Based on recent field research, the paper suggests an interpretative model of territorial government in France. Relations between national and local authorities as well as policy-making processes suggest that the centralized State has faced a major decline of its hegemony and that decentralization reforms have induced a polycentric dynamics. Seven basic characteristics and three key properties of the model are discussed. The emerging model fits neither a new localism nor a new centralism pattern. It is the product of on-going incremental trade-offs between centrifugal and centripetal rationales. This complexity reflects a situation that is under the rather conservative and tight control of national politicians holding multiple local elected mandates.

INTRODUCTION

Up to the late 1970s France had been considered as a quasi-ideal case of centralized state (De Tocqueville 1856). The authoritarian and rather unexpected decentralization policy launched in 1981 by François Mitterrand, the newly elected President of the Republic, raised enthusiasm and attracted international attention [START_REF] Hayward | Governing France. The One and Indivisible Republic[END_REF], Page and Goldsmith 1987[START_REF] Schmidt | Democratizing France. The Political and Administrative History of Decentralization[END_REF]). During the following twenty years additional modernization decisions were taken by ruling politicians and central ministries. End of July 2004 the conservative majority at the Parliament approved a new and relevant transfer of policy domains from the State to the regions, the départements and the communes.

Have reforms fundamentally changed it all? How far has the State role and influence been reduced or transformed? How far have local and regional authorities taken advantage of massive transfers? The purpose shall be to understand the current state of territorial government, its basic characteristics and dynamics, to identify the actual functioning of the vertical relationships between national and sub-national levels as well as to understand how public authorities and organizations belonging to the same institutional and territorial level manage horizontal interdependencies. It is neither to list the decentralization reforms and describe their formal content nor to explain why France has become so active modernizing its way to govern sub-national public affairs -since the 1950s around four hundred and twenty decrees have been issued by Paris to modernize administrative procedures.

The debate between new localism and new centralism that goes on in a number of European countries may seem quite irrelevant for the understanding of the current French situation. Territorial policy making and politics are basically run and regulated by a polycentric and informal configuration involving national ministries and sub-national authorities so that none of them plays a leading role and may act in a fully autonomous way. Intricate interdependencies and complex exchanges provide a normative tissue and a political fabric in which the various parties are embedded, which access is not easy to outsiders and that is non transparent for citizens.

Social science research had identified informal characteristics such as cooptation processes between State agencies and local notables [START_REF] Grémion | Le Pouvoir Périphérique: Bureaucratie et Notables dans le Système Politique Français[END_REF] or the emergence of cities as strong political entities [START_REF] Thoenig | De l'incertitude en gestion territoriale[END_REF]. They operated at the margins of the centralized State design well before the 1981 decentralization. They still exist in the early 2000s, but in a global setting where the hegemony of ministries in Paris and prefects in the provinces has declined to a large extent and the pure centralized model has vanished.

Research has also evidenced that less government and more governance approaches handle regional and local public affairs (Le Galès and Lequesne 1998). Policy networks, issue communities, urban regimes, and subsidiarity are usually associated with governance. Nevertheless government from below practices [START_REF] Sellers | Governing from Below[END_REF] do not imply a full withdrawal of the State, and participative policy making does not imply that the political class loses control. The State apparatus still matters. The innovation is that it is just one player among many others. Sub-national bodies enjoy much autonomy but they do not act in a autarkic manner.

French decentralization and modernization processes have stopped half way between centralization and disjointed pluralism models. A system is operating which is more than just a compromise. The aim of the paper is to characterize its components and its inner regulation. It is also to explain the roots of its sustainability and legitimacy.

French decentralization and territorial administration coincides with the triumph of the elected politicians over the State executive branch (including the government and the national bureaucrats such as the prefects). Multiple political office holders control the reform agenda in a rather conservative and selfish perspective. Often described as a half reform because transfer of power from the State to territorial institutions did not include transfer of power from the local political class to citizens and inhabitants, the 1981 decentralization policy enhanced the role of such grands élus. Its sponsors and socialist thinkers such as François Mitterrand, Prime Minister Pierre Mauroy and Gaston Defferre, his minister if Interior, were seasoned notables and multiple office holders. They framed a decentralization scheme that would strengthen the power base of their colleagues across the country and among the various political parties.

The interpretative model presented below relies mainly on observations and information collected during a series of six empirical field studies led between 1991 and 2002. Their respective topic and methods shall be listed whenever mentioned. Other sources and recent studies shall also be used and cited that cover additional facets.

SEVEN BASIC CHARACTERISTICS

Neither hierarchical authority nor bargaining between fully autonomous equals structure the way the national State and sub-national public authorities manage their actual interdependence and exchange relationships in France.

A quite old tradition exists that ranks the French case as being rather unique and complex [START_REF] Ashford | British Dogmatism and French Pragmatism[END_REF]. To a large degree the idea that it is some exception while inter-governmental would be easier to understand in most other democracies is not convincing. Part of the prejudice may derive from the quite early emphasis made by social scientists on informal processes and actual practices. Reforms designed and implemented in the last two decades have not made the situation more simple, to say the least.

Territorial policy-making and politics suggest in a recurrent manner the existence and the importance Seven basic characteristics structure the way territorial affairs are handled and the social structure in which public officials are embedded. They blend functional creativity and democratic conservatism, competition mechanisms and cooperation norms, institutional innovativeness and power struggles.

A dense and thick institutional web

Sub-national affairs are handled by an exceptionally high number of political public authorities that have different legal statuses and operate at different geographic levels.

France is vertically sub-divided in four main levels: communes, intercommunalities, départements, and regions. About 54.000 sub-national public authorities govern some jurisdiction dealing with public affairs, which means one for slightly more than one hundred inhabitants. The institutional density is spectacular. The number of communes, for instance, is approximately equivalent to the sum of the communes in all the other country members of the European Union (see appendix 1) Not many countries experience such a dense, creative and diverse institutional landscape. The contrast is striking with the often under-estimated importance given to local government as compared with national affairs. The conventional metaphor that France is made of two parts, Paris and the provinces, is questionable. The periphery has been deprived from institutional means of selfgovernment. Increasing privatization of urban services and public utilities has occurred (Lorrain and Stoker 1997). Nevertheless the rise of market economy has not induced much outsourcing or privatization, and has not weakened public institutions. About 20 specific statuses exist: municipal councils, general councils for départements, regional councils, agglomeration councils, commune councils, inter-municipal syndicates, urban communities, pays, etc. Each has policy domains to handle and a territory to cover.

At one end of the spectrum are classic democratic jurisdictions such as the commune, the département and the region. Citizens elect their office holders. These bodies have their own administration and raise fiscal revenues. At the other end, ad hoc configurations exist which raison d'être is to administer a functional task -collection of garbage, economic development, etc. They are governed by so-called indirect democratic principles. Participation to them is optional, depending from the discretionary will of local and regional councils. Their ruling bodies are composed of officials designated by such councils. Many of them can be terminated at any time. A variety of hybrid organs are also operating, some being mandatory for the communes being part of their territory, others not, some being designed by law, others not.

