Pyrite oxidation in coal-bearing strata is recognised as the main precursor to Acidic Mine Drainage (AMD) generation. Predicting AMD quality and quantity for remediation, or proposed extraction, requires assessment of interactions between oxidising fluids and pyrite, and between oxidation products and groundwater. Current predictive methods and models rarely account for individual mineral weathering rates, or their distribution within rock. Better constraints on the importance of such variables in controlling rock leachate are required to provide more reliable predictions of AMD quality. In this study assumptions made during modelling of AMD generation were tested including; homogeneity of rock chemical and physical characteristics, controls on the rate of embedded pyrite oxidation and oxidation front ingress. The main conclusions of this work are:• The ingress of a pyrite oxidation front into coal-bearing strata depends on dominant oxidant transport mechanism, pyrite morphology and rock pore-size distribution.• Although pyrite oxidation rates predicted from rate laws and derived from experimental weathering of coal-bearing strata agree, uncertainty in surface area of framboids produces at least an order of magnitude error in predicted rates.• Pyrite oxidation products in partly unsaturated rock are removed to solution via a cycle of dissolution and precipitation at the water-rock interface. Dissolution mainly occurs along rock cleavage planes, as does diffusion of dissolved oxidant.• Significant variance of whole seam S and pyrite wt % existed over a 30 m exposure of an analysed coal seam. Assuming a seam mean pyrite wt % to predict net acid producing potential for coal and shale seams may be unsuitable, at this scale at least.• Seasonal variation in AMD discharge chemistry indicates that base-flow is not necessarily representative of extreme poor quality leachate. Summer and winter storms, following relatively dry periods, tended to release the greatest volume of pyrite oxidation products.

"Principal Components Analysis (PCA) is an important mathematical technique widely used in the world of quantitative finance. The ultimate goal of this paper is to construct a portfolio with hedging positions, which is able to outperform the SPY benchmark in terms of the Sharpe ratio. Mathematical techniques implemented in this paper besides principle component analysis are the Sharpe ratio, ARMA, ARCH, GARCH, ACF, and Markowitz methodology. Information about these mathematical techniques is listed in the introduction section. Through conducting in sample analysis, out sample analysis, and back testing, it is demonstrated that the quantitative approach adopted in this paper, such as principle component analysis, can be used to find the major driving factor causing movements of a portfolio, and we can perform a more effective portfolio analysis by using principle component analysis to reduce the dimensions of a financial model."

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My research makes three contributions to the literature. The first contribution is to find supportive evidence for the augmented Taylor rule model with orthogonalized bond market variables I build to more accurately describe and forecast the behavior the Federal Reserve, with improved model’s fit both in and out-of-sample. The second contribution to the existing literature is that I find supportive evidence for a macro explanation of industrial firm behavior in the United States. The third contribution of this paper is that I provide a new aspect to understand the monetary policy and the monetary policy transmission mechanism for both monetary policy practitioners and researchers. This research proceeds as the following: Essay one provides a literature review for the research in this dissertation discussing background and theories for both the empirical and theoretical applications of the Taylor rule, a tool for the setting of the federal funds rate. The second essay is designed to understand the setting of monetary policy by the Federal Reserve. I show that augment a simple Taylor rule with bond market information can significantly improve the model’s fit, both in and out-of-sample. The improvement is enough to produce lower forecast errors than those of non-linear policy models. In addition, the inclusion of these bond market variables resolves the parameter instability of the Taylor rule documented in the literature, and implies that the lagged federal funds rate plays a much smaller role than that suggested in the previous studies. The third essay examines the impact of monetary shocks on corporate cash holdings. I find evidence that small industrial firms hold onto cash when monetary policy is too tight and large industrial firms do the reverse both in the short-run and in the long-run. Further tests examine whether the long lasting loose monetary policy results in the pileup of corporate cash holdings. The evidence supports the assumption that industrial firms take the “long lasting lower interest rate” environment to hoard cash to buffer the monetary policy effectiveness.

