Abst ract We present a novel method that constructs and navigates a network of local minima of potential elds deened over multi-dimensional spaces. Though motivated by problems of motion planning for robotic manipulators, similar techniques have been proposed for use in other domains such as molecular chemistry and drug design. The method is based on building a roadmap of paths connecting local...

Let h1, · · · , hn be positive integers. We study new sums m(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 min { r1 h1 , · · · , rn hn } and M(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 max { r1 h1 , · · · , rn hn } , the first of which times h1 · · ·hn is the number of lattice points in a pyramid of dimension n + 1. We show that m(h1, · · · , hn) (h1 − 1) · · · (hn − 1) = 1 + ∑ ∅6 =I⊆{1...

Dimensionality reduction is a commonly used step in many algorithms for visualization, classification, clustering and modeling. Most dimensionality reduction algorithms find a low dimensional embedding that preserves the structure of high-dimensional data points. This paper proposes Local Minima Embedding (LME), a technique to find a lowdimensional embedding that preserves the local minima stru...