# Formative Group Coursework

We form groups of 4, and shouldn't be much larger or smaller than this. It is quite a fun bit of coursework to do, and for this, we are expected to work independently.

At the end, the group gives a presentation about what they have done. For the exercise, we start with a problem, then come up with a research question. We can then start to model, then implement and test the model.

After this, we analyse the model to see the first results, understand the results and analyse them. We then find the analytical results or approximations and adapt the research question or simplify the model.

At the end, the results are presented to the rest of the students.

## Aims

- Clear research question
- Model specification
- Implementation of the model
- Set of model outputs to give tentative answer to the research question
- Short presentation on the outcomes of the project

## Topics

The topics can be chosen from a number of different topics which have been suggested by the lecturer. Can also choose something besides the ones given and this would need approval by the lecturer.

### Modelling Swarming Dynamics

This is the first topic suggested. How do the patterns of swarming emerge from the micro-rules. Swarms are big structures within herds or collections of animals, all adjusting their positions to move around in interesting patterns.

The original model on this was Greg Reynold's "boids" model. This is the most famous paper from the eighties, with a set of movement rules for the bots. Recommended to look at the paper, and see if we can possibly reproduce the results.

#### Example Research Questions

- What benefits does swarming give a group of boids?
- Can we evolve swarming rules for particular purposes (e.g., to monitor an environment)?
- What swarming rules would co-evolve with cooperation?
- What patterns arise from an interaction of a swarm with:
- Outside drivers -- e.g., predators, other food sources?
- Another swarm?

### Forest Fires

Forest fires are interesting to model, as they can influence lots of things. Does the forest fire influence the pattern of trees? How does this change based on the distribution of newer and older trees? How often the forest fire occurs?

The structure of the cluster size of the trees is related to the likelihood that the cluster will burn down. We can measure the cluster sizes of trees and the statistics of these will follow a pattern. There are lots of small clusters, with a tail that contains larger clusters.

#### Example Research Questions

- Given a landscpe:
- Where is best to put warning stations/detectors for earliest possible warnings?
- How to stop a fire?
- How to protect certain regions of landscape, such as settlements?
- Compare the efficiency of different ways to stop fires, what is best?

- Can we stop catastrophic losses in a cost efficient way?

### Wealth Distributions

Wealth distributions in society are generally quite skewed, such that most people own little to nothing, and very few people own most of the wealth. There is a lot of work to understand how these distributions fall about. These are power law distributions typically.

There are simple agent-based models that give rise to these assumptions. These models are where the agents trade with each other. There are many papers on this, and these can be implemented quite simply. We can simulate approximately \(1,000\) agents

#### Example Research Questions

- Can we build more realistic models (e.g., using heterogeneous agents)?
- Do the most efficient agents always become the richest?
- What rules do we need to constrain inequality (e.g., through tax)
- At the start of an equal society, is there any way to predict who is becoming rich? When can we predict this?
- What is the impact of crashes or external shocks to the system?

### Models of Segregation

People often segregate within cities by e.g., race, or wealth. People who are similar to each other tend to live near each other. Is there a way to understand this from simple micro-rules for relocation.

The main research paper for this is by Schelling.

#### Example Research Questions

- Can we reproduce the initial result?
- What about the inclusion of additional constraints to the model (e.g., can only move a certain distance, dependent on financial resources)?
- Schelling models on other types of networks?
- Inclusion of noise in movement decisions (where agents are not rational, and simply move randomly)?
- A model that co-evolves with the evolution of cooperation?

## Steps for the Coursework

- Form groups of 3-4 people, with complementary skills
- Read the original paper, what is interesting? What research questions does it answer, how does it answer them, what are the key results?
- Think about the shortcomings of the paper, does it leave any questions unanswered? Are any decisions badly justified?
- Extend the research question by developing some ideas on how to extend the paper
- Are these interesting? Is simulation needed?

Whilst doing this, we need to consider a tentative research question. We need to look at what the model extension could look like, what needs to be included or excluded, agents needed to be modelled, how to describe an agent and how it can be done in the timeframe allocated.

We then look at the model outputs to measure to answer the research question, and if the question is relevant or interesting. We may need some data to calibrate the model.

## Definitions

- Scaling, self-organization, optimization in a complex landscape: all recently developed ideas in statistical physics
- Solvability of the basic equations of motions
- Soluble
- Mean-field rate equation
- Random
- Greedy
- Asymptotic scaled wealth distribution
- Gaussian
- Fermi