Bernard Dinh

Emmanuel Ma Mung

French migratory policy and immigrant entrepreneurship

The objective of this paper is to focus on the inequalities facing immigrants in access to the labour market and the impact of these on immigrant entrepreneurship. Unlike in other areas of legislation regarding foreigners, there has been a tendency to increase legal discrimination for over a century. Whereas European states have become the destination countries of immigrants mainly since 1945, France has been a receiving country for much longer. It was a destination for neighbouring Europeans as well as for people from other continents for a long time, with systematic evidence since the second half of the nineteenth century (381,000 resident foreigners in 1851, one million in 1881). Most of the discriminatory measures of the 1930s are still in force today. However, a class of small entrepreneurs of foreign origin has asserted itself in the receiving society during the past three decades, partly compensating for the continuous decrease in the number of French native entrepreneurs.

Introduction

Among the inequalities of rights between nationals and foreigners 3 , the most well-known and the most accepted are those relating to rights of free movement and residence, and to public rights. However, other less-studied inequalities exist in the sphere of economic and social rights, particularly those concerning access by foreigners to the labour market 4 . Unlike other areas of legislation relating to foreigners, there has been a tendency to increase legal discrimination during the past century5 , because, resulting from "measures undertaken in haste and under the pressure of the time, many remained on a long-term basis or even permanently" [START_REF] Lochak | Police et travail. Aux origines de l'ordonnance du 2 novembre 1945[END_REF].

Measures aimed at banning certain occupations to foreigners were added subsequent to the others, and only those concerning European Union nationals were removed under the pressure of European legislation. French State policy towards self-employed immigrants is to regulate and restrict access to the trades. Nevertheless, restrictions and regulations have varied in degree depending on the era. Although the overall philosophy of the legislation has not evolved since the 1930s, it has been more or less strictly enforced in the intervening decades.

French migration policy has gone through various phases during the past century. First of all, there was the gradual institutionalisation of a migration policy, from a laissez-faire attitude to state intervention, then the free movement of immigrants in a context of minimal regulation and intervention by the State, to the current policy aiming to regulate and strictly control foreigners [START_REF] Ma Mung | Continuidad y fluctuaciones de la política migratoria francesa[END_REF][START_REF] Dinh | The ethnic neighbourhoods and "La République". The case of Faubourg Saint-Denis area[END_REF].

The first section provides an overview of France's experience as an immigration country and presents successive migration policies and regulations, while the second section is devoted to the legal context, notably bans and exclusions concerning foreigners, implemented by the authorities during the 1930s, encouraged and supported by certain trade associations. Most of these exclusions are still in force today. The third section presents a recent statistical characterisation6 of immigrant entrepreneurship 7 in France, which has developed within the confines of the discriminatory legislation of the past. This phenomenon constitutes a strong trend observed since the census of 1974, characterised by the appearance of this class of small entrepreneurs within the immigrant population in the 1970s, followed by decades of development.

Immigrant France

In contrast to its neighbours, particularly Germany 8 , France experienced a demographic deficit during the late nineteenth century and was from very early on obliged to rely on foreign labour -to 'adopt foreigners in order to survive'. Already in the mid-nineteenth et des Etudes Economiques (the French National Institute of Statistics and Economic Studies, INSEE) have since changed, and they now conduct an annual census based on a sample. Applied for the first time in 2004, the first results will be available in the second semester of 2009. 7 The definition of immigrant entrepreneurs applied in this study is: 'immigrant' people -according to the INSEE definition -who engage in activities as craftsmen, as traders or as paid heads of companies of ten or more employees. For convenience, this group is referred to as ACE ('Artisans, Commerçants, Chefs d'entreprise', meaning "craftsmen, shopkeepers, company heads with at least ten employees on the payroll"). 8 What was increasingly alarming for the French political leaders was the growing contrast with their German neighbour, whose army crushed the army of Napoleon III in 1870-1871. Nevertheless, at that time there was not yet a marked difference in population size between the two countries, both having a population close to 40 million. Forty years later however, France, divested of Alsace-Lorraine, did not even reach this threshold of 40 million inhabitants (39,600,000 in 1911 within its borders at that time), whereas the population of the German Empire exceeded 65 million [START_REF] Garden | La dynamique de la population française (1801-1914)[END_REF]. century, elements of policies (the 'Nationality' laws of 1851, 1889 9 and of 1927) aiming to attract immigrant workers were developed, yet a laissez-faire attitude of non-intervention prevailed until the 1930s. Moreover, France had the lowest overseas emigration rates of the larger countries of Europe in the late nineteenth and early twentieth centuries. French cities were often more attractive than American ones [START_REF] Haines | French Migration to the United States: 1820 to 1950[END_REF].

Whereas European states have become destination countries for immigrants mainly since 1945, France has been a target country for much longer. It has been a receiving country for neighbouring Europeans but also for people from other continents for a long time. The evidence is systematic since the second half of the nineteenth century -the first census in which the category of foreigners appears is 1851, when 381,000 foreigners were enumerated. By 1881 there were already one million foreigners.

The immigration into France of foreign population groups -inhabitants of the border zones or neighbouring countries on the eve of the First World War -was, on such a scale, a unique phenomenon in Europe 10 . The demographic imbalance between France and Europe contributed to the welcoming of people from other European countries, who did not have to resort to moving across the Atlantic to far-off America in order to find employment and a means of living.

"France is a country of immigration just like the Republic of Argentina or Australia. Every year, on average around 40,000 to 50,000 foreigners settle here and establish ties" (Leroy-Beaulieu, 1886) 11 . Neighbouring countries such as Belgium, Luxembourg, the Netherlands, Great Britain, Switzerland and Germany constituted source countries of emigration to France. Immigrants from these countries were mainly employed in the processing industries. Another migratory wave emerged in the years preceding the First World War, as is the case for Poles migrating to France [START_REF] Ponty | Polonais méconnus, histoire des travailleurs immigrés en France dans l'entre-deux-guerres[END_REF]. Afterward, from June 1919, the migratory phenomenon took on such a scale that France in 1930 was the country with the highest proportion of foreigners -515 for every 100,000 inhabitants compared to 492 in the United States of America [START_REF] Noiriel | Le creuset français, histoire de l'immigration XIXe-XXe siècles[END_REF]. 9 A decisive step in the history of the law on French nationality was reached when the word 'nationality' appeared for the first time in the title of a law governing access to French nationality in 1927. Decided after long debates (the proposal for the law dated back to 1882), the 1927 law became imperative just as much for demographic reasons (mainly a decrease in the birth rate) as because of compulsory military service from which foreigners were exempt. Thus, by completely revising the pre-existing legislation, the State introduced new measures aimed at facilitating foreigners' access to French nationality (Maillard, 2007). For an understanding of nationality issues in France, see the contribution of Jean [START_REF] Massot | Français par le sang, Français par la loi, Français par le choix[END_REF], "Français par le sang, Français par la loi, Français par le choix", Revue Européenne des Migrations Internationales, vol. 1, no. 2, pp. 9-19. 10 Already since the eighteenth century, the weak growth of the French population had been evident, increasing little before the end of the eighteenth century, approximately to 20 to 25 million inhabitants (Mauco, 1932). The need for an increased population and a qualified workforce for new industrial and commercial activities contributed to a regular immigration flow, the destinations of which were sometimes limited to areas like Corsica or localities like Calais, Longwy, or Sarrelouis, or in trades where there was a demand for labour (immigration of merchants or specialists of Italian, Portuguese, Dutch, Greek or Armenian origin). For example, we note Jean Baptiste Colbert's advice to King Louis XIV to import tinplate workers from Koblenz to work in French industries in order to compensate for the shortage of labour in these firms. Moreover, France welcomed Catholic refugees from England and Ireland and recruited foreign mercenaries. (See: Lequin, Y. (ed.) (1992), Histoire des étrangers et de l'immigration en France, Paris: Larousse. See also: d'Alteroche, B. ( 2002), De l'étranger à la seigneurie à l'étranger au royaume, XI-XVe siècle, L.G.D.J.). 11 Cited by Henri [START_REF] Bunle | Mouvements migratoires entre la France et l'étranger[END_REF], p. 67.

