Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Health benefits of reducing NO x emissions in the presence of epidemiological and atmospheric nonlinearities

Recent epidemiological evidence suggests that the logarithm of concentration is a better predictor of mortality risk from long-term exposure to ambient PM2.5 and NO2 than concentration itself. A log-concentration-response function (CRF) predicts a heightened excess risk per unit concentration at low levels of exposure that further increases as the air becomes less polluted. Using an adjoint air quality model, we estimate the public health benefits of reducing NO x emissions, on a per-ton and source-by-source basis. Our estimates of benefits-per-ton assume linear in concentration and log-concentration CRFs for NO2 and a CRF that is linear in concentration for O3. We apply risk coefficients estimated using the Canadian Census Health and Environment Cohort. We find that a log-concentration CRF for NO2 leads almost consistently to larger benefits-per-ton than a linear in concentration CRF (e.g., $500 000 ton-1 compared to$270 000 ton-1 for Ottawa). We observe that concentrations gradually decline due to widespread, progressive emissions abatement, entailing increasing health benefits as a result of (1) a log-concentration CRF for NO2 and (2) the nonlinear response of O3 to NO x emissions. Our results indicate that NO x abatement has the potential to incur substantial and increasing health benefits, by up to five times with 85% emission reductions, for Canada into the future

Gaseous air pollution and emergency hospital visits for hypertension in Beijing, China: a time-stratified case-crossover study

Background: A number of epidemiological studies have been conducted to research the adverse effects of air pollution on mortality and morbidity. Hypertension is the most important risk factor for cardiovascular mortality. However, few previous studies have examined the relationship between gaseous air pollution and morbidity for hypertension. ---------- Methods: Daily data on emergency hospital visits (EHVs) for hypertension were collected from the Peking University Third Hospital. Daily data on gaseous air pollutants (sulfur dioxide (SO2) and nitrogen dioxide (NO2)) and particulate matter less than 10 μm in aerodynamic diameter (PM10) were collected from the Beijing Municipal Environmental Monitoring Center. A time-stratified case-crossover design was conducted to evaluate the relationship between urban gaseous air pollution and EHVs for hypertension. Temperature and relative humidity were controlled for. ---------- Results: In the single air pollutant models, a 10 μg/m3 increase in SO2 and NO2 were significantly associated with EHVs for hypertension. The odds ratios (ORs) were 1.037 (95% confidence interval (CI): 1.004-1.071) for SO2 at lag 0 day, and 1.101 (95% CI: 1.038-1.168) for NO2 at lag 3 day. After controlling for PM10, the ORs associated with SO2 and NO2 were 1.025 (95% CI: 0.987-1.065) and 1.114 (95% CI: 1.037-1.195), respectively.---------- Conclusion: Elevated urban gaseous air pollution was associated with increased EHVs for hypertension in Beijing, China

A Semianalytical PDF of Downlink SINR for Femtocell Networks

This paper presents a derivation of the probability density function (PDF) of the signal-to-interference and noise ratio (SINR) for the downlink of a cell in multicellular networks. The mathematical model considers uncoordinated locations and transmission powers of base stations (BSs) which reflect accurately the deployment of randomly located femtocells in an indoor environment. The derivation is semianalytical, in that the PDF is obtained by analysis and can be easily calculated by employing standard numerical methods. Thus, it obviates the need for time-consuming simulation efforts. The derivation of the PDF takes into account practical propagation models including shadow fading. The effect of background noise is also considered. Numerical experiments are performed assuming various environments and deployment scenarios to examine the performance of femtocell networks. The results are compared with Monte Carlo simulations for verification purposes and show good agreement