Revealed cardinal preference

I prove that as long as we allow the marginal utility for money (lambda) to vary between purchases (similarly to the budget) then the quasi-linear and the ordinal budget-constrained models rationalize the same data. However, we know that lambda is approximately constant. I provide a simple constructive proof for the necessary and sufficient condition for the constant lambda rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical studies of consumer behavior. 'Go Cardinals!' It is the minimal requirement of any scientifi c theory that it is consistent with the data it is trying to explain. In the case of (Hicksian) consumer theory it was revealed preference -introduced by Samuelson (1938,1948) - that provided an empirical test to satisfy this need. At that time most of economic reasoning was done in terms of a competitive general equilibrium, a concept abstract enough so that it can be built on the ordinal preferences over baskets of goods - even if the extremely specialized ones of Arrow and Debreu. However, starting in the sixties, economics has moved beyond the 'invisible hand' explanation of how -even competitive- markets operate. A seemingly unavoidable step of this 'revolution' was that ever since, most economic research has been carried out in a partial equilibrium context. Now, the partial equilibrium approach does not mean that the rest of the markets are ignored, rather that they are held constant. In other words, there is a special commodity -call it money - that reflects the trade-offs of moving purchasing power across markets. As a result, the basic building block of consumer behavior in partial equilibrium is no longer the consumer's preferences over goods, rather her valuation of them, in terms of money. This new paradigm necessitates a new theory of revealed preference.

On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Surfactant protein-D and exposure to bioaerosols in wastewater and garbage workers.

PURPOSE: Bioaerosols and their constituents, such as endotoxins, are capable of causing an inflammatory reaction at the level of the lung-blood barrier, which becomes more permeable. Thus, it was hypothesized that occupational exposure to bioaerosols can increase leakage of surfactant protein-D (SP-D), a lung-specific protein, into the bloodstream. METHODS: SP-D was determined by ELISA in 316 wastewater workers, 67 garbage collectors, and 395 control subjects. Exposure was assessed with four interview-based indicators and by preliminary endotoxin measurements using the Limulus amoebocyte lysate assay. Influence of exposure on serum SP-D was assessed by multiple linear regression considering smoking, glomerular function, lung diseases, obesity, and other confounders. RESULTS: Overall, mean exposure levels to endotoxins were below 100 EU/m(3). However, special tasks of wastewater workers caused higher endotoxin exposure. SP-D concentration was slightly increased in this occupational group and associated with the occurrence of splashes and contact to raw sewage. No effect was found in garbage collectors. Smoking increased serum SP-D. No clinically relevant correlation between spirometry results and SP-D concentrations appeared. CONCLUSIONS: These results support the hypothesis that inhalation of bioaerosols, even at low concentrations, has a subclinical effect on the lung-blood barrier, the permeability of which increases without associated spirometric changes.

Determinació de la deposició atmosfèrica de metalls pesants a les Muntanyes de Prades (Tarragona) a partir dels bioindicadors Xanthoria parietina i Hypnum cupressiforme

En aquest estudi s’ha determinat la deposició atmosfèrica de metalls pesants a partir dels bioindicadors Xanthoria parietina (liquen) i Hypnum cupressiforme (molsa), en 16 punts de mostreig repartits per la zona on s’ubicarà el futur parc natural de les Muntanyes de Prades (Tarragona). A partir de la comparació de les concentracions obtingudes en aquest treball amb les d’altres estudis de plantejament equiparable, es va comprovar que la majoria de valors de concentració dels metalls eren similars als d’altres zones geogràfiques estudiades, a excepció del crom i el níquel, que presentaven valors clarament més elevats. A partir de proves estadístiques (ANOVA, regressions múltiples) es va determinar que existien diferències significatives entre les concentracions de metalls dels diferents punts de mostreig. També es van detectar correlacions significatives entre les concentracions dels punts de mostreig i la distància d’aquests respecte els focus potencials de contaminació que s’havien considerat prèviament. Amb les dades obtingudes a partir un petit anàlisi de la riquesa liquènica dels punts de mostreig, es va disposar d’informació extra per poder avaluar les fonts i el patró de distribució d’aquests contaminants.

