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Geographic information systems (GISs) are a highly influential tool in today's society, and are used in a growing number of applications, including planning, engineering, land management,and environmental study. As the field of GISs continues to expand, it is very important to observe and account for the error that is unavoidable in computerized maps. Currently, both statistical and non-statistical models are available to do so, although there is very little implementation of these methods. In this dissertation, I have focused on improving the methods available for analyzing error in GIS vector data. In particular, I am incorporating Bayesian methodology into the currently popular G-band error model through the inclusion of a prior distribution on point locations. This has the advantage of working well with a small number of points, and being able to synthesize information from multiple sources. I have also calculated the boundary of the confidence region explicitly, which has not been done before, and this will aid in the eventual inclusion of these methods in GIS software. Finally, I have included a statistical point deletion algorithm, designed for use in situations where map precision has surpassed map accuracy. It is very similar to the Douglas-Peucker algorithm, and can be used in a general line simplification situation, but has the advantage that it works with the error information that is already known about a map rather than adding unknown error. These contributions will make it more realistic for GIS users to implement techniques for error analysis. / Ph. D.

Yes / We describe a method for deriving the linear cortical magnification factor from positional error across the visual field. We compared magnification obtained from this method between normally sighted individuals and amblyopic individuals, who receive atypical visual input during development. The cortical magnification factor was derived for each subject from positional error at 32 locations in the visual field, using an established model of conformal mapping between retinal and cortical coordinates. Magnification of the normally sighted group matched estimates from previous physiological and neuroimaging studies in humans, confirming the validity of the approach. The estimate of magnification for the amblyopic group was significantly lower than the normal group: by 4.4 mm deg 1 at 18 eccentricity, assuming a constant scaling factor for both groups. These estimates, if correct, suggest a role for early visual experience in establishing retinotopic mapping in cortex. We discuss the implications of altered cortical magnification for cortical size, and consider other neural changes that may account for the amblyopic results.

The facts that relative consumption concerns may give rise both to positional and environmental externalities, and that these two externalities are increasingly transboundary require us to derive an optimal commodity tax in an international framework. The corrective tax policy decided at a national level is found to fail to internalize all positional and environmental externalities. The optimal tax policy under an international cooperative framework reflects correction for both global positional and environmental externalities. In this broader framework, we also characterize the provision of pollution abatement as an additional policy instrument. The results show that relative concerns for one of the private goods do not lead to any modification of the policy rule for public abatement.

This thesis addresses the problem of positional consensus of multi-agent systems. A positional consensus is achieved when the agents converge to a point. Some applications of this class of problem is in mid-air refueling of the aircraft or UAVs, targeting a geographical location, etc. In this research work some positional consensus algorithms have been developed. They can be categorized in two part (i) Broadcast control based algorithm (ii) Distributed control based algorithm. In case of broadcast based algorithm control strategies for a group of agents is developed to achieve positional consensus. The problem is constrained by the requirement that every agent must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. The mathematical formulation has been done in a linear programming framework that is computationally less intensive than earlier proposed methods. Moreover, a random perturbation input in the control command, that helps to achieve reasonable proximity among agents even for a large number of agents, which was not possible with the existing strategy in the literature, is introduced. This method is extended to achieve positional consensus at a pre-specified location. A comparison between the LP approach and the existing SOCP based approach is also presented. Some of the algorithm has been demonstrated successfully on a robotic platform made from LEGO Mindstorms NXT Robots. In the second case of broadcast based algorithm, a decentralized algorithm for a group of multiple autonomous agents to achieve positional consensus has been developed using the broadcast concept. Even here, the mathematical formulation has done using a linear programming framework. Each agent has some sensing radius and it is capable of sensing position and orientation with other agents within their sensing region. The method is computationally feasible and easy to implement. In case of distributed algorithms, a computationally efficient distributed rendezvous algorithm for a group of autonomous agents has been developed. The algorithm uses a rectilinear decision domain (RDD), as against the circular decision domain assumed in earlier work available in the literature. This helps in reducing its computational complexity considerably. An extensive mathematical analysis has been carried out to prove the convergence of the algorithm. The algorithm has also been demonstrated successfully on a robotic platform made from LEGO Mindstorms NXT Robots.

This thesis comprises three phases with a combined aim which was to investigate the effect of position on the lumbar intervertebral disc (IVD). The effect of position on the lumbar IVD in asymptomatic subjects and subjects with discogenic low back pain (DLBP) was explored using positional Magnetic Resonance Imaging (pMRI). Convenience samples of 11 asymptomatic and 34 DLBP subjects were recruited to have sagittal and axial pMRI scans performed in sitting (Neutral, Flexed and Extended), standing and lying (Supine and Prone extension) positions. The sagittal plane migration of the nucleus pulposus (NP) of each lumbar IVD in each position was measured from the sagittal and axial pMRI scans. Within and between group inferential analysis was performed using nonparametric tests. Both the asymptomatic and DLBP subjects’ demonstrated that position had statistically significant effects on the sagittal plane NP migration. Both groups demonstrated significantly greater posterior sagittal plane NP migration in Neutral and Flexed sitting positions compared to the other positions. However, between group comparisons identified that the asymptomatic subjects also demonstrated significantly greater posterior sagittal plane NP migration than the DLBP subjects. This pattern was more common in the upper lumbar IVDs (L1/2 and L2/3) between positions and less common in the lower IVDs (L4/5 and L5/S1) between positions. New knowledge regarding the behaviour of the lumbar IVD emerged from this research. The differences detected between the asymptomatic and DLBP subjects suggest that some current theories regarding DLBP may be incorrect. The results also support imaging of DLBP subjects in sitting positions as opposed to current supine positions. Although the limitations of the study reduce generalisation of the results, the implications for clinical practice, imaging and suggestions for further research from this work are important to improve understanding and conservative management of DLBP.