Gwenn Menvielle
email: gwenn.menvielle@inserm.fr

Julien Dugas

Jeanna-Eve Franck

Matthieu Carton

Brigitte Trétarre

Isabelle Stücker

Danièle Luce

Icare Group

Sylvie Cénée

Oumar Gaye

Florence Guida

Farida Lamkarkach

Loredana Radoï

Marie Sanchez

Diane Cyr

Annie Schmaus

Occupational prestige trajectory and the risk of lung and head and neck cancer among men and women in France

Keywords: Occupational prestige trajectory, alcohol, smoking, occupational exposures, respiratory cancer

Objectives: to investigate the associations between occupational prestige trajectories and lung and head and neck (HN) cancer risk, and to assess to what extent smoking and alcohol drinking and occupational exposures contribute to these associations.

Methods: Using data from the ICARE case-control study (controls (2676 men/715 women), lung cancers (2019 men/558 women), HN cancers (1793 men/305 women)), we defined occupational prestige trajectories using group-based modeling of longitudinal data. We conducted logistic regression models.

Results: Among men, a gradient was observed from the downward "low to very low" trajectory to the stable very high trajectory. The associations were reduced when adjusting for tobacco and alcohol consumption and occupational exposures. Among women, when compared to the stable high trajectory, there was an increased cancer risk in all trajectories. The associations remained globally unchanged or even increased after adjustment for tobacco and alcohol consumption, and did not change when adjusting for occupational exposures. The ORs were smaller for lung than for HN cancers in men.

Conclusion: Occupational prestige trajectory is strongly associated with lung and HN cancer risk in men and women.

Introduction

Incidence of lung and head and neck (HN) (lip, mouth, pharynx, larynx) cancers is high among men and increasing among women. [START_REF] Lortet-Tieulent | Convergence of decreasing male and increasing female incidence rates in major tobacco-related cancers in Europe in 1988-2010[END_REF] In 2012, the European standardized incidence rates were respectively 30.9 (per 100000 person years) for HN cancers and 74.5 for lung cancer in men, and 8.9 and 27.9 in women. [START_REF] Ferlay | Cancer incidence and mortality patterns in Europe: estimates for 40 countries in 2012[END_REF] Studies have consistently reported a strong association between socioeconomic status (SES) and lung and HN cancer incidence, with differences by gender and country. [START_REF] Faggiano | Socioeconomic differences in cancer incidence and mortality[END_REF] SES is a multidimensional construct. Higher education is associated with a higher sensitivity to and a better understanding of prevention messages and a better ability to change his/her behavior whereas income captures more material dimensions such as living conditions, good diet or access to health care. Occupational class, more closely linked to occupation itself, is another frequent indicator of SES. Several classifications exist for occupational class. Classifications such as the international Erikson and Goldthorpe's class categories (EGP) [START_REF] Erikson | The constant flux[END_REF] or the French PCS classification [START_REF] Desrosières | Les catégories socioprofessionnelles] Occupational class categories La Découverte[END_REF] are categorical and combine various dimensions such as the level of qualification, the employee/self-employed status, the work characteristics, the level of income or the supervisory position. Other classifications are hierarchical and allow ordering all occupations on the social ladder, either based on the combination of educational requirements and monetary payoffs, such as the International Socio-Economic Index of Occupational Status [START_REF] Ganzeboom | A standard international socio-economic index of occupational status[END_REF], or based on the popular degree of desirability of occupations, such as the Treiman's Standard International Occupational Prestige Scale. [START_REF] Treiman | Occupational prestige in comparative perspective-quantitative studies in social relations[END_REF] Most studies investigating socioeconomic inequalities in respiratory cancer incidence have focused on educational level or occupational class at one point in time and did not capture changes in SES over the life time. [START_REF] Boing | How much do smoking and alcohol consumption explain socioeconomic inequalities in head and neck cancer risk?[END_REF][START_REF] Menvielle | The role of smoking and diet in explaining educational inequalities in lung cancer incidence[END_REF][START_REF] Menvielle | Smoking, alcohol drinking, occupational exposures and social inequalities in hypopharyngeal and laryngeal cancer[END_REF][START_REF] Nkosi | Socioeconomic position and lung cancer risk: how important is the modeling of smoking?[END_REF][START_REF] Santi | Occupation and educational inequalities in laryngeal cancer: the use of a job index[END_REF] However, a few studies, most of them were case-control studies, have investigated the association between respiratory cancer incidence and occupational class over the life time, assessed either by the longest occupational class or by trajectories between two points in time. [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF][START_REF] Conway | Socioeconomic factors associated with risk of upper aerodigestive tract cancer in Europe[END_REF][START_REF] Marshall | Socioeconomic status, social mobility and cancer occurrence during working life: a case-control study among French electricity and gas workers[END_REF][START_REF] Melchior | Occupational class, occupational mobility and cancer incidence among middle-aged men and women: a prospective study of the French GAZEL cohort*[END_REF][START_REF] Menvielle | Smoking, alcohol drinking, occupational exposures and social inequalities in hypopharyngeal and laryngeal cancer[END_REF][START_REF] Schmeisser | Life course social mobility and risk of upper aerodigestive tract cancer in men[END_REF]) Therefore the available literature did not consider the development of SES over the whole working life. A hierarchical measure of occupational class available at various points in time over the working life may allow to identify specific social groups and therefore improve our understanding of socioeconomic inequalities in health.

Several studies have investigated the underlying mechanisms of the socioeconomic differences observed in respiratory cancer incidence trying to identify what risk factors could explain these inequalities. Smoking and alcohol drinking are the two main risk factors for these cancers and are strongly socially patterned. Whatever the SES indicator used, studies have generally reported that smoking and alcohol drinking partly accounted for these inequalities for lung cancer [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF][START_REF] Menvielle | The role of smoking and diet in explaining educational inequalities in lung cancer incidence[END_REF][START_REF] Menvielle | Quantifying the mediating effects of smoking and occupational exposures in the relation between education and lung cancer[END_REF]) and HN cancer [START_REF] Boing | How much do smoking and alcohol consumption explain socioeconomic inequalities in head and neck cancer risk?[END_REF][START_REF] Menvielle | Smoking, alcohol drinking, occupational exposures and social inequalities in hypopharyngeal and laryngeal cancer[END_REF][START_REF] Santi | Occupation and educational inequalities in laryngeal cancer: the use of a job index[END_REF] although in some studies, the associations were strongly attenuated or not any more significant after adjustment. [START_REF] Conway | Socioeconomic factors associated with risk of upper aerodigestive tract cancer in Europe[END_REF][START_REF] Melchior | Occupational class, occupational mobility and cancer incidence among middle-aged men and women: a prospective study of the French GAZEL cohort*[END_REF][START_REF] Nkosi | Socioeconomic position and lung cancer risk: how important is the modeling of smoking?[END_REF][START_REF] Schmeisser | Life course social mobility and risk of upper aerodigestive tract cancer in men[END_REF]) Few studies have investigated the contribution of occupational exposures to these inequalities and suggested a non-negligible role of these exposures. [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF][START_REF] Menvielle | Occupational exposures contribute to educational inequalities in lung cancer incidence among men: Evidence from the EPIC prospective cohort study[END_REF][START_REF] Menvielle | Quantifying the mediating effects of smoking and occupational exposures in the relation between education and lung cancer[END_REF][START_REF] Menvielle | Smoking, alcohol drinking, occupational exposures and social inequalities in hypopharyngeal and laryngeal cancer[END_REF][START_REF] Santi | Occupation and educational inequalities in laryngeal cancer: the use of a job index[END_REF] Finally, most studies focused on men [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF][START_REF] Marshall | Socioeconomic status, social mobility and cancer occurrence during working life: a case-control study among French electricity and gas workers[END_REF][START_REF] Melchior | Occupational class, occupational mobility and cancer incidence among middle-aged men and women: a prospective study of the French GAZEL cohort*[END_REF][START_REF] Schmeisser | Life course social mobility and risk of upper aerodigestive tract cancer in men[END_REF]) whereas the situation is likely to differ by gender due to gender differences in the social stratification, the social context, the consumption of tobacco and alcohol, the exposure to carcinogens, and the work history.

Finally the role of risk factors in socioeconomic inequalities in cancer risk may differ by SES indicator.

In particular, the association between health behavior and SES may be stronger when SES is assessed using a prestige indicator, that relates to people's status and social standing in society, than a measure based on employment relations, that is more linked to income and wealth. [START_REF] Chandola | Social inequality in coronary heart disease: a comparison of occupational classifications[END_REF][START_REF] Galobardes | Indicators of socioeconomic position (part 1)[END_REF]) Declining prestige may be associated with decreased self-esteem and psychological health, and might be particularly linked to changes in health behaviors as a way to cope with this adversity.

The aim of our analysis was, separately among men and women, first to investigate the association between occupational prestige trajectories and lung and HN cancer incidence and second to assess to what extent smoking, alcohol drinking and occupational exposures over the life time contributed to these inequalities.

Methods

Study population

The ICARE study is a multi-center population-based case-control study conducted in France from 2001 through 2007 in 10 French "départements" (administrative areas) covered by a cancer register.

The cases were all patients newly diagnosed during the study period with a primary, histologically confirmed malignant tumour of oral cavity, pharynx, sinonasal cavities, larynx and lung (International Classification of Diseases, 10 th Revision codes C00-C14, C30-C34) and who were aged 75 or less at diagnosis. The control group was selected from the general population of the same geographical areas (département) by random digit dialing, with frequency matching to all cases by sex and age.

Additional stratification was used to achieve a distribution by socioeconomic status among the controls comparable to that of the general population. Participation rates were 87.1% in lung cancer cases, 82.5% in HN cancer cases and 80.6% among controls. The study design has been described in details previously [START_REF] Luce | Investigation of occupational and environmental causes of respiratory cancers (ICARE): a multicenter, population-based case-control study in France[END_REF].

