Daniela Berti

Tarabout Introduction Gilles

Introduction

Daniela Berti, Gilles Tarabout

Introduction

DANIELA BERTI and GILLES TARABOUT

This volume has been prepared with a view to confront a widespread stereotype in academic studies about India. According to this stereotype, pre-colonial India consisted of territorial units with ill-defined, fuzzy boundaries. This is taken to be a specifically Indian characteristic as the very notion of territory in Indian civilization is said to be of secondary importance for cultural reasons (this notion may be part of a more general, and widespread way of opposing a reified West to an equally reified India). The arguments put forward may vary. However, they all converge to create the idea that, generally speaking, territory in India had, and still has, little value as a cognitive category. This book aims at radically reconsidering this perspective.

Social anthropology and the study of territory

For long the social sciences have largely ignored the question of territory. It is only from the 1980s onwards that geographers, whom one would think to have been concerned with this topic long ago, have really begun to interest themselves in territories, not only in their political but also in their symbolic dimension, as objects of discourse and representation. 1 Paradoxically, debates among them seem to have been initiated by a perception of the 'end of territory' as a consequence of globalization. According to some, the category had thus become obsolete at the very moment it came into focus. The trend concerns now all the social sciences, so much that the French Ministry of Education and Research recently (2003) advertised an offer to substantially fund projects that would study 'Space and territory: society, economy, culture, language, representations', stating that 'social sciences and humanities have mostly elaborated their knowledge by ignoring the spatial dimension of human actions', but that processes at work in the contemporary world (i.e.globalization) involve a great number of academic disciplines in the geographical turn 'spreading in the social sciences, not only -as would be obvious-in geography, but also in economy..., in urban sociology, in political sciences..., in anthropology, in history, in linguistics, in the genetics of populations, and in cognitive sciences. ' As far as anthropology is concerned, a similar diagnostic has been made in numerous recent publications. As one of them put it, 'the exploration of how notions of belonging, localities and identities are constructed seems particularly relevant in current political contexts of "globalisation"' (Lovell 1998b: 1). One of the first and most influent publications on this theme was a collection of papers edited in 1988 by Arjun Appadurai in a special number of Cultural Anthropology on 'Place and Voice in Anthropological Theory', where the focus was more specifically on the problem of 'culturally defined locations to which ethnographies refer' (Appadurai 1988: 16). The discussion was further elaborated in various later works. [START_REF] Gupta | Culture, Power, Place : Ethnography at the End of an Era[END_REF], for instance, emphasize that we should be raising questions about 'anthropology's implicit mapping of the world as a series of discrete, territorialized cultures', and that at a time when 'cultural difference is increasingly becoming deterritorialized because of mass migrations and transnational culture flows of a late capitalist, postcolonial world…, there is obviously a special interest in understanding the way that questions of identity and cultural difference are spatialized in new ways. The circumstances of an accelerating "global cultural ecumene"… make the project of exploring the intertwined processes of place making and people making in the complex cultural politics of the nation-state an especially vital part of the contemporary anthropological agenda' (Gupta and Ferguson 1997: 3-4).

In this general context of rethinking the anthropologist's location as well as the way identities may relate to space in a globalized world, there have been essays reflecting on the very notions of space and place as something that may be a 'problem' in contemporary anthropological theory, which 'arises, paradoxically, because the meaning of place too often seems to go without saying' (Rodman 1992: 640). 2 However, as the author argues, places are socially constructed with multiple meanings, and 'anthropologists would do well to follow geographers' renewed interest […] in reunifying location (i.e., the spatial distribution of socioeconomic activity such as trade networks), sense of place (or attachment to place), and locale (the setting in which a particular social activity occurs, such as a church) to yield a more rounded understanding of places as culturally and socially constructed in practice' (Rodman 1992: 643). 3 In a short but influent seminal paper 4 on 'heterotopias', Michel Foucault stressed that 'the present epoch will perhaps be above all the epoch of space' (Foucault 1986: 22). 'In any case', he wrote, 'I believe that the anxiety of our era has to do fundamentally with space, no doubt a great deal more than with time'. But this was not to be the same space as was known earlier. According to him, 'today the site has been substituted for extension which itself had replaced emplacement… Our epoch is one in which space takes for us the form of relations among sites ' (ibid.23). How much this intuition had foreseen later developments in the social sciences (and especially in anthropology) is evident in the fact that all the works previously mentioned deal mostly, if not exclusively, with the question of sites, of identities in relation to space. In other words, the 'geographical turn' in social science studies appears also to be overwhelmingly a culturalist turn. 5 For instance, geographer Bonnemaison argues that 'human territoriality may be defined by the cultural relationship that a group or a society maintains with... the web of places and the system of itineraries that frame its space. References to biological-like concepts of "closure" such as appropriation or frontiers is not always a prime necessity: territory in fact refers more to the notion of identity than to security' (Bonnemaison 1995: 71, our translation).

