Intersection homology of stratified fibrations and neighborhoods

We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.Comment: 45 page

Covering rough sets based on neighborhoods: An approach without using neighborhoods

Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin

Missing the Target

Buffalo is the nation’s third most impoverished city. Buffalo’s East Side and West Side neighborhoods are two of Buffalo’s most impoverished areas. If any two neighborhoods are in need of economic development, it is these two. And yet, despite spending billions of dollars on economic development programs each year, the State, County, and City have largely ignored these neighborhoods and their increasingly desperate residents. Programs, funds, and subsidies meant to help blighted neighborhoods have instead subsidized sprawl, rewarded large, non-local companies, and, even within Buffalo, done more for downtown law firms and upscale condos than for the East and West Side