Average Runtime of Quicksort

by JT Cho

It's always boggled my mind how statistics plays a role in the runtime analysis of various algorithms. The two seemingly distinct fields of Computer Science and Statistics mesh in a very surprising way - enabling one to make strong statements regarding the asymptotic complexity of an algorithm. In this article . . .

Bernoulli Laplace Model of Diffusion

by JT Cho

This post is a part of a series on stochastic theory. In this article, we will work through a standard theory problem on the Bernoulli-Laplace model of diffusion. I presume here that you have a basic understanding of what a Markov chain is. Problem Context Let's consider two urns, each . . .

Covariance Method for Principal Component Analysis

by JT Cho

I've been working on a couple of side projects recently, so I haven't had much time to do any math or CS related blog posts. However, in my research for a planned side-project involving Self Organizing Maps, I came upon a concept I had seen once before a long time . . .

Trigonometry of Correlation I

by JT Cho

I always find it super cool when recognizing key parallels between different branches of mathematics serendipitously. It allows me to employ techniques I have learned in other classes to derive valuable insight in a new topic, which sometimes (not always) makes the learning a bit easier. Today I will discuss . . .