Biased representation of homothetic preferences on homogeneous sets

In the homogeneous case of one-dimensional objects, we show that any preference relation that is positive and homothetic can be represented by a quantitative utility function and unique bias. This bias may favor or disfavor the preference for an object. In the first case, preferences are complete but not transitive and an object may be preferred even when its utility is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it may not be sufficient for an object to have a greater utility for be preferred. In this manner, the bias reflects the extent to which preferences depart from the maximization of a utility function.

Aspects thérapeutiques de la vitamine D: quels taux cibler avec quels traitements [Therapeutic goal of vitamin D: optimal serum level and dose requirements].

Therapeutic goal of vitamin D: optimal serum level and dose requirements Results of randomized controlled trials and meta-analyses investigating the effect of vitamin D supplementation on falls and fractures are inconsistent. The optimal serum level 25(OH) vitamin D for musculoskeletal and global health is > or = 30 ng/ml (75 nmol/l) for some experts and 20 ng/ml (50 nmol/l) for some others. A daily dose of vitamin D is better than high intermittent doses to reach this goal. High dose once-yearly vitamin D therapy may increase the incidence of fractures and falls. High serum level of vitamin D is probably harmful for the musculoskeletal system and health at large. The optimal benefits for musculoskeletal health are obtained with an 800 UI daily dose and a serum level of near 30 ng/ml (75 nmol/l).

Simultaneous determination of antidementia drugs by HPLC-MS: validation data of the method and plasma level determinations in 300 patients

Aims: A rapid and simple HPLC-MS method was developed for the simultaneousdetermination of antidementia drugs, including donepezil, galantamine, rivastigmineand its major metabolite NAP 226 - 90, and memantine, for TherapeuticDrug Monitoring (TDM). In the elderly population treated with antidementiadrugs, the presence of several comorbidities, drug interactions resulting frompolypharmacy, and variations in drug metabolism and elimination, are possiblefactors leading to the observed high interindividual variability in plasma levels.Although evidence for the benefit of TDM for antidementia drugs still remains tobe demonstrated, an individually adapted dosage through TDM might contributeto minimize the risk of adverse reactions and to increase the probability of efficienttherapeutic response. Methods: A solid-phase extraction procedure with amixed-mode cation exchange sorbent was used to isolate the drugs from 0.5 mL ofplasma. The compounds were analyzed on a reverse-phase column with a gradientelution consisting of an ammonium acetate buffer at pH 9.3 and acetonitrile anddetected by mass spectrometry in the single ion monitoring mode. Isotope-labeledinternal standards were used for quantification where possible. The validatedmethod was used to measure the plasma levels of antidementia drugs in 300patients treated with these drugs. Results: The method was validated accordingto international standards of validation, including the assessment of the trueness(-8 - 11 %), the imprecision (repeatability: 1-5%, intermediate imprecision:2 - 9 %), selectivity and matrix effects variability (less than 6 %). Furthermore,short and long-term stability of the analytes in plasma was ascertained. Themethod proved to be robust in the calibrated ranges of 1 - 300 ng/mL for rivastigmineand memantine and 2 - 300 mg/mL for donepezil, galantamine and NAP226 - 90. We recently published a full description of the method (1). We found ahigh interindividual variability in plasma levels of these drugs in a study populationof 300 patients. The plasma level measurements, with some preliminaryclinical and pharmacogenetic results, will be presented. Conclusion: A simpleLC-MS method was developed for plasma level determination of antidementiadrugs which was successfully used in a clinical study with 300 patients.

Water Level Changes in Iowa's Aquifers, 2008

This monthly report from the Iowa Department of Natural Resources is about the water quality management of Iowa's rivers, streams and lakes.

Water Level Changes in Iowa's Aquifers, 2008

This monthly report from the Iowa Department of Natural Resources is about the water quality management of Iowa's rivers, streams and lakes.

Optimal monetary and fiscal policy in a currency union

We lay out a tractable model for fiscal and monetary policy analysis in a currency union, and study its implications for the optimal design of such policies. Monetary policy is conducted by a common central bank, which sets the interest rate for the union as a whole. Fiscal policy is implemented at the countrylevel, through the choice of government spending. The model incorporates country-specific shocks and nominal rigidities. Under our assumptions, the optimal cooperative policy arrangement requires that inflation be stabilized at the union level by the common central bank, while fiscal policy is used by each country for stabilization purposes. By contrast, when the fiscal authorities act in a non-coordinated way, their joint actions lead to a suboptimal outcome, and make the common central bank face a trade-off between inflation and output gap stabilization at the union level.

