title: Characterising sound visualisations of specifications using refinement

authors: Pilbrow, Colin

subjects: specification

abstract: Visualisations can be used to help analyse, explore, and validate Z specifications. However, if visualisations contain errors or are used incorrectly then they can be misleading and harmful. The aim of this work is to characterise the soundness of visualisations of Z specifications. We achieve this by using refinement. We look for a refinement relation between a Z specification and its (claimed sound) visualisation. If the relation does not hold, then the visualisation is not sound. The main type of visualisation we investigate is state diagrams. These diagrams are useful for visualising the state and operations of Z specifications. We look at a variety of state diagrams styles before widening the scope to include μ-Chart visualisations and animated visualisations. We find that existing refinement methods should not be used for all types of visualisations. To characterise the soundness of partial visualisations we extend the standard rules to include unexamined states and restricted specifications. Finally, we include examples of the refinement rules being used on our visualisations. This lets us formally show whether each individual visualisation is sound or not.

text: Characterising sound visualisations of specifications using refinement Visualisations can be used to help analyse, explore, and validate Z specifications. However, if visualisations contain errors or are used incorrectly then they can be misleading and harmful. The aim of this work is to characterise the soundness of visualisations of Z specifications. We achieve this by using refinement. We look for a refinement relation between a Z specification and its (claimed sound) visualisation. If the relation does not hold, then the visualisation is not sound. The main type of visualisation we investigate is state diagrams. These diagrams are useful for visualising the state and operations of Z specifications. We look at a variety of state diagrams styles before widening the scope to include μ-Chart visualisations and animated visualisations. We find that existing refinement methods should not be used for all types of visualisations. To characterise the soundness of partial visualisations we extend the standard rules to include unexamined states and restricted specifications. Finally, we include examples of the refinement rules being used on our visualisations. This lets us formally show whether each individual visualisation is sound or not.

year: 2019

title: Geodesic geometry of some static axisymmetric vacuum spacetimes

authors: Harder, David M.

abstract: Solutions of Laplace's equation in terms of bispherical and toroidal coordinates are used to derive new exact exterior (vacuum), general relativistic fields, of static axially symmetric spacetimes. 
For each new metric we calculate the first Geroch relativistic multipole moments. By selecting solutions that have even multipole moments, and thus a plane of equatorial symmetry, we numerically generate the timelike geodesics of test particles confined to these planes. 
Approximate solutions of these orbits are calculated, fro~ which the precession of the perihelion is compared to that of the numerical results and those predicted by a method of Fernández-Jambrina and Hoenselaers (2001). Similar calculations are done in the bispherical case for the precession rate of the line of nodes of a perturbed circular orbit. 
Geodesics of zero angular momentum are also presented for various spacetimes. In general, it is observed that the trajectories of test particles can experience periods of gravitational repulsion. Furthermore, the toroidal solutions show that the period of oscillation of a test particle along the axis of a ring like mass distribution can increase as the mass of the source is increased. 
We also consider the application of bicyclide coordinates. In doing so the computation of Lamé-Wangerin functions are required. New results for the eigenfunctions for the Lamé equation of order  -1/2 are produced. Analytic and numerical results are compared. The multipole moments and timelike geodesics of this solution are also presented.

text: Geodesic geometry of some static axisymmetric vacuum spacetimes Solutions of Laplace's equation in terms of bispherical and toroidal coordinates are used to derive new exact exterior (vacuum), general relativistic fields, of static axially symmetric spacetimes. 
For each new metric we calculate the first Geroch relativistic multipole moments. By selecting solutions that have even multipole moments, and thus a plane of equatorial symmetry, we numerically generate the timelike geodesics of test particles confined to these planes. 
Approximate solutions of these orbits are calculated, fro~ which the precession of the perihelion is compared to that of the numerical results and those predicted by a method of Fernández-Jambrina and Hoenselaers (2001). Similar calculations are done in the bispherical case for the precession rate of the line of nodes of a perturbed circular orbit. 
Geodesics of zero angular momentum are also presented for various spacetimes. In general, it is observed that the trajectories of test particles can experience periods of gravitational repulsion. Furthermore, the toroidal solutions show that the period of oscillation of a test particle along the axis of a ring like mass distribution can increase as the mass of the source is increased. 
We also consider the application of bicyclide coordinates. In doing so the computation of Lamé-Wangerin functions are required. New results for the eigenfunctions for the Lamé equation of order  -1/2 are produced. Analytic and numerical results are compared. The multipole moments and timelike geodesics of this solution are also presented.

year: 2003

title: Hā Ora: secondary care barriers and enablers to early diagnosis of lung cancer for Māori communities.

authors: Kidd, Jacquie

subjects: Barriers

abstract: BACKGROUND: Lung Cancer is the leading cause of cancer deaths in Aotearoa New Zealand. Māori communities in particular have higher incidence and mortality rates from Lung Cancer. Diagnosis of lung cancer at an early stage can allow for curative treatment. This project aimed to document the barriers to early diagnosis and treatment of lung cancer in secondary care for Māori communities. 
METHODS: This project used a kaupapa Māori approach. Nine community hui (focus groups) and nine primary healthcare provider hui were carried out in five rural localities in the Midland region. Community hui included cancer patients, whānau (families), and other community members. Healthcare provider hui comprised staff members at the local primary healthcare centre, including General Practitioners and nurses. Hui data were thematically analysed. 
RESULTS: Barriers and enablers to early diagnosis of lung cancer were categorised into two broad themes: Specialist services and treatment, and whānau journey. The barriers and enablers that participants experienced in specialist services and treatment related to access to care, engagement with specialists, communication with specialist services and cultural values and respect, whereas barriers and enablers relating to the whānau journey focused on agency and the impact on whānau. 
CONCLUSIONS: The study highlighted the need to improve communication within and across healthcare services, the importance of understanding the cultural needs of patients and whānau and a health system strategy that meets these needs. Findings also demonstrated the resilience of Māori and the active efforts of whānau as carers to foster health literacy in future generations.

text: Hā Ora: secondary care barriers and enablers to early diagnosis of lung cancer for Māori communities. BACKGROUND: Lung Cancer is the leading cause of cancer deaths in Aotearoa New Zealand. Māori communities in particular have higher incidence and mortality rates from Lung Cancer. Diagnosis of lung cancer at an early stage can allow for curative treatment. This project aimed to document the barriers to early diagnosis and treatment of lung cancer in secondary care for Māori communities. 
METHODS: This project used a kaupapa Māori approach. Nine community hui (focus groups) and nine primary healthcare provider hui were carried out in five rural localities in the Midland region. Community hui included cancer patients, whānau (families), and other community members. Healthcare provider hui comprised staff members at the local primary healthcare centre, including General Practitioners and nurses. Hui data were thematically analysed. 
RESULTS: Barriers and enablers to early diagnosis of lung cancer were categorised into two broad themes: Specialist services and treatment, and whānau journey. The barriers and enablers that participants experienced in specialist services and treatment related to access to care, engagement with specialists, communication with specialist services and cultural values and respect, whereas barriers and enablers relating to the whānau journey focused on agency and the impact on whānau. 
CONCLUSIONS: The study highlighted the need to improve communication within and across healthcare services, the importance of understanding the cultural needs of patients and whānau and a health system strategy that meets these needs. Findings also demonstrated the resilience of Māori and the active efforts of whānau as carers to foster health literacy in future generations.

year: 2021