Raphaël M. Jungers

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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)
The resilience of Supervisory Control and Data Acquisition (SCADA) systems for electric power networks for certain cyber-attacks is considered. We analyze the vulnerability of the measurement system to false data attack on communicated measurements. The vulnerability analysis problem is shown to be NP-hard, meaning that unless P=NP there is no polynomial(More)
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 total number of elementary flux vectors which(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 totalreward and the(More)
We consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed, undirected graph. We are motivated by the task of deriving lower bounds for consensus protocols and by the so-called “definitive consensus conjecture” which states that for an undirected connected graph G with diameter D there exist D matrices whose(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)
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we(More)
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Rényi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node. The evolution of this(More)
Some questions related to the computation of the capacity of codes that avoid forbidden difference patterns are analysed. The maximal number of n-bit sequences whose pairwise differences do not contain some given forbidden difference patterns is known to increase exponentially with n; the coefficient of the exponent is the capacity of the forbidden(More)