Modeling and Simulating Social Systems with MATLAB · 2016. 9. 26. · Lecture 1 – Introduction to the Course and MATLAB Computational Social Science Olivia Woolley, Lloyd Sanders,

2016-09-26

ETH Zürich

Modeling and Simulating Social Systems with MATLAB

Lecture 1 – Introduction to the Course and MATLAB

Computational Social Science

Olivia Woolley, Lloyd Sanders, Dirk Helbing

2016-09-26

Modeling and Simulating Social Systems with MATLAB 2

Lecture 1 – Contents §  Content, rules, and goals of the course

§  Short motivation on Modeling and Simulation

§  MATLAB basics

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Modelling and Simulating Social Systems with MATLAB

Weekly lecture with exercises, each session will be split into about 40 minutes lecture and 60 minutes exercises / project work. We will put the lecture slides and other material on http://www.coss.ethz.ch/education/matlab.html and we will use GitHub (more on that later): github.com/msssm

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How to contact us

§  in the lecture, please do not hesitate to approach us with any questions you might have

§  via email to

[email protected] or [email protected]

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Mailing List §  Send an email to:

[email protected] §  with text:

SUBSCRIBE msssm Your Name §  E.g.

SUBSCRIBE msssm Karsten Donnay

§  Text to unsubscribe:

SIGNOFF msssm

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Purpose of the Mailing List §  Foster cooperation among students

1. Discuss technical issues

2. Discuss organizational issues

3. Share code

4. Share references to literature

5. Share references to datasets

6. Form and communicate groups

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Rules of the Mailing List 1.  Be nice.

2.  Be collaborative.

3.  Only small attachments. Add links to external resources.

4.  Do not spam.

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Examination Format

Students earn their credit points by:

1.  Implementing a model / running simulations / analyzing data from the social science literature in MATLAB

2.  Submitting a short proposal specifying their project

3.  Producing a seminar thesis (up to 15 pages)

4.  Presenting the results it in a 15 minute talk (The thesis should include a discussion of the model, its theory and properties, details of the simulation, parameter dependencies, results from data analyses, but also possible practical implications.)

§  Submission of the work through GitHub: github.com/msssm (more on that later on)

(also see the course description)

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Seminar thesis

Studying a scientific paper and/or a data set

Reproducing and extending results / running a simulation in MATLAB

Writing a report and giving a talk

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Project §  Implementation of a model of a social system in

MATLAB §  During the next 2-3 weeks:

§  Form a group of 2-4 students

§  Decide together on a topic and research question

There are a lot of different project topics available on the Project section of the course website but we encourage you to realize your own ideas for example with one of the datasets listed.

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Project §  If you are looking for inspiration:

§  A number of reports from the previous course are linked on the Project section of the website

§  Take a look what they did, maybe you would like to build up on their work…

§  If you are a Master/PhD student: §  Your project can, of course, be related to your research

topic

Please approach us in class or write us an email if you have any questions.

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Project §  Procedure:

§  Organize yourself into groups (use the mailing list!)

§  Carefully select a topic (and corresponding papers)

§  Think about which particular question you want to study

§  Each group has to submit a short 1-2 page proposal that very briefly describes what they are planning to do

§  You will give a 3 minute flash-talk on your proposal

§  More information will follow in the next lectures

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Flash Talks Each group will have to present their proposal in the

form of a flash talk:

§  Only 1 slide!

§  Only 3 minutes! (plus 2 minutes questions/feedback)

§  The entire 5th lecture (October 24) is reserved for these flash talks

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Projects from previous semesters

Sugarscape Civil violence Group dynamics

Trust Facebook social networks

Space syntax

Pedestrian dynamics Cycling strategies Tumour growth

Segregation Cancer Traffic dynamics

Swarms Sailing strategies Migration

Flocks Cockroaches Arab Revolutions

Civil war Queuing models Synchronized clapping

Game theory tournament

Game theory Language formation

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Schedule of the course §  The first lecture will be on the basic functionality

of MATLAB: matrix operations, data structures, conditional statements, statistics, plotting, etc.

§  In later lectures, we will introduce various modeling approaches from the social sciences: dynamical systems, cellular automata, game theory, networks, multi-agent systems, …

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Schedule of the course 26.09. 03.10. 10.10. 17.10. 24.10. 31.10. 07.11. 14.11. 21.11. 28.12. 05.12. 12.12. 19.12.

Introduction to MATLAB

Introduction to social science modelling and simulations Working on projects

(seminar thesis)

Handing in seminar thesis and giving a presentation

Flash Talks

Modeling overview

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Schedule of the course §  Please take note of the dates for the hand-in and

the oral presentation of your projects:

§  Deadline for project proposals: Sunday 23 October 2014 at midnight

§  Flash talks: Monday 24 October 2014

§  Deadline for project reports: Friday 16 December 2014 at midnight

§  Oral project presentations: 19 December to 20 December 2014

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Goals of the course: 1.  Acquiring understanding of the basics of MATLAB.

