Mathematical Foundations of Complex Networked Information Systems Po

Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in eve

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R. Kumar · Martin J. Wainwright Riccardo Zecchina

Mathematical Foundations of Complex Networked Information Systems Politecnico di Torino, Verrès, Italy 2009 Fabio Fagnani · Sophie M. Fosson Chiara Ravazzi  Editors

Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and NY Catharina Stroppel, Bonn Anna Wienhard, Heidelberg

More information about this series at http://www.springer.com/series/304

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Fondazione C.I.M.E., Firenze C.I.M.E. stands for Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Centre. Conceived in the early fifties, it was born in 1954 in Florence, Italy, and welcomed by the world mathematical community: it continues successfully, year for year, to this day. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities over the years. The main purpose and mode of functioning of the Centre may be summarised as follows: every year, during the summer, sessions on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. A Session is generally based on three or four main courses given by specialists of international renown, plus a certain number of seminars, and is held in an attractive rural location in Italy. The aim of a C.I.M.E. session is to bring to the attention of younger researchers the origins, development, and perspectives of some very active branch of mathematical research. The topics of the courses are generally of international resonance. The full immersion atmosphere of the courses and the daily exchange among participants are thus an initiation to international collaboration in mathematical research. C.I.M.E. Director Elvira MASCOLO Dipartimento di Matematica “U. Dini” Università di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]

C.I.M.E. Secretary Paolo SALANI Dipartimento di Matematica “U. Dini” Università di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]

For more information see CIME’s homepage: http://www.cime.unifi.it CIME activity is carried out with the collaboration and financial support of: - INdAM (Istituto Nazionale di Alta Matematica) - MIUR (Ministero dell’Universita’ e della Ricerca)

P.R. Kumar • Martin J. Wainwright • Riccardo Zecchina

Mathematical Foundations of Complex Networked Information Systems Politecnico di Torino, VerrJes, Italy 2009 Fabio Fagnani, Sophie M. Fosson, Chiara Ravazzi Editors

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Authors P.R. Kumar CSL and Department of ECE University of Illinois Urbana Illinois, USA

Martin J. Wainwright Department of Statistics UC Berkeley Berkeley California, USA

Riccardo Zecchina DISAT Politecnico di Torino Torino, Italy Editors Fabio Fagnani DISMA Politecnico di Torino Torino, Italy