Formal and informal support systems in a rural town and county : report of the research on mental health in Dannevirke Borough and County : a thesis presented in fulfilment of the requirements for the degree of Master of Philosophy at Massey University

The Dannevirke project was designed to provide a view into one rural borough and county in order to discern how that community provided services for those in need of emotional and psychological support. Professional human service providers and a representative sample, of the general population were interviewed to identify the formal and informal supports that were available to the community and to define mental health and mental illness. This project was based on two assumptions: 1) rural and small town life in New Zealand had networks of self-help and support and these networks were different from those found in the urban environment; 2) clinical and professional practitioners adopted unique responses to practice in a rural area. This study demonstrated that a rural community based on the romantic notion of a small homogenous, caring community was simplistic. Intrarural differences in the numerous settlements revealed a more complex fabric. The data did reflect an intricate and caring network of informal supports but it was unclear as to how different (e.g. more supportive) these rural networks were to those in an urban/suburban community. Respondents with low group membership and low visitation from family and friends reported a statistically significant low sense of psychological well-being using the Bradburn Well-Being Scale (1969). The actual roles these networks played in caregiving and prevention needed further inquiry. The pathways to service for people experiencing emotional/psychological problems were traced, including a ten year statistical analysis of inpatient psychiatric care. The general practitioner was identified by the respondents in the community and by other professionals as the primary gatekeeper for services, underlining the medical bias in their definitions of mental illness. Delivery of services by the professionals in the rural area was complicated by distance, minimal interprofessional coordination, shortage of specialist services, and a lack of ongoing professional education in the field of community mental health. Treatment in the community was favoured over sending the clients away for services and the local hospital was a unique resource for short-term respite care. The findings brought forth numerous questions including: What models of practice are effective for mental health care in the rural context? How do geographical distance and isolation affect community mental health practice? Does the urban base of most professional training prepare formal caregivers for life and practice in the rural setting? Specific recommendations for policy development and for further research were discussed

Asymptotically Optimal Bounds for (t,2) Broadcast Domination on Finite Grids

Let $G=(V,E)$ be a graph and $t,r$ be positive integers. The \emph{signal} that a tower vertex $T$ of signal strength $t$ supplies to a vertex $v$ is defined as $sig(T,v)=max(t-dist(T,v),0),$ where $dist(T,v)$ denotes the distance between the vertices $v$ and $T$. In 2015 Blessing, Insko, Johnson, and Mauretour defined a \emph{$(t,r)$ broadcast dominating set}, or simply a \emph{$(t,r)$ broadcast}, on $G$ as a set $\mathbb{T}\subseteq V$ such that the sum of all signals received at each vertex $v \in V$ from the set of towers $\mathbb{T}$ is at least $r$. The $(t,r)$ broadcast domination number of a finite graph $G$, denoted $\gamma_{t,r}(G)$, is the minimum cardinality over all $(t,r)$ broadcasts for $G$. Recent research has focused on bounding the $(t,r)$ broadcast domination number for the $m \times n$ grid graph $G_{m,n}$. In 2014, Grez and Farina bounded the $k$-distance domination number for grid graphs, equivalent to bounding $\gamma_{t,1}(G_{m,n})$. In 2015, Blessing et al. established bounds on $\gamma_{2,2}(G_{m,n})$, $\gamma_{3,2}(G_{m,n})$, and $\gamma_{3,3}(G_{m,n})$. In this paper, we take the next step and provide a tight upper bound on $\gamma_{t,2}(G_{m,n})$ for all $t>2$. We also prove the conjecture of Blessing et al. that their bound on $\gamma_{3,2}(G_{m,n})$ is tight for large values of $m$ and $n$.Comment: 8 pages, 4 figure

Structured penalties for functional linear models---partially empirical eigenvectors for regression

One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear model is often used to estimate the relationship between the predictor functions and scalar responses. Common approaches to the ill-posed problem of estimating a coefficient function typically involve two stages: regularization and estimation. Regularization is usually done via dimension reduction, projecting onto a predefined span of basis functions or a reduced set of eigenvectors (principal components). In contrast, we present a unified approach that directly incorporates spatial structure into the estimation process by exploiting the joint eigenproperties of the predictors and a linear penalty operator. In this sense, the components in the regression are `partially empirical' and the framework is provided by the generalized singular value decomposition (GSVD). The GSVD clarifies the penalized estimation process and informs the choice of penalty by making explicit the joint influence of the penalty and predictors on the bias, variance, and performance of the estimated coefficient function. Laboratory spectroscopy data and simulations are used to illustrate the concepts.Comment: 29 pages, 3 figures, 5 tables; typo/notational errors edited and intro revised per journal review proces

Thermal-structural panel buckling tests

The buckling characteristics of a titanium matrix composite hat-stiffened panel were experimentally examined for various combinations of thermal and mechanical loads. Panel failure was prevented by maintaining the applied loads below real-time critical buckling predictions. The test techniques used to apply the loads, minimize boundary were shown to compare well with a finite-element buckling analysis for previous panels. Comparisons between test predictions and analysis for this panel are ongoing