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Error propagation in sparse linear systems with peptide-protein incidence matrices

Peter Damaschke (Institutionen för data- och informationsteknik, Datavetenskap, Algoritmer (Chalmers) ; Institutionen för data- och informationsteknik, Datavetenskap, Bioinformatik (Chalmers)) ; Leonid Molokov (Institutionen för data- och informationsteknik, Datavetenskap, Algoritmer (Chalmers) ; Institutionen för data- och informationsteknik, Datavetenskap, Bioinformatik (Chalmers))
8th International Symposium on Bioinformatics Research and Applications ISBRA 2012, Lecture Notes in Bioinformatics (0302-9743). Vol. 7292 (2012), p. 72-83.
[Konferensbidrag, refereegranskat]

We study the additive errors in solutions to systems Ax=b of linear equations where vector b is corrupted, with a focus on systems where A is a 0,1-matrix with very sparse rows. We give a worst-case error bound in terms of an auxiliary LP, as well as graph-theoretic characterizations of the optimum of this error bound in the case of two variables per row. The LP solution indicates which measurements should be combined to minimize the additive error of any chosen variable. The results are applied to the problem of inferring the amounts of proteins in a mixture, given inaccurate measurements of the amounts of peptides after enzymatic digestion. Results on simulated data (but from real proteins split by trypsin) suggest that the errors of most variables blow up by very small factors only.

Nyckelord: protein mixture inference, linear system, error propagation, bipartite graph, shortest path



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Denna post skapades 2012-05-11. Senast ändrad 2015-02-11.
CPL Pubid: 157546