<p>The aim of this study is to illustrate, adapt and develop methods of survival analysis in analysing and estimating customer survival time in subscription-based businesses. Two particular objectives are studied. The rst objective is to redene the existing survival analysis techniques in business terms and to discuss their uses in order to understand various issues related to the customer-rm relationship.</p>

<p>Aggressive fiscal and monetary policies by governments of countries and central banks in developed markets could somehow push inflation to some very high level in the long run. Due to the decreasing of pension fund benefits and increasing inflation rate, pension companies are selling inflation-linked products to hedge against inflation risk. Such companies are seriously considering the possible effects of inflation volatility on their investment, and some of them tend to include inflationary allowances in the pension payment plan. In this dissertation we study the management of pension funds of the defined contribution type in the presence of inflation-recession. We study how the fund manager maximizes his fund&rsquo / s wealth when the salaries and stocks are affected by inflation. In this regard, we consider the case of a pension company which invests in a stock, inflation-linked bonds and a money market account, while basing its investment on the contribution of the plan member. We use a benchmarking approach and martingale methods to compute an optimal strategy which maximizes the fund wealth.</p>

While forage plays an important role in equine nutrition, little research has been conducted evaluating fiber utilization by young horses. Therefore, studies were conducted to compare in vivo digestibility and digesta passage in weanlings and mature horses (Exp 1) and yearlings and mature horses (Exp 2). All horses were fed forage-based diets at the same rate (on a metabolic BW basis; Exp 1: 67% alfalfa cubes, 33% concentrate; Exp 2: 75% timothy cubes, 25% concentrate). Ytterbium labeled hay and cobalt-ethylenediaminetetraacetic acid were used to estimate digesta mean retention time (MRT), while in vivo digestibility (DM, OM, and NDF) was measured using a total fecal collection method. Feed and water intake was similar between young and mature horses in both experiments. In Exp 1, there were no differences in digestibility or MRT due to age. The results suggested that weanling horses are capable of digesting a relatively high quality diet as efficiently as mature horses and that most of the development of the gastrointestinal tract occurs before 6 mo of age. In Exp 2, digestibility estimates were greater (P < 0.0311) for the yearlings than for the geldings. The increased digestive capacity of the yearlings was likely due to the longer MRT observed for the particulate phase in the yearlings (P = 0.0190). A third study was conducted to compare the microbial profiles of the feces of mares and foals. Fecal samples were collected from mare-foal pairs as the foal matured. The profiles of each pair, obtained using polymerase chain reaction-denaturing gradient gel electrophoresis, were compared and used to describe bacterial colonization in the foal. Mean similarity between mares and their foals on the day of parturition was low, but rapidly increased. Within 2 wk of parturition, similarity among mares and their foals was higher than among mature mares, suggesting that by 2 wk of age the bacterial species found in the foals’ gut are similar to those found in the mature horse. Collectively, the results from this series of experiments describe the early development of the foal’s digestive capacity.

Charnigo and Srinivasan originally developed compound estimators to nonparametrically estimate mean response functions and their derivatives simultaneously when there is one response variable and one covariate. The compound estimator maintains self consistency and almost optimal convergence rate. This dissertation studies, in part, compound estimation with multiple responses and/or covariates. An empirical comparison of compound estimation, local regression and spline smoothing is included, and near optimal convergence rates are established in the presence of multiple covariates. James and Stein proposed an estimator of the mean vector of a p dimensional multivariate normal distribution, which produces a smaller risk than the maximum likelihood estimator if p is at least 3. In this dissertation, we also extend their idea to a nonparametric regression setting. More specifically, we present Steinized local regression estimators of p mean response functions and their derivatives. We consider different covariance structures for the error terms, and whether or not a known upper bound for the estimation bias is assumed. We also apply Steinization to compound estimation, considering the application of Steinization to both pointwise estimators (for example, as obtained through local regression) and weight functions. Finally, the new methodology introduced in this dissertation will be demonstrated on numerical data illustrating the outcomes of a laboratory experiment in which radiation induces nanoparticles to scatter evanescent waves. The patterns of scattering, as represented by derivatives of multiple mean response functions, may be used to classify nanoparticles on their sizes and structures.