2.  Attaining practical knowledge of MATLAB necessary to run computer simulations.

3.  Understanding basic properties of social systems.

4.  Acquaintance with main quantitative modeling approaches for social systems.

5.  Implementing (simple) models of social systems, replicating and extending established models.

6.  Learning to pose a scientific research question

7.  Becoming confident in communicating scientific results in an academic context.

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Requisites of the Course §  Highly interdisciplinary course: Physics, Sociology, Game

Theory, Biology, Computer Science, Software Engineering…

This course requires:

1.  Hard work

2.  Curiosity and creativity

3.  Interest in scientific methods

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MATLAB §  Why MATLAB?

Language is quick to learn, easy to use, rich in functionality, good plotting abilities.

§  MATLAB is commercial software from MathWorks, but there are free MATLAB clones with limited functionality (Octave and Scilab).

§  Python SciPy packages similar to MATLAB

§  MATLAB can be downloaded from ides.ethz.ch

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What is a Social System?

§  A set of interdependent relationships, customs, and institutions that constitute a society. (Oxford English dictionary)

§  A social system is the patterned series of interrelationships existing between individuals, groups, and institutions and

forming a whole. (Merriam-Webster dictionary)

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What is a model?

§  A reduced abstraction of reality aimed at understanding certain components of a more complicated/complex whole.

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On Exactitude in Science . . . In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless… Source: Jorge Luis Borges, Collected Fictions, Translated by Andrew Hurley Copyright Penguin 1999

What is a model?

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Introduction to Modelling and Simulations §  Modelling and simulations allow us to formalize,

discover and even predict real-world phenomena.

§  Simulations are the instantiation of a process specified by a formal model.

§  Simulations allow us to study models that are not analytically tractable.

§  Simulations can also be very entertaining (a nice byproduct but not the main purpose of the course).

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Modelling and Simulation

Model

Social processes

Simulated data

Collected Data

Source: Gilbert and Troitzsch (2005)

Abstraction

Simulation

Data gathering

Similarity

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Emergence and Simulations §  Explaining macro-phenomena based on

micro-mechanisms

§  Especially relevant in a complex system.

§  Simulations can capture “Emergence”:

“Interactions among objects at one level give rise to different types of objects at another level.”

“The whole is more than the sum of its parts.”

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Emergence and Simulations

Courtesy of Iain Couzin

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Emergence of Tokyo transportation network

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Fig. 1 Network formation in Physarum polycephalum.

Atsushi Tero et al. Science 2010;327:439-442 Published by AAAS

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Fig. 2 Comparison of the Physarum networks with the Tokyo rail network.


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Fig. 4 Network dynamics for the simulation model.


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References §  Gilbert, N. and Troitzsch K.G. “Simulation for the Social Scientist” 2nd

Ed. Open Uni. Press (2005)

§  Epstein J.M. and Axtell R. “Growing Artificial Societies. Social science

from the bottom up” MIT Press (1996)

§  Epstein J.M. “Generative Social Science” Princeton Uni. Press (2006)

§  Tero, Atsushi, et al. "Rules for biologically inspired adaptive network

design." Science (2010).

§  Emergence: https://www.youtube.com/watch?v=aEaZHWXmbRw

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MATLAB environment

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What is MATLAB? §  MATLAB derives its name from matrix laboratory

§  Interpreted language §  No compilation like in C++ or Java §  The results of the commands are immediately

displayed

§  Procedural/imperative programming

§  Matrix/array/vector programming

§  (Object-oriented programming)

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Overview - What is MATLAB? §  MATLAB derives its name from matrix laboratory

§  Scalars §  Vectors §  Matrices

x11

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x11 x12 x13

x11

x12

x13

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x11 x12 x13

x21 x22 x23

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§  Scalars §  Vectors §  Matrices §  Multi-dimensional

x111 x121 x131

x211 x221 x231

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Pocket calculator §  MATLAB can be used as a pocket calculator:

>> 1+2+3

ans=

6

>> (1+2)/3

ans=

1

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Variables and operators §  Variable assignment is made with ‘=’

§  Variable names are case sensitive: §  Num, num, NUM are all different variables

>> num=10

num =

10

§  The semicolon ‘;’ cancels the validation display >> B=5;

>> C=10*B

C =

50

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Variables and operators §  Basic operators:

§  + - * / : addition subtraction multiplication division §  ^ : Exponentiation §  sqrt() : Square root §  % comment >> a=2; % First term

>> b=5; % Second term

>> c=9; % Third term

>> R=a*(sqrt(c) + b^2);

