Achraf Ghorbel
email: achraf.ghorbel@irisa.fr

Aurélie Lemaitre
email: aurelie.lemaitre@irisa.fr

Eric Anquetil
email: eric.anquetil@irisa.fr

Competitive hybrid exploration for off-line sketches structure recognition

We work on new strategies of exploration for interpretation of off-line sketches. A first approach (call IMISketch) was based on a competitive breadth-first exploration of the analysis tree allowing to evaluate simultaneously several possible hypotheses of recognition in a dynamic local context of document. A great advantage of this strategy is to be able to solicit the user during the decision process to avoid error accumulation in the analysis step. IMISketch strategy is very interesting but it can lead combinatory problems when addressing complex sketches. In this paper, we propose a new hybrid strategy for exploration. The recognition process alternates between a breadth-first and depth-first exploration. The strategy is totally driven by the grammatical description of the document. The paper demonstrates the interest of this new hybrid strategy method on handwritten 2D architectural floor plans containing walls, opening and furnitures.

Introduction

IMISketch [START_REF] Ghorbel | Interactive competitive breadth-first exploration for sketch interpretation[END_REF] is an interactive syntactic method for interpretation of structured documents. A priori structural knowledge of the document in IMISketch is expressed through a two-dimensional visual language based on production rules. This analyzer aims to interpret the image primitives. These primitives are line-segments and polygons. IMISketch adopts a breadth-first exploration unlike classical syntactic analysis methods [START_REF] Chan | An efficient syntactic approach to structural analysis of on-line handwritten mathematical expressions[END_REF] [2] [3] [8] based on depth-first exploration. Each branch of the tree is a possible hypothesis. The uncertainty is formalized by the attribution of scores to each hypothesis. If the ambiguities can not be resolved in an automatic manner, the user will be solicited by the analyzer to resolve the ambiguity. The user integration in the recognition loop avoids error ac-cumulation and thus a fastidious a posteriori correction. The first results of this method performed on the architectural plans containing walls and opening are promising [START_REF] Ghorbel | Interactive competitive breadth-first exploration for sketch interpretation[END_REF]. The presence of the user in the loop analysis requires a reasonable analysis time. For this, we proposed in [START_REF] Ghorbel | Optimization analysis based on a breadth-first exploration for a structural approach of sketches interpretation[END_REF] some optimizations to accelerate the interpretation.

When we analyze some architectural plans containing more complex furnitures, we note that the current IMISketch generates a lot of combinatory due to the presence of many basic primitives in a small zone.

In this paper, we focus on a new strategy of exploration to reduce the combinatory to obtain an analyzer that is really exploitable in the context of an interactive analysis. This strategy consists in passing from a method based only on breadth-first exploration to a hybrid method that alternates between breadth-first and depth-first exploration. At each step of analysis, the type of exploration will be induced by production rules of the two-dimensional grammar that will drive the analysis. The choice of exploration type is induced by the risk of the current interpretation relatively to its neighbours. An interpretation is called low-risk when the analyzer is sure to combine the right primitives that form an entity. Depth-first exploration is adopted in the low-risk interpretation cases. In other cases, the analyzer adopts a breadth-first exploration allowing to evaluate simultaneously several possible hypotheses of recognition in the current local context of the document. The complete system can be applied to off-line documents (images). We validate this new hybrid strategy on handwritten architectural plans. Some examples are illustrated in Figure 9.

The remaining of the paper is organized as follows. In the section 2, we introduce the principles of our existing interactive analysis method for interpreting sketches, IMISketch. The new hybrid strategy is described in section 3. Experimental results are reported in section 4 and finally, section 5 concludes the paper.

Overview of IMISketch

In this section, we present the different steps of the existing method IMISketch (cf. Figure 1). The first step is the extraction of basic primitives required for analysis. The second main step is to analyze these primitives and to use their structural arrangement in the document to identify the symbols. This phase is interactive: the analyzer can solicit the user to resolve ambiguity cases. The recognition of the document structure is managed by a grammatical analyzer that drives the calls of symbol classifiers to evaluate a scoring for each hypotheses. We now detail each step of analysis.

Preprocessing phase: Primitive extraction

The first step consists of extracting the necessary information from the structured document. This phase is generic and off-line and does not depend on the type of document to interpret. We have chosen to work only with line-segments, which represents the primitives of our analysis. We adopt the Kalman filter to extract these primitives [START_REF] Lemaitre | Text line extraction in handwritten document with kalman filter applied on low resolution image. Document Image Analysis for Libraries[END_REF] presented in figure 2.

Interactive breadth-first exploration: IMISketch

IMISketch analyzer explores the matching between the document structure defined by grammatical rules and the set of primitives contained in the document. The grammatical rules are expressed using the contextdriven constraint multiset grammars (CD-CMG) [START_REF] Macé | Eager interpretation of on-line hand-drawn structured documents: The dali methodology[END_REF]. In CD-CMG, when a production reduction occurs, it means that a multiset of elements is replaced by another one α. This reduction has impacts on the analysis of the document: now that new α elements exists in the document, it may be possible to add new others, positioned relatively to these α elements. The interpretation of α creates a new zone, called relative position to search the next elements to analyse in the document.

The primitive interpretation depends on its neighbourhood in structured documents: the structured document analysis requires a two-dimensional context. The analyzer begins by defining a spatial contextual focus that aims to limit the combinatory exploration due to the breadth-first exploration of the analysis tree.

Each primitive can be interpreted in several ways which led to a construction of an analysis tree. In the building of the analysis tree, the analyzer explores all the possible hypotheses of interpretation using breadthfirst exploration in the spatial context with the algorithm described in [START_REF] Ghorbel | Optimization analysis based on a breadth-first exploration for a structural approach of sketches interpretation[END_REF]. Each root is the production rule that would consume this primitive. Each node or leaf is the application of a production rule deduced from the previous node. The number of analysis trees corresponds to the number of possible interpretations for the current primitive.

Once the tree is constructed, we start the decision phase. The role of the decision process is to validate the right hypothesis among a set of competing hypotheses generated with a breadth first analysis. The analyzer solicits the user in case of ambiguity, i.e. when more than one hypothesis can be validate with almost the same score. Otherwise, the analyzer validates the best hypothesis.

When the correct root is validated, other roots are put on hold and the new roots are either the sons of this root if exists, or the waiting roots otherwise. The analyzer goes back to the first step (defining the local context). The analysis is complete when no more production rule is applicable.

IMISketch application on furniture

In this section, we present an example of interpretation produced by IMISketch. We want to analyze the primitives {1,...,6} illustrated in Figure 3 with the grammar described in Figure 4. In the grammar, each new interpreted element induces the creation of a new relative position for the search of the following elements to recognize. We are mainly interested in the combinatory at the analysis tree level. According to Figure 4, there are two ways to interpret the primitive '1':

• As wall: the Figure 5 shows the analysis tree corresponding to all the hypotheses generated by this interpretation.

• As a part of furniture: the Figure 6 shows the part of analysis tree corresponding to some hypotheses generated by this interpretation. We present just a part of the tree analysis for more clarity. This analysis tree generates a lot of combinatory, and we obtain several equivalent hypotheses.

Ps (1) Ps (1)

( ) ( ) ( ) P1 (2) P2 (
( ) ( ) ( ) ( ) 1 2 3 4 P1 (2) P2 (2) P1 (4) P2 (4) P1 (3) P2 (3) P2 (3) P1 (3) P2 (3) P2 (3)
P2 (2) P2 ( 5) P2 ( 6)

P2 (6) P2 (5)
P2 ( 4) P2 ( 5) P2 ( 6)

P2 (6) P2 (5)
P2 ( 4) P2 ( 5) P2 ( 6)

P2 (6) P2 (5)
P2 ( 2) P2 ( 5) P2 ( 6) P2 ( 6) P2 ( 5) P2 ( 6) P2 ( 5) P2 ( 6) P2 ( 5) P2 ( 6) P2 ( 5) P2 ( 6) P2 ( 5)

Breadth-first exploration P3 (1)
P3

P3

Despite

our previous optimizations on IMISKetch [START_REF] Ghorbel | Optimization analysis based on a breadth-first exploration for a structural approach of sketches interpretation[END_REF], the combinatorial problem remains a major problem especially when the documents are more complex than walls and openings. For example, the analysis tree for interpreting the primitive '1' in a component of furniture requires more than 50 nodes (Figure 6). We present in the next section, a new hybrid strategy to improve the exploration of the analysis tree.

Hybrid exploration

Symbols with a complex structure, such as furniture in the case of architectural floor plan, generates a lot of combinatory because they are composed of a big number of primitives interconnected in a reduced zone. Despite breadth-first exploration offers the possibility to choose between several possible hypotheses for interpreting primitives, this exploration generates a lot of combinatory. In opposite, the depth-first exploration avoids combinatorial problems but does not generate all hypotheses. This exploration may suggest a wrong interpretation of primitives.