Between 1920 and 1930, the official figures reveal a surplus of 1,150,000 entries of immigrant workers over departures [START_REF] Bunle | Mouvements migratoires entre la France et l'étranger[END_REF]. They arrived under the aegis of international bilateral agreements signed by France with Italy in 1904and 1906, Belgium in 1906, Poland and Italy in 1919, and finally with Czechoslovakia in 1920. This institutionalised a relationship between the receiving country, the origin countries and French companies, representing a strong convergence of interests. Until mid-1932, as passing border control was not compulsory, foreign immigration in France was de facto a free movement. The immigrant worker could enter without difficulty, as long as they did not make known their intention to occupy paid employment. They could then subsequently regularise their situation by presenting a contract of employment. During the 1920s, the United States of America had stopped allowing immigration and France welcomed many of those who might have otherwise gone to America.

The 1930s witnessed the dawn of a period of immigration restriction, becoming increasingly discriminatory and stringent until 1945. In that year, the Government passed a law that has acted as the legislative basis for immigration policy ever since. With the ordinance of November 1945 and the creation of the 'Office National d'Immigration' (ONI), the State took charge of migration management. Nevertheless, labour market forces remained very strong and the official recruitment of foreign labour covered only a minority of actual entrants. The overwhelming recourse to regularisation was one of the main features of foreign labour management during this time. Families arrived both in the years preceding the labour migration ban of 1974 and thereafter [START_REF] Cordeiro | L'immigration[END_REF].

After 1974, legislation that had previously focused on 'temporary workers' gradually shifted its priorities to those 'who came to France to stay'. The 1980s was a period of stabilisation and from the 1990s on, a tendency towards more control and stricter admission policies can be observed.

Legal context

Until the Great Depression of 1929, a laissez-faire policy of benign non-intervention prevailed. The Depression of the 1930s and the rise of xenophobic sentiments resulted for immigrants in a series of discriminatory measures aimed at salaried labour. Yet the economic crunch also affected tradesmen, craftsmen and professionals. Suspected of taking advantage of loopholes in the labour regulations, immigrants were accused of unfair competition. Trade organisations began to lobby against immigrant competition, evidence of deep-seated unity founded on a commitment to closely monitor immigrants. They called for other ways to restrict the number of immigrants setting up independent businesses, such as legislation similar to the law of 10 August 1932 regulating salaried labour, setting quotas for the number of immigrants in each business sector or region [START_REF] Schor | L'opinion française et les étrangers, 1919-1939[END_REF].

The decree of 8 August 1935 subjected immigrant business-owners to the same obligations that had been mandated in 1932 for immigrant salaried workers. It required the possession of a special identity card, a mechanism that made it possible to regulate the number of immigrants. To this day, many sectors of economic activity remain closed to immigrants, but nationals from EU member countries are in a privileged position, because they are entitled to practice the profession of their choice in the territory of any Member State. This legislation applied mainly to nationals from non-EU countries; in France, this means African and Asian immigrants. These restrictions were not lifted until 1984 by the law of 17 July. The modification of the residence permits regime exempting immigrants with a ten-year residence permit from the requirement to apply for a special immigrant business licence granted a large number of immigrants access to a new legal status, allowing the exercise of an independent activity. This covered more than two million foreigners. Holders of a temporary residence permit (one-year) remained subject to the obligation to apply for a 'foreign merchant' licence 12 . This applied to about 300,000 foreigners. This liberalisation can be explained by the Government's interest at the time in reducing unemployment among the foreign population. However, this intention is not explicitly stated in the official text of the law [START_REF] Ma Mung | France: the narrow path[END_REF].

One way of getting around these discriminatory restrictions was to acquire French citizenship. As a result, a large number of 'naturalised French citizens' engaged in business activities; 11.7 per cent of the naturalised French citizens were contractors or merchants in 1990, as opposed to 8.9 per cent of the native French citizens. Another strategy was to marry a French spouse who held the nominal title of head of the business. It is impossible to quantify the immigrant businesspeople who resorted to this strategy, but field studies indicate that it is a common practice. Likewise, a non-spouse who is a French national may hold the title of head of the business. Here again, the number of these businesspeople is difficult to establish (ibid.).

Nowadays, according to the Groupe d'étude et de lutte contre les discriminations (GELD, 2005) 13 , 5.2 million titular jobs are reserved for French nationals in three Government departments (State, Territory and Hospitals). Additionally, companies with a specific status that generate public utilities (La Poste, EDF-GDF, Air France) and public industrial establishments providing more than a million jobs are required to hire only French or European Union nationals. About fifty occupations are the object of limitations in relation to nationality, equating to 615,000 jobs 14 , or to the holding of French qualifications, equating to 625,000 jobs 15 . (For the exhaustive list of jobs that require French nationality or French qualifications, see the GELD report, pp. 22-32, available at: http://www.viepublique.fr/documents-vp/ged_emploisreserves.pdf.)

Faced with these discriminatory measures, immigrant businesses have developed within the confines of restrictive legislation. Understandably, foreigners gravitate towards the sectors subject to the least regulation on the basis of nationality: the grocery trades, other retail and wholesale trades, the restaurant sector, construction, the garment trade, and so on.

12 From 1935 to 1984, foreigners who wished to engage in trade had to apply for a special licence as 'foreign merchants'. These licences were only granted in very limited numbers by local administrations. 13 Research Group against Discrimination (formerly GED). 14 Health care professionals: physicians, dental surgeons, midwives, pharmacists or veterinarians; legal professionals: court-appointed administrators, estate brokers, attorneys, notary publics, bailiffs and licensed auctioneers; but also licensed architects, surveyors and certified public accountants, among others. Immigrants from non-EU countries are banned by law from a large number of other independent pursuits. This ranges from owning a newspaper, a television or radio broadcast agency, or a co-operative newspaper/magazine distribution business, to selling tobacco or alcoholic beverages or engaging in self-employment in the insurance sector as a broker, general agent, and so on (CERC, 1999). 15 Foreign physicians who work in French hospitals are a good and convincing example. Recruited to compensate for a lack of staff, they are paid just one third of what French physicians are paid, can neither run their own business nor work in a private firm, and have their career pathway blocked (National Union of Physicians with non-European Union Diplomas, SNPADHUE, 2006).

Immigrant entrepreneurs: A statistical overview

From a strictly quantitative standpoint, immigrant activity has in fact been marginal since 1945, but the number of foreign shopkeepers and craftspeople was higher before the First World War than today. The discriminatory measures and the overtly xenophobic and racist policies of the French Government before the Second World War were factors in the sharp drop in the proportion of immigrants among entrepreneurs. The 1911 census counted 121,000 foreign business-owners (as compared to 107,100 in 1999), and the percentage of selfemployed workers in the immigrant working population was much higher than it is today: 20.4 per cent in 1911 as compared to 6.9 per cent in 1999 [START_REF] Belin | Recensement de la population (French Annual Census of Statistics: SUSE file)[END_REF].

