Since Q commutes with homological shifts, for every spectrum ({X_cdot }), the shifts (C_cdot (X_n)[-n]) are also coalgebras over Q, and the transition maps in (10.7) are coalgebra maps, so that (C_cdot (X_cdot )) is also naturally a coalgebra over Q.
Note that the drawn variances correspond to fields with very slightly different spacings (varLambda_{mathrm{sq}}); however, it is easy to check numerically that for every spectrum considered here, the variance of a monochromatic field with wavelength (varLambda_{mathrm{sq}}) is inferior to the variance drawn on Fig. 4.
For a given search method and database, a list of candidate peptides is obtained for every spectrum analyzed.
The measurement scanning speed was equal to 50 nm/min, data was pitched every 0.5 nm and five accumulations were taken for every spectrum.
For every spectrum, the reported results from each database search method were compared against a list of the theoretical peptides generated from the known proteins to determine whether a true peptide hit exists in those results.
With this simulation, we tried to mimic the reality of the acquisition as closely as possible; therefore we incorporated summation over the integration time for every spectrum while simulating reference mirror movement, a discrete wavelength axis and a limited spectral resolution.
Our MAP detector returns a label L i MAP for every observed spectrum which is determined according to L i MAP = arg min ℓ ∈ { 1, …, m }, f ∈ D 1 2 | | y i − α i A f | | 2 − log p. where m is the number of signals in D, and p is the a priori probability of target class ℓ.
For every such spectrum, the sum formula of the sample molecule is known.
For every such spectrum, we computed all molecules such that the monoisotopic mass M0 has relative mass difference of at most α1 p.p.m.
For every experimental spectrum examined, we collect the scores of peptides in the database, and find good agreement between the collected score statistics and our theoretical distribution.
