| Name | Departement | |
|---|---|---|
| Sebastian Heinekamp | heinekas@student.ethz.ch | DPHYS |
| Tileman Conring | tconring@gmail.com | DPHYS |
| Fabian Wermelinger | fabianw@student.ethz.ch | DMAVT |
git://github.com/tconring/Arabian-Spring.git (read only)
A few months ago in some Arabian countries there were some kind of revolutionary movements. In some countries they were successful while in other countries they struggled. Our aim of this research project is to understand the mechanisms of the success of the Arabian spring. We want to build a society based on a small world graph with, e.g. three clusters, where each cluster represents a country adjacent to another. These clusters shall be formed with individual probabilities, generating different homogeneity of each country as such. With the focus on one country, we want to analyze the spreading of opinion changes between nodes (where each node has an agent assigned to) in that particular cluster based on an SIR(S) model. Further, the propagation of the opinion formation across the clusters shall be investigated. The probability of “infection” shall depend on local quantities such as the number of connected links to a node (clustering coefficient). This may result in a stronger influence of one particular node connected to another in the same cluster, but it may also spread across clusters since there will be nodes with connections to individual nodes of another cluster. In that case, a global quantity such as the link lengths of the two clusters in question may also influence the opinion spreading across them. In a first simplified step, we assume that links between nodes will exist during all times.
Fundamental Questions: How does the structure p of multiple s-connected networks influence the spreading of opinion formation based on an SIR(S) model, where p ranges from 0 (large-world, regular ring lattice) to 1 (disordered network, random) and s defines the probability that one node of a given network will be connected with a node of another network?
Expected Results: Prediction of a date where a certain amount of nodes of the main network has a mind state to uprise against the government and how long it will take from there on to spread over to the other networks, depending on their structure p and connectivity s. We assume that the opinion formation will be faster in a more random like network than it would be in a regular ring lattice.
Each network is an assembly of N nodes generated with independent functions. The output of these functions must be a sparse matrix S. See the MATLAB help for the sparse() function in order to generate sparse matrices in MATLAB.
If a network has N nodes, then there are N agents. Hence, the number of agents is determined by the size of the sparse matrix S. Agent information is stored in a structure array. See the MATLAB help for more information on structures in MATLAB. Each element (i.e. agent) in that array has several fields assigned to. Suppose agent(i) is the i-th agent in the array of agents, then the following fields are assigned to it:
- agent(i).state: The state variable defines the current mind state of the agent. It is a either 0 or 1, where 0 means pro regime and 1 means con regime.
- agent(i).nbr: The nbr variable is a list of integers to the j-th neighbor of the i-th agent. The length of that list is the number of agents who know agent i, and vice versa.
- agent(i).threshold: The threshold defines the willingness of an agent to jump over to the group of agents who are con regime. It is a floating point value on the interval [0 1], where 0 means that the agent will only change its mind if ALL of its immediate neighbors (and higher order neighbors, depending on par.nbrDepth) already possess a state of 1. On the otherhand, 1 means that the agent will step to the group even if ALL of its immediate (and higher order) neighbors still possess a state of 0. An agent with threshold 1 is a very radical one and can be seen as an initiator of a later riot.
- agent(i).citizen: The citizen variable defines one agents citizenship. That is, the membership to a certain cluster of the global network. The variable holds an integer representing the number of the cluster where agent(i) is resident of. For example, agent(i).citizen = 1 means that agent i is citizen of cluster 1. A node of cluster i shall be connected to a node of cluster j with probability p. Hence, the agent function takes a first argument p, followed by s arguments, where each of the s arguments is a sparse matrix S, generated with the network function.
The structure array of agents must be generated with an independent function, taking the global probability p and s sparse matrices S ( generated with the network function) as arguments.
- agent(i).state The state variable defines the current mind state of the agent. It is a numeric value on the interval [0 1], where 0 means pro regime and 1 means con regime. Hence, a state of 0.5 means undecided.
- agent(i).nbr The nbr variable is a list of integers to the j-th neighbor of the i-th agent. The length of that list is the number of agents who know agent i, and vice versa.
- agent(i).alpha The alpha variable is a scalar between 0 and 1. It defines the influence of agent i on its neighbors j. A value of 0 means no influence, whereas 1 means very high influence. However, the influence of agent i on its neighbor j can only take effect once the probability beta of infection is met. Beta defines the rate of infection of the SIR(S) model and is a global value, given to the solver function. The alpha value is a network dependent value.
- agent(i).citizen The citizen variable defines one agents citizenship. That is, the membership to a certain cluster of the global network. The variable holds an integer representing the number of the cluster where agent(i) is resident of. For example, agent(i).citizen = 1 means that agent i is citizen of cluster 1. A node of cluster i shall be connected to a node of cluster j with probability p. Hence, the agent function takes a first argument p, followed by s arguments, where each of the s arguments is a sparse matrix S, generated with the network function.
The solver function is an independent function taking an array of agents and a parameter structure as arguments. It implements the SIR(S) model and solves (or iterates) through a given amount of time. It generates a residual to track the development of the individual mind states over time.