Complex Systems Beyond the Metaphor

A successful one-week short course on Complex Systems Beyond the Metaphor: Your Mathematical Toolset was held in the UNSW School of Mathematics and Statistics on Feb 5-9, 2007. It introduced the mathematical foundations and tools needed for a solid understanding of complex systems, an area often known for purely metaphorical or 'hand-waving' explanations.

Aiming at a mathematically literate audience (e.g. engineers, quantitative biologists, computer modellers), leading Australian experts presented intensive introductions to the essential topics of complex systems theory, including self-organization, nonlinear dynamical systems, cellular automata, networks and statistical learning.

The speakers were David Green (Monash), Bob Marks (UNSW), Bruce Henry (UNSW), David Hill (ANU), Janet Wiles (UQ) and Matt Wand (UNSW)

The course may be repeated at some time in the future. If you may be interested in attending or have any suggestions to make, please email James Franklin.


Participants may be interested in the forthcoming Complex'07 conference on the Gold Coast in July 2007 ... flyer

Topics

• David Green: introduction to complexity definitions, measures
• complexity paradigms in nonlinear dynamics, networks, computation
• emergence, self-organisation, criticality, modularity, feedback, simulations, applications

• Bruce Henry: chaos
• fractals
• anomalous diffusion
• fractional calculus

• Janet Wiles: genetic networks
• cellular automata
• neural nets

Image modified from Pov Planet by Casey Uhrig, used with permission

• Robert Marks: the science and art of modelling
• generative social science theory and techniques
• agent-based models in designing markets, including learning

(Bob's notes)

• David Hill: complex networks introduction
• random graphs, small world, scale free
• network dynamics, synchronization, collapse
• network control

(Hill first lecture; Hill second lecture; Hill third lecture; Hill fourth lecture)

• Matt Wand: elements of statistical learning
• cross-validation, curse of dimensionality
• support vector machine classification
• semiparametric regression

Further information

Download brochure here (580kB), with details of program and speakers

Contact: Bruce Henry (UNSW)

Computing Tutorial Project: Price-Check!

During the week, students were challenged to attempt a small modelling project (download project). In groups of 2-4, participants had the opportunity to design and implement an agent-based model of the check-out area of a suburban supermarket.

Prizes were awarded in the following categories:

• The El Farrol Arthur Prize for Human Dynamics: 'Team Control' (Shane Stephens and Stephen Curiskis)
• The Eric Weisstein Prize for `Geeky Appeal': 'SuperSim' (Alex Ryan and Martin Wong)
• The Warhol Prize for Model Creativity: Carl Kneipp

Models contributed by their authors are here:

• SuperSim by Alex Ryan and Martin Wong. Download their NetLogo model file here
• Team Control by Shane Stephens and Stephen Curiskis. Implemented in Python. Files available upon request.

Our Sponsors

COSNet, the ARC Complex Open Systems Research Network, links scientists in the physical, biological and social sciences to research and develop tools for the self-organization of complex non-equilibrium systems

MASCOS, the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, conducts research on the mathematical and statistical modelling of complex systems. Its UNSW node is the local host of the course

AMSI, the Australian Mathematical Sciences Institute, coordinates research, industry linkages and education initiatives in the mathematical sciences

Course photos

Course participants at the AGSM

Presenters David Hill, Bob Marks, Bruce Henry and Janet Wiles with ICIAM President Ian Sloan