D.Phil. (Mathematical Statistics) / Fractional Brownian motion and its increment process, fractional Gaussian noise, are syn- onymous with the concept of long range dependence. A strictly stationary time series is said to exhibit long range dependence or long memory if its autocorrelations decrease to zero as a power of the lag, but their sum over all lags is not absolutely convergent. This phenomenon has been observed in numerous scientific areas such as hydrology, ethernet traffic data, stock returns and exchange rates, to name just a few. The extent of long memory dependence is characterized by the value of the so called Hurst exponent or Hurst coefficient H. Approximate normality and unbiasedness of the maximum likelihood estimate of H hold reasonably well for sample sizes as small as 20 if the mean and scale parameters are known. We show in a Monte Carlo study that if the latter two parameters are unknown, the bias and variance of the maximum likelihood estimate of H both increase substantially. We also show that the bias can be reduced by using a jackknife or parametric bootstrap proce- dure. However, in very large samples, maximum likelihood estimation becomes problematic because of the large dimension of the covariance matrix that must be inverted. We consider an approach for estimating the Hurst exponent by taking first order differ- ences of fractional Gaussian noise. We find that this differenced process has short memory and that, consequently, we may assume approximate independence between the estimates of the Hurst exponents in disjoint blocks of data. We split the data into a number of con- tiguous blocks, each containing a relatively small number of observations. Computation of the likelihood function in a block then presents no computational problem. We form a pseudo likelihood function consisting of the product of the likelihood functions in each of the blocks and provide a formula for the standard error of the resulting estimator of H. This formula is shown in a Monte Carlo study to provide a good approximation to the true standard error. Application of the methodology is illustrated in two data sets. The long memory property of a time series is primarily characterized by H. In general, such series are exceptionally long, therefore it is natural to enquire whether or not H remains constant over the full extent of the time series. We propose a number of tests for the hypothesis that H remains constant, against an alternative of a change in one or more values of H. Formulas are given to enable calculation of asymptotic p-values. We also propose a permutational procedure for evaluating exact p-values. The proposed tests are applied to three sets of data.

Approved for public release; distribution is unlimited / A group of lesser used analog control system design techniques, generally termed parameter plane methods, is examined through the use of an IBM compatible microcomputer program developed as part of this thesis. The coefficients of a system's characteristic polynomial are determined by the plant and any added compensators. As these coefficients are varied , so too are the roots of the characteristic equation and therefore the system response in terms of bandwidth, settling time, etc. In the parameter plane method, a designer selects two parameters of a system's compensator(s) . The parameters commonly represent such attributes as a compensator gain, pole, or zero but can be any linear system function. One or more system characteristics dictating desired system performance, such as relative damping or undamped natural frequency, are computer model inputs. The associated parameter values to achieve the input characteristics are output in graphical and/or tabular form. / http://archive.org/details/parameterplanean00kran / Lieutenant Commander, United States Navy

When an emerging outbreak occurs, stable parameter estimation and reliable projections of future incidence cases using limited (early) data can play an important role in optimal allocation of resources and in the development of effective public health intervention programs. However, the inverse parameter identification problem is ill-posed and cannot be solved with classical tools of computational mathematics. In this dissertation, various regularization methods are employed to incorporate stability in parameter estimation algorithms. The recovered parameters are then used to generate future incident curves as well as the carrying capacity of the epidemic and the turning point of the outbreak. For the nonlinear generalized Richards model of disease progression, we develop a novel iteratively regularized Gauss-Newton-type algorithm to reconstruct major characteristics of an emerging infection. This problem-oriented numerical scheme takes full advantage of a priori information available for our specific application in order to stabilize the iterative process. Another important aspect of our research is a reliable estimation of time-dependent transmission rate in a compartmental SEIR disease model. To that end, the ODE-constrained minimization problem is reduced to a linear Volterra integral equation of the first kind, and a combination of regularizing filters is employed to approximate the unknown transmission parameter in a stable manner. To justify our theoretical findings, extensive numerical experiments have been conducted with both synthetic and real data for various infectious diseases.

