Game Theory applied to gene expression analysis

Doctorate in Mathematics and Applications MAT/09 ii iii To Alessandra and Giovanna iv Acknowledgements Three years as a Ph.D student involved in a multidisciplinary field at the Department of Mathematics and at the Unit of Molecular Epidemiology gave me many opportunities to exchange opinions with a lot of people from completely different research area. Here I would like to take the opportunity to thank some persons that have been very important for the accomplishment of this thesis. First of all, I want to thank my friend and promotor Fioravante Patrone, for his enthusiastic, conscious and inspired supervision. At the time when I started my doctorate, I had already been co-worker of Fioravante for few enjoyable years, and I am not able to fully express my gratitude to him for his superb guidance in doing research in Game Theory, applied Mathematics and many other topics. My thanks also to Stefano Bonassi, for his continuing support and for having provided a tangible opportunity to focus my efforts on the application of Game Theory to gene expression analysis. and Gian Paolo Tonini for their cooperation and assistance in explaining me many biological aspects on which microarray technology is based. for profitable discussions on game theoretical topics of interest for my work. Furthermore, I want to express my gratitude to all my colleagues for creating a nice environment for doing research. I am grateful to my parents for their unceasing support, and to have given me the opportunity to enjoy Science in a loving environment when I was a young student. Last, but for sure not least, I thank my wife Alessandra-computer scientist v vi and mother-for her efforts in giving me all her strength all the time, also in the most difficult moments, successfully fulfilling her difficult job, and never subtracting a carefulness to our daughter Giovanna and me. She is without any doubt the most astonishingly talented person I have ever known.