Horses consume large amounts of fiber in their diet, which may affect digestibility and digesta rate of passage. The objective of these studies was to assess the effects of diet composition on digestibility and rate of passage in horses using mathematical models. Using previously published data, forage dry matter digestibility (DMD) was related to forage neutral detergent fiber (NDF) concentrations and crude protein (CP) concentrations (DMD = 66.1178 – 0.3410*NDF + 0.6356*CP, DM basis; P < 0.001). In a second experiment, horses were fed diets formulated to have high fiber (HF, n= 3; NDF = 55.3%, CP = 11.8%) or low fiber (LF, n = 3; NDF = 40.5%, CP = 13.3%) concentrations. The LF treatment had greater DM, organic matter, and gross energy digestibilities (P < 0.05), whereas the HF treatment had greater NDF digestibility (P < 0.05). Mathematical models were useful to determine mean retention time (MRT) and there were no differences between model MRT and algebraic MRT, or treatment. Some compartmental parameters were different between treatments (P < 0.05), indicating that dietary fiber may alter some components of digesta passage in horses.

HIV/AIDS is widely spread and ranks as the sixth biggest killer all over the world. Moreover, due to the rapid replication rate and the lack of proofreading mechanism of HIV virus, drug resistance is commonly found and is one of the reasons causing the failure of the treatment. Even though the drug resistance tests are provided to the patients and help choose more efficient drugs, such experiments may take up to two weeks to finish and are expensive. Because of the fast development of the computer, drug resistance prediction using machine learning is feasible. In order to accurately predict the HIV drug resistance, two main tasks need to be solved: how to encode the protein structure, extracting the more useful information and feeding it into the machine learning tools; and which kinds of machine learning tools to choose. In our research, we first proposed a new protein encoding algorithm, which could convert various sizes of proteins into a fixed size vector. This algorithm enables feeding the protein structure information to most state of the art machine learning algorithms. In the next step, we also proposed a new classification algorithm based on sparse representation. Following that, mean shift and quantile regression were included to help extract the feature information from the data. Our results show that encoding protein structure using our newly proposed method is very efficient, and has consistently higher accuracy regardless of type of machine learning tools. Furthermore, our new classification algorithm based on sparse representation is the first application of sparse representation performed on biological data, and the result is comparable to other state of the art classification algorithms, for example ANN, SVM and multiple regression. Following that, the mean shift and quantile regression provided us with the potentially most important drug resistant mutants, and such results might help biologists/chemists to determine which mutants are the most representative candidates for further research.

Decaying fossil fuel resources, international relation complexities, and the risks associated with nuclear power have led to an increased demand for alternative energy sources. Renewable energy sources offer adequate solutions to these challenges. Forecasting of solar energy has also increased over the past decade due to its use in photovoltaic (PV) system design, load balance in hybrid systems, and projected potential future PV system feasibility. Artificial neural networks (ANN) have been used successfully for solar energy forecasting. In this work, several meteorological variables from Saudi Arabia as a case study will be used to determine the most effective variables on Global Solar Radiation (GSR) prediction. Those variables will be used as inputs for a proposed GSR prediction model. This model will be applicable in different locations and conditions. This model has a simple structure and offers better results in terms of error between actual and predicted solar radiation values.

