Ultraviolet-visible spectroscopy provides color information on organic compounds during chemical reactions. Absorption spectra of a pH indicator during protonation show absorption bands from electronic transitions based on molecular structure. Information from the bands including the wavelength of maximum absorption and calculated molar extinction coefficient can provide specific parameters for the reactant (the indicator) and the product (the protonated indicator). However, these parameters never directly present what chemical reaction is occurring, which is typically only determined after identification of the compounds with other characterization methods. Here, we show that a geometric object, which was built out of the loci of chromaticity points for a polymer pH-indicator in CIELAB color space, indicates that the reaction is protonation. The object contains information about species, i.e., the pH-indicating portion and its protonated form. Each locus for different initial concentrations was a line segment, which corresponded to the protonation process. The segments for a polymer pH indicator with azobenzene as the pH-indicating dye portion at different initial concentrations created a planar triangle in CIELAB color space. For another polymer pH indicator of nitrophenol, the geometric space was a half line. The corresponding geometric equations may be specific to protonation including information about the chemical species.
In real-world dirty data, errors are often not randomly distributed. Rather, they tend to occur only under certain conditions, such as when the transaction is handled by a certain operator, or the weather is rainy. Leveraging such common conditions, or "cause conditions", the proposed data-cleansing algorithm resolves multi-tuple conflicts with high speed, achieves higher completeness, and runs with high accuracy in realistic settings. We first present complexity analyses of the problem, pointing out two subproblems that are NP-complete. We then introduce, for each subproblem, heuristics that work in sub-polynomial time. We also raise the issue that some previous studies overlook the notion of repaircompleteness, which means, having less number of unsolved conflicts in the resulting repairs. The proposed method is capable of obtaining a complete repair if we are allowed to preprocess the input set of constraints. The algorithms are tested with three sets of data and rules. The experiments show that, compared to the state-of-the-art methods for conditional functional dependencies-based and FD-based data cleansing, the proposed algorithm scales better with respect to the data size, is the only method that outputs complete repairs, and is more accurate especially when the error distribution is skewed.
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