Large deviation asymptotics for occupancy problems

In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the distribution of various interesting quantities (such as the fraction of cells that contain a given number of balls), these expressions are often of limited practical use. Approximations provide an attractive alternative, and in the present paper we consider a large deviation approximation as r and n tend to infinity. In order to analyze the problem we first consider a dynamical model, where the balls are placed in the cells sequentially and ``time'' corresponds to the number of balls that have already been thrown. A complete large deviation analysis of this ``process level'' problem is carried out, and the rate function for the original problem is then obtained via the contraction principle. The variational problem that characterizes this rate function is analyzed, and a fairly complete and explicit solution is obtained. The minimizing trajectories and minimal cost are identified up to two constants, and the constants are characterized as the unique solution to an elementary fixed point problem. These results are then used to solve a number of interesting problems, including an overflow problem and the partial coupon collector's problem.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000013

Multi-object spectroscopy of the field surrounding PKS 2126-158: Discovery of a z=0.66 galaxy group

The high-redshift radio-loud quasar PKS 2126-158 is found to have a large number of red galaxies in close apparent proximity. We use the Gemini Multi-Object Spectrograph (GMOS) on Gemini South to obtain optical spectra for a large fraction of these sources. We show that there is a group of galaxies at $z\sim0.66$, coincident with a metal-line absorption system seen in the quasar's optical spectrum. The multiplexing capabilities of GMOS also allow us to measure redshifts of many foreground galaxies in the field surrounding the quasar. The galaxy group has five confirmed members, and a further four fainter galaxies are possibly associated. All confirmed members exhibit early-type galaxy spectra, a rare situation for a Mg II absorbing system. We discuss the relationship of this group to the absorbing gas, and the possibility of gravitational lensing of the quasar due to the intervening galaxies.Comment: Monthly Notices of the Royal Astronomical Society, in press. 10 pages, 8 figure

Mediating exposure in public interactions

Mobile computing and public interactions together open up a new range of challenges in interaction design. To date a very gregarious model of interaction has been assumed. However, the public setting will invoke feelings of shyness and a desire to control the personal exposure associated with interactions. In this paper we discuss these issues and our initial tests of a system which affords a control beyond "engage or don't engage"

My blue heaven : Fox-Trot

https://digitalcommons.library.umaine.edu/mmb-vp/7259/thumbnail.jp

Measurement of cruelty in children: The Cruelty to Animals Inventory

Cruelty to animals may be a particularly pernicious aspect of problematic child development. Progress in understanding the development of the problem is limited due to the complex nature of cruelty as a construct, and limitations with current assessment measures. The Children and Animals Inventory (CAI) was developed as a brief self- and parent-report measure of F. R. Ascione''s (1993) 9 parameters of cruelty. The CAI emerged as a reliable, stable, and readily utilized measure of cruelty using parent and child reports. Children (especially the older children) reported higher rates of cruelty than their parents and boys reported more cruelty than girls. Self- and parent-reports showed good convergence with independent observations of cruelty versus nurturance during free interactions with domestic animals. The results indicate that cruelty to animals can be reliably measured using brief child and parent report measures

If It Wasn\u27t For You

https://digitalcommons.library.umaine.edu/mmb-vp/2890/thumbnail.jp

Estimating Waterfowl Densities in a Flooded Forest: a Comparison of Methods

During winter, aerial surveys are used to estimate densities of ducks that occupy open-water habitats. However, such surveys are ineffective for sampling forest-dwelling species, especially Aix sponsa (Wood Ducks), Anas platyrhynchos (Mallards), and Lophodytes cucullatus (Hooded Mergansers). We evaluated fixed-radius plot (FRP) and Reynolds and Goodrum variable-radius plot (VRP) methods for estimating waterfowl densities in a flooded hardwood bottomland. We constructed 15 elevated blinds on the Angelina River flood plain in eastern Texas and established a 1-ha FRP around each blind; color-coded markers were placed at fixed intervals from each blind. Observers surveyed waterfowl from blinds for 21 mornings during January–March, 1990. For FRPs, species, sex, and time a bird entered and exited the plot were recorded. For VRPs, similar data and estimated observer-to-bird distance were recorded. Data were arranged in a randomized block design and tested using 1-way analyses of variances. Wood Ducks, Mallards, and Hooded Mergansers comprised 68, 18, and 10% of the birds recorded, respectively. Wood Duck density estimates (per ha) for FRP, Reynolds VRP, and Goodrum VRP methods were 0.65, 0.49, and 1.00 (P \u3c 0.001), respectively; for Mallards, estimates were 0.27, 0.20, and 0.33 (P \u3c 0.001), respectively; and estimates were 0.09, 0.13, and 0.15 (P = 0.003) for Hooded Mergansers, respectively. Based on ease of implementation, complexity of data analyses, and precision of density estimates, the FRP and Goodrum VRP methods are recommended for sampling waterfowl in flooded forests

