Multiple linear regression is a widely used statistical method. Its application, especially in the sciences, social sciences, and economics assists administrators in evaluating programs and planners in predicting future situations. The method is so common that most institutions have in their computer operation some standard programs to deal with the calculations. These traditional approaches use the method of least squares and yield an unbiased estimate of the parameters. The general linear model used is Y = Xβ+ e, where E(e) = 0, E(ee`) = σ2In and X is (n x p) and full rank. The least squares estimate of the unknown parameter vector β is then given by β = (X'X)-1X̀Y. This approach, however, often produces unsatisfactory (or even inaccurate) results if the data vectors are ill-conditioned. Such ill-conditioning is a result of non-orthogonal data vectors and inter-correlation of response variables that are unfortunately quite common in all fields.In recent years it has become obvious that for these applications the unbiased estimate is not necessarily the best over-all in terms of mean square error. A biased estimate may actually be of more value in analysis and prediction. Ridge estimators are biased estimators that have proved useful in these cases. In their basic form β(k) = [(X'X) + kI]-1 X́Y, they differ from the least squares estimator in that they have a small positive constant added to the diagonal elements of the X́X matrix.This thesis will first deal with the situations in which the least squares approach is not adequate and the cases where the ridge estimate contributes to a usable solution. The significant work which has been done in the field will be surveyed and the main problem of determining an appropriate constant k for the ridge estimate will be considered.

No description available.

Thesis (M.S.)--University of South Africa. / Includes bibliographical references (leaves 200-202).

This thesis focuses on ridge regression (RR) and least absolute shrinkage and selection operator (lasso). Ridge properties are being investigated in great detail which include studying the bias, the variance and the mean squared error as a function of the tuning parameter. We also study the convexity of the trace of the mean squared error in terms of the tuning parameter. In addition, we examined some special properties of RR for factorial experiments. Not only do we review ridge properties, we also review lasso properties because they are somewhat similar. Rather than shrinking the estimates toward zero in RR, the lasso is able to provide a sparse solution, setting many coefficient estimates exaclty to zero. Furthermore, we try a new approach to solve the lasso problem by formulating it as a bilevel problem and implementing a new algorithm to solve this bilevel program. / Graduate

Wrinkle ridges are among the most common tectonic structures on the terrestrial planets and provide important records of the history of planetary strain and geodynamics. The observed broad arches and superposed narrow wrinkles are thought to be the surface manifestation of blind thrust faults, which terminate in near-surface volcanic sequences and cause folding and layer-parallel shear. However, the subsurface tectonic architecture associated with the ridges remains a matter of debate. Here we present direct observations of a wrinkle ridge thrust fault where it has been exposed by erosion in the southern wall of Melas Chasma on Mars. The thrust fault has been made resistant to erosion, likely due to volcanic intrusion, such that later erosional widening of the trough exposed the fault plane as a 70km long ridge extending into the chasma. A plane fit to this ridge crest reveals a thrust fault with a dip of 13 degrees (+8 degrees, -7 degrees) between 1 and 3.5km depth below the plateau surface, with no evidence for listric character in this depth range. This dip is significantly lower than the commonly assumed value of 30 degrees, which, if representative of other wrinkle ridges, indicates that global contraction on Mars may have been previously underestimated.

No description available.

Thesis advisor: Mark D. Behn / The global mid ocean ridge system is segmented by transform faults and non-transform discontinuities. Oceanic transform faults display distinct morphology characterized by a deep valley and shallow transverse ridges on either side of the valley. Although the morphology of oceanic transform faults is known to first order, there is no consensus on the processes that form the transform valley and/or the adjacent transverse ridges. To date, most models of transform morphology attribute these features to either transform-normal extension or to shear stresses induced by slip along the fault. In this thesis, I compile bathymetric data along 16 major transform faults on the Mid-Atlantic Ridge and identify the key morphological properties of each transform. Specifically, I estimate transform valley width, depth, and total relief measured from the valley floor to the adjacent transverse ridges. The strongest correlation is between the relief and maximum depth, but there is a weaker correlation between maximum depth and valley width. These morphologic properties are then compared to key fault parameters such as slip rate, fault-normal compression/extension rate, thermal area, and the seismic coupling ratio, which is defined as the fraction of total fault slip that occurs seismically. These comparisons are used to test models that describe mechanisms of the formation of the transform valley. The strongest correlation is between the fault thermal area and valley half width. This suggests that the width of the transform valley may be controlled by the shear stress applied to the fault as it slips. By contrast, the data are not consistent with a model in which the valley is created by extension across the fault, because our data show that the maximum transform valley depth increases with compression and not extension. / Thesis (MS) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.

