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As I read through “Information theoretic inequalities”, it felt like the icing on the cake: a simpler proof of a result from my Master’s thesis. The result itself wasn’t the focus of my Master’s but instead facilitated the proof of a number of other results, … Continue reading
My uncle’s in town and just reminded me of a puzzle that he’d asked me over ten years ago. A census worker goes to a house and the person who answers the door tells the census worker that she has three daughters. “I need to know … Continue reading
It was the spring of 2003; Toby Berger and I were both in the common room of Phillips Hall, and there was half an hour before his information theory class was set to start. Toby was advising my honors thesis, a project that was exploring … Continue reading
I just got back from a fourday camping trip for the Fourth. While roasting marshmallows and hiking along trails, I managed to fall into a few puzzles. Justin posed a puzzle that we’d formulated a while ago: a multiperson variation … Continue reading
The problem asks you to show that . If , then the solution is quite easy. Set the gradient equal to zero and solve the system of equations for . Since the function is convex, this is the minimum point, and … Continue reading
He’s met almost everyone else: Wiener, Bode, Bellman, Carnot, Tesla, Marconi, and of course, Shortz. Bad jokes aside, in an attempt to understand the inverse water filling solution from ratedistortion theory better, I put together some rough notes attempting to connect it and the sampling … Continue reading