A Deterministic Algorithm for the Vertex Connectivity Survivable Network Design Problem

In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u,v) for each pair of vertices u,v. We are also given a cost function on the set of edges. Our goal is to find the minimum cost subset of edges such that for every pair (u,v) of vertices we have r(u,v) vertex disjoint paths in the graph induced by the chosen edges. Recently, Chuzhoy and Khanna presented a randomized algorithm that achieves a factor of O(k^3 log n) for this problem where k is the maximum connectivity requirement. In this paper we derandomize their algorithm to get a deterministic O(k^3 log n) factor algorithm. Another problem of interest is the single source version of the problem, where there is a special vertex s and all non-zero connectivity requirements must involve s. We also give a deterministic O(k^2 log n) algorithm for this problem

The Effect of Household Characteristics on Poverty and Living Standards in South Africa

This paper uses panel data from South Africa to examine the effect of household characteristics on poverty and living standards and how they have changed over the five years following the dismantling of apartheid. I estimate the standard of living using two alternative methodologies. First, I use probit analysis to examine the poverty status of the household. Second I use quantile regressions to examine the standard of living of the household at different points on the income distribution. The main measure of the standard of living is per adult equivalent household income, which adjusts household income by the scale and composition adjusted household size. The estimation results show that the sex of the household head, the education attainment of the household head, ethnicity and region of residence have significant effects on both the poverty status and standard of living of the household.

On the Stability of Super-Earth Atmospheres

We investigate the stability of super Earth atmospheres around M stars using a 7-parameter, analytical framework. We construct stability diagrams in the parameter space of exoplanetary radius versus semi-major axis and elucidate the regions in which the atmospheres are stable against the condensation of their major constituents, out of the gas phase, on their permanent nightside hemispheres. We find that super Earth atmospheres which are nitrogen-dominated ("Earth-like") occupy a smaller region of allowed parameter space, compared to hydrogen-dominated atmospheres, because of the dual effects of diminished advection and enhanced radiative cooling. Furthermore, some super Earths which reside within the habitable zones of M stars may not possess stable atmospheres, depending on the mean molecular weight and infrared photospheric pressure of their atmospheres. We apply our stability diagrams to GJ 436b and GJ 1214b, and demonstrate that atmospheric compositions with high mean molecular weights are disfavoured if these exoplanets possess solid surfaces and shallow atmospheres. Finally, we construct stability diagrams tailored to the Kepler dataset, for G and K stars, and predict that about half of the exoplanet candidates are expected to habour stable atmospheres if Earth-like conditions are assumed. We include 55 Cancri e and CoRoT-7b in our stability diagram for G stars.Comment: Accepted by ApJ. 10 pages, 6 figures. No changes from previous version, except for added hypen in titl