Corruption and the Hadleyburg effect

We study the dynamics of corruption relying on two fundamental observations:(a) Given agents detected as corrupt are typically fired and replaced, the historical levels of corruption have an impact on current corruption throughthe distribution of corruption costs of old agents; (b) Institutions negatively affected by their agents' corrupt activities are likely to respond optimally to it thereby decreasing the payoff from being corrupt. We model this situation by considering an agent who is supposed to monitor acontractor's delivery of a product or service and can manipulate hisreports thus allowing the contractor to deliver lower quality in exchange for a bribe. Given the two generations of agents overlapping at any particular date, the administration sets an optimal level of quality in eachperiod. We find that (i) A unique steady state level of corruption exists;(ii) Regardless of the initial distribution, apart from an initial period,equilibrium sequences are decreasing and converge to the steady state, aresult we term the "Hadleyburg effect". We use these findings to study thedynamic response of corruption to both temporary and permanent shocks to theprofitability of corruption and we find that the "Hadleyburg effect" hasimportant positive and normative implications.

Ex post bargaining, labor coordination and wage formation at the firm level

We lay out a model of wage bargaining with two leading features:bargaining is ex post to relevant investments and there isindividual bargaining in firms without a Union. We compareindividual ex post bargaining to coordinated ex post bargainingand we analyze the effects on wage formation. As opposed to exante bargaining models, the costs of destroying the employmentrelationship play a crucial role in determining wages. Highfiring costs in particular yield a rent for employees. Ourtheory points to a employer size-wage effect that is independentof the production function and market power. We derive a simpleleast squares specification from the theoretical model thatallow us to estimate components of the wage premium fromcoordination. We reject the hypothesis that labor coordinationdoes not alter the extensive form of the bargaining game. Laborcoordination substantially increases bargaining power butdecreases labor's ability to pose costly threats to the firm.

The size and burden of mental disorders and other disorders of the brain in Europe 2010.

Aims: To provide 12-month prevalence and disability burden estimates of a broad range of mental and neurological disorders in the European Union (EU) and to compare these findings to previous estimates. Referring to our previous 2005 review, improved up-to-date data for the enlarged EU on a broader range of disorders than previously covered are needed for basic, clinical and public health research and policy decisions and to inform about the estimated number of persons affected in the EU. Method: Stepwise multi-method approach, consisting of systematic literature reviews, reanalyses of existing data sets, national surveys and expert consultations. Studies and data from all member states of the European Union (EU-27) plus Switzerland, Iceland and Norway were included. Supplementary information about neurological disorders is provided, although methodological constraints prohibited the derivation of overall prevalence estimates for mental and neurological disorders. Disease burden was measured by disability adjusted life years (DALY). Results: Prevalence: It is estimated that each year 38.2% of the EU population suffers from a mental disorder. Adjusted for age and comorbidity, this corresponds to 164.8 million persons affected. Compared to 2005 (27.4%) this higher estimate is entirely due to the inclusion of 14 new disorders also covering childhood/adolescence as well as the elderly. The estimated higher number of persons affected (2011: 165 m vs. 2005: 82 m) is due to coverage of childhood and old age populations, new disorders and of new EU membership states. The most frequent disorders are anxiety disorders (14.0%), insomnia (7.0%), major depression (6.9%), somatoform (6.3%), alcohol and drug dependence (>4%), ADHD (5%) in the young, and dementia (1-30%, depending on age). Except for substance use disorders and mental retardation, there were no substantial cultural or country variations. Although many sources, including national health insurance programs, reveal increases in sick leave, early retirement and treatment rates due to mental disorders, rates in the community have not increased with a few exceptions (i.e. dementia). There were also no consistent indications of improvements with regard to low treatment rates, delayed treatment provision and grossly inadequate treatment. Disability: Disorders of the brain and mental disorders in particular, contribute 26.6% of the total all cause burden, thus a greater proportion as compared to other regions of the world. The rank order of the most disabling diseases differs markedly by gender and age group; overall, the four most disabling single conditions were: depression, dementias, alcohol use disorders and stroke. Conclusion: In every year over a third of the total EU population suffers from mental disorders. The true size of "disorders of the brain" including neurological disorders is even considerably larger. Disorders of the brain are the largest contributor to the all cause morbidity burden as measured by DALY in the EU. No indications for increasing overall rates of mental disorders were found nor of improved care and treatment since 2005; less than one third of all cases receive any treatment, suggesting a considerable level of unmet needs. We conclude that the true size and burden of disorders of the brain in the EU was significantly underestimated in the past.Concerted priority action is needed at all levels, including substantially increased funding for basic, clinical and public health research in order to identify better strategies for improved prevention and treatment for isorders of the brain as the core health challenge of the 21st century. (C) 2011 Published by Elsevier B.V.