This was indeed what S. Feld and K.H. Basso observed in their 1996 review of the then existing literature on the subject, when they wrote that 'the recent topicalization of place by cultural anthropologists has mostly been concerned with theorizing social identities' (Feld and Basso 1996b: 4). According to them, recent research in anthropology theorized place 'largely from the standpoint of its contestation', a development that 'surely reflects the now acute world conditions of exile, displacement, disaporas, and inflamed borders, to say nothing of the increasingly tumultuous struggles by indigenous peoples and cultural minorities for ancestral homelands, land rights and retention of sacred places'. As a consequence, anthropologists have come to worry 'about places as sites of power struggles or about displacement as histories of annexation, absorption, and resistance ' (ibid.: 4-5).

This statement certainly accounts for the perspective taken in the two volumes edited by [START_REF] Appadurai | Introduction: Place and Voice in Anthropological Theory[END_REF] and [START_REF] Gupta | Culture, Power, Place : Ethnography at the End of an Era[END_REF]. However, as Feld and Basso noticed, ethnographic accounts centered on the social construction of particular localities 'were few and far between' (ibid. : 6). Their own collection of contributions (as well as [START_REF] Rodman | Empowering Place: Multilocality and Multivocality[END_REF], Hirsch and O'Hanlon 1995and Lovell 1998a) therefore endeavoured to explore the 'complex ways in which places anchor lives in social formations ranging widely in geographical location, in economic and political scale, and in accompanying realms of gender, race, class, and ethnicity' (Feld and Basso 1996b: 7).

To sum up, the spate of anthropological writing on space since the late 1980s appears to follow two main trends. One is concerned with the location of the anthropologists and the people they study in a globalized world said to be characterized by deterritorialized culture. The other deals with perceptions and experience of lived-in places. Despite their differences, the two approaches partake of common preoccupations. Both are mostly, if not exclusively, focused on the question of the definition of identities. And both scarcely -if at all-mention such a word as 'territory', except in its derivative form 'deterritorialization'. Instead, there is a full array of seemingly connected notions such as 'space', 'place', 'location', 'site', and 'landscape'. Suggestive as they may be in their own right, these concepts are quite distinct from the notion of territory, which seems to have altogether disappeared from the profession's interests. 6 In thirty-one years of the Annual Review of Anthropology, significantly, there is not one bibliographical review that mentions in its title 'territory', or concerns itself with the topic. How can we account for such a disinterest?

The main cause could well be the exclusive stress put on culture and identities that has led most anthropologists in recent times to distrust the very notion of territory by assimilating it -we suppose-with the notion of cultural or ethnic boundaries. There is now a widely shared 'discomfort with the idea of bounded cultural units', to use Appadurai's words (Appadurai 1988b: 20). Indeed, we too feel such a discomfort. But it is our contention that it has little to do with the question of territory, and that conflating the two notions, 'territory' and 'bounded cultural unit' (if it were to happen) would be groundless. They just are not coterminous, as territory does not primarily refer to culture or identity, but to rights.

Ordinary definitions of the term in standard dictionaries give, for instance, 'land, especially land under one ruler or government' or 'the land and waters under a jurisdiction'; 'a political subdivision of a country'; 'an area for which a person is responsible as a representative or agent: a salesperson's territory', etc. Clearly, the notion of territory refers to notions of jurisdiction, of power, of rights, 7 but does not necessarily relate to cultural units or to group identities. People within a salesperson's territory may not be aware of the existence and the limits of this territory, and certainly need not develop a common perception of identity. While rights of a like nature define mutually exclusive territories, rights of different nature define different kinds of territories that may overlap and combine over a single stretch of land. A territory may be discontinuous geographically, its limits may be fluid, fuzzy, contested. But only in some specific cases does it intersect with the question of cultural identities.

