Table I

Formal definitions of the various terms and notions used

The symbol convention used in this table is followed in the entire text.

Term usedFormal definition
Mass spectrum MA set {p1, p2, … } of peaks.
Peak pEach peak has an associated mass-to-charge ratio mz(p) and intensity(p).
Run RA series (M1, M2, … ) of mass spectra. A run corresponds to the output of an RPLC experiment.
Run T0SCX23AA run in a two-dimensional LC/LC MS experiment. The notation denotes the series A run of SCX fraction 23 of the sample collected at time point 0.
pqWe write pq for two peaks pεMi and qεMj if ij, i.e. p and qoccur in the same run, and p occurs in the same or an earlier spectrum than q.
Signal map fWe call f order-preserving if, for any pair (p,q) of peaks with pq, there exists a peak uεf(p), such that uv for all peaks vεf(q).
Alignment αGiven two 1D runs R with spectra (M1, M2, … ) and Swith spectra (N1, N2, … ), a function α that maps each spectrum in R to a set of spectra in S. α has the property that, for any two spectra Mi and Mj with ij, there exists a spectrum Nkεα(Mi), such that kl for all spectra Nlεα(Mj).