In this section, we propose a dynamic strategy to switch between a breadth-first exploration and a depthfirst exploration to reduce the combinatory. We improve the use of the existing CD-CMG grammar to drive this new strategy analysis. In our hybrid strategy, CD-CMG is not restricted to the modeling of the document but also used for the choice of the exploration strategy: either breadth-first exploration or depth-first exploration.

Breadth-first / Depth-first exploration

The CD-CMG grammar drives the exploration of the analysis tree. It enables to choose between breadth-first and depth-first exploration at each step of analysis.

• depth-first exploration: this exploration strategy is chosen if the production rule applied at the root of the analysis tree generates only one way to interpret the other primitives of the same group (interconnected primitives).

• breath-first exploration: if the interpretation of the root of the analysis tree generates several ways to interpret the primitives of the same group.

As we have said previously the depth-first exploration may not generate all the hypotheses. Consequently, we propose to reduce the risks by limiting the possible zone of application of the depth-first analysis. We implement this idea using the concept of relative position.

Reduced relative position Vs extended relative position

We recall that the relative position is the search zone that is created after the interpretation of each element in order to continue the analysis. In this analyzer, we combine two kinds of relative positions (Figure 7):

• Extended relative position: this position is the same to that used in previously IMISKetch. When this position is activated, the analyzer adopts the classical breadth-first exploration.

• Reduced relative position: this zone search is smaller and enables to adopt the depth-first exploration. This position is intended to collect interconnected primitives that are very close.

In the grammatical description, each interpreted elements can create the both kinds of relative positions. Thanks to these positions, the hybrid exploration is totally led by the grammatical description and can be adapted for the description of each element present in the document. If a created element is associated to two positions, the reduced position is used in priority. The transition from reduced position to extended position is established only after no rules of productions is applicable.

Example of hybrid exploration

In this section we return to the same example of section 2.3. Figure 3 illustrates the primitives to interpret and Figure 4 describes the production rules.

In the case of architectural floor plans, we consider that the close interconnected set of basic primitives belong either to the same furniture(toilet, table, bed) or to one or more walls and openings (doors, windows); the not interconnected primitives elements belong to the same or different elements. For this, we have described in the grammar that the walls create only extended relative positions. The furniture rule now creates two relative positions: reduced and extended.

Primitives {1, 2, 3, 4} are interconnected and form the group G1. Primitives {5, 6} are interconnected and form the group G2. By applying the production rules described in Figure 4, there are two ways to interpret the primitive '1': a wall or a component of furniture. Since the wall creates only an extended relative position, the analysis tree thus constructed is similar to IMISketch (Figure 5). Figure 8 shows the analysis tree obtained with the new exploration strategy about how to obtain furniture. The analyzer uses the reduced relative position to group primitives that can form a furniture by adopting an depth-first exploration. The group {1, 2, 3, 4} forms a table. The extended position is used to find another hypothesis of furniture. {1, 2, 3, 4, 5, 6} may form another furniture: toilet. With this new strategy, to interpret the primitive '1' as a component of a furniture, we pass from around 50 nodes with IMISketch to 7 nodes with the hybrid exploration. We have shown in this simple example, by applying our new strategy on six basic primitives, we won 86% of exploration of nodes. This new hybrid strategy also lets alleviate the competitive hypotheses. In our example, this new strategy allows to pass from 6 competing hypotheses (Figure 6) to 2 hypotheses (Figure 8).

Experimental results

In this section we report results obtained from the hybrid exploration strategy described in section 3 on the interactive method of document analysis. The aim of this strategy is to reduce the analysis time of the document to meet the criteria of acceptability and usability of the system.

The experiments were carried on 24 architectural plans of different complexity drawn by six different people. Each architectural plan is composed of a set of walls, opening (doors, windows and sliding windows) and furniture (single sink, double sinks, toilet, bathtub, square table, table with chairs, single bed, double bed, shower, couch). Figure 9 shows some examples of analyzed architectural plans and Figure 10 reports the total number of symbols of the database.

To evaluate our new exploration strategy, we adopt two experiments. The first one consists of comparing our new hybrid approach to IMISketch method (based on breadth-first exploration). In this experiment, we analyzed 7 architectural plans using IMISketch. This interpretation requires more than 5300 nodes per image and therefore a large computation time. The interpretation of the same plans with our new exploration strategy requires an average of 1713 nodes and thus acceptable computation time for an interactive method. This represents a gain of 70% (Figure 11). Today, the average computation time is 4 min per image. In future work, we will try to reduce the computation time to attain around 1 min 30: experimentally, it seems the ideal timing that allows the user to follow in real time the recognition process.

The second experiment evaluate the rate of structural recognition, i.e. the interpretation of primitives into walls, openings and furnitures, using our hybrid strategy and the presence of the user in the loop of analysis.

Figure 13 reports recognition rates based on 24 architectural handwritten plans with varying threshold of user solicitations. This figure shows the evolution of recognition rates related to the number of user solicitations. We can notice that the best compromise (recognition rates / user solicitations) is obtained with 12 user solicitations per image: it means that 4% of primitive interpretations require the user solicitation. 49% of user solicitations are useful to take the right decision which is not the best hypothesis proposed by the analyser. The structural recognition rates increase from 91% without user solicitations to 96% with user solicitations. The remaining errors (about 4%) are mostly due to badly drawn symbols.

With this strategy, we can deal with complex problems where the furniture is attached to wall.

Conculsion

In this paper, we have presented a hybrid strategy for solving combinatory generated by an interactive analysis for the sketch recognition. This strategy alternates between a breadth-first and depth-first exploration. Note that this hybrid exploration is driven by the grammar. This strategy has been validated and tested on an interactive analyzer for interpreting handwritten architectural floor plans.

Future work will focus on extending the experimental results on large image databases containing printed and vectored document architectural plans... We will also validate the criteria of acceptability and usability of the system by doing usage tests that will be conducted in collaboration with experts from the laboratory uses "Loustic" (http ://www.loustic.net/rennes).

Figure 1 .

 1 Figure 1. Synthetic scheme of IMISketch method for structured documents interpretation

Figure 2 .

 2 Figure 2. Extraction of primitives. The original drawing is in light gray, and the extracted primitives are in black.

Figure 4 .

 4 Figure 4. Example of production rules used for the architectural plans

Figure 5 .

 5 Figure 5. Analysis tree resulting from the interpretation of the primitive '1' as wall

Figure 6 .

 6 Figure 6. Part of the analysis tree resulting from the interpretation of the primitive '1' as furniture (should contain about 50 nodes)

Figure 7 .

 7 Figure 7. Example of two relative position a furniture component

Figure 8 .

 8 Figure 8. Analysis tree with Hybrid exploration: transformation of primitive '1' to table or toilet.

  Figure 12(a) and Figure 12(b) present examples of furniture that share a component with a wall. Figure 12(c) illustrates an example of furniture that has a component attached to wall. Figure 12(d) and Figure12(e)show examples of furniture that has a component attached to an opening. The interpretation of these cases is very difficult with IMISketch because large combinatory is generated ; but in these complex cases, the furniture are localized with the hybrid strategy.

Figure 13 .

 13 Figure 9. Examples of architectural floor plans

Table :

 :

	Name Name	Created l elements	Consumed elements Consumed elements
	Ps	Starting wall	Longest line in the document
	P1	Wall	Line at the end of an other wall
	P2	Sequence_Opening	Line at the end of an interpreted wall or Line at the end of an interpreted wall or sequence_Opening
	P3	Sequence_Furniture	A sequence and two colinear walls or a sequence and wall and a line wich are colinear
	P4	Door	A sequence and two colinear walls or a A sequence and two colinear walls or a sequence and wall and a line wich are colinear
	P5	Window	A sequence and two colinear walls or a sequence and wall and a line wich are colinear
	P6 P6	Furniture Furniture	A Sequence Furniture A Sequence_Furniture

Depth-first exploration : Breadth-first exploration

Figure 3. Primitives to interpret

Acknowledgment

The authors would like to thank all the people who took part in the experiments. This work partially benefits from the financial support of the ANR Project Mobisketch.


Keywords:

Part of the research leading to the present results have benefited from the financial support from the

Indigenous territoriality and political agenda in

 Bolivia (1970Bolivia ( -2010) )Laurent Lacroix SOGIP-IIAC/LAIOS EHESS !"#$%&'()*+&%,"(,-(.'*(/0/*+(1(2*++%., +%0$%.3(04.,5'.,"*(*.(0#*"60(/,$%.%74*(*"(8,$%)%*(9:;<=> ?=:=@(AB(C4D6*+"&>*B(E*)%&.0(6*($FG"&.%.4.(H0.0$I(6JD".+,/,$,#%0B(?=:?B(:<(9:@B(//K(L=><<K((

The recognition and respect of specific territories, whether of pre-colonial or colonial origin, has been one of the major claims made by indigenous peoples in Bolivia 2 . The current Constitution (2009) recognizes indigenous peoples as "any human collective that shares a cultural identity, a language, a historical tradition, institutions, a territoriality and a cosmovision whose existence is prior to the Spanish colonial invasion". Designated as "indigenous native peasant nations and peoples" (naciones y pueblos indígena originaria campesinos) in the current Constitution, they call for the establishment of autonomous territories integrated into the political administrative organization of the Bolivian State.