A major example of such an intersection is, of course, the modern nation-state, where a territory, a political regime, a people and a culture are claimed to be ideally one and the same. This late development can by no means be taken as the model for reflecting on territory -such a standpoint, we feel, acted as a deterrent for fully recognizing the existence of territories in India, as we shall be showing later. Rather, one should consider its specificity against the many other forms of territorial organization that were, and still are, prevalent in the world.

While the present contributions participate in a wider movement currently taking place in the social sciences, which tends to give full importance to conceptions of space, they also try to explore a category -territory-that has elicited remarkably little interest among anthropologists in recent years. We feel, however, that there is much to gain in such a study, the more so because nation-state centred interpretations have tended to obscure the understanding of the complex interplay of territories in social life.

At the same time, the essays in this volume try to relate to a more specific tradition of Indian studies, and to contest some of its own peculiar stereotypes. The paradox is that for this region of the world, the notion of territory was far from being simply ignored. On the contrary it has been the object of diverse speculations, many of them concluding that it was of secondary importance and quite dispensable. Our discussion will first review the various arguments that were put forward to justify such a stand, before evoking the few attempts made to stress anew the importance of territory in India.

Territory in India

The most enduring stereotype that characterizes so many studies of India is that in this society there were neither territories properly speaking nor boundaries, at least in pre-colonial times -an interpretation that has led scholars to assert for instance that 'territory cannot be seen as a primary constituent of the Indian state' (Wink 1986: 161), or that 'the Indian political tradition… ascribed but an ambiguous and subordinated place to territory' (Jaffrelot 1996: 75, our translation).

On the contrary, as has been said, the present collection of essays aims at showing through some well-defined cases the crucial import of territory in India since ancient times, not only in the definition and the regulation of effective social, political, and religious relationships, but also as a category that has explicit cognitive value, as an object of symbolic activity, representations, and debates. The scope is therefore wider than a study of political territories alone, as the very nature of the objections raised by various authors against valuing their importance could not but lead to take into account a diversity of domains related to the various conceptualizations of territory in India. A brief review of these positions may not be out of place.

In their manifesto launched in 1957 at the occasion of the first number of Contributions to Indian Sociology, with the intention to contest the importance that was given at the time to the notion of the village as a sociological unit, 8 L.Dumont and D.L.Pocock wrote that the 'territorial factor, the relation to the soil is not, in India as a whole, one of the primary factors in social organisation. It is a secondary factor in relation to the two fundamental factors of kinship and caste' (Dumont and Pocock 1957: 18). Dumont himself had elaborated on this notion in his monograph study on the Kallars of Tamil Nadu, where he made a detailed study of local territorial units. In this work he concluded that 'kinship remains the fundamental principle of organization, and it becomes a factor in political organization once it is qualified or mediated so to speak, by the territorial principle' [START_REF] Dumont | A South Indian Subcaste: Social Organization and Religion of the Pramalai Kallar[END_REF][START_REF] Dumont | A South Indian Subcaste: Social Organization and Religion of the Pramalai Kallar[END_REF]: 184). With nuances, this was more or less the position held by many other authors. For example, A.C. Mayer, writing at the same period, underlined the importance of locality in breeding 'village patriotism' (overriding, often, caste divisions), but concluded also that kinship is essential in defining territorial units: 'this makes the region a fluid and rather unsatisfactory structural concept…The "territory" of Ramkheri subcaste group is a variable kinship-territory' (Mayer 1960: 271-2). Similarly, Richard G. Fox found that in northern India 'the territorial state does not prove preeminent over local kin-defined political and economic bodies' (Fox 1971: 168). 9 In the present volume, Chapter 6 by Gérard Toffin is a critical contribution to this specific discussion and illustrates, among other things, that kinship and territory need not be set up as exclusive alternatives, but help mutually define each other. 10 As an important variant in the arguments conducive to a devaluation of territory in relation to caste, Dumont later developed an alternative theory, in which kinship lost its role in favour of what he called the caste system's 'ideology'. According to his well-known formula, 'the ideology ignores territory as such' (Dumont 1966: 196). There, 'ideology' relates to the basic opposition between purity and impurity, the fundamental logic behind the 'caste system' in Dumont's theory. Such an assertion, in his view, was not meant to deny the empirical evidence of territorial facts, on which he himself had worked in detail. However, his quest for an overarching structural principle giving coherence to 'Indian civilisation' (a preoccupation that went back to the first issue of Contributions to Indian Sociology in 1957) led him to an a priori subordination of what he called the empirical level to the ideological. In his words, the ideological level in India 'does not account for the territorial factor, ignores it and encompasses it' (ibid.: 67). Many essays in the present volume address and contest this perspective, for instance the contributions by Michel Angot and Gérard Colas (Chapters 1 and 2) that historicize the sharp contrast existing at the 'ideological level' between a Vedic ritualistic discourse, devaluing fixation in permanent places, and later Brahmanical developments, valuing the local entrenchment of gods.

