Efficient minimax strategies for square loss games

We consider online prediction problems where the loss between the prediction and the outcome is measured by the squared Euclidean distance and its generalization, the squared Mahalanobis distance. We derive the minimax solutions for the case where the prediction and action spaces are the simplex (this setup is sometimes called the Brier game) and the \ell_2 ball (this setup is related to Gaussian density estimation). We show that in both cases the value of each sub-game is a quadratic function of a simple statistic of the state, with coefficients that can be efficiently computed using an explicit recurrence relation. The resulting deterministic minimax strategy and randomized maximin strategy are linear functions of the statistic.

Removal of herbicides from aqueous solutions by modified forms of montmorillonite

This investigation for the removal of agricultural pollutants, imazaquin and atrazine was conducted using montmorillonite (MMT) exchanged with organic cations through ion exchange. The study found that the adsorption of the herbicides was affected by the degree of organic cation saturations, the size of organic cations and the different natures of the herbicides. The modified clays intercalated with the larger surfactant molecules at the higher concentrations tended to enhance the adsorption of imazaquin and atrazine. In particular, the organoclays were highly efficient for the removal of imazaquin while the adsorption of atrazine was minimal due to the different hydrophobicities. Both imazaquin and atrazine were influenced by the changes of pH. The amphoteric imazaquin exists as an anion at the pH 5–7 and the anionic imazaquin was protonated to a neutral and further a cationic form when the pH is lower. The weak base, atrazine was also protonated at lower pH values. The anionic imazaquin had a strong affinity to the organoclays on the external surface as well as in the interlayer space of the MMT through electrostatic and hydrophobic interactions. In this study, the electrostatic interaction can be the primary mechanism involved during the adsorption process. This study also investigated a comparative adsorption for the imazaquin and atrazine and the lower adsorption of atrazine was enhanced and this phenomenon was due to the synergetic effect. This work highlights a potential mechanism for the removal of specific persistence herbicides from the environment.

Efficient microwave hydrothermal preparation of nanocrystalline anatase TiO2 colloids

Titanium dioxide nanocrystals are an important commercial product used primarily in white pigments and abrasives, however, more recently the anatase form of TiO2 has become a major component in electrochemical and photoelectrochemical devices. An important property of titanium dioxide nanocrystals for electrical applications is the degree of crystallinity. Numerous preparation methods exist for the production of highly crystalline TiO2 particles. The majority of these processes require long reaction times, high pressures and temperatures (450–1400 °C). Recently, hydrothermal treatment of colloidal TiO2 suspensions has been shown to produce quality crystalline products at low temperatures (<250 °C). In this paper we extend this idea utilising a direct microwave heating source. A comparison between convection and microwave hydrothermal treatment of colloidal TiO2 is presented. The resulting highly crystalline TiO2 colloids were characterised using Raman spectroscopy, XRD, TEM, and electron diffraction. The results show that the microwave treatment of colloidal TiO2 gives comparable increases in crystallinity with respect to normal hydrothermal treatments while requiring significantly less time and energy than the hydrothermal convection treatment.