Regular systems of paths and families of convex sets in convex position

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five is in convex position. (If each pair of bodies have at most two common tangents it is enough to assume that every triple is in convex position, and likewise, if each pair of bodies have at most four common tangents it is enough to assume that every quadruple is in convex position.) This confirms a conjecture of Pach and Toth, and generalizes a theorem of Bisztriczky and Fejes Toth. Our results on families of convex bodies are consequences of more general Ramsey-type results about the crossing patterns of systems of graphs of continuous functions $f:[0,1] \to \mathbb{R}$. On our way towards proving the Pach-Toth conjecture we obtain a combinatorial characterization of such systems of graphs in which all subsystems of equal size induce equivalent crossing patterns. These highly organized structures are what we call regular systems of paths and they are natural generalizations of the notions of cups and caps from the famous theorem of Erdos and Szekeres. The characterization of regular systems is combinatorial and introduces some auxiliary structures which may be of independent interest

The Erd\H{o}s-Szekeres problem for non-crossing convex sets

We show an equivalence between a conjecture of Bisztriczky and Fejes T{\'o}th about arrangements of planar convex bodies and a conjecture of Goodman and Pollack about point sets in topological affine planes. As a corollary of this equivalence we improve the upper bound of Pach and T\'{o}th on the Erd\H{o}s-Szekeres theorem for disjoint convex bodies, as well as the recent upper bound obtained by Fox, Pach, Sudakov and Suk, on the Erd\H{o}s-Szekeres theorem for non-crossing convex bodies. Our methods also imply improvements on the positive fraction Erd\H{os}-Szekeres theorem for disjoint (and non-crossing) convex bodies, as well as a generalization of the partitioned Erd\H{o}s-Szekeres theorem of P\'{o}r and Valtr to arrangements of non-crossing convex bodies

The Shadows of a Cycle Cannot All Be Paths

A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three shadows of a cycle (i.e., a simple closed curve) in $\mathbb R^3$ to be paths (i.e., simple open curves). We also show two contrasting results: the three shadows of a path in $\mathbb R^3$ can all be cycles (although not all convex) and, for every $d\geq 1$, there exists a $d$-sphere embedded in $\mathbb R^{d+2}$ whose $d+2$ shadows have no holes (i.e., they deformation-retract onto a point).Comment: 6 pages, 10 figure

ARE ECONOMIC FUNDAMENTALS DRIVING FARMLAND VALUES?

Farmland, Land Value, Agricultural Finance, Land Economics/Use, Q14, Q15,

Psychiatric disorders, psychotropic medication use and falls among women: an observational study

BACKGROUND: Psychotropic agents known to cause sedation are associated with an increased risk of falls, but the role of psychiatric illness as an independent risk factor for falls is not clear. Thus, this study aimed to investigate the association between psychiatric disorders, psychotropic medication use and falls risk. METHODS: This study examined data collected from 1062 women aged 20-93 yr (median 50 yr) participating in the Geelong Osteoporosis Study, a large, ongoing, population-based study. Depressive and anxiety disorders for the preceding 12-month period were ascertained by clinical interview. Current medication use and falls history were self-reported. Participants were classified as fallers if they had fallen to the ground at least twice during the same 12-month period. Anthropometry, demographic, medical and lifestyle factors were determined. Logistic regression was used to test the associations, after adjusting for potential confounders. RESULTS: Fifty-six women (5.3%) were classified as fallers. Those meeting criteria for depression within the past 12 months had a 2.4-fold increased odds of falling (unadjusted OR = 2.4, 95% CI 1.2-4.5). Adjustment for age and mobility strengthened the relationship (adjusted OR = 2.7, 95% CI 1.4-5.2) between depression and falling, with results remaining unchanged following further adjustment for psychotropic medication use (adjusted OR = 2.7, 95% CI 1.3-5.6). In contrast, past (prior to 12-month) depression were not associated with falls. No association was observed between anxiety and falls risk. Falling was associated with psychotropic medication use (unadjusted OR = 2.8, 95% CI 1.5-5.2), as well as antidepressant (unadjusted OR = 2.4, 95% CI 1.2-4.8) and benzodiazepine use (unadjusted OR = 3.4, 95% CI 1.6-7.3); associations remained unchanged following adjustment for potential confounders. CONCLUSION: The likelihood of falls was increased among those with depression within the past 12 months, independent of psychotropic medication use and other recognised confounders, suggesting an independent effect of depression on falls risk. Psychotropic drug use was also confirmed as an independent risk factor for falls, but anxiety disorders were not. Further research into the underlying mechanisms is warranted

Extreme oxygen isotope zoning in garnet and zircon from a metachert block in melange reveals metasomatism at the peak of subduction metamorphism

A tectonic block of garnet quartzite in the amphibolite-facies melange of the Catalina Schist (Santa Catalina Island, California, USA) records the metasomatic pre-treatment of high-delta O-18 sediments as they enter the subduction zone. The block is primarily quartz, but contains two generations of garnet that record extreme oxygen isotope disequilibrium and inverse fractionations between garnet cores and matrix quartz. Rare millimeter-scale garnet crystals record prograde cation zoning patterns, whereas more abundant similar to 200-mu m-diameter crystals have the same composition as rims on the larger garnets. Garnets of both generations have high-delta O-18 cores (20.8 parts per thousand-26.3 parts per thousand, Vienna standard mean ocean water) that require an unusually high-delta O-18 protolith and lower-delta O-18, less variable rims (10.0 parts per thousand-11.2 parts per thousand). Matrix quartz values are homogeneous (13.6 parts per thousand). Zircon crystals contain detrital cores (delta O-18 = 4.7 parts per thousand-8.5 parts per thousand, 124.6 + 1.4/-2.9 Ma) with a characteristic igneous trace element composition likely sourced from arc volcanics, surrounded by zircon with metamorphic age (115.1 +/- 2.5 Ma) and trace element compositions that suggest growth in the presence of garnet. Metamorphic zircon decreases in delta O-18 from near-core (24.1 parts per thousand) to rim (12.4 parts per thousand), in equilibrium with zoned garnets. Collectively, the data document the subduction of a mixed high-delta O-18 siliceous ooze and/or volcanic ash protolith reaching temperatures of 550-625 degrees C prior to the nucleation of small garnets without influence from external fluids. Metasomatism was recorded in rims of both garnet and zircon populations as large volumes of broadly homogeneous subduction fluids stripped matrix quartz of its extremely high oxygen isotope signature. Thus, zoned garnet and zircon in high-delta O-18 subducted sediments offer a detailed window into subduction fluids

Effects of an evidence service on community-based AIDS service organizations' use of research evidence: A protocol for a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>To support the use of research evidence by community-based organizations (CBOs) we have developed 'Synthesized HIV/AIDS Research Evidence' (SHARE), which is an evidence service for those working in the HIV sector. SHARE consists of several components: an online searchable database of HIV-relevant systematic reviews (retrievable based on a taxonomy of topics related to HIV/AIDS and open text search); periodic email updates; access to user-friendly summaries; and peer relevance assessments. Our objective is to evaluate whether this 'full serve' evidence service increases the use of research evidence by CBOs as compared to a 'self-serve' evidence service.</p> <p>Methods/design</p> <p>We will conduct a two-arm randomized controlled trial (RCT), along with a follow-up qualitative process study to explore the findings in greater depth. All CBOs affiliated with Canadian AIDS Society (n = 120) will be invited to participate and will be randomized to receive either the 'full-serve' version of SHARE or the 'self-serve' version (a listing of relevant systematic reviews with links to records on PubMed and worksheets that help CBOs find and use research evidence) using a simple randomized design. All management and staff from each organization will be provided access to the version of SHARE that their organization is allocated to. The trial duration will be 10 months (two-month baseline period, six-month intervention period, and two month crossover period), the primary outcome measure will be the mean number of logins/month/organization (averaged across the number of users from each organization) between baseline and the end of the intervention period. The secondary outcome will be intention to use research evidence as measured by a survey administered to one key decision maker from each organization. For the qualitative study, one key organizational decision maker from 15 organizations in each trial arm (n = 30) will be purposively sampled. One-on-one semi-structured interviews will be conducted by telephone on their views about and their experiences with the evidence service they received, how helpful it was in their work, why it was helpful (or not helpful), what aspects were most and least helpful and why, and recommendations for next steps.</p> <p>Discussion</p> <p>To our knowledge, this will be the first RCT to evaluate the effects of an evidence service specifically designed to support CBOs in finding and using research evidence.</p> <p>Trial registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT01257724">NCT01257724</a></p