Let S be a set of n points in < d. We present an algorithm that uses the well-separated pair decomposition and computes the minimum spanning tree of S under any Lp or polyhedral metric. It has an expected running time of O(n logn) for uniform distributions. Experimentalresults show that this approachis practical. Under a variety of input distributions, the resultingimplementation is robust and ...

We give a characterization of uniformly convex Banach spaces in terms of a uniform version of the Kadec-Klee property. As an application we prove that if (xn) is a bounded sequence in a uniformly convex Banach space X which is ε-separated for some 0 < ε ≤ 2, then for all norm one vectors x ∈ X there exists a subsequence (xn j) of (xn) such that inf j =k x − (xn j − xn k) ≥ 1 + δ X (2 3 ε), wher...

For periodically driven systems, quantum tunnelling between classical resonant stability islands in phase space separated by invariant KAM curves or chaotic regions manifests itself by oscillatory motion of wavepackets centred on such an island, by mulitplet splittings of the quasienergy spectrum, and by phase space localization of the quasienergy states on symmetryrelated flux tubes. Qualitati...

We introduce a new number of new techniques for the construction of low-distortion embeddings of a finite metric space. These include a generic Gluing Lemma which avoids the overhead typically incurred from the näıve concatenation of maps for different scales of a space. We also give a significantly improved and quantitatively optimal version of the main structural theorem of Arora, Rao, and Va...