Teaching a University Course on the Mathematics of Gambling

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a course on the mathematics of gambling

Iterating bonferroni bounds

A general method is presented for generating improved Bonferroni bounds whenever an improvement on Booles inequality holds.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25646/1/0000198.pd

The red-sky enigma over Svalbard in December 2002

On 6 December 2002, during winter darkness, an extraordinary event occurred in the sky, as viewed from Longyearbyen (78° N, 15° E), Svalbard, Norway. At 07:30 UT the southeast sky was surprisingly lit up in a deep red colour. The light increased in intensity and spread out across the sky, and at 10:00 UT the illumination was observed to reach the zenith. The event died out at about 12:30 UT. Spectral measurements from the Auroral Station in Adventdalen confirm that the light was scattered sunlight. Even though the Sun was between 11.8 and 14.6deg below the horizon during the event, the measured intensities of scattered light on the southern horizon from the scanning photometers coincided with the rise and setting of the Sun. Calculations of actual heights, including refraction and atmospheric screening, indicate that the event most likely was scattered solar light from a target below the horizon. This is also confirmed by the OSIRIS instrument on board the Odin satellite. The deduced height profile indicates that the scattering target is located 18–23km up in the stratosphere at a latitude close to 73–75° N, southeast of Longyearbyen. The temperatures in this region were found to be low enough for Polar Stratospheric Clouds (PSC) to be formed. The target was also identified as PSC by the LIDAR systems at the Koldewey Station in Ny-Ålesund (79° N, 12° E). The event was most likely caused by solar illuminated type II Polar Stratospheric Clouds that scattered light towards Svalbard. Two types of scenarios are presented to explain how light is scattered.publishedVersio

Exile Vol. XVII No. 1

FICTION The Backyard Burial by Heather Johnson 9-11 French Persuasion by John Benes 18-22 In His Time by Keith Mcwalter 27-37 Time Ticking Off, Not Stopping by Holly Battles 39-40 ARTWORK by Roxy Sisson 13 by Bill Lutz 16 by Carol Belfatto 17 by Ned Bittinger 23 by Gail Lutsch 41 by Diane Ulmer 43 PHOTOGRAPHY by Tim Heth 3, 4, 5, 7, 9, 12, 15, 22, 38, 40, 44 by Rip Odell 15 by Maggie Hernandez 26, 42 POETRY For G. S. & A. B. T. by Paul Holbrook 2 Picture Writer by Julie Lockwood 6 Youth by Rufus Hurst 6 Today I Watched Flies Without Wings by Alice Merrill 6 Room 102 by Alice Merrill 6 The Flick by Debby Snyder 8 For P. E. H. by Timothy Cope 12 In Memory of Gertrude Stein by Michael Daugherty 14 Apogee Analogy by Paul Holbrook 15 First Impressions by Austin Hartman, Jr. 16 Count Jack Playing Peasant by Alice Merrill 24 Cherokee Arrowsmith by R. Crozier 24 road runs down valley by Fred Hoppe 25 Singularity by M. J. Wallace 25 Love\u27s Labour Lost by Tina Ostergard 25 Gnome by Cary Spear 25 Design and Layout: Keith McWalter 1 EXILE is the literary magazine of Denison University. It is entirely student-run and student edited, and receives operating funds from the Denison Campus Government Association. Submissions are edited anonymously and final actions are made independently by each staff. Printed by Ace News, Heath, Ohio.

Quantifying HIV transmission flow between high-prevalence hotspots and surrounding communities: a population-based study in Rakai, Uganda.

