To get some intuition, we begin with the group of real numbers R under addition. A trivial upper bound for the size of a sum set is |A + A| ≤ |A| 2+|A| 2 (equality is obtained when every pair of elements of A have a distinct sum). If we build A by taking elements of R at random, then we expect |A+A| to be very close to this upper bound, since the probability of a1+a2 = a3+a4 is very small (wher...

The Clifford tori in S constitue a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one ...

The retro-cue effect (RCE) describes superior working memory performance for validly cued stimulus locations long after encoding has ended. Importantly, this happens with delays beyond the range of iconic memory. In general, the RCE is a stable phenomenon that emerges under varied stimulus configurations and timing parameters. We investigated its susceptibility to dual-task interference to dete...

We derive a new representation of Lagrangian subspaces in the form ImΠT [ I X ] , where Π is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and X satisfies |Xij | ≤ { 1 if i = j, √ 2 if i = j. This representation allows us to limit element growth in the context of doubling algorithms for the computation of Lagrangian subspaces and the sol...