Complex Systems: Lecture Notes of the Les Houches Summer School 2006
Regular price
32.750 KD
inc. VAT
Couldn't load pickup availability
Table of contents
- Cover
- Previous sessionsvi
- Organizersix
- Lecturersix
- Seminar Speakersxi
- Participantsxiii
- Auditorsxvi
- Prefacexvii
- Contentsxxi
- Course 1. Introduction to phase transitions in random optimization problems1
- 1. Introduction5
- 2. Basic concepts: overview of static phase transitions in K-XORSAT8
- 3. Advanced methods (I): replicas25
- 4. Advanced methods (II): cavity34
- 5. Dynamical phase transitions and search algorithms41
- 6. Conclusions59
- Appendix A. A primer on large deviations60
- Appendix B. Inequalities of first and second moments62
- Appendix C. Corrections to the saddle-point calculation of <N2>63
- References64
- Course 2. Modern coding theory: the statistical mechanics and computer science point of view67
- 1. Introduction and outline71
- 2. Background: the channel coding problem72
- 3. Sparse graph codes82
- 4. The decoding problem for sparse graph codes89
- 5. Belief Propagation beyond coding theory110
- 6. Belief Propagation beyond the binary symmetric channel114
- 7. Open problems124
- Appendix A. A generating function calculation126
- References127
- Course 3. Mean field theory of spin glasses: statics and dynamics131
- 1. Introduction135
- 2. General considerations136
- 3. Mean field theory137
- 4. Many equilibrium states144
- 5. The explicit solution of the Sherrington Kirkpatrick model152
- 6. Bethe lattices163
- 7. Finite dimensions169
- 8. Some other applications174
- 9. Conclusions174
- References176
- Course 4. Random matrices, the Ulam Problem, directed polymers & growth models, and sequence matchin179
- 1. Introduction183
- 2. Random matrices: the Tracy-Widom distribution for the largest eigenvalue185
- 3. The longest common subsequence problem (or the Ulam problem)191
- 4. Directed polymers and growth models194
- 5. Sequence matching problem204
- 6. Conclusion211
- References214
- Course 5. Economies with interacting agents217
- 1. Introduction221
- 2. Models of segregation: a physical analogy224
- 3. Market relations231
- 4. Financial markets238
- 5. Contributions to public goods246
- 6. Conclusion252
- References253
- Course 6. Crackling noise and avalanches: scaling, critical phenomena, and the renormalization group257
- 1. Preamble261
- 2. What is crackling noise?261
- 3. Hysteresis and Barkhausen noise in magnets264
- 4. Why crackling noise?269
- 5. Self-similarity and its consequences276
- References286
- Course 7. Bootstrap and jamming percolation289
- 1. Introduction293
- 2. Bootstrap Percolation (BP)295
- 3. Jamming Percolation (JP)300
- 4. Related stochastic models307
- References308
- Course 8. Complex networks309
- 1. Introduction313
- 2. Network expansion and the small-world effect316
- 3. Degree distributions321
- 4. Further directions337
- References339
- Course 9. Minority games343
- 1. Introduction347
- 2. The minority game: definition and numerical simulations349
- 3. Exact solutions357
- 4. Application and extensions363
- 5. Conclusions370
- References370
- Course 10. Metastable states in glassy systems373
- 1. Introduction377
- 2. Mean-field Spin Glasses378
- 3. The complexity380
- 4. Supersymmetry breaking and structure of the states383
- 5. Models in finite dimension387
- 6. Conclusion391
- References392
- Course 11. Evolutionary dynamics395
- 1. Introduction and Questions399
- 2. Analysis of phenomenological models407
- 3. Acquisition of multiple beneficial mutations422
- 4. Recombination and sex435
- 5. Deleterious intermediaries and combinatoric possibilities437
- 6. Beyond the simplest questions440
- 7. The state of the field444
- 8. Acknowledgments445
- References445
- Course 12. Statistical modelling and analysis of biological networks447
- 1. A primer in Bayesian analysis452
- 2. Bayesian analysis of biological networks458
- 3. Applications464
- 4. Conclusion and outlook468
- References469
- Course 13. The slow dynamics of glassy materials: insights from computer simulations473
- References481
- Course 14. Epigenetic landscape and catastrophe theory: commentary on a correspondence483
- Selected Bibliography489
- Course 15. A hike in the phases of the 1-in-3 satisfiability491
- 1. Introduction495
- 2. Results496
- 3. Concluding remarks497
- References498
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 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
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