The faint-galaxy hosts of gamma-ray bursts

The observed redshifts and magnitudes of the host galaxies of gamma-ray bursts (GRBs) are compared with the predictions of three basic GRB models, in which the comoving rate density of GRBs is (1) proportional to the cosmic star formation rate density, (2) proportional to the total integrated stellar density and (3) constant. All three models make the assumption that at every epoch the probability of a GRB occuring in a galaxy is proportional to that galaxy's broad-band luminosity. No assumption is made that GRBs are standard candles or even that their luminosity function is narrow. All three rate density models are consistent with the observed GRB host galaxies to date, although model (2) is slightly disfavored relative to the others. Models (1) and (3) make very similar predictions for host galaxy magnitude and redshift distributions; these models will be probably not be distinguished without measurements of host-galaxy star-formation rates. The fraction of host galaxies fainter than 28 mag may constrain the faint end of the galaxy luminosity function at high redshift, or, if the fraction is observed to be low, may suggest that the bursters are expelled from low-luminosity hosts. In all models, the probability of finding a z<0.008 GRB among a sample of 11 GRBs is less than 10^(-4), strongly suggesting that GRB 980425, if associated with supernova 1998bw, represents a distinct class of GRBs.Comment: 7 pages, ApJ in press, revised to incorporate yet more new and revised observational result

A maximum-likelihood method for improving faint source flux and color estimates

Flux estimates for faint sources or transients are systematically biased high because there are far more truly faint sources than bright. Corrections which account for this effect are presented as a function of signal-to-noise ratio and the (true) slope of the faint-source number-flux relation. The corrections depend on the source being originally identified in the image in which it is being photometered. If a source has been identified in other data, the corrections are different; a prescription for calculating the corrections is presented. Implications of these corrections for analyses of surveys are discussed; the most important is that sources identified at signal-to-noise ratios of four or less are practically useless.Comment: 9 pp., accepted for publication in PAS

The oxygen-II luminosity density of the Universe

Equivalent widths of [OII] 3727 A lines are measured in 375 faint galaxy spectra taken as part of the Caltech Faint Galaxy Redshift Survey centered on the Hubble Deep Field. The sensitivity of the survey spectra to the [OII] line is computed as a function of magnitude, color and redshift. The luminosity function of galaxies in the [OII] line and the integrated luminosity density of the Universe in the [OII] line are computed as a function of redshift. It is found that the luminosity density in the [OII] line was a factor of ~10 higher at redshifts z~1 than it is at the present day. The simplest interpretation is that the star formation rate density of the Universe has declined dramatically since z~1.Comment: accepted for publication in Ap

A deductive statistical mechanics approach for granular matter

We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such a distribution is the equivalent of the Maxwell-Boltzmann's distribution in the kinetic theory of gasses. The comparison with a very extensive set of experimental and simulation data for packings of monosized spherical grains, reveals a remarkably good quantitative agreement with the theoretical predictions for the density fluctuations both at the grain level and at the global system level. Such agreement is robust over a broad range of packing fractions and it is observed in several distinct systems prepared by using different methods. The equilibrium distributions are characterized by only one parameter ($k$) which is a quantity very sensitive to changes in the structural organization. The thermodynamical equivalent of $k$ and its relation with the `granular temperature' are also discussed.Comment: 15 pages, 6 figure

The scale-dependence of relative galaxy bias: encouragement for the halo model description

We investigate the relationship between the colors, luminosities, and environments of galaxies in the Sloan Digital Sky Survey spectroscopic sample, using environmental measurements on scales ranging from 0.2 to 6 Mpc/h. We find: (1) that the relationship between color and environment persists even to the lowest luminosities we probe (absolute magnitude in the r band of about -14 for h=1); (2) at luminosities and colors for which the galaxy correlation function has a large amplitude, it also has a steep slope; and (3) in regions of a given overdensity on small scales (1 Mpc/h), the overdensity on large scales (6 Mpc/h) does not appear to relate to the recent star formation history of the galaxies. Of these results, the last has the most immediate application to galaxy formation theory. In particular, it lends support to the notion that a galaxy's properties are related only to the mass of its host dark matter halo, and not to the larger scale environment.Comment: submitted to ApJ; full resolution figures and slide material available at http://cosmo.nyu.edu/blanton/scale_density.htm

Probing Dark Matter Substructure in Lens Galaxies

We investigate the effects of numerous dark matter subhalos in a galaxy-sized halo on the events of strong lensing, to assess their presence as expected from the cold dark matter scenario. Lens galaxies are represented by a smooth ellipsoid in an external shear field and additional cold dark matter subhalos taken from Monte Carlo realizations which accord with recent N-body results. We also consider other possible perturbers, globular clusters and luminous dwarf satellites, for comparison. We then apply the models to the particular lens systems with four images, B1422+231 and PG1115+080, for which smooth lens models are unable to reproduce both the positions of the images and their radio flux ratios or dust-free optical flux ratios simultaneously. We show that the perturbations by both globular clusters and dwarf satellites are too small to change the flux ratios, whereas cold dark matter subhalos are most likely perturbers to reproduce the observed flux ratios in a statistically significant manner. This result suggests us the presence of numerous subhalos in lens galaxies, which is consistent with the results of cosmological N-body simulations.Comment: 19 pages, including 5 figures, ApJ in pres

Fingerprint for Network Topologies

A network's topology information can be given as an adjacency matrix. The bitmap of sorted adjacency matrix(BOSAM) is a network visualisation tool which can emphasise different network structures by just looking at reordered adjacent matrixes. A BOSAM picture resembles the shape of a flower and is characterised by a series of 'leaves'. Here we show and mathematically prove that for most networks, there is a self-similar relation between the envelope of the BOSAM leaves. This self-similar property allows us to use a single envelope to predict all other envelopes and therefore reconstruct the outline of a network's BOSAM picture. We analogise the BOSAM envelope to human's fingerprint as they share a number of common features, e.g. both are simple, easy to obtain, and strongly characteristic encoding essential information for identification.Comment: 12papes, 3 figures, in pres

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

A review of mammographic positioning image quality criteria for the craniocaudal projection

Detection of breast cancer is reliant on optimal breast positioning and the production of quality images. Two projections, the mediolateral (MLO) and craniocaudal (CC), are routinely performed. Determination of successful positioning and inclusion of all breast tissue is achieved through meeting stated image quality criteria. For the CC view, current image quality criteria are inconsistent. Absence of reliable anatomical markers, other than the nipple, further contribute to difficulties in assessing the quality of CC views. The aim of this paper was to explore published international quality standards to identify and find the origin of any CC positioning criteria which might provide for quantitative assessment. The pectoralis major (pectoral) muscle was identified as a key posterior anatomical structure to establish optimum breast tissue inclusion on mammographic projections. It forms the first two of the three main CC metrics that are frequently reported 1. visualisation of the pectoral muscle, 2. measurement of the posterior nipple line (PNL) and 3. depiction of retroglandular fat. This literature review explores the origin of the three metrics, and discusses three key publications, spanning 1992 to 1994, on which subsequent image quality standards have been based. The evidence base to support published CC metrics is sometimes not specified and more often the same set of publications are cited, most often without critical evaluation. To conclude, there remains uncertainty if the metrics explored for the CC view support objective evaluation and reproducibility to confirm optimal breast positioning and quality images