L\'{e}vy-based growth models

In the present paper, we give a condensed review, for the nonspecialist reader, of a new modelling framework for spatio-temporal processes, based on L\'{e}vy theory. We show the potential of the approach in stochastic geometry and spatial statistics by studying L\'{e}vy-based growth modelling of planar objects. The growth models considered are spatio-temporal stochastic processes on the circle. As a by product, flexible new models for space--time covariance functions on the circle are provided. An application of the L\'{e}vy-based growth models to tumour growth is discussed.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6130 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution

Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will first be shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform by the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axis. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized, this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a non parametric bootstrap based procedure is described, that provides confidence interval in addition to the estimates themselves and enables to construct an isotropy test procedure, that can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis is illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed

O VI and Multicomponent H I Absorption Associated with a Galaxy Group in the Direction of PG0953+415: Physical Conditions and Baryonic Content

We report the discovery of an O VI absorption system at z(abs) = 0.14232 in a high resolution FUV spectrum of PG0953+415 obtained with the Space Telescope Imaging Spectrograph (STIS). Both lines of the O VI 1032, 1038 doublet and multicomponent H I Lya absorption are detected, but the N V doublet and the strong lines of C II and Si III are not apparent. We examine the ionization mechanism of the O VI absorber and find that while theoretical considerations favor collisional ionization, it is difficult to observationally rule out photoionization. If the absorber is collisionally ionized, it may not be in equilibrium due to the rapid cooling of gas in the appropriate temperature range. Non-equilibrium collisionally ionized models are shown to be consistent with the observations. A WIYN survey of galaxy redshifts near the sight line has revealed a galaxy at a projected distance of 395 kpc separated by ~130 km/s from this absorber, and three additional galaxies are found within 130 km/s of this redshift with projected separations ranging from 1.0 Mpc to 3.0 Mpc. Combining the STIS observations of PG0953+415 with previous high S/N GHRS observations of H1821+643, we derive a large number of O VI absorbers per unit redshift, dN/dz ~20. We use this sample to obtain a first estimate of the cosmological mass density of the O VI systems at z ~ 0. If further observations confirm the large dN/dz derived for the O VI systems, then these absorbers trace a significant reservoir of baryonic matter at low redshift.Comment: Accepted for publication in Ap.J., vol. 542 (Oct. 10, 2000

The Structure of Isothermal, Self-gravitating Gas Spheres for Softened Gravity

A theory for the structure of isothermal, self-gravitating gas spheres in pressure equilibrium in a softened gravitational field is developed. The one parameter spline softening proposed by Hernquist & Katz (1989) is used. We show that the addition of this extra scale parameter implies that the set of equilibrium solutions constitute a one-parameter family, rather than the one and only one isothermal sphere solution for Newtonian gravity. We demonstrate the perhaps somewhat surprising result that for any finite choice of softening length and temperature, it is possible to deposit an arbitrarily large mass of gas in pressure equilibrium and with a non-singular density distribution inside of r_0 for any r_0 > 0. The theoretical predictions of our models are compared with the properties of the small, massive, quasi-isothermal gas clumps which typically form in numerical Tree-SPH simulations of 'passive' galaxy formation of Milky Way sized galaxies. We find reasonable agreement despite the neglect of rotational support in the models. We comment on whether the hydrodynamical resolution in our numerical simulation of galaxy formation is sufficient, and finally we conclude that one should be cautious, when comparing results of numerical simulations involving gravitational softening and hydrodynamical smoothing, with reality.Comment: 22 pages Latex + 12 figure

Estimation of sample spacing in stochastic processes

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies