Alternating sign matrices and domino tilings

We introduce a family of planar regions, called Aztec diamonds, and study the ways in which these regions can be tiled by dominoes. Our main result is a generating function that not only gives the number of domino tilings of the Aztec diamond of order $n$ but also provides information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Several proofs of the formula are given. The problem turns out to have connections with the alternating sign matrices of Mills, Robbins, and Rumsey, as well as the square ice model studied by Lieb

Bibliography of Sources on Dena’ina and Cook Inlet Anthropology Through 2016

This version 4.3 will be the final version for this bibliography, a project that was begun in 1993 by Greg Dixon. We have intentionally excluded all potential references for the year 2017. This version is about 29 pages longer and has about 211 entries added since the previous version 3.1 of 2012. Aaron Leggett has added over fifty sources many being rare items from newpapers and magazines. Also many corrections and additions were made to entries in earlier versions.I wish to thank Kenaitze Indian Tribe and the “Dena’ina Language Revitalization Project” for their support for several projects during 2017-2018, including this Vers. 4.3. Previous versions have had partial support from "Dena'ina Archiving, Training and Access" project (NSF-OPP 0326805, 2004) and from Lake Clark National Park. I thank Katherine Arndt of Alaska & Polar Regions at UAF for her careful proofreading

National Rugby League athletes and tendon tap reflex assessment: A matched cohort clinical study

BACKGROUND: Limited research suggests elite athletes may differ from non-athletes in clinical tendon tap reflex responses. METHODS: In this matched cohort study, 25 elite rugby league athletes were compared with 29 non-athletes to examine differences in tendon reflex responses. Relationships between reflex responses and lengths of players’ careers were also examined. Biceps, triceps, patellar and Achilles tendon reflexes were clinically assessed. RESULTS: Right and left reflexes were well correlated for each tendon (r(S) = 0.7–0.9). The elite rugby league athletes exhibited significantly weaker reflex responses than non-athletes in all four tendons (p < 0.005). Biceps reflexes demonstrated the largest difference and Achilles reflexes the smallest difference. Moderate negative correlations (r(S) = −0.3–0.6) were observed between reflex responses and lengths of players’ careers. CONCLUSIONS: Future research is required to further elucidate mechanisms resulting in the observed differences in tendon reflexes and to ensure clinical tendon tap examinations and findings can be interpreted appropriately in this athletic population