New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

38 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS
Figure 3.4.10: Histogram of peak heights from a randomly chosen spectrum. Note
that only peaks smaller than 500 are displayed. The curve in darker green is a spline
based approximation to the top mid-points of the histogram bars.
� x(Pi,s) < x(Pi,e) - the end point’s x value must be greater than the start
point’s x value.
� y(Pi,s) = 0 - the y value of the start point must equal to zero.
� y(Pi,e) = 0 - the y value of the end point must equal to zero.
� ∀Sk ∈ {S x(Pi,s) . . . S x(Pi,e) : Sk > 0} - the y values of all points between
the start and end point must be greater than zero.
Where x(·) returns the x and y(·) returns the y value of a given spectrum
point. Thus, we are scanning through a spectrum S looking for intersections
of the data curve with the x-axis. Everything between every two intersection
we call a candidate peak.
However, most of these candidate peaks found with this simple algorithm
are not actually real peaks. Most are overlaying single peaks either resulting
from poor resolution of the MALDI-TOF machine, because of isotopic
patterns, or highly complex peptide mixtures.