Collective decision-making on networked systems in presence of antagonistic interactions

Abstract

captures the alliances/rivalries between the political parties in the parliament. The idea is that the frustration of the parliamentary networks should correlate well with the duration of the government negotiation, and it is supported by the analysis of the legislative elections in 29 European countries in the last 40 years.The final contribution of this thesis is an analysis of the structure of (signed) Laplacian matrices and of their pseudoinverses. It is shown that the pseudoinverse of a Laplacian is in general a signed Laplacian, and in particular that the set of eventually exponentially positive Laplacian matrices (i.e., matrices whose exponential is a matrix with negative entries which becomes and stays positive at a certain power) is closed under stability and matrix pseudoinversion.The first person I need to thank is definitely my supervisor, Claudio Altafini. I am incredibly grateful for the opportunity of pursuing a PhD with you, your curiosity and passion for research are truly inspiring. Thank you for all your guidance and support, and for being available every time I needed help or got stuck. Grazie! I would also like to thank my co-supervisor, Anders Hansson, for his support and for always having kind words towards me, and for the many discussions on our shared interests, such as music, opera, gardening, and much more.I am grateful to Svante Gunnarsson, Martin Enqvist and Ninna Stensgård for providing a motivating, functioning and constructive work environment. To Alberto, Erik, Martin L., Gustaf, Jonatan and Anna, and all my colleagues at RT, thank you. Doing a PhD might feel lonely sometimes, and I am glad I have met so many nice, fun, and supportive colleagues and friends. Lunch walks, fika discussions, exchange of ideas at the reading group, workouts, dinners, BBQs, parties; in many occasions I have felt lucky to be part of the RT group. I treasure these memories. Kristoffer, Per, and Gustaf, I really appreciate all the help you have given me with thesis related issues in the last period.I would also like to thank my friends outside RT. Elisabeth, I so appreciate our discussions and dinners (with cake and wine of course); Oskar, thank you for the lunches and for teaching me Swedish customs. Many thanks also to France (Alessandro) and Giulio, for all the great times we have shared together since university, and to Arianna, Mattia, and la compagnia di Breda, for welcoming me so warmly every time I return to Italy.Finally, I want to thank my family. Thank you Olle, for being so supportive, caring and patient. I can't help but smile when I think about you. Un grazie speciale va ad Anna, Gianna e Luigi, per avermi sempre supportato (e sopportato direi) nei miei studi e sostenuto nelle mie scelte. Papà, per avermi insegnato a guardare il mondo con curiosità, ti penso spesso; mamma, per essere un ottimo esempio di donna forte e determinata; Anna, perchè so che posso sempre contare su di te (qui ci starebbe bene uno sticker).Thank you all!