Digital neighborhoods

Simple Neighborhoods

The purpose of this note is to state a collection of results, all related to questions of uniqueness of smooth neighborhoods of finite complexes as imbedded (nicely) in differentiable manifolds. The reported results will appear in subsequent papers, the first of which is [l ]. The approach taken is always via the theory of simple homotopy types (due to J. H. C. Whitehead), and the main theorem ...

Mapping digital divide in neighborhoods: Wi-Fi access in Baton Rouge, Louisiana

The independent neighborhoods process

A triangle T (r) in an r-uniform hypergraph is a set of r + 1 edges such that r of them share a common (r − 1)-set of vertices and the last edge contains the remaining vertex from each of the first r edges. Our main result is that the random greedy triangle-free process on n points terminates in an r-uniform hypergraph with independence number O((n log n)). As a consequence, using recent result...

Extended Conceptual Neighborhoods

Based on the smooth transition model for conceptual neighborhood graphs among binary topological relations, an extended model, the movement model, is proposed. A neighborhood relation between two topological relations describes one of the possible movements of one object with respect to the second one. The example of the construction of the graph for line-zone relations is provided. Such extend...

Neighborhoods as Nuisance Parameters

Deviations from the center within a robust neighborhood may naturally be considered an innnite dimensional nuisance parameter. Thus, in principle, the semiparametric method may be tried, which is to compute the scores function for the main parameter minus its orthogonal projection on the closed linear tangent space for the nuisance parameter, and then rescale for Fisher consistency. We derive s...