Functional redundancies and geographical overlaps exist. In extreme cases up to nine sub-national public authorities handle local development policies in the same commune. Piling up direct and indirect democracy, generalist and functional authorities, designs sophisticated webs of actors and jurisdictions. Despite values such as equality, uniformity across the territory of the Republic is not achieved, quite the opposite.

State agencies as local operators

Despite decentralization central state keeps the monopoly of designing and changing the status of public sub-national institutions. Organic changes are top down driven. For instance the ways to select, train and pay employees of local authorities, whether city managers or street cleaners, are defined by national laws. The ministry of Interior is in charge of designing standard formal charts communes should enforce for their public agencies.

Central institutions are major daily operators handling local policies, as if no clear-cut separation would exist between the sphere of local affairs the state has in charge and the sphere of local affairs sub-national authorities have in charge. Most national ministries operate at the grass roots level. They cover domains such as education, agricultural development, crime and law, public health, sports, roads, just to mention a few. 95 % of the state employees work outside Paris, in other locations than those of national headquarters. Such a ratio is unique within the OECD and EU member states. Many thousands of field agencies are spread across France. For instance the ministry of Finance heads five separate administrative networks. Each has specific units at three levels: regional, départemental, local. State employees located sub-nationally outnumber sub-national authority employees by 40 %. In some domains, they even deliver additional services and are not linked to national policies. For instance they collect taxes on behalf of local authorities. Local authorities pay a fee in return. In some domains, non-mandatory services get supplied in a market-type of approach. In engineering, national state ministries like Agriculture and Équipement compete with local authority controlled technical agencies and with private sector companies.

Inside the state apparatus partitioning is general practice, whether hierarchically or horizontally. Tasks are subdivided between specialized silos. Each state field agency handles in a monopolistic way a geographical area. It also tends to protect its turf from any interference by other state colleagues. This pattern induces a dilution of horizontal cooperation between state agencies. The unitary French state looks like a loosely coupled network. Even the prefect, supposed to be the ultimate incarnation of the state authority and the carrier of general interest in each region and département, hardly can coordinate.

Competition between public authorities

Perfect centralization defines a world in which order and action are governed from the top. Who does what when how and with whom is non ambiguous. The French scene suggests that this is not exactly what happens. Asymmetries are often relaxed. Transitivities are exceptions. Neither the regional council nor the general council have some sort of constitutional right on the chart of lower level bodies such as communes. Regions, départements and communes are separate independent entities not linked by subordination principles. No one is entitled to supervise and to act as a trustee for anybody else.

Regions, communes and départements may be called generalists. Core competences are legally assigned to each of them. But the actual division of domains is far more informal and subtle. Tasks that are mandatory for communes may be delegated to other levels such as syndicates of communes (waste disposal, busing, etc) or are sub-contracted to private companies (water management, cemeteries, public transportation, etc). More important, a public authority may take the initiative to enter a policy area that is not part of its own core portfolio but belongs to the core domain of another territorial level. Three, four when not five different authorities belonging to different levels fund and provide goods or services for the same territory. Even state field agencies join the game and add complexity. Here they set up a joint policy with a city. There they provide services that overlap or are redundant with services produced by the same city.

Local authorities take advantage of such legal relaxations. They define their own agenda of issues and portfolio of domains. To intervene or not in such and such sector becomes a strategic tool for political purposes. Even with few monies allocated to a domain, the council may show to the population that it cares about it. The initiative to cover a wide array of projects may satisfy tactic purposes and symbolic uses: hindering the intervention of potential competitors, putting pressure on third parties to spend their own money in a domain the latter would not have covered spontaneously, increasing the brand awareness of the council and the image of its political leaders.

Public affairs structure an open market where players might compete to expand their visibility or to control a dominant market share. The formal division of core domains between players does not regulate most of their acts and non-acts, even in domains like law and crime where precise limits give exclusive ownership to state police. Local authorities sign exchange and cooperation agreements with foreign countries. Politically fashionable issues like sustainable development attract attention from several public authorities while others such as drug addictions remain neglected, kept to the lowest required standards. Some institutions or levels still matter more than others. But cards keep being redistributed among the players. The division of work and the modes of exchange are diversified across the national territory. Sub-national government is driven by micro-contexts and multiple players who co-produce informal and flexible designs.

A complex set of inter-institutional patterns

Another stylized fact deals with autonomy and coordination. Quite extensive use is made of cooperation patterns, but within certain limits.

Coordination as an administrative mechanism by which the center makes the parts compatible does not work well. Policies requiring the intervention of various field agencies inside a same jurisdiction are a nightmare to coordinate and to manage. Each ministry tends to keep its own professional culture and to protect its own networks with local public authorities and elites.

Between sub-national public authorities, the picture looks quite identical. While massive differences exist between authorities of the same territorial level -for instance between rural and urban communes -in terms of population size, financial resources or functional needs, local councils are fiercely fighting to remain the sole legitimate and democratically appointed masters of their jurisdictions. Communes or regions are inclined to prefer mutual avoidance. Mergers giving birth to large size jurisdictions are considered as the ultimate threat, as a way to commit political suicide. Functional coordination achieved through various institutional arrangements such as communes of communes is widely practiced because it provides alternative routes to survival.

Hierarchy and polity are weak mechanisms. Nevertheless many joint ventures and alliances occur. Functional interests and ad hoc circumstances more than partisan politics push autonomous bodies to become limited partners.

Extensive use has been made of quasi-contractual partnerships and opportunistic joint ventures since the late 1980s. Co-funding provides an illustration state of territorial government. A research made about budgetary processes in two regional councils (Nord-Pas-de-Calais, Limousin) indicates that about two thirds of the budgets controlled by regional councils are spent for co-developed programs and allocated to co-funded projects (Gilbert and[START_REF] Thoenig | La gestion des services communaux[END_REF]1999b). In the 1990s, a region co-funded an annual average of more or less 1.300 single investment projects.

Strong incentives and procedural requirements exist which are set up by outside authorities such as the European Commission or the French government. Two major formal set-ups for public investment funding are European Structural Funds and so-called Plan Contracts between the State and the Regions (Gilbert and Thoenig 1999a). To be eligible for such multi-annual subsidies, subnational authorities have to match funds allocated. Projects are jointly prepared, decided and assessed. Facts show a wide use of co-funding. About half of the budget spent by a regional council is allocated to a co-funded project. Mutualisation practices go far beyond formal set-ups. About one quarter of local projects are funded on a spot ad hoc and one shot basis. Here five partners (a village, the département, the national ministry of Agriculture, the local Chamber of Agriculture, the region) each paying one fifth of the bill, join to buy a one thousand and hundred euro forest acquisition. There two parties (a regional council and an urban community council) spend sixteen million euros each to build a state research center.

