Lastly even with the reduction of size P then

Lastly, even with the reduction of size P, then the labelling may remain ambiguous. Indeed, in the case of overlaps, it is theoretically impossible to reduce P to 1 by definition. In the absence of a more thorough method of reduction of P, heuristic methods can be employed to assign a “score” to each possible member of P, to provide a ranked list of possible candidates. Such a ranked list allows for more rapid rejection of unlikely combinations, such as mass 2 being suggested as (2H)22+, rather than the more probable, H2+.
For the purposes of this work, a highly simplistic weighting scheme is utilised to roughly separate highly unlikely from possible elements. To do this, an assumed bulk composition multiplied by the natural abundance is used to assign a relative weight to the occurrence of each isotope. The product of the isotopic scores is the score for the final molecular ion. As an example, for an Fe–Mn alloy with 20at% Mn, the score for an 56Fe54Fe molecular GSK461364 would be (0.8×0.917)(0.8×0.058)=0.034, assuming no contaminant species. For elements typically not present in the bulk, but present in the analysis as contaminants (e.g. H and O), a weighting factor must be given, based upon the propensity of the material (in the case of H) to be present in the APT dataset – unfortunately, estimations for this can be quite arbitrary. However, as the quality of the ranking is only heuristic and not exact in nature, inaccuracies below order-of-magnitude levels often do not change the relative ranking of the elements of P.
Whilst it is now possible to generate a suggestion set P, and roughly rank P using compositional data, additional data regarding peak positions is required for the reduction step. This places an additional burden on operators – however this too can be partially automated. Unlike the peak identification stage, APT mass spectral peak detection fundamentals are not too dissimilar to other mass spectral methods. It has long been considered that peak detection methods can be effective in correctly extracting peaks from a mass spectral signal [10], specifically in the related mass spectral imaging technique of MALDI-TOF.
Such peak extraction methods compute the total peak area without a-priori peak shape assumptions. Indeed, considerable work has been conducted in the area, with comprehensive reviews of the relative strengths and weaknesses of these automated approaches [11]. In techniques such as MALDI-TOF, mass spectra are highly complex [12], and peaks can be present in high mass regions, such as ~10,000Da [13].
The MALDI-TOF tool “MaldiQUANT” was selected for the use in this work for the purposes of peak and background extraction [14], as it has been extensively developed. Comparative reviews for various signal processing techniques (such as wavelets [15], MEND [16]), are further discussed in detail elsewhere [17]. The optimisation of the peak extraction and identification steps for the context of APT are outside the scope of this work – peak detection here is used only to demonstrate the complete processing chain.
Similar to the method of Andreev [16], MaldiQuant was used to process time-domain signals, rather than the m/z domain, due to the non-linearity of the transform between the two domains, which results in artificially altered peak and background shapes. The output from MaldiQUANT which is relevant to this work is a set of detected peaks, and a background spectrum.
For this work, the method used was the wavelet “TopHat” mode [14], with a fixed Half-Width of 0.3amu1/2. The cutoff amplitude for thresholding the wavelet-processed signal was set by first manually ranging, then reducing the cutoff until the same number of ranges (within a small tolerance ~2 peaks) was identified by the automated detector as for the manual ranging. In a full implementation, pre-calibrated thresholds can be used. Automatic identification was performed on the peak positions, and the identity was assigned as the highest ranked species from the set of suggestions for each peak.