François Huet

Laboratory-scale identification of corrosion mechanisms by a novel pattern recognition system based on electrochemical noise measurements

Papers dealing with electrochemical noise measurements (ENM) published in scientific journals often propose advanced signal processing techniques, in particular to determine the corrosion mechanisms. Most of the time, this is done without first validating their measurements. However, validation is not possible by simply visualizing the time records; rather, it is necessary to measure the EN at different sampling frequencies and check the overlap of the power spectral densities (PSDs) in the common frequency ranges [1,2]. Such validation is mandatory because many commercial potentiostats do not have anti-aliasing filters before the analog-to-digital converters in the measurement channels. The aliasing of high-frequency signal components to frequencies below half of the sampling frequency corrupts the EN signal in both time and frequency domains. This explains the dramatic scatter of the PSDs of the thermal noise generated by dummy cells, as shown in the round-robin tests organized by the European Cooperative Group on Corrosion Monitoring of Nuclear Materials (ECG-COMON) [2,3].

The paper by Zhang et al. [4] presents EN results on the corrosion of 304 stainless steel (SS) in FeCl3 solution. Fig. 2 of that paper shows good overlap of the PSDs of the noise measured at 3 different sampling frequencies on a dummy cell with 3 resistors of 1 M in a star arrangement, as those used in the round-robin tests mentioned above. However, the typical PSDs of the potential and current fluctuations expected to correspond to the three corrosionrelated mechanisms of 304 SS (uniform corrosion, pitting corrosion and passivation) in Fig. 6 were particularly inaccurate. These PSDs were recalculated from the raw time records obtained during the review process at another journal. A simple linear detrending and a Hann window were applied on each block of 2048 points of the raw data with the software "psd-detrend_ECG-COMON.exe", available for free on the ECG-COMON website (www.ecg-comon.org) [1]. The results, shown in Fig. 1 below, are much more accurate than in Fig. 6 and allow a more thorough analysis of the ENM.

Even if the low-frequency parts of the PSDs could be improved by using a detrending method of order higher than 1 for the time records showing a high drift, the high-frequency parts are calculated with high precision. In the passivation case, the PSDs at frequencies above 0.1 Hz are due to the noise generated by the zero-resistance ammeter (ZRA) itself. Indeed, the amplitude of the potential PSD at 0.1 Hz is the same as for the 1 M dummy cell (10 -11 V 2 Hz - 1 , see Fig. 2a in Zhang et al.). Moreover, the current PSD increases with frequency above 0.1 Hz and reaches a plateau of amplitude 4  10 -21 V 2 Hz -1 at 1 Hz. This can only be explained by the fact that the PSD of the current noise was dominated by the regulation noise, which is equal to Vreg(f) / 4|Z| 2 (see Fig. 7 and Eq. 18 in Ref. 5) where Vreg is the regulation noise (voltage fluctuations around the DC value of 0 mV applied between the two electrodes by the ZRA) of the instrument. At high frequency, Vreg(f) does not depend on frequency while the impedance modulus decreases with increasing frequency, hence explaining the increase of the current PSD with frequency.

As a consequence, most of the fluctuations of the potential and current time records were due to the instrumentation and not to the passivation process, so that all the moments Estd, Eskew, Ekurt, Istd, Iskew, Ikurt, and Rn in Zhang et al. [4] cannot be attributed to the passivation process, which should not be considered in this study.

Figure 1 .

 1 Figure 1. Typical PSDs of the EN signals corresponding to the three corrosion mechanisms of


The latest crisis related to financial capitalism and mutations of the welfare state has been generating a new dynamic in the social economy of many advanced capitalist countries. Many politicians, institutions and movements are mobilising social economy (also called voluntary sector, third sector, etc.) as a solution to the current crisis. This is especially the case for cooperatives, which are now being promoted as an alternative to the drifts of financial capitalism. For example, on 1 July 2016, the occasion of the International Day of Cooperatives, ILO Director-General Guy Ryder issued a statement entitled "Cooperatives: An old idea, but more relevant than ever in today's world1 ". The International Co-operative Alliance (ICA), which has existed since 1895, defined a cooperative as "an autonomous association of persons united voluntarily to meet their common economic, social and cultural needs and aspirations through a jointly owned and democratically controlled enterprise", and based on the values of "self-help, self-responsibility, democracy, equality, equity and solidarity" [ICA, 1995]. Around the world, the cooperative movement has regrouped different types of organisations that have been experimented with in relation to many human activities, including consumer, worker, agricultural and housing cooperatives. The cooperative movement is a historic component of the social economy that remains very dynamic, and the emergence and the relatively old institutionalisation of specific actors, principles and rules to the cooperative have significantly influenced other forms of organisations in the social economy as association, mutual insurance [START_REF] Vienney | L'économie sociale[END_REF] or today's nongovernmental organizations and social enterprises.

The first cooperative developments emerged in Western Europe at the beginning of the nineteenth century in response to contradictions between the democratic and industrial revolutions. During the first half of the nineteenth century, the working classes experienced new forms of collective organisations as cooperatives in order to improve their working and living conditionsthe "Commerce Véridique et Social", founded in Lyon in 1835, or the "Rochdale Society of Equitable Pioneers" founded in the Manchester area in 1844, are emblematic examples of this periodand some social reformers as Robert Owen in England and Charles Fourier in France promoted a new organisation of society and relationship based on association and cooperation. In his study on "the social question", the sociologist Robert Castel remarks that "the association carries another conception of the social, whose achievement passes through the formation of collectives establishing relationships of interdependence among equal individuals2 " [Castel, 1995, p. 423]. During the nineteenth century, the cooperative movement saw a rapid economic development while being subjected to institutional and legal recognition in various countries, and the cooperatives became one of the largest social movements along with trade unionism and political socialism. During the first half of the twentieth century, the cooperative movement and specifically consumer cooperation were organised by wholesaling and retailing networks in many urban centres and rural areas and within the International Co-operative Alliance. The cooperative movement has actively participated in the democratisation of consumption and the improvement of daily life; it was in the centre of the political and cultural emancipations of the working classes and feminist movements, and it was a space for reflection and commitment for intellectuals in various parts of the world [Furlough and Strikwerda, 1999;[START_REF] Toucas | Les coopérateurs. Deux siècles de pratiques coopératives[END_REF][START_REF] Draperi | La République coopérative[END_REF]. Since its origins, and depending on the sociocultural contexts, the cooperative movement has been in tension among various practices and ideologies. In France during the nineteenth century, there were different traditions within the cooperative movement, such as liberalism, socialism, solidarism, Catholicism and paternalism [Gueslin, 1998;[START_REF] Ferraton | Associations et coopératives. Une autre histoire économique[END_REF][START_REF] Fretel | L'association entre libéralisme économique et État social : Une analyse des schèmes de justification de l'économie sociale aux XIXe et XXe siècles[END_REF]. The interwar period was a golden age for the French cooperative movementa period largely unrecognized even todaybut it was also a period of profound changes for French society and the forms of capitalism and state that prevailed during "the long nineteenth century" from the French Revolution to World War I (to use the formulation of the British Historian Eric Hobsbawm). The political and socioeconomic evolutions during the interwar period shook the ideological traditions in which the cooperative movement had evolved, and during the Great Depression the institutions of liberal capitalism and ideas of classical liberalism became unstable and partly rejected. If Keynesianism and Fascism "served as the ideological basis of the of the postwar "embedded liberal" order" [Blyth, 2002, p. 5], some other "neo" ideologies figured prominently in the debate and the institutional reconfiguration in France, such as neo-liberalism, neo-socialism and neo-corporatism [START_REF] Pirou | Néo-libéralisme, néo-corporatisme, néo-socialisme[END_REF]Audier, 2012], and neo-cooperation [START_REF] Furlough | Consumer Cooperation in France: The Politics of Consumption, 1834-1930[END_REF]. Economic ideas play a crucial role in the construction and transformation of institutional orders, especially during moments of economic uncertainty, and in constructing institutional solutions to the crises [START_REF] Blyth | Great transformations. Economic ideas and institutional change in the twentieth century[END_REF]. The cooperative ideology(ies) have also contributed to these institutional dynamics, particularly during the unstable interwar period. This working paper explores the evolution of French cooperative ideologies; it focuses specifically on the neo-liberal papers on cooperatives written by Bernard Lavergne and Hyacinthe Dubreuil, and on the socialist papers on cooperatives by George Fauquet and Marcel Mauss.

