On the Sensitivity of Solution Components in Linear Systems of Equations
SIAM Journal on Matrix Analysis and Applications
Shared Peptides in Mass Spectrometry Based Protein Quantification
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
The Parameterized Complexity of Some Geometric Problems in Unbounded Dimension
Parameterized and Exact Computation
On the hardness of approximating Max-Satisfy
Information Processing Letters
Structural Identifiability in Low-Rank Matrix Factorization
Algorithmica - Special Issue: Computation and Combinatorial Optimization; Guest Editors: Xiaodong Hu and Jie Wang
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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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.