Historically, indigenous peoples' territorial claims are intimately linked to Spanish colonization, an aspect of which has been the breaking up of pre-colonial territorialities that the main indigenous organizations today seek to reestablish or reconstitute. In spite of this historical character, the issue of indigenous territories has only emerged on the Bolivian national political agenda in the last forty years. This emergence appears at the juncture of three factors: the mobilization of indigenous organizations for the recognition of a series of rights (including territorial rights), successive national policies of state modernization since the beginning of the 1980s, and an international context favorable to the protection and promotion of indigenous peoples rights.

This particular juncture has presented itself twice and has led to remarkable progress in terms of indigenous territorial rights in Bolivia. The first instance occurred at the beginning of the 1990s as the liberal multicultural model won recognition throughout Latin America. The second instance took place at the end of the 2000s, following symbolically powerful political changes both on the national level, with the election of the union leader Evo Morales in 2005, and on the international scene, with the United Nations Declaration on the Rights of Indigenous Peoples in 2007. The conjunction of these events has led to the elaboration of a unique political Constitution adopted in 2009.

These elements contribute to explain the importance taken by indigenous issues in the contemporary Bolivian political field, particularly so in their territorial dimension. This article purports to assess the evolution of indigenous territorial issues during the past two years in Bolivia. To do so, the article briefly presents the two main indigenous organizations in the country, whose main agenda is of a territorial nature. Then, the two historical periods mentioned will be analyzed through a multiscalar framework to explore the interactions between the regional, national and international levels in terms of the political treatment of ethnic and territorial issues. The objective is to determine whether the current national and international context is really favorable to indigenous peoples in Bolivia.

Prominent indigenous actors in the mobilization

In Bolivia, the emergence of new indigenous movements, sometimes described as the "indian awakening", occurred at the beginning of the 1980s in two distinct regions: on the Altiplano (west of the country) and in the Lowlands (east of the country). Like many social, trade union, civic and political movements of the country, indigenous organizations are marked by regionalism. While they share many claims such as the institutionalization of an indigenous territoriality integrated to the general organization of the Bolivian State, and constantly express feelings of mutual solidarity, each of these organizations develops its own political strategy to reach its goals. Consequently, there has not been a unified indigenous movement in Bolivia to this day.

The Andes: from katarism to the Consejo Nacional de Ayllus y Markas de Qullasuyu (CONAMAQ)

The apparition of an indianist trade union movement known as the katarist movement3 at the beginning of the 1970s is the first expression of an "Indian awakening" in the Andean region. This movement rejects the assimilationist and paternalist policies deployed by the State since the 1930s, and insists on the cultural oppression of populations defined as Indian (Tiwanaku Manifesto in 1973). The katarist questioning culminates with the establishment of the Confederación Síndical Única de los Trabajadores Campesinos de Bolivia (CSUTCB) in 1979, the first national independent peasant trade union. Its creation is a highlight of the democratic transition in Bolivia (1978Bolivia ( -1982) ) and the union demonstrates strong capacities for mobilization until 1983, at which point the katarist movement comes to a halt. At the union level, its leaders struggle to propose a unifying project (Le Bot 1994). In electoral terms, they are extremely divided and accumulate failures on their respective sides [START_REF] Pacheco | El indianismo y los indios contemporeanos en Bolivia[END_REF]. Katarism loses significant momentum and concedes the vanguard of peasant unionism to the coca producers established in the tropical valleys of the Chaparé [START_REF] Ortega | Hallu hayllisa huti. Identificación étnica y procesos políticos en Bolivia[END_REF][START_REF] Mansilla | Política, Cultura y Etnicidad en Bolivia, Serie Fenómenos de colonialismo interno[END_REF].

In the Andes, the traditional organization (preceding trade unionism) is revalorized after having been reduced to its sole ritual dimension during forty years by the widespread movement of peasants' unionization. The communal and intercommunal political system is rehabilitated. The pre-Columbian form of Andean socio-territorial organization, the ayllu, is considered anew and becomes a first order claim. The union model does not disappear, however, and power at the local level is the subject of an acute competition between union leaders and so-called "traditional" authorities (Le Gouill 2007).

During the 1980s many indigenous organizations are developed as an alternative to the union model at the local, provincial and regional levels 4 while peasants' unions at the departmental level highlight the ethnic dimension of their organization 5 . In March 1997, the Consejo Nacional de Ayllus y Markas de Qullasuyu (CONAMAQ) is created, presenting itself as the representative organization of the "Indigenous Nationalities and Peoples of Bolivia's Highlands" 6 . This emergence amplifies the differentiation process between peasants' unions and indigenous organizations in the Andes. The latter re-appropriate indigenous terms to designate their authorities and develop their claim platforms around the key theme of the ayllu as a collective territory. Conversely, peasants' unions call for the granting of individual or familial plots of land.

The main objective of the CONAMAQ is to reconstitute territorial entities of pre-Columbian origin (ayllus, markas, suyus), which it sees as a necessary condition for "the political selfdetermination and guaranteed exercise of collective rights for indigenous peoples". The CONAMAQ primarily claims the "restitution of native communal lands usurped by the invaders", which would allow Andean communities to "reconstitute their own territorialitybased system of political organization", "their own organizational structures" (particularly economic and judicial ones), and their "own cosmovision" (cosmic vision of the ayllu). To do so, the CONAMAQ advocates a "constitutional recognition of indigenous native peoples' collective rights" and the instauration of a plurinational State.

Despite a growing visibility and intervention on the national political scene, the CONAMAQ willingly admits to a lack of coordination between its affiliates as well as the lack of a general political project, both of which limit its capacity for mobilization. Its leadership nonetheless tries to remedy these lack by strengthening its governance structure and by taking a proactive role in national debates.

In the Lowlands: the Confederación de los Pueblos Indígenas de Bolivia (CIDOB)

From the time of colonization to the 1980s, indigenous populations in the Bolivian Lowlands have been placed under a variety of authorities 7 . Dispersed and without representative organizations, some of these populations live with great difficulty under their assigned authorities while others try to escape their imposed livelihoods by establishing themselves in the forest, far from administrative centers, when such a possibility still exists. At the end of the 1970s these indigenous populations organize themselves under the aegis of a small group of anthropologists and establish in 1982 the Indigenous Platform of the Bolivian East, which rapidly transforms into the Indigenous Confederation of Bolivia while keeping its first acronym, CIDOB. Indigenous peoples from the Lowlands are now known and visible.

The new interethnic organization reflects the realization by many indigenous communities that they confronted a similar situation in terms of land spoliation, economic and political marginalization, and the absence of individual and collective rights. The ethnic character of the CIDOB rests on a twofold process of differentiation. First, with regard to small Andean peasants established in the Lowlands, organized through peasants' unions affiliated to the CSUTCB and primarily claiming the attribution of individual plots of land. CIDOB affiliates, on their part, seek to establish an organization that would be more autonomous from political parties and less vertical than trade unions, and look for means to gain the attribution of collective lands. The second differentiation is in opposition to local political and economic elites of foreign origin (descending from settlers or coming from new waves of international migrations) with whom CIDOB members are competing for access to natural resources. This elite controls the land market and contributes to the progress of the agrarian frontier, thereby threatening indigenous populations' living areas. The CIDOB thus fills a gap in terms of representative organizations in the Lowlands and challenges the notion of a uniquely Andean indianity in the national political imagination.

CIDOB's mission is to "defend the fundamental human rights of indigenous peoples in the country"8 . Among its numerous demands, the theme of territoriality appears simultaneously as central, federative and a source of mobilization. Obtaining territories and tenure is an absolute priority for indigenous peoples in the region. According to the CIDOB, the existence of an "indigenous territory" implies an integral spatial unity in which indigenous populations would collectively control natural resources, exercise their political and administrative autonomy, and uphold their histories and traditions. The territory is seen as the primary basis for indigenous peoples' development. It is perceived as a fundamental prerequisite for solving the many challenges faced by indigenous communities in the region such as economic poverty, low results in terms of health and education, and political marginalization [START_REF] Lema | Pueblos Indígenas de la Amazonía Boliviana. La Paz : PNUD, CAF[END_REF].

Consequently, the CIDOB orientates all its actions towards the obtaining of specific areas for indigenous peoples.

