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Article: Max-plus singular values[Show abstract] [Hide abstract]
ABSTRACT: In this paper we prove a new characterization of the max-plus singular values of a max-plus matrix, as the max-plus eigenvalues of an associated max-plus matrix pencil. This new characterization allows us to compute max-plus singular values quickly and accurately. As well as capturing the asymptotic behavior of the singular values of classical matrices whose entries are exponentially parameterized we show experimentally that max-plus singular values give order of magnitude approximations to the classical singular values of parameter independent classical matrices. We also discuss Hungarian scaling, which is a diagonal scaling strategy for preprocessing classical linear systems. We show that Hungarian scaling can dramatically reduce the 2-norm condition number and that this action can be explained using our new theory for max-plus singular values.Linear Algebra and its Applications 12/2015; 486:419-442. DOI:10.1016/j.laa.2015.08.019
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ABSTRACT: Several recent developments are brought together: (i) the new availability of a consensus, curated human metabolic network reconstruction (Recon2), approximately a third of whose steps are represented by transporters, (ii) the recognition that most successful (marketed) drugs, as well as natural products, bear significant similarities to the metabolites in Recon2, (iii) the recognition that to get into and out of cells such drugs hitchhike on the transporters that are part of normal intermediary metabolism, and the consequent recognition that for intact biomembrane Phospholipid Bilayer diffusion Is Negligible (PBIN), and (iv) the consequent recognition that we need to exploit this and to use more phenotypic assays to understand how drugs affect cells and organisms. I show in particular that lipophilicity is a very poor predictor of drug permeability, and that we need to (and can) bring together our knowledge of both pharmacology and systems biology modelling into a new systems pharmacology.10/2015; DOI:10.1016/j.pisc.2015.06.004
- 10/2015; DOI:10.1016/j.ebiom.2015.10.021
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