Estela Sánchez

On the Convexity of Games Corresponding to Sequencing Situations with Due Dates

This paper considers sequencing situations with due date criteria. Three different types of criteria are considered: the weighted penalty criterion, the weighted tardiness criterion and the completion time criterion. The main focus is on convexity of the associated cooperative games. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Intrinsic spontaneous activity and subthreshold oscillations in neurones of the rat dorsal column nuclei in culture

The basis of rhythmic activity observed at the dorsal column nuclei (DCN) is still open to debate. This study has investigated the electrophysiological properties of isolated DCN neurones deprived of any synaptic influence, using the perforated‐patch technique. About half of the DCN neurones (64/130) were spontaneously active. More than half of the spontaneous neurones (36/64) showed a low threshold membrane oscillation (LTO) with a mean frequency of 11.4 Hz (range: 4.3–22.1 Hz, n= 20; I= 0). Cells showing LTOs also invariably showed a rhythmic 1.2 Hz clustering activity (groups of 2–5 action potentials separated by silent LTO periods). Also, more than one‐third of the silent neurones presented clustering activity, always accompanied by LTOs, when slightly depolarised. The frequency of LTOs was voltage dependent and could be abolished by TTX (0.5 μM) and riluzole (30 μM), suggesting the participation of a sodium current. LTOs were also abolished by TEA (15 mM), which transformed clustering into tonic activity. In voltage clamp, most DCN neurones (85 %) showed a TTX‐/riluzole‐sensitive persistent sodium current (INa,p), which activated at about ‐60 mV and had a half‐maximum activation at −49.8 mV. An M‐like, non‐inactivating outward current was present in 95 % of DCN neurones, and TEA (15 mM) inhibited this current by 73.7 %. The non‐inactivating outward current was also inhibited by barium (1 mM) and linopirdine (10 μM), which suggests its M‐like nature; both drugs failed to block the LTOs, but induced a reduction in their frequency by 56 and 20 %, respectively. These results demonstrate for the first time that DCN neurones have a complex and intrinsically driven clustering discharge pattern, accompanied by subthreshold membrane oscillations. Subthreshold oscillations rely on the interplay of a persistent sodium current and a non‐inactivating TEA‐sensitive outward current.

Newly developed blockers of the M-current do not reduce spike frequency adaptation in cultured mouse sympathetic neurons

The M‐current (IK(M)) is believed to modulate neuronal excitability by producing spike frequency adaptation (SFA). Inhibitors of M‐channels, such as linopirdine and 10,10‐bis(4‐pyridinylmethyl)‐9(10H)‐anthracenone (XE991), enhance depolarization‐induced transmitter release and improve learning performance in animal models. As such, they are currently being tested for their therapeutic potential for treating Alzheimers disease. The activity of these blockers has been associated with the reduction of SFA and the depolarization of the membrane observed when IK(M) is inhibited. To test whether this is the case, the perforated patch technique was used to investigate the capacity of IK(M) inhibitors to alter the resting membrane potential and to reduce SFA in mouse superior cervical ganglion neurons in culture. Linopirdine and XE991 both proved to be potent blockers of IK(M) when the membrane potential was held at −30 mV (IC50 2.56 and 0.26 µm, respectively). However, their potency gradually declined upon membrane hyperpolarization and was almost null when the membrane potential was kept at −70 mV, indicating that their blocking activity was voltage dependent. Nevertheless, IK(M) could be inhibited at these hyperpolarized voltages by other inhibitors such as oxotremorine‐methiodide and barium. Under current‐clamp conditions, neither linopirdine (10 µm) nor XE991 (3 µm) was effective in reducing the SFA and both provoked only a small slowly developed depolarization of the membrane (2.27 and 3.0 mV, respectively). In contrast, both barium (1 mm) and oxotremorine‐methiodide (10 µm) depolarized mouse superior cervical ganglion neurons by about 10 mV and reduced the SFA. In contrast to classical IK(M) inhibitors, the activity of linopirdine and XE991 on the IK(M) is voltage dependent and, thus, these newly developed IK(M) blockers do not reduce the SFA. These results may shed light on the mode of action of these putative cognition enhancers in vivo.

On values for generalized characteristic functions

In this work we study a new generalization for the Shapley value. We consider games in coalitional form in which the characteristic function is defined on all possible orders. These games are useful to model some economic situations. Different axiomatic characterizations are found for the new value using marginality, balanced contributions, the potential and the consistency property.ZusammenfassungIn dieser Arbeit wird eine Verallgemeinerung des Shapley-Wertes eingeführt und untersucht. Bei den zugrundeliegenden Spielen in Koalitionsform, die zur Modellierung einiger ökonomischer Sachverhalte geeignet sind, ist die charakteristische Funktion über allen Reihenfolgen der Koalitionsbildung definiert. Basierend auf den bekannten Eigenschaften des Shapley-Wertes werden verschiedene axiomatische Charakterisierungen dargestellt.

The proportional rule for problems with constraints and claims

Abstract In this paper we study how to distribute a resource among different agents who have claims on it when there are some constraints in the problem. This kind of problem generalizes, for instance, the class of bankruptcy problems. We introduce two single-valued rules based on the principle of proportionality. Some properties of the rules are given and some axiomatic characterizations are found.

How to Distribute Costs Associated with a Delayed Project

In this paper we study how to distribute the cost caused by the delay of a project among the firms which are responsible for it. We present two rules, one based on serial cost sharing problems and the other, in game theory. Moreover, we introduce some desirable properties, inspired by well-known principles, and study which of them are satisfied by the rules.

Sequencing games without initial order

In this note we study uncertainty sequencing situations, i.e., one-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et al. (Eur J Oper Res 40:344–351, 1989). Moreover, we propose and characterize two simple cost allocation rules for uncertainty sequencing situations with equal processing times.

NTU PERT games

In this paper a new class of Non-Transferable Utility (NTU) games is introduced. We associate an NTU game to the PERT problem that arises from a method of operations research called Project Evaluation and Review Technique (PERT). The goal is to divide the slacks of time among the different activities involved in the project. We model this problem as an NTU game and we study some properties. It is shown that this class of NTU games has a non-empty core. Moreover, an easy expression for the compromise value is attained and an adjusted compromise value is defined.

Coalitional values and generalized characteristic functions

Abstract. We study coalitional values for games in generalized characteristic function form. There are two extensions of the Shapley value (Shapley (1953)) in this context, one introduced by Nowak and Radzik (1994) and the other introduced by us. We generalize both values to games with a priori unions in the same way that Owen (1977) did for the Shapley value, and we obtain an axiomatic characterization for both of them. Moreover we analyze the differences between them and study the consistency, the balanced contributions, and the potential.

Manipulation of optimal matchings via predonation of endowment

In this paper we answer a question posed by Sertel and Sanver (2002) on the manipulability of optimal matching rules in matching problems with endowments. We characterize the classes of consumption rules under which optimal matching rules can be manipulated via predonation of endowment.