Measure of occupational trajectory, smoking, alcohol drinking and occupational exposures

Subjects were interviewed face-to-face by trained interviewers, using a standardized questionnaire including detailed information about socio-demographic characteristics, lifetime tobacco and alcohol consumption (type, period of consumption, frequency of consumption and quantities consumed for each period), and lifetime occupational history (covering all jobs held for at least 1 month and periods of inactivity). For each job period, occupation and industrial activity were coded blind to the case-control status using respectively the International Standard Classification of Occupations 1968 (ISCO) (International Labour 1968) and the French Nomenclature of Activities (NAF).

Using each participant's work history, we defined lifecourse occupational prestige trajectory, using the Treiman's Standard International Occupational Prestige Scale (SIOPS), an internationally comparable scoring system. The score ranges from 14 for unskilled agricultural workers to 78 for physicians and some other occupations with higher education like university teachers. A SIOPS score was assigned to each job period based on the ISCO-code using the Ganzeboom conversion tool (Ganzeboom and Treiman). For periods with two or more parallel jobs, the maximum value of the scores attributed to these jobs was taken. Retirement was considered to end a subject's work history. As recommended by Treiman, intermediate phases of occupational inactivity (training, illness, unemployment) were assigned a score of 30 or the score of the previous occupation if lower than 30. A score of 30 roughly corresponds to the prestige scores of low-skilled manual jobs (such as machinist or plasterer) or low clerical work (such as mail distributor or warehouseman). Other periods of inactivity (e.g. housewife) were assigned a missing value for SIOPS. Members of the armed forces were assigned a score of 42. For each individual, we reconstructed a work history with one SIOPS score per year. People with missing SIOPS score for the whole job history were excluded from the analysis (7.2% of men and 8.0% of women). Then, we used group-based trajectory model on SIOPS repeated measures to identify distinct clusters of individuals following a similar longitudinal pattern separately for men and women. These clusters correspond to the occupational prestige trajectories analyzed in this paper. The fit of the models as well as the homogeneity within each trajectory led us to define 8 trajectories in men and in women (figure 1). We conducted sensitivity analyses excluding people with no SIOPS score for at least 20% (3.2% of men and 23.3% of women) or 30% of their job history (2.0% of men and 15.1% of women). The higher proportion in women accounts for housewife women.

In the lung cancer analyses, lifelong cigarette smoking was captured using an index specifically developed for this disease, the cumulative smoking index (CSI). The CSI takes into account total duration of smoking, time since cessation and average number of cigarettes smoked per day and is null for never smokers. In our data, the CSI varied linearly with lung cancer risk. [START_REF] Papadopoulos | Heavy smoking and lung cancer: are women at higher risk? Result of the ICARE study[END_REF] In the HN cancer analyses, lifelong tobacco consumption was measured using pack-years (restricted cubic splines separately in men and women), smoking status (never/current/former smoker) and the interaction between these variables. The average daily alcohol consumption was calculated as the number of drinks per day by adding the average lifetime daily consumption of each type of alcoholic beverage (restricted cubic splines separately in men and women).

Occupational exposure to asbestos and crystalline silica was assessed using job-exposure matrices (JEM) specifically developed for France. [START_REF] Févotte | Matgene: a program to develop job-exposure matrices in the general population in France[END_REF] For each combination of an ISCO and a NAF code, the JEM assigned a probability, an intensity and a frequency of exposure. The indices were provided for different calendar periods between 1947 and 2007 to account for possible variations in exposure over time. For each subject, we derived from its entire occupational history a cumulative level of exposure to asbestos and crystalline silica obtained as the sum over all jobs of the product of the exposure intensity, probability, frequency and duration (using midpoints of each class). Exposure to silica could not be studied in women due to the small number of subjects exposed.

Assessment of ever exposure to diesel motor exhaust (DME) was collected for each job period and based on self-report. This information was missing for about 13% of all job periods. We combined the ISCO code with the NAF code for each job period. Missing values for exposure to DME were replaced by the modal category observed in the same ISCO-NAF combination among subjects with complete data. DME exposure was assessed from the questionnaire on a case-by-case basis when the modal category included less than 60% of the subjects. The association between lung cancer and ever exposure to DME was similar when using this variable and when restricting the analysis to complete case data. [START_REF] Matrat | Occupational exposure to diesel motor exhaust and lung cancer: A dose-response relationship hidden by asbestos exposure adjustment? The ICARE study[END_REF] In lung cancer analyses, we adjusted for occupational exposures to asbestos (restricted cubic splines for men, ever/never for women), silica (restricted cubic splines for men) and DME (ever/never). In HN cancers analyses, we adjusted for occupational exposures to asbestos (restricted cubic splines for men, ever/never for women).

Logistic regression models were conducted separately for lung and HN cancers, and for men and women. The first model was adjusted for age and residence area. The second model was adjusted additionally for smoking (lung cancer) or alcohol and tobacco consumption (HN cancer). The third model included additional adjustment for occupational exposures. For a large proportion of women, their work history includes long periods of inactivity as housewife. Therefore, among women, we conducted an additional model adjusted for the number of years as housewife (as a continuous variable). Data with missing values on risk factors were excluded (smoking n=59, alcohol n=77, occupational exposures n=175, periods of inactivity as housewife n=129). All analyses were conducted using SAS 9.4 software (SAS Institute, Cary,NC). Overall, our analyses were based on 3391 controls (2676 men/715 women), 2577 lung cancers (2019 men/558 women), 2098 HN cancers (1793 men/305 women).

Results

We identified 8 occupational prestige trajectories in men and in women (figure 1). In men, there were 4 trajectories stable over the working life (stable low, stable middle, stable high, stable very high), 2 upward trajectories (very low to middle, low to high), and 2 slightly downward trajectories (low to very low, middle to low). In women, there were 4 stable trajectories (stable middle, stable middle+, stable high, stable very high), 2 upward trajectories (low to middle, low to high) and 2 downward trajectories (low to very low, middle to very low). In total, 19% of male controls and 27% of female controls experienced a downward trajectory. The respective percentages for an upward trajectory were 21% and 26%. The distribution of alcohol and tobacco consumption, the occupational exposure to asbestos, silica and DME as well as the number of years of inactivity as housewife are presented in table 1 by gender and occupational trajectories. The risk factors were more prevalent in the more socially deprived groups. Among men, these differences were especially pronounced for alcohol consumption in HN cancer cases. Among women, the stable very high trajectory, although based on very small numbers, displayed the worst profile with high alcohol and tobacco consumption.

The results of the logistic models are presented in tables 2 and 3.

In men, a gradient was observed amongst all occupational prestige trajectories. A decreased HN cancer risk was observed in the stable very high trajectory and an increased HN cancer risk was observed in all other trajectories when compared with the stable high trajectory. The increased risk was especially pronounced among men who experienced a low to very low or a stable low trajectory.

The risk in the upward trajectories was close to the risk of the group they joined. The associations were substantially reduced when adjusting for tobacco and alcohol consumption and for occupational exposures in all trajectories except in the low to high and in the stable very high trajectories where the ORs hardly changed. The ORs were statistically significant after full adjustment in all trajectories but the low to high and the stable very high trajectory. The pattern was similar for lung cancer, although the ORs were much lower than those observed for HN cancers. When compared with the stable very high trajectory, an significantly increased lung cancer risk was observed in all trajectories but the stable very high and the low to high trajectories . The associations were reduced when adjusting for smoking and then for occupational exposures (the OR although higher than 1 became non-significant for the low to middle trajectory).

In women, when compared to the stable high trajectory, there was an increased HN cancer risk in all trajectories in particular in the stable very high trajectory. The ORs were nonetheless significant only for the low to very low, stable middle and very high trajectories. After adjustment for tobacco and alcohol consumption, the associations remained globally unchanged or even increased. The ORs hardly changed when adjusting for the number of years as housewife, except for the stable very high trajectory. Contrary to men, the ORs were only slightly lower for lung than for HN cancer, and even higher and statistically significant for the low to high trajectory. When adjusting for smoking, the ORs increased for the low to very low, stable middle and stable middle+ trajectories, decreased and became non-significant for the low to high and the stable very high trajectories, and did not change for the other trajectories. For both lung and HN cancer analyses, additional adjustment for occupational exposures hardly changed the estimates.

Results from the sensitivity analyses excluding people with no SIOPS score for at least 20% or 30% of their job history led to similar conclusions (results not shown).

Discussion

Although there is now a substantial body of literature on SES and cancer risk, little is known on SES over the life time and cancer risk. Using a continuous variable for occupational prestige, we precisely modelled people's trajectories over the whole working life and identified 8 groups of occupational prestige trajectories in men and in women. This classification was more discriminatory than the French categorical occupational class classification; e.g. in our data, 47% of the women were clerks most of their working life. In men, we did not identify pronounced downward trajectories. However we observed a low and slightly downward trajectory that accounted for a non-negligible part of the population (4% of controls, 8% of lung cancers, 12% of HN cancers). This trajectory was characterized by a high consumption of alcohol. It is likely that alcohol played a role in this trajectory, probably both by impacting the first job at the bottom of the occupational prestige ladder and by preventing an upward trajectory over the life time.

Both in men and women, we identified a small group who experienced a stable very high occupational prestige trajectory. Among women, this extremely small group is very specific: when it is grouped with the much larger stable high trajectory and used as the reference category, no differences in respiratory cancer risk between occupational prestige trajectories appear any more.

That is why we kept this small group separate in our analyses. In men this socially very privileged group displayed the best health profile and our results suggest that a socioeconomic gradient in respiratory cancers risk exists until the very top of the social ladder. In women however, this socially very privileged group showed the highest lung and HN cancer risk, partly due to a high alcohol and tobacco consumption. We acknowledge that our estimates are based on small numbers and that no firm conclusion can be drawn. However, our results suggest that in this birth cohort, the most socially privileged women had the worst health behaviors, which may reflect their higher emancipation. [START_REF] Schaap | Female ever-smoking, education, emancipation and economic development in 19 European countries[END_REF][START_REF] Waldron | Patterns and causes of gender differences in smoking[END_REF] Before discussing the results, some methodological issues should be discussed. The ICARE study is among the largest case-control studies worldwide on respiratory cancers, with high participation rates (82.5% among HN cancer cases, 87.1% among lung cancer cases and 80.6% among controls).

