複雑システム数理特論

This lecture aims to explain the characteristics of structure and dynamics in complex systems, introduce modeling and analysis methods at the macroscopic and microscopic levels, and help students understand how the link between microscopic dynamics and macroscopic behavior is constructed.

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授業計画

1. Overview (10/07) 2. Iterative maps and stochastic iterative maps (10/14) 3. Thermodynamics and statistical mechanics (10/21) 4. Activated processes and glasses (10/28) 5. Cellular automata (11/04) 6. Statistical fields (11/11) 7. Computer simulations (11/18) 8. Scaling and renormalization (12/09) 9. Neural networks(12/16, 12/23) 10. Subdivided neural networks (01/06,01/13) 11. Models of mind (01/20)

授業の方法

Essentially the course is based on the lecture form.

成績評価方法

Grade will be evaluated based on the attendance rate and the final report.

履修上の注意

None in particular.

その他

＜授業情報＞ In the beginning of the lecture, a number of important concepts pertaining to the structure and dynamics of complex systems will be explained in order to familiarize students with the general properties of complex systems. This is followed by an introduction to modeling methods for the overall behavior of complex systems, including differential equation models, nonlinear dynamical systems, and stability analysis. The introduction of micro-models of complex systems will focus on cellular automata and particle and spin models for physical systems. The connection between micro and macro models will be introduced with a focus on phase transition theory and neural networks.