Bayesian and maximin optimal designs for heteroscedastic regression models

The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model. --

Maximin and Bayesian optimal designs for regression models

For many problems of statistical inference in regression modelling, the Fisher information matrix depends on certain nuisance parameters which are unknown and which enter the model nonlinearly. A common strategy to deal with this problem within the context of design is to construct maximin optimal designs as those designs which maximize the minimum value of a real valued (standardized) function of the Fisher information matrix, where the minimum is taken over a specified range of the unknown parameters. The maximin criterion is not differentiable and the construction of the associated optimal designs is therefore difficult to achieve in practice. In the present paper the relationship between maximin optimal designs and a class of Bayesian optimal designs for which the associated criteria are differentiable is explored. In particular, a general methodology for determining maximin optimal designs is introduced based on the fact that in many cases these designs can be obtained as weak limits of appropriate Bayesian optimal designs. --maximin optimal designs,Bayesian optimal designs,nonlinear regression models,parameter estimation,least favourable prior

External and internal noise surveys of London primary schools

Internal and external noise surveys have been carried out around schools in London, UK, to provide information on typical levels and sources to which children are exposed while at school. Noise levels were measured outside 142 schools, in areas away from flightpaths into major airports. 86% of the schools surveyed were exposed to noise from road traffic, the average external noise level outside a school being 57 dB LAeq. Detailed internal noise surveys have been carried out in 140 classrooms in 16 schools, together with classroom observations. It was found that noise levels inside classrooms depend upon the activities in which the children are engaged, with a difference of 20 dB LAeq between the 'quietest' and 'noisiest' activities. The average background noise level in classrooms exceeds the level recommended in current standards. The number of children in the classroom was found to affect noise levels. External noise influenced internal noise levels only when children were engaged in the quietest classroom activities. The effects of the age of the school buildings and types of window upon internal noise were examined but results were inconclusive

Artificial Neural Network Representations for Hierarchical Preference Structures

In this paper, we introduce two artificial neural network formulations that can be used to predict the preference ratings from the pairwise comparison matrices of the Analytic Hierarchy Process (AHP). First, we introduce a modified Hopfield network that can be used to exactly determine the vector of preference ratings associated with a positive reciprocal comparison matrix. The dynamics of this network are mathematically equivalent to the power method, a widely used numerical method for computing the principal eigenvectors of square matrices. However, we show that the Hopfield network representation is incapable of generalizing the preference patterns, and consequently is not suitable for approximating the preference ratings if the preference information is imprecise. Then we present a feed-forward neural network formulation that does have the ability to accurately approximate the preference ratings. A simulation experiment is used to verify the robustness of the feed-forward neural network formulation with respect to imprecise pairwise judgments. From the results of this experiment, we conclude that the feed-forward neural network formulation appears to be a powerful tool for analyzing discrete alternative multicriteria decision problems with imprecise or fuzzy ratio-scale preference judgments

Anatomy, morphology and evolution of the patella in squamate lizards and tuatara (Sphenodon punctatus)

The patella (kneecap) is the largest and best-known of the sesamoid bones, postulated to confer biomechanical advantages including increasing joint leverage and reinforcing the tendon against compression. It has evolved several times independently in amniotes, but despite apparently widespread occurrence in lizards, the patella remains poorly characterised in this group and is, as yet, completely undescribed in their nearest extant relative Sphenodon (Rhynchocephalia). Through radiography, osteological and fossil studies we examined patellar presence in diverse lizard and lepidosauromorph taxa, and using computed tomography, dissection and histology we investigated in greater depth the anatomy and morphology of the patella in 16 lizard species and 19 Sphenodon specimens. We have found the first unambiguous evidence of a mineralised patella in Sphenodon, which appears similar to the patella of lizards and shares several gross and microscopic anatomical features. Although there may be a common mature morphology, the squamate patella exhibits a great deal of variability in development (whether from a cartilage anlage or not, and in the number of mineralised centres) and composition (bone, mineralised cartilage or fibrotendinous tissue). Unlike in mammals and birds, the patella in certain lizards and Sphenodon appears to be a polymorphic trait. We have also explored the evolution of the patella through ancestral state reconstruction, finding that the patella is ancestral for lizards and possibly Lepidosauria as a whole. Clear evidence of the patella in rhynchocephalian or stem lepidosaurian fossil taxa would clarify the evolutionary origin(s) of the patella, but due to the small size of this bone and the opportunity for degradation or loss we could not definitively conclude presence or absence in the fossils examined. The pattern of evolution in lepidosaurs is unclear but our data suggest that the emergence of this sesamoid may be related to the evolution of secondary ossification centres and/or changes in knee joint conformation, where enhancement of extensor muscle leverage would be more beneficial.Sophie Regnault, Marc E. H. Jones, Andrew A. Pitsillides, John R. Hutchinso

Analysis and testing of two-dimensional vented Coanda ejectors with asymmetric variable area mixing sections

The analysis of asymmetric, curved (Coanda) ejector flow has been completed using a finite difference technique and a quasi-orthogonal streamline coordinate system. The boundary layer type jet mixing analysis accounts for the effect of streamline curvature in pressure gradients normal to the streamlines and on eddy viscosities. The analysis assured perfect gases, free of pressure discontinuities and flow separation and treated three compound flows of supersonic and subsonic streams. Flow parameters and ejector performance were measured in a vented Coanda flow geometry for the verification of the computer analysis. A primary converging nozzle with a discharge geometry of 0.003175 m x 0.2032 m was supplied with 0.283 cu m/sec of air at about 241.3 KPa absolute stagnation pressure and 82 C stagnation temperature. One mixing section geometry was used with a 0.127 m constant radius Coanda surface. Eight tests were run at spacing between the Coanda surface and primary nozzle 0.01915 m and 0.318 m and at three angles of Coanda turning: 22.5 deg, 45.0 deg, and 75.0 deg. The wall static pressures, the loci of maximum stagnation pressures, and the stagnation pressure profiles agree well between analytical and experimental results