Cases were recruited through a collaboration with the French network of cancer registries, which allowed a nearly complete identification of eligible cases. Controls were selected to have a socioeconomic distribution comparable to that of the general population of the same geographical area. Recall bias is a well-known weakness of case-control studies. Therefore, we paid special attention to data collection. Detailed information was collected by trained interviewers during faceto-face interviews, with a standardised questionnaire, and in a similar manner, among cases and controls.

We collected detailed information on lifetime tobacco and alcohol consumption, with information on the different types and quantity consumed for the different consumption periods. However, we did not account for differences in the type of tobacco smoked (brown or blond, use of filter) in our measure of lifelong smoking. We could identify occasional drinkers and exclude them from the 'never drinker' group. In France, in 2005, only 8.4% of individuals reported never having consumed alcohol, [START_REF] Legleye | Alcoholization, a complex phenomenon[END_REF] a proportion close to the proportion of never drinkers among controls in the ICARE study (8.6%). In addition, in France, in 2005, around 26% of men (age standardised figure) reported being never smokers, a proportion close to our figures (28%). [START_REF] Peretti-Watel | Les Français et la cigarette en 2005 : un divorce pas encore consommé[END_REF] However differential reporting between cases and controls cannot be excluded, and we cannot rule out an underestimation of tobacco or alcohol consumption, which may differ by SES. [START_REF] Huerta | Reliability of self-reported smoking history and age at initial tobacco use[END_REF] We nevertheless believe that any misreporting in lifetime tobacco or alcohol consumption is not likely to substantially affect our main conclusions.

Occupational exposures were assessed thanks to the lifetime job history. Self-reported occupational history is usually considered as reliable. [START_REF] Blair | Methodological issues regarding confounding and exposure misclassification in epidemiological studies of occupational exposures[END_REF]) Occupations were coded blind to the casecontrol status. Occupational exposure to asbestos and silica was assessed through specific JEMs developed for France. A JEM generates only non-differential misclassification which could result in an underestimation of the association between the carcinogens and cancer and an underestimation of the role of these occupational exposures in socioeconomic inequalities in respiratory cancers risk.

However previous studies have validated these JEMs. [START_REF] Guida | Risk of lung cancer associated with occupational exposure to mineral wools: Updating knowledge from a French population-based casecontrol study, the ICARE study[END_REF][START_REF] Lacourt | Temporal patterns of occupational asbestos exposure and risk of pleural mesothelioma[END_REF] In addition, lifetime prevalence of asbestos exposure among our male and female controls (24.3% and 4.1%) is comparable to an estimation from 2007 based on the general French population (26.7% and 2.7% resp.). [START_REF] Févotte | Matgene: a program to develop job-exposure matrices in the general population in France[END_REF]) Overall, we accounted for occupational exposures to asbestos and silica in a much more precise way than in previous studies on socioeconomic inequalities in cancer risk [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF][START_REF] Santi | Occupation and educational inequalities in laryngeal cancer: the use of a job index[END_REF]) due to both the detailed measure of exposures (weighted combination of intensity, duration, frequency, and probability) and the modeling of the association with cancer risk (splines). Regarding exposure to DME, we cannot exclude a recall bias. However, 26.2% of our male controls reported at least one job with DME exposure, a proportion close to that found in an Italian study. [START_REF] Richiardi | Occupational exposure to diesel exhausts and risk for lung cancer in a population-based case-control study in Italy[END_REF] We investigated the association between occupational prestige trajectory and lung and HN cancer risk using data from the ICARE study. Data for lung cancer have been previously included in a pooled analysis on social mobility for occupational prestige. [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF] However, in the latter study, trajectories were assessed using only the first and the last or longest occupation and occupational exposures were assessed in a crude way using ever employment in a job with known lung carcinogen exposure. We observed strong associations between occupational prestige trajectory and lung and HN cancer risk. These associations were reduced when adjusting for people's education but most remained elevated (results not shown), suggesting that education and prestige have an independent effect on cancer risk and do not account for the same dimensions of people's SEP. [START_REF] Galobardes | Indicators of socioeconomic position (part 1)[END_REF] The SIOPS classification has been developed for men and this may impact our results in women due to differences in occupational prestige between men and women for some occupations. However, prestige scores measure the classical sociological hypothesis that occupational status constitutes the single most important dimension in social interactions and this hierarchy is not likely to fundamentally differ by gender. Investigating work history in women is complexified because of inactivity periods as housewife. We chose to adjust for the duration of these episodes. Finally, we assessed occupational prestige using people's own occupation. Several studies have shown that women's but also men's health were related to their partner's SEP. [START_REF] Chandola | Social inequality in coronary heart disease: a comparison of occupational classifications[END_REF][START_REF] Skalicka | Effects of spouses' socioeconomic characteristics on mortality among men and women in a Norwegian longitudinal study[END_REF][START_REF] Torssander | Marital partner and mortality: the effects of the social positions of both spouses[END_REF] Therefore our results may be different when using the occupational prestige of the household. However the lifetime occupational history of the partner was not available in our study.

Our results confirm the substantial role of smoking and alcohol drinking in socioeconomic inequalities in respiratory cancers incidence in men. Consistently with most of the available literature [START_REF] Behrens | Occupational prestige, social mobility and the association with lung cancer in men[END_REF][START_REF] Boing | How much do smoking and alcohol consumption explain socioeconomic inequalities in head and neck cancer risk?[END_REF][START_REF] Menvielle | The role of smoking and diet in explaining educational inequalities in lung cancer incidence[END_REF][START_REF] Menvielle | Quantifying the mediating effects of smoking and occupational exposures in the relation between education and lung cancer[END_REF][START_REF] Menvielle | Smoking, alcohol drinking, occupational exposures and social inequalities in hypopharyngeal and laryngeal cancer[END_REF][START_REF] Santi | Occupation and educational inequalities in laryngeal cancer: the use of a job index[END_REF], we observed that these risk factors only partly accounted for these inequalities. We cannot rule out residual confounding by smoking and alcohol drinking. This would occur in all groups but may be larger among men with a low occupational prestige due to longer and heavier consumptions. However it is unlikely that residual confounding account for all remaining inequalities.

Our analyses stress the importance of work-related factors in socioeconomic inequalities in respiratory cancer incidence. Interestingly, we observe a stronger gradient relating occupational prestige to occupational exposures than to health behaviors in men. We may have underestimated the contribution of occupational exposures as we did not account for all carcinogens because of no data availability. For lung cancer, we adjusted for the three carcinogens with the highest number of attributable lung cancer cases [START_REF] Brown | Occupational cancer in Britain. Respiratory cancer sites: larynx, lung and mesothelioma[END_REF]) but could not include several known or suspected carcinogens for HN cancers (e.g. strong acid mists, wood dust or formaldehyde). This may explain why the decrease in socioeconomic inequalities after adjustment for occupational exposures was more pronounced for lung than HN cancers and residual confounding may be larger for HN cancers.

In women, although smoking and alcohol drinking contributed to socioeconomic inequalities in respiratory cancer incidence, the situation is more complex. Our results suggested that the women with the highest occupational prestige had the highest tobacco consumption: when compared with women with a stable high occupational prestige trajectory, adjustment for smoking decreased the risk of lung cancer for the stable very high trajectory and did not change or even increased the risk in the other groups. This is consistent with the literature that shows that France has now reached the last stage of the smoking epidemic: tobacco consumption is now among the highest SES women only in the oldest age group, i.e. among women born before 1955, close to our population (mean age of 60.4 in controls and 57.5 in cases). [START_REF] Bricard | Educational inequalities in smoking over the life cycle: an analysis by cohort and gender[END_REF] Although residual confounding due to misreporting of alcohol and tobacco consumption is likely to occur in women as in men, it is less clear to assess how this would have impacted the results because of the lack of gradient between SES and smoking. We observed a negligible contribution of occupational exposures to socioeconomic inequalities in respiratory cancers incidence. This reflects the low prevalence of these exposures in female occupations, at least for the high levels of exposure.

Finally, other risk factors such as poor diet [START_REF] Lagiou | Diet and upper-aerodigestive tract cancer in Europe: the ARCAGE study[END_REF][START_REF] Skuladottir | Does insufficient adjustment for smoking explain the preventive effects of fruit and vegetables on lung cancer?[END_REF]) or physical inactivity [START_REF] Steindorf | Physical activity and lung cancer risk in the European Prospective Investigation into Cancer and Nutrition Cohort[END_REF]) may account for part of the remaining inequalities. [START_REF] Malon | Compliance with French nutrition and health program recommendations is strongly associated with socioeconomic characteristics in the general adult population[END_REF][START_REF] Menai | Walking and cycling for commuting, leisure and errands: relations with individual characteristics and leisure-time physical activity in a cross-sectional survey (the ACTI-Cites project)[END_REF] There is also an increasing body of literature suggesting that exposure to infections may account for part of the worst health in low SES groups, either through a higher and/or an earlier exposure during the lifecourse and/or a higher vulnerability. [START_REF] Dowd | Early origins of health disparities: burden of infection, health, and socioeconomic status in U.S. children[END_REF] Although it has been very little investigated, this is likely to be more important for HN (through human papillomavirus infection) than for lung cancer (D 'Souza et al. 2007 ;[START_REF] Rotnaglova | HPV involvement in tonsillar cancer: prognostic significance and clinically relevant markers[END_REF]) and this could explain part of the remaining inequalities in HN cancer risk. Factors associated with SES during childhood (including infections) may also explain part of the remaining inequalities (Kelly-Irving et al.

2013

), especially in groups with low occupational prestige at the beginning of their carrier, as the first occupation is more closely linked to childhood SES. This may in particular account for the differences observed between men in the stable high and low to high occupational prestige trajectories for HN cancers risk. Future studies are needed to investigate these issues.

