Blog ⁽⁷⁾

An exploration of the critical brain hypothesis using a stochastic branching model to study, both theoretically (mean-field analysis) and empirically (in simulations), why neural systems might fine-tune or self-organize near criticality.

An exploration of phase transitions, through the lense of statistical mechanics, and a pedagogical example using the Ising model.

Classification of harmful brain activity in human patients from EEG recordings. This article is a formal write-up for a Kaggle competition I competed in hosted by Harvard Medical School.

Principal components analysis (PCA) is a method for unsupervised dimensionality reduction of data. This review gives a formal derivation and from-scratch implementation of PCA, with an example from genomics.

A rigorous exploration of the classic Gambler's Ruin problem in probability theory. This post analyzes the problem through its closed-form solution, and verifies the solution with a Monte Carlo simulation.

Support vector machines (SVMs) are a method for supervised learning of a binary classifier. This review provides a formal derivation of hard-margin SVMs, and implements them in Python with CVXOPT.

A historical and formal view of the Rosenblatt Perceptron algorithm, an early algorithm for supervised learning of a binary classifier.