A Mean-Risk Mixed Integer Nonlinear Program for Network Protection

Many of the infrastructure sectors that are considered to be crucial by the Department of Homeland Security include networked systems (physical and temporal) that function to move some commodity like electricity, people, or even communication from one location of importance to another. The costs associated with these flows make up the price of the network\u27s normal functionality. These networks have limited capacities, which cause the marginal cost of a unit of flow across an edge to increase as congestion builds. In order to limit the expense of a network\u27s normal demand we aim to increase the resilience of the system and specifically the resilience of the arc capacities. Divisions of critical infrastructure have faced difficulties in recent years as inadequate resources have been available for needed upgrades and repairs. Without being able to determine future factors that cause damage both minor and extreme to the networks, officials must decide how to best allocate the limited funds now so that these essential systems can withstand the heavy weight of society\u27s reliance. We model these resource allocation decisions using a two-stage stochastic program (SP) for the purpose of network protection. Starting with a general form for a basic two-stage SP, we enforce assumptions that specify characteristics key to this type of decision model. The second stage objective---which represents the price of the network\u27s routine functionality---is nonlinear, as it reflects the increasing marginal cost per unit of additional flow across an arc. After the model has been designed properly to reflect the network protection problem, we are left with a nonconvex, nonlinear, nonseparable risk-neutral program. This research focuses on key reformulation techniques that transform the problematic model into one that is convex, separable, and much more solvable. Our approach focuses on using perspective functions to convexify the feasibility set of the second stage and second order conic constraints to represent nonlinear constraints in a form that better allows the use of computational solvers. Once these methods have been applied to the risk-neutral model we introduce a risk measure into the first stage that allows us to control the balance between an efficient, solvable model and the need to hedge against extreme events. Using Benders cuts that exploit linear separability, we give a decomposition and solution algorithm for the general network model. The innovations included in this formulation are then implemented on a transportation network with given flow demand

The experience of living with age related macular degeneration:A longitudinal study into the impact of age related macular degeneration on quality of life

In this thesis I contribute to the understanding of the experience of living with Age-Related Macular Degeneration (AMD) and its impact on quality of life through the use of a pragmatically guided mixed methods approach. AMD is a condition resulting in the loss of central vision in old age which can have a huge impact on the lives of patients. This thesis includes: literature reviewing; qualitative meta-synthesis; surveys and descriptive statistics; observation; and analysis of in-depth interviewing, in order to build a picture of what it is like for older people to live with AMD. I present the findings from six separate studies each designed to answer specific research questions. I begin with a mixed methods study to determine how well the most commonly used measure of quality of life for AMD patients’ represents patient experiences. I then go on to investigate the experiences of patients with AMD through a meta-synthesis of qualitative research and finally present four of my own empirical studies three of which investigate the experiences of patients with different types of AMD: early dry AMD, treatable wet AMD and advanced wet AMD and the final study investigates what it is like for a couple living together with AMD. Throughout the qualitative studies I use Interpretative Phenomenological Analysis (IPA) to develop an understanding of the experiences and life contexts of patients with AMD. Through rigorous analysis, I identify a range of themes which highlight the shared and divergent experiences of individuals with AMD and the need to acknowledge patients’ past, present and potential future life contexts and experiences when providing services to older people with AMD. I relate the findings of the six studies to the wider psychological literature on chronic illness and make recommendations for services for patients with AMD to be provided holistically within a lifeworld-led health care model

Exploring the facilitators and barriers to physical activity in older people with sight loss.

This study aimed to explore facilitators and barriers to physical activity in older people with sight loss. Focus groups were conducted with 13 community dwelling older adults with sight loss ranging from poor to completely blind. Transcripts were analysed using an inductive thematic analysis. Facilitators and barriers are experienced in three ways: psychologically; through opportunity and access; and at a societal and policy level. Campaigns are needed to challenge unhelpful age-related stereotypes at both psychological and societal levels. Additionally, interventions grounded in evidence and theory should be trialled and evaluated for increasing physical activity in this population

Enhanced antibiotic distribution strategies and the potential impact of facial cleanliness and environmental improvements for the sustained control of trachoma: a modelling study.

BACKGROUND: Despite some success in controlling trachoma with repeated mass drug administration (MDA), some hyperendemic regions are not responding as fast as anticipated. Available data suggests that individuals with higher bacterial infection loads are less likely to resolve infection following a single dose of treatment, and thus remain a source of re-emergent infection following treatment. We assessed the potential impact of a new double-dose antibiotic distribution strategy in addition to enhanced facial cleanliness (F) and environmental improvements (E). METHODS: Using a within-community mathematical model of trachoma transmission we assessed the impact of a new double-dose antibiotic distribution strategy given 2 weeks apart, with and without enhanced F&E. We compared the annual double-dose strategy to single-dose annual MDA treatment in hyper-, meso- and hypoendemic settings, and to biannual MDA at 6-monthly intervals in hyperendemic communities. RESULTS: The findings from our mathematical model suggest that implementing the new double-dose strategy for 5 years or less was predicted to control infection more successfully than annual or 6-monthly treatment. Infection was controlled more readily if treatment was combined with enhanced F&E. The results appeared robust to variation in a number of key epidemiological parameters. To have long-term impact on transmission, enhanced F&E is essential for high transmission settings. CONCLUSION: Our current findings are based on simualtion modelling only, due to lack of epidemilogical data, however they do suggest that the  annual double-dose treatment strategy is encouraging for trachoma control. In high transmission settings, both MDA and enhanced F&E are needed for sustained control