A fundamental problem in systems biology consists of investigating robustness properties of genetic regulatory networks (GRNs) with respect to model uncertainty. This paper addresses this problem for GRNs where the coefficients are rationally affected by polytopic uncertainty, and where the saturation functions are not exactly known. First, it is shown that a condition for ensuring that the GRN...

In a Shapley-Shubik assignment problem with a supermodular output matrix, we consider games in which each firm makes a take-it-orleave-it salary offer to one applicant, and a match is made only when the offer is accepted by her. We consider both one-shot and multistage games. In either game, we show that there can be many equilibrium salary vectors which are higher or lower than the minimum com...

Abstract. This paper retakes previous work of the authors, about the relationship between non–quasi–competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in the literature that the loss of quasi–competitiveness is linked, in the long run as new firm...

Let X be a given nonempty closed convex subset in IR and let f : X×X −→ IR be a given bifunction with f(x, x) = 0 for all x ∈ X. We are interested in the following quasi-equilibrium problem { Find x ∈ K(x) such that f(x, y) ≥ 0 ∀ y ∈ K(x) (QEP ) where K(·) is a multivalued mapping X −→ 2 . When the mapping x −→ K(x) is such that K(x) = X for all x ∈ X, (QEP ) reduces naturally to the equilibriu...

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the si...