Shapley Supercluster Survey: Construction of the photometric catalogues and i-band data release

The Shapley Supercluster Survey is a multi-wavelength survey covering an area of ∼23 deg² (∼260 Mpc² at z = 0.048) around the supercluster core, including nine Abell and two poor clusters, having redshifts in the range 0.045–0.050. The survey aims to investigate the role of the cluster-scale mass assembly on the evolution of galaxies, mapping the effects of the environment from the cores of the clusters to their outskirts and along the filaments. The optical (ugri) imaging acquired with OmegaCAM on the VLT Survey Telescope is essential to achieve the project goals providing accurate multi-band photometry for the galaxy population down to m∗ + 6. We describe the methodology adopted to construct the optical catalogues and to separate extended and point-like sources. The catalogues reach average 5σ limiting magnitudes within a 3 arcsec diameter aperture of ugri = [24.4,24.6,24.1,23.3] and are 93 per cent complete down to ugri = [23.8,23.8,23.5,22.0] mag, corresponding to ∼m∗ r + 8.5. The data are highly uniform in terms of observing conditions and all acquired with seeing less than 1.1 arcsec full width at half-maximum. The median seeing in r band is 0.6 arcsec, corresponding to 0.56 kpc h⁻¹ 70 at z = 0.048. While the observations in the u, g and r bands are still ongoing, the i-band observations have been completed, and we present the i-band catalogue over the whole survey area. The latter is released and it will be regularly updated, through the use of the Virtual Observatory tools. This includes 734 319 sources down to i = 22.0 mag and it is the first optical homogeneous catalogue at such a depth, covering the central region of the Shapley supercluster

Shapley Supercluster Survey: Ram-Pressure Stripping vs. Tidal Interactions in the Shapley Supercluster

We present two new examples of galaxies undergoing transformation in the Shapley supercluster core. These low-mass (stellar mass from 0.4E10 to 1E10 Msun) galaxies are members of the two clusters SC-1329-313 (z=0.045) and SC-1327-312 (z=0.049). Integral-field spectroscopy complemented by imaging in ugriK bands and in Halpha narrow-band are used to disentangle the effects of tidal interaction (TI) and ram-pressure stripping (RPS). In both galaxies, SOS-61086 and SOS-90630, we observe one-sided extraplanar ionized gas extending respectively 30kpc and 41kpc in projection from their disks. The galaxies' gaseous disks are truncated and the kinematics of the stellar and gas components are decoupled, supporting the RPS scenario. The emission of the ionized gas extends in the direction of a possible companion for both galaxies suggesting a TI. The overall gas velocity field of SOS-61086 is reproduced by ad hoc N-body/hydrodynamical simulations of RPS acting almost face-on and starting about 250Myr ago, consistent with the age of the young stellar populations. A link between the observed gas stripping and the cluster-cluster interaction experienced by SC-1329-313 and A3562 is suggested. Simulations of ram pressure acting almost edge-on are able to fully reproduce the gas velocity field of SOS-90630, but cannot at the same time reproduce the extended tail of outflowing gas. This suggests that an additional disturbance from a TI is required. This study adds a piece of evidence that RPS may take place in different environments with different impacts and witnesses the possible effect of cluster-cluster merger on RPS.Comment: 27 pages, 28 figures, MNRAS accepte

ACCESS - V. Dissecting ram-pressure stripping through integral-field spectroscopy and multi-band imaging

We study the case of a bright (L>L*) barred spiral galaxy from the rich cluster A3558 in the Shapley supercluster core (z=0.05) undergoing ram-pressure stripping. Integral-field spectroscopy, complemented by multi-band imaging, allows us to reveal the impact of ram pressure on the interstellar medium. We study in detail the kinematics and the physical conditions of the ionized gas and the properties of the stellar populations. We observe one-sided extraplanar ionized gas along the full extent of the galaxy disc. Narrow-band Halpha imaging resolves this outflow into a complex of knots and filaments. The gas velocity field is complex with the extraplanar gas showing signature of rotation. In all parts of the galaxy, we find a significant contribution from shock excitation, as well as emission powered by star formation. Shock-ionized gas is associated with the turbulent gas outflow and highly attenuated by dust. All these findings cover the whole phenomenology of early-stage ram-pressure stripping. Intense, highly obscured star formation is taking place in the nucleus, probably related to the bar, and in a region 12 kpc South-West from the centre. In the SW region we identify a starburst characterized by a 5x increase in the star-formation rate over the last ~100 Myr, possibly related to the compression of the interstellar gas by the ram pressure. The scenario suggested by the observations is supported and refined by ad hoc N-body/hydrodynamical simulations which identify a rather narrow temporal range for the onset of ram-pressure stripping around t~60 Myr ago, and an angle between the galaxy rotation axis and the intra-cluster medium wind of ~45 deg. Taking into account that the galaxy is found ~1 Mpc from the cluster centre in a relatively low-density region, this study shows that ram-pressure stripping still acts efficiently on massive galaxies well outside the cluster cores.Comment: 46 pages, 21 figures, accepted for publication; MNRAS 201