We investigated the role of occupational prestige trajectories on respiratory cancers risk in men and women in France. Our results confirmed the existence of large socioeconomic inequalities both in men and women, but they also highlighted specific patterns that were not observed with other SES indicators. Our study therefore underlines the importance of using various measures of SES to fully understand the complex mechanisms at stake in socioeconomic inequalities in health.

Compliance with ethical standards

Fig1. :

 : Fig1.: Occupational prestige trajectories over the whole working life in men (upper panel) and women (lower panel). The ICARE case-control study,France, 2002France, -2005

Table 1 :

 1 Distribution of tobacco and alcohol consumption and occupational exposures by gender and 430 occupational prestige trajectories among controls, lung and head and neck cancers.The ICARE case- 431 control study, France, 2002-2005 432

		Occupational		Nb alcoholic	Light	Never	Pack-CSI*	Ever exposed to		Nb years as
		prestige trajectory		drink/day* drinkers** smokers years*		asbestos	silica	DME	housewife
			N	Mean	N (%)	N (%)	Mean Mean	N (%)	N (%)	N (%)	Mean
	CONTROLS
	Men	Low to very low	115	4.4	42 (36.5) 33 (28.7)	21.3	1.1	67 (58.3)	30 (26.1) 38 (33.0)	-
		Stable low	588	3.5	249 (42.4) 148 (25.2) 22.6	0.9	428 (72.8) 208 (35.4) 192 (32.7)	-
		Middle to low	382	3.2	159 (41.6) 99 (25.9)	22.8	1	272 (71.2)	99 (25.9) 100 (26.2)	-
		Low to middle	291	3.5	111 (38.1) 88 (30.2)	22.2	0.9	229 (78.7)	95 (32.7) 104 (35.7)	-
		Stable middle	492	2.9	247 (50.2) 124 (25.2) 21.8	0.9	293 (59.6) 111 (22.6) 151 (30.7)	-
		Low to high	272	2.6	129 (47.4) 76 (27.9)	17.9	0.8	141 (51.8)	32 (11.8) 68 (25.0)	-
		Stable high	464	2.4	234 (50.4) 136 (29.3) 18.9	0.9	100 (21.6)	32 (6.9) 50 (10.8)	-
		Stable very high	72	2.1	43 (59.7) 25 (34.7)	20.8	0.8	16 (22.2)	8 (11.1)	3 (4.2)	-
	Women Low to high	46	1.3	7 (15.2)	26 (56.5)	18.5	0.9	8 (17.4)	-	2 (4.4)	2.8
		Low to very low	134	0.9	38 (28.4) 104 (77.6) 19.8	1.1	36 (26.9)	-	10 (7.5)	5.1
		Low to middle	138	0.7	26 (18.8) 92 (66.7)	12.3	0.8	40 (29.0)	-	13 (9.4)	3.7
		Middle to very low	57	1.3	18 (31.6) 30 (52.6)	12.3	0.8	12 (21.1)	-	8 (14.0)	5.8
		Stable middle	97	1.1	26 (26.8) 62 (63.9)	11.2	0.7	26 (26.8)	-	10 (10.3)	2.5
		Stable middle+	120	1.1	24 (20.0) 81 (67.5)	13.6	0.9	14 (11.7)	-	7 (5.8)	2.4
		Stable high	120	1.0	19 (15.8) 76 (63.3)	17.4	1	8 (6.7)	-	4 (3.3)	0.6
		Stable very high	3	1.5	1 (33.3)	2 (66.7)	9.8	1.2	0 (0)	-	0 (0)	0.0
	LUNG CANCER
	Men	Low to very low	171	-	-	0(0)	-	1.7	119 (69.6)	56 (32.8) 51 (29.8)	-
		Stable low	701	-	-	14 (2.0)	-	1.7	578 (82.5) 347 (49.5) 261 (37.2)	-
		Middle to low	337	-	-	14 (4.2)	-	1.6	271 (80.4) 112 (33.2) 97 (28.8)	-
		Low to middle	180	-	-	5 (2.8)	-	1.6	150 (83.3)	80 (44.4) 66 (36.7)	-
		Stable middle	309	-	-	6 (1.9)	-	1.6	214 (69.3)	83 (26.9) 83 (26.9)	-
		Low to high	127	-	-	3(2.4)	-	1.6	65 (51.2)	23 (18.1) 28 (22.1)	-
		Stable high	164	-	-	4(2.4)	-	1.6	40 (24.4)	9 (5.5)	24 (14.6)	-
		Stable very high	30	-	-	2(6.7)	-	1.5	1 (3.3)	1(3.3)	4 (13.3)	-
	Women Low to high	39	-	-	14 (35.9)	-	1.6	5 (12.8)	-	6 (15.4)	1.9
		Low to very low	111	-	-	40 (36.0)	-	1.5	26 (23.4)	-	4 (3.6)	4.2
		Low to middle	96	-	-	21 (21.9)	-	1.6	33 (34.4)	-	12 (12.5)	2.8
		Middle to very low	46	-	-	11 (23.9)	-	1.5	8 (17.4)	-	7 (15.2)	4.2
		Stable middle	102	-	-	33 (32.4)	-	1.6	25 (24.5)	-	9 (8.8)	2.3
		Stable middle+	90	-	-	26 (28.9)	-	1.5	16 (17.8)	-	6 (6.7)	2.0
		Stable high	65	-	-	19 (29.2)	-	1.6	4 (6.2)	-	4 (6.2)	1.2
		Stable very high	9	-	-	0 (0)	-	1.6	0 (0)	-	0 (0)	0.2
	HEAD AND NECK CANCERS
	Men	Low to very low	207	11.3	17 (8.2)	6 (2.9)	39.9	-	152 (73.4)	-	-	-
		Stable low	700	8.4	98 (14.0)	23 (3.3)	40.2	-	568 (81.1)	-	-	-
		Middle to low	331	7.9	49 (14.8)	16 (4.8)	39.3	-	270 (81.6)	-	-	-
		Low to middle	146	7.4	21 (14.4)	11 (7.5)	40.8	-	114 (78.1)	-	-	-
		Stable middle	221	6.9	37 (16.7)	12 (5.4)	39.1	-	142 (64.3)	-	-	-
		Low to high	84	6.0	15 (17.9)	4 (4.8)	39.4	-	49 (58.3)	-	-	-
		Stable high	97	5.3	23 (23.7)	6 (6.2)	38.2	-	24 (24.7)	-	-	-
		Stable very high	7	4.9	0 (0)	0 (0)	46.6	-	1 (14.3)	-	-	-
	Women Low to high	15	2.3	4 (26.7)	8 (53.3)	24.8	-	5 (33.3)	-	-	4.9
		Low to very low	68	3.6	13 (19.1) 20 (29.4)	36.1	-	15 (22.1)	-	-	4.5
		Low to middle	61	3.7	7 (11.5)	10 (16.4)	33.2	-	11 (18.0)	-	-	4.0
		Middle to very low	28	3.6	5 (17.9)	6 (21.4)	27.8	-	10 (35.7)	-	-	6.4
		Stable middle	49	4.2	8 (16.3)	11 (22.5)	34.2	-	7 (14.3)	-	-	2.4

Table 2 :

 2 Odds ratios (OR) and 95% confidence intervals (CI) associated with occupational prestige trajectories for lung and head and neck cancers risk. Men (4695 men in the lung cancer analyses, 4469 men in the head and neck cancers analyses). The ICARE case-control study, France, 2002-2005 Model 1 further adjusted for smoking (lung cancer) or tobacco and alcohol consumption (HN cancer) 3: Model 2 further adjusted for occupational exposures (asbestos, silica and DME for lung cancer; asbestos for HN cancers)

	Occupational prestige	Lung cancer

Table 3 :

 3 Odds ratios (OR) and 95% confidence intervals (CI) associated with occupational prestige trajectories for lung and head and neck cancers risk.Women (1273 women in the lung cancer analyses, 1020 women in the head and neck cancers analyses). The ICARE case-control study,France, 2002France, -2005 Model with adjustment for years of inactivity (as a continuous variable)

	Lung cancer

62 (1.01-2.60) 1.62 (1.01-2.61)

					1.45 (0.86-2.45)	1.76 (0.93-3.32)	1.75 (0.93-3.30)
	Stable high	1	1	1	1	1	1
	Stable very high	5.17 (1.33-20.0)	3.48 (0.72-16.8)	3.48 (0.72-16.8)	7.

59 (1.68-34.3) 7.32 (1.23-43.5) 7.23 (1.22-43.3)

	Year of inactivity	0.99 (0.97-1.01)	0.98 (0.96-1.01)	0.98 (0.96-1.01)	1.

01 (0.99-1.03) 1.01 (0.98-1.03) 1.01 (0.98-1.03) 1

  : Model adjusted for age and residence area 2: Model 1 further adjusted for smoking (lung cancer) or tobacco and alcohol consumption (head and neck cancers) 3: Model 2 further adjusted for occupational exposures (asbestos and Diesel Motor Exhaust for lung cancer; asbestos for head and neck cancers)

(Danièle LuceThis work was supported by a grant from the French Agency for Food, Environmental and Occupational Health and Safety (ANSES) [grant number EST-2009/1/65]. The ICARE study was funded by French National Research Agency (ANR); French National Cancer Institute (INCA); French Agency for Food, Environmental and Occupational Health and Safety (ANSES); French Institute for Public Health Surveillance (InVS); Fondation pour la Recherche Médicale (FRM); Fondation de France; La Fondation ARC pour la Recherche sur le Cancer; Ministry of Labour (Direction Générale du Travail); and Ministry of Health (Direction Générale de la Santé).

Conflict of interest: The authors declare that they have no conflict of interest.

Informed consent: Informed consent was obtained from all participants included in the study.


Valentin Coirier
email: valentin.coirier@gmail.com

Alain Lescoat

Celine Chabanne

Maxime Fournet

Guillaume Coiffier

Stéphane Jouneau

Elisabeth Polard

Patrick Jego

Céline Chabanne

Patrick Jégo

Pulmonary arterial hypertension in four patients treated by leflunomide

Keywords:

teaching and research institutions in France or abroad, or from public or private research centers.