The Optical/Near-IR Colours of Red Quasars

We present quasi-simultaneous multi-colour optical/near-IR photometry for 157 radio selected quasars, forming an unbiassed sub-sample of the Parkes Flat-Spectrum Sample. Data are also presented for 12 optically selected QSOs, drawn from the Large Bright QSO Survey. The spectral energy distributions of the radio- and optically-selected sources are quite different. The optically selected QSOs are all very similar: they have blue spectral energy distributions curving downwards at shorter wavelengths. Roughly 90% of the radio-selected quasars have roughly power-law spectral energy distributions, with slopes ranging from Fν ∝ ν0 to Fν, ∝ ν-2. The remaining 10% have spectral energy distributions showing sharp peaks: these are radio galaxies and highly reddened quasars. Four radio sources were not detected down to magnitude limits of H ∼ 19 · 6. These are probably high redshift (z > 3) galaxies or quasars. We show that the colours of our red quasars lie close to the stellar locus in the optical: they will be hard to identify in surveys such as the Sloan Digital Sky Survey. If near-IR photometry is added, however, the red power-law sources can be clearly separated from the stellar locus: IR surveys such as 2MASS should be capable of finding these sources on the basis of their excess flux in the K-band

The Spectra of Red Quasars

We measure the spectral properties of a representative sub-sample of 187 quasars, drawn from the Parkes Half-Jansky, Flat-radio-spectrum Sample (PHFS). Quasars with a wide range of rest-frame optical/UV continuum slopes are included in the analysis: their colours range from 2 < B-K < 7. The median H-beta and [O III] emission-line equivalent widths of the red quasar sub-sample are a factor of ten weaker than those of the blue quasar sub-sample. Both the colours and the emission-line equivalent widths of the red quasars can be explained by the addition of a featureless red synchrotron continuum component to an otherwise normal blue quasar spectrum. The relative strengths of the blue and red components span two orders of magnitude at rest-frame 500nm. The blue component is weaker relative to the red component in low optical luminosity sources. This suggests that the fraction of accretion energy going into optical emission from the jet is greater in low luminosity quasars. This synchrotron model does not, however, fit around 10% of the quasars, which have both red colours and high equivalent width emission-lines. We hypothesise that these red, strong-lined quasars have intrinsically weak Big Blue Bumps. There is no discontinuity in spectral properties between the BL Lac objects in our sample and the other quasars. The synchrotron emission component only dominates the spectrum at longer wavelengths, so existing BL Lac surveys will be biassed against high redshift objects.Comment: 22 pages, 12 figures, accepted for publication in PASA. Data tables and composite spectra from the paper can be found at http://msowww.anu.edu.au/~pfrancis

Characteristic thought and imagery in the work of Henry Vaughan.

Early estimates of Vaughan's work have often emphasised its curious elements, the erudite, obscure or derivative, rather than that which is really characteristic. With a poet such as Vaughan, that is easy to do. Certainly the earliest critics of his poetry read it without any real attempt to lay aside their own preconceptions and enter into the world of seventeenth century thought. Though that fault led to distorted judgments about Vaughan, it nevertheless gave rise to a series of studies that, taken together, have explored the early seventeenth century to us in a way that has made possible a more balanced estimate of Vaughan as a poet in his own time. In this study we shall be concerned to examine some of the elements that are characteristic of Vaughan's work, and to see in what way and to what degree they are important