The first part of this article identifies some contextual elements concerning the evolution of the French cooperative movementespecially consumer cooperativesduring the economic boom of the 1920s and the crisis of the 1930s. It also presents general remarks on the evolution of economic ideas and institutions during this period. The second part focuses on analysing two cooperative propositions that fall within the emergence of neo-liberalism in France in the 1930s: the cooperative Order of Bernard Lavergne, the purpose of which was to empower consumers by liberalising both the market and the welfare state; and the cooperative organisation of work proposed by Hyacinthe Dubreuil, which aims to liberalise workers of modern corporations. The third part focuses on the role of cooperatives in the "Keynesian turn" of French socialism by exploring papers by two cooperative thinkers: George Fauquet, who promotes using the cooperative sector to integrate different kinds of cooperatives inside a mixed economy system; and Marcel Mauss, who believes cooperatives are a good way to enhance the empowerment of consumers and citizens with a view to nationalising the economy.

The metamorphosis of the French cooperative movement during the interwar period: Contextual perspectives

The first cooperative experiences in Europe emerged at the beginning of the nineteenth century, and between the nineteenth and the twentieth centuries, the consumer cooperation became ideologically and institutionally predominant in the French cooperative movement, even through consumer cooperation was divided between many networks and political groups. The rivalry between the two national consumer cooperative organisations, namely the Union Coopérative (which defended a "third way" between liberalism and socialism) and the Bourse des Coopératives Socialistes (which considered consumer cooperation to be the "third pillar of socialism") that lasted from the 1890s to 1912 is particularly representative of the divisions in the cooperative movement at the turn of the century [START_REF] Furlough | Consumer Cooperation in France: The Politics of Consumption, 1834-1930[END_REF]. The unification of consumer cooperative networks into a Fédération Nationale des Coopératives de Consommation (FNCC) on the eve of the First World War and the role of cooperators during that conflict gave new impetus to trade relations and political support for cooperatives during the interwar period -a period which represents the "golden age" of the French cooperative movement [START_REF] Toucas | Les coopérateurs. Deux siècles de pratiques coopératives[END_REF]. To understand the development of the cooperative movement in the context of the interwar period, we can distinguish two precise moments: the expansion of cooperatives in the economic boom of the 1920s (1.1) and the weakening of cooperatives after the 1930s crisis (1.2).

The French cooperative movement during the "Crazy Years"

The First World War had dramatic demographic, socio-economic and political consequences; in the years following it, the French economy saw a period of dynamic growth (around 6% per year). This economic growth was fuelled by the development of new industrial activities (in relation inter alia to electricity, chemistry and the automotive sector) and strong growth in productivity, as well as by the improvements in living and working conditions that accompanied the development of the welfare state [START_REF] Beaud | Histoire du capitalisme (1500-2010[END_REF]. The French regulation school suggests that the interwar period was characterised by an intensive mode of regulation (significant productivity gains) without mass consumption but with liberal wage labour regulation. The contradictions of this "hybrid" mode of regulation were the origin of the 1929 crisis, but it already showed its first signs of failure in the 1920s [START_REF] Boyer | Économie politique des capitalismes. Théorie de la régulation et des crises[END_REF][START_REF] Boyer | Économie politique des capitalismes. Théorie de la régulation et des crises[END_REF]. These economic contradictions can also partially explain the development of consumer cooperatives during the interwar period as a way to deal with the macroeconomic imbalance between production and consumption. From a political point of view, the National Bloc first took first power after the war, while socialists, communists and trades unionists were divided until the Lefts Cartel between radicals and socialists came to power in 1924. The right returned to power in 1926, but the uncertainties of political change weakened the foundations of the Third Republic; some historians speak about a French crisis of the "republican mystic" during the 1920s [START_REF] Milza | Histoire du XXème siècle Tome 1. De 1900 à 1945, la fin du monde européen[END_REF].

In addition to the economic boom and the emergence of a consumer society [START_REF] Furlough | Consumer Cooperation in France: The Politics of Consumption, 1834-1930[END_REF], the cooperative movement also benefitted from the state's help after the role of cooperatives was recognised during the war. In addition to providing food, clothing, education and agriculture support, cooperatives also offered a space of solidarity and politicisation. Their importance in the everyday lives of the working class helped consumer cooperatives grow from 876,000 members in 1914 to 2.3 million members in 1922 [START_REF] Toucas | Les coopérateurs. Deux siècles de pratiques coopératives[END_REF]. The cooperative movement came also closer to the Socialist and Communist Parties as well as to trade unions. However, for Charles Gide3 and his conception of a republic cooperative of consumers, it was mainly a period of intellectual consecration in the French and international cooperative movements [START_REF] Draperi | La République coopérative[END_REF]. At the end of the 1920s, some cooperative leaders and theorists expressed a desire to accelerate the second phase of the republic cooperative's development namely the abolition of wage labourand proposed merging worker and consumer cooperatives into one movement. However, the crisis of the 1930s ended this cooperative dynamic and the hope for a republic cooperative [START_REF] Toucas | Les coopérateurs. Deux siècles de pratiques coopératives[END_REF].

The French cooperative movement during the Great Depression

Different interpretations of the economic crisis that followed 1929 are still being proposed today [START_REF] Hautcoeur | La crise de 1929[END_REF], but in this article we follow the French regulation school's interpretation. This interpretation considers that the 1929 crisis was a crisis in the mode of accumulation, which was characterised by mass production without mass consumption; the fragility of this institutional configuration was succeeded by the new accumulation regime of Fordism (i.e. mass production with mass consumption) and Keynesianism regulation following the Second World War. However, the economic crisis quickly became a political crisis that entailed international events and the parliamentary democracy in France being called into question with the rise of fascism and many political scandals. The victory of the Popular Frontan alliance of left-wing movementsduring May 1936 legislative elections and the introduction of social reforms created both an important social movement and new perspectives for workers. However, effects of the Great Depression, international conflicts, the European crisis and many divisions in the Popular Front weakened the party and led to its break up in 1938 [START_REF] Milza | Histoire du XXème siècle Tome 1. De 1900 à 1945, la fin du monde européen[END_REF]. The economic and political transformations during the interwar period led to an ideological reconfiguration of French capitalism around three main ideologies: neo-liberalism, neocorporatism and neo-socialism [START_REF] Pirou | Néo-libéralisme, néo-corporatisme, néo-socialisme[END_REF]. Neo-liberals recognise a positive role for the state in the economy in terms of implementing unfettered competition and reducing inequalities; neo-corporatists propose enforcing the influence of corporations and professionals in organising the state and economy to fight liberalism excesses; and finally, neo-socialists reject integral collectivism and instead promote a mixed economy with planning and nationalization projects.

The 1930s crisis marked a return to divisions within the cooperative movement. These divisions were accentuated by management excesses that questioned the global project of cooperation, and economic depression and reductions in the state also directly impacted cooperativesmore specifically, producer cooperatives. The improvement of living conditions for workers and rural populations that accompanied the institutionalization of the welfare state weakened the ideal of the republic cooperative. The death of Charles Gide in 1932 deprived the movement of its major theorist in France, and the 1935 publication of George Fauquet's Secteur coopératif represented a symbolic turn for many cooperators who now left their utopia of a republic cooperative behind. 4 The reformist and pragmatic turn of the French cooperative movement is particularly evident in the FNCC, which promoted "neocooperative" values and practiced less radical. Historian Ellen Furlough summed up the trajectory of consumer cooperation in France during the interwar period as follows: "By the early 1920s, consumer cooperation seemed to be in a strong position. The FNCC sought vigorously to extend and strengthen the movement, and the new cooperatives founded after the war were flourishing. Yet the growth was accompanied by a transformation of both ideology and practice as neocooperation became the overarching framework. By the end of the 1920s, the elements that had distinguished cooperative from capitalist commerce were minimal. Cooperation had become a commercial sector within the largest capitalist economy; it mirrored many capitalist practices and assumption while retaining a few distinctively cooperative aspects" [Furlough, 1991, p. 259].

Box 1: The evolution of two consumer cooperative in the North of France in the late nineteenth and early twentieth centuries -L' "Union" de Lille and Amiens (Current research and the box is being drafted)

On the eve of the Second World War, cooperation remained one of the largest social movements in France despite the impact of the economic crisis. However, the interwar period represents a moment of profound ideological change in the French cooperative movement that we now consider through the writings of four cooperative thinkers of the 1920s and 1930s, namely Bernard Lavergne, Hyacinthe Dubreuil, George Fauquet and Marcel Mauss.

