Convexity as the one concept to bind them
A little bit more math to help us into the new year. This article is really very nice: What Shape is your Conjugate? A Survey of Computational Convex Analysis and its Applications (by Yves Lucet) This article is beautiful because it brings together many, and I mean really many, algorithms and unifies them all through applied convex analysis. For example, there is something in common among: Computing flows through networks Properties of alloys Image processing for IRM, ultrasound, ... Dynamic programming The magic in back of all of these concepts is convexity and how certain mappings preserve certain properties. The article is probably a bit fast for many readers, but truly insightful because of the scope of its coverage. It really priovides a common way to approach convexity in its many different forms.