A c c e p t e d M a n u s c r i p t

Introduction

Pulmonary arterial hypertension (PAH) is a rare disorder. PAH diagnosis is based on right heart catheterisation (RHC) [START_REF] Galiè | ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertension[END_REF], showing a mean pulmonary arterial pressure (mPAP) above 25 mmHg, associated with pulmonary capillary wedge pressure (PCWP) under 15 mmHg, in favour of pre-capillary pulmonary hypertension (PH). To confirm PAH, other aetiologies of pre-capillary PH (groups III and IV of the PH classification [START_REF] Galiè | ESC/ERS Guidelines for the diagnosis and treatment of pulmonary hypertension[END_REF]) must be excluded: PH due to lung disease or hypoxia (mainly chronic obstructive pulmonary disease and interstitial lung disease (ILD)) and chronic thromboembolic PH. PAH is confirmed after exclusion of these differential diagnoses (normal ventilation/perfusion lung scan and normal high-resolution computed tomography), and the next step is to perform aetiological investigations to determine the proper aetiological diagnosis allowing a specific treatment. PH of group I, corresponds to PAH [Appendix A, Table S1; See the supplementary material associated with this article online] and includes idiopathic PAH, heritable PAH, drugs and toxins induced PAH, PAH associated with connective tissue diseases (CTD), human immunodeficiency virus (HIV) infection, portal hypertension and congenital heart diseases.

In the 1960s, an epidemic of PAH in European women taking appetite-suppressant drugs [START_REF] Abenhaim | Appetite-suppressant drugs and the risk of primary pulmonary hypertension[END_REF] led to an improvement of PAH diagnosis and additional drugs increasing the risk of PAH were identified. In 2013, Montani et al. [START_REF] Montani | Drug-induced pulmonary arterial hypertension: a recent outbreak[END_REF] published a review identifying anorexigen drugs (aminorex, fenfluramine and derivatives, benfluorex, amphetamines), dasatinib, interferon alpha and beta as risk factors of drug-induced PAH.

Leflunomide is a selective inhibitor of de novo pyrimidine synthesis [START_REF] Breedveld | Leflunomide: mode of action in the treatment of rheumatoid arthritis[END_REF], prescribed for rheumatoid arthritis (RA) and psoriatic arthritis (PA). We report four cases of PAH following treatment by leflunomide.

Case-reports

The four patients were aged from 51 to 71 years-old at the time of the diagnosis of PAH (Table I). One patient received leflunomide 10mg per day, the three others received 20mg per day. Delay between leflunomide initiation and first symptoms of PAH ranged from 7 to 120 months. Two patients received leflunomide for RA, one for PA. The fourth patient was The four patients initially consulted for a recent dyspnea. At diagnosis, the dyspnea was estimated from grade II to IV using New York Heart Association (NYHA) functional grading.

After clinical examination, a cardiac aetiology of the dyspnea was suspected leading to transthoracic echocardiographic (TTE) evaluation. TTE found an increased estimated systolic pulmonary arterial pressure for all of them. PH was then confirmed by RHC (Table I) for all patients (mPAP between 35 and 48 mmHg), with haemodynamic profiles of pre-capillary PH (PCWP between 5 and 14 mmHg). Pulmonary vascular resistances (PVR) were increased and cardiac output (CO) decreased in all patients.

All patients underwent classical investigations for pre-capillary PH: biological evaluation for auto-immune disease, HIV serology, abdominal ultrasound scan, ventilation/perfusion lung scan and lung high-resolution computed tomography (CT). For patients 2 and 4, lung CT showed an aspect of ILD that was already known before initiation of leflunomide. ILD did not evolve on the new CT scan in comparison with the CT scan prior to leflunomide initiation.

Therefore PAH could not be secondary to the evolution of ILD. Other investigations for these two patients were negative. All investigations for patients 1 and 3 were also negative. For each patient, a pharmacovigilance reporting (declarations numbers RS20141210, RS20150927, RS20150576, RS20172152) was performed at the Rennes University Hospital pharmacovigilance centre, that conducted accountability investigations.

Leflunomide treatment was immediately stopped for two patients, five months after diagnosis for another and three years after diagnosis for the last one. Patients 1, 3 and 4 underwent specific PAH treatment. Patient 2 did not receive any PAH treatment. As recommended in case of serious adverse event, a wash-out procedure using cholestyramine was performed in patients 1 and 2 (8g three times a day, during 11 days); physicians in charge of patients 3 and 4 did not prescribe cholestyramine. Treatment strategy was determined during a multidisciplinary concertation, according to the ESC/ERS guidelines and adapted to the severity of PAH for each patient.

Evolution was evaluated according to the functional and haemodynamic parameters (Table II). Improvement was observed at the first follow-up visit after discontinuation of the treatment (between two and four months). For all patients, clinical or haemodynamic evolution was favourable.

A c c e p t e d M a n u s c r i p t

Discussion

We report four cases of PAH following treatment by leflunomide. Evolution (clinical, echocardiographic and/or haemodynamic) was favourable for all patients after discontinuation of leflunomide (without specific PAH treatment, for one patient) or introduction of a specific treatment for PAH.

Confirming the link between PAH and drug intake remains a great challenge, because PAH is always a rare complication occurring only in a very small proportion of exposed patients. Furthermore, in our four cases, re-administration of leflunomide was not possible, because of the serious adverse effect reported. We concluded to the diagnosis of PAH because precapillary PH was confirmed by RHC for all of them and there was no evidence for a PH group III aetiology: complementary explorations found neither worsening (patients 2 and 4) of an already known respiratory disease nor any argument for chronic thromboembolic disease. We then concluded to the diagnosis of drug-induced PAH after careful elimination of other aetiologies: before initiation of leflunomide, no patient had previous treatment at risk of druginduced PAH. No HIV infection was found, no cirrhotic or congenital heart disease was diagnosed. Heritable mutations were not investigated but a careful anamnesis ruled out any familial history of PAH. Imputability assessment methods for adverse drug reactions established the level of causality as possible (Naranjo [START_REF] Naranjo | A method for estimating the probability of adverse drug reactions[END_REF] and OMS algorithms) or plausible (French method). Haemodynamic improvement after treatment discontinuation, without introduction of PAH treatment in patient 2, is a strong evidence in favour of leflunomideinduced PAH. In 2012 Alvarez et al. [START_REF] Alvarez | Leflunomide-Induced Pulmonary Arterial Hypertension in a Young Woman with Rheumatoid Arthritis: A Case Report[END_REF], reported one case of PAH in a 28-year-old patient treated by leflunomide for RA. RHC was performed to confirm diagnosis, aetiological explorations were negative, evolution was favourable after leflunomide discontinuation and introduction of a specific PAH treatment (sildenafil, bosentan and acenocoumarol). Another case was published in 2004 by Martinez-Taboada et al. [START_REF] Martinez-Taboada | Pulmonary hypertension in a patient with rheumatoid arthritis treated with leflunomide[END_REF], reporting a 70-year-old patient also treated by leflunomide for RA. Diagnosis was not confirmed by haemodynamic explorations, but echocardiographic evolution was also favourable after discontinuation of leflunomide.

The conclusions of the investigations conducted by our pharmacovigilance centre were communicated to the European Medicines Agency, leading to the addition of "pulmonary hypertension" in the paragraph "special warnings and precautions for use" and "undesirable effects" of the package leaflet of leflunomide. The report of other cases will strengthen this hypothesis of leflunomide associated PAH.

A c c e p t e d M a n u s c r i p t

If the role of leflunomide in the development of PAH were confirmed, the question of its involvement in the pathophysiology of a specific pulmonary vascular disease would arise.

For other PAH inducing drugs, pathophysiology hypotheses have been suggested: inhibition of serotonin reuptake for fenfluramine and derivatives, ability to inhibit tyrosine kinase activity for dasatinib. Dasatinib might specifically inhibit a sub-family of kinases, named Src kinase, which would explain the specific effect of dasatinib and the absence of a class effect [START_REF] Montani | Pulmonary Arterial Hypertension in Patients Treated by Dasatinib[END_REF]. This hypothesis is supported by several studies demonstrating the role of Src tyrosine kinases in maintaining the integrity of the pulmonary vascular bed [START_REF] Pullamsetti | Role of Src Tyrosine Kinases in Experimental Pulmonary Hypertension[END_REF]. In 2013, Nagaraj et al. [START_REF] Nagaraj | Src tyrosine kinase is crucial for potassium channel function in human pulmonary arteries[END_REF] reported the co-localization of Src and TASK-1 (potassium channel) in the plasma membrane of human pulmonary arterial smooth muscle cells (hPASMCs). TASK-1 plays a role in the resting membrane potential of hPASMCs, therefore participating in the regulation of the pulmonary artery vascular tone. Nagarajet al. demonstrated that specific inhibition of Src results in the inhibition of TASK-1 (and others potassium channels), plasma membrane depolarization and hPASMCs contraction. The author concluded that Src tyrosine kinases control potassium channels (including TASK-1), which explains why their inhibition can lead to pulmonary vasoconstriction. Similarly, in vitro studies have also reported an inhibiting effect of leflunomide on this family of Src tyrosine kinases. These elements remain hypothetic and both the involvement and precise role of Src-kinases in the pathogenesis of leflunomideassociated PAH are still to be determined.

Leflunomide is a prodrug rapidly converted in the gastrointestinal tract and plasma in its metabolite [START_REF] Breedveld | Leflunomide: mode of action in the treatment of rheumatoid arthritis[END_REF], A77 1726. This metabolite inhibits de novo synthesis of pyrimidine ribonucleotides, regulating lymphocytes proliferation with an immunomodulatory effect. A77 1726 also named teriflunomide, has been recently authorised in the treatment of multiple sclerosis (relapsing-remitting form). Some of the classical adverse effects associated with leflunomide are also described with teriflunomide: systemic hypertension, hepatic cytolysis, cytopenia, peripheral neuropathy and alopecia. If the imputability of leflunomide in the development of PAH were confirmed, prescribers of teriflunomide should be attentive to the occurrence of PAH under treatment. Even if the accurate quantification of leflunomide prescriptions seems difficult to evaluate, the use of teriflunomide will significantly increase the number of patients exposed to A77 1726. For example, the French Authority of Health estimated in 2012 that 50 000 patients could benefit from a prescription of teriflunomide, in the treatment of multiple sclerosis [11]. Further observational studies and pharmacovigilance investigations are therefore needed to assess the risk of PAH in patients treated by teriflunomide in the future.

