In this thesis we study three different problems: convex ancient solutions to the power-of-mean curvature flow; Sharp inequalities; regularity results in some applications of optimal transportation. The second chapter is devoted to the power-of-mean curvature flow; We prove some estimates for convex ancient solutions (the existence time for the solution starts from -\infty) to the power-of-mean curvature flow, when the power is strictly greater than \frac{1}{2}. As an application, we prove that in two dimension, the blow-down of an entire convex translating solution, namely u_{h}=\frac{1}{h}u(h^{\frac{1}{1+\alpha}}x), locally uniformly converges to \frac{1}{1+\alpha}|x|^{1+\alpha} as h\rightarrow\infty. The second application is that for generalized curve shortening flow (convex curve evolving in its normal direction with speed equal to a power of its curvature), if the convex compact ancient solution sweeps the whole space \mathbb{R}^{2}, it must be a shrinking circle. Otherwise the solution must be defined in a strip region. In the first section of the third chapter, we prove a one-parameter family of sharp conformally invariant integral inequalities for functions on the $n$-dimensional unit ball. As a limiting case, we obtain an inequality that generalizes Carleman's inequality for harmonic functions in the plane to poly-harmonic functions in higher dimensions. The second section represents joint work with Tobias Weth and Rupert Frank; the main result is that, one can always put a sharp remainder term on the righthand side of the sharp fractional sobolev inequality. In the first section of the final chapter, under some suitable condition, we prove that the solution to the principal-agent problem must be C^{1}. The proof is based on a perturbation argument. The second section represents joint work with Emanuel Indrei; the main result is that, under (A3S) condition on the cost and c-convexity condition on the domains, the free boundary in the optimal partial transport problem is C^{1,\alpha}.

The motor control of anthropomorphic robotic systems is a challenging computational task mainly because of the high levels of redundancies such systems exhibit. Optimality principles provide a general strategy to resolve such redundancies in a task driven fashion. In particular closed loop optimisation, i.e., optimal feedback control (OFC), has served as a successful motor control model as it unifies important concepts such as costs, noise, sensory feedback and internal models into a coherent mathematical framework. Realising OFC on realistic anthropomorphic systems however is non-trivial: Firstly, such systems have typically large dimensionality and nonlinear dynamics, in which case the optimisation problem becomes computationally intractable. Approximative methods, like the iterative linear quadratic gaussian (ILQG), have been proposed to avoid this, however the transfer of solutions from idealised simulations to real hardware systems has proved to be challenging. Secondly, OFC relies on an accurate description of the system dynamics, which for many realistic control systems may be unknown, difficult to estimate, or subject to frequent systematic changes. Thirdly, many (especially biologically inspired) systems suffer from significant state or control dependent sources of noise, which are difficult to model in a generally valid fashion. This thesis addresses these issues with the aim to realise efficient OFC for anthropomorphic manipulators. First we investigate the implementation of OFC laws on anthropomorphic hardware. Using ILQG we optimally control a high-dimensional anthropomorphic manipulator without having to specify an explicit inverse kinematics, inverse dynamics or feedback control law. We achieve this by introducing a novel cost function that accounts for the physical constraints of the robot and a dynamics formulation that resolves discontinuities in the dynamics. The experimental hardware results reveal the benefits of OFC over traditional (open loop) optimal controllers in terms of energy efficiency and compliance, properties that are crucial for the control of modern anthropomorphic manipulators. We then propose a new framework of OFC with learned dynamics (OFC-LD) that, unlike classic approaches, does not rely on analytic dynamics functions but rather updates the internal dynamics model continuously from sensorimotor plant feedback. We demonstrate how this approach can compensate for unknown dynamics and for complex dynamic perturbations in an online fashion. A specific advantage of a learned dynamics model is that it contains the stochastic information (i.e., noise) from the plant data, which corresponds to the uncertainty in the system. Consequently one can exploit this information within OFC-LD in order to produce control laws that minimise the uncertainty in the system. In the domain of antagonistically actuated systems this approach leads to improved motor performance, which is achieved by co-contracting antagonistic actuators in order to reduce the negative effects of the noise. Most importantly the shape and source of the noise is unknown a priory and is solely learned from plant data. The model is successfully tested on an antagonistic series elastic actuator (SEA) that we have built for this purpose. The proposed OFC-LD model is not only applicable to robotic systems but also proves to be very useful in the modelling of biological motor control phenomena and we show how our model can be used to predict a wide range of human impedance control patterns during both, stationary and adaptation tasks.