In 1999, the number of immigrant entrepreneurs 16 was 166,222 -accounting for 10 per cent of all entrepreneurs. The most significant group is the Portuguese (15.8 per cent of immigrant entrepreneurs), followed by the Algerians (11.3 per cent) and Moroccans (10 per cent). They correspond to the most significant immigrant populations in France (Portuguese: 571,874;Algerian: 574,208;Moroccan: 522,504). Between 1990 and 1999, immigrant entrepreneurs experienced an evolution very different to that of the population of entrepreneurs at large (see table 1). On the one hand, the total number of entrepreneurs in France declined by 163,804, representing a decrease of 9 per cent. On the other hand, the number of immigrant entrepreneurs increased by 10,866 (+7 per cent) [START_REF] Ma Mung | The new landscape of immigrant entrepreneurship in France[END_REF]. This evolution is a continuation of the process observed since the census of 1975 [START_REF] Ma Mung | L'entreprenariat ethnique en France[END_REF][START_REF] Ma Mung | Commerçants maghrébins et asiatiques en France: agglomération parisienne et villes de l'Est[END_REF][START_REF] Dinh | L'entreprenariat ethnique en France[END_REF]. It is thus not a short-term phenomenon, but constitutes a strong trend characterised by the appearance of this class of small entrepreneurs within the immigrant population in the 1970s, followed by decades of development. However, this phenomenon can develop in very different ways depending on the entrepreneurial category (shopkeepers, craftspeople and company heads with at least ten employees on the payroll) and depending on the group's country of birth.

Three observations can be made here : Firstly, immigrant entrepreneurship is made up of small businesses. The number of immigrant 'company heads with at least ten employees on the payroll' is increasing, albeit at a modest rate (+3.8 per cent), whereas the entire category (immigrants + non-immigrants) is decreasing (-2.1 per cent). Despite this positive evolution, the proportion of immigrant heads of companies of with ten or more employees in the total immigrant ACE (7.3 per cent) remains lower than that of the nation as a whole (10.4 per cent). The proportion of small contractors among immigrant entrepreneurs is even more significant than is the case among the general population.

Secondly, a strong fall in the number of Spanish and Italian entrepreneurs is compensated for by the increase in the numbers of other immigrant entrepreneurs. A breakdown of the figures by country of birth shows strong differences (see table ). The number of entrepreneurs born in Spain has fallen by 31.4 per cent (-4,971). This fall is even greater among entrepreneurs born in Italy (-40.6 per cent; -10,717). Overall, nearly 16,000 Italian and Spanish entrepreneurs have disappeared.

This drop correlates with that of the immigrant working population with origins in these countries (Italy -36.8 per cent; Spain -32.6 per cent), itself due to the ageing of these populations17 and to a strong reduction in the flow of migrants coming from these countries18 . These changes point to the possible eventual disappearance of these groups of entrepreneurs. The sharp fall in the number of Italian and Spanish entrepreneurs is compensated for by a remarkable increase in the number of entrepreneurs originating from Morocco (+5,781), Turkey (+2,630) and Portugal (+2,058). The relative increase can be seen to be most marked among the Moroccans (+53.3 per cent) and Turks (+47.6 per cent). While the numbers originating from Vietnam, Laos and Cambodia are also remarkable (+34.2 per cent), the most pronounced increase is in the sub-Saharan African group (+87.3 per cent).

Thirdly, there is stagnation in the number of craftspeople, and an increase in the number of shopkeepers. The immigrant craft industry thus seems to be doing better than the French craft industry as a whole. Here again, however, the situation shows marked variation depending on the group in question. There has been an emphatic reduction in the number of Italian and Spanish craftspeople. Other groups, for example the Portuguese (+0.4 per cent), have maintained their levels, while yet others have experienced a conspicuous increase. Examples here are the South East Asians at +61.2 per cent, the Moroccans at +74.6 per cent and, most notably, the sub-Saharan Africans at +132.2 per cent. With 18,800 craftspeople, representing (in 1990) about a quarter of immigrant craftspeople, the Portuguese remain by far the principal group. The Italian craftspeople, even though they have lost half their manpower, still represent the second largest group (8,078), followed by the Algerians (7,155) whose number has increased by 24.8 per cent.

The situation is very different for shopkeepers, with their numbers increasing by 17.2 per cent. In terms of numbers, this branch of industry is more dynamic than the craft industry. However, here too it is important to examine the trends among the different groups. The Italians and the Spanish have lost about a quarter of their manpower, whereas the other groups display increases, some of them very significant. The most significant increases have been among the Moroccans (+2,676), the Turks (+1,517), the Portuguese (+1,374) and the sub-Saharan Africans (+2,908). The case of the Algerians is surprising, since they experienced a fall, albeit a slight one, in the number of shopkeepers (-0.5 per cent). Looking at the whole picture for 1999, one finds an almost perfect correspondence between these two categories of immigrant entrepreneurs, craftspeople making up 46.2 per cent, and shopkeepers comprising 46.5 per cent. This contrasts with the situation in 1990, when the former were proportionally more significant.

Focusing on the presence of different immigrant groups in entrepreneurial activities, the question is whether there is succession and replacement or cohabitation. The presence of immigrants in entrepreneurial activities is closely connected with the history of immigration and the various migratory waves that France has experienced. A group arrived in the 1950s and 1960s as immigrant workers, comprising Italians, Spanish, and later Algerians, many of whom became entrepreneurs. This group expanded its ranks and was joined by new entrepreneurs from other immigrant groups during the 1960s and 1970s, including the Portuguese and the Tunisians. Subsequently, in the 1980s and 1990s, these immigrants were joined by the Moroccans, the South East Asians and the Turks. More recently, in the 1990s, the Africans, the Indians, the Pakistanis and the Bangladeshis arrived.

It is possible to distinguish three phases in the entrepreneurial history of an immigrant group: a phase of installation and development, during which the number of entrepreneurs in the group rises strongly, and a phase of consolidation, during which the rate of recruitment makes only slight progress. Finally, there is a phase of decline where the number of entrepreneurs decreases. Immigrant groups are located at different phases according to the passage of time since their arrival.

The Spanish and Italians are in a phase of rapid decline. The Portuguese and Algerians, together with the Tunisians, are in a phase of consolidation, where their numbers are significant but recruitment is weak. We find the Moroccans, the South East Asians, the Turks and the Africans in a phase of installation and development. Nevertheless, it should be noted that, although the Italians and the Spanish are in a phase of decline, the proportion of entrepreneurs among their working population remains very high, compared to the average for all immigrants (respectively, 12.9 per cent and 8.5 per cent as against 7.3 per cent).

The existence of a class of entrepreneurs within these groups is a persistent rather than fortuitous phenomenon and represents an enduring change in their social structuring. In addition, it is not certain that the phases that one can identify from the tables will be exactly repeated in the future. Factors such as the development of Diasporas and circulatory economies can intervene in the development of a distinct group of immigrant entrepreneurs. These observations lead us to question whether the different groups successively replace each other, or whether they exist in a form of cohabitation. The census data do not allow us to answer this question, since the data at our disposal relate to a fixed point in time. Only a special longitudinal study could achieve this.