Dumont's theory has been widely criticised from different perspectives, 11 but his specific point about territory was in fact little, if at all discussed. While most of his critics did not address the issue, some did so, but often considered territory as a mere part of the politicoeconomic sphere, a reductionism that could not really confront Dumont's perspective. 12 Thus, in a way, it is somewhat paradoxical that Dumont has been one of the few anthropologists to have discussed at length the notion of territory as such, under various aspects -village community, village gods, territorial segmentation of castes, concepts of property, and royal power 13 -in order to demonstrate that it was of secondary importance in relation to caste and 'ideology'.

Another line of argument that has tended to devaluate the importance of territory in India pertains to a denial of the links between people -or some of them-with the place they live in. For instance Sanskritist Charles Malamoud suggested once that there is nowadays a 'weak "territoriality" of the Indian village', to be paralleled with the fact that 'ancestors in India have no earthly abode' [START_REF] Malamoud | Village and Forest in the Ideology of Brahmanic India[END_REF][START_REF] Malamoud | Village and Forest in the Ideology of Brahmanic India[END_REF]: 75 n.7). A similar reasoning has been made by anthropologist Yasushi [START_REF] Uchiyamada | Sacred Grove (kāvu): Ancestral Land of 'Landless Agricultural Labourers' in Kerala, India[END_REF] when he argued that depressed castes in Kerala, who bury their dead, develop more attachment to the land than upper castes who practise cremation. On the basis of factual observation, the argument is altogether unconvincing, since in this region members of high castes, too, define their identity through strong references to an ancestral land [START_REF] Tarabout | Au « royaume » des brahmanes, les guerriers sont rois: souveraineté, pouvoir et statut au Kérala[END_REF]) However, coming from a social anthropologist who certainly would not see himself as an 'Orientalist', such a repetition of the argument suggests how widespread can be the scholarly prejudices against the importance of territory in India.

It has to be acknowledged that the so-called 'ethnosociology' approach theorized by McKim Marriott has fostered a much more nuanced approach towards the relationship between people and the soil. Inspired by transactionalism, 'ethnosociology' interprets many characteristics of Indian society, particularly castes, in terms of a circulation of substances, especially bodily substances [START_REF] Marriott | Caste Systems[END_REF][START_REF] Marriott | India through Hindu Categories[END_REF]). The qualities of various beings are determined by the nature of 'coded substances' that are exchanged between all of them. Interactions are thus able to constantly modify beings. In order to regulate these fluxes and these influences, rules of avoidance or acceptance are established, which are at the core of caste society. This theoretical frame leaves no room for the notion of territory, strictly speaking. It may have encouraged some forms of 'locationism', so to say, but no interest in delimited jurisdictions. 14 Yet it has definitely opened up a new line of analysis conferring a crucial importance to the soil, in the sense of a geographical milieu linked to identities, or more precisely as an ecological environment with which people are in a constant exchange of 'substances'.

