Traditional analysis of aquifer tests uses the observed hydrograph at one well caused by pumping at another well for estimating transmissivity and storage coefficient of an aquifer. The analysis relies on Theis' or Jacob's approximate solution, which assumes aquifer homogeneity. Aquifers are inherently heterogeneous at different scales. If the observation well taps into a low permeability zone while the pumping well is located in a high permeable zone, the resulting situation contradicts the homogeneity assumption embedded in the traditional analysis. As a result, a practical but important question we ask: What do we derive from the traditional analysis? Using numerical experiments in synthetic aquifers, we answer this question. Results of the experiments indicate that the effective transmissivity, Teff , and storage coefficient, Seff , values vary with time, as well as the principal directions of the transmissivity, but both values approach their geometric means of the aquifer at large times. Analysis of the estimated transmissivity (T) and storage coefficient (S ) using well hydrographs from a single observation well shows that at early times, both the estimated T and S values vary with time. At late times, both estimates approach local averages near the observation well. The T value approaches but does not equal Teff , representing an average value over a broad area in the vicinity of the observation well while the S value converges to the value dominated by the storage coefficient near the observation wells (i.e., its average area is much smaller than that of the t value).

For over two decades, mathematicians and cryptologists have evaluated and presented the theoretical performance of Elliptic-curve scalar point-multiplication in projective geometry. Because computation in projective domain is composed of a wide array of formulations and computing optimizations, there is not a comprehensive performance comparison of point-multiplication using projective transformation available to verify its realistic efficiency in 64-bit x86 computing platforms. Today, research on explicit mathematical formulations in projective domain continues to excel by seeking higher computational efficiency and ease of realization. An explicit performance evaluation will help implementers choose better implementation methods and improve Elliptic-curve scalar point-multiplication. This paper was founded on the practical solution that obtaining realistic performance figures should be based on more precise computational cost metrics and specific computing platforms. As part of that solution, an empirical performance benchmark comparison between two approaches implementing projective Elliptic-curve scalar point-multiplication will be presented to provide the selection of, and subsequently ways to improve scalar point-multiplication technology executing in a 64-bit x86 runtime environment.

Receiver operating characteristic (ROC) curves are widely used in medical decision making. It was recognized in the last decade that only a specific region of the ROC curve is of clinical interest, which can be summarized by the partial area under the ROC curve (partial AUC). Early statistical methods for evaluating partial AUC assume that the data are from a specified underlying distribution. Nonparametric estimators of the partial AUC emerged recently, but there are theoretical issues to be addressed. In this dissertation, we propose two new nonparametric statistics, partially integrated ROC and partially integrated weighted ROC, for estimating partial AUC. We show that our partially integrated ROC statistic is a consistent estimator of the partial AUC, and derive its asymptotic distribution which is distribution free under the null hypothesis. In the partially integrated ROC statistic, when the ROC curve crosses the Uniform distribution function (CDF) and if the partial area evaluated contains the crossing point, or when there are multiple crossing, the partially integrated ROC statistic might not perform well. To address this issue, we propose the partially integrated weighted ROC statistic. This statistic evaluates the partially weighted AUC, where larger weight is given when the ROC curve is above the Uniform CDF and smaller weight is given when the ROC curve is below the Uniform CDF. We show that our partially integrated weighted ROC statistic is a consistent estimator of the partially weighted AUC. We derive its asymptotic distribution which is distribution free under the null hypothesis. We propose to apply our two nonparametric statistics to functional category analysis in microarray experiments. We define the functional category analysis to be the statistical identification of over-represented functional gene categories in a microarray experiment based on differential gene expression. We compare our statistics with existing methods for the functional category analysis both via simulation study and application to a real microarray data, and demonstrate that our two statistics are effective for identifying over-represented functional gene categories. We also emphasize the essential role of the empirical distribution function plots and the ROC curves in the functional category analysis.

The Receiver Operating Characteristic (ROC) curve is the plot of Sensitivity vs. 1- Specificity of a quantitative diagnostic test, for a wide range of cut-off points c. The empirical ROC curve is probably the most used nonparametric estimator of the ROC curve. The asymptotic properties of this estimator were first developed by Hsieh and Turnbull (1996) based on strong approximations for quantile processes. Jensen et al. (2000) provided a general method to obtain regional confidence bands for the empirical ROC curve, based on its asymptotic distribution. Since most biomarkers do not have high enough sensitivity and specificity to qualify for good diagnostic test, a combination of biomarkers may result in a better diagnostic test than each one taken alone. Su and Liu (1993) proved that, if the panel of biomarkers is multivariate normally distributed for both diseased and non-diseased populations, then the linear combination, using Fisher's linear discriminant coefficients, maximizes the area under the ROC curve of the newly formed diagnostic test, called the generalized ROC curve. In this dissertation, we will derive the asymptotic properties of the generalized empirical ROC curve, the nonparametric estimator of the generalized ROC curve, by using the empirical processes theory as in van der Vaart (1998). The pivotal result used in finding the asymptotic behavior of the proposed nonparametric is the result on random functions which incorporate estimators as developed by van der Vaart (1998). By using this powerful lemma we will be able to decompose an equivalent process into a sum of two other processes, usually called the brownian bridge and the drift term, via Donsker classes of functions. Using a uniform convergence rate result given by Pollard (1984), we derive the limiting process of the drift term. Due to the independence of the random samples, the asymptotic distribution of the generalized empirical ROC process will be the sum of the asymptotic distributions of the decomposed processes. For completeness, we will first re-derive the asymptotic properties of the empirical ROC curve in the univariate case, using the same technique described before. The methodology is used to combine biomarkers in order to discriminate lung cancer patients from normals.

