Notes
Technical notes.
Long-form explanations of mathematics, machine learning, and scientific computing, written to be read and worked through, with full derivations and code.
Lattice point visibility along powers of polynomials
A plain-language companion to our arXiv paper with Tristan Phillips, and to the two papers that followed: what happens to visibility when lines of sight bend into curves.
Gradient descent and the Adam optimizer
The workhorse of modern optimization, derived from first principles, with a from-scratch Python implementation of Adam.
Generalized evaluation of ordered sums of cosine products in an arithmetic sequence
A closed form for the ordered sum of cosine products, derived from the roots-of-unity factorization of odd powers.
The Confluence Analysis Program (CAP)
Open-source image analysis that measures cell confluence. Design, method, and results from the preprint.
Extending roots-of-unity factorization to sums and differences of even powers
Carrying the odd-power factorization over to even n, with harder trigonometric sums as exercises.
Magnetic fields and tau disaggregation in Alzheimer's disease, part 2: mechanisms
The physiological mechanisms by which static and alternating magnetic fields could act on tau aggregation.
Magnetic fields and tau disaggregation in Alzheimer's disease, part 1: the generator
The therapeutic case for exposing tau protein to static and alternating fields, and a bench-built field generator.
The quadratic sieve, implemented: factoring RSA semiprimes in Python
How the quadratic sieve finds smooth relations and turns them into a factorization, with a working implementation that breaks toy RSA keys.
Factoring sums and differences of odd powers with De Moivre's theorem
An alternate factorization via roots of unity, and an identity for evaluating trigonometric sums.