qmdaa:moro

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 qmdaa:moro [2007/09/18 12:51]steko lecture #2 qmdaa:moro [2018/08/04 00:01] (current) Both sides previous revision Previous revision 2007/09/18 14:02 steko lecture #32007/09/18 12:51 steko lecture #22007/09/18 12:04 steko created, lecture #1 Next revision Previous revision 2007/09/18 14:02 steko lecture #32007/09/18 12:51 steko lecture #22007/09/18 12:04 steko created, lecture #1 Line 46: Line 46: Philosophical positions Philosophical positions + ===== Lecture #2 ===== ===== Lecture #2 ===== Line 51: Line 52: Complex ≠ Complicated\\ Complex ≠ Complicated\\ Simple ≠ Easy\\ Simple ≠ Easy\\ - Multitude → complexity + Multitude → complexity ​but also simplicity - → simplicity + + - Chaotic systems + - Synergy systems + - Mesoscopic systems + + Complexity depends on the context of study. + + y = x^3 + a·x​ + + if <​m>​a=1​ or <​m>​a=-1​ the 2 resulting systems are qualitatively completely different. Mathematics catastrophe theory knows just 7 types of catastrophes described in mathematical terms. + + C. Renfrew 1978 + + Cellular Automata <​m>​{S_i}^{t+1} = R ({S^t}_{i-1},​{S^t}_{i},​{S^t}_{i+1})​ + + Power laws + + Independence ​→ No prediction + + ===== Lecture #3 ===== + + Fractals + * not a single statistics + * not only descriptive + * self-similar (scaling factors) + * defined by recursive algorithms + * fractional dimension compared to integer geometries (line=1, square=2, cube=3) + + Fractional dimension D characterizes how the mean depends on the size of the sample. + + Zipf 1949 + + Strange attractors are fractals (Lorentz) + + Self-organized Criticality
qmdaa/moro.txt · Last modified: 2018/08/04 00:01 (external edit)

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