On the odd cycle game and connected rules

We study the positional game where two players, Maker and Breaker, alternately select respectively 1 and b previously unclaimed edges of Kn. Maker wins if she succeeds in claiming all edges of some odd cycle in Kn and Breaker wins otherwise. Improving on a result of Bednarska and Pikhurko, we show that Maker wins the odd cycle game if b ≤ (4− √ 6)/5 +o(1)) n. We furthermore introduce “connected rules” and study the odd cycle game under them, both in the Maker-Breaker as well as in the Client-Waiter variant

Kinetic approaches to particle acceleration at cosmic ray modified shocks

Kinetic approaches provide an effective description of the process of particle acceleration at shock fronts and allow to take into account the dynamical reaction of the accelerated particles as well as the amplification of the turbulent magnetic field as due to streaming instability. The latter does in turn affect the maximum achievable momentum and thereby the acceleration process itself, in a chain of causality which is typical of non-linear systems. Here we provide a technical description of two of these kinetic approaches and show that they basically lead to the same conclusions. In particular we discuss the effects of shock modification on the spectral shape of the accelerated particles, on the maximum momentum, on the thermodynamic properties of the background fluid and on the escaping and advected fluxes of accelerated particles.Comment: 22 pages, 7 figures, accepted for publication in MNRA

Diabetes and disordered eating behaviours in a community-based sample of australian adolescents

Background:People with diabetes have been shown to be at risk for disordered eating compared to their non-diabetic peers. However, the majority of studies have been conducted in relatively small samples drawn from clinical diabetes settings or registries. Community-based samples are required to better understand disordered eating behaviours in this population. In a large community-based population sample of Australian adolescents, this study aimed to (1) investigate disordered eating behaviours in adolescents reporting a diagnosis of diabetes compared to their non-diabetic peers and (2) test associations between disordered eating behaviours and insulin restriction.Methods:Secondary school students (n = 4854; mean (SD) age 14.4 (1.6) years; 47% boys) completed an online survey, including self-reported presence of diabetes, demographics, weight status, substance use, insulin restriction and disordered eating behaviours. Clinically meaningful cut-offs for disordered eating behaviours were generated for analysis.Results:Disordered eating behaviours, specifically self-induced vomiting (diabetes 19.2%, no diabetes 3.3%; p p p p Conclusion:There was a high rate of disordered eating behaviours in adolescents with diabetes compared to their peers without diabetes. The findings of this study may have the potential to inform future health promotion, prevention, and early intervention approaches for those with comorbid diabetes and disordered eating behaviours. Future longitudinal studies are required to evaluate disordered eating behaviours in those with diabetes over time in community-based samples

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

Impacts of community resilience on the implementation of a mental health promotion program in rural Australia

Mental health promotion programs are important in rural communities but the factors which influence program effectiveness remain unclear. The aim of this mixed-methods study was to assess how community resilience affected the implementation of a mental health promotion program in rural Tasmania, Australia. Four study communities were selected based on population size, rurality, access to local support services, history of suicide within the community, and maturity of the mental health promotion program. Data from self-report questionnaires (n = 245), including items of Communities Advancing Resilience Toolkit (CART) assessment, and qualitative (focus group and interview) data from key local stakeholders (n = 24), were pooled to explore the factors perceived to be influencing program implementation. Survey results indicate the primary community resilience strengths across the four sites were related to the ‘Connection and Caring’ domain. The primary community resilience challenges related to resources. Qualitative findings suggested lack of communication and leadership are key barriers to effective program delivery and identified a need to provide ongoing support for program staff. Assessment of perceived community resilience may be helpful in informing the implementation of mental health promotion programs in rural areas and, in turn, improve the likelihood of their success and sustainability

Photolytic and thermolytic decomposition products from iron pentacarbonyl adsorbed on Y zeolite

Zeolite supported iron systems obtained by photolysis and thermolysis of Fe(CO)5/Na---Y adducts are characterized via evaluation of the respective magnetic isotherms taken with a FONER magnetometer at T = 4.2 K. Thermolysis under fast heating in inert gas and under fluidized shallow bed conditions completes within a few minutes at not, vert, similar 500 K, and gives iron clusters of which at least 70 to 90 wt% is smaller than 1 nm. Prolonged photolysis at 290 K in the same fluidized bed conditions does not result in the formation of ‘naked’ iron(O) clusters, but gives a limited fraction of magnetically coupled Fex(CO)y entities. Photodimerization cannot be excluded to be the main reaction path