Doctor of Philosophy / Department of Electrical and Computer Engineering / Sanjoy Das / The future energy grid is expected to operate in a decentralized fashion as a network of autonomous microgrids that are coordinated by a Distribution System Operator (DSO), which should allocate energy to them in an efficient manner. Each microgrid operating in either islanded or grid-connected mode may be considered to manage its own resources. This can take place through auctions with individual units of the microgrid as the agents. This research proposes efficient auction mechanisms for the energy grid, with is-landed and connected microgrids. The microgrid level auction is carried out by means of an intermediate agent called an aggregator. The individual consumer and producer units are modeled as selfish agents. With the microgrid in islanded mode, two aggregator-level auction classes are analyzed: (i) price-heterogeneous, and (ii) price homogeneous. Under the price heterogeneity paradigm, this research extends earlier work on the well-known, single-sided Kelly mechanism to double auctions. As in Kelly auctions, the proposed algorithm implements the bidding without using any agent level private infor-mation (i.e. generation capacity and utility functions). The proposed auction is shown to be an efficient mechanism that maximizes the social welfare, i.e. the sum of the utilities of all the agents. Furthermore, the research considers the situation where a subset of agents act as a coalition to redistribute the allocated energy and price using any other specific fairness criterion. The price homogeneous double auction algorithm proposed in this research ad-dresses the problem of price-anticipation, where each agent tries to influence the equilibri-um price of energy by placing strategic bids. As a result of this behavior, the auction’s efficiency is lowered. This research proposes a novel approach that is implemented by the aggregator, called virtual bidding, where the efficiency can be asymptotically maximized, even in the presence of price anticipatory bidders. Next, an auction mechanism for the energy grid, with multiple connected mi-crogrids is considered. A globally efficient bi-level auction algorithm is proposed. At the upper-level, the algorithm takes into account physical grid constraints in allocating energy to the microgrids. It is implemented by the DSO as a linear objective quadratic constraint problem that allows price heterogeneity across the aggregators. In parallel, each aggrega-tor implements its own lower-level price homogeneous auction with virtual bidding. The research concludes with a preliminary study on extending the DSO level auc-tion to multi-period day-ahead scheduling. It takes into account storage units and conven-tional generators that are present in the grid by formulating the auction as a mixed inte-ger linear programming problem.

Approved for public release; distribution is unlimited. / The use of higher-order statistics provides insight into signals which is not always available at lower orders. Additionally, Gaussian-distributed signals have the interesting characteristic of disappearing at higher orders. Because so much of the noise and inter- ference environment is Gaussian-distributed, higher-order statistics thus offer the promise of an additional method of noise reduction and interference mitigation. As communica- tions signals become more and more complex, any additional ability to reduce the effects of noise and interference will have a profound impact on communications, surveillance, and intelligence systems. / US Department of Defense author (civilian).

Bayesian subset selection suffers from three important difficulties: assigning priors over model space, assigning priors to all components of the regression coefficients vector given a specific model and Bayesian computational efficiency (Chen et al., 1999). These difficulties become more challenging in Bayesian quantile regression framework when one is interested in assigning priors that depend on different quantile levels. The objective of Bayesian quantile regression (BQR), which is a newly proposed tool, is to deal with unknown parameters and model uncertainty in quantile regression (QR). However, Bayesian subset selection in quantile regression models is usually a difficult issue due to the computational challenges and nonavailability of conjugate prior distributions that are dependent on the quantile level. These challenges are rarely addressed via either penalised likelihood function or stochastic search variable selection (SSVS). These methods typically use symmetric prior distributions for regression coefficients, such as the Gaussian and Laplace, which may be suitable for median regression. However, an extreme quantile regression should have different regression coefficients from the median regression, and thus the priors for quantile regression coefficients should depend on quantiles. This thesis focuses on three challenges: assigning standard quantile dependent prior distributions for the regression coefficients, assigning suitable quantile dependent priors over model space and achieving computational efficiency. The first of these challenges is studied in Chapter 2 in which a quantile dependent prior elicitation scheme is developed. In particular, an extension of the Zellners prior which allows for a conditional conjugate prior and quantile dependent prior on Bayesian quantile regression is proposed. The prior is generalised in Chapter 3 by introducing a ridge parameter to address important challenges that may arise in some applications, such as multicollinearity and overfitting problems. The proposed prior is also used in Chapter 4 for subset selection of the fixed and random coefficients in a linear mixedeffects QR model. In Chapter 5 we specify normal-exponential prior distributions for the regression coefficients which can provide adaptive shrinkage and represent an alternative model to the Bayesian Lasso quantile regression model. For the second challenge, we assign a quantile dependent prior over model space in Chapter 2. The prior is based on the percentage bend correlation which depends on the quantile level. This prior is novel and is used in Bayesian regression for the first time. For the third challenge of computational efficiency, Gibbs samplers are derived and setup to facilitate the computation of the proposed methods. In addition to the three major aforementioned challenges this thesis also addresses other important issues such as the regularisation in quantile regression and selecting both random and fixed effects in mixed quantile regression models.