The role of cooperatives in the emergence of French neo-liberalism: Bernard Lavergne and Hyacinthe Dubreuil

During the nineteenth century, cooperatives were a subject of discussion for few French liberal economists [START_REF] Ferraton | Associations et coopératives. Une autre histoire économique[END_REF], but the evolution of liberalism ideology during the interwar period led to new reflection on this subject. Around the 1930s, some French neo-liberals promoted the idea that the state could foster the development of consumer and worker cooperatives in order to organise the freemarket economy [Pirou, 1939, p. 42]. The cooperative writings of Bernard Lavergne (2.1) and Hyacinthe Dubreuil (2.2) are quite illustrative of the ambiguous relationship between the cooperative movement and French neo-liberalism.

The cooperative Order of Bernard Lavergne: The liberalisation of market and state by the consumers

Bernard Lavergne (1884Lavergne ( -1975) ) was an economist who theorized about and helped to develop the French consumer cooperatives movement. In particular, he and his professor Charles Gide together created La Revue des études coopératives 5 in 1921. He also contributed to the diffusion of neo-liberal ideas in France and was one of the organisers of the 1938 Walter Lippman Colloquium in Paris [Audier, 2012;[START_REF] Denord | Néo-libéralisme version française : Histoire d'une idéologie politique[END_REF].

Being critical of classical liberalism's limitations vis-à-vis explaining the evolution of capitalism and the emergence of the welfare state during the interwar period led Lavergne to proposing from marginalism theory a new theory of "consumer supremacy" to develop a neo-liberal organisation of the welfare state and the market capitalism: the cooperative Order [START_REF] Lavergne | L'ordre coopératif. Etude générale de la coopération de consommation[END_REF]1936]. He does not see the principle of free competition as being opposed to social justice, as "in the economic sense of the word, justice is a concept that is by definition amoral. It is simply the expression of the mechanic law of supply and demand" 6 [Lavergne, 1926, p. 61]. Social and economic inequalities are justified by the principle of "social opportunity", which reflects the "great inequality that exists between the talents and aptitudes of people" 7 [Lavergne, 1926, p. 584]. However, the concentration of capitalism and the oligopolies and cartels that existed during the interwar period question the liberalism principles, as when "the producers are not in competition, the capitalist regime becomes totally defective, not to say intolerable. Capitalism is based on a premise of competition" 8 [Lavergne, 1926, p. 45]. Lavergne's objective is to resolve the capitalist and democratic crisis by promoting the primacy of consumers on the marketwhich respects the "law of supply and demand"and the state, while simultaneously ensuring social justice considerations. Indeed, it is also in terms of "consumers born from state services" that citizens have "the right to also compete in the formation of general will and control of state machinery" 9 [Lavergne, 1926, p. 16]. However, to re-establish the prevalence of general interest in response to universal and equal suffrage, we need to create a complementary social suffrage in order to represent elites seeing as "the will and the competence of all elites, of all bodies that the culture and selflessness render them suitable to discern and wish the general good" 10 [ Lavergne, 1936, p. 61].

This double reform of the market and the state proposed by Lavergne is based on the emergence of a cooperative Order. He proposes giving the cooperative movement an autonomous doctrine of both socialism and liberalism that is also based on the latest scientific principles of marginalism theory. follow this theory, it is logical "to apply industrial management to consumer cooperatives […] if it is clear that public demand is the essential component of a product's value"11 [Lavergne, 1926, p. 37]. It is also necessary "to give at the entrepreneur any initiative" and "to dismiss any regime where economic management is exercised by authority, by obedience on direct orders from political power"12 [Lavergne, 1926, p. 37-38]. For Lavergne, the marginalism theory thus leads to a profound reformulation of the "cooperative trinity of formulae" that was formed around the abolition of profit, wage-labour and social classes. Firstly, cooperatives do not have to aim for the abolition of profitindeed, making profits is the goal for any enterprisebut should instead pursue a reasonable profit without transforming the efficiency of the capitalism production system. Secondly, we cannot abolish wage-labour given that modern technology creates "a necessary separation between a savers' community that, by mutual efforts, establishes enterprise, and a community of workers and engineers that puts assembled tools into service"13 [Lavergne, 1926, p. 68]; the cooperative Order can only improve employees' working conditions. Thirdly, social classes persist in the cooperative Order, but the "less unequal distribution" of wealth helps to "attenuate the class struggle which corrodes our modern societies"14 [Lavergne, 1926, p. 53]. Finally, the cooperative Order "is not something other than a powerful and methodical effort to introduce the greatest justice possible in economic relations, while accepting as given the individual selfishness and fundamental instincts of men, brief, while respecting the law of economic value which is essentially amoral"15 [Lavergne, 1926, p. 70].

Lavergne estimates that the cooperative Order will be realised by a double movement that arises from both the bottom of consumer cooperatives (and "emerges spontaneously from the soil") and the top of government cooperatives (which results from a state's willingness, bearing in mind that government cooperatives are similar to consumer cooperatives but instead have members that are legal entities, such as states, townships and local authorities). Lavergne's most important influence in the French cooperative movement was promoting a new kind of "government cooperative"or "régie coopérative" in Frenchin order to associate "in the democratic distribution of profitthe only result of the state managementthe fecundity on the free initiative and responsibility of private industries"16 [Lavergne, 1926, p. 485]. Lavergne observes that if consumer cooperatives have slightly developed in recent decades, the state will be unable to control the economy: "public authorities cannot be good industrialists or good merchants"17 [Lavergne, 1926, p. 485]. By balancing the economic efficiency of liberalism with the social justice of cooperative principles, "The cooperative Order permits socialisation without state control. It authorises an indefinite socialisation of economic enterprises without compromising either public liberties or private liberties. […]. It is the only social principle which manages to come out of the conflict of individual selfishness and human mediocrity, a just and liberal order" 18 [Lavergne, 1926, p. 47].

The cooperative organisation work of Hyacinthe Dubreuil: The liberalisation of labour and workers in the modern corporation

Despite publishing some best sellers, 19 Hyacinthe Dubreuil (1884Dubreuil ( -1975) ) is little known in the French cooperative movement. He started his career as a worker and trade unionist and later became a top official at the International Labour Office (ILO); he also influenced the emergence of management science in France. Close to neo-liberal and neo-corporatist reformers during interwar period, Dubreuil tried his entire life to promote a new way of organising work in modern firms based on cooperative principles [START_REF] Ribeill | De La République Industrielle de Hyacinthe Dubreuil aux groupes autonomes : une vieille idée proudhonienne sans avenir ?[END_REF]].

Dubreuil's personal history as a former worker led him to propose scientifically studying the discouragement of the working class in order to promote a "rational use of the human factor" 20 [Dubreuil, 1923, p. 15]. He suggested different causes for workers' discouragement (e.g., recruitment and redundancy, work organisation and conflicts, and low incomes) but was critical of the conventional wisdom concerning worker morale, seeing as "in the best interests of social production, it may be necessary to understand that labour will not show prodigies what it is capable either by narrow rules or by stupefying slavery of a robot discipline 21 [Dubreuil, 1923, p. 70]. If the workers' claims pass by their liberty within the organisation of the company, none of the socialist proposals (such as the abolition of private property, the conquest of state power and critiques against mechanization) represent solutions for the labour crisis in modern capitalism. Worker cooperatives are also not a solution, as "a same vice should hurt them if the worker can't find on worker cooperatives that the same mediocre and passive life, and this vice should be the cause of the relative stagnation of this kind of enterprise, which however already contains a partial application of cooperative principles. This internal obstacle follows, in my view, a false and arbitrary conception of equality" 22 [Dubreuil, 1923, p. 221]. Nevertheless, Dubreuil considers that "if we exclude worker cooperatives, we will not reject the cooperative principle. We will look instead to develop them, but in another form" 23 [Dubreuil, 1923, p. 151]. Examples of cooperatives 18 «L'ordre coopératif permet la socialisation sans étatisation, il autorise une socialisation indéfinie des entreprises économiques sans compromettre ni libertés publiques ni libertés privées. […] Il est le seul principe social qui réussisse à faire sortir du conflit des égoïsmes individuels et de la médiocrité humaine un ordre juste et libéral » [Lavergne, 1926, p. 47]. 19 Two of his books were published in English: Dubreuil, 1930, Robots or men? A French workman's experience in American industry, New-York, Harper & Brothers;and Dubreuil, 1939, A chance for everybody, A liberal basis for the organization of work, London, Chatto & Windus. 20 « Utilisation rationnelle du facteur humain » [Dubreuil, 1935, p. 199] 21 « Pour le plus grand intérêt de la production sociale, il faudra peut-être arriver à comprendre que jamais le Travail ne montrera les prodiges dont il est capable par le moyen de règles étroites, ni par l'esclavage abrutissant d'une discipline d'automates » [Dubreuil, 1923, p. 70]. 22 « Un même vice doit donc les frapper pour que l'ouvrier ne trouve dans les unes comme dans les autres que la même vie médiocre et « passive », et ce vice doit être la cause de la stagnation relative de ces entreprises, qui contiennent pourtant déjà une application partielle des principes coopératifs. Cet obstacle intérieur résulte, à mon sens, d'une conception fausse et arbitraire de l'égalité » [Dubreuil, 1923, p. 221]. 23 « Si nous écartons la coopérative de production, nous ne repousserons pas le principe coopératif. Nous chercherons au contraire à le développer, mais sous une autre forme » (1923, p. 151). such as the Familistère 24 show us that it is possible to liberate the workers in an industrial firm and thus "to also impart an entrepreneurial spirit in a worker" 25 [Dubreuil, 1935, p. 90].