Rhinitis due to acrylates : case report

Background: Acrylates and methacrylates (salts and esters of acrylic and metacrylic acid respectively), are monomers commonly found in polymer plastics, resins and glues, and are widely used in many industry sectors. The first adverse health effects described were skin reactions and asthma. Exposure to acrylates, for instance when using multicomponent glues, is now a well known cause of occupational asthma. Methods: We report the case of a rhinitis - and possible asthma - to acrylates, in a 38-year-old woman, working in a nail beauty salon. She was currently treated for hypertension, and otherwise known for obesity and seasonal rhinoconjunctivitis, but did not have any respiratory problem. Two years after starting this activity, she progressively started to complain of anosmia, rhinitis, and intermittent dyspnea. Her job consisted in decorating nails with a mixture of a polymer powder and a liquid monomer, after removing the previous artificial nail with a small sander. We assessed exposure to acrylates at her working place, both as dust (from sanded nails) and volatile compound (from the mixture described above), and she was asked to measure her peak flow values twice a day for ten days, in order to detect a possible relationship between her occupational activities, the symptoms and the peak flow values. Results: Measures made during the visit of the patient's place of work showed that the existing aspiration system was efficient for eliminating the dust produced by nail sanding, but not for eliminating the volatile components. Thus, occupational exposure to acrylates was demonstrated. Moreover, the peak flow measures showed an average decrease of almost 10 percent when the patient was at work, compared to when she stayed home. We concluded that she actually suffered from professional rhinitis and, possibly, professional asthma (not certain because of the limited number of peak flow measures per day). Conclusion: Although exposure to acrylates is a well known cause of occupational asthma, it should be emphasized that the exact mechanisms of action remain unknown, despite the abundant literature about it. Some professions, which tend to be more frequent nowadays (such as working in a nail beauty salon), can expose the worker to particular risks. This highlights the need of always inquiring not only about the profession, but also the related activities, when facing a case of suspected asthma.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1997), we explore new conditions on prefernce domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set {0, 1/2, 1}: indeed, we show that, there exists a one-to-one correspondence between solutions of an integer program defined on this set and the set of all Arrovian social welfare functions - without restrictions on the range.

Ramaderia extensiva com a eina de prevenció d'incendis i gestió del paisatge a Matadepera (Vallès Occidental)

Aquest es un estudi de la contribució d’un ramat mixt d’oví i cabrum a la gestió de les masses forestals per a la prevenció d’incendis al municipi de Matadepera. L’avaluació de l’acció del ramat s’ha efectuat mitjançant un estudi integrat a traves del coneixement local i l’estudi ecològic de les zones pasturades. La ramaderia extensiva i especialment els ramats d’ovelles i cabres han contribuït durant segles a la neteja del sotabosc mitjançant l’aprofitament productiu d’aquestes zones, per tant no es quelcom nou, sinó un reconeixement als serveis ecològics no productius de la ramaderia extensiva i com aquesta es eficaç en la prevenció d’incendis forestals.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On Strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin (1980)) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints.

Focus sur l'échantillonnage de la poussière sédimentée avec des lingettes électrostatiques dans l'évaluation de l'exposition aux micro-organismes

L'exposition aux microorganismes en environnement intérieur a été associée à la survenue de troubles respiratoires et symptômes allergiques chez les personnes exposées (1). Investiguer la relation dose-réponse entre exposition et effets sur la santé est essentiel dans la prévention de l'apparition de ces symptômes. Cependant, la mesure de l'exposition par prélèvement actif des bioaérosols est coûteuse et contraignante à mettre en place sur un grand nombre de sites en parallèle. C'est pourquoi les méthodes de prélèvement passif de la poussière sédimentée sont de plus en plus souvent envisagées pour répondre à cette problématique. Pour valider l'efficacité d'évaluation de l'exposition par ces dernières méthodes, il est nécessaire de montrer que la poussière sédimentée est bien représentative de la poussière inhalable. Le premier article cité dans cette note se propose de répondre à ce point. De plus, il faut identifier les facteurs qui peuvent influencer les concentrations en micro-organismes dans ces poussières sédimentées. Le deuxième article choisi dans cette note répond à ce dernier aspect.

Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

A general multiserver state-dependent queueing system

The work studies a general multiserver queue in which the service time of an arriving customer and the next interarrival period may depend on both the current waiting time and the server assigned to the arriving customer. Stability of the system is proved under general assumptions on the predetermined distributions describing the model. The proof exploits a combination of the Markov property of the workload process with a regenerative property of the process. The key idea leading to stability is a characterization of the limit behavior of the forward renewal process generated by regenerations. Extensions of the basic model are also studied.