Deriving the discrete-Fourier-transform-based epicycle approximation, proving an L2 error bound, with comments on the fast Fourier transform algorithm.
Demo!Proving probability convergence to the Born rule in flea-perturbed n-well quantum systems using arbitrary functions, extending previous work in https://arxiv.org/abs/2409.16457.
Dataset ablation experiment to determine if small LMs can learn AANNs (article + adjective + numeral + noun), a rare English grammatical phenomena. Reproduces and extends the study in https://arxiv.org/abs/2403.19827 with the addition of morphological tags.
Mathematical study of PageRank as a stochastic ranking algorithm by rigorously proving steady-state Markov chain theorems in the language of linear algebra.
Deriving, analyzing, and optimizing Eulerian and Lagrangian fluid simulation implementations, using grids, particles, and even quadtrees.
Demo!Experiment and analysis of rectifier electrical circuits, answering the question: How does root mean squared alternating voltage affect direct current after passing through a full bridge rectifier?