As response to the labour crisis during the interwar period, Dubreuil proposes a new organisation of work based on cooperatives principles. His aim is to reconcile the self-interest of workers and capitalists with the collective interest of the enterprise, and thus "to realise labour productivity at the same time as peace among these various actors" [Dubreuil, 1923, p. 120]. The main issue is to know "by what practical arrangements labour could be organised for workers in order to bring their conditions to the same level as their employers?" 26 [Dubreuil, 1935, p. 70]. The solution is to develop "the association virtue within labour, in order to obtain this art of liberty and responsibility" 27 which characterizes the entrepreneurial spirit [Dubreuil, 1923, p. 18]. Dubreuil proposes a new organization of companies basing on "every technically isolated subdivisions" would take the form of a working teams with a technical and budgetary autonomy. He offers the following elaboration: "The enterprise could be taken the aspect of juxtaposed cells, in which the sought-after equilibrium between the self-interest of each individual and the collective interest of enterprise could be established. All relations inside an enterprise, both among individuals and the group than the group and the enterprise, would tend to take the form of purely commercial relations, in which this notion of subordination, which is inexhaustible in the supply of conflicts, would disappear" 28 [Dubreuil, 1935, p. 115]. These autonomous unities of production could take the form of "cooperatives without capital". At the beginning of more productivity and social peace, the "advantage of this system increases even further in cooperative organisations where everyone is prompted to a proportional interest in his situation, to ensure performance excellence: at first in his personal ardour, then in the judicious choice of the best chief" 29 [Dubreuil, 1923, p. 75]. Indeed, the cooperative teams will be based on a "natural inequality determined by only the difference of capacities" 30 [Dubreuil, 1935, p. 220]. This is in contrast to "egalitarianism", which weakens worker cooperatives. The cooperative organisation of labour can be implemented by a principle of "promotion" that consists of "placing everyone at the starting line with equal opportunities as well as equal resources" 31 [Dubreuil, 1935, p. 224] in order to discover "men endowed with chief capacities" 32 [Dubreuil, 1935, p. 236]. The cooperative organisation of labour inside the modern corporation allows workers to be liberated while productivity is increased for employers, but it is also a new kind of corporate solidarity in that every autonomous team of workers assumes "aspects of a real school of social life" 33 [Dubreuil, 1935, p. 255].

After being viewed ambiguously by some neo-liberal and neo-corporatist reformersespecially during Vichy France (1940)(1941)(1942)(1943)(1944)) -Dubreuil's proposition to develop a cooperative organisation of labour was later taken up again in the 1970s by a French neoliberal think-thank (namely the "Hyacinthe Dubreuil Committee" 34 which was chaired by the influential neoliberal economist Jacques Rueff) as well as by self-management movements [START_REF] Ribeill | De La République Industrielle de Hyacinthe Dubreuil aux groupes autonomes : une vieille idée proudhonienne sans avenir ?[END_REF].

3 The role of cooperatives in the evolution of French socialism:

George Fauquet and Marcel Mauss

The evolution of French society during the interwar period and the growing influence of Keynesian ideas during the 1930s has progressively called into question the ideal of the republic cooperative as a way to integrate a cooperative sector within the welfare state. Two theorists and promoters of the French cooperative movement during the first half of the twentieth century, namely George Fauquet (3.1) and Marcel Mauss (3.2), are important witnesses of the reconfiguration of the relationship between socialism and cooperative movements during the interwar period.

The cooperative sector in the "Mixed Economy" by George Fauquet

Initially trained as a medical doctor, Fauquet became a senior official in the ILO's cooperative department during the interwar period. His professional activities and activism in the socialist movement enabled him to get close to the cooperative movement to the point that he held important related responsibilities. His socio-economic approach to cooperatives played an important role during the second half of the twentieth century, especially within French cooperative research (e.g., the writings of Claude Vienney).

Like other cooperative theorists of this period, Fauquet remarked that "ahead of the new forms of capitalism, ahead the increasing state power on economic life, the thinking on cooperatives cannot be attached to conceptions that arose during the last century" 35 [Fauquet, 1942, p. 5]. The cooperators previously had a vision of an "infinite development of cooperative institutions at the expense of the external environment which they had to absorb piece by piece, but which would stay until the total absorption an environment of free competition" 36 [Fauquet, 1942, p. 11]. However, in the modern economy cooperatives "can only aim to set up a sector" 37 [Fauquet, 1942, p. 15]. Critical of "theories that tended to draw up doctrinal barriers between the different forms of cooperation" 38 [Fauquet, 1942, p. 18], Fauquet promoted a unitary approach to the cooperative sector that combined all kinds of 33 « L'aspect d'une véritable école de vie sociale » [Dubreuil, 1935, p. 255]. 34 Comité Hyacinthe Dubreuilcomité d'action pour le développement des équipes autonomes d'entreprises 35 « En face des formes nouvelles du capitalisme, en face de l'emprise croissante de l'État sur la vie économique, la pensée coopérative ne peut rester attachée à des conceptions nées au cours du siècle dernier » [Fauquet, 1942, p. 5]. 36 « Un développement indéfini des instituions coopératives aux dépens d'un milieu extérieur qu'elles devaient absorber fraction par fraction, mais qui resterait jusqu'à l'absorption complète, le milieu de la libre concurrence » [Fauquet, 1942, p. 11]. 37 Les coopératives « peuvent seulement viser à en occuper un secteur » [Fauquet, 1942, p. 15]. 38 « Les théories qui tendaient à dresser des barrières doctrinales entre les différentes formes de la Coopération » [Fauquet, 1942, p. 18].

cooperatives, but the question was then how "to determine what place the cooperative sector intends to claim in an organized economy or in an organisation's process"39 [Fauquet, 1942, p. 12].

Fauquet distinguishes between the public sector, the capitalist sector, the private sector (which includes domestic, farmer and crafts economies) and the cooperative sector. In particular, the cooperative sector is composed of different "forms of cooperation that are already linked or tend to be interlinked, both morally and economically" 40 [Fauquet, 1942, p. 14]. This sector tends to merge with the private sector, but it struggles and competes with the capitalist sector. The aim of cooperative institutions is to reduce "the breadth of the central zone occupied by the market and the capitalist economy" 41 [Fauquet, 1942, p. 31]. This is done through a process of cooperatively integrating the initial and final economic phases, in which "man cannot be reduced to the role of a simple element of an impersonal system" 42 [Fauquet, 1942, p. 86]. The relationship between the cooperative and public sectors is more complicated, because "an economy organized through a cooperative effort differs profoundly from the other realised and planned of organized economy" as the public sector. Indeed, "cooperative link is a federative link" 43 which differs from links within the public sector [Fauquet, 1942, p. 45]. Furthermore, the public and cooperative sectors have common aspirations regarding "the substitution of the notion of organized service to that of the struggle for profit and domination" 44 [Fauquet, 1942, p. 48]. However, the public sector is not the only way to organise the economy, because the "state is, necessarily and by nature, a coercive force: if it invaded the entire economic life, man would be submitted to the most appalling tyranny" 45 [Fauquet, 1942, p. 50]. On the contrary, we must permit "a meeting of two systems, and, at the same time, the meeting of two principles". 46 This can be achieved through a flexible link between cooperatives and the state that creates "a relay chain between the control centres of the economy and the depths of social life" 47 [Fauquet, 1942, p. 50]. The cooperative sector has to find its own place in a mixed economy that is partly controlled by the state in order to widen "the field of social life where man ensures, for the common good, the responsible use of his liberty" 48 [Fauquet, 1942, p. 52]. When some commentators stressed that Fauquet had abandoned the utopia of the republic cooperative, however, he proposed also an alternative organisation of economic liberalism without falling into a collectivism system: "the automatic responses ensured at least theoretically the equilibrium of a liberal economy: it is from the free play of elements grouped federally into the cooperative organisations that the command economy can expect the same regulating action" 49 [Fauquet, 1942, p. 51].

