Modeling and Simulating Social Systems with MATLAB Lecture 5 - PowerPoint PPT Presentation

Modeling and Simulating Social Systems with MATLAB Lecture 5 – Cellular Automata Olivia Woolley, Stefano Balietti, Lloyd Sanders Computational Social Science (D GESS) 2015-10-26 ETH Zürich

Strategies for Research Projects  “Data project”:  Choose a dataset for which you have an interesting question  Come up with a research question that can be tested with that data  Implement an existing model form the scientific literature  Run simulations that either use the dataset as input or that reproduce certain aspects of the data 2015-10-26 2 Modelling and Simulating Social Systems with Matlab

Strategies for Research Projects  “Paper project”:  Choose a scientific paper (or several papers) on a modeling and simulation approach that looks interesting  Come up with a research question that builds upon the paper but is different from their research questions  Extend, simplify, modify, and/or combine existing models for testing your research question  Run simulations for your model and compare the results to the ones for the original model 2015-10-26 3 Modelling and Simulating Social Systems with Matlab

Repetition  D y n a m i c a l s y s t e m s d e s c r i b e d b y a s e t o f differential equations; numerical solutions can be calculated iteratively using Euler's method ( e x a m p l e s : L o t k a - Volterra and Kermack-McKendrick)  The values and ranges of parameters critically matter for the system dynamics (Example 2, epidemiological threshold)  Time resolution in Euler's method must be sufficiently high to capture “fast” system dynamics (Example 3)  MATLAB provides the commands ode23 and ode45 for solving differential equations (Example 3) 2015-10-26 4 4 Modelling and Simulating Social Systems with Matlab

Simulation Models  W h a t d o w e m e a n w h e n w e s p e a k o f (simulation) models?  Formalized (computational) representation of social (or other kinds of) dynamics  Reduction of complexity, i.e. highly simplifying assumptions  The goal is not to reproduce reality in general (only very specific aspects of it)  Formal framework to test and evaluate causal hypotheses against empirical data 2015-10-26 5 5 Modelling and Simulating Social Systems with Matlab

Simulation Models  Strength of (simulation) models?  Computational laboratory: test how micro dynamics lead to macro patters  Experiments with computer models are particularly useful in the social sciences, where experiments in the real world are typically not possible  Suitable where analytical models fail or where dynamics are too complex for analytical models 2015-10-26 6 6 Modelling and Simulating Social Systems with Matlab

Simulation Models  Weakness of (simulation) models?  The choice of model parameters and implementation details can have a strong influence on the simulation outcome  We can only model aspects of a system, i.e. the models are necessarily incomplete and reductionist  More complex models are generally not better (only when simplification is not possible)  It can be hard to relate simulation results to a realistic and relevant empirical question 2015-10-26 7 7 Modelling and Simulating Social Systems with Matlab

Simulation Models  How to we deal with the known limitations?  Simple models with only few parameters  Test whether simulation results depend on details of the implementation or model  Validate the model mechanism with observations and causal plausibility  Use empirical data to evaluate the predictive power of the simulation model 2015-10-26 8 8 Modelling and Simulating Social Systems with Matlab

Cellular Automaton (plural: Automata) 2015-10-26 9 9 Modelling and Simulating Social Systems with Matlab

Cellular Automaton (plural: Automata)  A cellular automaton is a set of rules, defining how the state of a cell in a grid is updated, depending on the states of its neighboring cells  Cellular-automata simulations are discrete in time and space 2015-10-26 10 10 Modelling and Simulating Social Systems with Matlab

Cellular Automaton  The grid can have an arbitrary number of dimensions: 1-dimensional cellular automaton 2-dimensional cellular automaton 2015-10-26 11 Modelling and Simulating Social Systems with Matlab

Moore Neighborhood  The cells are interacting with each neighbor cells, and the neighborhood can be defined in different ways, e.g. the M o o r e n e i g h b o r h o o d : 1 st order Moore neighborhood 2 nd order Moore neighborhood 2015-10-26 12 Modelling and Simulating Social Systems with Matlab

Von-Neumann Neighborhood  T h e c e l l s a r e i n t e r a c t i n g w i t h e a c h n e i g h b o r c e l l s , and the neighborhood can be defined in different ways, e.g. the V o n - N e u m a n n n e i g h b o r h o o d : 2 nd order Von-Neumann 1 st order Von-Neumann neighborhood neighborhood 2015-10-26 13 Modelling and Simulating Social Systems with Matlab

