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Notes on circulant matrices
Get PDFA note on the relation between (symmetric) circulant matrices and representations of the dihedral group
Kinetic modelling of metabolic pathways: Application to serine biosynthesis
Get PDFIn this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway using kinetic data from both experimental measurements and literature review. Our methodology is presented by using the example of serine biosynthesis in E. coli
Improving metabolic flux predictions using absolute gene expression data
Get PDFBackground:
Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for multicellular organisms, where cellular objectives differ greatly both between and within cell types. Moreover, for the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of interest rather than the rate of production of biomass per se.
Results:
An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method outperforms traditional approaches for predicting experimentally measured exometabolic flux that are reliant upon maximisation of the rate of biomass production.
Conclusion:
Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a requirement for knowledge of the biomass composition of the organism under the conditions of interest, the approach is likely to be of rather general utility. The method has been shown to predict fluxes reliably in single cellular systems. Subsequent work will investigate the method�s ability to generate condition- and tissue-specific flux predictions in multicellular organisms
The hyperbolic Schur decomposition (extended)
No full textWe propose a hyperbolic counterpart of the Schur decomposition, with the emphasis on the preservation of structures related to some given hyperbolic scalar product. We give results regarding the existence of such a decomposition and research the properties of its block triangular factor for various structured matrices
Integer-valued definable functions
Get PDFWe present a dichotomy, in terms of growth at infinity, of analytic
functions definable in the real exponential field which take integer values
at natural number inputs. Using a result concerning the density of rational
points on curves definable in this structure, we show that if a function
f : [0;1)n ! R is such that f(Nn) Z, then either supjxjr f(x) grows
faster than exp(r), for some > 0, or f is a polynomial over Q
Constraining flux balance analysis with genome-scale data
No full textBackground
Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for multicellular organism such as mammals, where cellular objectives differ greatly both between and within cell types. Moreover, for the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of interest rather than the rate of production of biomass per se.
Results
An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method outperforms traditional approaches for predicting experimentally measured metabolic flux that are reliant upon maximization of the rate of biomass production.
Conclusion
Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a requirement for knowledge of the biomass composition of the organism under the conditions of interest, the approach is likely to be of rather general utility. The method has been shown to reliably predict fluxes in single cellular systems, and is likely to be also to generate condition- and tissue-specific flux predictions in multicellular organisms
Employing pre-stress to generate finite cloaks for antiplane elastic waves
Get PDFIt is shown that nonlinear elastic pre-stress of neo-Hookean hyperelastic materials can be used as a mechanism to generate finite cloaks and thus render objects near-invisible to incoming antiplane elastic waves. This approach appears to negate the requirement for special cloaking metamaterials with inhomogeneous and anisotropic material properties in this case. These properties are induced naturally by virtue of the pre-stress. The size of the cloaking region can be altered at will by modification of the applied pre-stress
A fast algorithm for spectral interpolation of sampled data
Get PDFThis paper describes a fast algorithm to interpolate between samples of a bandwidth-limited signal that has been sampled at regular intervals. The algorithm is most suited to situations when a small amount of error in the interpolated values is acceptable, the larger the acceptable error, the more efficient is the algorithm. This can be useful in singnal processing, image processing and as an alternative to finite difference calculations. The same algorithm can be used to calculate the value of an degree polynomial at the degree Chebyshev points, given its values at the degree Chebyshev points, thus providing a fast algorithm for the approximate multiplicaltion of polynomials. This could be used in, for example, computer algebra systems. We consider signals of finite duration, but the same technique can be used to deal with infinite signals so could be used to achieve fast and power-efficient interpolation of streamed data. On a prarallel architecture, the algorithm also requires less inter-process communication than interpolation using a Fast Fourier Transform method
Improving metabolic flux predictions using absolute gene expression data
Get PDFBackground:
Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for multicellular organisms, where cellular objectives differ greatly both between and within cell types. Moreover, for the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of interest rather than the rate of production of biomass per se.
Results:
An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method outperforms traditional approaches for predicting experimentally measured exometabolic flux that are reliant upon maximisation of the rate of biomass production.
Conclusion:
Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a requirement for knowledge of the biomass composition of the organism under the conditions of interest, the approach is likely to be of rather general utility. The method has been shown to predict fluxes reliably in single cellular systems. Subsequent work will investigate the method�s ability to generate condition- and tissue-specific flux predictions in multicellular organisms
Reachability in One-Dimensional Controlled Polynomial Dynamical Systems
Get PDFn this paper we investigate a case of the reachability prob-
lem in controlled o-minimal dynamical systems. This problem can be formulated as follows. Given a controlled o-minimal dynamical system initial and target sets, find a finite choice of time points and control parameters applied at these points such that the target set is reachable from
the initial set. We prove that the existence of a finite control strategy is decidable and construct a polynomial complexity algorithm which generates finite control strategies for one-dimensional controlled polynomial
dynamical systems. For this algorithm we also show an upper bound on the numbers of switches in finite control strategies