The theoretical contribution of Fauquet does not stop at the cooperative sector; he also develops a new analysis of cooperative organisations that is designed like an association of individuals who are pursuing their aim using a common enterprise. The cooperative institutions are composed of "two elements jointly, one social and the other economic: an association of individuals who recognize on the one hand a similarity to some of their needs and on the other hand the possibility of better satisfying these needs through a common enterprise that by individual means; a common enterprise whose particular purpose responds precisely to the need to satisfy" 50 [Fauquet, 1942, p. 19]. Within a cooperative, the notion of democracy arises from the social relations between association members and the notion of service arises from management relations between enterprise members, but "if it fails in its moral task, a cooperative will fail in its economic task" 51 [Fauquet, 1942, p. 25]. The strength of cooperatives is precisely to promote moral relations between individuals and the society by associating persons and economic relations through a common enterprise: "the common action is both a condition and an ends to autonomy and independence for human individuals" 52 [Fauquet, 1942, p. 41]. If capitalist developments "have little by little detached economy from society and thus given birth to the dry realities that have served as a model for the abstractions of economists" 53 [Fauquet, 1942, p. 44], within cooperative institutions individuals "become aware of relations that unite them […]. As in all cooperation developments, they contribute to restoring the predominance of society in the economy" 54 [Fauquet, 1942, p. 36]. Even if Fauquet provides prominence to economic and management in his new theorization of the cooperative sector and institutions, he never forgets the humanist ideals of cooperation that previously existed in the republic cooperative. For Fauquet, "the first aim of cooperative institution is to improve the economic situation of its members; however, by the means that it uses, by the qualities that it both asks of its members and develops in them, it aims for and reaches the highest level. The goal of cooperation is then to make men who are responsible and in solidarity, who all rise to attain a full personal lives and together reach a full social life" 55 [Fauquet, 1942, p.42].

The socialist cooperative in the nationalisation of Marcel Mauss

Marcel Mauss was a French sociologist and anthropologist who is particularly well known for his book The Gift (1925). He was also very committed to the socialist and cooperative movements during the first half of the twentieth century. Influenced by Jean Jaures and Charles Gide, in his scientific papers and articles in popular newspapers he developed an original conception of socialist cooperation that combined his sociologist and socialist positions [START_REF] Dzimira | savant et politique[END_REF].

For Mauss, cooperative action is part of broader socialist action that also includes trade unions and the Socialist Partyin other words, the "three pillars of socialism". He already in 1899 stressed that "the trade union and socialist cooperative are the foundations of the future society […]. They constitute both the force and resistance of socialism; they are its means of creation" 56 [START_REF] Mauss | L'action socialiste[END_REF]. In addition to the cooperative papers he wrote during the interwar period, Mauss also shared reflections on cooperation in his writings about The Gift (1924) and the bolshevism (1924). However, it is a work that Mauss drafted in the 1920s but was edited in 2013 that interests us in relation to understanding his cooperative conception, namely The Nation [2013]. The historical process of nationalising economic and political life in our modern societies is intimately linked to the emergence of democratic socialism, but the concentration of capitalism after the First World War led to an exacerbation of social inequalities; indeed, "capitalism does not emerge declined, it comes out relatively augmented by the crisis; what was missing, it's it normal aspect; it is now monstrous and deranged" 57 [Mauss, 2013, p. 322]. Some large capitalist and international corporations concentrate economic power among "a group of relatively few great administrators, which contains many boards of directors and combines affairs with others affairs. There is already a concentration of powers, but these powers are not in the hands of the state" 58 [Mauss, 2013, p. 329]. Like others authors, Mauss estimates that to integrate the cooperative movement within a socialist action adapted to the economic context of the 1920s, the cooperative movement should take the capitalism concentration into account in its strategy. By socialism, Mauss means "ideas, forces, groups which tend in a modern nation to create the entire economic life. This process occurs in a nationalisation way, that is, through the establishment of an industrial and commercial property under control of the nation, through the establishment a form of collective property appropriate to various communities which make up the nation and who are currently more or less deprived" 59 [Mauss, 2013, p. 255]. The nationalisation process is based on a double "political-economic" movement that comes from the top through "the growing awareness and the direction of economic services of the nation" 60 , such as monetary policies and labour legislation. However, it is also a movement arising from the bottom that is defined as "mid-voluntary and midobligatory, mid-economic and mid-moral; it is supported by citizens arriving at the awareness of new interests and legal forms and then imposing them consciously and voluntarily on the state" 61 [Mauss, 2013, p. 296]. Three institutions play important roles in the bottom-up movement: trade unions (in establishing a labour democracy), mutual insurances (in establishing a mutual democracy) and cooperatives (in establishing a consumer democracy). It is the popular and democratic rules which characterise the foundation of these institutions, and Mauss prefers to use the term democracy (as opposed to socialism) in order to exceed "this eternal antinomic opposition of democracy and socialism that everyone opposes as if there were contradictory principles and as if it were not the same 56 « Le syndicat et la coopérative socialiste sont les fondements de la société future. […] Elles font la force et la résistance du socialisme ; elles sont ses moyens de création » [START_REF] Mauss | L'action socialiste[END_REF]. 57 « Le capitalisme ne sort pas diminué, il sort augmenté relativement de la crise ; ce qui a disparu, c'est son aspect normal ; il est monstrueux désormais et détraqué » [Mauss, 2013, p. 322]. 58 « Un groupe de grands administrateurs, relativement peu nombreux, figurant dans de nombreux conseils d'administration, abouchant les affaires les unes avec les autres. Il y a déjà concentration des pouvoirs, mais ces pouvoirs ne sont pas entre les mains de l'État » [Mauss, 2013, p. 329]. 59 Mauss « entend par socialisme, des idées, des forces, des groupes qui tendent dans une nation moderne à régler l'ensemble de la vie économique. Ce processus s'opère par voie de nationalisation, c'est-à-dire d'instauration de la propriété industrielle et commerciale sous le contrôle de la nation, par l'instauration d'une forme de propriété collective appropriée aux diverses collectivités dont se compose la nation et qui en sont actuellement plus ou moins privées » [Mauss, 2013, p. 255]. 60 « La prise de conscience et de direction des services économiques de la nation » [Mauss, 2013, p. 296]. 61 « Mi-volontaire et mi-obligatoire, mi-économique et mi-moral, il est le fait de citoyens arrivant à la conscience de nouveaux intérêts, de nouvelles formes juridiques et les imposant consciemment et volontairement à l'État » [Mauss, 2013, p. 296] emancipation movement of both the nation and the citizen" 62 [Mauss, 2013, p. 333]. However, Mauss remains critical of the worker, credit and agricultural cooperatives, as they are "related to the actual regime rather than to the future regime of the society. In fact, they are above all associations of little capitalists within a capitalist legal form" 63 [Mauss, 2013, p. 371]. Instead, he sees consumer cooperatives as having since their origin "a huge revolutionary ambition. In fact, only rare mass movements have what is right and are what they promised to be. Consumer cooperation immediately thinks to reform the regime not only of consummation, but also of production and property" 64 [Mauss, 2013, p. 373]. In a 1936 article in which Mauss discusses the conclusions of Fauquet's book (which he partially shares in the article), he nevertheless emphasises that it is consumer cooperation that "seems to be the one which has the most displaced economic and legal axes, which constitutes the most collective (and not individual) reserves, and creates the most public services" 65 [START_REF] Mauss | Note préliminaire sur le mouvement coopératif et spécialement sur le mouvement coopératif de consommation, plus spécialement sur le mouvement coopératif français[END_REF]. He concedes, that the cooperative movement has several limitations, such as a dependency on political changes, difficulties related to democratic and voluntary organisation, and risks of management and technical excesses at the expense of the cooperative ideal. Nonetheless, the French cooperative movement should follow the example of English cooperatives, which are veritable "centres of social life" 66 for workers, strikers and unemployed persons; indeed, English cooperatives "succeeded to maintain the movement, its ideal and its force". 67 However, "if cooperation has its internal and external limits, there is at least a point at which its limits are far away: it is when cooperation leaves the commercial, industrial and financial world and enters into the moral world. It is why […] I stay a socialist and workerist cooperator" 68 [START_REF] Mauss | Note préliminaire sur le mouvement coopératif et spécialement sur le mouvement coopératif de consommation, plus spécialement sur le mouvement coopératif français[END_REF]. 62 « Cette éternelle opposition antinomique de la démocratie et du socialisme, que les uns et les autres opposent comme s'il y avait des principes ici contradictoires, et s'il ne s'agissait pas du même mouvement d'émancipation, à la fois de la nation et du citoyen » [Mauss, 2013, p. 333]. 63 « Plutôt apparentées au régime actuel qu'au régime futur de la société. En fait, ce sont avant tout des associations de petits capitalistes sous une forme juridique capitaliste » [Mauss, 2013, p. 371]. 64 « Une immense ambition révolutionnaire. En fait, elle est un des rares mouvements des masses qui est bien ce qu'il avait promis d'être. Elle a tout de suite pensé à réformer le régime non seulement de la consommation, mais encore celui de la production et de la propriété » [Mauss, 2013, p. 373]. 65 « Parait être celle qui a le plus déplacé les axes économiques et juridiques, qui constitue le plus de réserves collectives et non individuelles, et rend le plus de services publics » [START_REF] Mauss | Note préliminaire sur le mouvement coopératif et spécialement sur le mouvement coopératif de consommation, plus spécialement sur le mouvement coopératif français[END_REF]. 66 « Centres de vie sociale » [START_REF] Mauss | Note préliminaire sur le mouvement coopératif et spécialement sur le mouvement coopératif de consommation, plus spécialement sur le mouvement coopératif français[END_REF]. 67 « Elles ont réussi à y maintenir le mouvement, son idéal et sa force » [START_REF] Mauss | Note préliminaire sur le mouvement coopératif et spécialement sur le mouvement coopératif de consommation, plus spécialement sur le mouvement coopératif français[END_REF] 68 « Si la coopération a ses limites internes et externes, il y a du moins un point où ces limites sont très lointaines : c'est lorsqu'elle sort du monde commercial ou industriel ou financier et qu'elle entre dans le monde moral. C'est pourquoi […] je reste un coopérateur socialiste et ouvriériste » [START_REF] Mauss | Note préliminaire sur le mouvement coopératif et spécialement sur le mouvement coopératif de consommation, plus spécialement sur le mouvement coopératif français[END_REF].