>> R

R =

56

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Data structures: Vectors §  Vectors are used to store a set of scalars

§  Vectors are defined by using square bracket [ ]

>> x=[0 2 4 10]

x =

0 2 4 10

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Data structures: Defining vectors

>> x=0:2:6

x =

0 2 4 6

§  Vectors can be used to generate a regular list of scalars by means of colon ‘:’ §  n1:k:n2 generate a vector of values going from n1 to n2

with step k

§  The default value of k is 1 >> x=2:5

x =

2 3 4 5

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Data structures: Accessing vectors

>> x=1:0.5:3;

>> x(2)

ans =

1.5

§  Access to the values contained in a vector §  x(i) return the ith element of vector x

§  x(i) is a scalar and can be assigned a new value >> x=1:5;

>> x(3)=10;

>> x

x =

1 2 10 4 5

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Data structures: Size of vectors

>> x=1:0.5:3;

>> s=length(x)

s =

5

§  Vectors operations §  The command length(x) return the size of the vector x

§  x(i) return an error if i>length(x) >> x=1:0.5:3;

>> x(6) ??? Index exceeds matrix dimensions.

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Data structures: Increase size of vectors

>> x=1:5;

>> x(6)=10;

>> x

x =

1 2 3 4 5 10

§  Vectors operations §  Vector sizes can be dynamically increased by

assigning a new value, outside the vector:

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Data structures: Increase size of vectors

>> x=1:5;

>> x(6)=10;

>> x

x =

1 2 3 4 5 10

§  Vectors operations §  Vector sizes can be dynamically increased by

assigning a new value, outside the vector:

Important: the first element of a vector has index 1

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Data structures: Sub-vectors

§  Vectors operations §  Subvectors can be addressed by using a colon §  x(i:j) return the sub vector of x starting from the ith

element to the jth one

>> x=1:0.2:2;

>> y=x(2:4);

>> y

y =

1.2 1.4 1.6

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Data structures: Matrices

§  Matrices are two dimensional vectors §  Can be defined by using semicolon into square

brackets [ ] >> x=[0 2 4 ; 1 3 5 ; 8 8 8]

x = 0 2 4 1 3 5 8 8 8

>> x=[1:4 ; 5:8 ; 1:2:7]

x = 1 2 3 4 5 6 7 8 1 3 5 7

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>> x=[0 2 4 ; 1 3 5 ; 8 8 8]

x = 0 2 4 1 3 5 8 8 8

>> y=x(2,3)

y =

5

§  Accessing the elements of a matrix §  x(i,j) return the value located at ith row and jth column §  i and j can be replaced by a colon ‘:’ to access the

entire line or column

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>> x=[0 2 4 ; 1 3 5 ; 8 8 8]

x = 0 2 4 1 3 5 8 8 8

>> y=x(2,:)

y =

1 3 5

§  Access to the values contained in a matrix §  x(i,j) return the value located at ith line and jth column §  i and j can be replaced by a colon ‘:’ to access the


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>> x=[0 2 4 ; 1 3 5 ; 8 8 8]

x = 0 2 4 1 3 5 8 8 8

>> y=x(:,3)

y =

4 5 8

§  Access to the values contained in a matrix §  x(i,j) return the value located at ith line and jth column §  i and j can be replaced by a colon ‘:’ to access the


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Matrices operations: Transpose §  Transpose matrix

§  Switches lines and columns §  transpose(x) or simply x’ >> x=[1:3 ; 4:6]

x = 1 2 3 4 5 6 >> transpose(x) x = 1 4 2 5 3 6 >> x’ x = 1 4 2 5 3 6

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Matrix operations §  Inter-matrices operations

§  C=A+B : returns C with C(i,j) = A(i,j)+B(i,j) §  C=A-B : returns C with C(i,j) = A(i,j)-B(i,j)

A and B must have the same size, unless one of them is a scalar

>> A=[1 2;3 4] ; B=[2 2;1 1];

>> C=A+B

C = 3 4 4 5

>> C=A-B

C = -1 0 2 3

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Matrix operations: Multiplication §  Inter-matrices operations

§  C=A*B is a matrix product. Returns C with C(i,j) = ∑ (k=1 to N) A(i,k)*B(k,j) N is the number of columns of A which must equal the

number of rows of B

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Element-wise multiplication §  Inter-matrices operations

§  C=A.*B returns C with C(i,j) = A(i,j)*B(i,j) A and B must have the same size, unless one of them is a scalar

>> A=[2 2 2;4 4 4];

>> B=[2 2 2;1 1 1];

>> C=A.*B C = 4 4 4 4 4 4

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Element-wise division §  Inter-matrices operations

§  C=A./B returns C with C(i,j) = A(i,j)/B(i,j) A and B must have the same size, unless one of them is a scalar