Master of Science / Department of Statistics / James W. Neill

Master of Science / Statistics / Weixing Song / In this report, an improved estimation procedure for the regression parameter in simple linear regression models with the Laplace measurement error is proposed. The estimation procedure is made feasible by a Tweedie type equality established for E(X|Z), where Z = X + U, X and U are independent, and U follows a Laplace distribution. When the density function of X is unknown, a kernel estimator for E(X|Z) is constructed in the estimation procedure. A leave-one-out cross validation bandwidth selection method is designed. The finite sample performance of the proposed estimation procedure is evaluated by simulation studies. Comparison study is also conducted to show the superiority of the proposed estimation procedure over some existing estimation methods.

Master of Science / Department of Architectural Engineering and Construction Science / Kimberly Kramer / The flying buttress is one of the most prominent characteristics of Gothic architecture. Understanding stress distribution from the upper vaulted nave (high vault) to the flying buttress system would contribute greatly to preservation efforts of such iconic structures. Many investigations have emphasized structural analysis of Gothic flying buttresses, but only limited research how architectural design affects load distribution throughout the Gothic members exist. The objective of this investigation was to inspire engineers and architectural preservationists to develop further research in Gothic structural analysis and restoration by increasing understanding how architectural design of flying buttresses affects the load path being transmitted from the main superstructure to the lateral force resisting system. Several flying buttress designs under similar analytical parameters were compared in order to understand how member geometries affect stress distribution. Because Gothic design is architecturally complex, finite element analysis method was used to obtain member stress distribution (regions of compressive and tensile stresses). Architectural elevation schematics of the flying buttresses of prominent Gothic cathedrals were referenced when modeling the structural members to a computer software program (RAM Elements).

M.Ing. (Electrical and Electronic Engineering) / Please refer to full text to view abstract

The Hungarian company Cool Tej (one of the companies that belong to British Cool Milk Group) performs losses on distributing milk to schools in one particular part of Hungary. Therefore, the milk distribution in Hungary is the issue that was further analysed and for which various solutions were found and evaluated.

Faculty of Science School of Animal ,Plant and Enviromental Sciences 9707660j McConnachie@ukzn.ac.za / Characteristics comprising an energy budget of Pseudocordylus melanotus melanotus were investigated in terms of limiting factors for the lizard’s distribution, and included measures of thermal biology, metabolism and digestive physiology. Pseudocordylus m. melanotus is rupicolous, is limited to the temperate parts of southern Africa and exhibits adaptations to these environments. The distribution of the lizard was modelled using two different climate envelope modelling techniques, which are discussed in terms of the energy budget and factors limiting the distribution of the lizard. Pseudocordylus m. melanotus exhibits wide thermal tolerances. It can withstand body temperatures (Tb) below freezing, but freezing of body water, which occurs at ca. -5 ºC, is lethal. The lower critical minimum temperature was a surprisingly high measure for an apparently cold-adapted lizard. In the laboratory, the selected body temperature (Tsel) was ca. 30 ºC. In the wild, lizards thermoregulate by shuttling between hot and cold microclimates, modifying body postures and regulating activity times, and select Tbs of ca. 29 ºC in summer and ca. 26 ºC in winter. Energy expenditure was measured over a range of temperatures. MR increases significantly with increasing temperature. Body mass and metabolic rate (MR) were significantly related at 30 ºC only. The lack of significance at other temperatures can be ascribed to the small range of body mass over which measures were made. Energy gain in P. m. melanotus was quantified in terms of prey capture rates and by measuring aspects of digestive physiology. Prey capture attempts were 35 % successful and occurred ca. every 2 h 30 min in the field. Lizards consumed a variety of arthropods, but mainly ate beetles. Digestive rate and appetite increased significantly with increasing temperature. Apparent digestive efficiency (ca. 94 %) and apparent assimilation efficiency (ca. 87.2 %) were not affected by temperature. iii Two energy budgets were calculated; one based mainly on laboratory measures and the other based on the thermal profile of lizard body temperature measured in the field. The laboratory energy budget was approximately half that of the field energy budget. The field energy budget, however, provided a more realistic view of energy expenditure since it covered almost the entire thermal range experienced by lizards. Between 592.53 kJ (field energy budget) and 940.06 kJ (laboratory energy budget) per year is required for a standard 30 g P. m. melanotus to remain in energy balance. This means that lizards need to consume between 73.55 and 116.69 g of mealworms per year, which equates to ca. 740 to 1200 average mealworms. Any energy gained over and above these requirements can be allocated to growth, reproduction and storage. In terms of the lizard’s distribution, it will be excluded from areas where the available thermal environment and prey abundance do not allow the lizard to maintain a positive energy balance. The lizard is apparently at the cold limit of its range, so predicted climate change in southern Africa is unlikely to have a significant effect on the distribution of the lizard. Suitable crevices are essential to the lizard’s survival, particularly during periods of extreme cold when lizards may experience Tbs where they are incapacitated, or effectively ‘comatose’, while in retreats.

With the ripples in the financial markets and economic stresses that occur around the world today, it would be beneficial to have some insight into the tools that help investors learn about the riskiness of their portfolios. At what value is one's portfolio in danger of being completely wiped out? We aim to further the understanding of values such as these and give an assessment of some risk measures by investing in an interactive portfolio, as well as estimating the values at risk and expected shortfalls of this portfolio.