Edge-colourings of graphs

All the results in this thesis are concerned with the classification of graphs by their chromatic class. We first extend earlier results of Fiorini and others to give a complete list of critical graphs of order at most ten. We give conditions for extending the edge-colouring of a nearly complete subgraph to the whole graph and use this result to prove a special case of Vizing's conjecture. We also use other methods to solve further cases of this conjecture. A major part of the thesis classifies those graphs with at most 4 vertices of maximum degree and this work is generalised to graphs with r vertices of maximum degree. We also completely classify all regular graphs G with degree at least 6/7|V(G)|. Finally we give some examples of even order critical graphs and introduce the concept of a supersnark

Nanoflow-nanospray mass spectrometry metabolomics reveals disruption of the urinary metabolite profiles of HIV-positive patients on combination antiretroviral therapy

Background: The use of combination antiretroviral therapy (cART) has substantially improved the outlook for patients with HIV infection. However, lifelong exposure to cART is also associated with adverse metabolic changes and an enhanced risk of renal, hepatic and cardiovascular dysfunction. This study investigated disruptions of the urinary metabolome of cART-exposed patients, thereby furthering our understanding of some of the side effects of pharmaceutical intervention. Methods: HIV-positive patients were recruited from an HIV clinic and divided into cART-naive and cART-exposed groups. HIV-negative patients were recruited from a sexual health clinic. All 89 subjects were white males. Targeted biochemistry analyses were performed on plasma samples. Urine samples were collected following an overnight fast and analysed with a highly sensitive untargeted metabolomic method using nanoflow/nanospray liquid chromatography-time of flight mass spectrometry. Datasets were analysed using projection modelling to detect metabolite markers of cART exposure. Results: Metabolites or parent compounds of all cART drugs were detected in urine extracts of all but one of the cART-exposed patients confirming adherence to the pharmaceutical regimen. Analysis of urine samples from patients on cART revealed significant reductions in selected bile acids, lipid, nucleoside and androgen metabolites. However, plasma concentrations of free or conjugated testosterone were unchanged indicating possible disruption of androgen transport or excretion in urine of patients on cART. Conclusions: Discovery-based metabolomics reveals the potential to identify novel markers of cART intervention and metabolite disruption in HIV-positive patients, which may enable the efficacy, compliance and side effects of these pharmaceutical mixtures to be investigated

Reducing contamination risk in cluster-randomized infectious disease-intervention trials

Background: Infectious disease interventions are increasingly tested using cluster-randomized trials (CRTs). These trial settings tend to involve a set of sampling units, such as villages, whose geographic arrangement may present a contamination risk in treatment exposure. The most widely used approach for reducing contamination in these settings is the so-called fried-egg design, which excludes the outer portion of all available clusters from the primary trial analysis. However, the fried-egg design ignores potential intra-cluster spatial heterogeneity and makes the outcome measure inherently less precise. Whereas the fried-egg design may be appropriate in specific settings, alternative methods to optimize the design of CRTs in other settings are lacking. Methods: We present a novel approach for CRT design that either fully includes or fully excludes available clusters in a defined study region, recognizing the potential for intra-cluster spatial heterogeneity. The approach includes an algorithm that allows investigators to identify the maximum number of clusters that could be included for a defined study region and maintain randomness in both the selection of included clusters and the allocation of clusters to either the treatment group or control group. The approach was applied to the design of a CRT testing the effectiveness of malaria vector-control interventions in southern Malawi. Conclusions: Those planning CRTs to evaluate interventions should consider the approach presented here during trial design. The approach provides a novel framework for reducing the risk of contamination among the CRT randomization units in settings where investigators determine the reduction of contamination risk as a high priority and where intra-cluster spatial heterogeneity is likely. By maintaining randomness in the allocation of clusters to either the treatment group or control group, the approach also permits a randomization-valid test of the primary trial hypothesis

Selected abstracts from the Breastfeeding and Feminism International Conference 2016