The phenomenon of succession is, however, observable on a local scale in certain Parisian districts, where one group succeeds another in the food or restaurant trade [START_REF] Ma Mung | Commerçants maghrébins et asiatiques en France: agglomération parisienne et villes de l'Est[END_REF]. The same phenomenon has been observed in the USA (Waldinger, 1987) and in the Netherlands [START_REF] Rath | A game of ethnic musical chairs? Immigrant businesses and the formation and succession of niches in the Amsterdam economy[END_REF]. However, very often cohabitation is observed, rather than replacement or succession. This is the case, for example, for the Faubourg Saint-Denis area in central Paris, where Turks, Chinese and Indo-Pakistanis share commercial space (Dinh, 2002[START_REF] Dinh | Le faubourg Saint-Denis, communauté ethnique marchande?[END_REF][START_REF] Dinh | The ethnic neighbourhoods and "La République". The case of Faubourg Saint-Denis area[END_REF].

Conclusion

The great number of jobs closed to foreigners has inestimable consequences in terms of processes of integration, and raises many questions about the efficacy of the fight against discrimination. Nevertheless, it did not prevent a class of small entrepreneurs of foreign origin from asserting itself in the host society. The strategies for getting around these discriminatory restrictions are numerous. Among them, the acquisition of French nationality remains the most evident and the most easily quantifiable.

Finally, in leaving foreigners with no option but to acquire French nationality, the French State effectively continued a policy of long-term immigration by encouraging the immigration of labour migrants with a vocation to stay in the country, transforming it into immigration of settlement.

The law of 17 July 1984 marked a step forward in facilitating access for immigrants with a ten-year residence permit to independent business activities. It remains the case that in many of the liberal professions, such as in medicine, foreign doctors are assigned to the most precarious positions and are paid 40 to 50 per cent less than their French colleagues with the same skills (SNPADHUE, 2008). This is despite the fact that they compensate for staff shortages in the French hospital system.

In other economic sectors where the jobs are considered to be menial tasks, such as in catering, security or cleaning, spontaneous strikes by undocumented workers in 2008 have highlighted a situation known to all: the employment of undocumented migrants, mainly sub-Saharan Africans, in the most difficult and worst-paid jobs. They pay their welfare contributions and taxes and contribute to French economic development without benefiting in return from the rights reserved for nationals. As French 'citoyens', that is "holders of a part of national sovereignty" [START_REF] Lochak | Etrangers et citoyens au regard du droit[END_REF], we have internalised the limits of the nation-state and the political consciousness that characterises it to such an extent that we consider it "as normal that there are foreigners, that is people who do not have the same rights as us" [START_REF] Kristeva | Etrangers à nous-mêmes[END_REF].

Table 1 -Changes in ACE immigrants from 1990 to 1999 (%)

 1

	ACE workforce	Total of the active population at work

MIGRINTER (International Migrations, Spaces and Societies) -University of Poitiers / CNRS

MIGRINTER (Migrations internationales, espaces et sociétés) -Université de Poitiers / CNRS : UMR 6588

In the French tradition, only the national is a citizen, whereas the foreigner has no authorisation to exercise the rights related to this quality. The difference between national citizens and non-citizen foreigners is far from being a marginal element of a foreigner's condition; it is on the contrary a central, essential element (the right to vote, access to public service jobs -which make up one-third of jobs available in the labour market, suspicion and penalisation of mixed marriages in France and in Europe, etc.)[START_REF] Lochak | Etrangers et citoyens au regard du droit[END_REF].

See Danielle Lochak's essential work in this area. Legal discrimination in social welfare provisions affecting foreigners living in France will not be dealt with here. In relation to that issue, please refer to the works of GISTI (2002), Le guide de la protection sociale des étrangers en France, Paris: La Découverte;[START_REF] Gacon | L'ouverture des frontières de la protection sociale. La couverture sociale des ressortissants des pays tiers[END_REF][START_REF] Toullier | En matière de protection sociale, fidélité à la logique Pasqua[END_REF].

This refers to discrimination not only sanctioned, but imposed, by texts, laws or regulations.

The most recent figures available date from 1999. The census methods of the Institut National de la Statistique

The over-60s represent 59.6 per cent and 51.6 per cent respectively, of the Italian and Spanish immigrants, as against 21.3 per cent for the whole population resident in France.

The number of immigrants coming from these countries since

is only 6,876 for Spain and 9,583 for Italy, with all social and professional categories grouped together.


Pascal Perrier
email: pascal.perrier@gipsa-lab.grenoble-inp.fr

Yohan Payan
email: yohan.payan@imag.fr

Isabelle Stéphanie

Mohammad Ali Buchaillard

Matthieu Nazari

Chabanas

Buchaillard

Stéphanie Buchaillard
email: stephanie.buchaillard@gmail.com

Mohammad Ali Nazari
email: mohammad.nazari@gipsa-lab.grenoble-inp.fr

Matthieu Chabanas
email: matthieu.chabanas@gipsa-lab.grenoble-inp.fr

Mohammad Ali Nazari

Biomechanical models to study speech

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Linguistic oral communication is a cognitive task in which humans share information by producing oro-facial gestures and generating acoustic signals. These gestures and signals are perceived, classified and interpreted in relation to a code, the linguistic code made of units of various sizes and of rules that specify how units can be assembled. In line with many authors, we think that linguistic units and rules have not been elaborated independently of the physical and cognitive systems that vehicle them in oral communication among humans [START_REF] Liljencrants | Numerical simulation of vowel quality systems: the role of perceptual contrast[END_REF][START_REF] Lindblom | Economy of speech gestures[END_REF][START_REF] Lindblom | Can the models of evolutionary biology be applied to phonetic problems[END_REF][START_REF] Lindblom | Phonetic universals in vowel systems[END_REF]Ohala,1983;[START_REF] Browman | Towards an articulatory phonology[END_REF][START_REF] Wilhelms-Tricarico | Development of a tongue and mouth floor model for normalization and biomechanical modeling[END_REF][START_REF] Boë | Tendencies in phonological structures: the influence of substance on form[END_REF][START_REF] Schwartz | The Dispersion-Focalization Theory of vowel systems[END_REF][START_REF] Schwartz | Phonology in a Theory of Perception-for-Action-Control[END_REF][START_REF] Schwartz | Linking the Dispersion-Focalization Theory (DFT) and the Maximum Utilization of the Available Distinctive Features (MUAF) principle in a Perception-for-Action-Control Theory (PACT)[END_REF][START_REF] Macneilage | The frame/content theory of evolution of speech production[END_REF]. We share their opinion in that the structures of languages and their diachronic evolutions are strongly influenced by the characteristics of the speech production and speech perception systems [START_REF] Fuchs | Is there a biological grounding of phonology? Determining factors, optimization and Communicative usage[END_REF], Fuchs & Perrier, 2009). This point of view is in opposition with some major linguistic theories (see among others [START_REF] Chomsky | The Sound Patterns of English[END_REF][START_REF] Prince | Optimality Theory: Constraint Interaction in Generative Grammar[END_REF] More specifically, for speech production, we think that anatomical and mechanical properties of the speech apparatus have to be taken into account in the study of languages. They should be considered in conjunction with general motor control mechanisms and strategies underlying the generation of skilled gestures in humans. The physical patterns carrying linguistic information in speech are typically associated with time varying articulatory and spectral patterns. These patterns are generated by displacements of the jaw, the tongue and the velum, by shaping of the deformable tongue and lips, and/or by vibrations of the vocal folds. These physical phenomena are deeply constrained, limited and determined by the physical nature of these articulators. All these constraints are likely to influence the structure of the phonological systems. Thus, [START_REF] Hamann | Retroflexion and retraction revised[END_REF] has suggested that an explanation for the absence of nonvelarized retroflexes in the inventory of world's languages could be the articulatory impossibility to generate retroflexion without tongue retraction. In the same vein, [START_REF] Hamann | Retroflexion of voiced stops: Data from Dhao, Thulung, Afar and German[END_REF] have suggested that the emergence of a voiced retroflex stop from a voiced alveolar or dental stop could arise from the specific articulatory requirements for voiced alveolar or dental stops.