A

  c c e p t e d M a n u s c r i p t treated by leflunomide for an undetermined CTD (insufficient diagnostic criteria for systemic sclerosis or systemic lupus erythematosus) with disabling arthralgia, a questionable indication for leflunomide.

A c c e p t e d M a n u s c r i p t

Table I :

 I Characteristics of patients at the moment of PH diagnosis delay between initiation of leflunomide et diagnosis of pulmonary arterial hypertension.

		Age at	Sex	Disease	Duration of	Dose of	NYHA FC	mPAP	PCWP	CO	PVR
		diagnosis	(M/F)		treatment*	leflunomide,	(I-IV)	(mmHg)	(mmHg)	(L/min)	(WU)
		(years)			(months)	at diagnosis
						(mg/d)
	1	51	F	PA	48	20	IV	48	14	4,47	7,6
	2	56	H	RA	7	20	II	38	9	4,5	6,4
	3	71	F	RA	120	10	IV	43	5	1,4	14,6
	4	59	M	uCTD	46	20	IV	35	8	3,77	7,1
	NYHA FC: New-York Hearth Association functional class; mPAP: mean pulmonary arterial pressure; PCW: pulmonary capillary wedge
	pressure; CO: cardiac output; PVR: pulmonary vascular resistance in Wood Units; PA: psoriatic arthritis; RA: rheumatoid arthritis; uCTD:
	undetermined connective tissue disease (not systemic sclerosis, not systemic erythematous lupus).

*

Table II :

 II Management of PAH and outcomes (last PAH evaluation) : pulmonary arterial hypertension; NYHA FC: New-York Hearth Association functional class; mPA: mean pulmonary arterial pressure; PCW: pulmonary capillary wedge pressure; CO: cardiac output; PVR: pulmonary vascular resistance in Wood Units. * last haemodynamic evaluation of the patient before article submission.

		PAH	PAH treatment	NYHA	mPAP	PCWP	CO	PVR
		treatment	at last	FC	(mmHg)	(mmHg)	(L/min)	(WU)
			evaluation*	(I-IV)
	Patient 1	epoprostenol,	ambrisentan,	II	33	8	7,2	3,47
		bosentan,	sildenafil
		treprostinil,
		ambrisentan,
		sildenafil
	Patient 2	no treatment	no treatment	II	31	11	6,4	3,1
	Patient 3	sildenafil,	sildenafil,	I	43	10	5	7
		bosentan	bosentan
	Patient 4	sildenafil	sildenafil	I	32	12	9,6	2,08

PAH

A c c e p t e d M a n u s c r i p t

Disclosure of interest

The authors report no conflicts of interest related to the article.

Appendix A. Supplementary data

Supplementary data (Table S1) associated with this article can be found in the online version at … A c c e p t e d M a n u s c r i p t


Isabelle Kermen
email: isabelle.kermen@univ-artois.fr

Presentation proposed by

This paper examines a teacher's activity to reconstruct her choices and a part of her professional knowledge. Three dimensions of the teacher's activity are considered in this study: i) a cognitive dimension concerning the tasks given to the students and the chemistry content involved, ii) a mediative dimension regarding the unfolding teaching session, iii) a personal dimension including the teacher's knowledge and beliefs about chemistry and chemistry teaching. The teacher's activity in the classroom results from choices made during the design and the implementation of the lesson plan which depend among other on the teacher's knowledge and on the results of his/her actions. We assume that the comparison of two successive sessions of two groups of a same form provides indicators, modifications and unchanged features of the unfolding sessions, to infer pedagogical content knowledge (PCK) and pedagogical knowledge (PK). Our purpose is to determine them and to characterise the conditions and also PK that contribute to the development of PCK.

The data are two video-recorded successive sessions of a 12 th grade form on the change criterion of chemical systems and of the teacher's interviews which took place just before and after the sessions. Several analyses follow: an analysis of the lesson plan to determine the tasks, of the unfolding teaching sessions to reveal the pedagogical strategies and the students' scaffolding, and of the teacher's comments to discover articulated knowledge. This first set of analyses provides tacit and expressed PCK and PK. The second analysis stage compares the two unfolding sessions and highlights the modifications that occurred, which are considered to be revealing the development of new PCK. A fine grain analysis of the chemistry content involved and of the classroom interactions allows to identify new PCK which also appear to be a consequence of PK involved.

Extended summary (1250 words exactly!)

This case study addresses a teacher's activity working on the change criterion of chemical systems in a 12 th grade form. The purpose is to reconstruct some pedagogical content knowledge (PCK) and pedagogical knowledge (PK) from the analysis of the teacher's actions and choices. The teacher's activity in the classroom relies upon the determinants of the teaching learning situation (students, content, syllabus, school…) and upon the beliefs and knowledge of the teacher. According to the framework of the double didactic and ergonomic approach [START_REF] Robert | Le système complexe et cohérent des pratiques des enseignants de mathématiques: Une double approche[END_REF][START_REF] Vandebrouck | Mathematics Classrooms: Students' Activities and Teachers' Practices[END_REF] five dimensions structure the analysis of the activity.

The cognitive dimension concerns the design of the tasks given to the students, the lesson plan and the chemical content involved; the mediative dimension concerns the implementation of the lesson plan and especially the choices of classroom organisation and of students' scaffolding. Three other dimensions include determinants that influence the teaching learning situation. The institutional dimension examines how the teacher takes the syllabus, the resources, and the institutional constraints into account. The social dimension is about the relationships with the people working in the school and the way the teacher takes the students' social background into account. The personal dimension includes the teacher's conceptions, knowledge and beliefs about chemistry, chemistry teaching. Inferring professional knowledge from the teacher's actions means that the focus is on the personal dimension, particularly on PCK and PK, and on the cognitive and mediative dimensions of the teacher's activity.

Drawing on the Morine-Dershimer and Kent's model (1999) for PK, [START_REF] Corrigan | Chemistry teacher education to promote understanding of learning through effective reflective practice[END_REF] highlights the role of three components, instructional models and strategies (PK-strategy), classroom management and organisation (PK-management), and classroom discourse and communication (PK-discourse). The PCK model [START_REF] Magnusson | Nature, sources and development of pedagogical content knowledge for science teaching[END_REF] includes five components among which, knowledge of students' understanding of the chemistry topic under consideration (PCK-student) and knowledge of instructional strategies (PCK-strategy) that enable the students to overcome their difficulties. According to literature reviews, PCKstrategy and PCK-student on the one hand [START_REF] Van Driel | Developing science teachers' pedagogical content knowledge[END_REF] and PK-strategy and PKmanagement on the other hand [START_REF] König | General Pedagogical Knowledge of Future Middle School Teachers: On the Complex Ecology of Teacher Education in the United States, Germany, and Taiwan[END_REF] are the core components of PCK and PK respectively. The teacher's activity in the classroom results from decisions taken during the planning and the implementation [START_REF] Wanlin | La pensée des enseignants pendant l'interaction en classe. Une revue de la littérature anglophone[END_REF]. They depend among other on the teacher's knowledge and on the results of his/her actions. The teacher's knowledge mobilized during actions is often tacit [START_REF] Van Driel | Professional development and reform in science education: The role of teachers' practical knowledge[END_REF]. Thus the analysis of actions leads to infer knowledge that is not articulated by the teacher. Nevertheless, an analysis of the teacher's comments on his/her actions provides expressed knowledge.

A chemistry teacher was filmed during two successive teaching sessions on the change criterion of chemical systems with the two groups of a 12 th grade form in the same afternoon. She enacted a new lesson plan for the first time. The teacher's choices are analysed to determine the knowledge that supports the decisions. The comparison of the two successive sessions provides indicators, such as modifications of the unfolding sessions, which are assumed to be adaptations of actions and reveal new knowledge. The purpose is to determine PCK and PK inferred from the teacher's choices analysis, and the conditions and PK that contribute to the development of PCK.

Methodology

The teacher (Dora) was briefly interviewed before and after the teaching sessions and was told to comment on her classroom videos some weeks later. She chose the second session.

A first analysis took place in three steps: i) the analysis of the lesson plan determined the tasks given to the students which informed about their nature and organisation; ii) the session transcript was split in episodes, each episode is delimited by the completion of a task, which revealed the work organisation enabling to determine the pedagogical strategies involved, and the interactions between the teacher and the students; iii) some comments made in the interviews led to infer knowledge and appreciate the reflexive ability of the teacher. The teacher's knowledge was actually inferred in each type of analysis. Then, the comparison of the two unfolding sessions revealed some modifications the reasons of which were examined in Dora's actions and comments and in some students' actions.

Results

In both sessions the students had to predict what could happen in the mixtures (two acids and their conjugated bases), to write a chemical equation, to express the chemical species concentrations in the mixtures etc… Dora changed the tasks organisation from session 1 to session 2. She removed two tasks, modified the order and duration of others. See table 1.

