Reaching consensus on a connected graph

We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a consensus is reached. In some cases we are able to show that this is minimised by $K_n$. We prove an upper bound for the case $p=0$ and give a family of graphs which asymptotically achieve this bound. In order to obtain the mean of the waiting time we also study a gambler's ruin process with delays. We give the mean absorption time and prove that it monotonically increases with $p\in[0,1/2]$ for symmetric delays

The role of beliefs in predicting adherence to nebulised therapy in adolescents with cystic fibrosis

Introduction: Sub-optimal treatment adherence in Cystic Fibrosis (CF) is commonplace, and is known to deteriorate in adolescence, increasing risk of early morbidity and mortality. Although, in other chronic conditions, research focusing on psychological models of beliefs, and in particular the Necessity-Concerns Framework, has proved promising to understand this problem, comparatively little exists within CF. Importantly, the devices used to deliver nebulised treatments in CF provide objective recording of dose consumption, offering a singular opportunity to overcome the largest barrier in adherence research - subjective adherence measurement. However, the existing studies in CF which have examined this model in these treatments, have either relied on subjective measurement of adherence, and/or inadequately adapted the measure used to assess these beliefs. Method: This thesis was completed in two parts. Study one developed a systematic process for adapting the BMQ-S into two versions, to separately capture necessity and concern beliefs of patients and their parents which may influence adherence behaviour to both categories of nebulised medications. This process included a modified two-round Delphi survey which elicited feedback from an expert panel on the value and clarity of the adapted questionnaires. Study two examined the relationship between beliefs elicited by the measures, and objectively-recorded adherence behaviour, to assess their relative utility in predicting adherence behaviour to nebulised treatments, from both patients’, and their parents’, beliefs. Results: In study one, consensus on the value of items in both questionnaires was positive, but more variable for clarity, causing two original items to be removed, eight revised, and three created in each of the adapted measures. Study two found no significant relationships between patients’ or parents’ necessity and concern beliefs, and objectively-recorded adherence behaviour, in either medication category, in the original or adapted measures. Although analyses were underpowered by inadequate sample sizes, findings suggest that the Necessity-Concerns Framework may relate to adherence differently between nebulised medication categories and respondents, and, most importantly, that the original measure may be superior in capturing these relations. Discussion: Although the results of this research are provisional, the novelty of design in both studies highlights several important considerations for future research, including the importance of assessing the psychometric properties of adapted belief measures, rather than assuming that refined versions will necessarily be superior to original versions. They also highlight the importance of considering parents beliefs when trying to understand adherence behaviour in adolescent populations

The older entrepreneurial event : entrepreneurial intentions in the third age

Policy on older workers has focused on increasing labour market participation either by encouraging those unemployed or inactive back into work or by encouraging people to work up to and beyond retirement age. It has been argued that older entrepreneurship might enable older individuals to extend their working lives and support them to fund their retirement. However, academic investigation of this phenomenon has been limited. Where research has been conducted, it has predominantly been investigated quantitatively (e.g Kautonen et al. 2009; Kautonen 2012; Walker & Webster 2007). Through the lens of Shapero’s (1982) Entrepreneurial Event (SEE) theory, this research sought to investigate the intentions of ‘older’ entrepreneurship and the subsequent business and personal outcomes of engaging in entrepreneurship for older individuals in the UK. A qualitative research design within a Constructivist paradigm was used. Aligning with the Constructivist standpoint, multiple methods in the form of a qualitative survey (n = 70) and 20 in depth interviews were undertaken with UK based older entrepreneurs. Data was thematically analysed. Findings on motivations behind third age entrepreneurship found in this study are similar to those reported across the literature on small firms in terms of the reportage of extrinsic and intrinsic motivators. However, current findings demonstrate that financial necessity does not appear to be a prevalent motivation for engaging in older entrepreneurship. Instead, importance was given to non-pecuniary motivating factors such as enjoyment and remaining active in older age. Motivations were also found to influence how the older entrepreneurs measured success in terms of business and personal outcomes. Success was not perceived only through traditional means related to growth and pecuniary earnings, with intrinsic motivations often prioritised over pecuniary factors for the majority of older entrepreneurs. Findings also verify that in the context of older entrepreneurship SEE theory appears to be an appropriate theoretical model for understanding the entrepreneurial intentions and behaviours of the study’s sample. However, findings suggest that the theory may be better presented so that the importance of context in the formation of entrepreneurial intention and behaviour is emphasised

