Chutes and Ladders with Large Spinners

We prove a conjecture from a 2011 College Mathematics Journal article addressing the expected number of turns in a Chutes and Ladders game when the spinner range is close to the length of the board. While the original paper approached the question using linear algebra and the theory of Markov processes, our main method uses combinatorics and recursion

Allee Effects May Slow the Spread of Parasites in a Coastal Marine Ecosystem

Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of uninfected wild juvenile Pacific salmon populations by ectoparasitic salmon lice (Lepeophtheirus salmonis) over a 4-year period. In a data set of 68,376 fish, we observed 85 occurrences of precopular pair formation among 1,259 preadult female and 613 adult male lice. The probability of pair formation was dependent on the local abundance of lice, but this mate limitation is likely offset somewhat by mate-searching dispersal of males among host fish. A mathematical model of macroparasite population dynamics that incorporates the empirical results suggests a high likelihood of a demographic Allee effect, which can cause the colonizing parasite populations to die out. These results may provide the first empirical evidence for Allee effects in a macroparasite. Furthermore, the data give a rare detailed view of Allee effects in colonization dynamics and suggest that Allee effects may dampen the spread of parasites in a coastal marine ecosystem

Development of a low-maintenance measurement approach to continuously estimate methane emissions: a case study

The chemical breakdown of organic matter in landfills represents a significant source of methane gas (CH4). Current estimates suggest that landfills are responsible for between 3% and 19% of global anthropogenic emissions. The net CH4 emissions resulting from biogeochemical processes and their modulation by microbes in landfills are poorly constrained by imprecise knowledge of environmental constraints. The uncertainty in absolute CH4 emissions from landfills is therefore considerable. This study investigates a new method to estimate the temporal variability of CH4 emissions using meteorological and CH4 concentration measurements downwind of a landfill site in Suffolk, UK from July to September 2014, taking advantage of the statistics that such a measurement approach offers versus shorter-term, but more complex and instantaneously accurate, flux snapshots. Methane emissions were calculated from CH4 concentrations measured 700 m from the perimeter of the landfill with observed concentrations ranging from background to 46.4 ppm. Using an atmospheric dispersion model, we estimate a mean emission flux of 709 μg m−2 s−1 over this period, with a maximum value of 6.21 mg m−2 s−1, reflecting the wide natural variability in biogeochemical and other environmental controls on net site emission. The emissions calculated suggest that meteorological conditions have an influence on the magnitude of CH4 emissions. We also investigate the factors responsible for the large variability observed in the estimated CH4 emissions, and suggest that the largest component arises from uncertainty in the spatial distribution of CH4 emissions within the landfill area. The results determined using the low-maintenance approach discussed in this paper suggest that a network of cheaper, less precise CH4 sensors could be used to measure a continuous CH4 emission time series from a landfill site, something that is not practical using far-field approaches such as tracer release methods. Even though there are limitations to the approach described here, this easy, low-maintenance, low-cost method could be used by landfill operators to estimate time-averaged CH4 emissions and their impact downwind by simultaneously monitoring plume advection and CH4 concentrations

Interviews with the Apollo lunar surface astronauts in support of planning for EVA systems design

Focused interviews were conducted with the Apollo astronauts who landed on the moon. The purpose of these interviews was to help define extravehicular activity (EVA) system requirements for future lunar and planetary missions.RTOP 199-06-1

Action video game play and transfer of navigation and spatial cognition skills in adolescents who are blind

For individuals who are blind, navigating independently in an unfamiliar environment represents a considerable challenge. Inspired by the rising popularity of video games, we have developed a novel approach to train navigation and spatial cognition skills in adolescents who are blind. Audio-based Environment Simulator (AbES) is a software application that allows for the virtual exploration of an existing building set in an action video game metaphor. Using this ludic-based approach to learning, we investigated the ability and efficacy of adolescents with early onset blindness to acquire spatial information gained from the exploration of a target virtual indoor environment. Following game play, participants were assessed on their ability to transfer and mentally manipulate acquired spatial information on a set of navigation tasks carried out in the real environment. Success in transfer of navigation skill performance was markedly high suggesting that interacting with AbES leads to the generation of an accurate spatial mental representation. Furthermore, there was a positive correlation between success in game play and navigation task performance. The role of virtual environments and gaming in the development of mental spatial representations is also discussed. We conclude that this game based learning approach can facilitate the transfer of spatial knowledge and further, can be used by individuals who are blind for the purposes of navigation in real-world environments