Similarities between speech rhythms [START_REF] Ohala | The temporal regulation of speech[END_REF] and natural oscillation frequencies of the mandible let think that timing in speech could be constrained by inertial and modal properties of the articulators [START_REF] Morimoto | Frequency dependant modulation of rythmic human jaw movements[END_REF]. Articulatory paths and formant transitions between sounds are determined by the deformation capabilities of the tongue and of the lips [START_REF] Perrier | Influences of tongue biomechanics on speech movements during the production of velar stop consonants: A modeling study[END_REF].

Hence, a careful analysis of the physical properties of the speech apparatus, including an anatomical, biomechanical and aerodynamic characterization should contribute significantly to the understanding of the structures of languages and of their evolutions. This has been well understood a long time ago by researchers like Perkell or Fujimura, who initiated pioneer works in physiological modeling of the tongue based on a description of muscle anatomy, muscle force generation mechanisms and tongue tissues mechanics [START_REF] Perkell | A physiologically oriented model of tongue activity in speech production[END_REF][START_REF] Kiritani | A computational model of the tongue Annual[END_REF][START_REF] Kakita | Computational model of the tongue: A revised version[END_REF]. Since these pioneer works, the tremendous increase of computational capabilities in computers and the improvements of anatomical, physiological and neuro-physiological knowledge of the oro-facial sphere have permitted the elaboration of more sophisticated and more realistic models (for the tongue: [START_REF] Kakita | Computation of mapping from muscular contraction patterns to formant patterns in vowel space[END_REF][START_REF] Hashimoto | Estimation of the muscular tensions of the human tongue by using a three-dimensional model of the tongue[END_REF][START_REF] Wilhelms-Tricarico | Physiological modeling of speech production: methods for modeling soft-tissue articulators[END_REF][START_REF] Payan | Synthesis of V-V sequences with a 2D biomechanical tongue model controlled by the Equilibrium Point Hypothesis[END_REF][START_REF] Sanguineti | A dynamic biomechanical model for neural control of speech production[END_REF][START_REF] Wilhelms-Tricarico | Development of a tongue and mouth floor model for normalization and biomechanical modeling[END_REF][START_REF] Dang | Construction and control of a physiological articulatory model[END_REF][START_REF] Perrier | 3D biomechanical tongue modelling to study speech production[END_REF][START_REF] Fujita | A computational tongue model and its clinical application[END_REF][START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF] for the face: [START_REF] Terzopoulos | Analysis and synthesis of facial Image sequences using physical and anatomical models[END_REF][START_REF] Lucero | A model of facial biomechanics for speech production[END_REF][START_REF] Gomi | A physiologically based model of perioral dynamics for various lip deformations in speech articulation[END_REF][START_REF] Kim | Model-based investigation of control and dynamics in human articulatory motion[END_REF][START_REF] Sifakis | Simulating speech with a physics-based facial muscle model[END_REF][START_REF] Nazari | Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation[END_REF] for the jaw: [START_REF] Flanagan | Control of human jaw and multijoints arm movements[END_REF], Laboissière et al., 1996[START_REF] Stavness | Predicting muscle patterns for hemimandibulectomy models[END_REF].

In this paper, the methodology elaborated in our group for the design of biomechanical models of speech articulators (more specifically tongue and lips) in the aim to study speech production is explained. The basic principles that guided our work are close to those proposed by [START_REF] Wilhelms-Tricarico | Physiological modeling of speech production: methods for modeling soft-tissue articulators[END_REF] or [START_REF] Sifakis | Simulating speech with a physics-based facial muscle model[END_REF]. Our models are continuous ones based on finite element structures, the meshes, as opposed to discrete models based on spring-mass networks such as those of by [START_REF] Kim | Model-based investigation of control and dynamics in human articulatory motion[END_REF], [START_REF] Dang | Construction and control of a physiological articulatory model[END_REF], [START_REF] Terzopoulos | Analysis and synthesis of facial Image sequences using physical and anatomical models[END_REF]. Muscle activation affects the mechanical properties of the mesh elements associated with the activated muscle; the mechanical properties of the mesh elements are non-linear. As compared to Wilhelms-Tricarico's or Sifakis et al.'s models, our muscle models are functional and then less accurate. However, in our models the interaction of the soft tissues with the external structures, the teeth, the palate, the cranial bones are modeled with contacts, and this was not the case in these two reference models.

In the current paper, the methodology that guided the design of oro-facial biomechanical models in Gipsa-lab is explained and examples of the most recent models are presented. Then, results are described that were obtained with simulations and are related to important issues in phonetics.

METHODOLOGY FOR THE DESIGN OF BIOMECHANICAL MODELS OF SPEECH

ARTICULATORS

From a methodological point of view, our approach is constrained by two important and somewhat contradictory requirements: (1) since the aim of our work is to use models in order to infer and to understand the impact of physical phenomena underlying speech production onto phonetic patterns of languages, these models have to be as realistic as possible; (2) due to limitations in terms of computational costs and computational accuracy, numerical models of physics have to be simplified and inaccurate descriptions of reality have to be tolerated as long as they are well identified and explained. Hence, our methodology is the result of a compromise that consists in representing major anatomical, physiological, neuro-physiological and physical features and in suggesting or tolerating a number of simplifications in the description of some other properties that are assumed to have impacts of secondary importance.

3D geometry

The 3D geometry of the modeled articulators has been extracted from medical images collected from human subjects thanks to Magnetic Resonance Imaging (MRI) techniques, cineradiographies and CT-scans (Figure 1). Both in MRI and in CT scans, subjects are in supine position, which influences tongue geometry due to the orientation of the gravity field. Cineradiographies are collected with the subject's head in vertical position, and they are used to correct the geometry extracted from 3D scans and to remove the effect of gravity in supine position, by taking into account tongue contours in the mid-sagittal plane [START_REF] Buchaillard | Activations musculaires et mouvements linguaux : modélisation en parole naturelle et pathologique[END_REF] Figure 1: Example of a 3D CT Scan (left) and of a mandible geometry (right) extracted from CT scan data. In the CT-scan, white regions correspond to bony structures and dark gray regions to empty regions (air). [START_REF] Buchaillard | Activations musculaires et mouvements linguaux : modélisation en parole naturelle et pathologique[END_REF]

Finite Element Modeling

Modeling of soft tissues' mechanical behaviors, such as those of the tongue, the lips, the face or the velum, requires the application of physical laws specified by continuum mechanics. These laws account, among others, for relations between stress and strain, and between forces and displacements, as well as for balance conditions of the soft body under the influence of external actions. An efficient numerical framework to implement these laws is the Finite Element Method (FEM) proposed by [START_REF] Turner | Stiffness and deflection analysis complex structures[END_REF]. FEM requires sub-dividing the body into a set of small elements (the FEM mesh) determined by nodes and edges. Mechanical equations are solved for each element individually and rules are applied to assemble elements back into the whole body in order to determine its global deformation and displacement. Other techniques exist to account for soft tissues mechanics, which rely on a discrete representation of the body based on a series of connected springs and masses. These techniques have been shown to be computationally less demanding and therefore faster than FEM, but they also have been shown to be less accurate and less stable [START_REF] Piterman | Chaos dans la modélisation des tissus mous[END_REF].