Partnerships may be lasting or spot, formalized or verbal. Cases are exceptional of tense when not conflicting situations emerging around the definition of the financial contribution each single participant party should pledge. Basically parties involved trust each other at all steps of the process, from the initial study of the project to the payment and the final evaluation, as suggested by direct observation of sessions of two regional councils, and corroborated by in-depth interviews of 42 State or local decision makers involved (Gilbert and[START_REF] Thoenig | La gestion des services communaux[END_REF]1999b).

The success of co-funding practices is amazing. Local authorities pro-actively look for issues that could be administered by quasi-contractual partnerships and projects that could become co-funded. State ministries play identical strategies. They want to find opportunities and ways to keep a role, to serve as partners, to increase their legitimacy as good citizens of local democracy.

A moderate level of democratic participation

One per cent of the inhabitants holds an elected mandate, mainly in rural municipal councils of less than 2000 inhabitants. In large urban communes the average percentage does not reach one half per thousand. France offers two opposite facets in terms of democratic participation.

As national surveys consistently show, the mayor of a commune is ranked as the political figure French citizens and inhabitants feels the closest to or likes the most, far ahead of the President of the Republic, the Prime minister, the member of the national Parliament or the regional councilman they elect. Compared with the State administration, local authorities are perceived as more efficient and responsive. While the commune remains the archetype of localism and old roots, the region has become a key element of territorial identity despite the fact that it has been established only twenty years ago as a full democratic institution (Observatoire Interrégional du Politique 2002).

On the other hand France does not rank among countries experiencing a lively local democratic participation [START_REF] Hoffmann-Martinot | Reform and modernization of urban government in France[END_REF]. Every sixth year, electors show an increasing lack of interest for municipal as well as regional elections. They also make more volatile choices in terms of parties and leaders. Voting less and in a more opportunistic way does not imply that people participate more on other political arenas. France has dragged its feet in the participatory revolution. Decentralization from the State to sub-national authorities was not followed by decentralization from the political class to the citizens. February 27, 2002, the national Parliament voted an institutional arrangement to increase direct democracy. The 50 communes with over 80.000 inhabitants have to create in a mandatory manner district councils open to the population, the process being managed under close control by local ruling politicians. More relevant set ups such as referenda or councils of citizens enjoying real autonomy might exist here and there. Their existence reflects the discretionary initiative of the ruling mayor and has no legal basis ensuring continuity.

Performance constrained actors

Local authorities in general look like typical formal bureaucracies. But this does by no mean imply that they function in a bureaucratic way, paralyzed by rigidities and poor efficiency.

The départements had been quite unanimously perceived as too small and unable to manage modern economic development policies. The creation from scratch of regions clearly was considered as the way to provide the adequate solutions. Surprisingly, far from remaining terminal authorities, départements have recovered strongly since the 1970s. More generally territorial jurisdictions have increased their performance ability in a spectacular manner. France had been lagging in terms of local infrastructure investments. While the state had helped quite much, a major turnaround was nevertheless achieved by the own efforts of modernization of the communes, regions and départements. Cities have substituted to 19 th century administrative clerks well-trained technicians and modern managers [START_REF] Lorrain | Les mairies urbaines et leurs personnels[END_REF] A survey made in 1996 on 266 city managers of communes of 15.000 inhabitants or more ( a sample of 15 % of the total) clearly suggests that y many standards French local public authorities achieve quite acceptable levels of efficiency and effectiveness (Thoenig and Burlen 1999a). They have been quite good on average at managing macro-financial crisis periods (Guengant 1995). They have kept their average annual expenses at a lower level than their revenues without salary cuts and lay-offs of staff. Techniques such as management control are of wide and professional use. A research made on the use of management tools on 487 communes of 12.000 inhabitants suggets that about 85% of their city managers combine modern human resource policies and analytical accounting techniques [START_REF] Thoenig | La gestion des services communaux[END_REF]. They provide at an acceptable cost and within rather balanced budgets rather above average public goods and services. Sub-national authorities, once considered as hopeless cases, are today perceived as relevant alternatives to central state. Miracles or even solutions, once provided by Paris, are expected today from regions and intercommunalities. Most regions and some cities have big chunks of money available for investment and current expenses that the national budget apparently does not any longer have.

Many communes or even départements may be too small geographically or too weak fiscally to recruit personnel. But the quasi-market structure described above provides flexibility -if a council lacks resources, it may most of the time find help from partners -and acts as an incentive pressure -citizens can compare and benchmark.

Constitutive reforms and incremental changes

Modernization reforms in general occur and get implemented in quite soft ways Problems are not addressed which would imply surgery to heal them. Politicians favor patience and pragmatism as a virtue. Incrementalism is considered as a wise style for a government to operate. The only exception was the brutal and comprehensive manner in which the 1981 decentralization reform was handled.

Old or "empty" institutions are not abolished by the will of the state, top down. France remains one of the very few European democracies that has not seen since the 1940s its parliament or central government reshape the general map of the communes and reduce by law their numbers, despite the fact that about 80 % of them host less than 20 % of the total population, each of them having less than 2.000 inhabitants. To decentralize to the local political elites the handling of major sub-national institutional issues could well imply that the State is weaker than expected, at least in territorial politics matters.

Innovation is most of the time generated locally. Paris just ratifies and legitimizes new solutions that had been built up here and there. Even before the law had been abolished that was forbidding local authorities to allocate grants to private firms, many municipalities had started to intervene in economic development matters. Experimentation has been recognized in 2003 by the French parliament as a constitutional right of local authorities. Since many years experimentations had been practiced sub-nationally. To some extent the state has recognized what was going on and given an impulse to widen initiatives.

The more incremental changes are made the more the level of factual autonomy of sub-national bodies is increasing. Faced with a specific problem the state designs a specific solution. As the result of the piling up by Paris of new institutional statuses and bodies devoted to inter-communal cooperation, communes, but also départements gain additional zones of discretion. They have more opportunities in terms of choosing which ad hoc body to join or not.

Unintended consequences are many. The major winner of decentralization policies may well be the département and its general council, considered in the 1970s as a terminal conservative body, and that plays today a key role in social affairs and road infrastructure. Transfers of policy domains from the State to local authorities may not get a unanimous support. The 2002-2004 decentralization launched by the center-right government under President Chirac has induced a majority of indifferent to negative opinions in public opinion. Disenchantment is gaining ground among reform activists and supporters.

THREE KEY SYSTEMIC PROPERTIES

Characteristics such as thickness, overlap, redundancy and competition, just to name a few of those underlined above, may appear as obstacles to modernization and rationalization. Their hegemony may imply that within 30 years, decentralization policies combined with the rise of urban regimes and the fiscal crisis of the State have not solved the paralysis of centralization and the arrogance of bureaucracies that had been underlined about the pre-1981 situation, but have increased even more chaos and disruption.

