for the same object) and suggests that environment does not have a strong influence on galaxy properties. A red sequence luminosity function can be followed to the limits of our photometry: we see no evidence of a weakening of the red sequence to $z=0.6$. The blue galaxy fraction rises with redshift, especially at fainter absolute magnitudes. We observe bright blue galaxies in clusters at $z > 0.4$ that are not encountered locally. Surface brightness selection effects preferentially influence the detectability of faint red galaxies, accounting for claims of evolution at the faint end.Comment: 21 pages. A series of figures for individual clusters (the full sample) will be made available on the MNRAS website. Accepted by MNRA

Morphological evolution in situ: Disk-dominated cluster red sequences at z ~ 1.25

We have carried out a joint photometric and structural analysis of red sequence galaxies in four clusters at a mean redshift of z ~ 1.25 using optical and near-IR HST imaging reaching to at least 3 magnitudes fainter than $M^*$. As expected, the photometry and overall galaxy sizes imply purely passive evolution of stellar populations in red sequence cluster galaxies. However, the morphologies of red sequence cluster galaxies at these redshifts show significant differences to those of local counterparts. Apart from the most massive galaxies, the high redshift red sequence galaxies are significantly diskier than their low redshift analogues. These galaxies also show significant colour gradients, again not present in their low redshift equivalents, most straightforwardly explained by radial age gradients. A clear implication of these findings is that red sequence cluster galaxies originally arrive on the sequence as disk-dominated galaxies whose disks subsequently fade or evolve secularly to end up as high S\'ersic index early-type galaxies (classical S0s or possibly ellipticals) at lower redshift. The apparent lack of growth seen in a comparison of high and low redshift red sequence galaxies implies that any evolution is internal and is unlikely to involve significant mergers. While significant star formation may have ended at high redshift, the cluster red sequence population continues to evolve (morphologically) for several Gyrs thereafter.Comment: Accepted by MNRA

The Fornax Spectroscopic Survey --- Low Surface Brightness Galaxies in Fornax

The Fornax Spectroscopic Survey is a large optical spectroscopic survey of ALL 14,000 objects with 16.5<Bj<19.7 in a 12 sq.deg area of sky centered on the Fornax Cluster. We are using the 400-fibre Two Degree Field spectrograph on the Anglo-Australian Telescope: the multiplex advantage of this system allows us to observe objects conventionally classified as `stars' as well as `galaxies'. This is the only way to minimise selection effects caused by image classification or assessing cluster membership. In this paper we present the first measurements of low surface brightness (LSB) galaxies we have detected both in the Fornax Cluster and among the background field galaxies. The new cluster members include some very low luminosity (M_B approx -11.5 mag) dwarf ellipticals, whereas the background LSB galaxies are luminous (-19.6<M_B<-17.0 mag) disk-like galaxies.Comment: To appear in "The Low Surface Brightness Universe", IAU Coll 171, eds. J.I. Davies et al., A.S.P. Conference Series. 8 pages, LaTex, 6 encapsulated ps-figures, requires paspconf.st

A Topological Characterization Of Knots and Links Arising From Site-Specific Recombination

We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or link substrate. We show that all knotted or linked products fall into a single family, and prove that the size of this family grows linearly with the cube of the minimum number of crossings. Additionally, we prove that the only possible products of an unknot substrate are either clasp knots and links or (2,m)-torus knots and links. Finally, in the (common) case of (2,m)-torus knot or link substrates whose products have minimal crossing number m+1, we prove that the types of products are tightly prescribed, and use this to examine previously uncharacterized experimental data.Comment: 18 pages, 3 tables, 18 figures. See also arXiv:0707.3775v1 for biological evidence for and applications of the model developed her

The Extinction Distribution in the Galaxy UGC 5041

We probe the dust extinction through the foreground disk of the overlapping galaxy pair UGC 5041 by analyzing B,I, and H band images. The inclined foreground disk of this infrared-selected pair is almost opaque in B at a projected distance of ~8kpc. From the images, we estimate directly the area-weighted distribution of differential near-IR extinction: it is nearly Gaussian with =0.6 and sigma=0.27. For a homogenous dust distribution and a Milky Way extinction curve, this corresponds to a face-on distribution p(tau) with a mean of =0.34 and sigma_V=0.15. For a clumpy dust model the optical depth estimate increases to =0.41 and sigma_V=0.19. Even though the galaxy pair is subject to different selection biases and our analysis is subject to different systematics, the result is consistent with existing case studies, indicating that ~0.3 is generic for late-type spirals near their half-light radii. We outline how to estimate from p(tau) by how much background quasars are underreresented, where projected within ~10kpc of nearby spirals, such as damped Ly-alpha absorbers or gravitational lenses; from our data we derive a factor of two deficit for flux-limited, optical surveys.Comment: 18 pages, 3 figures; To appear in the Astronomical Journa

Optical/near-infrared colours of early-type galaxies and constraints on their star formation histories

(abridged) We introduce and discuss the properties of a theoretical (B-K)-(J-K) integrated colour diagram for single-age, single-metallicity stellar populations. This combination of integrated colours is able to largely disentangle the well known age-metallicity degeneracy when the age of the population is greater than ~300 Myr. We discuss in detail the effect on this colour-colour diagram of alpha-enhanced metal abundance ratios, the presence of blue horizontal branch stars unaccounted for in the theoretical calibration, and of statistical colour fluctuations in low mass stellar systems. In the case of populations with multiple stellar generations, the luminosity-weighted mean age obtained from this diagram is shown to be heavily biased towards the youngest stellar components. We apply this method to several datasets for which optical and near-IR photometry are available in the literature. For the two Local Group dwarf galaxies NGC185 and NGC6822, the mean ages derived from the integrated colours are consistent with the star formation histories inferred independently from photometric observations of their resolved stellar populations. A sample of bright field and Virgo cluster elliptical galaxies is found to exhibit a range of luminosity-weighted mean ages from 3 to 14 Gyr, with a mean of 8 Gyr, independent of environment, and mean metallicities at or just above the solar value. Colour gradients are found in all of the galaxies studied, in the sense that central regions are redder. Aperture data for five Virgo early-type dwarf galaxies show that these galaxies appear to be shifted to lower mean metallicities and lower mean ages (range 1 to 6 Gyr) than their higher luminosity counterparts.Comment: (1) Liverpool John Moores University, UK; (2) University of Cardiff, UK; (3) University of Bristol, UK; (4) INAF-Osservatorio Astronomico di Collurania, I; 12 pages, 9 figures, MNRAS in pres

Metastable Flux Configurations and de Sitter Spaces

We derive stability conditions for the critical points of the no-scale scalar potential governing the dynamics of the complex structure moduli and the axio-dilaton in compactifications of type IIB string theory on Calabi-Yau three-folds. We discuss a concrete example of a T^6 orientifold. We then consider the four-dimensional theory obtained from compactifications of type IIB string theory on non-geometric backgrounds which are mirror to rigid Calabi-Yau manifolds and show that the complex structure moduli fields can be stabilized in terms of H_{RR} only, i.e. with no need of orientifold projection. The stabilization of all the fields at weak coupling, including the axio-dilaton, may require to break supersymmetry in the presence of H_{NS} flux or corrections to the scalar potential.Comment: 24 page