Exceptional Moufang quadrangles and structurable algebras

In 2000, J. Tits and R. Weiss classified all Moufang spherical buildings of rank two, also known as Moufang polygons. The hardest case in the classification consists of the Moufang quadrangles. They fall into different families, each of which can be described by an appropriate algebraic structure. For the exceptional quadrangles, this description is intricate and involves many different maps that are defined ad hoc and lack a proper explanation. In this paper, we relate these algebraic structures to two other classes of algebraic structures that had already been studied before, namely to Freudenthal triple systems and to structurable algebras. We show that these structures give new insight in the understanding of the corresponding Moufang quadrangles.Comment: 49 page

A new construction of Moufang quadrangles of type E6, E7 and E8

In the classification of Moufang polygons by J. Tits and R. Weiss, the most intricate case is by far the case of the exceptional Moufang quadrangles of type E6, E7 and E8, and in fact, the construction that they present is ad-hoc and lacking a deeper explanation. We will show how tensor products of two composition algebras can be used to construct these Moufang quadrangles in characteristic different from 2. As a byproduct, we will obtain a method to construct any Moufang quadrangle in characteristic different from two from a module for a Jordan algebra

Moufang sets and structurable division algebras

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. We extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, we show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. We also obtain explicit formulas for the root groups, the tau-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups

A Neural Network Demand System

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de Travail du Centre d'Economie de la Sorbonne 2013.81 - ISSN : 1955-611XWe introduce a new type of demand system using a feedforward artificial neural network. The neural network demand system is a flexible system that requires few hypotheses, has no roots in consumer theory but may be used to test it. We use the system to estimate demand elasticities on micro data of household consumption in Canada between 2004 and 2008, and compare the results to those of the quadratic almost ideal demand system.Nous présentons un nouveau type de système complet de demande utilisant un réseau de neurones artificiels. Le système de demande à réseau de neurones est un système flexible nécessitant un minimum d'hypothèses. Sa formulation ne provient pas de la théorie du consommateur, mais il peut être utilisé pour la tester. Nous appliquons ce système à l'estimation d'élasticités de la demande des ménages sur des micro données canadiennes de 2004 à 2008, et comparons les résultats à ceux obtenus à l'aide du système QUAIDS

The ports of Flanders: Key facts & figures

The publication contains statistical information concerning the Flemish ports

Drug policy for visceral leishmaniasis: a cost-effectiveness analysis.

OBJECTIVE: To facilitate the choice of the best visceral leishmaniasis (VL) treatment strategy for first-line health services in (VL)-endemic areas, we compared in a formal decision analysis the cost and the cost-effectiveness of the different available options. METHODS: We selected four drug regimens for VL on the basis of frequency of use, feasibility and reported efficacy studies. The point estimates and the range of plausible values of effectiveness and cost were retrieved from a literature review. A decision tree was constructed and the strategy minimizing the cost per death averted was selected. RESULTS: Treatment with amphotericin B deoxycholate was the most effective approach in the baseline analysis and averted 87.2% of all deaths attributable to VL. The least expensive and the most cost-effective treatment was the miltefosine regimen, and the most expensive and the least cost-effective was AmBisome treatment. The cost of drug and medical care are the main determinants of the cost-effectiveness ranking of the alternative schemes. Sensitivity analysis showed that antimonial was competitive with miltefosine in the low-resistance regions. CONCLUSION: In areas with >94% response rates to antimonials, generic sodium stibogluconate remains the most cost-effective option for VL treatment, mainly due to low drug cost. In other regions, miltefosine is the most cost-effective option of treatment, but its use as a first-line drug is limited by its teratogenicity and rapid resistance development. AmBisome in mono- or combination therapy is too expensive to compete in cost-effectiveness with the other regimens