Marriott did not himself elaborate much on the topic, but some of his ideas have been fruitfully developed by other scholars, most notably by E.V. [START_REF] Daniel | Fluid Signs: Being a Person the Tamil Way[END_REF]. Writing about the Tamil village he studied, Daniel begins by stressing the importance of the notion of soil: 'one of the most important relationships to a Tamil is that which exists between a person and the soil of his ūr [village]' (Daniel 1984: 63). 15 He then proceeds to discuss the notion of ūr, which is not always restricted to 'village' but may take different meanings according to situations. For example, it is an external space 'defined person-centrically in terms of its relevance to a given ego rather than in terms of a purely semantic category that refers to a bounded territory common to all Tamils at all times and in all places' (ibid.: 68). When ūr specifically refers to the village, the corresponding territory can be conceived according to two contrasting modes: either as an administrative unit with fixed and continuous limits; or as a lived space with the 'focus on the center of the village and with a vulnerable "frontier" or a periphery' (ibid.: 77) marked by 'shrines of sentinel deities, entering points of roads and streams, haunted tamarind trees that dot the edge of the village' (ibid.: 74).

Daniel's book has become a reference for any discussion on the symbolic dimension of the relationships that people have with land in India. Indeed, he achieved a tour de force by conciliating the idea of humoral transactions in constant flux, at the core of ethnosociological theory, and its criticism by Moffatt: 'Why are physical, spatial boundaries so important in south Indian villages if flow is so valued?' (Moffatt 1990: 225). In stressing the crucial cognitive importance in India of the various bonds that link people to the land, Daniel has been able to hold together the notion of a flux of exchanges between people and the soil, and the notion of village territory, though he remained somewhat ambiguous in his formulations about the latter's limits.

In preparing this volume, therefore, we were faced with two disparate sets of arguments concerning a possible relationship between soil and territory. One argued that a supposed lack of territoriality was linked to a supposed lack of attachment to ancestors. The other one stressed the existence of constant flows of exchange between soil and people, but nevertheless entertained also little concern for territory proper, in the sense we have defined above (with the exception of Daniel's work). It was then necessary that the present book bring its own perspective on the question, and three chapters deal with the subject: Chapter 3 by Phyllis Granoff, Chapter 4 by Caterina Guenzi and Sunita Singh, and Chapter 5 by Caroline and Filippo Osella. It should be clear, however, that while these chapters amply demonstrate the elaborateness of conceptions that stress the mutual determination of places and people, they do not claim to establish that it equates soil with territory. As has been underlined before, the notions are just not of the same nature, though obviously they may intersect. But it was felt to be important, in this volume, to show that there exist in India explicit discourses establishing the identities of people with reference to their native or living well-circumscribed places. 16 A third and last group of arguments may be described as the acknowledgment that territory did play a role in political relationships in ancient times (pre-colonial, or pre-Mughal, depending on the authors), but that it was no 'real' territory, so to say. Some would hold for instance that Hindu kingdoms, prior to the colonial period, were not so much defined by their limits than by the network of personal relationships that developed between the king and those who recognised his power. In this sense, the notion of territory is irrelevant, even 'fallacious' (Wink 1986: 47). Instead, 'we find a people-cum-territory or janapada, shot through with vested rights' (ibid.: 161). This notion was already pinpointed by Dumont when he argued that according to the (Brahmanical) model of Hindu kingship, territory was undifferentiated from its population (Dumont 1991: 489). 17 This standpoint, however, has been contradicted by other scholars using the same Sanskrit references as Dumont, and underlining the importance of territory in the exercise of royal power that these texts make clear. The historian of law R. [START_REF] Lingat | Les sources du droit dans le système traditionnel de l'Inde[END_REF], for instance, showed that in the Dharmaśāstra and the Manusmti, royal power is closely associated with the notion of kṣatra, 'a power which is territorial in character, not only because it is applied within a territory and ends at the frontiers of the kingdom, but because it is conceived... as a regal right on territory, akin to a proprietary right that gives a direct power on land and soil' [START_REF] Lingat | Les sources du droit dans le système traditionnel de l'Inde[END_REF]: 237, our translation). Lingat's conclusion, however, was seldom heard.

