Minimum neighborhood in a generalized cube

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let theta(G)(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove theta(G)(k) >= -1/2k(2) + (2n - 3/2)k - (n(2) - 2) for each n-dimensional generalized cube and each integer k satisfying n + 2 <= k <= 2n. Our result is an extension of a result presented by Fan and Lin [J. Fan, X. Lin, The t/k-diagnosability of the BC graphs, IEEE Trans. Comput. 54 (2) (2005) 176-184]. (c) 2005 Elsevier B.V. All rights reserved.

A lower bound on the size of k-neighborhood in generalized cubes

The determination of the minimum size of a k-neighborhood (i.e., a neighborhood of a set of k nodes) in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems. The generalized cubes include the hypercube and most hypercube variants as special cases. In this paper, we present a lower bound on the size of a k-neighborhood in n-dimensional generalized cubes, where 2n + 1 <= k <= 3n - 2. This lower bound is tight in that it is met by the n-dimensional hypercube. Our result is an extension of two previously known results. (c) 2005 Elsevier Inc. All rights reserved.

Climate change justice: getting motivated in the last chance saloon

A key reason for pessimism with respect to greenhouse gas emissions reduction relates to the ‘motivation problem’, whereby those who could make the biggest difference prima facie have the least incentive to act because they are most able to adapt: how can we motivate such people (and thereby everyone else) to accept, indeed to initiate, the changes to their lifestyles that are required for effective emissions reductions? This paper offers an account inspired by Rawls of the good of membership of ‘intergenerational cooperative union’ to achieve justice that provides a solution to the motivation problem.

Real estate investment in global financial centers: risk, return and contagion

Global financial activity is heavily concentrated in a small number of world cities –international financial centers. The office markets in those cities receive significant flows of investment capital. The growing specialization of activity in IFCs and innovations in real estate investment vehicles lock developer, occupier, investment, and finance markets together, creating common patterns of movement and transmitting shocks from one office market throughout the system. International real estate investment strategies that fail to recognize this common source of volatility and risk may fail to deliver the diversification benefits sought.