Group Feature Screening via the F Statistic.

Feature screening is crucial in the analysis of ultrahigh dimensional data, where the number of variables (features) is in an exponential order of the number of observations. In various ultrahigh dimensional data, variables are naturally grouped, giving us a good rationale to develop a screening method using joint effect of multiple variables. In this article, we propose a group screening procedure via the F-test statistic. The proposed method is a direct extension of the original sure independence screening procedure, when the group information is known, for example, from prior knowledge. Under certain regularity conditions, we prove that the proposed group screening procedure possesses the sure screening property that selects all effective groups with a probability approaching one at an exponential rate. We use simulations to demonstrate the advantages of the proposed method and show its application in a genome-wide association study. We conclude that the grouping method is very useful in the analysis of ultrahigh dimensional data, as the optimal F-test can detect true signals with desired properties.

Enhanced separation of water quality parameters in the DAF (Dissolved Air Flotation) system using ozone.

Dissolved Air Flotation (DAF) has been used in water and wastewater treatment because it has an excellent separation capability. It was found that the separation capability of the DAF system could be even more enhanced by ozone. Ozone was applied as a substitute for air in the DAF system, so that the system was named as the DOF (Dissolved Ozone Flotation) system. Ozone not only enhances coagulation as is well known, but also provides larger micro-bubble volume because the solubility of ozone in water is much higher than that of air. Ozone enhanced the separation rate of SS by 13.6%, and turbidity by 21% in the DOF system compared to the DAF system. T-P was also removed 7.7% more in the DOF system. 41.5% of color and 7.4% of COD(Cr) were enhanced in their removal rate. Coliform and heterotrophic bacteria were removed 54% and 57.3% more in the DOF system. Separation capability of the DOF system was greatly enhanced for most of the water quality parameters because ozone provides strong oxidation power with large volume of micro-bubbles.