Project: Playing With S3 Simulator.


This handout contains the information you need to get going on your project. There are two parts to the handout. This first part has information about due dates for the project, the report you will be preparing, grading criteria, and a list of which students are doing which projects to help you in forming a group if you choose to do so. The second part has a brief summary of your topic and a list of key words to help you head in the right direction. In the next couple of weeks, you will get one more handout which will contain problems for you to solve as part of your project.

The material I'm giving you really is just a bare-bones minimum to help direct you. You are responsible for finding references and doing your own investigating and learning. However please feel free to contact me, in person or by email, for help finding references or working the problems or for general guidance about the projects, and to give me feedback about how it is going.

Due Dates

There are three due dates for the project, October 11th, October 30th and November 22nd. These deadlines are explained in page 3. Turning this material in on time will count towards points in the determination of your total grade on the project.

On Wednesday, November 22nd your overall project report is due.

Each person will be responsible for preparing his/her own report, including writing up his/her own solutions to the problems.



Reports and Grading Criteria

Your report should include some version of the following 5 parts. They do not have to be arranged the way I list them here, but all should be included in your report in some form or another.



  1. (10 points) General Discussion Introduction and generalities for the project (could include why you chose this project, background about the field of application, goals of the project), definitions and results from Probability used in the project, definitions and discussion of results and ideas from the field of application used in the project. When you state mathematical results that you use, try to explain some of the mathematics behind why the results are true-present a derivation if you can, or, if that is too difficult, give a sketch or an intuitive idea of how it works.

  2. (25 points) Solutions to Problems Give your solutions to the problems I will provide for your topic. It is very important not only to give a correct answer but also to give a thorough explanation of your solution. You should have a clear explanation of each step, an analysis of what results apply to what step, etc. This is not like just working out a usual homework problem-explain in words what you are doing and write sentences. If you are going to support a theory by simulations you should attach print outs of those realizations.

  3. (6 points) References A list of the references that you used, people you consulted, people you worked with, places you found help. Included in the 6 points will be turning things on time with respect to your deadlines.

  4. (2 points) Comments Your comments on how interesting you found the project, whether you feel that the time you spent on this was worthwhile and whether it might help you in the future or lead to anything for you, and suggestions to me for improvements in case I do projects like this again.
  5. (7 points) Presentation This includes innovation in presenting the material of the report, clarity and neatness, flow, design and organization of the report, and creativity used in explaining the ideas.

Project Details

Modeling Biological phenomena is a very exciting and rich area of research in Mathematics. Interacting particle systems is one way of modeling. Loosely speaking in this set up, we mainly work on the lattice(s) Z, Z^2, where particles or infections spread according to pre-determined birth and death rates.

In this project we shall work closely with the simulator S3 to understand these processes better. We shall try to predict (based on simulations) properties of certain processes with regard to it initial distribution, birth/death rates etc.

key words to learn:

  1. Interacting particle systems.
  2. Predator prey systems.
  3. Exponential Random variable.
  4. Poisson process.
  5. Contact process.

Plan:

  1. October 11th Install the simulator from the web-site: http://gumby.syr.edu. Present a print out of a simulation of your favourite process.

  2. October 30th Read through the Tutorial. Submit at least two references that you have found for you project. An explanation or definition of at least two of the key words.

http://www.math.ubc.ca/~athreya/302/projects/sim.html
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