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Kernel methods are a well-studied approach for addressing regression problems by implicitly mapping input variables into possibly infinite-dimensional feature spaces, particularly in cases where standard linear regression fails to capture non-linear relationships in data. Therefore, the choice between standard linear regression and kernel regression can be seen as a tradeoff between constraints on the number of features and the number of training samples. Our results show that the Gaussian kernel consistently achieves the lowest mean squared error for the largest considered training size. At the same time, the standard ridge regression exhibits a higher mean squared error and lower fit time. We have proven algebraically that the solutions of standard ridge regression and kernel ridge regression are mathematically equivalent.

<P> A study of the reliability of semiconductor distributed feedback diode lasers is presented using the degree of polarisation of photoluminescence (DOP). Two figures of merit, v and w, are developed and used to characterise device aging times and performance. v measures the strain gradient between the top and middle of a device by calculating the difference in an area-averaged DOP between the middle and top of a fixed area of the device. w measures the average strain profile across the top of the device by taking the difference in an area-averaged DOP between the region immediately beneath the ridge and the regions to the immediate right and left of it. Further, the influence of aging and the nature of metal contact are explored as they relate to these metrics. </p> <P> Finite element fits to the DOP and rotated degree of polarisation of photoluminescence (ROP) are presented. The models thus generated are used to explain the nature of the strain observed in different devices. </p> / Thesis / Master of Applied Science (MASc)

Existing models of the hydrogeology in the Blue Ridge Province in the eastern United States generally assume a simplified two-layered system consisting of shallow unconsolidated and relatively homogeneous and porous regolith with a water-table aquifer that slowly supplies water downward to the underlying variably fractured crystalline bedrock. In these models, interconnected fractures in the crystalline bedrock act as conduits for predominantly downward vertical and limited horizontal flow. Fracture density is depthà limited and correlated with proximity to topographic lineaments. Current models consider the porous regolith as the primary water storage reservoir for the entire aquifer system. In this research, detailed hydrogeologic studies in the Blue Ridge Province in Floyd County, Virginia reveal a substantially different framework for groundwater flow. Recent acquisition of two-dimensional surface resistivity profiles collected using a variety of array techniques combined with borehole geophysical logs revealed new insights into this geologically complex province. Dipole-dipole arrays were particularly important in gathering high resolution resistivity profiles that document horizontal and vertical resistivity variation reflecting changes in subsurface geology and anomalous low resistivity areas in crystalline bedrock associated with fault zones. The shallow regolith contains unsaturated areas and also localized sand and clay prone facies with water table and confined aquifer conditions residing locally. Hydraulic heads between the shallow aquifer and the deeper fractured bedrock aquifer can vary by 20 m vertically. Within the crystalline bedrock are anomalous lower resistivity intervals associated with ancient fault shear zones. Brecciated rock adjacent to the shear zones, and the shear zones themselves, can be hydraulically conductive and serve as pathways for groundwater movement. Aquifer testing of the regolith-bedrock fracture system occurred over a 6-day period and produced rapid and relatively uniform drawdowns in surrounding wells completed in the fractured bedrock aquifers. The shallow aquifers experienced minimal drawdowns from the aquifer test indicating low vertical hydraulic conductivity and limited communication between the shallow and deeper bedrock aquifers. Water chemistry and chlorofluorocarbon (CFC) age dating analyses indicated significant differences between water samples from the shallow and deep aquifers. A new conceptual model for Blue Ridge aquifers is proposed based on these research findings. / Ph. D.

