I first became interested in networks when reading Matthew O'Jackson's 2010 paper describing their application to economics. During the 2014 ebola outbreak, there was a lot of concern over the disease spreading to the U.S.. I was caught up with work/classes at the time, but decided to use airline flight data to at least explore the question. The source … Continue reading Modeling Ebola Contagion Using Airline Networks in R

# Tag: mathematics

# Finding and Plotting Lorenz Solution using MATLAB

I use MATLAB to solve the following Lorenz initial value problem: $latex \begin{cases} x'=-10(x+y) \\ y'=-x(z+28)-y \\ z'=xy-\frac{8}{3}z \\ x(0)=y(0)=z(0)=5 \end{cases} $ I wrote a function, LorenzRK4IVP(), that takes the system of three differential equations as input and solves the system using the Runge-Kutta method with step size $latex h=.01$. I plot the strange attractor as … Continue reading Finding and Plotting Lorenz Solution using MATLAB

# Using Markov Chains to Model Mortgage Defaults in R

The goal of this post is to blend the material I've been learning in my night class with my day-job and R.If we have some object that switches between states over time according to fixed probabilities, we can model the long-term behavior of this object using Markov chains*.A good example is a mortgage. At any … Continue reading Using Markov Chains to Model Mortgage Defaults in R

# Cobb-Douglas Visualisation – I

I used excel to construct a visualization of the Cobb-Douglas production function (explicitly presented in the graph titles). The production function expresses the output of any given firm as a function of two inputs (labor and capital) and parameters (alpha and beta). When the sum of alpha and beta equals 1, it can be shown … Continue reading Cobb-Douglas Visualisation – I

# Dynamic Equilibrium Simulation

# Monte Carlo Simulation of Pi

Partially out of boredom and partially because I was inspired by the movie title “Life of Pi”, I decided to make a monte carlo simulator that could approximate the value of pi. Monte carlo simulations are used in everything from derivative pricing to biology (and, in this case, boredom alleviation). Basically, it’s good for solving … Continue reading Monte Carlo Simulation of Pi