In both sessions Dora adopted the same working modes: teacher's talks, collective dialogues, hands-on activities performed by students-pairs and students' individual reflection. Dora held detailed discussions to grasp the students' conceptual difficulties and let them express their arguments. Dora commented on the students' understanding, on the unfolding sessions and gave some reasons for the changes she made. See table 2. Discussion Dora's pedagogical strategy is student-centred and fruitful because the students expressed their ideas which, in turn, enabled Dora to make the problem solving progress and involve them in the process. Each session analyses provide tacit or expressed PCK and PK (see examples 1, 2 in table 2). The comparison of the two unfolding sessions shows that Dora's pedagogical strategy is stable (tacit PK), she used the same working modes but adapted some questions and some tasks orders (see examples 3, 4, 5 in table 2). These modifications result from reflection during action [START_REF] Park | Revisiting the Conceptualisation of Pedagogical Content Knowledge (PCK): PCK as a Conceptual Tool to Understand Teachers as Professionals[END_REF], and aim to avoid students misunderstandings and to provide a more direct way to the problem solving. The analysis of the modifications and of the associated comments supports the development of new PCK. It was made possible by the enacted student-centred strategy based on existing tacit PK and by the teacher's reflexive ability. 1) prompted the students to explain why they think so 2) claimed that reason is an hypothesis that will be tested during the session 3) reminded that hypothesis when she recapitulated the problem to the students I expect the students will say nothing happen in mixture 1 because all amounts are equal contrary to mixture 2 no comment no comment or not watched students predict a chemical change comparing the amount of species (expressed PCK-student) taking that idea into account is a way to involve the students solving the problem (tacit PCK-strategy) holding a detailed discussion with a student enables the expression of his/her reasoning (tacit PK-strategy) example 2 group2 : Chloé wrote four species on the left of the chemical equation and was wondering about the species she could write on the right.

individual reflection 1) asked for an explanation 2) tried to make the student change her mind leading a detailed discussion with her about the reactivity of the species student's reasoning not anticipated she wrote all species on the left of the chemical equation and did not know what to write on the right.I didn't expect that but it is logical they think so.

this mistake means the student doesn't imagine that some species will be consumed and some others will be produced the students struggle to write a chemical equation when confronted to a system comprising all species about to react and to be produced (expressed new PCK-student) holding a detailed discussion with a student enables the expression of his/her reasoning (tacit PK-strategy)

  Pierre wrote a chemical equation which does not respect the composition of the initial state of the mixture (two acids and two bases), but interprets what happened in the acid solution individual reflection 1) asked for an explanation 2) corrected the error telling him he should take the predominant species of each solution into account 3) did not ask for the detailed composition of each solution with group 2, as she did with group 1 in episode 1 student's reasoning not anticipated he forgot to take the relevant species in the initial state of the mixture in the chemical equation video not watched it is difficult for a student to take only the majority solute of an acid or base solution into account to predict what could happen in a mixture (expressed PCK-student) it is no useful to remind the detailed composition of each acide or base solution, since the students are asked to predict what could happen in a mixture of four solutions (tacit new PCK-strategy) holding a detailed discussion with a student enables the expression of his/her reasoning (tacit PK-strategy) chemical change before writing a chemical equation confused the students (expressed new PCKstudent) writing the chemical equation should be done before looking for any chemical change (expressed new PCKreaction quotient before the concentrations ratio does not enable the students to determine the direction of chemical change (expressed new PCK-student) the initial reaction quotient calculus should be made after the concentrations ratio calculus (expressed new PCKstrategy)

twice underlined tasks are not proposed to group 2 table 1: episodes and tasks of the unfolding sessions teacher comments during interviews students actions working mode teacher actions before the unfolding session in the following up interview faced to the classroom video reconstructed PCK and PK

	episode	duration objective of the task	working mode		episode duration objective of the task	working mode
		1	11min introducing the solutions	teacher's talk and collective dialogue		1	6min30	introducing the mixtures to be made	teacher's talk
		2 group 1: Vincent stated that a 4min introducing the mixtures to be made chemical change will occur in	teacher's talk		2	7min writing a chemical equation	students' reflection
	example 1	3 prediction based on the same 6min30 Looking for a possible chemical change mixture 2 because the amount of the acids is collective different group2: Lucile made the same dialogue	teacher's talk and collective dialogue		3	9min	reflecting on how to detect a chemical change	teacher's talk and collective dialogue
		4 reason	7min	writing a chemical equation	students' reflection and collective dialogue		4	8min30	expressing concentrations	the	initial	students' reflection
	group 1	5 6 7	14min making the mixtures 13min reflecting on how to detect a chemical change 7min expressing the equilibrium constant	hands-on experiments in pairs teacher's talk and collective dialogue students' reflection and student correcting at the blackboard	group 2	5 6 7	14min making the mixtures 14min Looking for a possible chemical change 11min30 how to use the pH value to determine the concentrations ratio in the final state	hands-on experiments in pairs teacher's talk and collective dialogue teacher's talk and collective dialogue
		8	11min expressing the initial concentrations	collective dialogue and students' reflection		8	5min measuring the pH	hands-on experiments in pairs
		9	8min30	expressing the initial reaction quotient	students' reflection and collective dialogue		9	17min30	calculating the concentrations ratio in the final state of the system	students' reflection and teacher's talks
		10	8min30	how to use the pH value to determine the concentrations ratio in the final state	teacher's talk and students' reflection		10	4min	expressing the initial reaction quotient	teacher's talk and students' reflection
		11	5min	measuring the pH	hands-on experiments in pairs
		12	8min30	calculating the concentrations ratio in the final state of the system	students' reflection

table 2 : some examples of reconstructed PCK and PK

 2


V Démery

D S Dean

T C Hammant

R R Horgan

R Podgornik

Overscreening in a 1D lattice Coulomb gas model of ionic liquids

Keywords: 82, 45, Gj -Electrolytes 05, 20, Jj -Statistical mechanics of classical fluids 88, 80, fh -Supercapacitors

Overscreening in the charge distribution of ionic liquids at electrified interfaces is shown to proceed from purely electrostatic and steric interactions in an exactly soluble onedimensional lattice Coulomb gas model. Being not a mean-field effect, our results suggest that even in higher-dimensional systems the overscreening could be accounted for by a more accurate treatment of the basic lattice Coulomb gas model, that goes beyond the mean-field level of approximation, without any additional interactions.

Room temperature ionic liquids (RTILs) are Coulomb fluids with large, asymmetric ions, and are used as electrolytes in fuel and solar cells, batteries and supercapacitors, to name but a few important applications [1]. As pointed out in several seminal contributions by Kornyshev [2], the size of the ionic species leads in general to crowding and lattice saturation, thus engendering a fundamentally different behavior of ionic liquids at charged interfaces as compared to aqueous electrolytes. In some particular cases several aspects of this behavior can be captured on a mean-field level by the lattice Coulomb gas (LCG) model [2,3].

Steric effects stipulate that the capacitance of ionic liquids decays at large applied voltages while at the point of zero charge (PZC) it can exhibit a maximum as well as a minimum (and is thus a non-monotonic function of applied voltage) depending on the lattice packing fraction [4], whereas for dilute electrolytes the capacitance at PZC is always a minimum [2]. X-ray reflectivity [5], SFA [6] and AFM [7] studies at electrified interfaces reveal an alternating charge distribution starting with an overscreening cationic layer, at the negatively charged substrate, which decays roughly exponentially into the bulk liquid with a periodicity comparable with the size of ionic species [8]. This observed charge layering is expected to be a generic feature of RTILs at charged interfaces resulting from an interplay between steric effects and strong electrostatic coupling. While the dependence of the differential capacity can be predicted within the meanfield solution of the LCG model [4], the overscreening and alternate charge layering at an electrified interface cannot.

In order to explain overcharging and charge oscillations, Bazant et al. [9] proposed a phenomenological theory based on a Landau-Ginzburg-like functional containing the standard LCG free energy [10] but with an additional higher-order potential-gradient term, similar to what is found in Cahn-Hilliard models, and then solving it on a mean-field level. However, this higher-order gradient term can also be seen [11] as stemming from a decomposition of the Coulomb interaction into a long-distance mean-field-like component and a non-mean-field strongcoupling component [12]. This alternative interpretation motivates a more detailed non-mean-field analysis of the original Kornyshev LCG model in order to go beyond the limitations of the mean-field approximation. We thus propose an exact analysis, albeit in one dimension, that demonstrates the full physical phenomenology of the LCG model, and in particular shows that overscreening emerges naturally from this model without the introduction of any new physical interactions.

We solve exactly the statistical mechanics of a onedimensional LCG in a standard capacitor configuration, with a method that generalizes other treatments of the point-like, or continuous, one-dimensional Coulomb gas models extensively used in the study of electrolytes [13]. We consider a system where charges q (cations) or -q (anions) are located on a line at lattice points with lattice spacing a and a total size of M points. The Hamiltonian for one-dimensional Coulomb interactions (corresponding to sheets of charge in 3D) is

βH = - γ 4 M -1 i,j=0 |i -j|S i S j (1)
where γ = βq 2 a 0 is the ratio of the electrostatic over thermal energy, or equivalently of the lattice spacing over the (1D) Bjerrum length B = βq 2 / 0 . Here S i is a classical spin variable taking the value S i = 1 if there is a cation at lattice site i, S i = -1, if there is an anion, and S i = 0 if the site is unoccupied. We will impose overall electroneutrality on the system, stipulating that i S i = 0. The grand canonical partition function can then be written as

Ξ = Tr Si µ M -1 i=0 |Si| +π -π exp βH[S i ] + iψ M -1 i=0 S i dψ 2π , (2)
where µ is the fugacity of both anions and cations, assuming for simplicity that the ionic liquid is symmetric. Carrying out a Hubbard-Stratonovich transformation, the grand canonical partition function can be expressed as a path integral over a field φ j on the lattice, while the integral over ψ corresponds to the integral over φ 0 , but runs over an interval of length 2π. The partition function then assumes the form

Ξ = M -1 j=0 dφ j √ 2πγ exp(-S[φ]) , (3)
where

S[φ] = M -2 j=0 (φ j+1 -φ j ) 2 2γ - M -1 j=0 log(1 + 2µ cos(φ j )). ( 4
)
In the case where there are external charges on the boundaries of the system, +qQ on the site -1 and -qQ on the site M , i.e. in a capacitor configuration, we need to add iQ(φ -1 -φ M ) to the action (4). The field φ can be identified with the fluctuating electrostatic potential via the relation V = -iφ/βq. One can show that the saddle-point equation for the above functional integral, δS δφj | φMF = 0, reduces to the mean-field equations of Kornyshev [2] and Borukhov et al. [10], if one takes the continuous limit (a → 0 with the maximal charge density q/a kept constant).