This thesis is concerned with the problem of selection of important variables in Principal Component Analysis (PCA) in such a way that the selected subsets of variables retain, as much as possible, the overall multivariate structure of the complete data. Throughout the thesis, the criteria used in order to meet this requirement are collectively referred to as measures of Multivariate Association (MVA). Most of the currently available selection methods may lead to inappropriate subsets, while Krzanowskis (1987) M(subscript)2-Procrustes criterion successfully identifies structure-bearing variables particularly when groups are present in the data. Our major objective, however, is to utilize the idea of multivariate association to select subsets of the original variables which preserve any (unknown) multivariate structure that may be present in the data.The first part of the thesis is devoted to a study of the choice of the number of components (say, k) to be used in the variable selection process. Various methods that exist in the literature for choosing k are described, and comparative studies on these methods are reviewed. Currently available methods based exclusively on the eigenvalues of the covariance or correlation matrices, and those based on cross-validation are unsatisfactory. Hence, we propose a new technique for choosing k based on the bootstrap methodology. A full comparative study of this new technique and the cross-validatory choice of k proposed by Eastment and Krzanowski (1982) is then carried out using data simulated from Monte Carlo experiment.The remainder of the thesis focuses on variable selection in PCA using measures of MVA. Various existing selection methods are described, and comparative studies on these methods available in the literature are reviewed. New methods for selecting variables, based of measures of MVA are then proposed and compared ++ / among themselves as well as with the M(subscript)2-procrustes criterion. This comparison is based on Monte Carlo simulation, and the behaviour of the selection methods is assessed in terms of the performance of the selected variables.In summary, the Monte Carlo results suggest that the proposed bootstrap technique for choosing k generally performs better than the cross-validatory technique of Eastment and Krzanowski (1982). Similarly, the Monte Carlo comparison of the variable selection methods shows that the proposed methods are comparable with or better than Krzanowskis (1987) M(subscript)2-procrustes criterion. These conclusions are mainly based on data simulated by means of Monte Carlo experiments. However, these techniques for choosing k and the various variable selection techniques are also evaluated on some real data sets. Some comments on alternative approaches and suggestions for possible extensions conclude the thesis.

NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere.

The Singular Value Decomposition is one of the most useful matrix factorizations in applied linear algebra, the Principal Component Analysis has been called one of the most valuable results of applied linear algebra. How and why principal component analysis is intimately related to the technique of singular value decomposition is shown. Their properties and applications are described. Assumptions behind this techniques as well as possible extensions to overcome these limitations are considered. This understanding leads to the real world applications, in particular, image processing of neurons. Noise reduction, and edge detection of neuron images are investigated.

The purpose of this research is to address the problem of fault diagnosis of sensors which measure a set of direct redundant variables. This study proposes: 1. A method for linear senor fault diagnosis 2. An analysis of isolability and detectability of sensor faults 3. A stochastic method for the decision process 4. A nonlinear approach to sensor fault diagnosis. In this study, first a geometrical approach to sensor fault detection is proposed. The sensor fault is isolated based on the direction of residuals found from a residual generator. This residual generator can be constructed from an input-output model in model based methods or from a Principal Component Analysis (PCA) based model in data driven methods. Using this residual generator and the assumption of white Gaussian noise, the effect of noise on the isolability is studied, and the minimum magnitude of isolable fault in each sensor is found based on the distribution of noise in the measurement system. Next, for the decision process a probabilistic approach to sensor fault diagnosis is presented. Unlike most existing probabilistic approaches to fault diagnosis, which are based on Bayesian Belief Networks, in this approach the probabilistic model is directly extracted from a parity equation. The relevant parity equation can be found using a model of the system or through PCA analysis of data measured from the system. In addition, a sensor detectability index is introduced that specifies the level of detectability of sensor faults in a set of redundant sensors. This index depends only on the internal relationships of the variables of the system and noise level. Finally, the proposed linear sensor fault diagnosis approach has been extended to nonlinear method by separating the space of measurements into several local linear regions. This classification has been performed by application of Mixture of Probabilistic PCA (MPPCA). The proposed linear and nonlinear methods are tested on three different systems. The linear method is applied to sensor fault diagnosis in a smart structure and to the Tennessee Eastman process model, and the nonlinear method is applied to a data set collected from a fully instrumented HVAC system.

