Random line tessellations of the plane: statistical properties of many-sided cells

We consider a family of random line tessellations of the Euclidean plane introduced in a much more formal context by Hug and Schneider [Geom. Funct. Anal. 17, 156 (2007)] and described by a parameter \alpha\geq 1. For \alpha=1 the zero-cell (that is, the cell containing the origin) coincides with the Crofton cell of a Poisson line tessellation, and for \alpha=2 it coincides with the typical Poisson-Voronoi cell. Let p_n(\alpha) be the probability for the zero-cell to have n sides. By the methods of statistical mechanics we construct the asymptotic expansion of \log p_n(\alpha) up to terms that vanish as n\to\infty. In the large-n limit the cell is shown to become circular. The circle is centered at the origin when \alpha>1, but gets delocalized for the Crofton cell, \alpha=1, which is a singular point of the parameter range. The large-n expansion of \log p_n(1) is therefore different from that of the general case and we show how to carry it out. As a corollary we obtain the analogous expansion for the {\it typical} n-sided cell of a Poisson line tessellation.Comment: 26 pages, 3 figure

Baseline characteristics, response to and outcome of antiretroviral therapy among patients with HIV-1, HIV-2 and dual infection in Burkina Faso.

In an urban district hospital in Burkina Faso we investigated the relative proportions of HIV-1, HIV-2 and HIV-1/2 among those tested, the baseline sociodemographic and clinical characteristics, and the response to and outcome of antiretroviral therapy (ART). A total of 7368 individuals (male=32%; median age=34 years) were included in the analysis over a 6 year period (2002-2008). The proportions of HIV-1, HIV-2 and dual infection were 94%, 2.5% and 3.6%, respectively. HIV-1-infected individuals were younger, whereas HIV-2-infected individuals were more likely to be male, have higher CD4 counts and be asymptomatic on presentation. ART was started in 4255 adult patients who were followed up for a total of 8679 person-years, during which time 469 deaths occurred. Mortality differences by serotype were not statistically significant, but were generally worse for HIV-2 and HIV-1/2 after controlling for age, CD4 count and WHO stage. Among severely immune-deficient patients, mortality was higher for HIV-2 than HIV-1. CD4 count recovery was poorest for HIV-2. HIV-2 and dually infected patients appeared to do less well on ART than HIV-1 patients. Reasons may include differences in age at baseline, lower intrinsic immune recovery in HIV-2, use of ineffective ART regimens (inappropriate prescribing) by clinicians, and poor drug adherence

Geostatistical and Statistical Classification of Sea-Ice Properties and Provinces from SAR Data

Recent drastic reductions in the Arctic sea-ice cover have raised an interest in understanding the role of sea ice in the global system as well as pointed out a need to understand the physical processes that lead to such changes. Satellite remote-sensing data provide important information about remote ice areas, and Synthetic Aperture Radar (SAR) data have the advantages of penetration of the omnipresent cloud cover and of high spatial resolution. A challenge addressed in this paper is how to extract information on sea-ice types and sea-ice processes from SAR data. We introduce, validate and apply geostatistical and statistical approaches to automated classification of sea ice from SAR data, to be used as individual tools for mapping sea-ice properties and provinces or in combination. A key concept of the geostatistical classification method is the analysis of spatial surface structures and their anisotropies, more generally, of spatial surface roughness, at variable, intermediate-sized scales. The geostatistical approach utilizes vario parameters extracted from directional vario functions, the parameters can be mapped or combined into feature vectors for classification. The method is flexible with respect to window sizes and parameter types and detects anisotropies. In two applications to RADARSAT and ERS-2 SAR data from the area near Point Barrow, Alaska, it is demonstrated that vario-parameter maps may be utilized to distinguish regions of different sea-ice characteristics in the Beaufort Sea, the Chukchi Sea and in Elson Lagoon. In a third and a fourth case study the analysis is taken further by utilizing multi-parameter feature vectors as inputs for unsupervised and supervised statistical classification. Field measurements and high-resolution aerial observations serve as basis for validation of the geostatistical-statistical classification methods. A combination of supervised classification and vario-parameter mapping yields best results, correctly identifying several sea-ice provinces in the shore-fast ice and the pack ice. Notably, sea ice does not have to be static to be classifiable with respect to spatial structures. In consequence, the geostatistical-statistical classification may be applied to detect changes in ice dynamics, kinematics or environmental changes, such as increased melt ponding, increased snowfall or changes in the equilibrium line