The three-parameter lognormal distribution is widely used in many areas of science. Some modifications have been proposed to improve the maximum likelihood estimator. In some cases, however, the modified maximum likelihood estimates do not exist or the procedure encounters multiple estimates. The purpose of this research is focused on estimating the threshold or location parameter , because when is known, then the other two estimated parameters are obtained from the first two MLE equations. In this research, a method for constructing confidence intervals, confidence limits, and point estimator for the threshold parameter is proposed. Monte-Carlo simulation, bisection method, and SAS/IML were used to accomplish this objective. The bias of the point estimator and mean square error (MSE) criteria were used throughout extensive simulation to evaluate the performance of the proposed method. The result shows that the proposed method can provide quite accurate estimates.

Complex networks is an interdisciplinary research area which focuses on the study of properties of complex systems that have many functional or structural subunits. Community detection algorithms are one of the major approaches to analyse complex networks with multilevel or overlapping community structures. This research work focuses on constructing a novel community detection approach for simplification of a given complex demographic network. The general process of the abstraction from concrete problems as well as the general definition of communities have not been well defined and all the existing methods are derived from specific backgrounds, leaving the reliabilities in other fields open to ques- tion. This specificity of the existing methods reveals the need for a general approach for community definition and detection. Here, we devise a general procedure to find community structures in concrete problems by classifying the concrete networks into two basic types: Transmission networks and Similarity networks. The relation among nodes in transmission networks are constructed by material transmission and the ones in similarity network are constructed by the similarity in properties of the nodes. We show that both the types can be represented based upon an unified graph model. Based on the model, we propose a generic approach, Relation Strength Measurement (RSM), to define the communities. We have demonstrated that the Effective Resistance Function (ERF), from the Klein and Randic’s electrical network model, is applicable for quantifying the relation among nodes. We have also introduced a community threshold parameter (CP) based on which, the RSM algorithm categorizes the network nodes into communities. We have compared the performance of our algorithm with other well known community detection methods. The simulation results show that the algorithm accurately obtains the division of community structure both in real-world and synthetic networks.

The manifold boundary approximation method, MBAM is a new technique used in approximating systems of equations using parameter reduction. This method and other approximation methods are introduced and described. Several current issues in performing MBAM are discussed in further detail. These issues significantly slow down the process of MBAM and create a barrier of entry for those wishing to use the method without a strong background in mathematics. A solution is proposed to automatically reparameterize models and evaluate specific types of variables approaching limits -- significantly speeding up the process of MBAM. An implementation of the solution is discussed.

Theanine is a free, non-protein amino acid found in Camellia sinensis (tea) leaves. It is the main amino acid component in tea and contributes 1 to 2% of the dry weight of tea leaves. The content of amino acids is a key green tea quality parameter. High grade teas contain high amounts of theanine. It is responsible for the sweet, brothy umami taste of green tea. To date there is no international standard method for the analysis of theanine in tea samples. Several methods with different advantages and disadvantages have been reported but most of them are unsuitable for routine quality control analysis in commercial tea samples. In this study, a high performance liquid chromatography (HPLC) method with evaporative light scattering detection for the determination of theanine in tea samples has been developed. Chromatographic separation of theanine was achieved by reverse phase HPLC using a phenyl-hexyl column and isocratic water elution within 8 minutes. The method requires no sample derivatization and includes simple sample clean-up. Applying the same chromatographic conditions to a widely available C18 column, separation of theanine was achieved within 10 minutes. The successful application of the C18 column renders this method widely applicable. The method is linear over several orders of magnitude and the LOD are 11.53 and 10.83 μg/ml and the LOQ are 39.44 and 35.10 μg/ml for the phenyl-hexyl and C18 column, respectively. Simple but effective sample preparation and polyvinylpolypyrrolidone pre-treatment, along with the short analysis time facilitates high sample throughput (~40 samples can be prepared in an 8 hour day with overnight analysis by HPLCELSD). The method is selective, precise, accurate and practical for the quantification of theanine in tea extracts and was successfully used to determine theanine content in a variety of tea samples. The sensitivity and simplicity of this method renders it suitable for use in routine theanine analysis in quality control laboratories. Green tea, a simple refreshing beverage, has been believed to have therapeutic uses for centuries. Scientists have recognized that the wide range of physiological functions of green tea is due to the presence of catechins. An increasing body of evidence is showing that methylated forms of catechins have potent inhibitory activities to allergies. In addition to the methylated catechins, another relative novel group of catechins exists, namely digallated catechins. The medicinal value of these compounds is not yet known, but it is reasonable to speculate that the antioxidant capacity of digallated catechins will be superior to that of epigallocatechin gallate due to the 3 additional hydroxyl groups provided by the second gallic acid moiety. In this study reverse phase UPLC/ESI-MS/MS was effectively applied to investigate the presence of digallated and methylated catechins in crude tea extract. Low abundance catechins (-)-epigallocatechin-(O-3”-methyl) gallate ([M + H]+, m/z 473) and (-)-epicatechin-3-(O-3”-methyl) gallate ([M + H]+, m/z 457) were successfully detected at 31.9 and 37.5 minutes, respectively. The 2 digallated catechins investigated could not be detected, possibly due to being present at concentrations below the limit of detection. Compared to conventional HPLC/ESI-MS/MS, increased resolution and sensitivity, 80% less use of solvent and significantly reduced analysis times were observed. / Dissertation (MSc)--University of Pretoria, 2009. / Biochemistry / unrestricted

