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).
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.
Thanks for the explanation! My only concern now is the validity of the meaning of the principal eigenvalue: "λ determines how much influence people share with each other through their connections. If λ is small then the CEO has a lot of influence, if it is large then he has little." It seems to depend on λ>1 or λ<1. Also, has this method been applied in practice, if you know?
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.
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.
I understand this. But let's say I ran some experiments and collected some data in an attempt to disprove theory X. What does it mean for me to say that at the 99% confidence level X is still true, but at the 98% confidence level it is not true? I just find it a bit spooky, is all.
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?
I'm quite clear if you read more than one sentence.
It's the way this guy responded to a comment of a blog about the paper. It just seems like a bad place to post a real unfixable flaw to the paper. Assuming the commenter is right (also possibly a bad assumption) why not put some effort into your response that will be read by every computer science and math person you'll ever work with in the future. For instance how does one respond, follow up, contact this guy? I have to go google him wtf. It's the equivalent to nitpicking. In the end someone else will have to pick up the pieces of what he said and analyze it and rewrite it and repost it. So to me he seems like the guy from QA that no one wants to work with - a bad team player.
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!
Sudoku is very boring. If I wanted to spend my time solving small value NP-complete problems I might as well go out and solve TSPs over and over again.
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.
We agree it is strange that this idea has not been done by now. We keep expecting that we will find it around the corner, but so far it has not actually shown up. Basecamp is a great product for many elements of managing projects, but I feel it still falls short on the visualization end of things. They look to pretty openly support 3rd party extensions and they are on our road-map of data to visualize.
You must not have been the only person to notice this. The definition is on pg 6 in the pdf above.