Generalized van der Waerden Game on an Infinite Board

Consider the following Maker-Breaker game. Fix a finite subset $S\subset\mathbb{N}$ of the naturals. The players Maker and Breaker take turns choosing previously unclaimed natural numbers. Maker wins by eventually building a copy $aS+b$ of $S$, where $a\in\mathbb{N}\setminus\{0\}$ and $b\in\mathbb{Z}$. This is a generalization of a game analyzed by Beck. We show that Maker can win in $|S|$ moves if $|S|\leq 3$. When $|S|=4$, we show that Maker can always win in $5$ or less moves, and describe all $S$ such that Maker can win in $4$ moves. If $|S|\geq 5$, Maker has no winning strategy in $|S|$ moves.Comment: 10 pages, 6 figure

Kiloparsec-scale Spatial Offsets in Double-peaked Narrow-line Active Galactic Nuclei. I. Markers for Selection of Compelling Dual Active Galactic Nucleus Candidates

Merger-remnant galaxies with kpc-scale separation dual active galactic nuclei (AGNs) should be widespread as a consequence of galaxy mergers and triggered gas accretion onto supermassive black holes, yet very few dual AGNs have been observed. Galaxies with double-peaked narrow AGN emission lines in the Sloan Digital Sky Survey are plausible dual AGN candidates, but their double-peaked profiles could also be the result of gas kinematics or AGN-driven outflows and jets on small or large scales. To help distinguish between these scenarios, we have obtained spatial profiles of the AGN emission via follow-up long-slit spectroscopy of 81 double-peaked narrow-line AGNs in SDSS at 0.03 < z < 0.36 using Lick, Palomar, and MMT Observatories. We find that all 81 systems exhibit double AGN emission components with ~kpc projected spatial separations on the sky, which suggests that they are produced by kpc-scale dual AGNs or kpc-scale outflows, jets, or rotating gaseous disks. In addition, we find that the subsample (58%) of the objects with spatially compact emission components may be preferentially produced by dual AGNs, while the subsample (42%) with spatially extended emission components may be preferentially produced by AGN outflows. We also find that for 32% of the sample the two AGN emission components are preferentially aligned with the host galaxy major axis, as expected for dual AGNs orbiting in the host galaxy potential. Our results both narrow the list of possible physical mechanisms producing the double AGN components, and suggest several observational criteria for selecting the most promising dual AGN candidates from the full sample of double-peaked narrow-line AGNs. Using these criteria, we determine the 17 most compelling dual AGN candidates in our sample.Comment: 12 pages, 8 figures, published in ApJ. Modified from original version to reflect referee's comment

How to Embed a Librarian

Librarians were embedded in two Vanderbilt University courses in 2006. The largest undergraduate program is Human and Organization Development at the Peabody College of Education and Human Development. As part of an integrated approach, the librarians proposed an “embedded librarian” for a freshmen course of 107 students. A librarian audited a course. As a member of the class, she was informed about the assignments. She scheduled optional workshops that were tailored to the students needs. At the Owen Graduate School of Management, an embedded librarian worked with 65 undergraduate students from a variety of non-business majors at Vanderbilt. They participated in the intensive 4-week “Accelerator” summer program. The purpose of embedding a librarian was to instill business information fluency and to stress the value of information in academic and real-world situations. Highlighting their experiences, the embedded librarians and a course professor will present their observations and discuss expected outcomes. They will give advice for those who want to institute this program in their own institutions

Analysis of the Relationship Between Diet and Exercise Beliefs and Actual Behaviors Among Breast Cancer Survivors in Northwest Ohio

Introduction: Studies have shown that a diet high in fruit and vegetable intake, as well as a routine including daily exercise or physical activity, can independently affect relapse rates and survivorship in breast cancer patients. Fruits and vegetables contain powerful anti-oxidant molecules, capable of preventing tumor formation and proliferation. Exercise can lower circulating levels of estrogen, the female hormone responsible for tumor proliferation in the estrogen-sensitive form of the disease. The most beneficial results have been shown in women who exercise and consume a diet rich in fruits and vegetables. We studied the attitudes towards and behaviors related to fruit and vegetable intake and exercise in a cohort of breast cancer survivors in northwest Ohio. Materials and Methods: Data were gathered from a survey sent out by the Northwest Ohio Branch of the Susan G. Komen For the Cure Foundation. We assessed and evaluated survivors’ self-reported beliefs, attitudes, and behaviors regarding exercise and fruit and vegetable intake. Results: Nearly half of the survivors (46.5%) reported being unsure or in disagreement with the statement “Eating at least 5 servings of fruits and/or vegetables per day will reduce the risk of breast cancer recurrence.” Only 46.8% of those in agreement with the previous statement actually report eating at least 5 fruits and/or vegetables per day. With respect to exercise, 32.9% reported being unsure or in disagreement with the statement “Engaging in regular physical activity will reduce the risk of breast cancer recurrence.” Only 68.5% of those in agreement with the previous statement report any physical activity in the past 30 days. Conclusions: Many breast cancer survivors do not appear to be aware of the benefits of diet and exercise. Further, a large proportion of those who are aware of the benefits do not adapt a healthy diet and exercise as part of their lifestyle. A majority of these survivors see a primary care physician, which we believe is the best venue to bridge this education gap. It is apparent by the pattern our data shows that more needs to be done to educate breast cancer survivors about the benefits of exercise and fruit and vegetable intake. Steps need to be taken to ensure that those who are educated also remain motivated to engage in a healthy lifestyle with the hopes of avoiding breast cancer recurrence