Ground-water geology along the northwest foot of the Blue Ridge between Arnold Valley and Elkton, Virginia The area discussed in this report lies along the northwest flank of the Blue Ridge in Rockbridge, Augusta, and Rockingham counties, Virginia. It spans the boundary between the Blue Ridge and the Great Valley physiographic provinces. The southeastern (Blue Ridge) portion of the area is mountainous and underlain by Precambrian crystalline and lower Cambrian elastic rocks. It is a major water catchment area for the eastern edge of the Shenandoah Valley and is chiefly a National Forest preserve. Cambriancarbonate rocks and fine-grained elastics underlie the relatively level areas between the mountains and the major subsequent streams near their base. A thick unconsolidated mantle which slopes gently away from the mountains conceals bedrock over much of the area. Major well fields have been developed on level alluvial floodplains and terraces adjacent to the rivers. Some produce several million gallons of water each day from bedrock aquifers at depth of from 50 to over 700 feet. The average temperature within the area is about 55°F. Average annual precipitation is approximately 41 inches and is greatest in the mountains. About six inches becomes ground-water recharge. Artificial withdrawal by wells would increase the rate of recharge. Evapotranspiration frequently exceeds total precipitation during the summer and early autumn. Most streams which drain the Blue Ridge are perennial near the headwaters and intermittent northwest of the mountains. They may be influent to bedrock aquifers within or near the base of the mountains and near the confluence with subsequent streams where the clay mantle is deeply eroded, but are effluent in the intervening reaches. The perennial streams are dominantly effluent. The major rivers are sub•sequent and effluent. They receive surface drainage and overflow of ground-water reservoirs from the Blue Ridge and from dominantly carbonate terranes to the west and northwest. Streamflow of the major streams represents approximately one third of the average annual areal precipitation. The stratigraphic sequence within the area from older to younger is designated as fellows: Precambrian crystalline rocks; Precambrian-Lower Cambrian Catoctin Greenstone and Swift Run Formations; LowerCambrian elastics; Lower Cambrian Tomstown (Shady) Delomite; Lower Cambrian Waynesboro (Rome) Formation; Middle Cambrian Elbrook Formation; and the Upper Cambrian Conococheague Limestone. The Precambrian igneous and metamorphic rocks, and the lower portion of the Lower Cambrian elastics are normally relatively poor aquifers. Minor production is obtained from fractured zones at locations within the mountains. The Antietam formation, the upper portion of the Lower Cambrianelastics, is a major potential aquifer. One well in Buena Vista produces over 600 gpm of water of low mineralization. Similar sites abound along the base of the Blue Ridge. The Tomstown Dolomite is a major aquifer at Waynesboro where the DuPont well field produces over 11,000,000 gpd. The producing characteristics of the Tomstown formation near the mountains at locations remote from the major rivers, where it is commonly concealed by a thick impermeable mantle of clay, are virtually unknown. Thick beds of limestone and dolomite in the Waynesboro Formationare prolific aquifers at Glasgow and near Elkton. Argillaceous portions of the formation are commonly aquicludes although secondary permeability may be developed by fracturing. Several wells produce over 1000 gpm from aquifers in the Elbrookand Conococheague formations near Grottoes and south of Elkton. With some exceptions, the water produced from these formations is harder than that produced from older formations to the east. A mantle of Cenozoic gravel and clay up to 400 feet thick overlies the bedrock over wide areas. The lower portion consists primarily of silty clay which is largely residual. Near the base of the mountains where it is thickest. it consists largely of leached colluvial material derived from the adjacent formations. It is characteristically an aquiclude which inhibits direct downward percolation of water to the underlying bedrock. Water encountered in the bedrock below it is commonly under mild artesian head. The upper portion of the mantle consists dominantly of alluvial and colluvial gravel with a sandy clay matrix and discontinuous beds of sand or of sandy or silty clay. It lies unconformably over residual clay and bedrock and is probably of Pleistocene age. It grades into talus near the foot of the mountains. The Cenozoic mantle yields only small amounts of water of variable quality to domestic wells although several large springs issue from it. The structural geology of the area is complex. Interpretation is complicated by facies changes and poor exposure. Fractures produced by deformation of the brittle rocks provide permeability. The main effect of the structure is its effect on the distribution of potential aquifers. The occurrence of ground water within the area is probably influenced more by topography, distribution of the unconsolidated mantle, and lithologic characteristics of the bedrock than by structure. Calcium and magnesium bicarbonate is the principal chemical constituents of ground water produced from major wells and springs within the area. Water from the carbonate aquifers is commonly moderately hard (61-120 ppm as CaC03). Nearly all of the hardness is temporary(carbonate) and is approximately equivalent to the alkalinity. Concentrations of deleterious substances are low. Water from the elastic rocks is characterized of low mineralization and pH. It is corrosive to ferrous metals. The temperature of well waters varies from 12° to 15°c. (54° - 59°F.)with few exceptions. Quality of ground water can commonly be correlated with the geologic formation from which it is produced. The concentration of total dissolved solids in waters from the bedrock aquifers tends to increase with decreasing age of the aquifer and with distance from the mountains. Water from limestone is commonly more highly mineralized than that from dolomite. Waters from. the same formation tends to be more highly mineralized west of the major rivers than they are to the east. Mineralization of most of the waters studied is derived from the dissolution of the carbonate aquifers and is controlled by equilibrium relations between dolomite, calcite, and dissolved carbon dioxide. The degree of saturation of waters with respect to solid calcite and dolomite can be determined semiquantitatively by comparison of the equilibrium pH computed from water analyses with the measured pH. Waters from typical dolomite reservoirs are supersaturated with respect to dolomite. The ratio of the concentration of calcium to the concentration of magnesium of most samples reflects the composition of the reservoir rock. Most samples contain more calcium than magnesium. Relationships between the calcium-magnesium ratio, the total mineralization, and the degree of saturation of water samples with respect to the solid carbonates are useful to relate the geology of the area to its hydrology. The quality of river water fluctuates widely with meteorologic variations, but that of ground-water produced from bedrock in adjacent wells east of the river remains relatively constant. Recharge to the wells at depth is evidently sufficient to prevent downward percolation of appreciable quantities of surface flow into the good bores although pumping levels are commonly below river level. The quality of the water suggests that recharge is dominantly from the east. Dolomite aquifers underlying floodplain and terrace deposits east of the major rivers are most favorable for the industrial development of ground-water resources. Prospective areas are outlined. Wells located in minor stream valleys near the boundary between the Blue Ridge and the Valley also offers prospects of production from Antietam or Tomstownaquifers. Test-drilling is warranted. Drilling of test wells should be the first step of industrial site investigation. The location of wells should be based upon a detailed local surface geological investigation. / Doctor of Philosophy

