Quasigeometric Distributions and Extra Inning Baseball Games

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and the game had to be stopped at that point. Under the new rules, the All-Star Game must be played until there is a winner, no matter how long it takes, so the managers need to consider the possibility of a long extra inning game. This should lead the managers to ask themselves what the probability is that the game will last 12 innings. What about 20 innings? Longer? In this paper, we address these questions and several other questions related to the game of baseball. Our methods use a variation on the well-studied geometric distribution called the quasigeometric distribution. We begin by reviewing some of the literature on applications of mathematics to baseball. In the second section we will define the quasigeometric distribution and examine several of its properties. The final two sections examine the applications of this distribution to models of scoring patterns in baseball games and, more specifically, the length of extra inning games

Electron beam X-Y deflection system Final report

Design and fabrication of electron beam X-Y deflection system for retrofit on welding gun

Predicting uncertainty in sediment transport and landscape evolution - the influence of initial surface conditions

© 2015. Numerical landscape evolution models were initially developed to examine natural catchment hydrology and geomorphology and have become a common tool to examine geomorphic behaviour over a range of time and space scales. These models all use a digital elevation model (DEM) as a representation of the landscape surface and a significant issue is the quality and resolution of this surface. Here we focus on how subtle perturbations or roughness on the DEM surface can produce alternative model results. This study is carried out by randomly varying the elevations of the DEM surface and examining the effect on sediment transport rates and geomorphology for a proposed rehabilitation design for a post-mining landscape using multiple landscape realisations with increasing magnitudes of random changes. We show that an increasing magnitude of random surface variability does not appear to have any significant effect on sediment transport over millennial time scales. However, the random surface variability greatly changes the temporal pattern or delivery of sediment output. A significant finding is that all simulations at the end of the 10,000 year modelled period are geomorphologically similar and present a geomorphological equifinality. However, the individual patterns of erosion and deposition were different for repeat simulations with a different sequence of random perturbations. The alternative positions of random perturbations strongly influence local patterns of hillslope erosion and evolution together with the pattern and behaviour of deposition. The findings demonstrate the complex feedbacks that occur even within a simple modelled system

Integrated optical directional coupler biosensor

We present measurements on biomolecular binding reactions, using a new type of integrated optical biosensor based on a planar directional coupler structure. The device is fabricated by Ag+-Na+ ion-exchange in glass and definition of the sensing region is achieved by use of transparent fluoropolymer isolation layers formed by thermal evaporation. The suitability of the sensor for application to the detection of environmental pollutants is considered

Stratigraphy of stable isotope ratios and leaf structure within an African rainforest canopy with implications for primate isotope ecology

The canopy effect describes vertical variation in the isotope ratios of carbon (δ(13)C), oxygen (δ(18)O) and partially nitrogen (δ(15)N) within plants throughout a closed canopy forest, and may facilitate the study of canopy feeding niches in arboreal primates. However, the nuanced relationship between leaf height, sunlight exposure and the resulting variation in isotope ratios and leaf mass per area (LMA) has not been documented for an African rainforest. Here, we present δ(13)C, δ(18)O and δ(15)N values of leaves (n = 321) systematically collected from 58 primate food plants throughout the canopy (0.3 to 42 m) in Côte d’Ivoire, West Africa. Besides leaf sample height and light availability, we measured leaf nitrogen and carbon content (%N, %C), as well as LMA (n = 214) to address the plants’ vertical resource allocations. We found significant variation in δ(13)C, δ(18)O and δ(15)N, as well as LMA in response to height in combination with light availability and tree species, with low canopy leaves depleted in (13)C, (18)O and (15)N and slightly higher in %N compared to higher canopy strata. While this vertical isotopic variation was not well reflected in the δ(13)C and δ(15)N of arboreal primates from this forest, it did correspond well to primate δ(18)O values

Compensation of Strong Thermal Lensing in High Optical Power Cavities

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors such as Advanced LIGO, we show that strong thermal lenses form in accordance with predictions and that they can be compensated using an intra-cavity compensation plate heated on its cylindrical surface. We show that high finesse ~1400 can be achieved in cavities with internal compensation plates, and that the cavity mode structure can be maintained by thermal compensation. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.Comment: 8 page

Interactions of asbestos-activated macrophages with an experimental fibrosarcoma

Supernatants from in vivo asbestos-activated macrophages failed to show any cytostatic activity against a syngeneic fibrosarcoma cell line in vitro. UICC chrysotile-induced peritoneal exudate cells also failed to demonstrate any growth inhibitory effect on the same cells in Winn assays of tumor growth. Mixing UICC crocidolite with inoculated tumor cells resulted in a dose-dependent inhibition of tumor growth; this could, however, be explained by a direct cytostatic effect on the tumor cells of high doses of crocidolite, which was observed in vitro