On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

The strength of badenya ties: siblings and social security in old age – the case of urban Burkina Faso

In urban Burkina Faso, siblings play a decisive role in local social security. Badenya, the unity of children of the same mother, compensates in particular for the economic failure of an eldest son no longer in a position to fulfill his familial duties. Although the institution of badenya is strengthened as it increasingly comes into play to help a family avoid social marginalization, it is also overburdened, which makes its future uncertain. This article enhances the anthropological understanding of kinship by focusing on sibling relationships. Findings are based on interviews conducted between 2007 and 2010 with two generations in households in Bobo-Dioulasso and on participant-observation over the course of more than a dozen research stays since 1989.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Oxygenated polycyclic aromatic hydrocarbons and azaarenes in urban soils: A comparison of a tropical city (Bangkok) with two temperate cities (Bratislava and Gothenburg)

Environmental conditions in the tropics favor the formation of polar polycyclic aromatic compound (polar PACs, such as oxygenated PAHs [OPAHs] and azaarenes [AZAs]), but little is known about these hazardous compounds in tropical soils. The objectives of this work were to determine (i) the level of contamination of soils (0–5 and 5–10 cm layers) from the tropical metropolis of Bangkok (Thailand) with OPAHs and AZAs and (ii) the influence of urban emission sources and soil properties on the distribution of PACs. We hypothesized that the higher solar insolation and microbial activity in the tropics than in the temperate zone will lead to enhanced secondary formation of OPAHs. Hence, OPAH to related parent-PAH ratios will be higher in the tropical soils of Bangkok than in temperate soils of Bratislava and Gothenburg. The concentrations of ∑15OPAHs (range: 12–269 ng g−1) and ∑4AZAs (0.1–31 ng g−1) measured in soils of Bangkok were lower than those in several cities of the industrialized temperate zone. The ∑15OPAHs (r = 0.86, p < 0.01) and ∑4AZAs (r = 0.67, p < 0.01) correlated significantly with those of ∑20PAHs highlighting similar sources and related fate. The octanol–water partition coefficient did not explain the transport to the subsoil, indicating soil mixing as the reason for the polar PAC load of the lower soil layer. Data on PAC concentrations in soils of Bratislava and Gothenburg were taken from published literature. The individual OPAH to parent-PAH ratios in soils of Bangkok were mostly higher than those of Bratislava and Gothenburg (e.g. 9-fluorenone/fluorene concentration ratio was 12.2 ± 6.7, 5.6 ± 2.4, and 0.7 ± 02 in Bangkok, Bratislava and Gothenburg soils, respectively) supporting the view that tropical environmental conditions and higher microbial activity likely lead to higher OPAH to parent-PAH ratios in tropical than in temperate soils.