crossing_statistics

Final project for the 2022 Serrapilheira QBio Training Program Computation Methods Course.

In this project, we efficiently generate trajectories of an two-dimensional Ornstein-Uhlenbeck process and compile their first-encounter statistics. To do so, we implement two Julia modules for pseudo-random generation and slightly generalizable integration for linear stochastic differentiable equations. We then generate a dataset of encounter events and visualize our data using a histogram of the first-encounter times and an animation of the time-evolution of the motion.

Project structure

project/
*    ├── data/
     ├── docs/
*    ├── figs/
     ├── scripts/
*    └── README.md

The scripts/ folder contains three scripts to be run using Julia 1.8, as well as the modules PRNG.jl, for pseudo-random number generation, and SDE.jl for linear stochastic differential equation integration. To run the scripts, one simply needs to call

julia ./scripts/script.jl

In the docs/ folder one finds the report.Rmd R Markdown file, compiled into a .pdf using knitr with pdflatex.

Required packages

The Julia scripts require base Julia >=1.8, as well as the DelimitedFiles and Plots package. The JuliaCall package on R is required for compiling the report.