Notebooks will be uploaded for each support class.
Support Class 1.ipynb
- basic linear algebra in python
- simple random walk animation
- function SRW, a simple random walk with arguements p (probability steping up), tmax (when to terminate the walk) and N (number of replications)
- empirical distribution calculated at a fixed time (hist plot over possible states at time n)
- simulation with periodic boundary conditions (modulus L (L =10))
- simulation with closed boundary conditions (reflects at 10 and 0)
Support Class 2.ipynb
- Polya urn model
- empirical tail (1 - CDF)
- Gershgorin disk theorem
Support Class 3.ipynb
- general plotting techniques in matplotlib http://matplotlib.org/1.5.3/api/pyplot_api.html#matplotlib.pyplot.plot
Support Class 4.ipynb
- Kingman's Coalescent
- CTMC (waiting times, exponentially distributed)
Support Class 5.ipynb
- Orenstein-Uhlenbeck Process
- simulated by finite difference approximation (taking the Weiner incremenet by sampling from normal distributioon with zero mean and dt vaiance)
- simulated using
sdeint
(python stochastic differential equations, numerical integration)
Support Class 6.ipynb
- Moran model (similar to wright-fisher but continuous time)
- CTMC with waiting times
- introduction to networks and using the
networkx
package in python - degree distribution, clustering, transitivity, distance, largest component
Support Class 7.ipynb
- Erods-Renyi random graphs
- compare degree distribution to binomial distribution
- expected size of largest component for multiple realisations
- expected local clustering coefficient for multiple realisations
- Wigner semi-circle law
Support Class 8.ipynb
- compare degree distribution to poisson distribution
- Barabsai-albert model
- empirical tail distribution
- expected degree of nearest neighbour given node has degree k
For Latex, I recommend you to use Overleaf (particularly useful for RSG as can have multiple people working on the same document at the same time - plus you can chat to each other on there): https://www.overleaf.com/
For GitHub help, check out https://www.gitkraken.com/
Steps to download GitKraken:
- Download the .deb file
- open terminal and go into your downloads (cd Downloads)
sudo dpkg -i name.deb
- log in with you github
Useful links for the assignments:
- Log Normal Distribution: https://en.wikipedia.org/wiki/Log-normal_distribution
- Log Normal Scipy Documentstion: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html
- KDE plot visualisation: https://mathisonian.github.io/kde/
- Fokker-Planck Equation: book Stochastic Processes in physics and chemistry - N.G. Van Kampen
- Ornstein-Uhlenbeck process: https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process#Fokker%E2%80%93Planck_equation_representation
- Colour options in matplotlib https://xkcd.com/color/rgb/