I think your subset sum problem (the rock piles) is decent. However, for it to be useful I think you have to make it clear which class it is in (NP) and why (it is easy to check a solution and 2^n is not polynomial in n).
I don't understand the interpretation of the principal eigenvalue either. Perhaps there is a more suitable interpretation in the directed case, but I'm not sure of that either.
I think this method is generally known as eigenvector centrality, that is to say, the entries in the vector x are generally known as eigenvector centralities. I think this method is quite popular, but I do not know who uses it or how often.
Under mild conditions of the undirected graph (basically that it is not bipartite and that it is connected) one can use the Perron-Frobenius theorem. So, to remove the ambiguity you are concerned with consider that you want an x s.t. all the entries in x are positive. Then PF guarantees that the largest eigenvalue of A has multiplicity one and its associated eigenspace is one-dimensional. PF also guarantees that the eigenvector associated with the largest eigenvalue has positive entries and is the only eigenvector with positive entries. So, you want the largest eigenvalue (which is positive) and the unique positive valued eigenvector associated with it. Finally, to obtain this eigenvector/value pair one can use the power method which this author recommends.
This is why different communities accept p-values at certain levels (typically <0.05). You have to live with some amount of uncertainty when the data generating mechanism is random... that is unfortunately the nature of the beast.
The claim is that the proof is unfixable. Proofs are either right or wrong. Good academics are supposed to checks proofs of their colleagues. There is no claim as to the merit of contributions made by Deolalikar. So, why exactly do these academics infuriate you?
If you find Sudoku boring you just need to add more constraints. For example, try solving one by considering some ordering on the entries (say, Left-to-Right then Top-to-Bottom) and only allow yourself to fill in entries in that order... then time yourself!
Wait... hasn't this idea come and gone about 10 times in the last 10 years. I remember when I begged 37 signals to add this as a small feature about 4 years ago and they laughed it off. Also, some of the text in the biographies seem a bit exaggerated.
Sounds like an amazing idea... strikingly similar to the idea I pitched to YC in an interview in November, 2006 :-/. I guess they didn't like our team or progress. Bummer.
I can't believe no one has mentioned this, but it seems to me the most important thing is how well you can erase the marker. Assuming it works well you should demonstrate this. I simply will not buy a whiteboard without knowing how well it will work over time. Also, I've used Georgia Pacific Mark-R-Board which costs about 1/3 of your product and it works just fine. That made me chuckle when I read the cost comparison in your FAQ.
I'm not sure you've actually addressed his concern. I think the ability to use one (in an engineering sense) and get seemingly good results is separate from the issue of fully utilizing them. You are likely better off using a much more hands off tool that requires little knowledge of the underlying mechanism (to his point, d trees and svm).
I cannot let comments like this stand. I have seen little difference between students from the top few schools and the rest. If you are only doing an undergrad I see little reason to hold these top 4 on such a pedestal. Any school in the top 20 or even probably 40 are more than a java school at the undergraduate level. The differences are marginal. However, if you plan to go to graduate school I would certainly try to attend one of the top 4 schools.
You must not have been the only person to notice this. The definition is on pg 6 in the pdf above.