Congruences between modular forms and lowering the level mod l^n

In this article we study the behavior of inertia groups for modularGalois mod l^n representations and in some cases we give a generalizationof Ribet s lowering the level result (cf. [Rib90]).

Evolutionary rates of Jurassic ammonites in relation to sea-level fluctuations

An analysis is presented of the diversity and faunal turnover of Jurassic ammonites related to transgressive /regressive events. The data set contained 400 genera and 1548 species belonging to 67 ammonite zones covering the entire Jurassic System. These data were used in the construction of faunal turnover curves and ammonite diversities, that correlate with sea-level fluctuation curves. Twenty-four events of ammonite faunal turnover are analyzed throughout the Jurassic. The most important took place at the Sinemurian-Carixian boundary, latest Carixian-Middle Domerian, Domerian-Toarcian boundary, latest Middle Toarcian-Late Toarcian, Toarcian-Aalenian boundary, latest Aalenian-earliest Bajocian, latest Early Bajocian-earliest Late Bojocian, Early Bathonian-Middle Bathonian boundary, latest Middle Bathonian-earliest Late Bathonian, latest Bathonian-Early Callovian, earliest Early Oxfordian-Middle Oxfordian, earliest Late Oxfordian-latest Oxfordian, latest Early Kimmeridgian, Late Kimmeridgian, middle Early Tithonian and Early Tithonian-Late Tithonian boundary. More than 75 percent of these turnovers correlate with regressive-transgressive cycles in the Exxon, and /or Hallam's sea-level curves. Inmost cases the extinction events coincide with regressive intervals, whereas origination and radiation events are related to transgressive cycles. The turnovers frequently coincide with major or minor discontinuities in the Subbetic basin (Betic Cordillera).

How well do individuals predict the selling prices of their homes?

Self-reported home values are widely used as a measure of housing wealth by researchers employing a variety of data sets and studying a number of different individual and household level decisions. The accuracy of this measure is an open empirical question, and requires some type of market assessment of the values reported. In this research, we study the predictive power of self-reported housing wealth when estimating sales prices utilizing the Health and Retirement Study. We find that homeowners, on average, overestimate the value of their properties by between 5% and 10%. More importantly, we are the first to document a strong correlation between accuracy and the economic conditions at the time of the purchase of the property (measured by the prevalent interest rate, the growth of household income, and the growth of median housing prices). While most individuals overestimate the value of their properties, those who bought during more difficult economic times tend to be more accurate, and in some cases even underestimate the value of their house. These results establish a surprisingly strong, likely permanent, and in many cases long-lived, effect of the initial conditions surrounding the purchases of properties, on how individuals value them. This cyclicality of the overestimation of house prices can provide some explanations for the difficulties currently faced by many homeowners, who were expecting large appreciations in home value to rescue them in case of increases in interest rates which could jeopardize their ability to live up to their financial commitments.

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, andthe firm decides the best subset to offer at any given moment to maximize expected revenue. The resultingdynamic program for the firm is intractable and approximated by a deterministic linear programcalled the CDLP which has an exponential number of columns. However, under the choice-set paradigmwhen the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has beenproposed but finding an entering column has been shown to be NP-hard. In this paper, starting with aconcave program formulation based on segment-level consideration sets called SDCP, we add a class ofconstraints called product constraints, that project onto subsets of intersections. In addition we proposea natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methodson the benchmark data sets in the literature. Both the product constraints and the ?SDCP method arevery simple and easy to implement and are applicable to the case of overlapping segment considerationsets. In our computational testing on the benchmark data sets in the literature, SDCP with productconstraints achieves the CDLP value at a fraction of the CPU time taken by column generation and webelieve is a very promising approach for quickly approximating CDLP when segment consideration setsoverlap and the consideration sets themselves are relatively small.

