We investigate the properties of excess dark current accumulated during the 100-second full-frame readout of the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) detectors. This excess dark current, called "readout dark", gives rise to ambient background gradients and hot columns in each ACS/WFC image. While readout dark signal is removed from science images during the bias correction step in CALACS, the additional noise from the readout dark is currently not taken into account. We develop a method to estimate the readout dark noise properties in ACS/WFC observations. We update the error (ERR) extensions of superbias images to include the appropriate noise from the ambient readout dark gradient and stable hot columns. In recent data, this amounts to about 5 e-/pixel added variance in the rows farthest from the WFC serial registers, and about 7 to 30 e-/pixel added variance along the stable hot columns. We also flag unstable hot columns in the superbias data quality (DQ) extensions. The new reference file pipeline for ACS/WFC implements these updates to our superbias creation process.
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Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools. less 2ff7e9595c
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