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jeremykun.wordpress.com | ||
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www.jeremykun.com
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| | | | | Last time we left off with a tantalizing conjecture: a random graph with edge probability $ p = 5/n$ is almost surely a connected graph. We arrived at that conjecture from some ad-hoc data analysis, so let's go back and treat it with some more rigorous mathematical techniques. As we do, we'll discover some very interesting "threshold theorems" that essentially say a random graph will either certainly have a property, or it will certainly not have it. | |
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www.jeremykun.com
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| | | | | This is a guest post by my friend and colleague Adam Lelkes. Adam's interests are in algebra and theoretical computer science. This gem came up because Adam gave a talk on probabilistic computation in which he discussed this technique. Problem: Simulate a fair coin given only access to a biased coin. Solution: (in Python) def fairCoin(biasedCoin): coin1, coin2 = 0,0 while coin1 == coin2: coin1, coin2 = biasedCoin(), biasedCoin() return coin1 Discussion: This is originally von Neumann's clever idea. | |
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www.jeremykun.com
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| | | | | Or how to detect and correct errors Last time we made a quick tour through the main theorems of Claude Shannon, which essentially solved the following two problems about communicating over a digital channel. What is the best encoding for information when you are guaranteed that your communication channel is error free? Are there any encoding schemes that can recover from random noise introduced during transmission? The answers to these questions were purely mathematical theorems, of course. | |
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keymaterial.net
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| | | One weird hobby of mine is reasonable properties of cryptographic schemes that nobody promised they do or don't have. Whether that's invisible salamanders or binding through shared secrets, anything that isn't just boring IND-CCA2 or existential unforgeability is just delightful material to construct vulnerabilities with. Normally, with a signature scheme, you have the public key... | ||
