Mass spectrum *M* | A set {*p*_{1}, *p*_{2}, … } of peaks. |

Peak *p* | Each peak has an associated mass-to-charge ratio mz(*p*) and intensity(*p*). |

Run *R* | A series (*M*_{1}, *M*_{2}, … ) of mass spectra. A run corresponds to the output of an RPLC experiment. |

Run T0SCX23A | A 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. |

*p* ≤ *q* | We write *p* ≤ *q* for two peaks *pεM*_{i} and qεM_{j} if *i*≤ *j*, *i.e. p* and *q*occur in the same run, and *p* occurs in the same or an earlier spectrum than *q*. |

Signal map *f* | We call *f order-preserving* if, for any pair (*p*,*q*) of peaks with *p* ≤ *q*, there exists a peak *uεf*(*p*), such that *u* ≤ *v* for all peaks *vεf*(*q*). |

Alignment α | Given two 1D runs *R* with spectra (*M*_{1}, *M*_{2}, … ) and *S*with spectra (*N*_{1}, *N*_{2}, … ), 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 *M*_{i} and M_{j} with i ≤ *j*, there exists a spectrum *N*_{k}εα(M_{i}), such that k ≤ *l* for all spectra *N*_{l}εα(*M*_{j}). |