Container of (min, +)-linear systems

Based on the (min,+)-linear system theory, the work developed here takes the set membership approach as a starting point in order to obtain a container for ultimately pseudo-periodic functions representative of Discrete Event Dynamic Systems. Such a container, by approximating the exact system, ensures to entirely include it in a guaranteed way. To reach that point, the container introduced in this paper is given as an interval, the bounds of which are a convex function for the upper approximation and a concave function for the lower approximation. Thanks to the characteristics of the bounds, the aim is both to reduce data storage (that can be very high when exact functions are handled) and to reduce the algorithm complexity of the operations of sum, inf-convolution and subadditive closure. These operations are integrated into inclusion functions, the algorithms of which are of linear or quasi-linear complexity

Extrasynaptic and Postsynaptic Receptors in Glycinergic and GABAergic Neurotransmission: A Division of Labor?

Glycine and GABA mediate inhibitory neurotransmission in the spinal cord and central nervous system. The general concept of neurotransmission is now challenged by the contribution of both phasic activation of postsynaptic glycine and GABAA receptors (GlyRs and GABAARs, respectively) and tonic activity of these receptors located at extrasynaptic sites. GlyR and GABAAR kinetics depend on several parameters, including subunit composition, subsynaptic localization and activation mode. Postsynaptic and extrasynaptic receptors display different subunit compositions and are activated by fast presynaptic and slow paracrine release of neurotransmitters, respectively. GlyR and GABAAR functional properties also rely on their aggregation level, which is higher at postsynaptic densities than at extrasynaptic loci. Finally, these receptors can co-aggregate at mixed inhibitory postsynaptic densities where they cross-modulate their activity, providing another parameter of functional complexity. GlyR and GABAAR density at postsynaptic sites results from the balance between their internalization and insertion in the plasma membrane, but also on their lateral diffusion from and to the postsynaptic loci. The dynamic exchange of receptors between synaptic and extrasynaptic sites and their functional adaptation in terms of kinetics point out a new adaptive process of inhibitory neurotransmission

Représentation Tridimensionnelle de la Dynamique des Graphes d'Evénements Temporisés Généralisés

Les Graphes d\u27Evénements Temporisés (GET) ordinaires admettent une relation de transfert linéaire dans les algèbres de type (min,+). Ces relations de transfert peuvent être décrites au moyen de séries ultimement périodiques représentables dans le plan 2. Ce papier tente une représentation graphique analogue pour les GET Généralisés, c\u27est-à-dire les GET dont les arcs sont valués. La représentation nécessite une dimension supplémentaire permettant de tenir compte du gain de ces systèmes qui est algébriquement modélisé par l\u27introduction de nouveaux opérateurs. Cette représentation est une extension naturelle de celle utilisée pour les GET ordinaires. Il est en outre montré que pour les GETG possédant une propriété de périodicité il est possible de considérer la théorie de la résiduation pour synthétiser des lois de commande