BACKGROUND: International and global organisations advocate targeting interventions to areas of high HIV prevalence (ie, hotspots). To better understand the potential benefits of geo-targeted control, we assessed the extent to which HIV hotspots along Lake Victoria sustain transmission in neighbouring populations in south-central Uganda. METHODS: We did a population-based survey in Rakai, Uganda, using data from the Rakai Community Cohort Study. The study surveyed all individuals aged 15-49 years in four high-prevalence Lake Victoria fishing communities and 36 neighbouring inland communities. Viral RNA was deep sequenced from participants infected with HIV who were antiretroviral therapy-naive during the observation period. Phylogenetic analysis was used to infer partial HIV transmission networks, including direction of transmission. Reconstructed networks were interpreted through data for current residence and migration history. HIV transmission flows within and between high-prevalence and low-prevalence areas were quantified adjusting for incomplete sampling of the population. FINDINGS: Between Aug 10, 2011, and Jan 30, 2015, data were collected for the Rakai Community Cohort Study. 25 882 individuals participated, including an estimated 75·7% of the lakeside population and 16·2% of the inland population in the Rakai region of Uganda. 5142 participants were HIV-positive (2703 [13·7%] in inland and 2439 [40·1%] in fishing communities). 3878 (75·4%) people who were HIV-positive did not report antiretroviral therapy use, of whom 2652 (68·4%) had virus deep-sequenced at sufficient quality for phylogenetic analysis. 446 transmission networks were reconstructed, including 293 linked pairs with inferred direction of transmission. Adjusting for incomplete sampling, an estimated 5·7% (95% credibility interval 4·4-7·3) of transmissions occurred within lakeside areas, 89·2% (86·0-91·8) within inland areas, 1·3% (0·6-2·6) from lakeside to inland areas, and 3·7% (2·3-5·8) from inland to lakeside areas. INTERPRETATION: Cross-community HIV transmissions between Lake Victoria hotspots and surrounding inland populations are infrequent and when they occur, virus more commonly flows into rather than out of hotspots. This result suggests that targeted interventions to these hotspots will not alone control the epidemic in inland populations, where most transmissions occur. Thus, geographical targeting of high prevalence areas might not be effective for broader epidemic control depending on underlying epidemic dynamics. FUNDING: The Bill & Melinda Gates Foundation, the National Institute of Allergy and Infectious Diseases, the National Institute of Mental Health, the National Institute of Child Health and Development, the Division of Intramural Research of the National Institute for Allergy and Infectious Diseases, the World Bank, the Doris Duke Charitable Foundation, the Johns Hopkins University Center for AIDS Research, and the President's Emergency Plan for AIDS Relief through the Centers for Disease Control and Prevention

Quantifying HIV transmission flow between high-prevalence hotspots and surrounding communities: a population-based study in Rakai, Uganda

Background International and global organisations advocate targeting interventions to areas of high HIV prevalence (ie, hotspots). To better understand the potential benefits of geo-targeted control, we assessed the extent to which HIV hotspots along Lake Victoria sustain transmission in neighbouring populations in south-central Uganda. Methods We did a population-based survey in Rakai, Uganda, using data from the Rakai Community Cohort Study. The study surveyed all individuals aged 15–49 years in four high-prevalence Lake Victoria fishing communities and 36 neighbouring inland communities. Viral RNA was deep sequenced from participants infected with HIV who were antiretroviral therapy-naive during the observation period. Phylogenetic analysis was used to infer partial HIV transmission networks, including direction of transmission. Reconstructed networks were interpreted through data for current residence and migration history. HIV transmission flows within and between high-prevalence and low-prevalence areas were quantified adjusting for incomplete sampling of the population. Findings Between Aug 10, 2011, and Jan 30, 2015, data were collected for the Rakai Community Cohort Study. 25 882 individuals participated, including an estimated 75·7% of the lakeside population and 16·2% of the inland population in the Rakai region of Uganda. 5142 participants were HIV-positive (2703 [13·7%] in inland and 2439 [40·1%] in fishing communities). 3878 (75·4%) people who were HIV-positive did not report antiretroviral therapy use, of whom 2652 (68·4%) had virus deep-sequenced at sufficient quality for phylogenetic analysis. 446 transmission networks were reconstructed, including 293 linked pairs with inferred direction of transmission. Adjusting for incomplete sampling, an estimated 5·7% (95% credibility interval 4·4–7·3) of transmissions occurred within lakeside areas, 89·2% (86·0–91·8) within inland areas, 1·3% (0·6–2·6) from lakeside to inland areas, and 3·7% (2·3–5·8) from inland to lakeside areas. Interpretation Cross-community HIV transmissions between Lake Victoria hotspots and surrounding inland populations are infrequent and when they occur, virus more commonly flows into rather than out of hotspots. This result suggests that targeted interventions to these hotspots will not alone control the epidemic in inland populations, where most transmissions occur. Thus, geographical targeting of high prevalence areas might not be effective for broader epidemic control depending on underlying epidemic dynamics. Funding The Bill & Melinda Gates Foundation, the National Institute of Allergy and Infectious Diseases, the National Institute of Mental Health, the National Institute of Child Health and Development, the Division of Intramural Research of the National Institute for Allergy and Infectious Diseases, the World Bank, the Doris Duke Charitable Foundation, the Johns Hopkins University Center for AIDS Research, and the President's Emergency Plan for AIDS Relief through the Centers for Disease Control and Prevention

The sampling theory of neutral alleles and an urn model in population genetics

The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46946/1/285_2004_Article_BF00276386.pd