The Confederation has quickly established itself as an important and influent actor in the Bolivian political life. In a few years it has presented innovative reform projects that redefine the nation and the role of the State while leading large-scale mobilizations resulting in the acquisition of new rights for indigenous populations. The results of its activity is such that "the dominant actor in indigenous movements has been displaced geographically from the Andes to the East" (Calla Ortega & Molina Barrios 2000: 27). Since the 1990s, the CIDOB has successfully put the issues of indigenous territories and respect for sociocultural difference among the main themes of the national political agenda (Lacroix 2011a).

The 1990s : liberal multiculturalism and indigenous territoriality

During the 1990s, Bolivia has undergone, as most Latin-American countries have, a neoliberal process of political modernization of the State, which has resulted, among other effects, in a political-administrative reorganization and the implementation of multicultural policies. The latter implied constitutional reforms to recognize the multicultural and pluriethnic character of national societies. Included in a wider movement of participative decentralization of the State, neo-indigenist policies were implemented, recognizing specific rights for indigenous peoples [START_REF] Gros | Ser diferente por (para) ser moderno, o las paradojas de la identidad. Algunas reflexiones sobre la construccón de una nueva frontera étnica en América latina[END_REF]. The CIDOB has played a key role in these changes. Its mobilizations and propositions have accompanied every step of the establishment of liberal multiculturalism under the government of Sánchez de Lozada (1993Lozada ( -1997)). Such policy was adopted in response to demands from the Lowlands indigenous confederation and Andean indigenous organizations as well as to the economic and political orientations imposed by international agencies. These agencies will, on their own side, create a favorable context for indigenous rights.

2.1 A few precedents (1988)(1989)(1990)(1991)(1992) In 1989, the International Labor Organization (OIT) Convention 169 "on indigenous and tribal peoples in independent countries" is an important step in the recognition of indigenous peoples rights. Defining these peoples as agents of their own development, the Convention prompts the States to respect their territories, which are loosely defined as the areas that the peoples concerned traditionally occupy9 . This international norm consolidates the actions led by Lowlands's indigenous organizations in Bolivia. As soon as 1988, the CIDOB suggested to the Bolivian State the instauration of protected indigenous territories. The proposition follows two territorial claims made by organizations in the department of Beni, where areas of occupations are threatened by forestry activities in spite of their protected areas status (Lehm 1999).

Under pressure from Lowlands's indigenous organizations, the Bolivian State for the first time recognizes the regional aspect of the territorial issue for indigenous populations and accepted the idea of indigenous territories. A few months before the ILO Convention was published, the 17 th February Supreme Resolution 205 862 recognizes the "national and social necessity to recognize, assign and own territorial areas in favor of forest-dwelling groups and communities native to the Oriente and Bolivian Amazon" (article 1). In spite of these norms, the Bolivian State takes its time to grant territories. The CIDOB mobilizes against the scaling down of living areas for Lowlands's indigenous populations and demanded territories. In August 1990, it organizes a "March for territory and dignity". The mobilization is a shock for the national society as it reveals the range of cultural diversity of the country. This action is supported by a wide part of the population and inspires Andean indigenous organizations to break up with peasants' unions. It expresses the explicit will from indigenous peoples in the Lowlands to become active members of a plural and democratic nation (Libermann Cruz & Godínez Gutiérrez 1992) and starts to evoke the necessity of a new Constitution towards the instauration of a plurinational State [START_REF] Albó | El retorno del Indio[END_REF].

Following the march, the Bolivian state recognizes by supreme decrees four indigenous territories in 199010 and five others in 1991 11 . In 1992, president Paz Zamora's government ratifies ILO Convention 169 and revives the project for a Latin American and Caribbean Indigenous Peoples Development Fund. It officializes intercultural and bilingual education and adopts a law on the Environment that recognizes indigenous peoples' right to participate, administer and exploit natural resources in protected areas. Finally, it authorizes the creation of an indigenous forest protection force on recognized territories in 1990 [START_REF] Marinissen | Legislación boliviana y Pueblos Indígenas. Inventario y análisis en la perspectiva de las demandas indígenas[END_REF].

These advances were secured by the CIDOB in a favorable context for indigenous peoples rights. At the international level, the period sees important norms adopted such as the ILO Convention 169 (1989), the celebrations of the Discovery of Americas (1992), the declaration of an international year for indigenous peoples, and the proclamation of an international decade for the world's indigenous peoples by the UN (1993). In this particular context, the impact of the mobilization led by the CIDOB is strengthened by the indigenist policy specific to the government of president Paz Zamora.

The CIDOB maintains its activism through a second impressive initiative. It elaborates a draft Indigenous Law that synthetizes claims shared by all its affiliates and proposes political solutions. This document defines the indigenous territory in the following terms: "Indigenous territories are the lands traditionally occupied or owned by indigenous peoples (…) which constitute their natural habitat and the socio-economic space used for their productive activities, hunting, fishing, collecting, farming, raising stock (…) as well as imprescriptible areas necessary to guarantee the demographic growth and their sustainable development" (art. 9). These territories are inalienable and indivisible (art. 10). The State must guarantee the collective ownership of these territories to the populations concerned and bestow upon them the right to administer and manage natural resources (art. 11 &19). Indigenous peoples must be consulted prior to any authorization to exploit the subterranean resources of their territories (art. 12).

A national commission is given the task to prepare an Indigenous Peoples Bill based on CIDOB's document. Terminological and conceptual dissensions rapidly appear around the notions of "peoples", "territories" and "territorial right". The political Constitution of the time does not recognize indigenous populations as peoples then, or their traditional authorities. The "indigenous territory as defined by the CIDOB would imply a complete reorganization of the national space and would need the organization of a constituent assembly. Eventually, all political parties represented in the Parliament reject the CIDOB's Indigenous Law, which is assessed as unconstitutional by the Congress.

The effects of neo-indigenism on indigenous territoriality (1994-2005)

The CIDOB's political proposition is not discredited, however. Indigenous organizations' claims are taken into account, albeit in a particular way, by president Sánchez de Lozada's government (1993)(1994)(1995)(1996)(1997) as part of the vast project of reworking the national legislative framework that he has undertaken to modernize the State and pursue the neoliberal reforms implemented since 1985.

The 1967 Constitutions is revised. Bolivia is now defined as a unitary, multiethnic and pluricultural republic (art.1). It grants the status of "peoples" to indigenous populations, recognizes their rights and their "native communal areas"12 . It offers them the possibility of legal assistance (art. 116) and eliminates the criteria of literacy to enter elections (art. 221), which facilitates the electoral participation of many indigenous organizations. These constitutional provisions open new perspectives for indigenous populations, in two legal fields especially.

The 1994 law on Popular Participation instigates a municipalization of the national territory through a system of local participative democracy. The effects are significant for indigenous populations. For the first time, their communities are judicially recognized and constitute, along with peasants communities and urban districts associations, the basic territorial organization (OTB) of the participative decentralization. The principal effect of municipalization is to generate a growing presence of indigenous representatives both in town councils and in "vigilance committees" in charge of controlling the implementation of the five-yearly participatory plan of municipal development.

In spite of remarkable progress in terms of citizenship, participation and political representation, the political and administrative re-ordering of the country does not consider at all the kind of territoriality claimed by indigenous organizations as it is exclusively based on the municipalization of the national territory. In 1996 the Bolivian State attempts to address this issue when it is constrained to engage a reform of the agrarian legislation. This reform is recommended by international organizations (World Bank and international cooperation agencies) and called for by various indigenous, peasants, economic and non-governmental organizations; it occurs in an international context where indigenous peoples issues command growing attention 13 .

In accordance with article 171 of the Constitution and with ILO Convention 169, the law of the National Institute of Agrarian Reform (NIAR) provides for the dotation of Native Community Lands (tierras comunitarias de origen -TCO) to indigenous peoples. TCOs are defined as "geographical spaces constituting the settlement of indigenous and native communities to which they have traditionally accessed and where they maintain and develop their own forms of economic, social and cultural organization in order to secure their survival and development. They are inalienable, indivisible, irreversible, collective, composed by communities or associations of communities, exempt from seizure, and imprescriptible" (art.41, 5). The "TCO denomination comprises the concept of indigenous territory" (art. 3).

Seventeen articles precise the status of these TCOs, the process for their granting, and plan for the participation of indigenous organizations to national and departmental agrarian commissions.

Native Community Lands constitute a form of agrarian collective property in which indigenous title-holders can develop internally their own system of economic, social and cultural organization. From a juridical point of view, TCOs exclusively pertain to the agrarian domain and do not have any particular institutional competency.

The NIAR law has immediate effects. A wave of submissions for community areas floods the whole country. The CIDOB and its affiliates open the way, rapidly followed by Andean indigenous organizations affiliated to the CONAMAQ (which was created just a few months after the promulgation of the law on agrarian reform). A vast movement of ethnic territoriality is triggered in Bolivia. In 2007, more than 150 TCOs have been granted, covering 36% of the national territory, according to State figures. New territorial claims have been made and this coverage could reach 42% in the coming years [START_REF] Lacroix | Hacia una nueva gobernanza territorial indígena en Bolivia[END_REF].

