March 5, 2025

Perturbations to Flow Networks

We discuss how to find a min cut with the minimum number of edges via a perturbative argument on flow networks.

February 23, 2025

Derivation of OLS

We formulate and solve for OLS as the solution to a minimization problem.

February 22, 2025

Bias-Variance, Randomness, and Gauss-Markov

We use the bias-variance decomposition in machine learning as a backdrop to explore some probability-theoretic ways of thinking. We also make a comparison between the bias in Gauss-Markov and in bias-variance.

February 10, 2025

Gauss Equation

We take two traces of the Gauss equation to get a scalar relationship between intrinsic and extrinsic curvature quantities of an embedding.

October 26, 2024

A Geometer's Derivation of the Graph Laplacian

The graph Laplacian is central in spectral graph theory, but its link to the standard Laplacian is often unclear. We show both represent the difference between a function and its local average.