Streams are integrative systems spanning multiple spatial and temporal scales. Stream researchers, land-use managers, and policy decision makers must consider the downstream displacement of streams when approaching questions about stream ecosystems. The study of how anthropogenic land-use influences streams demands an ecosystem perspective, and this dissertation is an example of applying large scale analyses of stream reach responses, and linking the activity of humans in the landscape to stream structure and function. I investigate whether rural development and agriculture land-cover types influence abiotic and biotic stream responses. I establish a method for considering land-cover as an independent variable at multiple scales throughout a streams' watershed using hydraulic modeling. The travel time required for water to drain from the watershed to a stream reach provided a continuous index to delimit watershed sub portions along a spatial continuum. Within travel time zones (TTZs), I consider land-use at increasingly larger scales relative to a stream reach within which biotic responses are typically measured. By partitioning land-cover in TTZs, I was able to determine the spatial scale at which land-cover was most likely to influence in-stream responses. I quantified a suite of physical and biotic responses typical to the aquatic ecology literature, and found that streams did not respond much to rural development. Rural development influenced suspended and depositional sediments, and likely altered watershed hydrology though I was unable to find significant evidence supporting a hydrologic effect. Subtle differences in assemblages suggest that differences in sediment dynamics influenced macroinvertebrates and fish. Using the Land Cover Cascade (LCC) design, I link the influence of land-cover to biotic responses through a suite of multivariate models, focusing on sediment dynamics in an attempt to capture the subtle influence of hydrology and sediment dynamics. My dissertation provides future researchers with improved methods for considering land-cover as an independent variable, as well as introduces multivariate models that link land-cover to sediment dynamics and biota. My dissertation will assist future research projects in identifying specific mechanisms associated with stream responses to disturbance. / Ph. D.

Physical and geophysical data collected at the Fractured Rock Research Site in Floyd County, Virginia indicate that recharge rates to the subsurface are controlled by a small scale thrust fault associated with regional thrust faulting within the Blue Ridge Province. Recharge rates appear to be correlated to spatial variation in the hydraulic conductivity of the regolith, which has been influenced by weathering rates and the metamorphic and structural history of the underlying parent material. Previous studies conducted at the Fractured Rock Research Site suggest that recharge potential can be separated into two regions: one over a vertically oriented shear zone associated with the small scale thrust fault, and the other overlying a thrust fault hanging wall. The angle of dip of the thrust fault shear zone and the fracturing within the crystalline rock adjacent to the fault plane appear to serve as geologic controls that preferentially direct infiltrated meteoric water to a deeper confined aquifer. The structural competence of the granulite gneiss thrust fault hanging wall appears to act as a barrier to deeper groundwater recharge, causing the formation of a shallow semi-confined aquifer within the overlying regolith. In-situ analysis of matric potential and moisture content shows two distinctly different recharge processes that are spatially correlated with the structure of the shallow subsurface (regolith overlying the vertically oriented shear zone and regolith overlying the thrust fault hanging wall), and have been shown to have strong temporal correlations with the dynamics of the underlying saturated conditions. Recharge flux estimates within the regolith overlying the thrust fault hanging wall are uncharacteristically high, and appear to be offset within the monitored region by the upward hydraulic gradient associated with the potentiometric surface of the underlying semi-confined aquifer. Because of the influence exerted by the upward hydraulic gradient on matric potential within the unsaturated regolith overlying the semi-confined aquifer, accurate recharge estimates could not be obtained from the matric potential data recorded by the tensiometers along this portion of the transect. Recharge flux within the regolith overlying the vertically oriented shear zone is strongly controlled by the orientation and aerial extent of the thrust fault shear zone, and highlights the importance of accurate delineation of recharge areas in crystalline rock aquifer systems. / Master of Science

A solution to the regression model y = xβ+ε is usually obtained using ordinary least squares. However, when the condition of multicollinearity exists among the regressor variables, then many qualities of this solution deteriorate. The qualities include the variances, the length, the stability, and the prediction capabilities of the solution. An analysis called ridge regression introduced a solution to combat this deterioration (Hoerl and Kennard, 1970a). The method uses a solution biased by a parameter k. Many methods have been developed to determine an optimal value of k. This study chose to investigate three little used methods of determining k: the PRESS statistic, Mallows' C_k. statistic, and DF-trace. The study compared the prediction capabilities of the three methods using data that contained various levels of both collinearity and leverage. This was completed by using a Monte Carlo experiment. / Master of Science

Master of Science