Anatomy and physiology

Face and tongue anatomies are very complex. Mucosa, skin tissues, fat tissues, muscular tissues, ligaments and collagens are mixed with each other. Their respective boundaries are not clear and all these different kinds of tissues are unevenly distributed spatially. In many parts of the tongue fibers belonging to different muscles and oriented along various directions are interwoven. Our models do not account in details for this complexity. Based on dissections results [START_REF] Miyawaki | A study on the musculature of the human tongue: Observations on transparent preparations of serial sections[END_REF][START_REF] Takemoto | Morphological analysis of the human tongue musculature for three dimensional modelling[END_REF], on MRI images (Gilbert & Napadow, 2005) on data provided by the Visual Human Project (National Library of Medicine, USA, www.nlm.nih.gov/research/visible), and on anatomical atlases [START_REF] Netter | Atlas d'anatomie humaine[END_REF], we have proposed a simplified description of the anatomy, in which muscles are represented by a set of contiguous elements within the FEM mesh and by a set of macrofibers oriented for each muscle along the main direction of its fibers. The mesh models the elastic behavior of the tissues via a constitutive law representing the relation between stress and strain. Both linear and nonlinear laws have been used, which is done in the linear case simply with the specification of the Young's modulus and the assumption of incompressibility. The macrofibers are connected to the Finite Element mesh and they exert strain on it. The shape of the FEM mesh elements has been adapted, in order to fit as well as possible the global geometry of each muscle (main direction and crosssection). The connections of the tongue with the mandible and the hyoid bone and of the face tissues with the skull have been carefully described. The insertions of the muscles on the bony structures and within the soft tissues have been also determined with accuracy. They are of particular importance, since they determine the main directions of the macrofibers and, consequently, of the muscle forces exerted on the FEM mesh.

In its last version the 3D model of the tongue includes eleven independent muscle units, controlling the intrinsic muscles (the posterior, medium, and anterior parts of the Genioglossus, the Superior Longitudinalis, the Inferior Longitudinalis, the Verticalis, and the Transversalis), the extrinsic muscles (Hyoglossus and Styloglossus) and the mouth floor muscles (Geniohyoid and Mylohyoid), The face model includes also eleven independent muscle units, the Levator Labii Superioris Alaeque Nasi, Depressor Labii Inferioris, the Levator and Depressor Anguli Oris, the Zygomaticus, the Risorius, the Buccinator, the Mentalis and the Peripheral and Marginal parts of the Orbicularis Oris. Examples of these muscle implementations are given in figure 3. right, macrofibers for the posterior genioglossus and the styloglossus in the tongue model [START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]. Bottom panel: left, volumetric description of the orbicularis oris in the face model; right: macrofibers for the main muscles in the face model (left side only) [START_REF] Nazari | Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation[END_REF]

Mechanical aspects

Mechanical aspects include mass, damping factors, elastic properties of tissues, muscle force generation mechanisms, as well as boundary conditions (i.e., in our models, contacts between structures). The mass depends on material's mass density and volume. For the bony parts, the density is 2000kg/m 3 . For soft tissues, the density was chosen to be close to the density of water, i.e. 1040kg/m 3 . Damping factors have been chosen to be close and greater than critical damping in the range of movement frequencies observed in speech (from 1 to 20Hz). This allows the articulators moving rapidly, without generating physical instabilities.

Elastic properties of soft tissues were determined from measures made on tongue's and cheek pieces removed from a fresh cadaver [START_REF] Ohayon | Non linear elastic properties of the lingual and facial tissues assessed by indentation technique[END_REF], and from complementary measures made on living subjects [START_REF] Schiavone | A light sterilizable pipette device for the in vivo estimation of human soft tissues constitutive laws[END_REF]. These measures provide information about the relation between the intensity of an external stress applied to the tissues and the corresponding tissues deformation. This relation was found to be non-linear: a given increase of the stress has a smaller impact when deformation is large than when it is small (i.e. the stiffness increases for large deformation). This could be modeled by elements made of hyperelastic material [START_REF] Ohayon | Non linear elastic properties of the lingual and facial tissues assessed by indentation technique[END_REF]. In our models, these mechanical properties are modeled isotropically: they are exactly the same in all directions. This isotropic approach was chosen for sake of simplicity. It should be acknowledged that this does not match experimental results. Indeed, muscles have been shown to be rather transversely isotropic: their mechanical properties are fairly identical in directions orthogonal to the long muscle fibers, but they are different in the direction of these fibers.

Pharyngeal walls

The tongue model is embedded in a vocal tract and connected to the jaw and the hyoid bone. Vocal tract boundaries are the mandible, the hard and the soft palate, and the pharyngeal walls (Figure 4). The geometry of the mandible, the teeth, the hard palate, the soft palate and the pharyngeal walls were extracted from MRI images [START_REF] Badin | Three-dimensional linear articulatory modeling of tongue, lips and face, based on MRI and video images[END_REF]. In the current version of the model the mandible is fixed. In addition the soft palate and the pharyngeal walls are represented as solid structures. The hyoid bone is mobile and connected with springs to lower bony structures in the laryngeal and chest regions [START_REF] Perrier | 3D biomechanical tongue modelling to study speech production[END_REF][START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]. Boundary conditions correspond to contacts of the tongue blade and tongue tip with palate and upper teeth, and of the lower part of the tongue tip with the lower teeth and inner surface of the mandible [START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]. The face model includes contacts between upper and lower lips, as well as contact between lips and teeth [START_REF] Nazari | Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation[END_REF].

Muscle model

A muscle generates a force along the direction of its long fibers. This force tends to shorten the muscle and varies non-linearly with the length and the shortening rate of the long fibers [START_REF] Mcmahon | Muscles, Reflexes, and Locomotion[END_REF]. In addition, when a muscle is activated, it becomes stiffer in the direction orthogonal to its long fibers [START_REF] Mcmahon | Muscles, Reflexes, and Locomotion[END_REF] (the so-called "stress stiffening effect"). In our modeling approach, these phenomena are accounted for [START_REF] Nazari | Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation[END_REF]. A muscle force is generated according to the Equilibrium-Point Hypothesis [START_REF] Feldman | Once more on the Equilibrium-Point hypothesis ( model) for motor control[END_REF], which specifies that force varies as an exponential function of the muscle length (see below). In addition, this force decreases when the shortening rate increases. The stress stiffening effect is modeled thanks to changes in the relation between force and deformation.