In spite of strong territorial demand, indigenous territoriality remains precarious. By bestowing TCOs on indigenous populations, the Bolivian State gives them spaces of collective settlement rather than territories. These populations do not enjoy exclusive or priority rights in their collective property, nor decentralized resources to manage them. This situation of judicial and political in-betweenness encourages a superposition of rights, generating many social conflicts between TCO-holding populations and various agents (extractive companies, pastoralists, farmers) that are legally or illegally established on areas bestowed on indigenous peoples [START_REF] De | Territorios Indígenas en las Tierras Bajas de Bolivia. Un análisis de su estado a[END_REF]CIDOB 2000).

The CIDOB proposes to transform TCOs into indigenous jurisdictions integrated to the political and administrative framework of the State in order to remedy this situation, advocating for "indigenous autonomies". To do so, a new political constitution proves necessary. In this perspective, the CIDOB will be mobilized for a whole decade alongside other social actors, calling for the establishment of a constituent assembly whose main objective would be to institutionalize autonomous indigenous territories.

A new political and territorial paradigm

Evo Morales' access to power (2005), the elaboration of a new Constitution establishing a plurinational State ( 2009), and the United Nations Declaration on the Rights of Indigenous Peoples (2007) generate great hopes for Bolivian indigenous organizations. Each of these three facts have contributed to installing indigenous territoriality as one of the principal themes of political debate in recent years, and have created a historical opportunity to institutionalize indigenous territories.

A favorable context: Morales and the UN

The majority of Bolivian indigenous organizations support Evo Morales and his party, el Movimiento al Socialismo (MAS). In their ascension towards power, Morales and the MAS have offered a tangible political alternative for numerous indigenous leaders who participated in municipal elections by granting them a relative autonomy both in terms of nominating candidates and of electoral programs. The MAS thus captured indigenous organizations' sympathy, which have become a loyal electorate in national elections. Once in power, Evo Morales made many declarations of good intentions to indigenous peoples, and he is a selfproclaimed defender of their rights on the international scene. Some of the first measures of this government were aimed at indigenous peoples situations.

The National Plan for Economic Development presented in June 2006 has the core objective of constructing a "multinational and communitarian State" that would put an end to historical "colonialism", "neoliberalism", and "the exclusion of indigenous peoples" through a "recognition and a valorization of indigenous and peasant communal economies. The Plan is inspired by the "Andean-Amazonian capitalism" project elaborated by vice-president Garcia Linera, which consists in "the construction of a strong State that regulates the growth of industrial economy, extracts its benefits and transfers them towards the communitarian sphere to provide for specifically Andean and Amazonian forms of self-organization and mercantile development" (Garcia Linera 2005).

In November 2006, the Ley de Reconducción Comunitaria de la Reforma Agraria reconsiders the 1996 NIAR law. Among other changes, it provides for the priority (or even systematic) attribution of expropriated lands to "indigenous native peasant communities" (art. 34) as well as an active support to micro businesses and communitarian enterprises in terms of production, productivity and market exploration (art. 7). In 2007, two decrees regulate the socio-environmental control of oil and gas activities on indigenous peoples' and peasants' communities' lands that had been planned for in the 2005 Hydrocarbon law. The 1997 Mining Code is modified to allow indigenous peoples to claim rights, in particular the right to consultation over mining exploration on their lands.

The impact of all these measures remains somewhat limited. The new agrarian legislation does not include any new guarantee for TCOs, and new regulations on extractive activities in indigenous collective settlement areas have only worsened the tensions with the third parties (enterprise and individuals) who exploit oil and mineral resources. Further, Morales waits until the United Nations Declaration on the Rights of Indigenous Peoples to adopt some substantive measure about indigenous peoples.

The adoption of the international standard rejoices indigenous organizations in the country. The text had been negotiated for over twenty years and the object of numerous debates between indigenous peoples and the States. The Declaration affirms indigenous peoples right to self-determination and, consequently, their right to freely determine their political status and economic, social and cultural development (art.3), their right to be autonomous and manage their internal and local affairs (art.4). Bolivian indigenous organizations present a draft law to include this declaration in the national law and organize several demonstrations to secure such integration. Facing mobilization and enthusiasm, the Morales government elevates the 46 articles of the United Nations Declaration on the Rights of Indigenous Peoples to the rank of law of the Republic (law 3760, 7 th November 2007). For indigenous organizations, this measure is a first step towards the formalization of the international text pending its translation into the new Constitution. Its development, however, is delayed. The heated debates between the government and the opposition generate important social conflicts. The Constituent Assembly is adjourned and threatened of dissolution on several occasions during its mandate. The main indigenous and peasant organizations of the country, who became allied in a Pact of National Unity14 , have ensured the survival of the process by exercising pressure on delegates and by formulating numerous propositions during the debates.

Thus, the United Nations Declaration on the Rights of Indigenous Peoples comes at a right time when, in Bolivia, the political situation and the constitutional debates seem in a deadlock [START_REF] Lacroix | Refundación del modelo nacional y tensiones políticas[END_REF]. The international standard allows indigenous organizations to obtain minimum guarantees for the inclusion of indigenous peoples rights, especially those concerning their territories, and the constitutional incorporation of the concept of indigenous autonomy.

Political constitution and ethnic territoriality

A defining character of the 2009 Bolivian Constitution is to institute a "unitary State with plurinational law" (art.1). It secures indigenous peoples rights to self-determination, to autonomy, to self-government, to culture, to the recognition of indigenous institutions, and to the consolidation of territorial entities respectful of the unity of the State (art.2 & 30). The constitution recognizes their systems of government (art. 11 & 26). These fundamental principles are developed in fifty general articles with reference to socio-cultural difference, that is one-eighth of all constitutional articles. These articles detail the State model, the local system of indigenous government, indigenous peoples rights (in political, health and educational matters), the protection of traditional knowledge, and State support for indigenous economic development. Specific articles are concerned with the rights of "indigenous native peasant nations and peoples", indigenous peoples representation on and participation to the Plurinational Constitutional Tribunal, to the Plurinational Electoral Council, and to departmental and municipal councils.

The territorial and ethnic issue is discussed under the term "indigenous native peasant territorial entities". It is thematically divided into jurisdictions, autonomies, and natural resource management. The territories, municipalities and regions constituting "ancestral territories" for "indigenous native peasant nations and peoples" potentially are such territorial entities (art. 291 & 192). These entities are fully jurisdictions (art. 180, 191-193).

The conceded autonomy is "the expression of the right to self-government as the exercise of the right of self-determination by indigenous native peasant nations and peoples whose population shares a territory, a culture, a history, languages and specific judicial, political, social, economic organizations or institutions" (art. 290). "Each territorial entity (…) will elaborate its own status in accordance with its own norms and procedures and within the framework of the Constitution and the Autonomies and Decentralization Law" (art. 293). "indigenous native peasant nations and peoples" territories will assume the competencies of municipalities and regions according to their status" (art. 305). They can exercise these competencies "exclusively or in competition" (idem). These competencies bear, among other aspects, on the definition and implementation of local development (economic, cultural, social) plans, the development and maintenance of infrastructure, healthcare, the administration of indigenous justice, the protection of natural and cultural heritage, the relations with external organizations and institutions (idem).

"The exploitation of natural resources in a given place will be subject to a consultation process with the local population affected" (art.352). In the case of "indigenous native peasant nations and peoples", this consultation will respect their norms and procedures (idem). The benefits generated by resource exploitation will be primarily assigned to indigenous native peasant peoples (art. 353). The "entirety of indigenous native peasant territory" is recognized, which includes "the right to land, to the exclusive use and enjoyment of renewable natural resources as per legal provisions; free prior and informed consultation, and benefit-sharing stemming from the exploitation of natural resources from their territories (…) the definition of their development in accordance with their cultural criteria and life principles. (…) Indigenous native peasant territory comprises areas for the use and conservation of natural resources as well as areas for the social, spiritual and cultural reproduction" (art. 402). The State recognizes, protects and guarantees the individual and communitarian or collective ownership of the land (art. 393).

The notion of indigenous territoriality as defined by the Constitution satisfies the CIDOB and CONAMAQ expectations, for which indigenous territories must be granted autonomous governments by the State and must assume competencies similar to other subnational jurisdictions. To sum up, Bolivia is engaged towards the instauration of indigenous jurisdictions fully integrated to the political and administrative organization of the country; these could allow indigenous peoples to take on political, legal and normative autonomy with executive, administrative, patrimonial, territorial and jurisdictional dimensions, in accordance with the legal field of the State (CIDOB 2008).

