The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs

The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the competitor’s prices. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.     

E- and R-optimality of block designs for treatment-control comparisons

Abstract

We study optimal block designs for comparing a set of test treatments with a control treatment. We provide the class of all E-optimal approximate block designs, which is characterized by simple linear constraints. Based on this characterization, we obtain a class of E-optimal exact designs for unequal block sizes. In the studied model, we provide a statistical interpretation for wide classes of E-optimal designs. Moreover, we show that all approximate A-optimal designs and a large class of A-optimal exact designs for treatment-control comparisons are also R-optimal. This reinforces the observation that A-optimal designs perform well even for rectangular confidence regions.     

Inspection errors in link sampling

Results of an investigation into the sensitivity to two types of inspection error of link sampling procedures described by Harischchandra and Srivenkataramana are reported. Relevant compound distributions are derived. Some comparisons with results obtained in a similar investigation for standard double sampling are also given.     

Dorfman-sterrett screening (group testing) schemes and the effects of faulty inspection

The Dorfman screening procedure is based on first testing a group of items as a whole, proceeding to individual testing only if the group-test indicates existence of at least one nonconforming item. A modification suggested by Sterrett allows for reintroduct-ion of group testing of all items, not yet tested individually, when an item is classified as nonconforming by an individual test. Effects of faulty test inspection on the properties of the modified procedures are studied.     

Deserts and oases: the continuing concentration of population in the American Mountain West

The Mountain West is a region that seems to be simultaneously rural and urban. With its wide-open spaces, many national parks, monuments, and forests, and high degree of federal land ownership the West appears as the quintessential rural area. However, over 70 percent of the West's population live in metropolitan areas. This simultaneous rural and urban nature of the West is important in understanding the changing population geography of the region. We examine this by focusing on changing patterns of population concentration among metro and nonmetro counties. Unlike other regions in the US, the Mountain West has never experienced a period of counterurbanization or population deconcentration. Not only is current in-migration to the region increasingly concentrated in old and new metro areas, it is also concentrated in a select number of nonmetro areas as well—particularly nonmetro counties adjacent to metro areas, in retirement destinations, and in recreation centers.     

The contours of demography: Estimates and projections

This paper considers the scope of demography and the various research approaches that legitimately could claim the label. As a small field lacking security in academic structures, demography has been unusually sensitive to demand factors, including those associated with perceived population problems. International health is cited as an area of increased demographic presence; reasons for this development are explored. The technology for performing research in demography is improving more rapidly than in many other areas of the social sciences, and thus is helping to improve the relative standing of the field. Taking a demand-oriented approach, the paper identifies several promising research areas in which demographers will be called on to address issues of national and international concern.