Hydrothermally Emplaced, Lower Mississippian, Tripolitic Chert and Its Possible Relationship to the Tri-State Lead-Zinc Mining District

Across the southern Ozark Region, northern Arkansas, southwestern Missouri, and northeastern Oklahoma, exposures of the Lower Mississippian Boone Formation and its equivalents exhibit well-developed tripolitic chert that has been mined, more or less continuously, for at least 80 years. The tripolitic chert is a replacement of an interval within the basal portion of the upper Boone Formation in Arkansas and Oklahoma, and equivalent to the Elsey Formation in Missouri. The movement of silica-rich, hydrothermal fluids appears to have been much like that of a confined aquifer. It followed the basal upper Boone Formation (Arkansas) = Elsey Formation (Missouri) and was bound below by an impermeable interval at the top of the lower Boone Formation (Arkansas) = Reeds Spring Formation (Missouri), and above by the base of the upper Boone Formation (Arkansas) = Burlington-Keokuk (Missouri). The first hydrothermal event incompletely silicified the basal upper Boone = Elsey Formation. After leaching of the remnant carbonate, thus forming the tripolitic chert, a second hydrothermal event deposited terminated and doubly terminated quartz crystals, and druse in the tripolitic chert voids. This hydrothermal event may have pro-duced the Mississippi Valley-Type (MVT) lead-zinc deposits in northeast Oklahoma and southwestern Missouri. The famous deposits at Picher, Oklahoma, and Joplin, Missouri, appear to be positioned in the apparent path of the hydrothermal fluid migration. While timing of these hydrothermal events is unclear, they may reflect lateral secretion produced by the Ouachita Orogeny in the Late Pennsylvanian

ON THE CONNECTIONS BETWEEN SEMIDEFINITE OPTIMIZATION AND VECTOR OPTIMIZATION

This paper works out connections between semidefinite optimization and vector optimization. It is shown that well-known semidefinite optimization problems are scalarized versions of a general vector optimization problem. This scalarization leads to the minimization of the trace or the maximal eigenvalue

Hybrid Newton-type method for a class of semismooth equations

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem

Analyzing 2D gel images using a two-component empirical bayes model

<p>Abstract</p> <p>Background</p> <p>Two-dimensional polyacrylomide gel electrophoresis (2D gel, 2D PAGE, 2-DE) is a powerful tool for analyzing the proteome of a organism. Differential analysis of 2D gel images aims at finding proteins that change under different conditions, which leads to large-scale hypothesis testing as in microarray data analysis. Two-component empirical Bayes (EB) models have been widely discussed for large-scale hypothesis testing and applied in the context of genomic data. They have not been implemented for the differential analysis of 2D gel data. In the literature, the mixture and null densities of the test statistics are estimated separately. The estimation of the mixture density does not take into account assumptions about the null density. Thus, there is no guarantee that the estimated null component will be no greater than the mixture density as it should be.</p> <p>Results</p> <p>We present an implementation of a two-component EB model for the analysis of 2D gel images. In contrast to the published estimation method, we propose to estimate the mixture and null densities simultaneously using a constrained estimation approach, which relies on an iteratively re-weighted least-squares algorithm. The assumption about the null density is naturally taken into account in the estimation of the mixture density. This strategy is illustrated using a set of 2D gel images from a factorial experiment. The proposed approach is validated using a set of simulated gels.</p> <p>Conclusions</p> <p>The two-component EB model is a very useful for large-scale hypothesis testing. In proteomic analysis, the theoretical null density is often not appropriate. We demonstrate how to implement a two-component EB model for analyzing a set of 2D gel images. We show that it is necessary to estimate the mixture density and empirical null component simultaneously. The proposed constrained estimation method always yields valid estimates and more stable results. The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.</p

An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering

In this work we study an interior penalty method for a finite-dimensional large-scale linear complementarity problem (LCP) arising often from the discretization of stochastic optimal problems in financial engineering. In this approach, we approximate the LCP by a nonlinear algebraic equation containing a penalty term linked to the logarithmic barrier function for constrained optimization problems. We show that the penalty equation has a solution and establish a convergence theory for the approximate solutions. A smooth Newton method is proposed for solving the penalty equation and properties of the Jacobian matrix in the Newton method have been investigated. Numerical experimental results using three non-trivial test examples are presented to demonstrate the rates of convergence, efficiency and usefulness of the method for solving practical problems