From norms to implementation: the challenge of indigenous autonomies

The Autonomies and Decentralization Law (LMAD) was promulgated in July 2010. The text was long awaited by civil society organizations, especially indigenous and regionalist organizations, as it determines the general frame of departmental, regional, municipal and "indigenous native peasant" (indigena originario campesino, IOC) autonomies defined in the Constitution. A first reading of this complex and (over)detailed text allows an exposition of some general principles on the specific issue of IOC autonomies.

Among the eighteen fundamental principles for the autonomy system (territorial integrity of the State, self-government, hierarchical insubordination of autonomous territorial entities, voluntary access to autonomy, etc.), let us firstly highlight the principle of "Indigenous Native peasant nations and peoples preexistence" that guarantees, according to the Constitution and UN Declaration, "their self-determination, their right to autonomy, to self-government, to their culture, to the recognition of their institutions and the consolidation of their territorial entities" (art. 1 & 5). The preexistence principle also makes room for multiple pathways to autonomy.

The indigenous native peasant autonomy (AIOC) regime is exclusively granted to indigenous native peasant nations and peoples who are defined as "peoples and nations who existed prior to invasion and settlement, who constitute a sociopolitical unit, developed through history, with a common and shared organization, culture, institutions, law, rituality, religion, and language, among other characteristics. They are established in a given ancestral territory and have their own institutions" (art. 6.II).

These indigenous peoples may be granted autonomy from a territory, a region, a municipality or municipal district (art. 44 &28). Concerning the last three levels, the AIOC regime can be obtained through a locally initiated referendum (art. 50-52) after certification by the Ministry of Autonomies of the ancestral territory nature of these territorial units (art. 56). For territories (TIOCs), the ministerial certification rests on the viability of government (viabilidad gubernativa), which is assessed through an evaluation of the political organization and an analysis of the territorial development plan, and on a minimal demographic base calculated from the latest census results. The required demographic limit is 10 000 inhabitants for the Andes (4000 in exceptional cases), and 1000 inhabitants for the Lowlands (art. 58). On a more pragmatic level, these provisions mean that indigenous peoples who already have a TCO status have an easier access to a TIOC insofar as some information is already gathered.

Once the AIOC is granted, the deliberative organs of these territorial entities have to develop an "autonomic status" which must be approved by referendum and by 2/3 of the territorial entity's population (art. 53 & 54). These statuses must consider non-indigenous minorities by guaranteeing constitutional rights, and must present a strategic vision for the development of the territorial entity (art. 61 &62). Once the autonomic status enters into force, the indigenous government can exercise the legislative, deliberative, and regulating powers, and taken on their given competencies (art. 45 & 55).

These competencies involve health services, housing, drinkable water, telecommunications, cultural heritage, natural resources, biodiversity and the environment, rural and productive development, planning, territorial organization, tourism, transport, and natural risks management (art. 81-97). Educational competencies will be defined in a separate law (art. 84). All AIOC territorial entities constitute fully jurisdictions (art. 8). They are integrated to the general financial regime. Their resources mostly come from decentralized State funds whose management is subject to precise regulations shared by all subnational territorial entities (art. 106-131).

The indigenous territory (TIOC) is the greatest innovation in the political and administrative organization of the Bolivian State among all territorial entities defined in the LMAD. The TIOC results from the conversion of Native Community Lands (determined in the 1996 agrarian regime) into territorial jurisdictions with autonomous powers, as well as budgets and competencies similar to those of municipalities. It is defined as an "ancestral territory on which collective or native community lands have been constituted and duly consolidated in accordance with the law, and which have entered this category through the corresponding agrarian procedure (…) an indigenous native peasant government will be formed in it. This territory will be approved by law as a territorial unit, thereby acquiring a double character", agrarian and jurisdictional (art. 6.I.2).

In line with the Constitution, the law on Autonomies recognizes many rights mentioned in the UN Declaration (self-determination, autonomy, self-government) and satisfies Bolivian indigenous organizations aspirations. What is, however, the actual situation of indigenous autonomies in Bolivia? Although complex to sum up, the situation can be presented as follows.

Until now, only one out of two hundred TCOs has presented an autonomic status to the State (the first step to convert a TCO into an indigenous autonomous territory), Raqaypampa in the Cochabamba department. This status must now be submitted to the Constitutional tribunal. In other cases, obstacles are many. Among these, one is the fact that the majority of TCOs have not been granted tenure, thereby making the conversion into indigenous territory impossible. Further, the conditions set out in the LMAD are contested by indigenous organizations, particularly the demographic rule and the territorial continuity rule, that appear too stringent and restrictive for many indigenous peoples wishing to access territorial autonomy.

In parallel, a municipal dynamic has been engaged. Eleven out of the three-hundred-andthirty-six municipal governments have started the process to obtain the indigenous autonomy regime 15 and peasants organizations that compete for local power. The Autonomies ministry mediates to try and appease the conflicts and move the process forward in a consensual manner.

While it may appear innovative in legislation, the indigenous autonomy process is a source of detachment between the Morales government and indigenous organizations. The latter have had to mobilize on many occasions to negotiate adjustments that would incorporate their demands. These tensions extend the difficulties that have appeared in the relations between the parties since the adoption of the Constitution in 2009.

Indigenous organizations now keep watch. The steps to obtain the autonomy regime are many and each one represents a source of potential conflicts. The challenge consists in avoiding similar delays and faults as with the INRA law. 15 years after its promulgation, many TCOs have not been granted tenure nor have been identified and demarcated. To this already sensitive territorial situation, the issue of prior consultation of indigenous peoples over extractive activities on their territories only adds a new level of conflict with the Morales government. In other words, the concrete conditions for the instauration of a plurinational State and the implementation of self-determination for indigenous peoples are currently at stake in Bolivia.

By way of conclusion

With the new Constitution and the Autonomies and Decentralization Law, the Bolivian State seems to respond to territorial claims by indigenous organizations while incorporating international indigenous peoples rights. In the last four decades, two moments have proved decisive in the political consideration of indigenous territories in Bolivia. In the 1990s, the State grants indigenous peoples who so wish with Native Community Lands (TCOs). Although this form of territorial recognition does not fully consider the notion of territoriality developed by indigenous organizations (as it does not grant any competency in terms of public management and finances), it nonetheless generates a pre-territorialization of indigenous peoples through a demarcation of their areas of collective settlement. Then, in the last decade, indigenous territoriality has taken on a new dimension by integrating political projects linked to the process of "national re-foundation". Indigenous territories are now recognized as fully jurisdictions by the political Constitution of the Bolivian state.

These are two precise historical moments, characterized by the convergence of indigenous (through mobilizations and propositions) and indigenist (through recognition of rights and support policies) dynamics on both national and international levels. This juncture rests on a complex circulation of agents working at different levels (local, national, international) to elaborate norms, public policies and specific programs for indigenous peoples. In the Bolivian case, such historical coincidence clearly appeared first in the 1990s, and then in the last few years with the emergence of new international standards for indigenous peoples rights, of a State modernization process involving a global or partial consideration of indigenous issues, and of indigenous peoples mobilizations on both local and international levels for the implementation or claiming of rights. The interaction between these dynamics is generally occurring, in Bolivia as in most Latin-American States, in a normative field that is conducive to the eminently constitutionalist, legalist and pacific strategies of indigenous peoples in Latin America.

In all likelihood, the constitutional adoption of a plurinational State engages Bolivia towards a paradigmatic change in the governance of territorial(ized) entities, especially ethnic ones. The principles of liberal multiculturalism that were predominant in the 1990s are abandoned (Lacroix 2011b). Bolivia thus seems to direct itself towards an unheard of "post multicultural" political model [START_REF] Grey | Now we are citizens: indigenous in postmulticultural Bolivia[END_REF] that fully integrates the United Nations Declaration on the Rights of Indigenous Peoples and that grasps the indigenous question as a central and transversal political issue for a new societal project. Like indigenous autonomies, all the manifestations of the plurinational State have to be defined. The CIDOB and CONAMAQ have entered a probably long period of careful watch to ensure the effective implementation of the Bolivian Constitutions. In this perspective, these two organizations should maintain their particular place on the national and international political scenes in the coming years.

  . Five of them have developed their autonomic status. Six others are being discussed. Some of them have moved slowly forward because of local disagreement between indigenous 15 Chipaya, Pampas Aullagas, Totora and Salinas de Mendoza in the Oruro department; Tarabuco, Mojocoya and Huacaya in the Chuquisaca department; Charazani and Jesús de Machaka in the La Paz department; Charagua in the Santa Cruz department; Chayanta in the Potosí department.

  This perspective is reached at the end of a cycle of social and political unrest that sees four successive presidents of the Republic between 2000 and 2005. The last of them, Evo Morales, is elected in December 2005 during early general elections. In accordance with his electoral engagements, Morales organizes a constituent assembly(2006)(2007)(2008), which writes a new constitution approved by referendum in January 2009. The text integrates the full United Nations Declaration on the Rights of Indigenous Peoples (2007) and plans for the establishment of "indigenous autonomies".

