Sensitivity of the limit shape of sample clouds from meta densities

The paper focuses on a class of light-tailed multivariate probability distributions. These are obtained via a transformation of the margins from a heavy-tailed original distribution. This class was introduced in Balkema et al. (J. Multivariate Anal. 101 (2010) 1738-1754). As shown there, for the light-tailed meta distribution the sample clouds, properly scaled, converge onto a deterministic set. The shape of the limit set gives a good description of the relation between extreme observations in different directions. This paper investigates how sensitive the limit shape is to changes in the underlying heavy-tailed distribution. Copulas fit in well with multivariate extremes. By Galambos's theorem, existence of directional derivatives in the upper endpoint of the copula is necessary and sufficient for convergence of the multivariate extremes provided the marginal maxima converge. The copula of the max-stable limit distribution does not depend on the margins. So margins seem to play a subsidiary role in multivariate extremes. The theory and examples presented in this paper cast a different light on the significance of margins. For light-tailed meta distributions, the asymptotic behaviour is very sensitive to perturbations of the underlying heavy-tailed original distribution, it may change drastically even when the asymptotic behaviour of the heavy-tailed density is not affected.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ370 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Asymptotic independence for unimodal densities

Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (dfs). Dfs are rarely available in an explicit form, especially in the multivariate case. Often we are given the form of the density or, via the shape of the data clouds, one can obtain a good geometric image of the asymptotic shape of the level sets of the density. This paper establishes a simple sufficient condition for asymptotic independence for light-tailed densities in terms of this asymptotic shape. This condition extends Sibuya's classic result on asymptotic independence for Gaussian densities.Comment: 33 pages, 4 figure

An HI survey of the Centaurus and Sculptor Groups - Constraints on the space density of low mass galaxies

We present results of two 21-cm HI surveys performed with the Australia Telescope Compact Array in the nearby Centaurus A and Sculptor galaxy groups. These surveys are sensitive to compact HI clouds and galaxies with HI masses as low as 3E+06 Msun, and are therefore among the most sensitive extragalactic HI surveys to date. The surveys consist of sparsely spaced pointings that sample approximately 2% of the groups' area on the sky. We detected previously known group members, but we found no new HI clouds or galaxies down to the sensitivity limit of the surveys. If the HI mass function had a faint end slope of alpha = 1.5 below M_{HI} = 10^{7.5} Msun in these groups, we would have expected ~3 new objects. Cold dark matter theories of galaxy formation predict the existence of a large number low mass DM sub-halos that might appear as tiny satellites in galaxy groups. Our results support and extend similar conclusions derived from previous HI surveys that a HI rich population of these satellites does not exist.Comment: Accepted for publication in A&

High Metallicity Mg II Absorbers in the z < 1 Lyman alpha Forest of PKS 0454+039: Giant LSB Galaxies?

We report the discovery of two iron-group enhanced high-metallicity Mg II absorbers in a search through 28 Lyman Alpha forest clouds along the PKS 0454+039 sight line. Based upon our survey and the measured redshift number densities of W_r(MgII) <= 0.3 A absorbers and Lyman Alpha absorbers at z ~ 1, we suggest that roughly 5% of Lyman Alpha absorbers at z < 1 will exhibit "weak" Mg II absorption to a 5-sigma W_r(2796) detection limit of 0.02 A. The two discovered absorbers, at redshifts z = 0.6248 and z = 0.9315, have W_r(Lya) = 0.33 and 0.15 A, respectively. Based upon photoionization modeling, the H I column densities are inferred to be in the range 15.8 <= log N(HI) <= 16.8 cm^-2. For the z = 0.6428 absorber, if the abundance pattern is solar, then the cloud has [Fe/H] > -1; if its gas-phase abundance follows that of depleted clouds in our Galaxy, then [Fe/H] > 0 is inferred. For the z = 0.9315 absorber, the metallicity is [Fe/H] > 0, whether the abundance pattern is solar or suffers depletion. Imaging and spectroscopic studies of the PKS 0454+039 field reveal no candidate luminous objects at these redshifts. We discuss the possibility that these Mg II absorbers may arise in the class of "giant" low surface brightness galaxies, which have [Fe/H] >= -1, and even [Fe/H] >= 0, in their extended disks. We tentatively suggest that a substantial fraction of these "weak" Mg II absorbers may select low surface brightness galaxies out to z ~ 1.Comment: Accepted The Astrophysical Journal; 25 pages; 6 encapsulated figure

Automated Classification of Airborne Laser Scanning Point Clouds

Making sense of the physical world has always been at the core of mapping. Up until recently, this has always dependent on using the human eye. Using airborne lasers, it has become possible to quickly "see" more of the world in many more dimensions. The resulting enormous point clouds serve as data sources for applications far beyond the original mapping purposes ranging from flooding protection and forestry to threat mitigation. In order to process these large quantities of data, novel methods are required. In this contribution, we develop models to automatically classify ground cover and soil types. Using the logic of machine learning, we critically review the advantages of supervised and unsupervised methods. Focusing on decision trees, we improve accuracy by including beam vector components and using a genetic algorithm. We find that our approach delivers consistently high quality classifications, surpassing classical methods

The impact of local stellar radiation on the HI column density distribution

It is often assumed that local sources of ionizing radiation have little impact on the distribution of HI in the post-reionization Universe. While this is a good assumption for the IGM, analytic arguments suggest that local sources may typically be more important than the background radiation for high column density absorbers (N_HI > 10^17 /cm^2). We post-process cosmological simulations with accurate radiation transport to investigate the impact of local stellar sources on the HI distribution. We demonstrate that the limited numerical resolution and the simplified treatment of the ISM that are typical of current cosmological simulations provide significant challenges, but that many of the problems can be overcome by taking two steps. First, using ISM particles rather than stellar particles as sources results in a much better sampling of the source distribution. Second, by rescaling the source luminosities so that the amount of radiation escaping into the IGM agrees with that required to produce the observed background, many of the results become insensitive to errors in the predicted fraction of the radiation that escapes the immediate vicinity of the sources. By adopting this strategy and by varying the assumptions about the structure of the unresolved ISM, we conclude that we can robustly estimate the effect of local sources for column densities N_HI << 10^21 /cm^2. However, neither the escape fraction of ionizing radiation nor the effect of local sources on the abundance of N_HI >~ 10^21 systems can be predicted with confidence. We find that local stellar radiation is unimportant for N_HI << 10^17, but that it can affect Lyman Limit and DLA systems. For 10^18 < N_HI < 10^21 the impact of local sources increases with redshift. At z = 5 the abundance of absorbers with N_HI >> 10^17 is substantially reduced, but at z = 0 the reduction only becomes significant for N_HI >~ 10^21 /cm^2.Comment: 19 pages, 12 figures; Accepted for publication in MNRA