Writing y i = φ i and defining

p 1/2 (y, y ) = 1 √ πγ exp - (y -y ) 2 γ (5)
we introduce the symmetric operator

K(y, y ) = p 1/2 (y, z)(1 + 2µ cos(z))p 1/2 (z, y ) dz, ( 6
)
whose action is defined on a function f as Kf (y) = ∞ -∞ dy K(y, y )f (y ). This allows us to write the grand potential Ω Q at fixed external charges ±Q as (7) which we can now write as

exp(-βΩ Q ) = π -π dx e iQx p 1/2 K M p 1/2 e -iQx ,
exp(-βΩ Q ) = ψ Q |K M |ψ Q . ( 8
)
by defining ψ Q (y) = p 1/2 exp(-iQy) and writing operator matrix elements in ket notation as

f |D|g = π -π dx f * (x)Dg(x), (9)
for functions f and g and an operator D, and where f * denotes the complex conjugate of f . If instead of fixing the charge at the boundaries one keeps fixed the potential difference between them, ∆V = ∆ν/βq, it is easy to show that exp(-βΩ ∆ν ) = dσ exp(-∆νσ -βΩ σ ), (10) where Ω ∆ν is now the grand potential at imposed external potential difference. It follows that the average charge and differential capacity both as a function of the imposed potential difference are given by

Q ∆ν = - ∂(βΩ ∆ν ) ∂∆ν and c ∆ν = ∂ Q ∆ν ∂∆ν . (11)
To obtain the charge density we need to know the average charge number S i on site i. Therefore, we just need to replace 1 + 2µ cos(y i ) with i 2µ sin(y i ) in eq. ( 6), via a new operator

L(y, y ) = i ∞ -∞ p 1/2 (y, z)2µ sin(z)p 1/2 (z, y ) dz. (12)
Putting charges Q and -Q on the left and right boundaries, the mean charge density on site i is then

S i = ψ Q |K i LK M -i-1 |ψ Q ψ Q |K M |ψ Q . ( 13
)
In order to compute the thermodynamic quantities derived here, we need to evaluate the indicated matrix elements numerically. The domain of definition of the operators K and L depends on the choice of the surface charge Q. We define the Q-dependent class of functions where the set Z -Q is the set i -Q, where i is integer. Such functions are stable under the action of K and the action of K is given by

f (x) = k∈Z-Q fk exp(ikx), (14)
Kf k = e -γk 2 /4 e -γk 2 /4 fk +µ e -γ(k+1) 2 /4 fk+1 + e -γ(k-1) 2 /4 fk-1 . ( 15
)
The action of the operator K and L, can thus be carried out numerically in this Fourier representation. Numerical computations are performed by truncating the Fourier components at a maximum wave vector k max . This approximation is valid if γk 2 max 1 which means that in the cases studied here we can take k max = 25.

Numerically one can compute i) the grand potential of the system and the disjoining pressure giving the effective interaction between the two bounding layers; ii) the differential capacitance as a function of the voltage difference between the boundaries; and iii) the dependence of the charge density on the lattice position.

First, we look at the grand potential Ω as a function of the size of the system M for given charges ±Q on the boundaries. The discrete pressure on the boundaries is P = Ω M -Ω M +1 and tends to the bulk pressure P b when M is large. The actual force acting on the boundaries of the system is given by the disjoining pressure P d = P -P b that follows from the free enthalpy G M = Ω M + MP b , which is plotted in fig. 1. at high density and for different values of Q. The mean-field results are also shown for comparison.

We observe two salient features of the disjoining pressure: i) it is attractive when the system size is small and goes to zero for orders of magnitude M > 2Q ii) it exhibits oscillations of positive/negative pressure when M is even/odd. When the size of the system is large, the boundary charges are completely screened by the ions, and the plates only feel the bulk pressure; when the boundary layers are close to each other, not enough space is available for ions to screen the boundary charges and they thus attract each other because of their opposite charge. Having an even number of sites obviously stabilizes the system compared to an odd number; however, this effect vanishes as the size increases. This behavior is not seen within the mean-field approximation and is due to the fact that an odd number of sites cannot all be filled due to the electroneutrality condition, and this induces a high energy cost when µ is large. When the system becomes large this effect is asymptotically negligible, and it does not show up at lower densities. The mean-field result does not show these oscillations, but the general trend agrees with the exact result as well as with the continuous model meanfield results [14]. Another difference that is not shown here is that the bulk pressure is lower in the exact result than in the mean-field result.

The bulk pressure too has some subtle properties. It is given by P b = ln(λ 0 ), where λ 0 is the highest eigenvalue of K. But the operator K acts on the set of functions ( 14), which depends on the non-integer part of Q, θ = Q -Q ∈ [0, 1). Thus, we may expect that the bulk pressure depends on θ. This is indeed the case, but this dependence is very small: ∆P b /P b ∼ 10 -3 . This dependence corresponds to the so-called θ-vacuum introduced in ref. [15] for a standard Coulomb gas.

We next analyze the differential capacitance as a function of the boundary voltage difference for M = 100 sites and γ = 1 at high density (µ = 10) in fig. 2 and low density (µ = 0.1) in fig. 3. Two phenomena emerge in the behavior of capacitance: i) the capacitance has a dip at PZC; ii) the capacitance exhibits oscillations, distinctly visible at low densities. The PZC dip appears at low µ and confirms the continuum mean-field results of Kornyshev [2]. The oscillations stem from the θ-dependence of the bulk pressure inducing an extensive θ-dependence of the grand potential, which then exhibits minima at θ * corresponding to boundary charges Q ∈ Z + θ * . When the imposed voltage varies, the average charge exhibits plateaus at these selected charges, and the jumps between plateaus induce the peaks in the capacitance. These peaks become weaker as the system gets smaller or as the temperature increases.

The mean-field capacitance exhibits exactly the same trends but without oscillations, which is consistent with the absence of plateaus in the average charge. Again our mean-field results coincide with those of ref. [2].

Next we analyze the charge density profile in the vicinity of one of the boundaries (left); the same profile with opposite charge is obviously found close to the other boundary. First we note that for small packing fractions (µ = 1) the charge density shows a monotonic variation as a function of the separation from the boundary, fig. 4, and agrees with the mean-field result [10]. As we increase the packing fraction (µ > 1, fig. 5) the overscreening effect starts to dominate the behavior of the charge density and clear charge layering emerges: a counterion layer is followed by a coion layer with their thicknesses equal to the lattice unit. This corresponds closely to the experimentally observed situation [5] and approximately to the results of the model of Bazant et al. [9] if the packing fraction is not too large.

The charge distribution exhibits the following phenomenology: i) the amplitude of the oscillations varies continuously with the boundary charge Q, being maximal for half-integer values and zero for integer charges, due to the fact that in 1D one can have perfect screening only for integer values of Q; ii) the overcharging oscillations are damped with a characteristic length ξ, with ξ ∼ µ. The characteristic lengthscale of the overscreening oscillations can be obtained from the two highest eigenvalues of the transfer matrix K, λ 0 and λ 1 , and the definition of the correlation length ξ = (ln | λ0 λ1 |) -1 . Analytic computations of these eigenvalues for k max = 1 and Q = 0, and for k max = 0.5 and Q = 0.5 indeed give ξ ∼ µ.

When γ is small the mean-field approximation gives an accurate account of the capacitance and density profile in the system as shown in fig. 6. From this figure it is clear that the mean-field approximation works best for large applied voltages, which is also physically reasonable as the mean-field density profile imposed by the external potential is larger and thus relatively more important than any fluctuations.

Since the mean-field results show no overscreening, it must be a specific feature of the exact result for the same LCG model. We thus conclude that in order to describe the overscreening phenomena in ionic liquids one needs to go beyond the mean-field level of approximation. There appears to be no need to modify the original LCG Hamiltonian but it is essential to retain its discretized lattice form as opposed to its continuum limit. Based on our results, valid in 1D, we conclude that an approximation akin to the strong-coupling limit, as defined for ordinary Coulomb fluids [START_REF] Naji | Exotic Electrostatics: Unusual Features of Electrostatic Interactions between Macroions[END_REF], could be pertinent. However, deriving such an approximation systematically for a lattice Coulomb gas, where there are multiple length scales, is an open problem. * * * DSD acknowledges support from the Institut Universitaire de France. RP acknowledges support of The Leverhulme Trust and illuminating discussions with S. Perkin, D. Harries and U. Raviv.

Fig. 1 :

 1 Fig. 1: (Colour on-line) Dimensionless free enthalpy βGM as a function of the system size M , for the fugacity µ = 100: solid line: exact, Q = 5; dashed line: mean field, Q = 5; dash-dotted line: exact, Q = 0; dotted line: mean field, Q = 0.

Fig. 2 :

 2 Fig. 2: (Colour on-line) Capacitance as a function of the voltage drop for µ = 10 and γ = 1: exact result (solid line) and meanfield result (dashed line).

Fig. 3 :

 3 Fig. 3: (Colour on-line) Capacitance as a function of the voltage drop for µ = 0.1 and γ = 1: exact result (solid line) and meanfield result (dashed line). For smaller γ the non-monotonicity gradually disappears and the exact solution approaches the mean-field result of Kornyshev [2].

Fig. 4 :

 4 Fig. 4: (Colour on-line) Mean charge density close to the left electrode (located at x = -1) as a function of the position for Q = 0.5, γ = 1 and µ = 1: exact result (solid line) and meanfield result (dashed line).

Fig. 5 :

 5 Fig. 5: (Colour on-line) Exact result for the mean charge density close to the left electrode (located at x = -1) as a function of the position for Q = 0.5, for γ = 1 and different values of the fugacity.

Fig. 6 :

 6 Fig. 6: (Colour on-line) Capacitance as a function of the voltage drop for µ = 1 and γ = 0.1: exact result (solid line) and meanfield result (dashed line). Inset: charge density as a function of the position close to the left electrode, for Q = 5.