I’ve been iterating back and forth between Mathematica and my own simplifications, trying to clean up the formulas that feed into the efficiency calculation so that we can analyze them further.

Unfortunately, I’m currently frustrated by two problems that I’ve poured about six hours into now.

First, I’ve successfully reproduced the probabilities of all the various experimental outcomes, but when I collect them together and calculate the Chernoff distance C2 found on page 3, my values are consistently higher than the authors’. I’ve checked and re-checked my work and I can’t find any mistakes. Either there is a misprint in the article or I’m incorrectly using some function in Mathematica. I emailed the authors, asking for their code, and I’ll also try to consult with a Mathematica veteran. (Another pair of eyes would be really helpful right now.)

Second, I’m trying to perform an eigendecomposition of the evolution matrix. The eigenvalues I obtained by simplifying Mathematica’s symbolic calculation and plugging in the parameters I’m using match up with those yielded directly by a numerical Mathematica calculation. However, the eigenvectors don’t. For some reason, Mathematica returns a different set of eigenvectors, depending on whether I calculate symbolically and then substitute parameters, or whether I substitute parameters and then calculate numerically.

At this point, I’m out of ideas until I find a fresh pair of eyes to confirm that I’m not doing something crazy.

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‘Baby Rudin’ is to learning analysis as artificial insemination is to sexual reproduction. It’s not good, it’s not bad, and there are more fun ways of going about it, but at least it gets the job done.

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This is a great little intro to topology… and one more reason to love Dover books for their tiny, inexpensive textbooks.

Well-motivated and lots of interesting problems. I can’t compare it much to other topology books, but my general impression is that it covers less than Munkres.

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Statistics as a mathematical field was invented to turn imperfect information into usable generalizations. In an age of door-to-door censuses, phone surveys, and weather stations, it let humans make strong predictions about their world.

The impending rise of ubiquitous sensors detecting everything from weather to traffic to human relationships will supplant the need for statistics. Why sample data when you can have it all?

That said, statistics won’t entirely disappear. It will still be useful in making sense of experimental data since lab experiments simulate only a single case, and others may not even exist to be monitored. It will also still be useful in situations in which the extra cost of obtaining ubiquitous data is not worth the extra accuracy achieved over traditional statistical and sampling methods. Yet, even in this case, as the infrastructure for ubiquitous data is laid out, it will become more and more practical and economical to start using it.

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