Some Minimalist Dynamics Wan Ahmad Tajuddin Wan Abdullah Department of Physics, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia and Faculty of Computer Science and Information Technology, Universiti Malaya, 50603 Kuala Lumpur, Malaysia

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

► 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

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

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

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

• 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

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

Economics Wealth exchange Yakovenko money conserved → Gibbsian

With saving propensity non-thermal Chatterjee et al.

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

Price evolution - initial distribution gaussian 1:1 money:goods 100:1 money:goods

► ‘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?

Variance in price Mean price Price variance Initial ratio of goods

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

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

Wealth distribution

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

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

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

+ passing, positioning

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

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

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

noise intelligence learning

ขอบคุณ Thank you