Let M = M, +, <, 0, S be a linear o-minimal expansion of an ordered group, and G = G, ⊕, eG an n-dimensional group definable in M. We show that if G is definably connected w...
We show that a positive definite integral ternary form can be reduced with O(M(s) log2 s) bit operations, where s is the binary encoding length of the form and M(s) is the bit-com...
In this paper we investigate the Erd¨os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We pr...
: A distributed system is scalable if the rate at which it completes its computation and communication tasks does not depend on its size. As an example, the scalability of a peer-t...
The Helly number of a family of sets with empty intersection is the size of its largest inclusionwise minimal sub-family with empty intersection. Let F be a finite family of open...