IT is well known that, when the classical conditions on a metric d( , ) for a set X are relaxed by omitting the requirement d(x, y) = 0 only if z = y, there is no difficulty in generalizing the standard theorems of metric spaces, in particular those concerning metrization of topological spaces. On the other hand, if one attempts to omit the requirement of symmetry, the appropriate generalizations are not obvious. Such unsymmetric distance functions have been studied before by Wilson (9), who used the term quasi-metrics, Ribeiro (6), and others. To my knowledge, there has been no previous attempt to systematize the study of these quasi-metrics.Any distance function d( , ) on a set X (i.e. any non-negative real-valued function d( , ) denned on the product X x X and satisfying the triangle inequality) has the property that the open d-spheres (i.e. sets of the form {y : d(x,y)

Background: The approach and style of leaders is known to be an important factor influencing the translation of research evidence into nursing practice. However, questions remain as to what types of roles are most effective and the specific mechanisms through which influence is achieved. Objectives: The aim of the study was to enhance understanding of the mechanisms by which key nursing roles lead the implementation of evidence-based practice across different care settings and countries and the contextual factors that influence them. Design: The study employed a qualitative descriptive approach. Settings: Data collection was undertaken in acute care and primary/community health care settings in Australia, Canada, England and Sweden. Participants: 55 individuals representing different levels of the nursing leadership structure (executive to frontline), roles (managers and facilitators), sectors (acute and primary/community) and countries. Methods: Individual semi-structured interviews were conducted with all participants exploring their roles and experiences of leading evidence-based practice. Data were analysed through a process of qualitative content analysis. Results: Different countries had varying structural arrangements and roles to support evidence-based nursing practice. At a crosscountry level, three main themes were identified relating to different mechanisms for enacting evidence-based practice, contextual influences at a policy, organisational and service delivery level and challenges of leading evidence-based practice. Conclusions: National policies around quality and performance shape priorities for evidencebased practice, which in turn influences the roles and mechanisms for implementation that are given prominence. There is a need to maintain a balance between the mechanisms of managing and monitoring performance and facilitating critical questioning and reflection in and on practice. This requires a careful blending of managerial and facilitative leadership. The findings have implications for theory, practice, education and research relating to implementation and evidence-based practice.

This paper describes the rationale and process for developing a set of Aboriginal patient journey mapping tools with Aboriginal patients, health professionals, support workers, educators and researchers in the Managing Two Worlds Together project between 2008 and 2015. Aboriginal patients and their families from rural and remote areas, and healthcare providers in urban, rural and remote settings, shared their perceptions of the barriers and enablers to quality care in interviews and focus groups, and individual patient journey case studies were documented. Data were thematically analysed. In the absence of suitable existing tools, a new analytical framework and mapping approach was developed. The utility of the tools in other settings was then tested with health professionals, and the tools were further modified for use in quality improvement in health and education settings in South Australia and the Northern Territory. A central set of patient journey mapping tools with flexible adaptations, a workbook, and five sets of case studies describing how staff adapted and used the tools at different sites are available for wider use.

Background Appropriate choice of research design is essential to rightly understand the research problem and derive optimal solutions. The Comorbidity Action in the North project sought to better meet the needs of local people affected by drug, alcohol and mental health comorbidity. The aim of the study focused on the needs of Aboriginal peoples and on developing a truly representative research process. A methodology evolved that best suited working with members of a marginalised Aboriginal community. This paper discusses the process of co-design of a Western methodology (participatory action research) in conjunction with the Indigenous methodologies Dadirri and Ganma. This co-design enabled an international PhD student to work respectfully with Aboriginal community members and Elders, health professionals and consumers, and non-Indigenous service providers in a drug and alcohol and mental health comorbidity project in Adelaide, South Australia. Methods The PhD student, Aboriginal Elder mentor, Aboriginal Working Party, and supervisors (the research team) sought to co-design a methodology and applied it to address the following challenges: the PhD student was an international student with no existing relationship with local Aboriginal community members; many Aboriginal people deeply distrust Western research due to past poor practices and a lack of implementation of findings into practice; Aboriginal people often remain unheard, unacknowledged and unrecognised in research projects; drug and alcohol and mental health comorbidity experiences are often distressing for Aboriginal community members and their families; attempts to access comorbidity care often result in limited or no access; and Aboriginal community members experience acts of racism and discrimination as health professionals and consumers of health and support services. The research team considered deeply how knowledge is shared, interpreted, owned and controlled, by whom and how, within research, co-morbidity care and community settings. The PhD student was supported to co-design a methodology that was equitable, democratic, liberating and life-enhancing, with real potential to develop feasible solutions. Results The resulting combined Participatory Action Research (PAR)-Dadirri-Ganma methodology sought to create a bridge across Western and Aboriginal knowledges, understanding and experiences. Foundation pillars of this bridge were mentoring of the PhD student by senior Elders, who explained and demonstrated the critical importance of Yarning (consulting) and Indigenous methodologies of Dadirri (deep listening) and Ganma (two-way knowledge sharing), and discussions among all involved about the principles of Western PAR. Conclusions Concepts within this paper are shared from the perspective of the PhD student with the permission and support of local Elders and Working Group members. The intention is to share what was learned for the benefit of other students, research projects and community members who are beginning a similar journey.