Author Archives: K

High Throughput

In late 2011, I gave cheek swabs to National Geographic to trace my genetic genealogy. The samples looked at markers from my Y chromosome and mitochondrial DNA: the first was passed down from my father from his father from his … Continue reading

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Passing Notes in Class

I just got back from a four-day 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 multi-person variation … Continue reading

Posted in Information Theory, Papers, Puzzle | Leave a comment

Fool Me Once

I recently started watching Penn and Teller’s Fool Me, a show in which magicians try to fool Penn and Teller for a shot to perform in Vegas. After one of the episodes, there was a trick that I couldn’t even begin … Continue reading

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Complexity and Asymptotes

A friend pointed out to me that the statement that the final divide-and-conquer Fibonacci algorithm from the previous post could run in time was a bit misleading. The objection was that I had assumed that the matrix multiplication would not depend on … Continue reading

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Code Monkey

During my years as a student, I sometimes encountered a disdain in others for writing code. In some cases, the term “code monkey” would get used against someone who enjoyed writing code. Something never quite felt right about that term. … Continue reading

Posted in Programming, Signal Processing | 1 Comment

Voting Paradox

Inspired by the upcoming elections, I spent a little time yesterday trying to think up an example in which people could potentially have logically consistent beliefs individually but as a whole produce logically inconsistent outcomes. The result of that effort … Continue reading

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Walking Downhill

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

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4 Prisoners

The end of the 100 Prisoners post asked if there is a way to show that there does not exist a strategy that meets the coupon collector lower bound for release when there are prisoners. Let’s first establish strategies for … Continue reading

Posted in Probability, Puzzle | Leave a comment

Shannon Meets Shannon

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 rate-distortion theory better, I put together some rough notes attempting to connect it and the sampling … Continue reading

Posted in Information Theory, Signal Processing | 1 Comment

100 Prisoners

100 prisoners are condemned to life in prison, or so they think. One day the warden assembles all of the prisoners together and offers them a deal: “Starting tomorrow, I will select a prisoner at random every day and send … Continue reading

Posted in Probability, Puzzle | 3 Comments