## Mathematics

**2-butterfly derangement** â€” 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** â€” 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** â€” 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** â€” 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** â€”

**A Terrible Summary - The Risks of Reporting on Research** â€” 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** â€”

**First-order methods for stochastic optimization** â€” 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** â€” The aim of this post is to highlight the utility of non-negative factorization (NMF) in data analysis through examples. In a different post, weâ€™ll talk

**Obituaries: Harold Kuhn (1925â€“2014)** â€”

**3-Manifolds** â€”

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