Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

Catalase in fluvial biofilms: a comparison between different extraction methods and example of application in a metal-polluted river

Antioxidant enzymes are involved in important processes of cell detoxification during oxidative stress and have, therefore, been used as biomarkers in algae. Nevertheless, their limited use in fluvial biofilms may be due to the complexity of such communities. Here, a comparison between different extraction methods was performed to obtain a reliable method for catalase extraction from fluvial biofilms. Homogenization followed by glass bead disruption appeared to be the best compromise for catalase extraction. This method was then applied to a field study in a metal-polluted stream (Riou Mort, France). The most polluted sites were characterized by a catalase activity 4–6 times lower than in the low-polluted site. Results of the comparison process and its application are promising for the use of catalase activity as an early warning biomarker of toxicity using biofilms in the laboratory and in the field