1. Some Minimalist Dynamics
Wan Ahmad Tajuddin Wan Abdullah
Department of Physics, Faculty of Science, Universiti Malaya, Kuala Lumpur, Malaysia
and
Faculty of Computer Science and Information Technology, Universiti Malaya, Kuala Lumpur, Malaysia

2. Complexity Nature - complex at many levels
Physics: series expansions, truncations of series, statistical approximations, reduction analyses, system isolation, etc.
microbehaviour of components
↓ collective, emergent
macrolevel characteristics of system

3. ► get as close as possible to reality - better models and more accurate calculations
► minimalist models - capture the principal dynamics necessary, just sufficient for macrobehaviour
Identify, understand underlying dynamics principally responsible for macrophenomena

4. Monte Carlo simulation
simulation - integration of equations of motion.
noise/entropy/ignorance – probabilities
Prob(macro) = Folding(Prob(micro))
= ∫...π...Prob(macro|micro)Prob(micro|micro)...Prob(micro)...
Monte Carlo - integration of probability distributions

5. minimalist Ignore parameters not affecting macrobehaviour
(~ 'averaged out')

6. Some minimalist models
Lattice gas and fluids
atoms/molecules on lattice
→ vortices, turbulence flow
Cellular automata
lattice, neighborhood digital interactions
→ (1d,nn) dynamics: static, cycles, chaos, complex

7. • Protein folding
on-lattice, hydrophobic/hydrophylic nodes
→ insights into folding landscapes
• Genetic algorithms
Binary strings, mutation, cross-over, selection
→ parallel stochastic exploration of energy landscape,
optimization

8. Neural networks Traffic binary/bipolar, threshold, automata
→ gradient-descent dynamics,
optimization
associative (Hebb) learning
→ logic
Traffic
lattice, look-ahead interactions
→ dynamical phases: smooth flow, stop-and-start jams

9. Economics
Wealth exchange Yakovenko money conserved
→ Gibbsian

10. With saving propensity
non-thermal
Chatterjee et al.

11. Kinetic trading Trading rules: Local Zero temperature - deterministic
Conservative in money+ goods changing prices, money value
Scale independence of money, goods

12. Price evolution - initial distribution gaussian
1:1 money:goods :1 money:goods

13. ► ‘pump’ – for zero b states: push to higher h
► dissipative (in h) – tendency to move to lowest state
► ‘pump’ – for zero b states: push to higher h
long time behaviour – equilibration?

14. Variance in price
Mean price
Price variance
Initial ratio of goods

15. Demand curve
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6
0.1
0.3
0.5
0.7
0.9
Initial available goods (fraction)
Mean price (after 5 iterations)
25 agents
50 agents
100 agts
200 agts
400 agts

16. ‘greed’/rational/profit maximization
– where did it come from?
independence on number of agents?

17. Wealth distribution

20. Soccer? :-) dribble, shoot, move, strength, fermions
go for ball, go for goal
preliminary

21. +---------------------------------------------------+
| |
| h |
| h h y |
| y |
| h y |
[ ]
[ y ]
[ b h hY y g ]
[ h ]
| h y |
| h |
| h y y |
| y |

22. +---------------------------------------------------+
| |
| h |
| y |
| h |
| y |
[ ]
[ h y ]
[ hy ]
[ b h hY y g ]
[ hhy ]
[ y ]
[ h ]

23. + passing, positioning

24. +---------------------------------------------------+
| |
| y |
| h |
[ h ]
[ hy ]
[ hyy ]
[ b h h Hyy g ]
[ hyy ]
[ hh ]
[ ]
| yy |

25. +---------------------------------------------------+
| |
| y |
[ o hhh ]
[ y ]
[ hhhy y ]
[ b h yh hyy g ]
[ y y ]
[ ]
[ y ]
| h |

26. +---------------------------------------------------+
| |
| hh |
| h |
[ ]
[ y y ]
[ hy y ]
[ b h hyy g o
[ hy y ]
[ h ]
[ yy ]
| h |
| h |

27. noise
intelligence
learning

28. ขอบคุณ
Thank you