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Why does yeast ferment? A flux balance analysis study
Get PDFAdvances in biological techniques have led to the availability of genome-scale metabolic reconstructions for yeast. The size and complexity of such networks impose limits on what types of analyses one can perform. Constraint-based modelling overcomes some of these restrictions by using physicochemical constraints to describe the potential behaviour of an organism. FBA (flux balance analysis) highlights flux patterns through a network that serves to achieve a particular objective and requires a minimal amount of data to make quantitative inferences about network behaviour. Even though FBA is a powerful tool for system predictions, its general formulation sometimes results in unrealistic flux patterns. A typical example is fermentation in yeast: ethanol is produced during aerobic growth in excess glucose, but this pattern is not present in a typical FBA solution. In the present paper, we examine the issue of yeast fermentation against respiration during growth. We have studied a number of hypotheses from the modelling perspective, and novel formulations of the FBA approach have been tested. By making the observation that more respiration requires the synthesis of more mitochondria, an energy cost related to mitochondrial synthesis is added to the FBA formulation. Results, although still approximate, are closer to experimental observations than earlier FBA analyses, at least on the issue of fermentation
Natural hp-BEM for the electric field integral equation with singular solutions
Get PDFWe apply the -version of the boundary element
method (BEM) for the numerical solution of the electric field
integral equation (EFIE) on a Lipschitz polyhedral surface .
The underlying meshes are supposed to be quasi-uniform triangulations of \G,
and the approximations are based on either Raviart-Thomas or Brezzi-Douglas-Marini
families of surface elements.
Non-smoothness of leads to singularities in the solution
of the EFIE, severely affecting convergence rates of the BEM.
However, the singular behaviour of the solution can be explicitly
specified using a finite set of power functions (vertex-, edge-, and
vertex-edge singularities). In this paper we use this fact to
perform an a priori error analysis of the -BEM on quasi-uniform meshes.
We prove precise error estimates in terms of the polynomial degree ,
the mesh size , and the singularity exponents
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
Get PDFA new algorithm is developed for computing , where is an matrix and is with . The algorithm works for any , its computational cost is dominated by the formation of products of with matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix or a sequence on an equally spaced grid of points . It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the recent analysis of Al-Mohy and Higham [\emph{SIAM J. Matrix Anal.\ Appl.} 31 (2009), pp.\ 970--989], which provides sharp truncation error bounds expressed in terms of the quantities for a few values of , where the norms are estimated using a matrix norm estimator. Shifting and balancing are used as preprocessing steps to reduce the cost of the algorithm. Numerical experiments show that the algorithm performs in a numerically stable fashion across a wide range of problems, and analysis of rounding errors and of the conditioning of the problem provides theoretical support. Experimental comparisons with MATLAB codes based on Krylov subspace, Chebyshev polynomial, and Laguerre polynomial methods show the new algorithm to be sometimes much superior in terms of computational cost and accuracy. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form that arise in exponential integrators, where the are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension built by augmenting with additional rows and columns, and the algorithm of this paper can therefore be employed
Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups
Get PDFFor a group G and X a subset of G the commuting graph of G on X, denoted by C(G,X), is the graph whose vertex set is X with x, y � X joined by an edge if x =/= y and x and y commute. If the elements in X are involutions, then C(G,X) is called a commuting involution graph. This paper studies C(G,X) when G is a 4-dimensional projective symplectic group and X a G-conjugacy class of involutions, determining the diameters and structure of the discs of these graphs
Adversarial Smoothed Analysis
Get PDFThe purpose of this note is to extend the results on uniform smoothed analysis of condition numbers from BCL07 to the case where the perturbation follows a radially symmetric probability distribution. In particular, we will show that the bounds derived in BCL07 still hold in the case of distributions whose density has a singularity at the center of the perturbation, which we call adversarial
EST_MINRES: An Optimal Iterative Solver for Symmetric Indefinite Systems stemming from Mixed Approximation
Get PDFWe discuss the design and implementation of a suite of functions for solving symmetric indefinite linear systems associated with mixed approximation of systems of PDEs. The novel feature of our iterative solver is the incorporation of error control in the natural "energy" norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error. We describe a "proof of concept" MATLAB implementation of this algorithm and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package (cf. ACM Transactions on Mathematical Software 33, Article 14, 2007)
Rule Systems for Run-time Monitoring: from EAGLE to RULER
Get PDFIn Barringer et al. (2004,Vol. 2937, LNCS), EAGLE was introduced as a general purpose rule-based temporal logic for specifying run-time monitors. A novel interpretative trace-checking scheme via stepwise transformation of an EAGLE monitoring formula was defined and implemented. However, even though EAGLE presents an elegant formalism for the expression of complex trace properties, EAGLE's interpretation scheme is complex and appears difficult to implement efficiently. In this article, we introduce RULER, a primitive conditional rule-based system, which has a simple and easily implemented algorithm for effective run-time checking, and into which one can compile a wide range of temporal logics and other specification formalisms used for run-time verification. As a formal demonstration, we provide a translation scheme for linear-time propositional temporal logic with a proof of translation correctness. We then introduce a parameterized version of RULER, in which rule names may have rule-expression or data parameters, which then coincides with the same expressivity as EAGLE with data arguments. RULER with just rule-expression parameters extend the expressiveness of RULER strictly beyond the class of context-free languages. For the language classes expressible in propositional RULER, the addition of rule-expression and data parameters enables more compact translations. Finally, we outline a few simple syntactic extensions of ‘core’ RULER that can lead to further conciseness of specification but still enabling easy and efficient implementation
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
Get PDFA new algorithm is developed for computing , where is an matrix and is with . The algorithm works for any , its computational cost is dominated by the formation of products of with matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix or a sequence on an equally spaced grid of points . It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the recent analysis of Al-Mohy and Higham [\emph{SIAM J. Matrix Anal.\ Appl.} 31 (2009), pp.\ 970-989], which provides sharp truncation error bounds expressed in terms of the quantities for a few values of , where the norms are estimated using a matrix norm estimator. Shifting and balancing are used as preprocessing steps to reduce the cost of the algorithm. Numerical experiments show that the algorithm performs in a numerically stable fashion across a wide range of problems, and analysis of rounding errors and of the conditioning of the problem provides theoretical support. Experimental comparisons with two Krylov-based MATLAB codes show the new algorithm to be sometimes much superior in terms of computational cost and accuracy. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form that arise in exponential integrators, where the are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension built by augmenting with additional rows and columns, and the algorithm of this paper can therefore be employed
Bubbles and crashes in a Black-Scholes model with delay
Get PDFThis paper studies the asymptotic behaviour of an affine stochastic functional
differential equation modelling the evolution of the cumulative return of a
risky security. In the model, the traders of the security determine their
investment strategy by comparing short-- and long--run moving averages of the
security's returns. We show that the cumulative returns either obey the Law of
the Iterated Logarithm, but have dependent increments, or exhibit asymptotic
behaviour that can be interpreted as a runaway bubble or crash