The fact is that chaos is not prevailing. Analysis suggests that some level of integration is achieved and that some collective action is possible between the various levels and players. Three main social constructs may be identified that provide in a latent way social regulation and political integration: hypercentralization of power inside local and regional entities, mutual dependence between the State and the sub-national authorities, accumulation of electoral mandates. They diffuse implicit but widely shared norms policy-makers learn by trial and error. They also are pragmatic, action-focused. They make the handling of public affairs less volatile, uncertain and complicated to handle.

They civilize conflicts and anarchy

Centralization of power at the sub-national level

Sub-national authorities are formally administered according to a parliamentary pattern. Inside each commune, département or region, citizens elect the members of a council. Acting as a collective body in an identical way than a parliament, the council members define policies and supervise implementation. Throughout this procedure an equality principle is institutionalized: each person has one vote. Decisions and nominations are the consequences of the aggregation of a majority of individual preferences.

In daily practice local democracy does not function exactly the way legal frameworks define authority and legitimacy. Power dynamics and asymmetric relationships emerge which are quite different. Public affairs are governed in a highly centralized manner. One role is by far dominant if not hegemonic: the president of the council.

The paradox of local power is quite visible in cities, as suggested by a series of case studies on10 rural and 10 urban municipalities -in-depth interview of their 40 elected officials and administrative officers -and observation of policymaking processes in 14 communes of more than 15.000 inhabitants in domains like budget, taxation, infrastructure building and urban renewal policies. [START_REF] Thoenig | De l'incertitude en gestion territoriale[END_REF]. The mayor is chosen among and elected by the municipal council. He chairs its sessions. He also heads the municipal bureau, a political body that is responsible for the execution of the wills of the council and supervises the city bureaucracy. To some extent a political majority or group delegates to one of its members some specific tasks to handle while keeping formal control of his acts and non-acts. In most municipalities evidence persistently shows that the mayor, far from being a peer, becomes the boss of his colleagues. He makes his supporters dependent from him far more than he depends from them. Power inside the municipal polity polarizes around him.

A mayor acts as a structural hole in a network. He provides integration solutions when it is missing while needed in action contexts. Municipal centralization combines two skills. The president of the council becomes the main when not monopolistic linkage between multiple arenas or worlds, and heterogeneous logics of action. At the same time he protects the rents he is benefiting from, fights the emergence of any direct linkage between them that would occur outside his control, and does even increase barriers. Divide and rule, partitioning and integrating, fuel the process (see appendix 2).

Four main arenas and logics of action are under the control of the mayor or president: administrative agencies, politics and policy-making, relationships with the population, foreign affairs.

The mayor fully controls municipal public agencies. He hires and fires the city manager (secrétaire general), an administrative officer. Both work very closely together. They share a common interest. The city manager relies on his exclusive access to the mayor's office. He therefore keeps under strong command a rather large number of staff and missions. The municipality being often the main employer of the commune means that a wide electoral basis may be available. Mayoral legitimacy and budgetary control are his key resources to establish his hierarchical authority inside the administrative machinery. (Thoenig and Burlen 1998a and b). The mayor can rely on the city manager not only because he appoints him, but also because the latter provides the mayor with a critical resource: the bureaucrats endorse his policy preferences. While other city council members sit on the municipal bureau, with the rank of adjunct mayors, most of the time they have no real influence and are even forbidden direct access to the municipal agencies. Many mayors are quite cautious not to offer them opportunities or rights (permanent office, signature, etc) that may jeopardize his hegemony. De facto he simultaneously acts as the prime minister and as a minister for finance, welfare, public works, etc. of the commune. From a broader perspective, nobody else in the commune has any capacity to run and coordinate the administrative machine.

The mayor also controls the agenda of the municipal council. His wills and preferences become those of his political majority. Far from being a representative of a party machine, he acts as the head of a broad coalition. In principle citizens have to choose among competing lists of candidates for council membership. To elect the mayor among its members is the task of the council. In fact the candidates for mayorship are publicly known in advance. Their name makes a difference for the citizens who vote.

Given the fact that there are no limits to the number of times council members can be re-elected, a mayor can run as long as he wants. He selects the persons who shall join his list for the next election. To set up a coalition reflecting the main characteristics of the electorate in terms of gender, age, residence or geographic/ethnic origins, matters a lot. National partisan politics is more a burden than a resource. The first task a new mayor should achieve is to make his political career immune from interferences of his own party national and even local organization. Facts confirm that in terms of local government the strongest party is not the national party but the party of the mayor. A municipal council is therefore structured around two different social roles: the mayor, the councilmen. The former is the least common denominator of the latter.

A third key domain covers the relationships with the inhabitants. Mayors and presidents of councils allocate much attention to them. In some cases quite much money is spent to improve their image and to attribute success to some personal characteristics of them. In a symmetric way the solution to problems expressed by people is perceived as a personal favor, as linked to the influence and discretionary will of a single actor: the mayor himself, even when he strictly conforms to law and rules or when third parties have the final decision to make.

Caring about such relationships and customizing to individuals means that the mayor expects to get an electoral return back in the future and keeps control. The more a request is individualized, the easier the mayor may either satisfy it -by giving an instruction to the specific agency which handles it, which a basic councilman cannot do -or just give the proof that he has tried the best -in case delivery is not feasible.

Another outcome of a personalized treatment of demands is structural. Making aggregation of single demands quite difficult to occur means that collective action is less likely to emerge and that general causes are less likely to find advocates. Fractions inside the municipal council are less able to pick requests from the population and use them as partisan politics issues without the consent of the mayor.

Foreign affairs are the fourth and perhaps most decisive factor allowing centralization to occur and last as legitimate. Many outside public authorities manage policy domains that have consequences for the commune, and allocate attention or resources that matter for the mayoral entrepreneur. He builds a monopole around relationships with key outside institutions. He -and nobody else among the council members -spends time remaining in touch and negotiating with the general council, the regional council, State agents like the prefect, public financial institutions in Paris, the European Commission representatives, etc. The portfolio also includes public utility companies and firms that are potential job providers or urban developers. The wider his network of easy access to extra-municipal decision makers, the more he acts as a powerful broker when not as the rain maker inside his commune. He knows in advance what initiatives third parties may take, which opportunities are available, whom to contact in order to speed up a request or to get some extra funding.

Centralization induces long tenures. French mayors are world's champions in terms of longevity in power, despite the fact that recent years have seen some higher turnover (Hoffmann-Martinot 2000). On average they remain in power for thirteen years. Not to centralize is a way to commit early political suicide.

Centralization induces a major relaxation of checks and balances principles [START_REF] Thoenig | Pouvoirs et contrepouvoirs locaux: rendre la démocratie aux citoyens[END_REF]. A mayor, a president of the general council or of the regional council acts simultaneously as the chief of the executive and the boss of the legislative branch for many years in a row. Issues at stake have a low public visibility. Some form of patronage may develop.