From Tupac Katari who was the leader of an « native » rebellion on the Bolivian Altiplano in 1781. On the katarist movement, see, among other works, those by Jean-PierreLavaud (1981[START_REF] Lavaud | Identité et Politique : le courant Tupac Katari en Bolivie, document de travail 24[END_REF], Diego[START_REF] Pacheco | El indianismo y los indios contemporeanos en Bolivia[END_REF] and Yvon Le Bot (1994).

Among others: the Aymaras, Kechuas, Tupiguaranies National Council united by ayllus and communities (AKTUPAC) in 1986, the Unique Confederation of Kollasuyu-Bolivia Ayllus-Communities-Capitanias (CUAKK-B) in 1987, the Cabildo of Urinsaya Native communities in 1990, the South Oruro Ayllus Federation

(FASOR) in 1988, the North Potosí Federation of Native Ayllus (FAO-NP) in 1993, etc.5 For instance, the Unitary Chuquisaca Workers Peasant Native Trade Federation (FSUTCOH), or the Peasant Native Workers Trade Union Federation of Potosí (FSUTCOP).6 Extracts from documents produced by the organization.7 The authority of local settlers, then of Jesuit and Franciscan missionnaries between 1681 and 1767, then of local administrators or hacienda bosses between 1768 and1953, and finally the authority of various agents (State, catholic church, Summer Institute of Linguistics until the 1980s or 1990s in some regions)

Excerpts from the organization's archives.

Especially articles 13 to 19.

The Siriono Indigenous Territory; the multiethnic Isiboro-Sécure National Park; the Chiman Indigenous Territory; the Multiethnic Indigenous Territory.

The Araona Territory; the Pilon Lajas Biosphere Reserve; the Yuqui Territory; the Chiquitano Territory No1; the Mataco Territory.

Article 171 of the Constitution : Reconocimiento de derechos de pueblos indígenas I. Se reconocen, se respetan y protegen en el marco de la ley, los derechos sociales, económicos y culturales de los pueblos indígenas que habitan en el territorio nacional, especialmente los relativos a sus tierras comunitarias de origen, garantizando el uso y aprovechamiento sostenible de los recursos naturales, a su identidad, valores, lenguas, costumbres e instituciones. II. El Estado reconoce la personalidad jurídica de las comunidades indígenas y campesinas y de las asociaciones y sindicatos campesinos. III. Las autoridades naturales de las comunidades indígenas y campesinas podrán ejercer funciones de administración y aplicación de normas propias como solución alternativa de conflictos, en conformidad a sus costumbres y procedimientos, siempre que no sean contrarias a esta Constitución y las leyes. La ley compatibilizará estas funciones con las atribuciones de los Poderes del Estado.

In 1994, the Un adopted a Draft Declaration on the Rights of Indigenous Peoples, establishes an International Day for Indigenous Peoples (9 th August) and organizes the International Conference on population and development in Cairo. In 1995 it announces the first international decade for Indigenous Peoples on the theme of "Indigenous populations: partnership in action"(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004) during which the Declaration on the Rights of Indigenous Peoples is developed. In 1996, Rigoberta Menchu receives the Nobel Peace Prize and launches the issue of indigenous peoples on the international political and media scene.

The Pact of National Unity brings together the Confederación Sindical Única de los Trabajadores Campesinos de Bolivia (CSUTCB), the Confederación Nacional de Mujeres Campesinas Indígenas Originarias de Bolivia Bartolina Sisa (CNMCIOB-BS), the Confederación Sindical de Comunidades Interculturales de Bolivia (CSCIB), CONAMAQ and CIDOB. This inter-sectorial alliance is created in 2004. It has a double objective: the instauration of a Constituent Assembly and to support Evo Morales' Movimiento al Socialismo political project. Following a series of conflicts with the Morales government and the peasants' organisations, CIDOB and CONAMAQ have left the Pact of National Unity in 2011.

European

Research Council as part of the seventh Framework-program of the European Union in light of the funding convention ERC-2009-AdG-20090415-SOGIP for the research project "Scales of Governance and Indigenous Peoples Human Rights: the meanings and issues of self-determination in the time of globalization" (http://www.sogip.ehess.fr). I thank Martin Préaud, member of the SOGIP team, for the english translation of this text. Access to the original text : http://www.antropologia.cat/quaderns-e-194

Résumé

La Bolivie semble s'engager vers l'institutionnalisation de territoires autochtones intégrés à l'organisation politico-administrative de l'Etat. Ce processus se traduirait par l'instauration de circonscriptions et de juridictions ethniques autonomes. Cet article propose une lecture croisée considérant à la fois la mobilisation des organisations autochtones pour leurs droits, les débats nationaux autour des questions de territoires et d'autochtonie et l'évolution du contexte international au cours des quatre dernières décennies pour tenter de mieux comprendre les effets d'imbrication d'échelles de gouvernance qui ont mené à cet horizon politique en Bolivie.

Mots-clés : Bolivie -peuples autochtones -territoire -autonomie -traitement politique Summary Bolivia seems to engage towards the integration of indigenous territories into the institutional, political and administrative organization of the State. This process would result in the introduction of autonomous ethnic districts and jurisdictions. This paper proposes a cross reading, simultaneously considering the mobilization of indigenous organizations, national debates on issues of territories and ethnicity and the evolution of the international context in the last four decades. The objective is to better understand the complex interactions between scales of governance that have led to this renewed political landscape in in Bolivia.


S Laurens

S Tordeux

Explicit computation of the electrostatic energy for an elliptical charged disc

This letter describes a method for obtaining an explicit expression for the electrostatic energy of a charged elliptical innitely thin disc. The charge distribution is assumed to be polynomial. Such explicit values for this energy are fundamental for assessing the accuracy of boundary element codes. The main tools used are an extension of Copson's method and a diagonalization, given by Leppington and Levine, of the single-layer potential operator associated with the electrostatic potential created by a distribution of charges on the elliptical disc.

Introduction

In recent years, integral equations have become an essential tool for solving both industrial and scientic problems in electromagnetism and acoustics. The assessment of the accuracy delivered by such codes, in particular in their handling of the singular integrals involved, is a major issue. Here, we present a method for deriving an analytical expression for the electrostatic energy of a charged elliptical innitely thin plate, providing a means for the validation of these codes.

Let us denote by A = (x 1 , x 2 ) ∈ R 2 with x 2 1 /a 2 + x 2 2 /b 2 -1 < 0 and a > b the ellipse with major and minor semi-axes a and b. Let f be the electrostatic potential generated by a density of charges σ distributed over A:

f (x) = 1 4π A σ(y) |x -y| ds y for all x in A, (1)
with x = (x 1 , x 2 ). The units have been chosen such that the electric permittivity of air is 1. The electrostatic energy I can be expressed in either the two following forms:

I σ = A f (x) σ(x)ds x = A 1 4π A σ(x) σ(y) |x -y| ds x ds y .
(

) 2
Email address: sophie.laurens@insa-toulouse.fr (S. Laurens) We aim in this letter at proving and numerically illustrating the following theorem, where ε is the eccentricity of the ellipse A given by ε = 1 -b 2 /a 2 .

Theorem 1.1. Let σ(x) = α 0 + α 1 x 1 /a + α 2 x 2 /b, with α ∈ R 3 , be the distribution of charges over A. The corresponding electrostatic energy is given by

I σ = 8ab 2 15π 5α 2 0 + α 2 2 K(ε) + α 2 1 -α 2 2 K(ε) -E(ε) ε 2 ,
with K(ε) and E(ε) the complete elliptic integrals of the rst and second kind

K(ε) = π/2 0 dφ 1 -ε 2 sin 2 φ and E(ε) = π/2 0 1 -ε 2 sin 2 φ dφ. ( 3
)
2. Diagonalization of the electrostatic energy

Following [START_REF] Leppington | Reexion and transmission at a plane screen with periodically arranged circular or elliptical apertures[END_REF], we consider the spheroidal coordinate system (θ, ϕ) giving a parametrization of A in terms of the unit half-sphere

x 1 = a sin θ cos ϕ and x 2 = b sin θ sin ϕ, with θ ∈ [0, π/2], ϕ ∈ [0, 2π]. (4)
The elemental area associated with the new variables is ab cos θ sin θ dθdϕ. In these spheroidal coordinates, the electrostatic potential f dened in (1) and the electrostatic energy can also be written in terms of θ and ϕ as

       f (θ, ϕ) = ab 4π π/2 0 2π 0 g(θ ′ , ϕ ′ ) d(θ, ϕ, θ ′ , ϕ ′ ) sin θ ′ dθ ′ dϕ ′ , I σ = ab π/2 0 2π 0 f (θ, ϕ)g(θ, ϕ) sin θ dθdϕ,
with g(θ, ϕ) = σ(θ, ϕ) cos θ and d(θ, ϕ, θ ′ , ϕ ′ ) the distance separating x from y d = |x -y| expressed in the spheroidal coordinates (4). The next step consists in introducing a well chosen spectral basis for the halfsphere involving the even Legendre functions Q m n normalized by

