The universal Faber-Jackson relation

Composition of the Universal Relation

We prove that the communication complexity of the k-fold composition of the universal relation on n bits is (1 o(1))kn when k = o( p n= logn). Warning: Essentially this paper has been published in Advances in Computational Complexity Theory and is hence subject to copyright restrictions. It is for personal use only.

Zeros of the derivatives of Faber polynomials associated with a universal covering map

For a compact set E ⊂ C containing more than two points, we study asymptotic behavior of normalized zero counting measures {μk} of the derivatives of Faber polynomials associated with E. For example if E has empty interior, we prove that {μk} converges in the weakstar topology to a measure whose support is the boundary of g(D), where g : {|z| > r} ∪ {∞} → C\E is a universal covering map such th...

The Communication Complexity of the Universal Relation

Consider the following communication problem. Alice gets a word x 2 f0; 1gn and Bob gets a word y 2 f0; 1gn. Alice and Bob are told that x 6= y. Their goal is to find an index 1 i n such that xi 6= yi (the index i should be known to both of them). This problem is one of the most basic communication problems. It arises naturally from the correspondence between circuit depth and communication com...

The Nested Universal Relation Database Model

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The Nested Universal Relation Data Model