One argument that has been put forward was to affirm that, since every Hindu sovereign considered himself to be virtually a Universal Ruler, there was no room for the notion of territory, which thus had little pertinence for defining kingdoms. Based on texts and rituals that predate our era, this conception of kingship has been widely circulated and may be found in Buddhism as well as in the claims of any local Hindu chieftain of the recent past. We should however not confuse the image of power that these chieftains may have wanted to project, and the nature of this power. Some authors have been cautious enough in this respect and have considered that the symbolic order that was thus proclaimed, probably had only but 'a distant relationship with reality' and that, eventually, 'if there is an idea to remember, it is that kings ruled over a limited territory in the constant expectative of a war' (Biardeau 1982: 31 ff., our translation). Others have been less cautious. There has been for instance the suggestion that 'in the Hindu classical conceptions, the territorial extent was less important than its religious signification' (Jaffrelot 1996: 75, our translation;also Galey 1989).

Moreover, even authors who have recognized the past importance of the notion of territory in the relationships between kingdoms, have often dismissed the existence of their precise delimitation. Thus, according to some, 'the country was divided into political entities whose borders were defined by their centre rather than the peripheries, the opposite of the concept of limes, limits between states. That system continued till the reign of the Mughals' (Dupont and Landy 2005: 48). And even if the past existence of frontiers 'in the sense of zonal regions', with their fortified outposts and toll-bars, is readily acknowledged, 'this is no evidence that linear boundaries were known' (Embree 197: 260).

Obviously, such conclusions rely on a comparison with an ideal-type of territory that closely corresponds to the specific form it has assumed in the modern nation-state [START_REF] Anderson | Imagined Communities[END_REF][START_REF] Goswami | From Swadeshi to Swaraj: Nation, Economy, Territory in Colonial South Asia, 1870 to 1907[END_REF]. In our view, as already pointed out, such a stand is detrimental for developing any fruitful analysis of the relationships that may exist between societies and space: such a definition of 'territory' necessarily ends up in an a priori negation of any territorial logic in societies prior to the appearance of the modern nation-state; and even within today's nation-states, the analysis would be applicable only at one level, that of the nation, and not at various scales of observation within it. In the wake we would lose any ability to shed light on the historical processes by which this specific form of territorial construction has emerged, or on the rather recent manifestations it has entailed in terms of 'ethnicity'. We stand by our definition of territory as primarily a notion about jurisdiction, and we argue that, yes, territories in India have been for centuries inseparable from the exercise of political power, and, yes, these territories were often known in very precise terms through well-defined limits. The last part of the volume is thus dedicated to this discussion. Two chapters (Chapter 7 by Gilles Tarabout and Chapter 8 by Daniela Berti) are case studies of territorial entanglements between religious and political jurisdictions. A third and ultimate chapter by Christiane Brosius illustrates some aspects of the current 'ethnicization' of politics in contemporary India, as a recent development of territorial conceptions within the nationstate.

Before concluding this review, it has to be stated that besides the general trends that have been presented, there has been also many works that have provided descriptions and analyses conclusively showing the importance of soil and territory in India, in observed individual and social practices as well as in explicit discourses. 18 Historian Nicholas Dirks has for instance criticised Dumont for his devaluation of the importance of territory (said to be secondary in relation to kinship) in the latter's monograph on Kallars: 'My ethnographic construction of the Kallars in Pudukottai leads me to challenge Dumont's theory on a number of important points. Territory, for example, plays a major role at every level of social definition. It is so embedded within social and political forms that we cannot say that it merely mediates the political and social domains as Dumont suggests' (Dirks 1993: 258). Other authors have underlined the importance and relevance of territory for a great variety of social contexts, such as the regional configuration of caste relationships [START_REF] Miller | Caste and Territory in Malabar[END_REF], the elaboration of a mythical past by inhabitants of urban neighbourhoods [START_REF] Parkhill | What's Taking Place: Neighborhood Ramlilas in Banaras[END_REF], the power that is still today exercised by local deities within their specific jurisdiction [START_REF] Sax | Mountain Goddess: Gender and Politics in a Himalayan Pilgrimage[END_REF][START_REF] Berti | La parole des dieux[END_REF][START_REF] Tarabout | Corps possédés et signatures territoriales au Kérala[END_REF], the prevalence of localized codes of conduct for Brahmans [START_REF] Chakrabarti | Cult Region: The Puranas and the Making of the Cultural Territory of Bengal[END_REF], 19 the bonds that migrant workers keep with their village of origin [START_REF] Racine | Les attaches de l'homme. Enracinement paysan et logiques migratoires en Inde du Sud[END_REF], the territorial selfrepresentation of commercial networks found in some merchant castes [START_REF] Mines | The Warriors Merchants: Textiles, Trade, and Territory in South India[END_REF], or the enduring links that married women maintain with their natal family [START_REF] Sax | Residence and Ritual in the Garhwal Himalayas[END_REF] or village [START_REF] Lambert | Caste, Gender and Locality in Rural Rajasthan[END_REF]. In the latter case, Lambert has shown that the birth-place is a significant dimension of one's identity, and that the stress put either on caste or on kinship, or on place in order to define one's identity, may be of a strategic nature. The author does not limit her critique to the question of the supposed subordination of territory to caste, but extends it also to its alleged exclusion from the system of conscious ideas and values: 'local identity is an indigenous value and thereby constitutes an aspect of conscious ideology different from that of caste' (Lambert 1996: 116).