Advances in technology have led to fully integrated operator consoles which offer a broad range of solutions. Industry's move towards networking has resulted in the operator consoles being located at critical sites throughout the plant-floor. However, a lot of programming effort is required in order to use these consoles effectively. <p>The project addressed the problem by developing a software interface for the future user in a distributed automation environment. The system developed is capable of operating on IBM industrial computers, connected through a communications network on a DAE environment. By using the functions provided, the future user is insulated from the lower level control sequences of the operator interface and need only be concerned about the operation of these functions. <p>A description of the development of each phase project is given, and the purpose and operation subroutines are also presented in this report. / Master of Science

Since the introduction of the lipid emulsion formulation in 1986, propofol has become established for induction as well as for maintenance of anaesthesia in veterinary practice1 including cats2;3-8. Propofol is rapidly metabolized by hepatic glucuronidation in most species and it has also been shown to undergo extrahepatic metabolism9-13, so that total body clearance may exceed liver blood flow in certain species. Because of their highly carniverous diet, cats are little exposed to antiherbivory compounds so that they have become deficient in UGP-glucuronosyltransferase (UGT)14. Consequently, a number of drugs are eliminated slowly15;16, often giving rise to prolonged half-lives of the parent drugs. Cats are therefore sensitive to the adverse effects of many drugs and toxins that are normally glucuronidated before elimination. It is therefore likely that the disposition of propofol may differ markedly from that of humans and other animal species17. Adam et al18 reported that for the cremophor propofol formulation in cats, volumes of distribution were smaller and elimination halflives were longer than those of pigs, rats and rabbits. In addition, pulmonary uptake has been demonstrated to occur in cats,19 however propofol’s pharmacokinetics have not been studied formally. The purpose of this study was to determine the pharmacokinetic behaviour of propofol after single intravenous injections. In comparison with man, the apparent central volume of distribution in domestic cats is small (0.56L.kg-1 body weight vs. 0.228L.kg-1) for the human pharmacokinetic parameter set of Marsh et al20 and the clearance (0.0086 L.kg-1.min-1 vs. 0.027 L.kg- 1.min-1) is approximately 2½ times slower in cats when compared with humans. Slow clearance should not influence recovery from anaesthesia following standard induction doses, because the early decreases in blood concentrations are predominantly due to redistribution of drug to various tissues (similar to the disposition of thiopentone which exhibits a slow total body clearance21. However it is possible that drug may accumulate within the body after prolonged infusions, resulting in delayed recovery times. This phenomenon is best described by calculating “context-sensitive” decrement-times by computer simulation22-24. Computer software♣ were used to calculate the 20%, 50% and 80% context-sensitive decrement times for the cat pharmacokinetic model. For comparative purposes, similar calculations were performed for an adult human male (weight 70 kg) using the pharmacokinetic parameter-set of Marsh et al20. Assuming that recovery from anaesthesia occurs after a 50% decrease in blood concentrations has taken place, it is apparent from the 50% context-senstive decrement-time graph that for infusions lasting up to 20 minutes (during which concentrations are kept constant), recovery can be expected to be rapid and predictable. However if infusions are administered for longer than 20 minutes, the recovery times of the “average” cat increase rapidly, reaching a plateau of 36 minutes, while recovery times of the human remain short, albeit increasing slowly. Awakening times become dramatically prolonged and unpredictable in both cats and