Partial melting of basic dykes in the contact aureoles of two shallow-level, gabbro-pyroxenite intrusions, Fuerteventura

THESIS ABSTRACT Low-pressure anatexis of basic dykes gave rise to unusual, zebra-like migmatites, in the contact metamorphic aureoles of two layered gabbro-pyroxenite intrusions, PXl and PX2, in the root zone of an ocean island, Fuerteventura Basal Complex (Canary Islands). This thesis focuses on the understanding of processes attributing to the partial melting and formation of these migmatites, characterised by a dense network of closely spaced, millimetre-wide leucocratic segregations with perfectly preserved igneous textures. The presence of fluids are required to decrease the solidus of basic igneous lithologies, to allow partial melting in such aloes-pressure (1-2 kb) environment. An oxygen isotope study was thus carried out on dykes inside and beyond the PX2 aureole, in order to decipher the nature and origin of such fluids. Low or negative δ18O values were obtained for whole rocks and mineral-separates, decreasing towards the contact, with the intrusion itself retaining fairly high values. This trend has been attributed to the advection of meteoric water during magma emplacement, with increasing fluid/rock ratios (higher dyke intensities towards the intrusion acting as fluid-pathways) and higher temperatures promoting increasing exchange during recrystallisation. A comparison of whole rock and mineral major- and trace- element data allowed the redistribution of elements .between different mineral phases and generations, during contact metamorphism and partial melting to be assessed. Certain trace-elements, e.g. Zr, Hf, Y, and REEs, were internally redistributed during contact metamorphic recrystallisation, causing- the enrichment of neocrystallised diopsides compared to relict phenocrysts. This has been assigned to the liberation of trace elements on the breakdown of primary minerals, kaersutite and sphene, on entering the thermal aureole. Major and trace element compositions of minerals in migmatite melanosomes and leucosomes are almost identical, pointing to a syn- or post- solidus reequilibration on cooling of the migmatite terrain. The mineralogical, textural and geochemical evolution of dykes in a contact metamorphic aureole, is recorded around an apophysis of the PX1 intrusion, where there is evidence of incipient partial melting. Hydrothermal mineral pseudomorphs in the outer parts of the aureole are progressively replaced by dry mineral assemblages, with increasingly recrystallised diopside and evidence of partial melting -the extent of which varies from one lithology to another. The appearance of more mafic lithologies towards the intrusion, with lower whole rock SiO2 and mobile element abundances, e.g. Rb, Cs, K, has been explained by the migration and accumulation of feldspathic material into leucosomes outside the samples. A micro-structural study of leucosomes and leucocratic pods, with the aid of high-resolution X-ray computed micro-tomography (HRXµCT), allowing the visualization and quantification of shapes and orientations, was carried out in order to better understand the processes of melt segregation in the PX1 aureole. Leucocratic pods, representing former amygdales, are considered as natural strain ellipsoids. Their short axes are oriented perpendicular to leucosome planes, which sub-parallel the intrusive contact. Leucosomes thus effectively represent foliation planes. This implies that the direction of maximum shortening, during migmatisation, was perpendicular to the orientation of leucosomes, contradicting earlier models that suggest leucosomes represent tension veins. RESUME DE LA THESE Un phénomène rare de fusion partielle de filons basiques à basse pression a été étudié dans les auréoles de contact de deux intrusions litées de gabbro-pyroxénite, PX1 et PX2, localisées dans le soubassement de l'île volcanique de Fuerteventura aux Canaries. Cette anatexie a engendré des migmatites finement zébrées d'aspect très inhabituel, dont les processus de formation ont été étudiés dans le présent travail. Ces roches sont caractérisées par un réseau dense de veinules leucocrates d'épaisseur millimétrique, dont les textures ignées sont parfaitement préservées. La fusion partielle de roches basiques à basse pression (1-2 kbar) requiert la présence d'eau afin d'abaisser le solidus du système à des températures géologiquement réalistes. Une étude comparative des isotopes de l'oxygène a ainsi été menée sur des filons respectivement affectés et non affectés par le métamorphisme de contact, afin de confirmer la présence de ces fluides, de déterminer l'importance de leur interaction avec les roches et leur origine. Des valeurs de δ180 basses ou négatives ont été mesurées sur roche totale et minéraux séparés, décroissantes en direction du contact, alors que l'intrusion elle-même a conservé des valeurs élevées. Ce gradient a été attribué à l'advection d'eau météorique durant la mise en place du magma, les températures les plus élevées favorisant d'autant plus la circulation des fluides et les échanges isotopiques durant la recristallisation des roches. Cette recristallisation engendré une redistribution chimique complète des éléments entre les différentes générations de minéraux résultant du métamorphisme de contact et de l'anatexie, mise en évidence par microanalyse. Certains éléments traces comme Zr, Hf, Y et les REE ont été concentrés dans le diopside néoformé consécutivement à la déstabilisation de minéraux primaires riches en ces éléments comme la kaersutite ou le sphène. Les compositions en éléments majeurs et traces des minéraux des mélanosomes et leucosomes des migmatites sont pratiquement identiques, indiquant une rééquilibration syn- à postsolidus lors du refroidissement de l'auréole de contact. La transformation progressive des filons basiques au niveau de leur minéralogie, textures et composition chimique a pu être observée en détail à l'approche du contact d'une apophyse de l'intrusion PX1. La paragenèse magmatique initiale n'est jamais préservée, les faciès les plus distants du contact