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

An ATM distributed simulator for network management research

Due to the high cost of a large ATM network working up to full strength to apply our ideas about network management, i.e., dynamic virtual path (VP) management and fault restoration, we developed a distributed simulation platform for performing our experiments. This platform also had to be capable of other sorts of tests, such as connection admission control (CAC) algorithms, routing algorithms, and accounting and charging methods. The platform was posed as a very simple, event-oriented and scalable simulation. The main goal was the simulation of a working ATM backbone network with a potentially large number of nodes (hundreds). As research into control algorithms and low-level, or rather cell-level methods, was beyond the scope of this study, the simulation took place at a connection level, i.e., there was no real traffic of cells. The simulated network behaved like a real network accepting and rejecting SNMP ones, or experimental tools using the API node

Experimental Modeling and Control Strategies on an Open Mobile Robot Platform PRIM

This research work deals with the problem of modeling and design of low level speed controller for the mobile robot PRIM. The main objective is to develop an effective educational tool. On one hand, the interests in using the open mobile platform PRIM consist in integrating several highly related subjects to the automatic control theory in an educational context, by embracing the subjects of communications, signal processing, sensor fusion and hardware design, amongst others. On the other hand, the idea is to implement useful navigation strategies such that the robot can be served as a mobile multimedia information point. It is in this context, when navigation strategies are oriented to goal achievement, that a local model predictive control is attained. Hence, such studies are presented as a very interesting control strategy in order to develop the future capabilities of the system

Rhodium(I) catalyzed [2+2+2] cycloaddition reactions: experimental and theoretical studies

The [2+2+2] cycloaddition reaction involves the formation of three carbon-carbon bonds in one single step using alkynes, alkenes, nitriles, carbonyls and other unsaturated reagents as reactants. This is one of the most elegant methods for the construction of polycyclic aromatic compounds and heteroaromatic, which have important academic and industrial uses. The thesis is divided into ten chapters including six related publications. The first study based on the Wilkinson’s catalyst, RhCl(PPh3)3, compares the reaction mechanism of the [2+2+2] cycloaddition process of acetylene with the cycloaddition obtained for the model of the complex, RhCl(PH3)3. In an attempt to reduce computational costs in DFT studies, this research project aimed to substitute PPh3 ligands for PH3, despite the electronic and steric effects produced by PPh3 ligands being significantly different to those created by PH3 ones. In this first study, detailed theoretical calculations were performed to determine the reaction mechanism of the two complexes. Despite some differences being detected, it was found that modelling PPh3 by PH3 in the catalyst helps to reduce the computational cost significantly while at the same time providing qualitatively acceptable results. Taking into account the results obtained in this earlier study, the model of the Wilkinson’s catalyst, RhCl(PH3)3, was applied to study different [2+2+2] cycloaddition reactions with unsaturated systems conducted in the laboratory. Our research group found that in the case of totally closed systems, specifically 15- and 25-membered azamacrocycles can afford benzenic compounds, except in the case of 20-membered azamacrocycle (20-MAA) which was inactive with the Wilkinson’s catalyst. In this study, theoretical calculations allowed to determine the origin of the different reactivity of the 20-MAA, where it was found that the activation barrier of the oxidative addition of two alkynes is higher than those obtained for the 15- and 25-membered macrocycles. This barrier was attributed primarily to the interaction energy, which corresponds to the energy that is released when the two deformed reagents interact in the transition state. The main factor that helped to provide an explanation to the different reactivity observed was that the 20-MAA had a more stable and delocalized HOMO orbital in the oxidative addition step. Moreover, we observed that the formation of a strained ten-membered ring during the cycloaddition of 20-MAA presents significant steric hindrance. Furthermore, in Chapter 5, an electrochemical study is presented in collaboration with Prof. Anny Jutand from Paris. This work allowed studying the main steps of the catalytic cycle of the [2+2+2] cycloaddition reaction between diynes with a monoalkyne. First kinetic data were obtained of the [2+2+2] cycloaddition process catalyzed by the Wilkinson’s catalyst, where it was observed that the rate-determining step of the reaction can change depending on the structure of the starting reagents. In the case of the [2+2+2] cycloaddition reaction involving two alkynes and one alkene in the same molecule (enediynes), it is well known that the oxidative coupling may occur between two alkynes giving the corresponding metallacyclopentadiene, or between one alkyne and the alkene affording the metallacyclopentene complex. Wilkinson’s model was used in DFT calculations to analyze the different factors that may influence in the reaction mechanism. Here it was observed that the cyclic enediynes always prefer the oxidative coupling between two alkynes moieties, while the acyclic cases have different preferences depending on the linker and the substituents used in the alkynes. Moreover, the Wilkinson’s model was used to explain the experimental results achieved in Chapter 7 where the [2+2+2] cycloaddition reaction of enediynes is studied varying the position of the double bond in the starting reagent. It was observed that enediynes type yne-ene-yne preferred the standard [2+2+2] cycloaddition reaction, while enediynes type yne-yne-ene suffered β-hydride elimination followed a reductive elimination of Wilkinson’s catalyst giving cyclohexadiene compounds, which are isomers from those that would be obtained through standard [2+2+2] cycloaddition reactions. Finally, the last chapter of this thesis is based on the use of DFT calculations to determine the reaction mechanism when the macrocycles are treated with transition metals that are inactive to the [2+2+2] cycloaddition reaction, but which are thermally active leading to new polycyclic compounds. Thus, a domino process was described combining an ene reaction and a Diels-Alder cycloaddition.