π 0 Q m n (cos θ) Q m n ′ (cos θ) sin θdθ = δ n,n ′ .
(

) 5
This basis yields a block diagonalization of the convolution operator (see [START_REF] Leppington | Reexion and transmission at a plane screen with periodically arranged circular or elliptical apertures[END_REF])

1 d = 1 √ ab ∞ n=0 n m=-n n-m even n m ′ =-n n-m ′ even d n mm ′ Q m n (cos θ) Q m ′ n (cos θ ′ ) e i(mϕ-m ′ ϕ ′ ) , with d n mm ′ = Q m n (0) Q m ′ n (0) 2n + 1 2π 0 e i(m-m ′ )ϕ b a cos 2 ϕ + a b sin 2 ϕ dϕ. (6)
The functions f and g can be expanded in this basis as

u(θ, ϕ) = ∞ n=0 n m=-n n-m even u m n Q m n (cos θ) e imϕ with u = f or g (7)
with

u m n = 1 π π/2 0 2π 0 u(θ, ϕ) Q m n (cos θ) e -imϕ sin(θ)dθdϕ.
(8) Due to (6), coecients f m n are related to g m n by

f m n = √ ab 4 n m ′ =-n n-m ′ even d n mm ′ g m ′ n ′ . (9)
Moreover, the orthogonal properties of the spectral basis yield

I σ = π 4 (ab) 3/2 n,m,m ′ d n mm ′ g m n g m ′ n ,
where we have lightened the notation by making the range of the summation index implicit. Indices n, n ′ are varying from 0 to ∞, and m, m ′ are such that |m| ≤ n, |m ′ | ≤ n ′ , with n -m and n -m ′ even. Substituting expression (6) for d n mm ′ and introducing the eccentricity of the ellipse ε, we get

I σ = π ab 2 n,m,m ′ g m n g m ′ n Q m n (0) Q m ′ n (0) 2n + 1 π/2 0 cos(m -m ′ )ϕ 1 -ε 2 cos 2 ϕ
dϕ.

(10)

Electrostatic energy for an ane distribution of charges

This section is dedicated to the calculation of the electrostatic energy generated by an ane density of charges.

Proof of Theorem 1.1. Let σ 0 (x) = 1, σ 1 (x) = x 1 /a and σ 2 (x) = x 2 /b. In view of the symmetry of A with respect to x 1 and x 2 , we have

A 1 4π A σ i (x)σ j (y) |x -y| ds x ds y = 0 for i = j.
Consequently, the electrostatic energy I σ can be expanded as

I σ = α 2 0 I σ0 + α 2 1 I σ1 + α 2 2 I σ2
The result will follow from the computation of I σ0 , I σ1 and I σ2 .

Computation of I σ0

For σ(x) = σ 0 (x) = 1, the function g(θ, ϕ) = cos θ does not depend on ϕ. The g m n coecients are independent from a and b, and since g m n = 0 for all 3 m = 0, the function g can be expanded as g(θ) = +∞ n=0 g 0 n Q 0 n (cos θ) . Due to (10), the electrostatic energy I σ0 depends only on a and b and is given by

I σ0 (a, b) = π ab 2 +∞ n=0 |g 0 n | 2 Q 0 n (0) 2 2n + 1 π/2 0 dϕ 1 -ε 2 cos 2 ϕ = κ ab 2 K(ε), (11)
with ε = 1 -b 2 /a 2 and κ a constant depending neither on a nor on b. The constant κ is deduced from the classical case of an unit circle which has been detailed for example in [START_REF] Laurens | Lower and upper bounds for the Rayleigh conductivity of a perforated plate[END_REF]

I σ0 (1, 1) = C 1 4π C 1 |x -y| ds x ds y = 4/3. ( 12
)
Comparing ( 11) and ( 12), this yields to κ = 8/3π since K(0) = π/2. Therefore,

I σ0 = 8 3π ab 2 K(ε).
(13)

Computation of I σ1

For σ(x) = σ 1 (x) = x 1 /a, the function g is given by g(θ, ϕ) = sin θ cos θ cos ϕ. In that case, the g m n are zero except for |m| = 1. By denition of the Legendre functions, we have

Q -1 n = -Q 1 n .
As the function g is even, it emerges that g -1 n = -g 1 n , and thus

I σ1 = πab 2 n g 1 n Q 1 n (0) 2 2n + 1 2 π/2 0 dϕ 1 -ε 2 cos 2 ϕ + 2 π/2 0 cos 2ϕ dϕ 1 -ε 2 cos 2 ϕ .
Due to (3), it emerges that

I σ1 (a, b) = κ ab 2 K(ε) -E(ε) ε 2 . ( 14
)
To determine the constant κ, we consider again the case of an unit circle. In this case, I σ1 can be explicitly computed (see the Appendix A), and is given by I σ1 (1, 1) = 2/15. Evaluating (14) at a = b = 1 we get

I σ1 (1, 1) = κ π 4 since lim ε→0 K(ε) -E(ε) ε 2 = π 4 . (15)
It follows that κ = 8/15π and therefore we have

I σ1 = 8 15π ab 2 K(ε) -E(ε) ε 2 .
(16)

Computation of I σ2

For I σ2 , we consider σ(x) = σ 2 (x) = x 2 /b, meaning that g(θ, ϕ) = sin θ cos θ sin ϕ. We still have g m n = 0 except for |m| = 1, but in that case, g -1 n = g 1 n . Thus

I σ2 = πab 2 +∞ n=0 g 1 n Q 1 n (0) 2 2n + 1 2 π/2 0 dϕ 1 -ε 2 cos 2 ϕ -2 π/2 0 cos 2ϕ dϕ 1 -ε 2 cos 2 ϕ
Moreover, both integrals I σ1 and I σ2 are equal on C by symmetry. We obtain

I σ2 = 8 15π ab 2 K(ε) - K(ε) -E(ε) ε 2 .
(17)

Numerical tests and conclusion

Tables 1 and2 give a comparison of the exact values given by an analytical expression with numerical approximate values obtained by the boundary element code CESC of CERFACS with P 1 continuous elements. It can be observed that the two values coincide at least up to the fourth decimal digit. Table 3 shows the maximum relative error for each of the cases of Tables 1 and2 ε rel 0.055 0 /00 0.195 0 /00 9.1 × 10 -4 0 /00 0.334 0 /00 | in per mil for an elliptical disc for b = 0.5 and a = 0.5 : 0.05 : 1.5.

Table 1 :

 1 cases, which is less than 0.35 per mil. Exact and computed values of the electrostatic energy, I exact , for an elliptical disc with minor axis b = 0.5, given by (13), (16), (17) .

		a	0.5		0.7		0.9	1.1	1.3	1.5
	I comp σ0 I exact σ0	0.1666 0.1666	0.2741 0.2741	0.3939 0.3939	0.5234 0.5234	0.6608 0.6608	0.8048 0.8048
	I comp σ1 I exact σ1	×10 -1 0.0417 0.1455 0.3651 0.7535 1.3715 2.2781 ×10 -1 0.0417 0.1456 0.3656 0.7543 1.3717 2.2800
	I comp σ2 I exact σ2	×10 -2 0.4167 0.6280 0.8426 1.0585 1.2748 1.4910 ×10 -2 0.4167 0.6280 0.8427 1.0586 1.2748 1.4911
								σ i	and I comp σ i
		a	0.75		0.9		1.05	1.2	1.35	1.5
	I comp σ I exact σ	2.7734 2.7736	3.6157 3.6159	4.5162 4.5165	5.4706 5.4708	6.4761 6.4763	7.5313 7.5316

Table 2 :

 2 Ane density of charges σ = x1 + 2x2 + 3 for an elliptical disc with b = 0.5.

	I σ0	I σ1	I σ2	I σ

Table 3 :

 3 Maximum value of the relative error ε rel = max |I exact

	σ i	-I comp σ i

Acknowledgements

The authors would like to express their thanks to A. Bendali (INSA) for fruitful discussions and M. Fares (CERFACS) for the numerical computations achieved with the CERFACS code CESC. Part of this work was supported by the French National Research Agency under grant no. ANR-08-SYSC-001.

Appendix A. The case of an unit circle disc

Let C be the circle with radius 1. We aim here at computing the integral

This integral is rewritten in polar coordinates (r, φ for x and ρ, φ ′ for y) as

and evaluated using to the formula (3.4.5) of [3, p70] 2π 0 cos φ dφ

This leads to

This integral is symmetric in ρ and r, and since 2π 0 cos 2 φ ′ dφ ′ = π, we have