Table of contents A1. Infant feeding and poverty: a public health perspective in a global context Lisa H. Amir A2. Mothers’ experiences with galactagogues for lactation: an exploratory cross sectional study Alessandra Bazzano, Shelley Thibeau, Katherine P. Theall A3. The motherhood journey and breastfeeding: from self-efficacy to resilience and social stigma Anna Blair, Karin Cadwell A4. Breastfeeding as an evolutionary adaptive behavior Emily A. Bronson A5. Conflict-of-interest in public health policy: as real as that logo on your website Elizabeth C. Brooks A6. Co-opting sisterhood and motherhood: behind the scenes of Similac’s aggressive social media campaigns Jodine Chase A7. The exclusion of women from the definition of exclusive breastfeeding Ellen Chetwynd, Rebecca Costello, Kathryn Wouk A8. Healthy maternity policies in the workplace: a state health department’s experience with the “Bring Your Infant to Work” program Lindsey Dermid-Gray A9. Implications for a paradigm shift: factors related to breastfeeding among African American women Stephanie Devane-Johnson, Cheryl Woods Giscombe, Miriam Labbok A10. Social experiences of breastfeeding: building bridges between research and policy: an ESRC-funded seminar series in the UK Sally Dowling A11. Manager’s perspectives of lactation breaks Melanie Fraser A12. The challenging second night: a dialogue from two perspectives Jane Grassley, Deborah McCarter-Spaulding, Becky Spencer A13. The role of lactation consultants in two council breastfeeding services in Melbourne, Australia – some preliminary impressions Jennifer Hocking, Pranee Liamputtong A14. Integrating social marketing and community engagement concepts in community breastfeeding programs Sheree H. Keitt, Harumi Reis-Reilly A15. What happens before and after the maternity stay? Creating a community-wide Ten Steps approach Miriam Labbok A16. #RVABREASTFEEDS: cultivating a breastfeeding-friendly community Leslie Lytle A17. Public health vs. free trade: a longitudinal analysis of a global policy to protect breastfeeding Mary Ann Merz A18. Legislative advocacy and grassroots organizing for improved breastfeeding laws in Virginia Kate Noon A19. Breastfeeding and the rights of incarcerated women Krista M Olson A20. Barriers and support for Puerto Rican breastfeeding working mothers Ana M. Parrilla-Rodríguez, José J. Gorrín-Peralta Melissa Pellicier, Zeleida M. Vázquez-Rivera A21. Pumping at work: a daily struggle for Puerto Rican breastfeeding mothers in spite of the law Melissa Pellicier A22. “I saw a wrong and I wanted to stand up for what I thought was right:” a narrative study on becoming a breastfeeding activist Jennifer L. Pemberton A23. Peer breastfeeding support: advocacy and action Catherine McEvilly Pestl A24. Good intentions: a study of breastfeeding intention and postpartum realities among first-time Central Brooklyn mothers Jennifer Pierre, Philip Noyes, Khushbu Srivastava, Sharon Marshall-Taylor A25. Women describing the infant feeding choice: the impact of the WIC breastfeeding classes on infant feeding practices in Ionia, Michigan Jennifer Proto, Sarah Hyland Laurie Brinks A26. Local and state programs and national partnership to reduce disparities through community breastfeeding support Harumi Reis-Reilly, Martelle Esposito, Megan Phillippi A27. Beyond black breastfeeding week: instagram image content analysis for #blackwomendobreastfeed/#bwdbf Cynthia L. Sears, Delores James, Cedric Harville, Kristina Carswell A28. Stakeholder views of breastfeeding education in the K-12 environment: a review of the literature Nicola Singletary, L. Suzanne Goodell, April Fogleman A29. “The Breastfeeding Transition”: a framework for explaining changes in global breastfeeding rates as related to large-scale forces shaping the status of women Paige Hall Smith A30. Breastfeeding, contraception, and ethics, oh my! Advocacy and informed decision-making in the post-partum period Alison M. Stuebe, Amy G. Bryant, Anne Drapkin Lyerly A31. A hard day’s night: juggling nighttime breastfeeding, sleep, and work Cecilia Tomori A32. Empowering change in Indian country through breastfeeding education Amanda L. Watkins, Joan E. Dodgson A33. Servants and “Little Mothers” take charge: work, class, and breastfeeding rates in the early 20th-century U.S. Jacqueline H. Wol

Star multigraphs with three vertices of maximum degree.

The graphs we consider here are either simple graphs, that is they have no loops or multiple edges, or are multigraphs, that is they may have more than one edge joining a pair of vertices, but again have no loops. In particular we shall consider a special kind of multigraph, called a star-multigraph: this is a multigraph which contains a vertex v*, called the star-centre, which is incident with each non-simple edge. An edge-colouring of a multigraph G is a map ø: E(G)→, where is a set of colours and E(G) is the set of edges of G, such that no two edges receiving the same colour have a vertex in common. The chromatic index, or edge-chromatic numberχ′(G) of G is the least value of || for which an edge-colouring of G exists. Generalizing a well-known theorem of Vizing [14], we showed in [6] that, for a star-multigraph G, where Δ(G) denotes the maximum degree (that is, the maximum number of edges incident with a vertex) of G. Star-multigraphs for which χ′(G) = Δ(G) are said to be Class 1, and otherwise they are Class 2

A degree of concern? UK first degrees in science, technology and mathematics.

This note summarises a full report setting out the background information and initial findings of a project to explore the background to the widespread concerns over the supply of skilled people needed to maintain the UK as a leading knowledge economy. Phase I of the project concentrates on science, technology and mathematics (STM) first degree courses in the UK. The report is designed to underpin a wider study of the fitness for purpose of UK STM Higher Education (HE) into the middle of the next decade and beyond, and includes a wide range of data on STM A-levels, STM first degree courses and the first destination of STM graduates