Trade-offs in resource allocation underlie key life history traits of organisms. My dissertation focuses on the size-number trade-off in clonal broods of offspring using the polyembryonic wasp, Copidosoma bakeri parasitizing immature stages of the moth Agrotis ipsilon. I aim to characterize responses of wasp brood size and individual body mass by manipulating the environments in order to understand the allocation pattern in the size number trade-off. In reviewing the functional forms of trade-off relationships in relation to resource constraints, I distinguish among three main trade-off types based on graphical representations of the relationship between the trade-off variables: linear, convex (inverse), and concave. The size-number trade-off in C. bakeri shows convex relationship. Characteristics of the trade-off are sex specific: female broods have larger body mass but smaller brood size than do male broods. When food intake of the host was increased, the trade-off between wasp body mass and brood size for both sexes shifts toward both higher wasp brood size and higher body mass. When the host has better access to food late in development, the size-number trade-off curve moves up and to the right on the graph. However, the trait combinations shift along the same trade-off curve toward greater wasp body mass but smaller brood size when the host development time is shorter due to more resources in early in development. I also investigate temperature effects on the size-number trade-off. C. bakeri brood size significantly increases with high temperature early in host development. There is no shift in the allocation pattern of the size-number trade-off with temperature. Finally, I test effects of body mass on longevity, fecundity, and mating competitiveness of C. bakeri. Larger body size increases female longevity, and mated females produce more eggs than unmated females. There are no significant relationships between male body mass and longevity or mating competitiveness. Mating reduces male longevity independent of body mass. The different impact of body mass on fitness between male and female wasps suggests the observed sex-specific allocation patterns of the size-number trade-off. Implications of the experiments and possible follow-up work are discussed.

<p>The purpose of this study is to examine what affects the changes in credit spreads. A</p><p>regression model was performed where the explanatory variables were; volatility,</p><p>SP&500 index, interest-rate level the slope of yield curve and the dependent</p><p>variable was credit spread for each of CSUSDA, CSUSDBBB, and CSUSDB. We</p><p>found a positive correlation between these independent variables (Volatility, S&P</p><p>500index) and a negative correlation between interest-rate level and credit spreads.</p><p>These results were consistent with our hypothesis. However, the link between the</p><p>slope of yield curve and credit spreads was positive and that was inconsistent with</p><p>our hypothesis and some previous studies. The conclusion of this paper was a</p><p>change in credit spread is related to the variables that we used in our model. And</p><p>these variables explained about 50 per cent of this change.</p>

The conventional Zernike polynomial fit of circular aperture interferograms is reviewed and a more quantitative and statistical analysis is added. Some conventional questions such as the required number of polynomials, sampling requirements, and how to determine the optimum references surface are answered. Then, the analysis is applied to the polynomial fit of noncircular aperture interferograms and axicon interferograms. The problems and limitations of using Zernike polynomials are presented. A method of obtaining the surface figure error information from several smaller subaperture interferograms is analyzed. The limitations of the analysis for testing a large flat, a large parabola, or an aspheric surface are presented. The analysis is compared with the local connection method using overlapped wavefront information. Finally, the subaperture interferogram analysis is used to average several interferograms and to analyze lateral shearing interferograms.

We use a simulation model to generate tree-ring like data with systematic growth forcings and subject it to two methods of standardization: Regional Curve Standardization (RCS) and Negative Exponential Curve Standardization (NECS). The coherency between very low frequency forcings (hundreds of years) and the chronologies was higher when RCS was used to detrend the component series. There was no difference between standardization methods at decadal or annual time scales. We found that the detectability of systematic forcings was heavily dependent on amplitude and wavelength of the input signal as well as the number of trees simulated. These results imply that for very long tree-ring chronologies where the analyst is interested in low-frequency variability, RCS is a better method for detrending series if the requirements for that method can be met. However, in the majority of situations NECS is an acceptable detrending method. Most critically, we found that multi-centennial signals can be recovered using both methods.

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熱帶曲線(tropical curves) 是定義在熱帶半環(tropical semiring) 上的代數曲線。熱帶曲線是古典代數曲線經由某些賦值(valuation) 的映像，所以許多重要的代數曲線性質也同樣發生在熱帶曲線上。本篇論文我們試著將熱帶曲線圖形化。 首先，我們根據熱帶曲線的理論發展出幾個繪出熱帶曲線的演算法。再者，我們以電腦程式語言Python 去實現這些算演算法。我們發展的是跨平台的程式碼，可以在Linux, Mac OS X, Windows 等作業系統執行。 / Tropical curves are algebraic curves dened over the tropical semiring. They are the images of classical algebraic curves under some valuation maps, so reect many important properties of classical algebraic curves. In this thesis, we try to visualize tropical curves. We study the theory of tropical curves and develop several algorithms to draw the graphs of tropical curves. Furthermore, we implement these algorithms in Python programming language. These codes are cross-platform, running on Linux, Mac OS X, and Windows.