We prove that for every ε ∈ (0, 1) there exists Cε ∈ (0,∞) with the following property. If (X, d) is a compact metric space and μ is a Borel probability measure on X then there exists a compact subset S ⊆ X that embeds into an ultrametric space with distortion O(1/ε), and a probability measure ν supported on S satisfying ν (Bd(x, r)) 6 (μ(Bd(x,Cεr)) 1−ε for all x ∈ X and r ∈ (0,∞). The dependen...

Let u be the equilibrium potential of a compact set K in R. An electrostatic skeleton of K is a positive measure μ such that the closed support S of μ has connected complement and no interior, and the Newtonian (or logarithmic, when n = 2) potential of μ is equal to u near infinity. We prove the existence of an electrostatic skeleton for every convex polytope. Our proof raises several interesti...

We present a new method for the skeletonization of 2-dimensional or 3-dimensional objects. First, we introduce two local measures, and d, to characterize skeleton points, whose good localizaa tion is ensured by Euclidean distance mapping techniques. These measures allow us to control the detail of the resulting skeleton. Thresholding these measures generally does not yield well-deened skeleton:...

Algorithmic skeletons have proved to be a good solution to the problem of implementing parallel applications with specify communication structures. They define the overall structure of the computation, hiding the complex communication details. Nowadays, the different frameworks available offer a fixed set of skeletons. The programmer can implement efficient programs if the computation and commu...

BACKGROUND The demography and pattern of disease of skeletal assemblages may not accurately reflect those of the living population of which they were once a part. The hypothesis tested here was that skeletons from a mass disaster would more closely approximate to a living population than those from a conventional cemetery. METHOD Six hundred skeletons recovered from a Black Death plague pit i...

It has been discovered during the past few years that demosponges of the order Verongida such as Aplysina cavernicola exhibit chitin-based skeletons. Verongida sponges are well known to produce bioactive brominated tyrosine derivatives. We could recently demonstrate that brominated compounds do not exclusively occur in the cellular matrix but also in the skeletons of the marine sponges Aplysina...

We give a concise definition of mitered offset surfaces for nonconvex polytopes in R, along with a proof of existence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconvex polytopes. The geometric, topological, and algorithmic features of such skeletons are investigated, including a classification of their constructing events in t...

The fundamental idea behind the construction is rather simple: in essence, we wish the tiles to organize themselves into larger and larger images of the in ated tiles (these images are \supertiles"). Each of these supertiles is to be associated with a small amount of information| its alleged position with respect to its parent supertile. This information resides on a \skeleton" of edges; these ...