The day-of-the-week effect is a market anomaly that manifests as the cyclical behaviour of traders in the market. This market anomaly was first observed by M.F.M. Osborne (1959). The literature distinguishes between two types of cyclical effects in the market: the cyclical pattern of mean returns and the cyclical pattern of volatility in returns. This dissertation studies and reports on cyclical patterns in the South African market, seeking evidence of the existence of the day-of-the-week effect. In addition, the dissertation aims to investigate the implications of such an effect on hedge fund managers in South Africa. The phenomenon of cyclical volatility and mean returns patterns (day-of-the-week effect) in the South African All-share index returns are investigated by making use of four generalised heteroskedastic conditional autoregressive (GARCH) models. These were based on Nelson's (1991) Exponential GARCH (EGARCH) models. In order to account for the risk taken by investors in the market Engle et al's, (1987) 'in-Mean' (risk factor) effects were also incorporated into the model. To avoid the dummy variable trap, two different approaches were tested for viability in testing for the day-of- the-week effect. In the first approach, one day is omitted from the equation so as to avoid multi-colinearity in the model. The second approach allows for the restriction of the daily dummy variables where all the parameters of the daily dummy variables adds up to zero. This dissertation found evidence of a mean returns effect and a volatility effect (day-of-the- week effect) in South Africa's All-share index returns data (where Wednesdays have been omitted from the GARCH equations). This holds significant implications for hedge fund managers. as hedge funds are very sensitive to volatility patterns in the market, because of their leveraged trading activities. As a result of adverse price movements, hedge fund managers employ strict risk management processes and constantly rebalance their portfolios according to a mandate, to avoid incurring losses. This rebalancing typically involves the simultaneous opening of new positions and closing out of existing positions. Hedge fund managers run the risk of incurring losses should they rebalance their portfolios on days on which the volatility in market returns is high. This study proves the existence of the day-of-the-week effect in the South African market. These results are further confirmed by the evidence of the trading volumes of the JSE's All-share index data for the period of the study. The mean returns effect (high mean returns) and low volatility found on Thursdays, coincide with the evidence that trading volumes on the JSE on Thursdays are the highest of all the days of the week. The volatility effect on Fridays, (high volatility in returns) is similarly correlated with the evidence of the trading volumes found in the JSE's All-share index data for the period of the study. Accordingly. hedge fund managers would be advised to avoid rebalancing their portfolios on Fridays, which show evidence of high volatility patterns. Hedge fund managers are advised to rather rebalance their portfolios on Thursdays, which show evidence of high mean returns patterns, low volatility patterns and high liquidity. / Thesis (M.Com. (Risk Management))--North-West University, Potchefstroom Campus, 2006.

The emergence of closed-loop Brayton cycle power plants, such as the PBMR, resulted in the need to simulate start-up transients for industrial multi-stage axial flow compressors operating at subsonic conditions. This implies that the delivery pressure and power requirements must be predicted for different mass flow rates and rotational speeds while operating in the first and fourth quadrants on the compressor performance charts. Therefore, an analytical performance prediction model for subsonic multi-stage axial flow compressors had to be developed that can be integrated into a generic network analysis software code such as Flownex. For this purpose, performance calculations based on one-dimensional mean-line analysis demonstrated good accuracy, provided that the correct models for losses, incidence and deviation are used. Such a model is therefore the focus of this study. A preliminary analytical performance prediction code, with the capability of interchanging between different deviation and loss models is presented. Reasonably complex loss models are integrated in association with the correct incidence and deviation models in a software package called "Engineering Equation Solver" (EES). The total pressure loss calculations are based on a superposition of theoretically separable loss components that include the following: blade profile losses, secondary losses and annulus losses. The fundamental conservation equations for mass, momentum and energy for compressible "rotating pipe" flow were implemented into the performance prediction code. Performance prediction models were validated against experimental data and evaluated according to their ease of implementation. Verification was done by comparing simulation results with experimental work done by Von Backstrom. This includes a calculation to determine the uncertainty in the experimental results. Furthermore, since the conventional definition of isentropic efficiency breaks down at the boundaries of quadrants on the performance charts, a new non-dimensional power formulation is presented that allows for the calculation of the compressor power in all of the relevant quadrants. Good comparison was found between simulation results and measurements in the first and fourth quadrant of operation. / Thesis (M.Ing. (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2007.

Dowel-type steel to timber connections are commonly used in timber structure. The load carrying capacity and the stress distribution within the connection area are complicated and the failure behavior of a connection depends on many parameters. The main purpose of this thesis was to verify, using the data obtained from previous experiments, the conventional design method of European Code 5(EC5) (hand calculation) for dowel type joints subjected to pure bending moment and other alternative design methods based on the finite element method (FEM) including the use of the mean stress approach and the extended finite element method (XFEM). Finite element models were created in the software ABAQUS. The models were then used to predict the load bearing capacity and compare this to the experimental results. In addition parametric studies were performed with modifications of material properties and other parameters. The closest prediction in relation to the test results was obtained using XFEM where the predicted capacity was 3.82% larger than the experimental result. An extension of the mean stress method going from a 2D-formulation to a 3D-formulation was verified as well. A general conclusion drawn from this work is that the numerical modelling approaches used should also be suitable for application to complex connections and situations involving other loading situations than pure tension.