We have heard so far at this meeting from the practical-minded men of radio astronomy. Faced with the problem: ‘my map has sidelobes and noise on it’, they promptly reach for the nearest available weapons — ‘cleaners, polishers and kneaders’. All these use varying amounts of subjective human judgement, as for example in ‘window cleaning’. The ideas of the maximum entropy method are intriguing, ...

We will derive two results of the primal simplex method by constructing simple LP instances on 0-1 polytopes. First, for any 0-1 polytope and any of its two vertices, we can construct an LP instance for which the simplex method finds a path between them, whose length is at most the dimension of the polytope. This proves a well-known result that the diameter of any 0-1 polytope is bounded by its...

Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 s m=4, a monotone circuit computing CLIQUE(m; s) contains at least (1=2)1:8 min( p s 1=2;m=(4s)) gates: If a non-monotone circuit computes CLIQUE using a \small" amount of negation,...