Game of Life  N i = Number of 1 s t order Moore neighbors to cell i that are activated .  For each cell i : 1. D e a c t i v a t e active cell iff N i < 2 o r N i >3. 2. A c t i v a t e inactive cell iff N i =3 i 2015-10-26 14 Modelling and Simulating Social Systems with Matlab

Game of Life  N i = Number of 1 s t order Moore neighbors to cell i that are activated .  For each cell i : 1. Deactivate active cell if N i <2 or N i >3. 2. Activate inactive cell if N i =3 2015-10-26 15 15 Modelling and Simulating Social Systems with Matlab

Game of Life  Want to see the Game of Life in action? Type: l i f e 2015-10-26 16 16 Modelling and Simulating Social Systems with Matlab

Complex Patterns  “ Gosper Glider Gun”: 2015-10-26 17 17 Modelling and Simulating Social Systems with Matlab

Game of Life: Some Bits of History 1970: Conway presents the Game of Life; discovery of the glider (speed c/4) and the standard spaceships (speed c/2); discovery of the Gosper glider gun (first pattern found with indefinite growth) 1971: First garden of eden (pattern that has no parent pattern and can only occur at generation 0) was discovered; first patter with quadratic growth (breeder) 1989: Discovery of the first spaceships with velocities c/3 and c/4 1996: Game of Life simulated in Game of Life 2000: A Turing machine was built in Game of Life 2004: Construction of the largest interesting pattern so far: caterpillar spaceship with speed 17c/45 consisting of 11,880,063 alive cells 2013: The first complete replicator (a pattern that produces an exact copy of itself) was built 2014: Game of Life wiki contains more than 3000 interesting patterns 2015-10-26 18 Modelling and Simulating Social Systems with Matlab

Surprising discoveries continue  “The loafer” is a very small spaceship  It is the slowest known orthogonal spaceship (speed of c/7)  It was discovered only in 2013 2015-10-26 19 Modelling and Simulating Social Systems with Matlab

Life in Life  The Game of Life can be used to simulate the Game of Life: h t t p : / / w w w . y o u t u b e . c o m / w a t c h ? v = x P 5 - i I e K X E 8 2015-10-26 20 20 Modelling and Simulating Social Systems with Matlab

Life in Life  The Game of Life can be used to calculate everything (if a Turing machine can): http://www.youtube.com/watch?v=My8AsV7bA94 2015-10-26 21 21 Modelling and Simulating Social Systems with Matlab

1-dimensional Cellular Automata 2015-10-26 22 22 Modelling and Simulating Social Systems with Matlab

Cellular Automaton: Principles 1. S e l f O r g a n i z a t i o n : Patterns appear from random start patterns 2. Emergence: High-level phenomena can appear such as gliders, glider guns, etc. 3. Complexity: Simple rules produce complex phenomena 2015-10-26 23 23 Modelling and Simulating Social Systems with Matlab

Highway Simulation  Simple example of a 1-dimensional cellular automaton  Rules for each car at cell i : S t a y : I f t h e c e l l d i r e c t l y t o t h e r i g h t i s o c c u p i e d . 1. Move : Otherwise, move one step to the right, with 2. probability p Move to the next cell, with the probability p 2015-10-26 24 24 Modelling and Simulating Social Systems with Matlab

Highway Simulation  We have prepared some files for the highway simulations:  d r a w _ c a r . m : Draws a car, with the function draw_car(x0, y0, w, h)  simulate_cars.m : Runs the simulation, with the function simulate_cars(moveProb, inFlow, withGraphics) 2015-10-26 25 25 Modelling and Simulating Social Systems with Matlab

Highway Simulation  Running the simulation is done like this: s i m u l a t e _ c a r s ( 0 . 9 , 0 . 2 , t r u e ) 2015-10-26 26 26 Modelling and Simulating Social Systems with Matlab

Kermack-McKendrick Model  In lecture 4, we introduced the Kermack- McKendrick model, used for simulating disease spreading  We will now implement the model again, but this time instead of using differential equations we use the approach of cellular automata 2015-10-26 27 27 Modelling and Simulating Social Systems with Matlab

Kermack-McKendrick model 2015-10-26 28 Modelling and Simulating Social Systems with Matlab