Conclusion

The cooperative movement is today one of the most important social movements in the world, and the recent crisis of financial capitalism has given a new impetus to many cooperative initiatives in various socioeconomic activities. Sometimes presented as an economic alternative to "(neo)liberalism" the 'market economy' or 'capitalism', the cooperatives are also considered a way to "modernise" the welfare state in the trend of the new public management and to promote a kind of "corporate social responsibility" and new "social entrepreneurship". A certain number of historical tensions still remain in cooperatives and social economy initiatives, for example between philanthropy and self-help, and we can find even today different ideological positions that are structured around liberalism, socialism, Catholicism, Protestantism, et cetera. These initiatives inherit from an ambiguous tradition and reinvent (often without knowing it) cooperative practices and ideologies from other times. More specifically, the interwar period can be seen as a veritable ideological and institutional laboratory of "the short twentieth century" (to use again the formulation of Eric Hobsbawm) until the last crisis of 2008. The ambiguity of the role played by the social economy and some cooperatives in the "neoliberal" policies that followed the 1980s in many advanced capitalist countries is not surprising if we remind ourselves of neoliberal thinkers' interest in the cooperative movement during the 1930s. The "government cooperative" proposed by Lavergne can be compared to the "public-private partnership" that is developing today; Lavergne's "cooperative Order" is sometimes close to the "social market economy" promoted by the European Union or the project of "Big society" by David Cameron. The new cooperative organisation of work promoted by Hyacinthe Dubreuil brings to mind The New Spirit of Capitalism published by Eve Chiapello and Luc Boltanski [1999[START_REF] Boltanski | The New Spirit of Capitalism[END_REF], in which they illustrate how capitalism abandoned the hierarchical Fordist work organisation starting in the middle of the 1970s and developed a new networkbased organization founded on employee initiative and relative work autonomy (but with more material and psychological insecurity for workers)a new organization of work also called the neoliberal enterprise [START_REF] Coutrot | L'entreprise néo-libérale, nouvelle utopie capitaliste ?[END_REF]. Conversely, some cooperatives and social economy initiatives, particularly in countries deeply affected by the crisis and by austerity policies, renew with practices and ideologies that had developed in the labour and socialist movement. The position of George Fauquet on a unified cooperative sector complementary to the public sector in order to control and reduce the capitalist sector was also a position shared by many socialist promoters of a unified social economy or third sector during the 1980s; today, economists such as Christophe Ramaux consider the social economy one of the pillars of the social state [Ramaux, 2010]. The considerations of Marcel Mauss about reciprocity, the cooperative movement and socialism are also found today more or less explicitly in solidarity economy theories and movements [START_REF] Laville | Avec Mauss et Polanyi, vers une théorie de l'économie plurielle[END_REF][Laville, , 2010] ] and in "the commons" and its struggles [START_REF] Dardot | Commun. Essai sur la révolution au XXIe siècle[END_REF].

The historical investigation of the cooperative movement and the lessons that economists can draw from this research can help us not only understand the contemporary and future dynamics of social economy and cooperatives, but also, more broadly, present another perspective on the history and the current issues of capitalism dynamics. The cooperative movement has a long and rich history, especially in Western Europeeven if this history is largely unrecognised by economists and in the social sciences in general. Historians on both sides of the Channel acknowledge the same fact: cooperative history is underrepresented. The British historian Nicole Roberston notes that "the co-operative movement deserves to occupy an important place in economic and social history. Compared to the attention given by historians to the Labour Party and trade unions, however, it is generally under-represented in labour history" [Robertson, 2010, p. 4]. French historian Michel Dreyfus made a similar remark quite close: "an essential component of the social economy, cooperation is, with mutuality, the oldest and the most powerful social movement in our country […]. However, and paradoxically, the history of cooperation, which had its moment of glory particularly during the 1920s […] was later abandoned for decades by historians of the social movement 69 " [Dreyfus, 2005, p. 13]. Concerning the interest of economists in the cooperative, the assessment is even more bitter. While the cooperative was the subject of important discussions among political economy during the nineteenth century (e.g. John Stuart Mill, Karl Marx, Léon Walras, Charles Gide, etc.) and during the first half of the twentieth century (the "cooperative manifesto of French intellectuals and academics" was initiated by personalities such as Albert Aftalion, Charles Gide, Elie Halévy, Marcel Mauss, Charles Rist, etc.), contemporary economists have largely abandoned discussions of cooperative economy, despite recent theoretical proposals from a Marxist and institutionalist perspective, and for many years it has been challenged by mainstream economists. Today, however, it is a major issue in the defence of pluralism in economics. In this regard, the conclusion of Albert Hirschman in The Passions and the Interests, remains a pressing issue today: "I conclude that both critics and defenders of capitalism could improve upon the arguments through knowledge of the episode in intellectual history that has been recounted here. This is probably all one can ask of history, and of the history of ideas in particular: not to resolve the issues, but to raise the level of the debates" [Hirschman, 1977, p. 135].

69 "Composante essentielle de l'économie sociale, la coopération est, avec la mutualité, le mouvement social le plus ancien et le plus puissant de notre pays. […] Pourtant, et de façon paradoxale, l'histoire de la coopération, qui a eu son heure de gloire, en particulier dans les décennies 1920 […] a été ensuite délaissée durant des décennies par les historiens du mouvement social » [Dreyfus, 2005, p. 13].

http://www.ilo.org/global/about-the-ilo/how-the-ilo-works/ilo-director-general/statements-andspeeches/WCMS_495232/lang--en/index.htm

2 Translations are mine unless otherwise noted. « L'association porte une autre conception du social, dont la réalisation passe par la constitution de collectifs instituant des rapports d'interdépendances entre individus égaux »[Castel, 1995, p. 423].