Motor control

The choice for a motor control model was strongly influenced by our hypotheses about the relations between phonological units and their physical realizations. We do think that the discrete nature of the phonological inputs is mirrored in the motor control variables, and that the physical continuum of the articulatory movements and of the acoustic signal is the result of the interaction between discrete sequences of motor commands and the physical properties of the speech apparatus (Perrier et al., 1996a). Thus, our model of speech motor control is a "target-based" model, in which the targets are specific sets of motor commands associated with the phonological units. To implement this view of speech motor control, we used Feldman's Equilibrium-Point Hypothesis and its associated -model [START_REF] Feldman | Once more on the Equilibrium-Point hypothesis ( model) for motor control[END_REF]. According to this hypothesis a movement is generated from a discrete sequence of target motor commands from which the continuous time variation of the motor control variables is determined by shifting them at a constant rate between successive target values. The motor control variables are called and they are muscle threshold lengths: when a muscle is shorter than the value, it does not generate any active force (it behaves like a passive spring); when a muscle is longer than , it generates a force that tends to shorten it and to bring it back to length . Muscle force increases exponentially with the difference between the actual muscle length and the threshold . When two or more muscles are active, the resulting position of the articulator corresponds to a mechanical equilibrium between the different muscles forces. Feldman's hypothesis suggests that the mechanical equilibrium is controlled by the Central Nervous System via the specification of the thresholds of all active muscles.

Thus physical targets in speech production are not specified as articulatory positions, but as dynamical equilibrium positions. This property is very important and has provided a powerful modeling framework to account for the physical variability observed for a given phonological input according to speaking style, speaking rate or phonetic context (Perrier et al., 1996a;Perrier et al., 1996b) (see also below).

Evaluation

The evaluation of the models is based on comparisons of simulations results with experimental data collected on human speakers. Comparisons do not consist of a computation of any kind of average error between experimental trajectories and simulated ones. Indeed, in spite of the fact that our biomechanical models are based on data collected on human speakers and account as carefully as possible for physiological and physical properties, such a comparison would not make much sense. Some physical parameters in the model cannot be actually measured on living subjects, as for example the damping factors, or the variation of stiffness with muscle activation, or the global level of muscle activation. In addition the model is symmetrical in reference to the mid-sagittal plane, which is never really the case in humans. In addition, in spite our wish to be as accurate and realistic as possible, we had to tolerate some simplifications, such as the hypothesis of tissue isotropy or the application of muscle forces via macrofibers. These discrepancies with real human beings are not supposed to induce strong differences between simulations and data. However, they do not allow a point-topoint comparison of trajectories. Rather, comparisons are based on a number of more macroscopic factors that are key factors in terms of motor control or in terms of speech production, such as vocal tract shape, movement amplitude, movement duration, amplitude of the velocity peak within a movement, velocity profiles (time variation of the velocity during a movement), maximum level of force, position of acceleration peaks….

This will be illustrated in the section below.

EXAMPLES OF SIMULATION RESULTS RELATED TO ISSUES IN PHONETICS

In this section, some examples of results will be presented, that have potential implications for the studies of languages.

Tongue muscle activation for vowel /i/ -Possible consequences of control inaccuracies

With the vocal tract model presented Figure 4, 300 simulations have been carried out, in order to find out the muscle activations underlying the production of the main French oral vowels. These simulations have been assessed in the articulatory domain by comparing real 3D tongue shapes with the simulated ones, as well as in the acoustic domain by looking at the frequencies of the three first spectral maxima (formants) of the acoustic signal generated from the simulated tongue shape. The three formants are extracted from the synthetic signal generated from the 3D vocal tract shape with a Kelly-Lochbaum model implemented by [START_REF] Story | A parametric model of the vocal tract area function for vowel and consonant simulation[END_REF]. Initial activation patterns have been proposed on the basis of electromyographic data collected by [START_REF] Miyawaki | A preliminary report on the electromyographic study of the activity of lingual muscles[END_REF] and [START_REF] Baer | Electromyography of the tongue muscles during vowels in /pVp/ environment[END_REF] for Japanese and English vowels. From these initial patterns, variations were provided to the motor commands in order to generate realistic tongue shapes. To do so, our approach was, on the one hand, to make the simulated tongue shapes in the midsagittal plane as close as possible to tongue shapes classically presented for French oral vowels in the literature and observed by means of cineradiographic data (see for example [START_REF] Bothorel | Cinéradiographie des voyelles et des consonnes du français (Cineradiography of vowels and consonants in French)[END_REF]. On the other hand, we tried to get a good match between the synthetic formant values generated from the simulated tongue shape and the formant patterns classically given in the literature. The tongue shape thus obtained for vowel /i/ is depicted on Figure 5 [START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]. The corresponding formant values are F1=321Hz, F2=2095 Hz and F3=2988Hz. They correspond very well to the average values proposed for this vowel in French in Calliope (1984). The classical articulatory characteristics of this vowel are well replicated: the highest point of the tongue is located in its front part (alveo-palatal region), the back part is clearly pushed forward and it widens the pharyngeal cavity, the front part is grooved along the mid-sagittal direction. This is in agreement with general descriptions of the 3D shape of vowel /i/ (for example in [START_REF] Lundberg | Three-dimensional tongue surface reconstruction: Practical considerations for ultrasound data[END_REF] and with 3D data measured for this vowel with anatomic MRI on the native speaker of French 1 who served as reference to build up the tongue model.

The main tongue muscles underlying the production of this tongue shape are the posterior part of the genioglossus (GGp), its anterior part (GGa), the styloglossus (Sty) and the transversalis (Trans). In addition contacts are observed between the hard palate and the upper dental arch on one hand and the tongue lateral borders on the other hand. Our simulations reveal that GGp and Sty activations are responsible for tongue elevation, that GGp activation also allows the anterior positioning, and that the grooving of the anterior part is due to GGa activation. Transversalis activation facilitates these different shapings by limiting tongue deformation in the transversal direction. These findings are consistent with the EMG studies by Baer et al. (1998). As compared to these important and basic experimental results, our model brings a significant amount of new information, since it enables to understand the contribution of each muscle in the tongue shape of this vowel An analysis of the consequences of small variations of muscle activations has shown that they essentially affect the size of the constriction due to variations of the grooving amplitude, the front positioning of the tongue being stabilized by the contacts with the palate and the teeth [START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]. This finding shows that the correct production of vowel /i/ requires an accurate coordination of GGa and Trans muscles, in order to produce the appropriate grooving amplitude. Any inaccuracy in this coordination, due either to changes in motor commands or to variation in the relative timing of these commands, is likely to induce a transformation from a vowel /i/ to a more constricted articulation. This kind of inaccuracy could be at the origin of linguistic changes, where the vowel /i/ becomes a glide /j/ in vowel-to-vowel transitions (see [START_REF] Ladefoged | The sounds of the world's languages[END_REF][START_REF] Calliope ; Masson Chitoran | From hiatus to diphthong: the evolution of vowel sequences in Romance[END_REF][START_REF] Padgett | Glides, vowels, and features[END_REF]

Role of inertia and dynamics: vowel reduction

Vowel reduction associated with an increase in speaking rate is a well-known variation particularly well illustrated by the experimental study of /dud/ variability carried out by [START_REF] Lindblom | Spectrogaphic study of vowel reduction[END_REF]. On the basis of simulations run with a mass-spring model, [START_REF] Lindblom | Spectrogaphic study of vowel reduction[END_REF] could reproduce the measured spectrographic patterns by decreasing the time allowed for the vowel production between the two consonants. Doing so Lindblom suggested that articulatory inertial and dynamical properties would be the main factors of vowel reduction in fast speaking rate condition. However, the question remained whether realistic vowel reduction patterns can be obtained without changing the target articulatory commands underlying the production of the inter-consonantal vowel. [START_REF] Loevenbruck | Vocalic reduction: prediction of acoustic and articulatory variabilities with invariant motor commands[END_REF], using a slightly more realistic spring mass model controlled by the Equilibrium Point Hypothesis, suggested that vowel reduction can be obtained without any change in target vowel commands, just by reducing 1 Courtesy of Pierre Badin, Gipsa-lab, CNRS, Grenoble, France. movements' durations. A more accurate assessment is now possible by using our realistic biomechanical models.