étant constitués d'un assemblage pseudomorphique hydrothermal. Ce dernier est progressivement remplacé par des assemblages anhydres incluant du diopside néoformé, puis apparaissent les premiers signes de fusion partielle, dont l'importance varie fortement d'une lithologie à l'autre. L'apparition de faciès plus basiques en direction du contact, avec des teneurs réduites en SiO2 et en éléments incompatibles tels Rb, Cs, K, a été attribuée à l'échappement de leucosomes feldspathiques hors du système. Une étude microstructurale de la distribution spatiale du matériel leucocrate au sein des migmatites par microtomographie X de haute résolution (HRXµCT) a été menée pour mieux comprendre les processus de ségrégation des liquides dans l'auréole de PX1. De petites entités ovoïdes, représentant d'anciennes structures amygdalaires au sein des filons, ont été considérées comme des ellipsoïdes marqueurs de la déformation finie. Leur petit axe est orienté perpendiculairement aux plans définis par les leucosomes, eux-mêmes subparallèles au contact intrusif. Les leucosomes matérialisent donc des plans de clivage. Ainsi, la direction de raccourcissement maximum durant la fusion partielle était perpendiculaire à l'orientation des leucosomes, contrairement à ce qui a été dit dans de précédentes publications, qui suggéraient que les leucosomes représentaient des veines de tension. RESUME DE LA THESE (POUR LE GRAND PUBLIC) L'observation directe du soubassement d'une île volcanique est une occasion rare, accessible dans le «complexe de base » de l'île canarienne de Fuerteventura. Ce dernier a enregistré divers phénomènes magmatiques, métamorphiques et de fusion partielle induits par l'intrusion répétée de magmas alimentant des appareils volcaniques sus jacents, sous forme de petits plutons, essaims de filons et complexes annulaires de gabbros alcalins, pyroxénites, syénites et carbonatites. Dans ce contexte de flux de chaleur élevé, des filons basiques ont subi une fusion partielle au contact de deux intrusions de gabbro-pyroxénite, un phénomène extrêmement rare à une profondeur aussi réduite, estimée à quelque 3-6 km. Les produits de cette fusion partielle sont des liquides très riches en feldspath, concentrés en un réseau dense de veinules blanches (leucosomes) au sein du matériau résiduel sombre non fondu (mélanosome) pour former ce qu'on appelle des migmatites. Outre les aspects pétrologiques liés à la formation de ces migmatites, l'intérêt majeur du phénomène réside dans le fait qu'il puisse représenter la source des magmas évolués parfois observés sur les îles océaniques. A des pressions aussi faibles que dans le soubassement de Fuerteventura (1-2 Kbar), la présence de fluides abondants est nécessaire pour abaisser la température de début de fusion des roches (solidus) à des valeurs géologiquement réalistes. Des expériences ont montré que même en présence de plusieurs %-poids d'eau, une température de 1000°C était encore nécessaire pour obtenir une proportion de liquide équivalente à celle observée sur le terrain, soit 25%. Or les magmas alcalins des îles océaniques, bien qu'hydratés, n'en contiennent de loin pas autant, ce qui implique une source d'eau externe. Une étude isotopique de l'oxygène a été entreprise afin de tester cette hypothèse. Les valeurs obtenues en 5180 sont basses ou négatives et indiquent l'influence d'eau d'origine météorique. Cette eau de pluie se serait infiltrée le long des filons depuis la surface du volcan et les aurait complètement hydrothermalisés en profondeur (situation encore visible à l'extérieur de l'auréole de contact), leur permettant ainsi de stocker l'eau nécessaire à leur fusion partielle ultérieure. L'interaction entre eau de pluie et filons a été d'autant plus importante que ces derniers étaient proches du contact avec l'intrusion, ce qui suggère que la circulation de ces eaux et leur interaction avec les roches a été favorisée par la chaleur fournie par l'intrusion elle-même. Un autre aspect de ce travail s'est focalisé sur la redistribution des éléments traces au sein des minéraux des filons basiques durant le métamorphisme de contact et la fusion partielle. Ainsi, le pyroxène de seconde génération est-il sensiblement enrichi en traces telles Zr, Hf, Y et les terres rares, par rapport au pyroxène magmatique originel, en relation avec la déstabilisation de minéraux primaires riches en ces éléments tels le sphène et la kaersutite. Cependant, les compositions en éléments majeurs et traces des minéraux recristallisés des migmatites sont pratiquement les mêmes dans les leucosomes et les mélanosomes, suggérant une rééquilibration chimique complète durant le refroidissement de ces lithologies. Si certaines migmatites se sont comportées en système chimiquement fermé (hormis l'eau météorique), d'autres filons ont manifestement perdu une partie de leurs leucosomes, ainsi qu'en témoigne leur composition progressivement appauvrie en silice et autres éléments incompatibles mobiles, tels K et Rb à l'approche du contact de l'intrusion. Parallèlement à cette évolution chimique, les paragenèses hydrothermales distantes du contact sont progressivement remplacées par des paragenèses anhydres, puis par l'apparition des premiers leucosomes, tandis que les textures magmatiques initiales sont complètement effacées au profit d'une combinaison de textures magmatique dans les leucosomes et en mosaïque dans les mélanosomes. Enfin, la distribution spatiale des liquides de fusion partielle a été étudiée par microtomographie X de haute résolution, dans des filons contenant des entités ovoïdes leucocrates, sans doute d'anciennes amygdales à zéolites. Ces dernières ont été considérées comme des ellipsoïdes de la déformation finie. L'orientation de leur petit axe, perpendiculaire au plan défini par les veinules de leucosomes, indique que ces derniers représentent des plans de clivage perpendiculaires à la direction de raccourcissement maximum. Ainsi, la ségrégation des liquides de fusion partielle se serait faite dans les plans de compression et non dans des plans de dilatation, contrairement à ce que laisserait penser le sens commun.

