$\newcommand\cC{\mathcal C} \newcommand\F{\mathbb F}$

We show that low degree polynomials can be efficiently recovered when some of their values are corrupted (without knowing where they are corrupted). This is a result from error-correcting codes.

$\newcommand\E{\mathbb E}$ $\newcommand\eps\varepsilon$

In Cedric Villani’s book, he explains optimal transport with bread.

Indepenent subsets of vectors inspire the definition of the matroid. We also introduce graphical matroids, and other equivalent definitions. Finally, we look at the connection to problems solvable by the greedy algorithm.

Reference: Oxley Chapter 1.

We discuss Laplace’s method, Gaussian decomposition (the H-S trick), and applications to the replica method and free energy computations.

We compute the free energy for the Curie-Weiss model and verify that the mean-field approximation predicts the correct free energy density. This article follows the approach in Information, Physics, and Computation, example 4.11.