Essentially, there are two competing propositions on tax base choices. The optimal tax theory on taxation asserts that the broader the tax base the better the tax. On the other hand, some public choice proponents have argued that, at the constitutional level, we should choose to restrict the power to tax and thus limit the available base. These theories assert fundamentally different views on the state and its citizens. Within the traditional optimal tax framework, governments maximize residents utility and tax base broadening lowers the tax rate, thus there is a revenue neutral response. When, however, governments do not choose to maximize residents utility, then increases in the tax base can have an impact on governments revenues and spending. In order to determine if tax bases influence government spending data on forty-eight states were compiled for the years 1977 through 1992. A state finance system of equations was developed. Using three-stage least squares estimation in a fixed effects econometric model, the relationship between the broadness of a tax base and state government spending was estimated. The state sales tax base was the tax base used to study this relationship. The results of this estimation found that states with broader sales tax bases had higher spending, all else equal. This result suggest that governments do not act as if they maximize resident utility when making tax base and rate decisions, otherwise base broadness would have no impact on spending. An additional result from this empirical analysis, is that tax base and rates are inversely related, but the relationship does not lead to revenue-neutral adjustments.

This thesis first describes the reverse method of transformer design. An existing magnetic model for full-core shell-type transformers, based on circuit theory, is summarised. A magneto-static finite element model is introduced and two sample transformers are analysed. The magnetic model based on finite element analysis is shown to be more accurate than the model based on circuit theory. Partial-core resonant transformers are then introduced and their characteristics are explained using an equivalent circuit model. A method of measuring the winding inductances under resonant operation is developed and used to investigate the characteristics of two different tuning methods. A finite element model of the partial-core resonant transformer is developed by adopting the model for full-core shell-type transformers. The model results accurately match the measured inductance variation characteristics of three sample transformers and predict the onset of core saturation in both axial-offset and centre-gap arrangements. A new design of partial-core resonant transformer is arrived at, having an alternative core and winding layout, as well as multiple winding taps. The finite element model is extended to accommodate the new design and a framework of analysis tools is developed. A general design methodology for partial-core resonant transformers with fixed inductance is developed. A multiple design method is applied to obtain an optimal design for a given set of specifications and restrictions. The design methodology is then extended to devices with variable inductance. Three design examples of partial-core resonant transformers with variable inductance are presented. In the first two design examples, existing devices are replaced. The new transformer designs are significantly lighter and the saturation effects are removed. The third design example is a kitset for high-voltage testing, with the capability to test any hydro-generator stator in New Zealand. The kitset is built and tested in the laboratory, demonstrating design capability. Other significant test results, for which no models have yet been developed, are also presented. Heating effects in the core are reduced by adopting an alternative core construction method, where the laminations are stacked radially, rather than in the usual parallel direction. The new kitset is yet to be used in the field.

Estimation procedures and optimal designs for estimation of the individual parameters and of the global parameters are discussed under various conditions of prior knowledge. The extension to nonlinear parametrization of the response function ís based on the asymptotical validity of the results for the linear parametrization. For the case where the error variance and the dispersion matrix are unknown, an iterative estimation procedure is suggested. An example based on dental plaque pH profiles demonstrates the improvement that is achieved (a) through using the optimal design or a design that ís close to the optimal, and (b) through taking into account prior information. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Ambulanssjuksköterskor upplever att antalet uppdrag ökar och att tillgängligheten på ambulanser minskar. Speciellt för de allvarligaste uppdragen. Det upplevs också som att en del patienter ringer efter ambulans eller åker lite mer frekvent än vad som kan anses brukligt. Att ge dem adekvat hjälp samt frigöra ambulansresurser till mer akuta uppdrag borde gagna både den enskilda patienten samt ambulanssjukvården. Syftet med studien var att genom journalgranskning kartlägga mångbesökare och jämföra den prehospitala bedömningen med den slutdiagnos som ges på sjukhuset för att undersöka om de erbjuds en optimal vårdnivå. Studien är genomförd med en kvantitativ ansats där en retrospektiv journalgranskning använts för att finna de som åkt ambulans, i Skaraborg, till en vårdinstans fyra gånger eller fler under 2014. Resultatet visade att två tredjedelar av patienterna i kategorin var födda före 1950. De sökte i störst utsträckning för andningsbesvär, bröstsmärtor, buksmärta samt infektion. Endast 2,8% bedömdes ha psykiska besvär och 2,9% transporterades till en vårdcentral. Det visade sig också att en tredjedel av de patienter som räknades som mångbesökare aldrig lades in på sjukhuset. Av de som definierades som mångbesökare var 68 % över 60 år. Flera av dessa patienter skulle fått bättre hjälp om individuella vårdplaner tagits fram som utgått från en personcentrerad vård där hänsyn tagits till varje individs situation och egen åsikt. Det skulle också göra att flera av dessa ej behövt åka till en akutmottagning vilket antas givit ett minskat vårdlidande och högre tillgänglighet på akutambulanser.

