Graph Saturation in Multipartite Graphs

Let $G$ be a fixed graph and let ${\mathcal F}$ be a family of graphs. A subgraph $J$ of $G$ is ${\mathcal F}$-saturated if no member of ${\mathcal F}$ is a subgraph of $J$, but for any edge $e$ in $E(G)-E(J)$, some element of ${\mathcal F}$ is a subgraph of $J+e$. We let $\text{ex}({\mathcal F},G)$ and $\text{sat}({\mathcal F},G)$ denote the maximum and minimum size of an ${\mathcal F}$-saturated subgraph of $G$, respectively. If no element of ${\mathcal F}$ is a subgraph of $G$, then $\text{sat}({\mathcal F},G) = \text{ex}({\mathcal F}, G) = |E(G)|$. In this paper, for $k\ge 3$ and $n\ge 100$ we determine $\text{sat}(K_3,K_k^n)$, where $K_k^n$ is the complete balanced $k$-partite graph with partite sets of size $n$. We also give several families of constructions of $K_t$-saturated subgraphs of $K_k^n$ for $t\ge 4$. Our results and constructions provide an informative contrast to recent results on the edge-density version of $\text{ex}(K_t,K_k^n)$ from [A. Bondy, J. Shen, S. Thomass\'e, and C. Thomassen, Density conditions for triangles in multipartite graphs, Combinatorica 26 (2006), 121--131] and [F. Pfender, Complete subgraphs in multipartite graphs, Combinatorica 32 (2012), no. 4, 483--495].Comment: 16 pages, 4 figure

Monte Carlo Simulation of a Knudsen Effusion Mass Spectrometer Sampling System

Knudsen flow is easily simulated with a Monte Carlo method. In this study we develop a Visual Basic for Excel (VBA) code to simulate the molecular beam from a vaporizing solid. The system at NASA Glenn uses the restricted collimation method of Chatillon and colleagues, which consists of two apertures between the effusion cell and the ionizer. The diameter of the first aperture is smaller than the diameter of the effusion cell orifice, so the ionizer effectively only sees inside the effusion cell. The code is able to calculate the transmission coefficient through the cell orifice, through the cell orifice and the first aperture, and through the cell orifice and first and second aperatures. Calculated transmission coefficients through the cell orifice are compared to tabulated values to validate the code. Then transmission coefficients are calculated through the cell orifice and both apertures to the ionizer. This allows the geometry (aperture spacing and diameters) of the sampling system the sampling system to be optimized. Calculated transmission factors are also compared to literature values calculated via an analytic method

Thermodynamic Studies of High Temperature Materials Via Knudsen Cell Mass Spectrometry

The Knudsen Cell technique is a classic technique from high temperature chemistry for studying condensed phase/vapor equilibria. It is based on a small enclosure, usually about 1 cm in diameter by 1 cm high, with an orifice of well-defined geometry. This forms a molecular beam which is analyzed with mass spectrometry. There are many applications to both fundamental and applied problems with high temperature materials. Specific measurements include vapor pressures and vapor compositions above solids, activities of alloy components, and fundamental gas/solid reactions. The basic system is shown. Our system can accommodate a wide range of samples, temperatures, and attachments, such as gas inlets. It is one of only about ten such systems world-wide

Monte Carlo simulation of a Knudsen effusion mass spectrometer sampling system

RATIONALE: Knudsen effusion mass spectrometry (KEMS) shows improved performance with the restricted collimation method of Chatillon and colleagues, which consists of two apertures between the Knudsen cell orifice and the ionizer. These apertures define the shape and position of the molecular beam independently of the sample and effusion orifice and as a result reduce background and improve sampling from the Knudsen cell.Modeling of the molecular beam in restricted collimation allows optimization of the apertures’ diameters and spacing. METHODS:Knudsen flow is easily simulated with a Monte Carlo method. In this study a Visual Basic for Excel (VBA) code is developed to simulate the molecular beam originating from a vaporizing condensed phase in a Knudsen cell and passing through the cell orifice and the two apertures. RESULTS: The code is able to calculate the transmission coefficient through the cell orifice, through the cell orifice and the first aperture, and through the cell orifice and first and second apertures. Also calculated are the angular distributions of the effusate density emerging from the cell and average number of collisions with the orifice walls. CONCLUSIONS: This code allows the geometry (aperture spacing and diameters) of the sampling system to be optimized for maximum transmission. The calculated effusate distributions and low average number of orifice wall collisions illustrated the advantages of restricted collimation. Calculated transmission factors are also compared to literature values calculated via the analytical method of Chatillon and colleagues

Genetic and environmental influences on sleep quality in middle‐aged men: a twin study

Poor sleep quality is a risk factor for a number of cognitive and physiological age-related disorders. Identifying factors underlying sleep quality are important in understanding the etiology of these age-related health disorders. We investigated the extent to which genes and the environment contribute to subjective sleep quality in middle-aged male twins using the classical twin design. We used the Pittsburgh Sleep Quality Index to measure sleep quality in 1218 middle-aged twin men from the Vietnam Era Twin Study of Aging (mean age = 55.4 years; range 51-60; 339 monozygotic twin pairs, 257 dizygotic twin pairs, 26 unpaired twins). The mean PSQI global score was 5.6 [SD = 3.6; range 0-20]. Based on univariate twin models, 34% of variability in the global PSQI score was due to additive genetic effects (heritability) and 66% was attributed to individual-specific environmental factors. Common environment did not contribute to the variability. Similarly, the heritability of poor sleep-a dichotomous measure based on the cut-off of global PSQI>5-was 31%, with no contribution of the common environment. Heritability of six of the seven PSQI component scores (subjective sleep quality, sleep latency, sleep duration, habitual sleep efficiency, sleep disturbances, and daytime dysfunction) ranged from 0.15 to 0.31, whereas no genetic influences contributed to the use of sleeping medication. Additive genetic influences contribute to approximately one-third of the variability of global subjective sleep quality. Our results in middle-aged men constitute a first step towards examination of the genetic relationship between sleep and other facets of aging.Accepted manuscrip

Second generation Robo-AO instruments and systems

The prototype Robo-AO system at the Palomar Observatory 1.5-m telescope is the world's first fully automated laser adaptive optics instrument. Scientific operations commenced in June 2012 and more than 12,000 observations have since been performed at the ~0.12" visible-light diffraction limit. Two new infrared cameras providing high-speed tip-tilt sensing and a 2' field-of-view will be integrated in 2014. In addition to a Robo-AO clone for the 2-m IGO and the natural guide star variant KAPAO at the 1-m Table Mountain telescope, a second generation of facility-class Robo-AO systems are in development for the 2.2-m University of Hawai'i and 3-m IRTF telescopes which will provide higher Strehl ratios, sharper imaging, ~0.07", and correction to {\lambda} = 400 nm.Comment: 11 pages, 4 figures, 3 table

Gaps in the Saturation Spectrum of Trees

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n, H), while the maximum size is the well studied extremal number, ex(n, H). The saturation spectrum for a graph H is the set of sizes of H-saturated graphs between sat(n, H) and ex(n, H). In this paper we show that paths, trees with a vertex adjacent to many leaves, and brooms have a gap in the saturation spectrum