An update on the middle levels problem

The middle levels problem is to find a Hamilton cycle in the middle levels, M_{2k+1}, of the Hasse diagram of B_{2k+1} (the partially ordered set of subsets of a 2k+1-element set ordered by inclusion). Previously, the best result was that M_{2k+1} is Hamiltonian for all positive k through k=15. In this note we announce that M_{33} and M_{35} have Hamilton cycles. The result was achieved by an algorithmic improvement that made it possible to find a Hamilton path in a reduced graph of complementary necklace pairs having 129,644,790 vertices, using a 64-bit personal computer.Comment: 11 pages, 5 figure

The effect of prior probabilities on quantification and propagation of imprecise probabilities resulting from small datasets

This paper outlines a methodology for Bayesian multimodel uncertainty quantification (UQ) and propagation and presents an investigation into the effect of prior probabilities on the resulting uncertainties. The UQ methodology is adapted from the information-theoretic method previously presented by the authors (Zhang and Shields, 2018) to a fully Bayesian construction that enables greater flexibility in quantifying uncertainty in probability model form. Being Bayesian in nature and rooted in UQ from small datasets, prior probabilities in both probability model form and model parameters are shown to have a significant impact on quantified uncertainties and, consequently, on the uncertainties propagated through a physics-based model. These effects are specifically investigated for a simplified plate buckling problem with uncertainties in material properties derived from a small number of experiments using noninformative priors and priors derived from past studies of varying appropriateness. It is illustrated that prior probabilities can have a significant impact on multimodel UQ for small datasets and inappropriate (but seemingly reasonable) priors may even have lingering effects that bias probabilities even for large datasets. When applied to uncertainty propagation, this may result in probability bounds on response quantities that do not include the true probabilities.Comment: 36 pages, 12 figure

Macroeconomic Shocks, Job Security and Health: Evidence from the Mining Industry

How do exogenous changes in the macroeconomic environment affect workers’ perceived job security, and consequently, their mental and physical health? To answer this question, we exploit variation in world commodity prices over the period 2001-17 and analyse panel data that includes detailed classifications of mining workers. We find that commodity price increases cause increases in perceived job security, which in turn, significantly and substantively improve the mental health of workers. In contrast, we find no effects on physical health. Our results imply that the estimated welfare costs of recessions are much larger when the effects of job insecurity, and not only unemployment, are considered

Development of user guidelines for ECAS display design, volume 1

Experiment computer application software (ECAS) display design and command usage guidelines were developed, which if followed by spacelab experiments, would standardize methods and techniques for data presentation and commanding via ECAS. These guidelines would provide some commonality among experiments which would enhance crew training and flight operations. The guidelines are applicable to all onboard experiment displays, whether allocated by ECAS or a dedicated experiment processor. A brief description of the spacelab data display system characteristics and of the services provided by the experiment computer operating system is included. Guidelines concerning data presentation and layout of alphanumeric and graphic information are presented along with guidelines concerning keyboard commanding and command feedback

A review of melt and vapor growth techniques for polydiacetylene thin films for nonlinear optical applications

Methods for the growth of polydiacetylene thin films by melt and vapor growth and their subsequent polymerization are summarized. Films with random orientations were obtained when glass or quartz were used as substrates in the vapor growth process. Oriented polydiacetylene films were fabricated by the vapor deposition of diacetylene monomer onto oriented polydiacetylene on a glass substrate and its subsequent polymerization by UV light. A method for the growth of oriented thin films by a melt-shear growth process as well as a method of film growth by seeded recrstallization from the melt between glass plates, that may be applied to the growth of polydiacetylene films, are described. Moreover, a method is presented for the fabrication of single crystal thin films of polyacetylenes by irradiation of the surface of diacetylene single crystals to a depth between 100 and 2000 angstroms