Error Propagation in Sparse Linear Systems with Peptide-Protein Incidence Matrices

Damaschke, Peter; Molokov, Leonid

doi:10.1007/978-3-642-30191-9_7

Cited by 1 publication

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“…We are particularly interested in the reconstruction of protein mixtures after enzymatic digestion into peptides which can be identified and measured. Most peptides come from only one or two candidate proteins, and simulated protein digestion data suggest that already equations with at most two variables suffice to infer most of the protein amounts, provided that all measurements are correct [2]. A practical issue is that, as a result of experimental errors, some of the measured values in b may be corrupted.…”

Section: Introductionmentioning

confidence: 99%

“…Related Literature: In [2] we considered an error model where all b i are changed by at most some small , and we gave graph-theoretic and LP methods for controlling the error in the solution vector x. The motivation for the present study is that, besides general measurement inaccuracies, a number k of measured amounts may be totally wrong and should be detected first.…”

Section: Introductionmentioning

confidence: 99%

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Fixed-Parameter Tractability of Error Correction in Graphical Linear Systems

Damaschke

Eğecioǧlu

Molokov

2013

WALCOM: Algorithms and Computation

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Abstract.In an overdetermined and feasible system of linear equations Ax = b, let vector b be corrupted, in the way that at most k entries are off their true values. Assume that we can check in the restricted system given by any minimal dependent set of rows, the correctness of all corresponding values in b. Furthermore, A has only coefficients 0 and 1, with at most two 1s in each row. We wish to recover the correct values in b and x as much as possible. The problem arises in a certain chemical mixture inference application in molecular biology, where every observable reaction product stems from at most two candidate substances. After formalization we prove that the problem is NP-hard but fixed-parameter tractable in k. The FPT result relies on the small girth of certain graphs.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%