Computational Geometry Column 42

A compendium of thirty previously published open problems in computational geometry is presented.Comment: 7 pages; 72 reference

Expected Changes in the Workforce and Implications for Labor Markets

[Excerpt] While many have written about possible effects of the baby boom on the U.S. economy, few have recognized that this demographic transition provides analysts with a unique and valuable opportunity to investigate how the labor market works. Specifically, as baby boomers move up the age distribution, they impart a one-time shock to the supply of potential workers in each age bracket. Because this change is exogenous, many of the tools labor economists typically apply can be utilized to predict how the aging of the baby boom will alter key labor market outcomes. Theoretical and empirical models which (either implicitly or explicitly) hold constant structural parameters in order to work through the effects of an exogenous shock are well-suited to address this issue

Expected Changes in the Workforce and Implications for Labor Markets

This paper examines the likely effects of the aging of the baby boom on labor force attachment, unemployment, and wages. Labor market trends between now and 2020 are the focus of analysis, when the majority of the baby boom generation will confront its retirement decision. We begin by reviewing past labor force trends and discussing important limitations of existing projection methods. Key elements needed to project the consequences of the demographic shock facing the labor market are identified. The task of developing a fully specified economic model to examine the effect of the aging of the baby boom on the labor market is as yet incomplete. On the basis of the best available evidence, we suggest the following conclusions can be drawn: The trend towards earlier retirement will slow and perhaps reverse in the next few decades. Unemployment should fall among older workers and the aggregate full-employment unemployment rate should also decline as the baby boom ages. The aging of the baby boom will not depress wages substantially, either for older workers or for other demographic groups.

Entropy "floor" and effervescent heating of intracluster gas

Recent X-ray observations of clusters of galaxies have shown that the entropy of the intracluster medium (ICM), even at radii as large as half the virial radius, is higher than that expected from gravitational processes alone. This is thought to be the result of nongravitational processes influencing the physical state of the ICM. In this paper, we investigate whether heating by a central AGN can explain the distribution of excess entropy as a function of radius. The AGN is assumed to inject buoyant bubbles into the ICM, which heat the ambient medium by doing pdV work as they rise and expand. Several authors have suggested that this "effervescent heating" mechanism could allow the central regions of clusters to avoid the ``cooling catastrophe''. Here we study the effect of effervescent heating at large radii. Our calculations show that such a heating mechanism is able to solve the entropy problem. The only free parameters of the model are the time-averaged luminosity and the AGN lifetime. The results are mainly sensitive to the total energy injected into the cluster. Our model predicts that the total energy injected by AGN should be roughly proportional to the cluster mass. The expected correlation is consistent with a linear relation between the mass of the central black hole(s) and the mass of the cluster, which is reminiscent of the Magorrian relation between the black hole and bulge mass.Comment: accepted for Ap

Aging, Job Satisfaction, and Job Performance

The national trend to earlier retirement is surprising in light of conventional wisdom holding that older workers are healthy, satisfied and productive employees -- sometimes even more so than their younger counterparts. This paper examines whether conventional wisdom is wrong by reviewing existing studies and noting some of their most important shortcomings. New empirical evidence is provided on the links between aging, job satisfaction, and job performance using data from a nationally representative survey of workers

An Algorithmic Study of Manufacturing Paperclips and Other Folded Structures

We study algorithmic aspects of bending wires and sheet metal into a specified structure. Problems of this type are closely related to the question of deciding whether a simple non-self-intersecting wire structure (a carpenter's ruler) can be straightened, a problem that was open for several years and has only recently been solved in the affirmative. If we impose some of the constraints that are imposed by the manufacturing process, we obtain quite different results. In particular, we study the variant of the carpenter's ruler problem in which there is a restriction that only one joint can be modified at a time. For a linkage that does not self-intersect or self-touch, the recent results of Connelly et al. and Streinu imply that it can always be straightened, modifying one joint at a time. However, we show that for a linkage with even a single vertex degeneracy, it becomes NP-hard to decide if it can be straightened while altering only one joint at a time. If we add the restriction that each joint can be altered at most once, we show that the problem is NP-complete even without vertex degeneracies. In the special case, arising in wire forming manufacturing, that each joint can be altered at most once, and must be done sequentially from one or both ends of the linkage, we give an efficient algorithm to determine if a linkage can be straightened.Comment: 28 pages, 14 figures, Latex, to appear in Computational Geometry - Theory and Application