Many domains, such as emergency assistance, agriculture, construction, and planetary exploration, will increasingly require effective coordination of teams of robots and humans to accomplish a collection of spatially distributed heterogeneous tasks. Such coordination problems range from those that require loosely coordinated teams in which agents independently perform their assigned tasks, to those that require tightly coordinated teams where all actions of the team members need to be tightly synchronized. The scenarios of interest to this thesis lie between these two extremes, where some tasks are independent and others are related by constraints such as precedence, simultaneity, or proximity. These constraints may be a result of different factors including the complementary capabilities of different types of agents which require them to cooperate to achieve certain goals. The manner in which the constraints are satisfied influences the overall utility of the team. This thesis explores the problem of task allocation, scheduling, and routing for heterogeneous teams with such cross-schedule dependencies. We first describe and position this coordination problem in the larger space of multi-robot task allocation problems and propose an enhanced taxonomy for this space of problems. Recognizing that solution quality is important in many domains, we then present a mathematical programming approach to computing a bounded-optimal solution to the task allocation, scheduling and routing problem with cross-schedule dependencies. Specifically, we present a branch-and-price algorithm operating on a set-partitioning formulation of the problem, with side constraints. This bounded optimal “anytime” algorithm computes progressively better solutions and bounds, until it eventually terminates with the optimal solution. By examining the behavior of this algorithm, we gain insight into the impact on problem difficulty of various problem features, particularly different types of cross-schedule dependencies. Lastly, the thesis presents a flexible execution strategy for the resulting team plans with cross-schedule dependencies, and results demonstrating the approach on a team of indoor robots

Planning is an essential part of intelligent behavior and a ubiquitous task for both humans and rational agents. One framework for planning in the presence of uncertainty is probabilistic planning, in which actions are described by a probability distribution over their possible outcomes. Probabilistic planning has been applied to different real-world scenarios such as public health, sustainability and robotics; however, the usage of probabilistic planning in practice is limited due to the poor performance of existing planners. In this thesis, we introduce a novel approach to effectively solve probabilistic planning problems by relaxing them into short-sighted problems. A short-sighted problem is a relaxed problem in which the state space of the original problem is pruned and artificial goals are added to heuristically estimate the cost of reaching an original goal from the pruned states. Differently from previously proposed relaxations, short-sighted problems maintain the original structure of actions and no restrictions are imposed in the maximum number of actions that can be executed. Therefore, the solutions for short-sighted problems take into consideration all the probabilistic outcomes of actions and their probabilities. In this thesis, we also study different criteria to generate short-sighted problems, i.e., how to prune the state space, and the relation between the obtained short-sighted models and previously proposed relaxation approaches. We present different planning algorithms that use short-sighted problems in order to solve probabilistic planning problems. These algorithms iteratively generate and execute optimal policies for short-sighted problems until the goal of the original problem is reached. We also formally analyze the introduced algorithms, focusing on their optimality guarantees with respect to the original probabilistic problem. Finally, this thesis contributes a rich empirical comparison between our algorithms and state-of-the-art probabilistic planners.

In this dissertation I present my approach and findings regarding the development of a simulation model for a small scale renewable energy system. A brief introduction provides the reader with the background as to why there is a need for such a simulation package. The project objectives, research methodology and the research contributions originating from the project is also described. A literature study was done on all the relevant technologies constituting the renewable energy system as well as the techniques required to model the system. A system breakdown identified the various sub modules as well as how they interface with each other. The simulation model was tested by using Alexander bay, South Africa, as a case study. The results obtained from the various modules were discussed and found to correlate with what was expected. Although not contained within the project’s scope, an additional analysis of the effect of the wind data’s resolution on the probable power output of a wind turbine was performed leading to a hypothesis regarding the estimation of a more accurate probable power output extrapolation from data with a coarse resolution. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013

The South African Department of Science and Technology is striving to develop a means of producing hydrogen gas in remote and civil areas through the use of renewable energy sources. For the purposes of creating such mobile hydrogen production facilities, a small-scale hydrogen production system based on renewable energy sources needs to be developed and modelled. This system is to serve as a pilot plant for further development of a large scale mobile hydrogen production facility. This work focuses on the characterisation of sizing algorithms for renewable energy sources which can determine component configurations that satisfy power requirements of the system. Additionally, optimal sizing techniques must be developed which can output an optimal plant configuration to a user based on cost and efficiency. To this end, a literature study was done on all the components that make up a renewable energy hydrogen system. The techniques researched were then applied to create algorithms capable of correctly sizing the required components of such a plant. These techniques were integrated into an application created in the LabVIEW environment, which is capable of outputting an optimal plant configuration based on the specific needs of a client. A case study was defined with which the results of the simulation models were verified. Using this work, a future, more comprehensive system may be developed and commercialised, building from the techniques implemented here. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013