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Aggregation in complex systems

16-hour module, term 1, 2011/12, module leader: R.S.MacKay.

Thursdays 10.00-12.00, in the TCC lecture room (B0.15a) or by videolink from partner institutions.

Starts 13 October 2011, no lecture 10 November, last lecture 8 December.

Available for credit at Warwick as MA5Q3 Complexity Science (24 CATS). To obtain credit, candidates must write up a chapter of notes for the module. The lectures can be taken as starting point, but substantial independent reading (and potentially new research) will be required as a complement (24 CATS normally requires a 30-hour module, so work equivalent to 14 extra hours of lectures is needed). Deadline: 29 February 2012.


This module will address hierarchical aggregation procedures for complex systems. It is NOT about many other uses of the word "aggregation".

For present purposes a "complex system" is a large collection of interdependent units. Given a description at the level of individual units ("microscopic") it might be fruitful to partition the collection into groups of units which can be considered to be "super-units" with effective interactions between them. The nicest situation is where the new system is in the same class as the old one, because one can then imagine iterating the procedure.

Potential outcomes are:

- efficient ways to compute quantities for complex systems

- insight into the macroscopic behaviour

Challenges are:

- the choice of partition

- practical implementation

Contexts to be studied include:

- equilibrium statistical mechanics

- shortest paths in graphs

- selfish traffic flow

- Markov processes

- multi-agent games

- oscillator networks

The content is very much research (and literature search) in progress. Participants will be expected to engage in the process.

A short paper setting out some of the directions (was prepared for an EC FET call). Our grant proposal HACS for this call.

Summary presentation of the scope of the module (pdf) (converted from ppt)

On oscillator networks: CameroonLecturesPart1 (pdf); plus perhaps useful UHypPseudoDiscreteTime (pdf)

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