From 1889 until his death in 1932, Charles Gide develop a program of integral cooperativisation of the economy the Cooperative Republicbased on primacy of the consumer, which pass by three principle steps : firstly cooperativisation of trade, secondly cooperativisation of industrial production and a third phase to cooperativise agriculture. See an English translation in CharlesGide, 1921, Consumers' Co-Operative Societies, Manchester, Cooperative Union Limited.

The project of Republic cooperative disappeared in northern countries after the Second World War, but it reappeared during the 1960s with independence struggles in third world countries, as Guyana which achieved independence from the United Kingdom on 1966 and became officially the Co-operative Republic of Guyana on 1970[Draperi, 2012, p. 232-252].

« Remettre la gestion industrielle aux coopératives de consommateurs […] s'il est exact que la demande du public est l'élément essentiel de la valeur des produits »[Lavergne, 1926, p. 37].

« Laisser au chef de l'entreprise toute initiative, par conséquent l'obligation logique où l'on se trouve d'écarter tout régime où la gestion économique est exercée par voie d'autorité, par obéissance aux ordres directs du pouvoir politique »[Lavergne, 1926, p. 37-38].

« Une séparation nécessaire entre la collectivité des épargnants qui, de leurs efforts associés, fondent l'entreprise, et la collectivité des salariés et ingénieurs qui mettent en services l'outillage assemblé »[Lavergne, 1926, p. 68].

« D'atténuer la lutte des classes qui ronge nos sociétés modernes »[Lavergne, 1926, p. 53].

L'Ordre coopératif « n'est autre chose qu'un effort puissant et méthodique pour introduire la plus grande justice possible dans les relations économiques, tout en acceptant comme donné l'égoïsme individuel et les instants fondamentaux de l'homme, bref, tout en respectant la loi de la valeur économique qui, par essence, est amorale»[Lavergne, 1926, p. 70].

« A la répartition démocratique du profit -seul fruit de la gestion d'Étatla fécondité de la libre initiative et de la responsabilité de l'industrie privée »[Lavergne, 1926, p. 485].

« Les pouvoirs publics ne sauraient être bon industriel, ni bon commerçant »[Lavergne, 1926, p. 518]

« Déterminer quelle place il [le secteur coopératif] entend revendiquer dans l'économie organisée ou en voie d'organisation »[Fauquet, 1942, p. 12].


Achraf Lamlih

Philippe Freitas

Mohamed-Moez Moez Belhaj

Jérémie Salles

Vincent Kerzérho

Fabien Soulier

Serge Bernard

Rouyer Tristan

Sylvain Bonhommeau

Tristan Rouyer

A Hybrid Bioimpedance Spectroscopy Architecture for a Wide Frequency Exploration of Tissue Electrical Properties

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

I. INTRODUCTION

Bioimpedance spectroscopy (BIS) is a technique increasingly used for measuring the electrical properties of biological tissues [START_REF] Grimnes | Bioimpedance and Bioelectricity Basics[END_REF]. Since bioimpedance is a function of the physiological processes, variations of the composition of biological tissues can be seen as variations of the electrical impedance of the tissue.

In order to measure bioimpedance, current stimulation is generally used. Thus, a current containing a single or multiple frequencies is injected in the tissue under test via electrodes, the bio-modulated response voltage is then measured to determine the impedance transfer function.

Due to its non-invasive nature, its low cost and its ability to achieve low-power consumption, BIS is a suitable technique for long periods of monitoring. In fact, its use can improve the quality of healthcare delivered through earlier diagnosis and less invasive procedures.

Choosing an integrated system architecture for BIS is a difficult task as it is ruled by several constraints such as precision, bandwidth and measurement time. In the literature, two types of architectures could be found, frequency sweep based architectures and multitone-based architectures. These architectures provide different trade-offs between measurement time and precision. This paper presents a hybrid architecture providing fast measurements while maximizing precision. It has been defined for biological tissue electrical properties exploration over a wide frequency range. Its critical blocks are optimized for a bandwidth up to 10 MHz, an example of the design optimization is detailed for the current driver.

II. BIS ARCHITECTURES

A. Constraints

Building an integrated system for BIS is very dependent on the application and ruled by several constraints. The main constraints facing a BIS integrated system designer are bandwidth, precision and measurement time.

In the literature, many applications using single frequency bioimpedance measurements can be found. However, for a rigorous characterization of the biological tissue composition, the complex impedance needs to be analyzed over a large range of frequencies. In fact, each tissue molecule has a different response to a given frequency. Indeed the electrical permittivity of biological tissues decreases in three main steps corresponding to three dispersions [START_REF] Schwan | Electrical properties of tissue and cell suspensions[END_REF] : the α dispersion (10 Hz to 10 KHz), the β dispersion (10 KHz to 10 MHz) and the γ dispersion (≥ 10 MHz ). Since α and β dispersions are associated with the most relevant biological aspects [START_REF] Dastjerdi | Designing and implementing bioimpedance spectroscopy device by measuring impedance in a mouse tissue[END_REF], BIS integrated systems should be able to cover at least over these frequency ranges (10 Hz to 10 MHz). The Signal to Noise Ratio (SNR) is used as a precision metric. SNR cannot be improved by increasing the amplitude of the excitation signal, since it is limited by the safety requirements. Thus, care must be taken in order to maximize SNR over the frequency range of interest. Finally, in order to respect the system invariance criterion, measurement time should be as short as possible.

In general, two types of architectures could be found in the literature. Frequency sweep based architectures provide maximum precision while having long measurement times. On the other hand, multitone-based architectures provide short measurement times but their precision decreases with the number of frequency components in the excitation signal.

B. Multitone architectures

In BIS applications where the properties of the tissue under test are rapidly changing over time, fast BIS should be performed in order to respect the system invariance criterion. A solution is to use multitone signals in order to cover the chosen frequency range in a short time frame. However the energy of the signal is spread among its frequency points. Thus, multitone-based architectures provide short measurement times but their precision decreases with the number of frequency components contained in the excitation signal.

In the signal generation side, memory registers containing the binary multitone signal are sampled by a clock. The result is fed to a Digital-to-Analog Converter (DAC) that transforms the binary signal to pre-defined voltage levels. A Low Pass Filter (LPF) is used in order to get rid of the high frequency quantization noise. A current driver is then used to convert the multitone voltage to an excitation current.

In the response analysis side, an Instrumentation Amplifier (IA) is used to amplify the bio-modulated signal, an Analogto-Digital Converter (ADC) is used to convert the amplified signal to the digital domain, then a Discrete Fourier Transform is computed in order to determine the phase and amplitude of the frequency components of interest.

C. Frequency sweep architectures

The signal to noise ratio (SNR) is a critical criterion in order to assess the quality of the excitation signal, and thus the measurement precision. The SNR cannot be improved by increasing the amplitude of the excitation signal, since it is limited by the safety requirements. In BIS applications where high precision is needed, frequency sweep architectures are used in order to have a maximal SNR, since the energy of the signal is concentrated over a single frequency point each time.

In the signal generation side, a Phase locked Loop (PLL) is generally used as a frequency multiplier to get the higher frequency. On the negative feedback path, successive divisions are then performed to get the frequency components of interest. The digital signal is then scaled and delayed multiple times and the sum of the results is used to construct a sine wave of the targeted frequency. The scale coefficients and the phase shifts are computed so that the constructed signal has the lowest total harmonic distorsion possible [START_REF] David-Grignot | On-chip generation of sine-wave summing digital signals: an analytic study considering implementation constraints[END_REF]. A current driver is then used to convert the constructed sine wave voltage to an excitation current.

In the response analysis side, an IA is used to amplify the bio-modulated signal, then a lock-in amplifier followed by a low rate ADC feed the memory with bit words representing the real and the imaginary parts of the impedance.