Virtual environments for the transfer of navigation skills in the blind: a comparison of directed instruction vs. video game based learning approaches

For profoundly blind individuals, navigating in an unfamiliar building can represent a significant challenge. We investigated the use of an audio-based, virtual environment called Audio-based Environment Simulator (AbES) that can be explored for the purposes of learning the layout of an unfamiliar, complex indoor environment. Furthermore, we compared two modes of interaction with AbES. In one group, blind participants implicitly learned the layout of a target environment while playing an exploratory, goal-directed video game. By comparison, a second group was explicitly taught the same layout following a standard route and instructions provided by a sighted facilitator. As a control, a third group interacted with AbES while playing an exploratory, goal-directed video game however, the explored environment did not correspond to the target layout. Following interaction with AbES, a series of route navigation tasks were carried out in the virtual and physical building represented in the training environment to assess the transfer of acquired spatial information. We found that participants from both modes of interaction were able to transfer the spatial knowledge gained as indexed by their successful route navigation performance. This transfer was not apparent in the control participants. Most notably, the game-based learning strategy was also associated with enhanced performance when participants were required to find alternate routes and short cuts within the target building suggesting that a ludic-based training approach may provide for a more flexible mental representation of the environment. Furthermore, outcome comparisons between early and late blind individuals suggested that greater prior visual experience did not have a significant effect on overall navigation performance following training. Finally, performance did not appear to be associated with other factors of interest such as age, gender, and verbal memory recall. We conclude that the highly interactive and immersive exploration of the virtual environment greatly engages a blind user to develop skills akin to positive near transfer of learning. Learning through a game play strategy appears to confer certain behavioral advantages with respect to how spatial information is acquired and ultimately manipulated for navigation

X- and gamma-ray observations of the 15 November 1991 Solar Flare

This work expands the current understanding of the 15 November 1991 Solar Flare. The flare was a well observed event in radio to gamma-rays and is the first flare to be extensively studied with the benefit of detailed soft and hard X-ray images. In this work, we add data from all four instruments on the Compton Gamma Ray Observatory. Using these data we determined that the accelerated electron spectrum above 170 keV is best fit with a power law with a spectral index of −4.6, while the accelerated proton spectrum above 0.6 MeV is fit with a power law of spectral index −4.5. From this we computed lower limits for the energy content of these particles of∼1023 ergs (electrons) and ∼1027 ergs (ions above 0.6 MeV). These particles do not have enough energy to produce the white-light emission observed from this event. We computed a time constant of 26+20−15 s for the 2.223 MeV neutron capture line, which is consistent at the 2σ level with the lowest values of ∼70 s found for other flares. The mechanism for this short capture time may be better understood after analyses of high energy EGRET data that show potential evidence for pion emission near ∼100 MeV

Energetic proton spectra in the 11 June 1991 solar flare

We have studied a subset of the 11 June 1991 solar flare γ-ray data that we believe arise from soft proton or ion spectra. Using data from the COMPTEL instrument on the Compton Observatory we discuss the gamma-ray intensities at 2.223 MeV, 4–7 MeV, and 8–30 MeV in terms of the parent proton spectrum responsible for the emission

The Locations of Gamma-Ray Bursts Measured by COMPTEL

The COMPTEL instrument on the Compton Gamma Ray Observatory is used to measure the locations of gamma-ray bursts through direct imaging of MeV photons. In a comprehensive search, we have detected and localized 29 bursts observed between 1991 April 19 and 1995 May 31. The average location accuracy of these events is 1.25\arcdeg (1$\sigma$), including a systematic error of \sim0.5\arcdeg, which is verified through comparison with Interplanetary Network (IPN) timing annuli. The combination of COMPTEL and IPN measurements results in locations for 26 of the bursts with an average ``error box'' area of only $\sim$0.3 deg$^2$ (1$\sigma$). We find that the angular distribution of COMPTEL burst locations is consistent with large-scale isotropy and that there is no statistically significant evidence of small-angle auto-correlations. We conclude that there is no compelling evidence for burst repetition since no more than two of the events (or $\sim$7% of the 29 bursts) could possibly have come from the same source. We also find that there is no significant correlation between the burst locations and either Abell clusters of galaxies or radio-quiet quasars. Agreement between individual COMPTEL locations and IPN annuli places a lower limit of $\sim$100~AU (95% confidence) on the distance to the stronger bursts.Comment: Accepted for publication in the Astrophysical Journal, 1998 Jan. 1, Vol. 492. 33 pages, 9 figures, 5 table