Thus, territorial facts in India have imposed themselves on the attention of numerous observers, and could be negated or said to be of secondary importance only when there exists interpretative prejudice. At the same time, they still open a wide array of questions for discussion and interpretation. The present volume aims at addressing some of them. Without trying to be exhaustive in any way, given the immensity and the complexity of the Indian subcontinent, it is based on a diversified set of studies, varied both in historical and regional scope. The book therefore combines a great diversity of sources (ethnography, archives, texts and inscriptions), used by authors who have specialized in different disciplines (Indology, history of religion, social anthropology). Such diverse approaches and methodologies have been organized together in order to provide contrasting pictures of the plural conceptions and symbolic manipulations of territory in the Indian world. Three contributions by Sanskritists, each a specialist of a different period and of different texts, will precede papers of anthropological perspective. They introduce a necessary historicity, as some objections to the importance of territory in India relied on interpretations of Brahmanical texts, taken to express some kind of timeless cultural disinterest for attachment to place, for territory, and for boundaries.

Summary

Without strictly following a chronological order, the succession of contributions is arranged so as to begin with the ancient period and end with today's developments. However, the main objective in organizing the book has been to deal step by step with the arguments that have just been presented. The volume is thus divided into three main parts. The first, 'Emergence of Divine Territories in Brahmanical Texts', is a preliminary discussion of some 'ideological' aspects of territory in ancient India. The second, 'Land, Soil, and Sense of Belonging', deals not so much with territory per se than with the allegation that cultural or theological reasons prevent some people in India from developing attachment with their native or living place. The third and most developed part, 'Religious and Political Territories', is a discussion of various kinds of territorial jurisdictions -with a last development about today's Hindutva claims for an 'ethnicized' national territory [START_REF] Jaffrelot | La question du territoire en Inde : de l'universalisme aux particularismes ?[END_REF].

EMERGENCE OF DIVINE TERRITORIES IN BRAHMANICAL TEXTS

We begin with a preliminary question: to what extent are there ideas in Brahmanical thinking that actually point to a devaluation of the notion of territory (and to what extent do they relate to practice)?

The first chapter by Michel Angot shows that Vedic texts definitely expressed a strong devaluation of the notion of localized, bounded place, and conversely put an extreme positive value on open space -at least as far as the Gods were concerned. While the hierarchy of values is unambiguous in these texts, understanding the way it did inform practice may prove more conjectural. Certainly, this was well in line with the way public sacrifices, the srauta rituals, could not be reiterated in the same spot, and with the full symbolism of such rituals. But, as pointed out by the author himself, these texts bear on ritual practice and on conceptions about the divine realm, and should not be taken as directly applying to the social world. As a matter of fact, even if these values are plainly congruent with the standard hypothesis of a nomadic origin of the Vedic first people, the development of Vedic rituals as elaborated in the ritual literature corresponds to a period when they applied for centuries within a well settled agricultural society. Today itself, Vedic srauta rituals may occasionally be re-enacted (with their valuation on open space) in the contemporary, well-territorialized Indian society. Clearly, values inform social life, but not necessarily in a mechanical way. In terms of a general theory, this should lead one to be very cautious about ideas about the 'spirit', the 'ethos' of a society or an economic system (Max Weber), or the 'ideology' of Indian civilization (Louis Dumont). In the specific perspective of the present volume, the positive value given to open space and the correlated devaluation of bounded places did apply well to the Vedic vision of the divine, but it may well have been circumscribed to this particular context in the developments of religion and society in India, and does not mean that Vedic society was devoid of territories, or that the ideology presented here was the only existing model. Contemporary ritual contexts that are proper to the Brahmans are still associated with Vedic deities that are 'delocalized', but often coexist at the same time with other models in which gods and goddesses are grounded in a specific territory, owned by them. 20 Chapter 2 by Gérard Colas suggests some aspects of the historical shift in Brahmanical traditions from Vedic speculations towards later, very different conceptions. Epigraphic and textual sources of the fourth and fifth centuries C.E. refer to sedentary deities installed in temples in villages and towns. This sedentary character goes hand in hand with the existence of physical images of the divine (absent from Vedic references). Gods now have a physical body, more or less anthropomorphic, and are actors within a local society. The texts and inscriptions bear witness to the sometimes heated debates about the development of temple rituals and the possible implication of Brahmans in them. They testify also to the growing body of lands donated to them for the maintenance of cults. But if the link between divine image and temple ground is assumed quite early in the texts, there is a reluctance to admit that gods themselves may become landowners, and it takes many centuries for the literate society to accept it through various phraseologies. It is in this context that explicit discourses on divine territory appear -discourses that are plural and sometimes contradictory.

