Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Alarm systems and catastrophes from a diverse point of view

Using a chain of urns, we build a Bayesian nonparametric alarm system to predict catastrophic events, such as epidemics, black outs, etc. Differently from other alarm systems in the literature, our model is constantly updated on the basis of the available information, according to the Bayesian paradigm. The papers contains both theoretical and empirical results. In particular, we test our alarm system on a well-known time series of sunspots.

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<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 ^ .

Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

Deposition and biokinetics of inhaled nanoparticles

Particle biokinetics is important in hazard identification and characterization of inhaled particles. Such studies intend to convert external to internal exposure or biologically effective dose, and may help to set limits in that way. Here we focus on the biokinetics of inhaled nanometer sized particles in comparison to micrometer sized ones.The presented approach ranges from inhaled particle deposition probability and retention in the respiratory tract to biokinetics and clearance of particles out of the respiratory tract. Particle transport into the blood circulation (translocation), towards secondary target organs and tissues (accumulation), and out of the body (clearance) is considered. The macroscopically assessed amount of particles in the respiratory tract and secondary target organs provides dose estimates for toxicological studies on the level of the whole organism. Complementary, microscopic analyses at the individual particle level provide detailed information about which cells and subcellular components are the target of inhaled particles. These studies contribute to shed light on mechanisms and modes of action eventually leading to adverse health effects by inhaled nanoparticles.We review current methods for macroscopic and microscopic analyses of particle deposition, retention and clearance. Existing macroscopic knowledge on particle biokinetics and microscopic views on particle organ interactions are discussed comparing nanometer and micrometer sized particles. We emphasize the importance for quantitative analyses and the use of particle doses derived from real world exposures.

Virologic failure and second-line antiretroviral therapy in children in South Africa--the IeDEA Southern Africa collaboration

Background: With expanding pediatric antiretroviral therapy (ART) access, children will begin to experience treatment failure and require second-line therapy. We evaluated the probability and determinants of virologic failure and switching in children in South Africa. Methods: Pooled analysis of routine individual data from children who initiated ART in 7 South African treatment programs with 6-monthly viral load and CD4 monitoring produced Kaplan-Meier estimates of probability of virologic failure (2 consecutive unsuppressed viral loads with the second being >1000 copies/mL, after ≥24 weeks of therapy) and switch to second-line. Cox-proportional hazards models stratified by program were used to determine predictors of these outcomes. Results: The 3-year probability of virologic failure among 5485 children was 19.3% (95% confidence interval: 17.6 to 21.1). Use of nevirapine or ritonavir alone in the initial regimen (compared with efavirenz) and exposure to prevention of mother to child transmission regimens were independently associated with failure [adjusted hazard ratios (95% confidence interval): 1.77 (1.11 to 2.83), 2.39 (1.57 to 3.64) and 1.40 (1.02 to 1.92), respectively]. Among 252 children with ≥1 year follow-up after failure, 38% were switched to second-line. Median (interquartile range) months between failure and switch was 5.7 (2.9-11.0). Conclusions: Triple ART based on nevirapine or ritonavir as a single protease inhibitor seems to be associated with a higher risk of virologic failure. A low proportion of virologically failing children were switched.

Single Molecular Conductance of Tolanes: Experimental and Theoretical Study on the Junction Evolution Dependent on the Anchoring Group

Employing a scanning tunneling microscopy based beak junction technique and mechanically controlled break junction experiments, we investigated tolane (diphenylacetylene)-type single molecular junctions having four different anchoring groups (SH, pyridyl (PY), NH2, and CN) at a solid/liquid interface. The combination of current–distance and current–voltage measurements and their quantitative statistical analysis revealed the following sequence for junction formation probability and stability: PY > SH > NH2 > CN. For all single molecular junctions investigated, we observed the evolution through multiple junction configurations, with a particularly well-defined binding geometry for PY. The comparison of density functional theory type model calculations and molecular dynamics simulations with the experimental results revealed structure and mechanistic details of the evolution of the different types of (single) molecular junctions upon stretching quantitatively.

ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.