Prior to 1960, most countries over the world used traditional economic indicators to represent their social status. Economists mostly used Gross National Product, GNP, as a measurement of the social welfare standard of a country or a society. However, with the progress of the development, the traditional economic indicators were unable to follow the progress of social welfares. Therefore, it made economists hard to measure the status of social welfares. Sen (1977) thought that the development of human beings is not restricted to the increase of average disposable incomes only. He thought that people should use the indicators with more information to measure the distinctive diversity of welfares. Bauer (1966) first stated the social indicators as a measurement of social status and trends. Then, the so-called ¡§Social Indicators Movement¡¨ was aroused by Bauer¡¦s theory. As a result, to measure the development of a society entirely, people could determine the development from the medicine, health, economy, environment, and welfare aspects. In the researches about social developments, there were many discussions in building indicators of social welfare, quality of living, basic fulfillment, and development of welfare. The research is trying to establish a system of social indicators to measure the development from every aspect and selecting the social indicator index with representative indicators as a measurement of society development. Moreover, this research would analyze the systems of social indicators in Taiwan from 1982 to 2002 to see if the government made an appropriate allocation of resources in the executions of related policies. The research refers to 20 related indicator systems in Taiwan and overseas as their times of quotes and principles of selecting indicators to sum up 9 probable indicators. Then, the Principal Component Analysis method and the Varian method are adopted as research methods to abstract factors. Moreover, there are two abstracted factors. One is economic and environment factor and another one is medical welfare and unemployment factor. The research uses weighted method to find out the synthetic indicators in Taiwan from 1982 to 2002. The weighted multiple gained from factor analysis for the two factors is 0.8353 and 0.1647. Based on the data mining and analysis from second information, three scores were acquired, economic and environment factor, medical welfare and unemployment factor, and entirely performance. Each of these three scores shows the trend and the change year by year. The last, according the result from this analysis, the policy and recommendation was brought up.

To have a voice link with other diving partners or surface personnel, divers need to put on a communication mask. The second stage regulator or mouthpiece is equipped with a circuit to pick up the voice of the diver. Then the voice is frequency-modulates into ultrasonic signal to be transmitted into water. A receiver on the other side picks up the ultrasonic signal and demodulates it back to voice, and plays back in diver's earphone set. This technology is mature but not widely adopted for its price. Most divers still use their favorite way to communicate with each other, i.e. DSL (divers' sign language.) As more and more intelligent machines or robots are built to help divers for their underwater task, divers not only need to exchange messages with their human partners but also machines. However, it seems that there are not many input devices available other than push buttons or joysticks. We know that divers¡¦hands are always busy with holding tools or gauges. Additional input devices will further complicate their movement, also distract their attention for safety measures. With this consideration, this paper intends to develop an algorithm to read the DSL as input commands for computer-aided diving system. To simplify the image processing part of the problem, we attach an LED at the tip of each finger. The gesture or the hand sign is then captured by a CCD camera. After thresholding, there will only five or less than five bright spots left in the image. The remaining part of the task is to design a classifier that can identify if the unknown sign is one from the pool. Furthermore, a constraint imposed is that the algorithm should work without knowing all of the signs in advance. This is an analogy to that human can recognize a face is someone known seen before or a stranger. We modify the concept of eigenfaces developed by Turk and Pentland into eigenhands. The idea is to choose geometrical properties of the bright spots (finger tips), like distance from fingertips to the centroid or the total area of the polygon with fingertips as its vertices as the features of the corresponding hand sign. All these features are quantitative, so we can put several features together to construct a vector to represent a specific hand sign. These vectors are treated as the raw data of the hand signs, and an essential subset or subspace can be spanned by the eigen vectors of the first few large corresponding values. It is less than the total number of hand signed involved. The projection of the raw vector along these eigen vectors are called the principal components of the hand sign. Principal components are abstract but they can serve as keys to match the candidate from a larger pool. With these types of simple geometrical features, the success rate of cross identification among 30 different subjects' 16 gestures varies to 91.04% .