My Math Forum Degree of freedom in signal processing (gravity) NP Complete

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 November 21st, 2013, 05:43 AM #2 Senior Member   Joined: Jan 2013 Posts: 209 Thanks: 3 Re: Degree of freedom in signal processing (gravity) NP Comp Actually, what I should have said is Minimum Clique Cover, a set of cliques covering all nodes once each which has the least cliques of all ways to do that, because nomatter what you do there will always be at least that many things that have to be perpendicular to eachother. The useful thing about a node-dimensional hypersphere surface is if you have each clique moving around randomly in its own lower dimensional hypersphere (of as many dimensions as that clique size) then for each pair of hyperspheres we have 2 continuous surfaces whose every point is the same distance to every point on the other hypersphere. If you move randomly in both, you have not gotten closer or farther to any part of any other hypersphere. Even if you travel an infinite distance of all paths in each hypersphere individually, you have travelled no distance relative to the other hyperspheres. The distance to them is always sqrt(2) a quarter turn. But where are these hyperspheres is the question... They should be whichever pairs of nodes have a random spread of dot product (blurring around sqrt(2) distance said the flat way) because... Theres no randomness anywhere else, all gone from holding those lacking an edge as perpendicular. If we knew how to exactly hold them perpendicular.

 Tags complete, degree, freedom, gravity, processing, signal

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