Lecturer: Susana Gomes
Teaching Assistant: Kamran Pentland
All lectures and support classes will be in room D1.07, but they will also be streamed on MS Teams if somebody is in self-isolation.
Most of the course materials will also be uploaded to the MA933 Team. If you are not on the Team and would like to be added, please email the lecturer.
Kamran will upload jupyter notebooks for your support classes. These will be on his github page.
Class test - Wednesday 12 January 2022, 10:00 (UK time) in D1.07
Submit worksheets here.
For the procedure for the class test, see this page.
Below is the 2019 information for reference.
Below is some of the information from 2019/20 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.
- list of exam topics UPDATED 7.12.!
- Written class test (about 3 hours) on Friday January 17 (week 2 of term 2), 10-1pm in D1.07, counts 80/100.
No books allowed, please only come with writing material and have your student ID number ready to put on the exam booklet.
Previous class tests (ONLY 2 HOURS) from 2014 (pdf), 2015 (pdf), 2016 (pdf), 2017 (pdf) and 2018 (pdf)
- homework counts 20/100 marks
- course notes (last updated 04.12.): notes_ma933_19.pdf
- final version of course notes from last year: 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
sheet 1: due Friday 18.10., 12pm noon
Random walk, Pólya urn models, generator matrices
- sheet 2: due Friday 15.11., 12pm noon
Kingman's coalescent, Ornstein-Uhlenbeck process, Moran model, birth-death chains
- sheet 3: due Friday 17.1., 12pm noon
Geometric Brownian motion, Barabasi-Albert model, Erdos Renyi random graphs, contact process
CHANGES 6.12.: Q3.5 is not for credit! Total mark for sheet changed to 50.
18.12.: Q3(a) and (b) have been clarified in the online version, please have a look.
- 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 processesNOT EXAMINABLE
- hand-out 6: Heavy tails, extreme value statistics, see also extremes.ipynb for illustrations
For class material see Emma's Github page
Moran model on sheet 2: moran_model.ipynb
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.
- 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, 2006)
The Structure and Function of Complex Networks (M.E.J. Newman; SIAM Review 45(2), 167–256, 2003)