Mathematical Sciences- Journal Articles
http://hdl.handle.net/10468/89
2018-02-18T21:51:44ZThe Gamma characteristic of reconstructed PET images: Implications for ROI analysis
http://hdl.handle.net/10468/5245
The Gamma characteristic of reconstructed PET images: Implications for ROI analysis
Mou, Tian; Huang, Jian; O'Sullivan, Finbarr
The basic emission process associated with PET imaging is Poisson in nature. Reconstructed images inherit some aspects of this—regional variability is typically proportional to the regional mean. Iterative reconstruction using expectation maximization (EM), widely used in clinical imaging now, impose positivity constraints that impact noise properties. The present work is motivated by analysis of data from a physical phantom study of a PET/CT scanner in routine clinical use. Both traditional filtered back-projection (FBP) and EM reconstructions of the images are considered. FBP images are quite Gaussian but the EM reconstructions exhibit Gamma-like skewness. The Gamma structure has implications for how reconstructed PET images might be processed statistically. Post-reconstruction inference— model fitting and diagnostics for regions of interest are of particular interest. Although the relevant Gamma parameterization is not within the framework of generalized linear models (GLM), iteratively re-weighted least squares (IRLS) techniques, which are often used to find the maximum likelihood estimates of a GLM, can be adapted for analysis in this setting. Our work highlights the use of a Gamma-based probability transform in producing normalized residuals as model diagnostics. The approach is demonstrated for quality assurance analyses associated with physical phantom studies—recovering estimates of local bias and variance characteristics in an operational scanner. Numerical simulations show that when the Gamma assumption is reasonable, gains in efficiency are obtained. The work shows that the adaptation of standard analysis methods to accommodate the Gamma structure is straightforward and beneficial.
2017-11-23T00:00:00ZThe influence of process parameters on the physical characteristics of ceramic microneedles, evaluated using a factorial design
http://hdl.handle.net/10468/4851
The influence of process parameters on the physical characteristics of ceramic microneedles, evaluated using a factorial design
Carracedo-Taboada, Marta; O'Sullivan, Kathleen; McAuliffe, Michael A. P.; Vucen, Sonja; O'Sullivan, Caroline
Salguero, Jorge; Ares, Enrique
The paper presents the application of the factorial Design of Experiments (DoE) to evaluate the influence of process parameters on the physical characteristics of ceramic microneedles (CMN). In this study, an understanding of the fabrication process was achieved by performing a DoE based on varying two levels of five parameters. Statistical analyses were performed on the data to investigate whether the process parameters have a significant effect on the production of a patch of 25 microneedles (MN) with sharp tips. The study showed that four out of five main effects as well as an interaction between two parameters were significant.
2017-10-05T00:00:00ZThe constrained optimisation of small linear arrays of heaving point absorbers. Part I: The influence of spacing
http://hdl.handle.net/10468/4839
The constrained optimisation of small linear arrays of heaving point absorbers. Part I: The influence of spacing
McGuinness, Justin P. L.; Thomas, Gareth
This paper describes the optimisation of small arrays of Wave Energy Converters (WECs) of point absorber type. The WECs are spherical in shape and operate in heave alone and a linear array of five devices is considered. Previous work is extended by considering the constrained performance of the array members, where an uaniper limit on WEC displacements is enforced. Two opimisations are performed. In each case, the objective function is defined as the mean of the averaged interaction factor ovehe non-dimensional length of the array. The first considers the array layout fixed at a geometry previously identified as optimal in an unconstrained regime and optimises the displacements of the WECs subject to constraints. The second allows both the WEC positions and displacements to vary as optimisation variables. It is shown that the optimal layout of the constrained arrays is different from the unconstrained case. Applying constrained motions results in optimal layouts that are more separated, with less grouping of WECs and this will have practical considerations. The effect of the constraints varies depending on the incident wave angle. In some cases, performance is reduced drastically and stability of performance is improved, while in other cases there is a degradation of performance. Thus, a trade-off between performance and stability of performance is seen when displacement constraints are applied.
2017-07-18T00:00:00ZSpectral data for simply periodic solutions of the sinh-Gordon equation
http://hdl.handle.net/10468/4821
Spectral data for simply periodic solutions of the sinh-Gordon equation
Klein, Sebastian
This note summarizes results that were obtained by the author in his habilitation thesis concerning the development of a spectral theory for simply periodic, 2-dimensional, complex-valued solutions u of the sinh-Gordon equation. Spectral data for such solutions are defined for periodic Cauchy data on a line (following Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data of such Cauchy data is answered. Finally a Jacobi variety for the spectral curve is constructed, and this is used to study the asymptotic behavior of the spectral data corresponding to actual simply periodic solutions of the sinh-Gordon equation on strips of positive height.
2017-04-04T00:00:00Z