The polarization of power on one sole person has dramatically expanded from communes to départements. The case is even more spectacular at the regional level: 10 years only after their creation, 17 out of 21 regional councils were already governed by one dominant integrator: their president. Functional institutions running according to indirect democracy procedures -their leaders are nominated by the councils running the member authorities, not by the citizens of their district -should be added to the list. Decentralization from the State has helped diffuse and legitimize centralization in sub-national authorities

The State territorial embeddedness: from local cooptation to institutionalization of collective action

Cross-regulation and cooptation of local notables were key processes used by State bureaucracies to face territorial public affairs in pre-decentralized France (Thoenig 1975, Crozier and[START_REF] Crozier | The regulation of complex organized systems[END_REF]. Observation shows that in the current post-centralized system they still are in use, but have lost much of their importance.

In the early 2000s as in the early 1970s, State administrative pyramids keep functioning in a quite flexible manner. They show much sensitivity to local specificities and particularistic requests. They do not apply in a blind and rigid ways impersonal criteria. Grass roots agents take much distance with rules and headquarters. Inside their ministerial hierarchical pyramid, they even behave as advocates of causes and vested interests rooted in the local territory in which they are supposed to act as representatives of the state policy and enforce its wills. Flexibility in action and endorsement of localism are two basic processes that reinforce each other.

State agents invest much time and care building up local relational networks and getting support from local elected officials like mayors of communes or presidents of councils. They may even prefer to help the latter get their problems solved than control whether their acts and non-acts do conform to the legal and financial procedures defined by the State. For a prefect a major failure to avoid is to lose access to and confidence from the political elites who are located in his geographical jurisdiction. This also implies that the more state agencies are embedded in the local territorial jurisdictions, the less their headquarters can control them. Hierarchical coordination between bureaucratic silos is quite difficult to generate inside the State apparatus while the local dominant elected politician becomes, even without any explicit intervention, the common reference for each of them.

A major function of cross regulation is to build local political capital. State representatives working in field agencies internalize values and stakes that are those carried and shared by local groups. These values and stakes may in many cases be somewhat different from those emitted by the national headquarter. For grass roots agencies local embeddedness is a resource, not a constraint. Their agents are perceived by those they administer as human, sensitive, doing the best they can. In return State agencies rally local support. For instance the national police gets vital information from the public and invaluable support from municipalities.

Decentralization pushes national bureaucracies to be even more sensitive to achieve local political capital. The only problem is that, as compared with the old days of centralization, Paris has now many less resources to allocate at a time when local notables were substituted by heads of autonomous institutions. Cooptation and cross-regulation are insufficient mechanisms for the State apparatus to remain a relevant player in territorial affairs.

Within the last 20 years, most legal and financial controls of sub-national authority acts were transferred from ministries and prefects to autonomous judiciary bodies such as Regional Courts of Accounts. Facing increased competition from the firms, State agencies also have lost their quasi-monopoly on technical and administrative expertise. Several policy domains linked to transportation, social affairs, professional training and economic development have been transferred by the State to local authorities. By comparison local authorities have increased their resources and their autonomy in a relevant way. State public agencies do less by themselves than in the past, distribute less money and rely less on technical standards to impose their will. Faced with increasing budgetary shortages, Paris decentralizes the leftovers of the Welfare State to sub-national authorities.

Secondary analysis of case studies dealing with inter-organizational management of policies such as forests, industrial and domestic waste collection and treatment , crime and law, regional parks, and urban zoning indicate that a major change has occurred. Another model of governance has been endorsed and developed by the State: institutionalization of collective action [START_REF] Duran | L'Etat et la gestion publique territoriale[END_REF].

Being less able to pay the piper and call the tune, central government develops policy tools such as constitutive policies,. Specific arenas are supplied to territorial actors to address new issues in a context where traditional jurisdictions are too small and rigid to handle mobile problems, multiple public and private actors are involved in setting up solutions and implementing them, and uncertain technologies are used to handle problems difficult to define. Procedures and approaches are set up such as quasi-neighborhood and public hearings that enable single issue groups and private interests to express and share some common definition of specific problems to address. In parallel to democratically elected councils, ad hoc policy arenas exist that have a consultative role. Powerful and traditional institutions like chambers of commerce or agriculture, but also single-issue groups, economic lobbies and firms join public agencies and politicians to help identify specific problems and their causes, coordinate efforts to address them and elaborate in a quasiconsensual manner an action-oriented blueprint. Non-profit associations, moral entrepreneurs, citizen groups invest attention and energy Such participation schemes, one per policy domain, give birth to a kind of functional or administrative democracy. It is more than pure consultation and less than power sharing. It remains widely understood that the legitimate political bodies keep the final decision and that elected politicians remain in charge.

Touchy local issues like crime and law, for instance, have become co-governed and co-produced by such arrangements, as suggested by a field research made in three different regions and combining in-depth interviews of 64 State representatives (judges, police officers and prefects) and 8 mayors with direct observation of coordination meetings and the conduct of police interventions in real time. (Gatto and Thoenig 1993). Transportation [START_REF] Purenne | L'action publique par le bas. Les transports urbains de la Communauté urbaine de Lyon[END_REF], economic development [START_REF] Douillet | Action publique et territoire. Le changement de l'action publique au regard des politiques de développement territorial[END_REF], public housing among other domains illustrate how common such a phenomenon has become. Even policy domains that were pure monopolies of the State -such as R and D or higher education -have become extremely sensitive to the emergence of specific regional wills and initiatives.

One key consequence is that the mayor or the president of a territorial council becomes inside his territorial jurisdiction a much stronger actor than before and even than the prefect and the State representatives. This undisputed leader clearly stands now as the common denominator between multiple and weakened state units that are unable to coordinate their acts by themselves. His action platform and his power stakes shape a cognitive framework each of them does appropriate and all share.

The surprise is that nevertheless the State territorial role is still valued and desired by local politicians. While state field agencies have lost their former hegemony, they still matter for local politicians. One reason is that stronger local authorities use weaker bureaucrats for strategic purposes of their own. State field agencies offer access to decision-makers. Local and regional politicians use their managers as intermediaries, brokers and advocates to get some problems handled and some requests satisfied when third parties are influential in decision-making. State agencies supply non-partisan mediation. Their representatives are facilitators of local policy-making. Local administrators take advantage of the fact that state bureaucrats, while rather sensitive to territorial specificities, do not belong to the sphere of politics. Some prestige is linked to their status. Their careers are quite immune from outside influences. Mayors who are members of a same syndicate in charge of local development favor the intervention of a engineer of the ministry of Public Works to run their joint venture. Technical criteria and advice certified by state administrators are considered as a shelter against patronage and discretionary power. A collateral effect of state mediation is that some convergence is ensured between policy areas in neighboring jurisdictions. Similar issues are put on the agendas. Identical choice criteria are enacted. State agents share a common educational and cognitive background. In many cases communes or regions adopt action frameworks that are designed by state administrations and benchmarked through cross-regulation.

