No lectures next week (28.11. and 29.11.) due to strike action.
Class takes place Wednesday 27.11., 10-11 in D1.07!
See calendar for up to date timetable.
Lectures: Thu 11-1 and Fri 11-12 in D1.07
Classes: Fri 12-1 in D1.07
- 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)