>> A=[2 2 2;4 4 4];

>> B=[2 2 2;1 1 1];

>> C=A./B C = 1 1 1 4 4 4

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Matrices operations: Division §  Inter-matrices operations

§  x=A\b returns the solution of the linear equation A*x=b A is a n-by-n matrix and b is a column vector of size n

>> A=[3 2 -1; 2 -2 4; -1 0.5 -1];

>> b=[1;-2;0];

>> x=A\b

x = 1 -2 -2

3x + 2y � z = 12x� 2y + 4z = �2

�x +12y � z = 0 Attention:

/ (slash) and \ (back slash) are different operators

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Matrices: Creating

§  Matrices can also created by these commands: rand(n, m) a matrix of size n x m, containing random numbers [0,1] zeros(n, m), ones(n, m) a matrix containing 0 or 1 for all elements

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Matrices Dimensions

>> A = zeros(3,4);

>> size(A)

ans =

3 4

>> size(A,1)

ans =

3

>> size(A,2)

ans =

4

§  size() returns info about a matrix’s dimensions.

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The for loop

§  Vectors are often processed with loops in order to access and process each value, one after the other: §  Syntax : for i=x

…. end

§  With -  i the name of the running variable -  x a vector containing the sequence of values assigned to i

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The for loop

>> for i=1:3

i^2

end

i =

1

i =

4

i =

9

§  MATLAB waits for the keyword end before computing the result.

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The for loop

>> for i=1:3

y(i)=i^2;

end

>> y

y =

1 4 9

§  MATLAB waits for the keyword end before computing the result.

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Conditional statements: if

§  The keyword if is used to test a condition §  Syntax :

if (condition) ..sequence of commands.. end

§  The condition is a Boolean operation §  The sequence of commands is executed if the tested

condition is true

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Logical operators

§  Logical operators §  < , > : less than, greater than §  == : equal to §  && : and §  || : or §  ~ : not ( ~true is false) §  (1 stands for true, 0 stands for false)

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Conditional statements: Example

>> threshold=5;

>> x=4.5;

>> if (x<threshold)

diff = threshold - x;

end

>> diff

diff =

0.5

§  An example:

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Conditional statements: else §  The keyword else is optional

§  Syntax : if (condition)

..sequence of commands n°1..

else

..sequence of commands n°2..

end

>> if (x<threshold)

diff = threshold - x ;

else

diff = x – threshold;

end

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Scripts and functions §  External files used to store and save sequences

of commands.

§  Scripts: §  Simple sequence of commands §  Global variables

§  Functions: §  Dedicated to a particular task §  Inputs and outputs §  Local variables

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Scripts and functions §  Scripts :

§  Create .m file, e.g. sumVector.m. §  Type commands in the file. §  Type the file name, .e.g sumVector, in the command

window or run code from text editor with open file %sum of 4 values in x x=[1 3 5 7]; R=x(1)+x(2)+x(3)+x(4); R

sumVector.m

>> sumVector

R = 16

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Scripts and functions §  Make sure that the file is in your working

directory!

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Scripts and functions §  Functions :

§  Create .m file, e.g. absoluteVal.m §  Declare inputs and outputs in the first line of the file,

function [out1, out2, …] = functionName (in1, in2, …) e.g. function [R] = absoluteVal(x)

§  Use the function in the command window functionName(in1, in2, …) e.g. absoluteVal(x)

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Scripts and functions

function [R] = absoluteVal(x) % Compute the absolute value of x if (x<0) R = -x ; else R = x ; end

absoluteVal.m

>> A=absoluteVal(-5);

>> A

A =

5

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Scripts and functions

function [R] = absoluteVal(x) % Compute the absolute value of x if (x<0) R = -x ; else R = x ; end

absoluteVal.m

>> A=absoluteVal(-5);

>> A

A =

5

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Exercise 1

§  Compute: a) b)

c) §  Slides/exercises:

http://www.coss.ethz.ch/education/matlab.html

25510718

×

+ ∑=

100

0ii

∑=

−10

5

2 )(i

ii

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Exercise 2

§  Solve for x:

452232223321432

4321

4321

4321

4321

=++−

=−−−

=+−+

=+−−

xxxxxxxxxxxxxxxx

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Exercise 3 §  Fibonacci sequence: write a function which

computes the Fibonacci sequence of a given number n and returns the result in a vector.

§  The Fibonacci sequence F(n) is given by :

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References §  http://www.mathworks.ch/products/matlab/

index.html

§  http://www.mathworks.ch/matlabcentral/index.html

§  https://ides.ethz.ch/

Documents

Modeling and Simulating Social Systems with MATLAB · 2016. 9. 26. · Lecture 1 – Introduction to the Course and MATLAB Computational Social Science Olivia Woolley, Lloyd Sanders,