To get the prefect involved in municipal affairs or to receive some help from a State engineer allows the mayor not to become too exclusively dependent from the president of the general council and the bureaucracy he heads. The mayor avoids for instance the département or the region to become too powerful, to dictate its own terms. State local presence and intervention guarantees that public affairs as markets remain oligopolistic. State representatives offer an alternative channel and rationale to political agents and partisan intermediaries. The mayor has not to pay a price to more powerful local politicians. Being dependent from the good will of a bureaucrat keeps politics out of the picture.

State public agencies lower open wild competition between local authorities.

Their presence prevents the weakest to become prisoners of the strongest.

Accumulation of political mandates

Presidential and mayoral centralization simplifies government inside each subnational authority at the micro level.

Nevertheless tens of thousands autonomous bodies and territories combined with the absence of hierarchical subordination links between them does not help some form of coordination and integration.

A major constitutive process operates at a meso level. Six to seven hundred elected officials -sometimes called grands notables or grands élus -supply integration capacity between separate geo-institutional levels and across partitioned territories. Cumulating two or more electoral mandates is the way for a local administrator and politician to join such a very influential and exclusive club.

French laws allow the same person to exert at the same time more than one electoral mandate. A municipal council member may also be a regional council member and a national senator in Paris, or a member of the European parliament in Strasbourg. Law puts some modest restrictions to accumulating national/European and local mandates. For instance it is not allowed to be a president of the regional and a president of a general council. An extensive use is made of elected local mandate accumulation. Around two thirds of the members of general councils also act as local mayors, not counting those who are mere municipal council members.

Top positions are concentrated in a few hands. National as well as European electoral mandates are linked with sub-national electoral mandates. The polarization of authority is also occurring between regional mandates and subregional mandates such as municipal offices. Accumulation rate is even more impressive when mandates in sub-national authorities not directly elected by the population such as urban communities and communes of communes are taken into account and added to the portfolio.

A Matthew effect is at work. Top mandates go to powerful politicians. To be a mayor of a large city or a president of a regional council increases the probability of simultaneously being a member of the national parliament. A member of the general council is more likely to be the mayor of the most populated commune of his district than a mere member of a municipal council of a small village in the same district. Citizens give a premium to accumulation. A candidate already holding another elected office has two to three times more chances to be elected by them than a competitor who is not. About half of the presidents of general councils and three quarters of the presidents of regional councils also sit on the benches of the national Parliament.

Multiple mandate positions are rather safe jobs. Influence derived from accumulation amounts to more than the sum of the single mandates. The key reason is that their holder can control in one pair of hands different resources and be at the same time present at several levels of government, from Paris down to the commune, know-how, information and networks linked to one role being connected with those linked to the other roles.

Despite low turnover and some patronage, accumulation is more an opportunity than a liability. Good reasons explain why voters do not jeopardize accumulation. It provides them with opportunities. Citizens have a direct channel of access to Paris and central agencies: their mayor, who happens also to be a senator. Even mayors of surrounding communes may find helpful to support their colleague who, on top of mayor and senator, also is a member of the regional council. The bottom expects the grand élu to be a by-passer, a broker, an advocate of local causes at the top.

As state agents do, grands élus provide alternative channels of mediation. But they are much more effective and powerful. No accumulation of mandates exists inside state hierarchies. A prefect cannot at the same time be his own subordinate and his own superior. A senator who also is mayor is not prisoner of hierarchies. Through him local inhabitants benefit from a very short circuit to get access to Paris while there may be at least two when not three anonymous intermediaries or levels inside the state administrative circuits. The fact that grands élus preside one if not two sub-national councils gives them a second advantage. They control more resources and coordinate wider policy domains, and are not prisoners of silos. A third difference is linked to democratic legitimacy. State agents are not elected.

Multiple mandate holders exert more power and influence than state agencies. At the same time they do not try to keep state agencies out of the game. They also govern in a centralized and personalized manner that is identical to the leadership style adopted by single mandate elected official. But they do it with even more strength. They divide and rule. They are policy integrators. They frame mid-term horizons. They induce coordination in action between multiple actors, private and public. To pile up multiple hats on the same head becomes a collective solution in a world that is institutionally differentiated and politically scattered as the French scene is. To some extent a grand élu acts as an institutional facilitator.

The accumulation process gives birth to a specific style of policy-making. While grands élus show muscles to impose their own preferences and reward their friends, they are keen not to punish their enemies too much. Territorial justice is a criterion that often overcomes partisan loyalties. Everybody should be entitled to a fair minimal share of the public pie. Communes run by opposition parties may even get a better treatment from the grand élu chairing the general council than communes run by friends of his own electoral majority [START_REF] Gilbert | Les co-financements entre collectivités publiques. Une étude prototype[END_REF]. 89 % of regional funds are allocated without any opposition and even any debate among political majorities and minorities inside the council (Gilbert and Thoenig 1999b). Political majorities get constructed and deconstructed according to criteria that do not just fit ideological cleavages and partisan coalitions.

POWER BASES AND CONSERVATIVE AGENDAS

Ideological debates about comprehensive redesigns in the field of territorial government have been quite shy since the early 1990s. Politicians do not rank its reform as a top priority issue in their electoral platforms. Unlike Great Britain and Italy, for instance, French political leaders, left and right, seem to be quite cautious when not agnostic. So-called 'New' approaches dealing with public management, centralism or localism, are considered with skepticism for managerial purposes and inappropriate for political reasons.

Modernization of territorial politics and policy making nevertheless keeps been fueled by a stream of initiatives and reforms taken at all levels. About 70 relevant new laws or decrees have been issued by the State in the last 10 years. Most if not all of them are favoring incremental change. The sub-national system evolves and is driven by adjustments as if a kind of blue-print would exist that would set limits to how far changes could occur or could be acceptable to the polity. A kind of implicit action agenda exists. To understand its existence and its content, one has to recall the fact that there is no explicit legal definition of the domains of territorial affairs the State administration is in charge of.

Agenda setting and political muscles are mainly in the hands of elected politicians whose feet are locally embedded and whose hands are nationally active. Ratios of mandate accumulation have remained quite constant in the last 16 years (6 different legislatures and 5 changes of parliamentary majority). Around 90% of the members of the Parliament simultaneously hold one when not two elected mandates in sub-national authorities. About half of the senators are also busy as mayors. An average of a third of the deputies hold two other local mandates. Even ministers of the Prime Minister cabinet may keep local mandates, and many do.

To some extent the most powerful political party in France is neither the party of the President of the Republic nor the opposition party. This social configuration regroups in an informal manner most of such grands élus, a 'party' in which right and left wing politicians are equals and colleagues. It benefits from key influence in one specific policy domain: territorial government. The accumulation of mandates makes the blending when not the confusion between local and national agendas, between State offices and sub-national offices, constraining. State elites care about national and local affairs at the same time.

The national political class is made of influent local administrators, and viceversa.

