Edge-choosability of multicircuits

AbstractA multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). The List-Colouring Conjecture (LCC) is that every multigraph G has edge-choosability (list chromatic index) ch′(G) equal to its chromatic index χ′(G). In this paper the LCC is proved first for multicircuits, and then, building on results of Peterson and Woodall, for any multigraph G in which every block is bipartite or a multicircuit or has at most four vertices or has underlying simple graph of the form K1, 1, p

The average degree of a multigraph critical with respect to edge or total choosability

AbstractLet G be a multigraph with maximum degree at most Δ⩾3 such that ch′(G)>Δ or ch″(G)>Δ+1 and G is minimal with this property. A new proof is given for the result (which was already known, apart from a simple calculation) that the average degree of G is greater than 2Δ except possibly in the second case when Δ=5

Exploring concepts of health with male prisoners in three category-C English prisons

Lay understandings of health and illness have a well established track record and a plethora of research now exists which has examined these issues. However, there is a dearth of research which has examined the perspectives of those who are imprisoned. This paper attempts to address this research gap. The paper is timely given that calls have been made to examine lay perspectives in different geographical locations and a need to re-examine health promotion approaches in prison settings. Qualitative data from thirty-six male sentenced prisoners from three prisons in England were collected. The data was analysed in accordance with Attride-Stirling's (2001) thematic network approach. Although the men's perceptions of health were broadly similar to the general population, some interesting findings emerged which were directly related to prison life and its associated structures. These included access to the outdoors and time out of their prison cell, as well as maintaining relationships with family members through visits. The paper proposes that prisoners' lay views should be given higher priority given that prison health has traditionally been associated with medical treatment and the bio-medical paradigm more generally. It also suggests that in order to fulfil the World Health Organization's (WHO) vision of viewing prisons as health promoting settings, lay views should be recognised to shape future health promotion policy and practice

A multidisciplinary approach for generating globally consistent data on mesophotic, deep-pelagic, and bathyal biological communities

Approaches to measuring marine biological parameters remain almost as diverse as the researchers who measure them. However, understanding the patterns of diversity in ocean life over different temporal and geographic scales requires consistent data and information on the potential environmental drivers. As a group of marine scientists from different disciplines, we suggest a formalized, consistent framework of 20 biological, chemical, physical, and socioeconomic parameters that we consider the most important for describing environmental and biological variability. We call our proposed framework the General Ocean Survey and Sampling Iterative Protocol (GOSSIP). We hope that this framework will establish a consistent approach to data collection, enabling further collaboration between marine scientists from different disciplines to advance knowledge of the ocean (deep-sea and mesophotic coral ecosystems)

Using funnel plots in public health surveillance

<p>Abstract</p> <p>Background</p> <p>Public health surveillance is often concerned with the analysis of health outcomes over small areas. Funnel plots have been proposed as a useful tool for assessing and visualizing surveillance data, but their full utility has not been appreciated (for example, in the incorporation and interpretation of risk factors).</p> <p>Methods</p> <p>We investigate a way to simultaneously focus funnel plot analyses on direct policy implications while visually incorporating model fit and the effects of risk factors. Health survey data representing modifiable and nonmodifiable risk factors are used in an analysis of 2007 small area motor vehicle mortality rates in Alberta, Canada.</p> <p>Results</p> <p>Small area variations in motor vehicle mortality in Alberta were well explained by the suite of modifiable and nonmodifiable risk factors. Funnel plots of raw rates and of risk adjusted rates lead to different conclusions; the analysis process highlights opportunities for intervention as risk factors are incorporated into the model. Maps based on funnel plot methods identify areas worthy of further investigation.</p> <p>Conclusions</p> <p>Funnel plots provide a useful tool to explore small area data and to routinely incorporate covariate relationships in surveillance analyses. The exploratory process has at each step a direct and useful policy-related result. Dealing thoughtfully with statistical overdispersion is a cornerstone to fully understanding funnel plots.</p

Damage Limitation: Learning Lessons from Complaints and Appeals Staff on the Handling of Student Grievance

Against a backdrop of rising student complaints in higher education (HE) and debate about students as consumers, increasing attention is turning to institutional processes for dealing with complaints and appeals. This paper draws on a nationwide survey across UK HE to explore the unique experiences of Complaints and Appeals staff. The research provides important new insights into the perceived benefits of student complaints as well as the challenges. The findings indicate a need to change the culture around complaints to help address issues such as time taken to resolve formal complaints, expectations of students and impact on student/staff relationships. Drawing on theoretical models of service failure from the business sector, combined with a co-production model of HE, we conclude with recommendations about how complaints and appeals might be regarded as a learning opportunity leading to improved channels of communication and dissemination, as well as offering continuing professional development opportunitie

Co-limitation towards lower latitudes shapes global forest diversity gradients

The latitudinal diversity gradient (LDG) is one of the most recognized global patterns of species richness exhibited across a wide range of taxa. Numerous hypotheses have been proposed in the past two centuries to explain LDG, but rigorous tests of the drivers of LDGs have been limited by a lack of high-quality global species richness data. Here we produce a high-resolution (0.025° × 0.025°) map of local tree species richness using a global forest inventory database with individual tree information and local biophysical characteristics from ~1.3 million sample plots. We then quantify drivers of local tree species richness patterns across latitudes. Generally, annual mean temperature was a dominant predictor of tree species richness, which is most consistent with the metabolic theory of biodiversity (MTB). However, MTB underestimated LDG in the tropics, where high species richness was also moderated by topographic, soil and anthropogenic factors operating at local scales. Given that local landscape variables operate synergistically with bioclimatic factors in shaping the global LDG pattern, we suggest that MTB be extended to account for co-limitation by subordinate drivers

www.elsevier.com/locate/disc Tutte polynomial expansions for 2-separable graphs

Let ˆG be a graph obtained from a graph G with no loops or coloops by replacing each edge e = uw of G by a connected graph He that has only the vertices u and w incommonwith the rest of ˆG. Two mutually dual formulas are proved for the Tutte polynomial of ˆG interms of parameters of the graphs He and (in the one case) ow polynomials of subgraphs of G or (in the other case) tension polynomials of contractions of G. This generalizes the results of Rea