Scaling limits for the Lego discrepancy

For the Lego discrepancy with M bins, which is equivalent with a chi^2-statistic with M bins, we present a procedure to calculate the moment generating function of the probability distribution perturbatively if M and N, the number of uniformly and randomly distributed data points, become large. Furthermore, we present a phase diagram for various limits of the probability distribution in terms of the standardized variable if M and N become infinite.Comment: 16 page

The Magnitude-Size Relation of Galaxies out to z ~ 1

As part of the Deep Extragalactic Evolutionary Probe (DEEP) survey, a sample of 190 field galaxies (I_{814} <= 23.5) in the ``Groth Survey Strip'' has been used to analyze the magnitude-size relation over the range 0.1 < z < 1.1. The survey is statistically complete to this magnitude limit. All galaxies have photometric structural parameters, including bulge fractions (B/T), from Hubble Space Telescope images, and spectroscopic redshifts from the Keck Telescope. The analysis includes a determination of the survey selection function in the magnitude-size plane as a function of redshift, which mainly drops faint galaxies at large distances. Our results suggest that selection effects play a very important role. A first analysis treats disk-dominated galaxies with B/T < 0.5. If selection effects are ignored, the mean disk surface brightness (averaged over all galaxies) increases by ~1.3 mag from z = 0.1 to 0.9. However, most of this change is plausibly due to comparing low luminosity galaxies in nearby redshift bins to high luminosity galaxies in distant bins. If this effect is allowed for, no discernible evolution remains in the disk surface brightness of bright (M_B < -19) disk-dominated galaxies. A second analysis treats all galaxies by substituting half-light radius for disk scale length, with similar conclusions. Indeed, at all redshifts, the bulk of galaxies is consistent with the magnitude-size envelope of local galaxies, i.e., with little or no evolution in surface brightness. In the two highest redshift bins (z > 0.7), a handful of luminous, high surface brightness galaxies appears that occupies a region of the magnitude-size plane rarely populated by local galaxies. Their wide range of colors and bulge fractions points to a variety of possible origins.Comment: 19 pages, 12 figures. Accepted for publication in the Astrophysical Journa

The Optimisation of Stochastic Grammars to Enable Cost-Effective Probabilistic Structural Testing

The effectiveness of probabilistic structural testing depends on the characteristics of the probability distribution from which test inputs are sampled at random. Metaheuristic search has been shown to be a practical method of optimis- ing the characteristics of such distributions. However, the applicability of the existing search-based algorithm is lim- ited by the requirement that the software’s inputs must be a fixed number of numeric values. In this paper we relax this limitation by means of a new representation for the probability distribution. The repre- sentation is based on stochastic context-free grammars but incorporates two novel extensions: conditional production weights and the aggregation of terminal symbols represent- ing numeric values. We demonstrate that an algorithm which combines the new representation with hill-climbing search is able to effi- ciently derive probability distributions suitable for testing software with structurally-complex input domains

A new parameter space study of cosmological microlensing

Cosmological gravitational microlensing is a useful technique for understanding the structure of the inner parts of a quasar, especially the accretion disk and the central supermassive black hole. So far, most of the cosmological microlensing studies have focused on single objects from ~90 currently known lensed quasars. However, present and planned all-sky surveys are expected to discover thousands of new lensed systems. Using a graphics processing unit (GPU) accelerated ray-shooting code, we have generated 2550 magnification maps uniformly across the convergence ({\kappa}) and shear ({\gamma}) parameter space of interest to microlensing. We examine the effect of random realizations of the microlens positions on map properties such as the magnification probability distribution (MPD). It is shown that for most of the parameter space a single map is representative of an average behaviour. All of the simulations have been carried out on the GPU-Supercomputer for Theoretical Astrophysics Research (gSTAR).Comment: 16 pages, 10 figures, accepted for publication in MNRA

The VIMOS Public Extragalactic Redshift Survey (VIPERS): On the correct recovery of the count-in-cell probability distribution function

We compare three methods to measure the count-in-cell probability density function of galaxies in a spectroscopic redshift survey. From this comparison we found that when the sampling is low (the average number of object per cell is around unity) it is necessary to use a parametric method to model the galaxy distribution. We used a set of mock catalogues of VIPERS, in order to verify if we were able to reconstruct the cell-count probability distribution once the observational strategy is applied. We find that in the simulated catalogues, the probability distribution of galaxies is better represented by a Gamma expansion than a Skewed Log-Normal. Finally, we correct the cell-count probability distribution function from the angular selection effect of the VIMOS instrument and study the redshift and absolute magnitude dependency of the underlying galaxy density function in VIPERS from redshift $0.5$ to $1.1$. We found very weak evolution of the probability density distribution function and that it is well approximated, independently from the chosen tracers, by a Gamma distribution.Comment: 14 pages, 11 figures, 2 table

What is Holding Back Convnets for Detection?

Convolutional neural networks have recently shown excellent results in general object detection and many other tasks. Albeit very effective, they involve many user-defined design choices. In this paper we want to better understand these choices by inspecting two key aspects "what did the network learn?", and "what can the network learn?". We exploit new annotations (Pascal3D+), to enable a new empirical analysis of the R-CNN detector. Despite common belief, our results indicate that existing state-of-the-art convnet architectures are not invariant to various appearance factors. In fact, all considered networks have similar weak points which cannot be mitigated by simply increasing the training data (architectural changes are needed). We show that overall performance can improve when using image renderings for data augmentation. We report the best known results on the Pascal3D+ detection and view-point estimation tasks