Mathematics
2-butterfly derangement — The hallmark of the Cooley-Tukey algorithm for Fast Fourier Transform is the butterfly network, which helps reduce $O(n^2)$ computations to $O(n log n)$. Butterflies are
Maximum weighted independent set - connected component — Given a weighted connected component, what is the weight of the maximum independent set, and how many different sets have this weight? A Petersen graph
Maximum weighted independent set - singletons and forest — Gus wants to open franchises of his restaurant, Los Pollos Hermanos, along Central Avenue. There are $n$ possible locations for franchises, where location i is
Rational numbers in decimal — In decimal representation, rational numbers either terminate after a finite number of digits or produce a repeating sequence. Conversely, any repeating decimal can be converted
Generalized heaps —
A Terrible Summary - The Risks of Reporting on Research — Two reasons why I think that A Beautiful Algorithm? The Risks of Automating Online Transactions is way off in its report on an otherwise interesting
Continued Fractions —
First-order methods for stochastic optimization — Optimization, particularly deterministic (convex) optimization, is essential to many learning algorithms (regression, support vector machines, matrix factorization etc). This post discusses first-order/gradient-based optimization approaches that
Nonnegative Matrix Factorization, 1 — The aim of this post is to highlight the utility of non-negative factorization (NMF) in data analysis through examples. In a different post, we’ll talk
Obituaries: Harold Kuhn (1925–2014) —
3-Manifolds —
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