Municipal sludge as source of nitrogen and phosphorus in perennial pasture Eragrostis curvula production: Agronomic benefits and environmental impacts

Land application of sludge has been shown to improve soil properties and aid crop growth, but the possibility of constituent nutrients such as nitrogen and phosphorus reaching environmentally toxic levels has caused governing authorities to set limits to how much sludge can be applied to agronomic land. The high nitrogen utilisation potential of pasture grasses suggests that more sludge can be used in this cropping system without the risk of excess nitrates. This study investigates the effect of exceeding the South African sludge application limit on hay yield, soil nitrates and phosphorus. Field plots were arranged in a complete block design comprising 4 replications of 4 treatments planted to Eragrostis curvula. The treatments consisted of 0, 4, 8 and 16 Mg∙ha-1 anaerobically digested sludge. Soil samples were collected before treatment application and at the end of each growing season for N, P, NO3-, NH4+, and Bray-1P analyses. Plant samples were collected at flowering stage for hay yield and N and P uptake determination. Statistical analyses were conducted using analysis of variance (ANOVA) and general linear model (GLM) procedures of Windows SAS 9.0 to evaluate the effect of sludge application rates on hay yield. Results over 4 growing seasons indicate that exceeding the recommended limit increased hay yield by 4% in a dry season (11.7 vs. 12.36 Mg∙ha-1) and by 16% in a wet season (14.19 vs. 17.31 Mg∙ha-1) and also increased nitrogen uptake by 15%. Sludge applied at double the recommended limit did not cause the accumulation of nitrate and ammonium in the soil, however, both total and Bray-1P were doubled. The study shows that the potential long-term environmental risk of doubling the sludge application rate norm would be from labile P accumulation in the soil profile despite a sludge P:Fe molar ratio of less than unity.Keywords: sludge, Eragrostis curvula, nitrogen, phosphorus, leachin

Attitudes towards bystander cardiopulmonary resuscitation:Results from a cross-sectional general population survey

Survival from out-of-hospital cardiac arrest (OHCA) varies across the developed world. Although not all OHCA are recoverable, the survival rate in Scotland is lower than in comparable countries, with higher average survival rates of 7.9% in England and 9% across Europe. The purpose of this paper is to explore the barriers, facilitators and public attitudes to administering bystander cardiopulmonary resuscitation (CPR) which could inform future policy and initiatives to improve the rate of bystander CPR. Data was collected via a cross-sectional general population survey of 1027 adults in Scotland. 52% of respondents had been trained in CPR. Of those who were not trained, two fifths (42%) expressed a willingness to receive CPR training. Fewer than half (49%) felt confident administering CPR, rising to 82% if they were talked through it by a call handler. Multivariate analyses identified that people in social grade C2DE were less likely than those in social grade ABC1 to be CPR trained and less confident to administer CPR if talked through by a call handler. The older a person was, the less likely they were to be CPR trained, show willingness to be CPR trained or be confident to administer bystander CPR with or without instruction from an emergency call handler. These findings are particularly relevant considering that most OHCA happen in the homes of older people. In a developed country such as Scotland with widely available CPR training, only half of the adult population reported feeling confident about administering bystander CPR. Further efforts tailored specifically for people who are older, unemployed and have a lower social grade are required to increase knowledge, confidence and uptake of training in bystander CPR