In Bayesian disease mapping, one needs to specify a neighborhood structure to make inference on the underlying geographical relative risks. We propose a model in which the neighborhood structure is part of the parameter space. We retain the Markov property of the usual Bayesian spatial models: given the neighborhood graph, the disease rates follow a conditional autoregressive model. However, th...

Researchers measuring racial inequality of neighborhood environment across metropolitan areas (MAs) have traditionally employed segregation measures, yet such measures are limited for incorporating a third axis of information, including neighborhood opportunity. Using Census 2000 tract-level data for the largest U.S. MAs, we introduce the interquartile-range overlap statistic to summarize the s...

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

neighborhood attachment is closely related to concrete and abstract conceptions that set the scene for a variety of interactions among the residents. it is on the basis of social-physical location which happens over time. neighborhood attachment also enhances the possibility of residents’ social participation in urban neighborhoods and has a bilateral relationship with residents’ satisfaction. ...

The choice of a closed regular neighborhood of a finite polyhedron embedded in a manifold enables one to write the ambient space as a union of two manifolds, the neighborhood and its complement, glued along a common boundary component. Poincaré duality embeddings are a homotopy theoretic version of this in which the manifolds are replaced by Poincaré spaces and the gluing is now done with respe...

For a compact monotonically normal space X we prove: (1) X has a dense set of points with a well-ordered neighborhood base (and so X is co-absolute with a compact orderable space); (2) each point of X has a well-ordered neighborhood πbase (answering a question of Arhangel’skii); (3) X is hereditarily paracompact iff X has countable tightness. In the process we introduce weak-tightness, a notion...

Given a bounded metric space X, the set of closed sets of X supports a metric, the Hausdorff metric. Whether X is bounded or not, there is a compact, locally compact topology on the space of closed sets. If A,B ⊂ X are closed sets, define their Hausdorff distance dH(A,B) to be the number inf { r | B is in the r − neighborhood of A andA is in the r − neighborhood of B }. We can say this more pre...

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder’s theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of σ(T ). As applications, we show that if T is algebraically M -hyponormal, or if T is algebraically paranormal, then the generalized Weyl’s theore...

An important technique for exploratory data analysis is to form a mapping from the high-dimensional data space to a low-dimensional representation space such that neighborhoods are preserved. A popular method for achieving this is Kohonen's self-organizing map (SOM) algorithm. However, in its original form, this requires the user to choose the values of several parameters heuristically to achie...

Agent-based modeling and simulation, based on the cellular automata paradigm, is an approach to modeling complex systems comprised of interacting autonomous agents. Open questions in agent-based simulation focus on scale-up issues encountered in simulating large numbers of agents. Specifically, how many agents can be included in a workable agent-based simulation? One of the basic tenets of agen...