For this study, we used the two dimensional version of the vocal tract model. This model has been extensively described in [START_REF] Payan | Synthesis of V-V sequences with a 2D biomechanical tongue model controlled by the Equilibrium Point Hypothesis[END_REF] and [START_REF] Perrier | Influences of tongue biomechanics on speech movements during the production of velar stop consonants: A modeling study[END_REF]. As compared to the description that is provided above of the more recent 3D model, some points should be made clear though. The Finite Element mesh is a representation of the projection of the tongue in the mid-sagittal plane. Just as in the 3D model the internal geometry of the mesh has been designed to facilitate the anatomical representation of the muscles. However, the restriction of the mesh to a 2D representation has two noticeable consequences. First, only the muscles that have a clear and direct impact on the tongue contour in the midsagittal plane are modeled. These muscles are the posterior and anterior parts of the Genioglossus, the Hyoglossus, the Styloglossus, the Verticalis and the inferior and superior Longitudinalis. The role of the transversalis is consequently not accounted for. Second, the non-compressibility constraint is not implemented in relation to the 3D volume of the tongue, but in relation to the 2D surface of the Finite Element mesh. In addition, the elastic properties of the mesh elements are not described by a constitutive law relating stress and strain, but directly via the Young Modulus. Hence, the tissue stiffening associated with muscle activation is modeled by a linear increase of the Young Modulus with muscle activation (according to Feldman's model the activation is the difference between the actual muscle length and the motor command , and takes also into account the rate of muscle length change).

The study of the vowel reduction phenomenon with this model consisted in observing the impact of speaking rate increase on the tongue shape reached for the vowel. It has been assessed for /kik/ and /kak/ sequences. The targets for /k/, /a/ and /i/ have been determined with an optimal planning model described in [START_REF] Perrier | Speech planning for V 1 CV 2 sequences: Influence of the planned sequence[END_REF]. This model minimizes the articulatory effort while ensuring that targets in the acoustic domain are reached. It takes into account the fact that the jaw is fixed in the model. Results are presented in Figure 6. They are evaluated with respect to the hypothesis suggested by [START_REF] Loevenbruck | Vocalic reduction: prediction of acoustic and articulatory variabilities with invariant motor commands[END_REF] on the basis of the tongue shape actually reached for vowels /i/ and /a/. These tongue shapes are compared to the rest position of the tongue model (close to a schwa) and to the other tongue shapes generated with this model for the other French oral vowels. In addition, general information about "standard" vocal tract configurations measured on human speakers in the mid-sagittal plane (such as the X-ray views available in [START_REF] Bothorel | Cinéradiographie des voyelles et des consonnes du français (Cineradiography of vowels and consonants in French)[END_REF]) is taken into account. For both speaking rates the timings of motor commands are the same for both sequences. For each sequence target motor commands are identical in both speaking rates. It can be observed on Figure 6 that the impact of speaking rate increase is different according to the sequence. For fast speaking rate, the tongue shape reached for /a/ is very close to the central schwa configuration, without any clear constriction in the vocal tract (right top panel). Under the same conditions, the shape reached for /i/ is close to an /e/ configuration. Indeed, the right bottom panel of Figure 6 shows that this tongue shape still corresponds to a high and front vowel. However, as shown by the global orientation of the nodes trajectories in the palatal region from /k/ to /i/, this tongue shape is less high and less front than under normal speaking rate conditions (Figure 6, bottom panel, left), These results are consistent with the acoustical observations made by Gendrot & Adda-Decker (2009) from a large corpus of multi-speaker spontaneous speech. Thus, the simulations made with a realistic biomechanical model confirm the trends of the observations made by using more simple models, and make them more specific thanks to the integration of global constraints on tongue deformation.

The fact that vowel dependent articulatory (and acoustic) variability can be realistically accounted for with constant underlying motor targets, just by varying the timing of the motor command patterns is interesting and important in the context of the study of the interface between (invariant) phonology and (variable) phonetics.

CONCLUSIONS

Elaborating realistic biomechanical models of the speech articulators is a longterm task, requiring the collection of many data of different kinds about the anatomical, physiological and mechanical characteristics of the peripheral speech production system, and necessitating the use of complex and powerful mathematical methods. At first glance it seems very far from major linguistic issues. However in the context of substance-based approaches of language studies, this methodology contributes efficiently to quantitatively evaluate possible interactions between the structures of languages, their variations and their evolutions and the physical characteristics of the peripheral speech production apparatus. The study of the muscle activations underlying the vowel /i/ and of the sensitivity of this vowel to variations in the activations' amplitudes and in their time coordination has provided a basis for a further study of sounds' changes that could originate in these variations. The study of vowel reduction has shown that variable articulatory and acoustic patterns can be found for constant motor commands simply by varying their timing. Thus, biomechanical models of speech production offer a powerful research context to quantitatively study the interface between invariant phonological inputs and variable phonetic outputs, with a possible emphasis of the role (and the status) of the prosody in this interface.

Figure 2 :

 2 Figure 2: FEM meshes used for the tongue model (left, Buchaillard et al., 2009) and the face model (right, Nazari et al., 2010) In our model we have used a well-acknowledged commercial FEM Package called ANSYS TM . It guarantees the best possible accuracy of numerical modeling. FEM meshes defined for the tongue and the face models are shown in figure 2. They are made of hexahedral elements. The orientations and sizes of the elements have been determined in order to facilitate the modeling of muscle anatomy within each articulator and in the face (see below).

Figure 3 :

 3 Figure 3: Examples of anatomical muscle implementations. Top panel: left, localization of the anterior (dark gray), medium (light gray) and posterior (gray) parts of the genioglossus in the tongue;right, macrofibers for the posterior genioglossus and the styloglossus in the tongue model[START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]. Bottom panel: left, volumetric description of the orbicularis oris in the face model; right: macrofibers for the main muscles in the face model (left side only)[START_REF] Nazari | Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation[END_REF]

Figure 4 :

 4 Figure4: The 3D vocal tract model[START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]

Figure 5 :

 5 Figure 5: Tongue shape simulated for vowel /i/. Left panel: view from the front; Middle panel: View from the back; Right panel superimposition with the MRI data recorded from a native speaker of French (triangular mesh)[START_REF] Buchaillard | A biomechanical model of cardinal vowel production: Muscle activations and the impact of gravity on tongue positioning[END_REF]

Figure 6 :

 6 Figure 6: Impact of speaking rate on /kVk/ articulatory patterns simulated with a 2D biomechanical model of the vocal tract. Top panel: sequence /kak/, bottom panel: sequence /kik/; Left: normal speaking rate; right: fast speaking rate. In each plot the mid-sagittal tongue contour is represented for the first consonant /k/ (upper contour) and for the vowel (lower contour). Trajectories of nodes located on the upper tongue contour are depicted for the whole /kVk/ sequence

ACKNOWLDEGMENTS

This work has been funded by grants provided by the CNRS (POPAART Project, PR2 French-Germany Program), by the French-German University (Project Pilios) and by the Agence Nationale de la Recherche (Project Skullspeech, ANR-08-BLAN-0272).