humans if propofol concentrations are required to decrease by 80% for recovery to occur. Under these circumstances the 80% decrement time after a two-hour infusion is approximately two hours in cats and 45 minutes in humans. On the other hand, if dosing is conservative, so that blood concentrations need to decrease by only 20% for awakening to occur, then recovery times are short and predictable, being only a few minutes, regardless of the duration of the preceding infusion. These findings are in accordance with those of Pascoe et al25 who reported that cats took longer to recover after a short (30 min) infusion than after a long (150 min) infusion. In their crossover study, the propofol infusion rates were adjusted so that the cats were maintained at a light level of anaesthesia at which they responded sluggishly to pedal stimulation. It is therefore likely that propofol concentrations were kept steady and were similar during the 30-minute as well as during the 150-minute infusions. Delayed recovery has also been reported when propofol was administered to cats on consecutive days26. Conclusions and clinical relevance: We recommend that propofol infusions be administered to cats only for fairly short procedures and that for prolonged surgery, maintenance of anaesthesia should be accomplished using other drugs. In order to decrease the propofol dose, premedication and analgesic supplements should be co-administered to provide “balanced” anaesthesia. ♣ TIVA Trainer version 8, author Frank Engbers, Leiden University Medical Centre Copyright / Dissertation (MMedVet)--University of Pretoria, 2009. / Companion Animal Clinical Studies / unrestricted

Although Essential Tremor (ET) is the most common type of tremor, many patients are left without satisfactory treatment options. One potential alternative treatment to medication or surgery is a wearable tremor-suppressing device. However, optimizing the effectiveness of such a device requires knowledge of which muscles/joints are most responsible for tremor. To answer this question, current efforts simulate tremor propagation using a model of the neuromusculoskeletal dynamics of the upper limb. To guide efforts to identify realistic model parameters and use the model to determine the mechanical origin of tremor, we performed preliminary parameter estimation work and a thorough sensitivity analysis of this tremor propagation model. The tremor propagation model included muscle activation inputs to the 15 major superficial muscles and joint displacement outputs in the 7 main degrees of freedom (DOF) from the shoulder to the wrist, resulting in 105 input-output relationships. We calculated the mean normalized sensitivities of all outputs to all 107 model parameters over the tremor band (4 to 8 Hz), resulting in approximately 12,000 sensitivities. We found that sensitivities were relatively constant in the tremor band, except for shoulder adduction-abduction, which exhibited a large peak in sensitivity between 4 and 5 Hz. Averaged across the tremor band, the system was most sensitive to select elements of inertia, muscle force, muscle moment arm, damping, muscle time constants, and stiffness (in that order). The 19 highest all-input-excitation sensitivities were between 1.2 and 4.57, meaning a 100% change in parameter value produces 120-457% change in tremor. Conversely, the model includes many parameters to which the outputs are relatively insensitive. For example, the sensitivities to almost one third of the 107 parameters are below 0.1, meaning a 100% change in parameter value produces only a 10% change in tremor. To gain additional insight, we compared the sensitivities of the full model to those of a simpler model including only two inputs and two outputs. Analyzing the two-input two-output model revealed patterns in sensitivity which persist in the full model. The sensitivities of the full model were further compared to past studies that performed rudimentary sensitivity analyses and were found to match while adding significantly more parameter-specific sensitivity information. Future work will extend this sensitivity analysis to tremor at the hand, where it matters most.