## Complex Systems: Lecture Notes of the Les Houches Summer School 2006There has been recently some interdisciplinary convergence on a number of precise topics which can be considered as prototypes of complex systems. This convergence is best appreciated at the level of the techniques needed to deal with these systems, which include: 1) A domain of research around a multiple point where statistical physics, information theory, algorithmic computer science, and more theoretical (probabilistic) computer science meet: this covers some aspects of error correcting codes, stochastic optimization algorithms, typical case complexity and phase transitions, constraint satisfaction problems. 2) The study of collective behavior of interacting agents, its impact on understanding some types of economical and financial problems, their link to population and epidemics dynamics, game theory, social, biological and computer networks and evolution. The present book is the written version of the lectures given during the Les Houches summer school session on "Complex Systems", devoted to these emerging interdisciplinary fields. The lectures consist both in a number of long methodological courses (probability theory, statistical physics of disordered systems, information theory, network structure and evolution, agent-based economics and numerical methods) and more specific, 'problem oriented' courses. Lecturers are all leading experts in their field; they have summarized recent results in a clear and authoritative manner. The "Les Houches lecture notes" have a long tradition of excellence and are often found to be useful for a number of years after they were written. The book is of interest to students and researchers with various backgrounds: probability theory, computer science, information theory, physics, finance, biology, etc. · Topical and comprehensive survey of the emerging, interdisciplinary field of "Complex Systems", covered by recognized world experts · "Les Houches lectures notes": a long tradition of excellence and long-lasting impact · Of interest to a broad audience (mathematics, physics, biology, informatics, finance, geology, etc.) · Some applications may have concrete impact · Selected topics in complex systems: forefront of research in the field |

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### Contents

the statistical mechanics and computer science point of view | 67 |

statics and dynamics | 131 |

Course 4 Random matrices the Ulam Problem directed polymers growth models and sequence matching | 179 |

Course 5 Economies with interacting agents | 217 |

scaling critical phenomena and the renormalization group | 257 |

Course 7 Bootstrap and jamming percolation | 289 |

Course 8 Complex networks | 309 |

Course 9 Minority games | 343 |

Course 10 Metastable states in glassy systems | 373 |

Course 11 Evolutionary dynamics | 395 |

Course 12 Statistical modelling and analysis of biological networks | 447 |

insights from computer simulations | 473 |

commentary on a correspondence | 483 |

Course 15 A hike in the phases of the 1in3 satisfiability | 491 |

### Other editions - View all

Complex Systems: Lecture Notes of the Les Houches Summer School 2006 Jean-Philippe Bouchaud,Marc Mezard,J. Dalibard No preview available - 2007 |

### Common terms and phrases

3-XORSAT agents algorithm approximation asymptotic avalanche average behaviour Belief Propagation beneficial mutations channel codeword complex compute configuration consider correlations corresponding critical decoding defined degree distribution denote density depends dominated DPLL dynamics edges ensemble entropy equation equilibrium evolution evolutionary example exponent exponentially factor graph finite fixed fluctuations formula free energy function Gaussian genes genome giant component given interactions lattice LDPC Lett limit magnetization matrix mean field mean field theory metastable Mézard minority game mutation rate mutations networks nodes optimal parameter Parisi particles percolation phase transition Phys population power law probability distribution problem random graphs random matrix random variable ratio replica satisfiable scaling Section sequence solution spin glasses stochastic strategy structure symmetry temperature theoretical theory threshold tion Tracy-Widom distribution typical vertex vertices zero

### Popular passages

Page vi - Scattering theory. Recent developments in field theory. Nuclear interaction; strong interactions. High energy electrons. Experiments in high...

Page v - ECOLE DE PHYSIQUE DES HOUCHES Service inter-universitaire commun à l'Université Joseph Fourier de Grenoble et à l'Institut National Polytechnique de Grenoble Subventionné par le Ministère de l'Éducation Nationale, de l'Enseignement Supérieur et de la Recherche, le Centre National de la Recherche Scientifique, le Commissariat à l'Énergie Atomique Membres du conseil d'administration : Yannick Vallée (président), Paul Jacquet (vice-président), Cécile...

Page xv - University of Calgary 2500, University Drive, NW Calgary Alberta T2N 1N4 Canada Professor K.-F.

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Page xx - The staff of the School, especially Brigitte Rousset and Isabelle Lelievre, have been of great help for the preparation and development of the school, and we would like to thank them warmly on behalf of all students and lecturers.