Fitting the curve in Excel®:Systematic curve fitting of laboratory and remotely sensed planetary spectra

Spectroscopy in planetary science often provides the only information regarding the compositional and mineralogical make up of planetary surfaces. The methods employed when curve fitting and modelling spectra can be confusing and difficult to visualize and comprehend. Researchers who are new to working with spectra may find inadequate help or documentation in the scientific literature or in the software packages available for curve fitting. This problem also extends to the parameterization of spectra and the dissemination of derived metrics. Often, when derived metrics are reported, such as band centres, the discussion of exactly how the metrics were derived, or if there was any systematic curve fitting performed, is not included. Herein we provide both recommendations and methods for curve fitting and explanations of the terms and methods used. Techniques to curve fit spectral data of various types are demonstrated using simple-to-understand mathematics and equations written to be used in Microsoft Excel® software, free of macros, in a cut-and-paste fashion that allows one to curve fit spectra in a reasonably user-friendly manner. The procedures use empirical curve fitting, include visualizations, and ameliorates many of the unknowns one may encounter when using black-box commercial software. The provided framework is a comprehensive record of the curve fitting parameters used, the derived metrics, and is intended to be an example of a format for dissemination when curve fitting data

Why Take Painkillers?

Accounts of the nature of unpleasant pain have proliferated over the past decade, but there has been little systematic investigation of which of them can accommodate its badness. This paper is such a study. In its sights are two targets: those who deny the non-instrumental disvalue of pain's unpleasantness; and those who allow it but deny that it can be accommodated by the view—advanced by me and others—that unpleasant pains are interoceptive experiences with evaluative content. Against the former, I argue that pain's unpleasantness does indeed have noninstrumental disvalue; against the latter I argue both that my critics’ own desire-theoretic accounts of pain's unpleasantness cannot accommodate such disvalue, and that my evaluativist view can—either by appealing to “anti-unpleasantness” desires or by exploiting pain's perceptuality

Improving Existing Delay Analysis Techniques for the Establishment of Delay Liabilities

Delay analysis and schedule compression are normally treated as separate, independent, aspects of the study of delays and their effects on the completion of construction projects. This paper examines the feasibility of integrating the delay analysis and schedule compression functions into a broad-scoped two-stage process. The main issue is shown to be the kind of delay analysis required for each stage of the process and seven existing techniques are illustrated for use in conjunction with schedule compression. Some necessary modifications to these techniques are identified together with a typology for categorising each technique

Combination technique based second moment analysis for elliptic PDEs on random domains

In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance with leading order in the amplitude of the random domain perturbation. The partial differential equation for the covariance is a tensor product Dirichlet problem which can efficiently be determined by Galerkin’s method in the sparse tensor product space. We show that this Galerkin approximation coincides with the solution derived from the combination technique if the detail spaces in the related multiscale hierarchy are constructed with respect to Galerkin projections. This means that the combination technique does not impose an additional error in our construction. Numerical experiments quantify and qualify the proposed method

Second moment analysis for Robin boundary value problems on random domains

We consider the numerical solution of Robin boundary value problems on random domains. The proposed method computes the mean and the variance of the random solution with leading order in the amplitude of the random boundary perturbation relative to an unperturbed, nominal domain. The variance is computed as the trace of the solution’s two-point correlation which satisfies a deterministic boundary value problem on the tensor product of the nominal domain. We solve this moderate high-dimensional problem by either a low-rank approximation by means of the pivoted Cholesky decomposition or the combination technique. Both approaches are presented and compared by numerical experiments with respect to their efficiency