On Minimum Average Stretch Spanning Trees in Polygonal 2-trees

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on $n$ vertices, we present an algorithm to compute a minimum average stretch spanning tree in $O(n \log n)$ time. This algorithm also finds a minimum fundamental cycle basis in polygonal 2-trees.Comment: 17 pages, 12 figure

Distribution of the delay time and the dwell time for wave reflection from a long random potential

We re-examine and correct an earlier derivation of the distribution of the Wigner phase delay time for wave reflection from a long one-dimensional disordered conductor treated in the continuum limit. We then numerically compare the distributions of the Wigner phase delay time and the dwell time, the latter being obtained by the use of an infinitesimal imaginary potential as a clock, and investigate the effects of strong disorder and a periodic (discrete) lattice background. We find that the two distributions coincide even for strong disorder, but only for energies well away from the band-edges.Comment: Final version with minor corrections in text, 4 pages, 2 PS figure

Propagating and evanescent waves in absorbing media

We compare the behavior of propagating and evanescent light waves in absorbing media with that of electrons in the presence of inelastic scattering. The imaginary part of the dielectric constant results primarily in an exponential decay of a propagating wave, but a phase shift for an evanescent wave. We then describe how the scattering of quantum particles out of a particular coherent channel can be modeled by introducing an imaginary part to the potential in analogy with the optical case. The imaginary part of the potential causes additional scattering which can dominate and actually prevent absorption of the wave for large enough values of the imaginary part. We also discuss the problem of maximizing the absorption of a wave and point out that the existence of a bound state greatly aids absorption. We illustrate this point by considering the absorption of light at the surface of a metal.Comment: Brief Review, to appear in the American Journal of Physics, http://www.kzoo.edu/ajp

An empirical study of the transition from paid work to self-employment

We explore the relationship between the probability of a transition from paid work to self-employment and three explanatory variables: paid income, predicted income, and income for ability. We use panel data for heads of households from the PSID SRC sample for eight pairs of years. Our results show that therelationship between paid income and self-employment is not linear. We then break up paid income into two components: a)predicted income based on human capital, demographic, and locational variables, and b) income for ability. Again, we find nolinear relationship between self-employment and either predicted income or income for ability. We then test for curvilinear relationships between these three variables (i.e., paid income, predicted income, and income for ability) and the transition to self-employment. We find that individuals with low incomes are more likely to take up self-employment. Further, income for ability is a stronger predictor of the transition to self-employment than predicted income. We show that the relationship between ability and self-employment is U shaped: very low ability and very high ability individuals are more likely to take up self-employment than medium ability individuals. We use prospect theory to explain this result.Entrepreneurship; self-employment; opportunity costs; value creation;