MA933 - Module Resources

Module information for 2023/24

Teaching Assistant: Andrew Nugent

Lectures: Tuesdays 10:00-12:00 and Fridays 10:00-11:00

Support classes: Fridays 11:00-12:00

All lectures and support classes will be in room D1.07 unless otherwise advised.

The course materials (slides, problem sheets, notes,...) will be uploaded to the MA933 Team. If you are not on the Team by the end of week 1, and would like to be added, please email the lecturer.

Andrew will upload Jupyter Notebooks for your support classes. These will be on his github page.

Assessment deadlines - you should submit your assignments here.
Assignment 1 - Tuesday 31 October 2023, 5pm (UK time)
Assignment 2Link opens in a new window - Tuesday 28 November 2023, 5pm (UK time)
Assignment 3Link opens in a new window - Friday 15 December 2023, 12 noon (UK time)

Class test - Wednesday 17 January 2024, 09:30 (UK time) in R1.15, Floor 1, Ramphal Building (at the top of Library Road)
For the procedure for the class test, see this page.

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Historical resources

Previous lecturers for MA933 were Stefan Grosskinsky and Robert MacKay, and previous TAs were Emma Southall and Kamran Pentland. Thank you all of them for their lecture notes and github repositories which we are all using :)

Below is some of the information from previous years for your reference (including previous class tests for revision, old lecture notes, and old handouts). I will follow most of Stefan's lecture notes but I aim to type my own during this term.

Assessment

list of exam topics UPDATED 7.12.!
Previous class tests (ONLY 2 HOURS) from 2014 (pdf), 2015 (pdf), 2016 (pdf), 2017 (pdf), 2018 (pdf), and 2019 (pdf).

Notes

course notes (last updated 04.12.2019): notes_ma933_19.pdf
final version of course notes from 2019: notes_ma933_18.pdf
the first part of notes for the former module CO905 Stochastic models of complex systems provide a slightly more complete introduction to Markov chains and might be useful for background reading

Hand-outs

hand-out 1: linear algebra
hand-out 2: characteristic functions, Gaussian, LLN, CLT
hand-out 3: Poisson processes
hand-out 4: Random sequential update, Gillespie algorithm
~~hand-out 5: Generating functions, branching processes~~ NOT EXAMINABLE
hand-out 6: Heavy tails, extreme value statistics, see also extremes.ipynb for illustrations

Classes

For old problems classes material see Emma's Github page and Kamran's Github page.

Moran model on sheet 2: moran_model.ipynb

Contact process on sheet 3: contact_process.ipynb, contact.c, sample output for system size 512 contact_n512.zip

Python is far too slow for this kind of simulation. You can use contact.c on the SCRTP machines you have access to (for machine names see slides for week 2 on this page by Dave Quigley).
Compile the code on the command line with: gcc -lgsl -lgslcblas -O9 -ooutputname contact.c
then type in command line: nohup ./outputname &
in the same directory, the nohup in front will cause the programme to finish even if you log out (no-hangup).
Adapt the code using a text editor and recompile, should be obvious which changes to make for (a), for (b) you will have to introduce a test function to stop the code when the absorbing state is reached.
For up to 500 realizations codes only run a few minutes which is fine. If you run longer jobs, you HAVE to follow these instructions how to use 'nice', also good to find which other machines are online.

Additional stuff

very useful tutorial slides on Fundamentals of Heavy Tails by J. Nair, A. Wierman and B. Zwart
tutorial on stochastic matrices including the google matrix and pagerank algorithm by D. Margalit and J. Rabinoff
review papers on complex networks:
Complex networks: Structure and dynamics (Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.-U.; Physics Reports 424 (4-5), 175-308, 2006Link opens in a new window)
The Structure and Function of Complex Networks (M.E.J. Newman; SIAM Review 45(2), 167–256, 2003Link opens in a new window)