Quite powerful associations are headed by grands élus who happen also to be key parliamentary legislators. The most established one is the national association of mayors. Described as the most powerful but invisible political lobby in national local politics (Le Lidec 2001), it gathers around 85% of the 36.000 mayors. Other associations mobilize the activism of elected politicians according to their mandates: presidents of the regional councils, presidents of general councils, mayors of middle size cities or presidents of agglomeration councils. Because party cleavages may differ or their mutual interests may sometime clash, as a consequence of increased sub-national institutional differentiation, grands élus experience some difficulty to propose reform options that are consensual among their local constituency. This is specially the case for the senators who are elected not by the population but by local 'colleagues' such as the mayors and the general council members. The best they can do is to stand against any reform initiative that may basically jeopardize the current system, for instance that may merge communes or suppress the département. Inside their own political party they fight reform platforms. They also deter governmental initiatives and kill legislative proposals that would destabilize the current situation. They also deter governmental initiatives and kill legislative proposals that would destabilize the current situation. These "guardians of local autonomy" share an implicit non-partisan common agenda. Five basic properties of the system are to be safeguarded. Any reform that would modify them should be killed such as:

Establishing a formal subordination between sub-national authorities, one level having constitutive rights on another level Forbidding the accumulation of mandates between all levels Putting an end to centralization of power in the hands of the president of the council, which means more checks and balances, and more decentralization from elected bodies to the population Abolishing one of the three main sub-national levels (region, département, commune) Lowering the influence of the State machinery and putting an end to its operational role in sub-national government.

For instance, socialist Prime Minister Lionel Jospin seriously considered in 1999-2000 to end any accumulation of electoral mandates of any kind. Polls suggested strong support public opinion. But he faced open blackmailing inside his own party in terms of sponsorship of his candidacy for the upcoming presidential election. The law he had prepared to enforce more democratic participation by the people was never submitted to the parliament.

While quite massive policy domains and authority have been transferred from the State to sub-national institutions between 1981 and 2004, no relevant transfer of power has ever been considered from the local politicians to the population. The majority of right as well as left politicians do not support the idea to expand checks and balances in local government-for instance to get the executive body or the mayor directly elected as such by the citizens, and apart from the council members election. Free referenda, initiatives by the population, and any other sort of modern form of citizen participation are considered as threatening perspectives to representative democracy, sometimes labeled as 'non-republican' principles Twice in the recent years State decentralization policies have reinforced institutional differentiation and autonomy between sub-national levels. Prime Minister Jean-Pierre Raffarin had to leave aside any attempt to create some subordination relationships of the département to the region or of the commune to the département. The first decentralization operated in the early 1980s faced no resistance for two reasons. It did not jeopardize the basic properties. The socialist government managed it in an authoritarian way during its first hundred days, leaving no voice and option to the Parliament and local resistance. In 2002 and 2003 the process turned into a nightmare for the center-right government He had made extensive consultation of local elites prior to the final draft of a law and its discussion by the Parliament. Lacking support from President Chirac, the Prime Minister had to bargain major compromises to get most of the grands élus belonging to his own parliamentary majority approve his law. Any attempt to subordinate in a way or another the département to the region or the commune to the département had to be dropped.

To keep both the region and the département, to add local functional institutions without massively decreasing the number of the communes, to ask the State to fund cities and villages that are fiscally poor, not to decentralize policy domains where budget cuts would be needed, are options that have consequences and costs. Facing increasingly differentiated institutional interests -regions, départements, communes of agglomeration, cities, etc.-the political class is unable to suggest in a consensual way which level should be favored and which one should be suppressed. It externalizes the political responsibility to the government in Paris and the financial costs to the State ministry of Budget, which means the national taxpayers [START_REF] Gilbert | Le risque institutionnel dans la prospective des finances locales[END_REF]. Local authorities such as communes and general councils prefer by far the State than the region or themselves to equalize fiscal revenues. And the State is trapped by and in local interests. Grants to local and regional authorities represent the major expense item of the State after the public debt. Their total amount is currently increasing by 5% each year.

Territorial government may be close to fiscal collapse, but public debates are still difficult to launch: who outside the inner circle of grands élus is legitimate to express a political voice and able to suggest alternatives to a system that is so complicate? The policy agenda setting is out of reach of public opinion. The lack of central discretionary authority on state-local financial relationships is just one facet of a much broader picture. National steering of sub-national public affairs is poorly effective for State political and bureaucratic officials, whether prefects or heads of national ministries. The initiative taken by surprise by President Mitterrand and his minister of Interior in 1981 was the exception to the rule. The Presidency of the Republic itself is if not weaker at least more prudent than one would expect from a political regime as the French State seems to be on paper [START_REF] Hayward | Governing From the Centre. Core Executive Coordination in France[END_REF]. The State administrative elites are like Gulliver: their feet are trapped in a local system that is difficult to clarify, simplify and make less costly, either by more localism or by new centralism.

ACKNOWLEDGEMENT

The author would like to thank Jack Hayward, Ed Page, Guy Peters and Denis Saint-Martin for their comments on an earlier draft of the paper.


Mariam Abdallah

Fabien Soulier

Serge Bernard

Lionel Gouyet

Guy Cathébras

Low-noise and Low-power Front-end for True-tripolar ENG Amplifier

I. INTRODUCTION

In the context of incurable neurological diseases, such as epilepsy, Parkinson's disease, stroke or spinal cord injury, surgical or pharmacological solutions are not always satisfactory restoration of sensory-motor functions affected. A workaround is then to interface the nervous system with a stimulating prosthesis by measuring electroneurogram (ENG). We are particularly interested in the acquisition of ENG signals at the peripheral nervous system which presents the opportunity to improve the functional electrical stimulation (FES) [START_REF] Wodlinger | Recovery of neural activity from nerve cuff electrodes[END_REF] [START_REF] Riso | Performance of alternative amplifier configurations for tripolar nerve cuff recorded ENG[END_REF]. Cuff electrodes which had been developed and most used in the last twenty years [START_REF] Al-Shueli | Simulated Nerve Signal Generation for Multi-Electrode Cuff system testing[END_REF][START_REF] Gouyet | A new Configuration of Multipolar cuff Electrode and dedicated IC for Afferent Signal Recording[END_REF] are established as a safe and reliable method of chronically recording the ENG comparing to intra-fascicular and sieve electrode [START_REF] Djilas | Interpretation of muscle spindle afferent nerve response to passive muscle stretch recorded with thin-film longitudinal intrafascicular electrodes[END_REF][START_REF] Kawada | A sieve electrode as a potential autonomic neural interface for bio-nic medicine[END_REF]. Typically, the neural activity measured by these electrodes is only microvolt's (1-5 µV in the 1Hz-3 kHz [START_REF] Haugland | Skin contact force information in sensory nerve signals recorded by implanted cuff electrodes[END_REF]). Moreover, the electromyogram (EMG) generated by active muscle activity which has signal amplitude in the order of 1mV presents one of the main noise sources and causes the interference with the recorded ENG. So minimizing these kinds of interferences is a main objective to be able to exploit neural signals.