D. Proposed hybrid architecture

When analyzing the two architectures previously detailed, an integrated circuit designer could notice that the constraints vary all over the α and β frequency ranges. In fact, at the α dispersion, the frequency sweep architecture has longer measurement times since we process the measurement chain entirely for each frequency. Moreover, for response analysis, the LPF establishment time is significant since it operates at low frequencies. At the β dispersion, the multitone architecture needs high sampling frequencies for the generation side in order to push further quantization noise. On the other hand, for the response analysis side, a high frequency ADC is needed which brings design complexity. Moreover, at the β frequency range, the bioimpedance magnitudes are low (tens of Ohms to several Ohms). Thus, the energy of each of the frequency components contained in the multitone excitation signal is low, making the specifications of the IA difficult to reach.

Fig. 1 shows the proposed architecture, it is a combination of the frequency sweep and the multitone architectures described in subsections II-B and II-C. It uses a finite state machine in order to choose the multitone generation and analysis for the frequencies of the α frequency region (10 Hz to 10 KHz), then it switches to the frequency sweep architecture for the β frequency region (10 kHz to 10 MHz) using the different multiplexers and demultiplexers. The current driver and the instrumentation amplifier are common blocks to the two architectures. Thus, their design process is critical since they

Io- Io+ V1 V2 V1 V2 Vin- Vin+ V3 V3 V4 Vdd V4 M1B M1A M2B M3B M2A M3A M4B M4A M5A M5B M6B M6A M7A M7B M11A M11B M12B M10A M12A M10B M11C M11D M8A M8B R M9A M9B Vref M13A M13B Ibias Idpb Idpa Vref Vref Vref
Ibias Ibias Ibias Fig. 2. Current driver architecture should be able to cover both the α and β frequency ranges. As an example, the current driver design and optimization is detailed in the next section.

III. CURRENT DRIVER DESIGN AND OPTIMIZATION

The current driver is a critical block of the presented architecture. Since α and β dispersions are associated with the most relevant biological aspects [START_REF] Dastjerdi | Designing and implementing bioimpedance spectroscopy device by measuring impedance in a mouse tissue[END_REF], the current should have a constant amplitude over these frequency ranges. This is achieved by having a large output impedance compared to the load. In fact, at lower frequencies, the sum of the electrodesinterface and tissue impedances have the highest magnitudes. Whereas at higher frequencies, stray capacitance represents the biggest challenge since it shunts the output resistance of the current driver which reduces its value.

A. Topology

Fig. 2 shows the architecture of the current driver [START_REF] Lamlih | Wideband fully differential current driver with optimized output impedance for bioimpedance measurements[END_REF]. It is a symmetrical fully-differential Operational Transconductance Amplifier (OTA). The first stage of the OTA consists of a degenerated differential pair. A degeneration resistance was added to the M1 transistors in order to enhance the linearity of the transfer function and to maximize the range of input voltage. The current across the differential pair branches has been set in order to have a bandwidth of operation covering the α and β frequency dispersions.

The output stage is a critical part of the current driver structure. It needs to provide a high output impedance while enabling a maximum output swing. Using regulated cascode current mirrors as the output stage architecture provides the best compromise between a high output resistance and the lowest output voltage. Since the OTA is fully-differential, a common-mode feedback (CMFB) loop is implemented to stabilize the common-mode output voltage at half supply [START_REF] Sansen | Analog Design Essentials[END_REF]. Due to low supply voltage specifications and in order to compensate for process variations, the output DC level is tunable using an independent reference voltage (Vref).

B. Output impedance increasing

The output stage of the current driver is critical. It has to provide an output current proportional to the input current at the high impedance output node. The output current amplitude needs to be constant regardless of loading. The important factors defining the performance of the output stage are thus output impedance, minimum output voltage and accuracy.

Bandwidth specifications imposed by the application require the use of short channel MOSFETs. A size reduction of the transistors leads to a decrease in the output resistance. Simple current mirror blocks or basic cascode structures are unable to provide an acceptable output resistance, especially at low frequencies where the load (electrode-tissue interface impedance) displays the highest impedance magnitudes, generating measurements errors in that frequency range. Therefore, improved output stage architectures for higher performances should be used.

Regulated cascode current mirror have the highest output impedance compared to simple or Wilson cascodes. It uses negative feedback in order to enhance the output impedance.

The improved regulated cascode shown in Fig. 3 is the basic block of the output stage. In order to minimize loading effects, the transistor M 6B is used to enhance the output impedance by a gm * ro factor compared to basic cascode structures. The output impedance of the improved regulated cascode can be written as :

Rout = ro M4 * ro M6 * gm M6 * ro M5 * gm M5 (1)
The main drawback of the regulated cascode is the output minimum voltage, which is equal to V th + 2V ef f . This could be improved to around 2V ef f by using the M 6 transistors in weak inversion. Although the matching of the M 6 transistors will be affected when operating in weak inversion, the loop gain of the structure is so important that the matching errors are negligible.

In order to enhance the accuracy of the current mirror, the drain to source voltages of M 3B and M 4B should be equalized. Since the V ds of M 4B is imposed by the gate voltage of M 6B , the proposed solution consists in using in a mesh an M 6BB transistor of similar size as M 6B biased with the same current, together with an M 2BB transistor of similar V gs as M 2B :

V ds M 4B = V gs M 6B
(2)

V gs M 6B = V gs M 6BB
(3)

V ds M 3B = V gs M 2BB -V gs M 2B + V gs M 6BB (4)
V ds M 3B = V gs M 6BB = V ds M 4B (5)

C. Results

The current driver was designed in a 0.18 µm AMS CMOS process operating at 1.8 V power supply. The current driver is capable of providing currents up to 600 µA peak to peak. The circuit design, simulations and layout were developed with Cadence suite using the toolkit provided by the foundry.

The Frequency response of the current driver transconductance is presented in Fig. 4. It has a transconductance of 860 µS up to 4 MHz decreasing to 854 µS at 8 MHz. The cutting frequency is located at 67 MHz. The current driver was loaded with a 1 kΩ resistor with only its intrinsic stray capacitance. Total Harmonic Distortion (THD) was simulated for a 400 µA peak to peak output current. The simulation results have showed a THD below 0.3% at low frequencies increasing to 0.6% at 8 MHz. The frequency response of the output impedance of the current driver is presented in Fig. 5. The output impedance is to 79 MΩ at DC up to 1 KHz. It decreases to 3.6 MΩ at 100 KHz, and to 324 kΩ at 1 MHz. The low frequency output impedance magnitudes are suitable for exploring the physiological processes occurring in the α region. At higher frequencies, the output impedance values are several orders of magnitude higher than the electrode-tissue impedance, since it is expected to decrease in the β region. A research presented in [START_REF] Rahal | A comparison study of electrodes for neonate electrical impedance tomography[END_REF] shows a comparison of the impedance magnitudes of several Ag/AgCl commercial electrodes in the frequency range (10 Hz-1 MHz), The average electrode-tissue impedance magnitudes were higher than 10 KΩ for frequencies below 10 KHz, equal to 5 KΩ at 10 KHz and 337 Ω at 1 MHz. The current driver output impedance results compared to the electrode-tissue magnitudes presented in [START_REF] Rahal | A comparison study of electrodes for neonate electrical impedance tomography[END_REF] show that it is capable of providing measurements with an error of 0.02% at 10 KHz and 0.1% at 1 MHz.

IV. CONCLUSION

A hybrid architecture for bioimpedance spectroscopy has been presented. This new architecture has been defined for a wide exploration of the electrical properties of the biological tissue. It combines the frequency sweep and multitone measurement techniques, thus providing fast measurement time and maximal precision over the α and β dispersions. Moreover, using the multitone measurement over the α dispersion and a frequency sweep over the β dispersion, enable the system architect to overcome the design challenges faced when using each technique separately. The current driver and the instrumentation amplifier are common blocks to the two measurement techniques, they have been designed in order to cover a frequency range of 10 Hz to 10 MHz. As an example, the current driver design and optimization using 0.18 µm CMOS AMS process has been presented.

Fig. 1 .

 1 Fig. 1. Hybrid bioimpedance spectroscopy architecture

Fig. 3 .

 3 Fig. 3. Improved regulated cascode architecture

Fig. 4 .

 4 Fig. 4. Current driver bandwidth

Fig. 5 .

 5 Fig. 5. Output impedance of the current driver

ACKNOWLEDGMENT

This research was part of the MERLIN-POPSTAR project funded by Ifremer and a Phd funded by Ifremer and labex Numev. We thank our colleagues from Ifremer/REM/RDT and RBE, CNRS, UM and IRD who provided insight and expertise that greatly assisted the research.