CO905 Stochastic models of complex systems
Online Course Materials (2013)
IN 2016/17 THIS MODULES RUNS AS A TCC COURSE, PLEASE VISIT THE NEW WEBPAGE.
Lecturer: Stefan Grosskinsky
Lectures: Thu 1011 and Fri 1012 in D1.07
Classes: Thu 1617 in D1.07
VIVAS on Firday 15.3. in D1.07, viva schedule, viva topics
Notes
 NEWpreliminary complete version of the notes: notes_co905_13.pdf
 Last year's course notes: notes_co905_12.pdf
See here for all of last year's online materials.  For students with a good knowledge in probability the notes of the course MA4H3 have useful background material on stochastic particle systems.
Changes/Related Events
 15.3. Vivas 94pm, see schedule above
 On Thursday 14.3.: Revision lecture 1011, no class in the afternoon
 Class at 4pm on Thursday 21.2. is cancelled due to the miniproject fair in Complexity
 First lecture on Thu 10.01.2013
 Last lecture Thursday 14.3. at 10 (revision)
Vivas are Friday 15.3.
Problem Sheets
 NEW part in Q3.3.c)sheet3: Moran model, Kingman's coalescent, exclusion process
 sheet2: Birthdeath processes, contact process
 sheet1: Generators/eigenvalues, branching processes, random walks
Handouts
 handout5: Connection between stochastic particle systems and PDEs (done for TASEP and Burgers equation)
 handout4: Proof of Thm 3.6 (nonexaminable)
 handout3: Characteristic function, Gaussians, LLN, CLT
 handout2: Poisson process, random sequential update, exponentials
 handout1: Generating functions, branching processes
Matlab and C stuff
 NEWBasic C code traffic.c and Matlab file traffic.m for the TASEP (Q3.3), to be adapted.
This compiles with gcc traffic.c on a CSC machine, try gcc O5 traffic.c to speed it up in case it runs too slow.
If you want to compile on your own machine, you might have to adapt the random number generator, e.g. replace lrand48() by rand() and srand48(seed) by srand(seed). But note that rand() is typically 'too bad', so to get good results you should run the code with 48 on a CSC machine, or copy the Mersenne Twister from the code for the contact process.
 Basic C code traffic_q23.c for Q3.3.c) Visualize output e.g. with Matlab using imagesc. Note that this code uses OPEN boundary conditions.
 Simple C program for the contact process using the Mersenne Twister: contact_mt.zip
You should have all files in the same directory. If initializing with system time does not work use your own favourite integer.
 You can find a list with CSC machines here, where you can run QUICK programmes ONLY, without submitting to the COW.
DO NEVER RUN ANYTHING ON GODZILLA!!
to compile on command line: gcc lm O9 contact_mt.c
 Wikibooks on Matlab and C_Programming
 Some links to Mersenne Twister:
http://www.math.sci.hiroshimau.ac.jp/~mmat/MT/VERSIONS/CLANG/clang.html
http://en.wikipedia.org/wiki/Mersenne_Twister
Suggested Books
 Gardiner: Handbook of Stochastic Methods (Springer).
 Grimmett, Stirzaker: Probability and Random Processes (Oxford).
 Grimmett: Probability on Graphs (CUP). (available online here)
 Mendez, Fedotov, Horsthemke: ReactionTransport Systems, Springer 2010.
Additional Literature
 A.B. Kolomeisky et al: Phase diagram of onedimensional driven lattice gases with open boundaries, J. Phys. A: Math. Gen. 31 6911 (1998)
 tutorials on the Ising model, including Monte Carlo simulation methods: http://www.nd.edu/~mcbg/tutorials/2006/tutorial/ising.html, http://pages.physics.cornell.edu/sethna/teaching/Simulations/LMC.html
 on MC methods without detailed balance: H. Suwa, S. Todo: Markov Chain Monte Carlo Method without Detailed balance, PRL 105, 120603 (2010)
review: M. Bachmann: Monte Carlo simulations, Lecture Notes of the 42nd IFF Spring School Macromolecular Systems in Soft and Living Matter, Forschungszentrum Juelich  M.T. Araujo, E. Drigo Filho: A General Solution of the FokkerPlanck Equation, JSP 146(3), 610619 (2012)610619 (2012)
 N. Goldenfeld, C. Woese: Life is physics: evolution as a collective phenomenon far from equilibrium, Annual Review of Condensed Matter Physics 2, 375399 (2011)
 R.A. Blythe: Ordering in voter models on networks: exact reduction to a singlecoordinate diffusion, J. Phys. A: Math. Theor. 43 385003 (2010)
 R.A. Blythe, A.J. McKane: Stochastic Models of Evolution in Genetics, Ecology and Linguistics, J. Stat. Mech.: Theor. Exp. (2007) P07018

Frank Kelly: The Mathematics of Traffic in Networks