The normal approximation is notoriously [1][2] bad when the binomial proportion you're trying to estimate is small and you don't have a big n. If one still wants a closed-form out-of-the-box formula (to avoid the exact resolution you suggested), one can use the Wilson approximation for instance.
As you said the PageRank is just one of the many features used by the ranking algorithm. I highly doubt that there is any patent issue here (it's "just" an eigenvector computation), and there is a ton of literature and practical evidence that you can build very good web-search ranking technologies without PageRank.
It would seem very surprising to me that one can patent a feature used in an algorithm for commercial purpose...
The work of Zubrzycki is impressive. For having studied acoustics quite a bit, I'm very impressed by the fact that the sound manages to have both a very short attack an a very good sustain (thanks to the wheel). Controlling the vibration of a bowed string must have been extremely difficult... For the interested reader, there's a more detailed article here:
http://tygodnik.onet.pl/zmysly/the-da-vinci-tone-in-english/...
Well if I were Google, I would make sure that the Incognito mode of Chrome prevents targeting except for adwords/adsense.
Pretty easy to do when you control the browser...
There are some gross simplifications here:
8. Wavelets are not "recursive Fourier analysis". If you want to make it simple, it's more like a spatially localized Fourier extension. I agree that they are under-used though.
9. SVM: the "kernel trick" is a big deal because sometimes defining a vector-space of linear features out of non-vector objects won't give you a good performance, and you'd better define a dot-product.
10. Deep Nets are not only bigger neural networks. The buzz is about how you train them. It's about improving how you train a net in general.
I would say that the next bing thing is more:
Realizing even more that Neural Nets is an optimization problem, and instead of using some heuristics, wait for some Russian mathematician to derive the right SGD schedule / batch solver for the problem. Then what the 1,000 of Google computers have been able to do for the cat face detector, we'll be able to do it on a smartphone chip.
People have to realize that Deep Learning is a bit of a "brute force" solution for the moment (each node is a linear model). We need to derive smarter algorithms.
[1]: http://en.wikipedia.org/wiki/Binomial_proportion_confidence_...
[2]: http://projecteuclid.org/download/pdf_1/euclid.ss/1009213286