Comparison of potential adjustment variables representing primary intellectual level in epidemiological studies on neurotoxicity

BACKGROUND: Primary intellectual abilities (PIA) are a confounder in epidemiological studies on neurotoxicity. A good measure of this confounder should be independent of age as PIA is an intrinsic ability. Furthermore, as PIA is related to health endpoints, any measure of PIA should reveal this association. This study is aimed at comparing vocabulary test, diploma and age at end of schooling properties as measures of PIA in a non-exposed population of workers. METHODS: The design was a cross-sectional study of 413 non-exposed workers (203 women and 210 men) selected from a health check-up center. The effect of age on the vocabulary score was assessed using an analysis of covariance adjusted for diploma. Relationships between neuropsychological performances and vocabulary score, diploma and end of schooling age were, respectively, assessed using multiple linear regressions adjusted for age and gender. RESULTS: Vocabulary score increased significantly with age, both for men and women. The increase was 0.14 word per year for women, and 0.18 word per year for men. The explained variance of the models evaluating the relationships between age at end of schooling, diploma, vocabulary test, and neuropsychological performances was quite similar for the three measures of PIA. CONCLUSIONS: Vocabulary score was found to be age-related, even after adjustment for diploma. No difference was found between these three variables in terms of their relationship to neuropsychological endpoints. Moreover, the literature shows that vocabulary test performances are influenced by exposure to neurotoxic agents. These results suggest that vocabulary score could be of interest for participants of similar ages and similar diplomas. Otherwise, the other two variables would be better PIA measures in neurotoxicology studies.