Multihop networks must pass messages between source and destination nodes via intermediate links and nodes. Assuming propagation delay is ignored, the mean amount of time the average message stays in a multihop network is directly proportional to the mean distance, in hops, between nodes. Thus, the aggregate link capacity of the network is also directly proportional to this "mean internodal dis...

In this paper, bounds on the mean power-weighted nearest neighbor distance are derived. Previous work concentrates mainly on the infinite sample limit, whereas our bounds hold for any sample size. The results are expected to be of importance for example in statistical physics, nonparametric statistics and computational geometry, where they are related to the structure of matter as well as prope...

BACKGROUND Running economy and performance in middle distance running depend on several physiological factors, which include anthropometric variables, functional characteristics, training volume and intensity. Since little information is available about hematological predictors of middle distance running time, we investigated whether some hematological parameters may be associated with middle d...

We use Monte Carlo methods to calculate the mean end-to-end distance of randomly branched polymer molecules. Molecular realisations are brown on the square and simple cubic lattices, and consist of N bifunctional monomers and N, polyfunctional branching units of functionality f. We treat three cases in which the monomer branches are either random walks, self-avoiding walks (saw), or SAW'S excep...

• Networks have been found through simulated annealing with mean internodal distances lower than any previously reported for a given number of nodes $N$ with a maximum of $p$ outgoing links per node. These networks form the closest known approximations to Moore networks. However, the improvements in mean internodal distance obtained are relatively small (a few percent) and this improvement decr...

Let M be a compact Riemannian manifold. For x, y G M, denote by p(x,y) the distance between x and y, i.e., the infimum of lengths of continuous piecewise C paths between x and y. (Notice that for geodesically complete manifolds there is always a path from x to y of length p(x,y).) The invariants of M based on the distance p are called metrical invariants. Most of them are related to the geometr...

Given any graph G with vertex set V(G), let r(G) _~'-1-, where deg(x) is the degree of x in G. x V(G) de g (x) Further, let a(G) denote the mean distance between vertices of G, i .e ., u(G) =. F .-d(x,y) I IV(T ,) where d(x,y) is the length of the shortest path connecting x and y in G, and the sum is taken over all pairs {x,y} of distinct vertices. The following attractive conjecture was made b...

The need to quantify distance between two groups of objects is prevalent throughout the signal processing world. The difference of group means computed using the Euclidean, or `2 distance, is one of the predominant distance measures used to compare feature vectors and groups of vectors, but many problems arise with it when high data dimensionality is present. Maximum mean discrepancy (MMD) is a...