How to find a syphilitic with the Lambert W-function and Fibonacci numbers

I said a few vague words on the All Things Considered piece about the Dorfman protocol for syphilis screening, which is an early example of the exploitation of sparsity to improve signal detection.  Jeffrey Shallit follows up with a really nice explanation of the method at his blog.  Good stuff in the comments, too, especially this souped-up recursive Dorfman suggested by Gareth McCaughan, in which Fibonacci numbers arise in a mysterious way!

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2 thoughts on “How to find a syphilitic with the Lambert W-function and Fibonacci numbers

  1. Andrei Caldararu says:

    A much more interesting question in my opinion is what to do if you have no idea what the total number of people with the disease is. If you know there is at most one person sick, you can do it in log_2-tests. If you know almost everyone has it, you’d better test everyone. The Dorfman test is linear in n, still. I don’t quite know how to distinguish between the linear and logarithmic cases, but I am sure this is known.

  2. JSE says:

    Andrei’s problem is kind of a hybrid between the Dorfman protocol and the Bayesian Roulette in the previous post!

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