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The concept of elementary flux vector is valuable in a number of applications of metabolic engineering. For instance, in metabolic flux analysis, each admissible flux vector can be expressed as a non-negative linear combination of a small number of elementary flux vectors. However a critical issue concerns the number of elementary flux vectors which may be… (More)

We study the problem of approximating the joint spectral radius (JSR) of a finite set of matrices. Our approach is based on the analysis of the underlying switched linear system via inequalities imposed between multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class… (More)

For a given finite set Σ of matrices with nonnegative integer entries we study the growth of max t (Σ) = max{{A1. .. At : Ai ∈ Σ}. We show how to determine in polynomial time whether the growth with t is bounded, polynomial, or exponential, and we characterize precisely all possible behaviors.

Overlap-free words are words over the binary alphabet A = {a, b} that do not contain factors of the form xvxvx, where x ∈ A and v ∈ A *. We analyze the asymptotic growth of the number u n of overlap-free words of length n as n → ∞. We obtain explicit formulas for the minimal and maximal rates of growth of u n in terms of spectral characteristics (the joint… (More)

— We consider questions related to the computation of the capacity of codes that avoid forbidden difference patterns. The maximal number of n-bit sequences whose pairwise differences do not contain some given forbidden difference patterns increases exponentially with n and the exponent is the capacity of the forbidden patterns. In [11] Moision, Orlitsky and… (More)

The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts – including ranking websites – and can be interpreted as the average portion of time spent at the node by an infinite random walk. We consider the problem of maximizing the PageRank of a node by selecting some of… (More)

Keywords: Skolem-Pisot problem Exponential polynomials Continuous time dynamical system Decidability Ordinary differential equations a b s t r a c t We study decidability and complexity questions related to a continuous analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity of a linear recurrent sequence. In particular, we show that the… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t The concept of elementary flux vector is valuable in a number of… (More)

— The question of knowing whether the Policy Iteration algorithm (PI) for solving stationary Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 25 years. Recently, an example on which PI requires an exponential number of iterations to converge was proposed for the total-reward and… (More)

The concept of Elementary Flux Modes (EFMs) has been of central importance in a number of studies involving the analysis of metabolism. In Provost and Bastin (2007) this concept is used to translate the metabolic networks of the different phases of CHO cell cultures into macroscopic bioreactions linking extracellular substrates to products. However, a… (More)