Stable marriage with general preferences

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable marriage where preferences are allowed to have ties and to be incomplete. As a result, we prove that deciding the existence of a stable matching in our model is NP-complete. Complementing this negative result we present a polynomial-time algorithm for the above decision problem in a significant class of instances where the preferences are asymmetric. We also present a linear programming formulation whose feasibility fully characterizes the existence of stable matchings in this special case. Finally, we use our model to study a long standing open problem regarding the existence of cyclic 3D stable matchings. In particular, we prove that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP-complete, showing this way that a natural attempt to resolve the existence (or not) of 3D stable matchings is bound to fail.Comment: This is an extended version of a paper to appear at the The 7th International Symposium on Algorithmic Game Theory (SAGT 2014

Possibility and necessity modals in Gbe and Surinamese Creoles

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The physical properties of a jet-nebulizer and their relevance for the histamine provocation test

We have examined the physical properties of eight specimens of a frequently used jet-nebulizer (Wiesbadener Doppelinhalator). For each nebulizer, under various conditions we measured driving pressure, solution output, solute output, particle concentration and size distribution in the aerosol, and the change of solute concentration in the storage vessel. Using histamine acid phosphate solutions in distilled water, there was considerable variability between the nebulizers in solute output (range about a factor 3). Solute output was strongly related to driving pressure (r2 = 0.89), to solution output (r2 = 0.96) and to particle concentration (r2 = 0.87). The particle size distributions of the eight nebulizers were very similar. The volume median aerodynamic diameter (VMAD) of the stable evaporated particles was on average 0.33 micrograms (geometric standard deviation of 1.78), which implies a VMAD of the primary droplets of about 3.2 micrograms. In fifteen subjects with bronchial hyperreactivity, a twofold increase of histamine output of the nebulizer without a change in particle size resulted on average in a twofold decrease of the histamine concentration that caused a 20 per cent fall (PC20) in FEV1. At constant histamine output the administration of dry particles instead of direct nebulization of (partly) saturated droplets into the mouth increased PC20 by a factor 2. This difference could not be explained by a changed deposition in the hypopharynx. There were large interindividual differences in the response to the altered aerosol characteristics. We conclude that the physical properties of the administered aerosols should be carefully controlled since they influence the biological response to inhaled histamine. The solute output of the investigated jet-nebulizer can satisfactorily be validated by weighing, for which an equation is given. In bronchial provocation testing, administration of dry particles is recommende