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A RIDGE (Region of IncreaseD Gene Expression), as defined by previous studies, is a consecutive set of active genes on a chromosome that span a region around 110 kbp long. This study investigated RIDGE formation by focusing on the well-defined, immunological important MHC locus. Macrophages were assayed for gene expression levels using the Affymetrix MG-U74Av2 chip are were either 1) uninfected, 2) primed with IFN-g, 3) viral activated with mCMV, or 4) both primed and viral activated. Gene expression data from these conditions was studied using data structures and new software developed for the visualisation and handling of structured functional genomic data. Specifically, the data was used to study RIDGE structures and investigate whether physically linked genes were also functionally related, and exhibited co-expression and potentially co-regulation. A greater number of RIDGEs with a greater number of members than expected by chance were found. Observed RIDGEs featured functional associations between RIDGE members (mainly explored via GO, UniProt, and Ingenuity), shared upstream control elements (via PROMO, TRANSFAC, and ClustalW), and similar gene expression profiles. Furthermore RIDGE formation cannot be explained by sequence duplication events alone. When the analysis was extended to the entire mouse genome, it became apparent that known genomic loci (for example the protocadherin loci) were more likely to contain more and longer RIDGEs. RIDGEs outside such loci tended towards single-gene RIDGEs unaffected by the conditions of study. New RIDGEs were also uncovered in the cascading response to IFNg priming and mCMV infection, as found by investigating an extensive time series during the first 12 hours after treatment. Existing RIDGEs were found to be elongated having more members the further the cascade progress.