Complex Systems Lecture Notes of the les Houches Summer School 2006

There 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 mu...

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Hlavní autoři: Bouchaud, Jean-Philippe, Mézard, Marc, Dalibard, Jean
Médium: E-kniha
Jazyk:angličtina
Vydáno: Chantilly Elsevier Science & Technology 2007
Elsevier Science
Vydání:1
Edice:Les Houches
Témata:
Komplexes System
ISBN:9780444530066, 0444530061
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  • Front cover -- Complex Systems -- Copyright page -- Previous sessions -- Organizers -- Lecturers -- Seminar Speakers -- Participants -- Auditors -- Preface -- Contents -- Course 1. Introduction to phase transitions in random optimization problems -- 1. Introduction -- 2. Basic concepts: overview of static phase transitions in K-XORSAT -- 3. Advanced methods (I): replicas -- 4. Advanced methods (II): cavity -- 5. Dynamical phase transitions and search algorithms -- 6. Conclusions -- Appendix A. A primer on large deviations -- Appendix B. Inequalities of first and second moments -- Appendix C. Corrections to the saddle-point calculation of &lt -- N2&gt -- -- References -- Course 2. Modern coding theory: the statistical mechanics and computer science point of view -- 1. Introduction and outline -- 2. Background: the channel coding problem -- 3. Sparse graph codes -- 4. The decoding problem for sparse graph codes -- 5. Belief Propagation beyond coding theory -- 6. Belief Propagation beyond the binary symmetric channel -- 7. Open problems -- Appendix A. A generating function calculation -- References -- Course 3. Mean field theory of spin glasses: statics and dynamics -- 1. Introduction -- 2. General considerations -- 3. Mean field theory -- 4. Many equilibrium states -- 5. The explicit solution of the Sherrington Kirkpatrick model -- 6. Bethe lattices -- 7. Finite dimensions -- 8. Some other applications -- 9. Conclusions -- References -- Course 4. Random matrices, the Ulam Problem, directed polymers &amp -- growth models, and sequence matching -- 1. Introduction -- 2. Random matrices: the Tracy-Widom distribution for the largest eigenvalue -- 3. The longest common subsequence problem (or the Ulam problem) -- 4. Directed polymers and growth models -- 5. Sequence matching problem -- 6. Conclusion -- References
  • Course 5. Economies with interacting agents -- 1. Introduction -- 2. Models of segregation: a physical analogy -- 3. Market relations -- 4. Financial markets -- 5. Contributions to public goods -- 6. Conclusion -- References -- Course 6. Crackling noise and avalanches: scaling, critical phenomena, and the renormalization group -- 1. Preamble -- 2. What is crackling noise? -- 3. Hysteresis and Barkhausen noise in magnets -- 4. Why crackling noise? -- 5. Self-similarity and its consequences -- References -- Course 7. Bootstrap and jamming percolation -- 1. Introduction -- 2. Bootstrap Percolation (BP) -- 3. Jamming Percolation (JP) -- 4. Related stochastic models -- References -- Course 8. Complex networks -- 1. Introduction -- 2. Network expansion and the small-world effect -- 3. Degree distributions -- 4. Further directions -- References -- Course 9. Minority games -- 1. Introduction -- 2. The minority game: definition and numerical simulations -- 3. Exact solutions -- 4. Application and extensions -- 5. Conclusions -- References -- Course 10. Metastable states in glassy systems -- 1. Introduction -- 2. Mean-field Spin Glasses -- 3. The complexity -- 4. Supersymmetry breaking and structure of the states -- 5. Models in finite dimension -- 6. Conclusion -- References -- Course 11. Evolutionary dynamics -- 1. Introduction and Questions -- 2. Analysis of phenomenological models -- 3. Acquisition of multiple beneficial mutations -- 4. Recombination and sex -- 5. Deleterious intermediaries and combinatoric possibilities -- 6. Beyond the simplest questions -- 7. The state of the field -- 8. Acknowledgments -- References -- Course 12. Statistical modelling and analysis of biological networks -- 1. A primer in Bayesian analysis -- 2. Bayesian analysis of biological networks -- 3. Applications -- 4. Conclusion and outlook -- References
  • Course 13. The slow dynamics of glassy materials: insights from computer simulations -- References -- Course 14. Epigenetic landscape and catastrophe theory: commentary on a correspondence -- Selected Bibliography -- Course 15. A hike in the phases of the 1-in-3 satisfiability -- 1. Introduction -- 2. Results -- 3. Concluding remarks -- References