There exist two amplifier configurations associated with the tripolar electrode (figure 1). First, the quasi-tripole proposed by R.Stein et al. [START_REF] Stein | Principles underlying new methods for chronic neural recording[END_REF] and J.Hoffer [START_REF] Hoffer | Long-term peripheral nerve activity during behavior in the rabbit: The control of locomotion[END_REF] is shown in figure 2 (a). This configuration is based on a screening effect achieved by shorting the outer poles. Secondly, the truetripole configuration consists of linear combination of signals coming from the three poles (V_in1, V_in2, V_in3).

V_out = A (V_in1 -(V_in2 + V_in3)/2) (1)
This combination is usually realized thanks to differential amplifiers as shown in the figure 2 (b). The true-tripole has several advantages over the quasi-tripole such as: less 1 Authors are with the DEMAR team (INRIA), in the Laboratoire d'Informatique, Robotique et Microélectronique de Montpellier, 161 rue Ada, 34392 Montpellier, France. Email: Firstname.Lastname@lirmm.fr. 2 University Montpellier Sud de France. 3 Centre National de la Recherche Scientifique. 4 TRAD, formerly with the DEMAR team. Email: lionel.gouyet@trad.fr. sensitivity to interface impedance, better signal-to-noise ratio (SNR) and EMG rejection [START_REF] Pachnis | Passive Neutralization of Myoelectric Interference from Neural Recording Tripoles[END_REF]. The drawback is that truetripole needs three differential amplifiers where the quasitripole requires only one.

In this paper, we present true-tripolar preamplifier followed by a variable-gain instrumentation amplifier (IA). This preamplifier is designed at a transistor level in order to reduce the size, power consumption and noise by limiting the number of transistors. First, we present the overall structure of the acquisition channel and the detailed design of the preamplifier. The third section gives the electrical performances of the designed amplifier. A brief discussion is then interpreted and finally, the last section gives some concluding points and perspectives.

II. MATERIAL AND METHOD

The acquisition system is designed as an application specific integrated circuit (ASIC) and contains several channels. Each channel is composed of an IA associated with a preamplifier as shown in the figure 3.

A. Overview of the structure

The circuit is designed with the AMS CMOS 0.35µm technology, with 3.3V supply. The preamplifier provides three functions which are: -to combine the input signals as shown in the equation ( 1), -to barely amplify the neural signal to an acceptable SNR, -and to present a differential output to the IA. Nevertheless, in the aim to increase and adjust the total gain of the structure this first stage is followed by an IA with variable gain. The latter is numerically controlled by a configurable network of switches and resistors in order to obtain a range of gain going from 6 dB to 80 dB for the second stage. We will use a Nexys2 FPGA card for this purpose. The SNR optimization of the IA is less critical than the preamplifier one thus it's realized with operational amplifiers from the AMS standard library.

B. Preamplifier

The preamplifier is designed like a differential pair whose negative input transistor is split into only two transistors (two times smaller than the positive input, figure 4). This way, it provides the same functionality as the classical true-tripolar structure with a single (3-input) differential amplifier instead of three, and with a size similar to a quasi-tripole amplifier. To improve the noise performances, we chose to use the PMOS transistors for the pair and we have optimized the size to (W/L= 150/7.5 µm). The active load is made with NMOS transistors. Two diodes were added in parallel to bias the output voltage to 1.65V approximately. The gain of the differential pair is given by: A= gm p / gm n [START_REF] Al-Shueli | Simulated Nerve Signal Generation for Multi-Electrode Cuff system testing[END_REF] Where gm p represents the transconductance of the P-MOS transistors connected to the inputs V_in2 and V_in3 while gm n is the transconductance of the diode connected to NMOS transistors at the bottom of the schematic. To achieve the gain of 100 with consumption of I_bias= 12 µA we have to chose an active load transistor size (W/L= 55/40) and diode of size (W/L=2/164.3).

III. RESULTS

A. Gains AND Rejection

Triantis et al. have shown that the EMG bio-potential has a linear spatial variation inside an insulated cuff [START_REF] Triantis | Experimental Assessment of Imbalance Conditions in a Tripolar Cuff for ENG Recordings[END_REF]. Therefore, to suppress this parasitical signal the preamplifier needs to reject: -the common mode

V_in1= V_in2= V_in3

(3)

-the differential parasitic mode

V_in1=0, V_in2= -V_in3 (4)
To characterize the preamplifier, we have to simulate the output with these two modes and compare it to the main mode which is orthogonal to both.

V_in1= -2 V_in2= -2 V_in3 (5) DC and AC simulations were performed for these three modes (figure 5). The results are presented in the figures 6 and 7. The main results of these simulations are:

-more than 150dB rejection ratio for the common and differential modes compared to main one.

-dynamic range of about ±5 mV.

B. Bandwidth and noise

Fig. 7 shows 200 kHz bandwidth that is far above the needs for ENG acquisition (tenths of kHz). The estimated flicker noise due to input and load transistors is below the µV on the required bandwidth.

IV. DISCUSSION

Simulations show that we succeeded to achieve the requirement for the true-tripolar amplifier with much less transistors than the usual structure keeping the power consumption under 12 µA for 3.3 V supply. The simulated rejection ratios seem very encouraging. Nevertheless, some mismatches were not simulated and the results have now to be confirmed by real measurements with the fabricated ASIC. Moreover, the estimated noise does not take in account all the sources in the circuit but only the input and load transistors, and may be measured as well.

V. CONCLUSION

In this paper, we have focused on the first stage of an acquisition system for recording electrical signal from peripheral nerves. Whereas the classical true-tripolar configuration offers an interesting parasitic signal rejection at the cost of multiplying the number of transistors, the amplifier presented in this work provides a very simple low noise, low power way to implement the true-tripolar functionality. It offers the ability to integrate large number of channels into a single ASIC. We are working now on an experimental setup for the characterization of the ASIC to confirm simulations results presented here. ACKNOWLEDGMENT Part of this work is supported by the Intense PSPC project.

Figure 1 .

 1 Figure 1. Tripolar cuff electrode.

Figure 2 .

 2 Figure 2. Tripolar ENG amplifier configurations (adapted from [11]). (a) quasi-tripole, (b) true-tripole.

Figure 3 .

 3 Figure 3. Overview of the true-tripolar acquisition system

Figure 4 .

 4 Figure 4. Three input preamplifier schematic.

Figure 5 .

 5 Figure 5. The three simulated modes used for preamplifier characterization: (a) comon mode, (b) differential parasitic mode, (c) main mode.

Figure 6 .

 6 Figure 6. DC simulation result for main (b), common (a) and differential modes (c).

Figure 7 .

 7 Figure 7. AC simulation result for main (b) and common (a) modes .Differential mode is too low to be simulated.