Taken together, these two chapters concur in their analysis of the decisive evolution in Brahmanical theories and ritual practices that lead from an uncompromised positive valuation of open space in the Vedic period, at least for the gods, to the latter's radical inscription in lands and territories. Clearly, when speaking about territory, the Brahmanical 'ideology' -to use Dumont's expression-is much more complex than a mere reference to Vedic speculation would suggest, not only in matters of land and society, but also in theological elaboration. The process has been a tense one, spanning centuries, but there is clearly no ground today to define Brahmanical conceptions of territory, even in the religious sphere, by referring merely to the early Vedic period. On the contrary, the process itself suggests the strength of territorial realities in Indian society for at least two thousand years, so much so that these forced themselves into the divine world.

LAND, SOIL, AND SENSE OF BELONGING

The following set of three chapters investigates a concept related to territory, but distinct from it, as already underlined: the concept of soil, and more generally the relationships between lands and identities. There are two points that are sought to be made.

At the general level of anthropological theory, the first illustrates that the interrelations between places and people do not necessarily entail the existence of a territory in the sense of a jurisdiction, as previously discussed. Nevertheless, it suggests also that 'space' does not exist as such (a point elaborately discussed in [START_REF] Casey | How to Get from Space to Place in a Fairly Short Stretch of Time. Phenomenological Prolegomena[END_REF], and that land, in the sense of places or soil, cannot be dissociated from society in all its heterogeneities and particularities.

At the level of this volume's specific argument, the second point is to underline the importance in India of these perceptions for understanding how people come to identify themselves, or be identified by others, with the land -that is, how they claim, or are said to 'belong' to it.

This sense of belonging is addressed here in three ways. Chapter 3, by Phyllis Granoff, is a study of identifications made in medieval Buddhist, Jain, and Hindu texts between regions and the people living there or originating from them. These are strongly worded stereotypes in which the people's characteristics, qualities, and behaviour are said to be determined by the very place where they live or where they come from. Such kinds of prejudice, Granoff argues, may well have been of immediate import for the delimitation of so-called sectarian divisions of the time, where religious sectarian identities may have papered over deep social divisions grounded on regional differentiation. In her words, 'ritual was merely put in the service of a more fundamental marker of difference to give what was not originally a religious difference a definitely religious tone.'

The other two chapters in this part are based on micro-level field studies. Through a study of present-day Varanasi astrologers, Caterina Guenzi and Sunita Singh (Chapter 4) are able to show that Brahmanical elaborations and practices of geomancy are based on a typology of soils and on their supposed respective interactions with different classes of society. Land enables astrologers to divine good or bad prospects for its inhabitants, as they share its effects on them according to their own respective qualities, and as in turn they affect land's characteristics. One aspect of Brahmanical 'ideology', therefore, provides for a luminous illustration of the extent to which land, person, and society may be mutually determined.

Caroline and Filippo Osella's study of the interactions between land and people as they are conceived in Central Kerala (Chapter 5) amply corroborates this statement. By examining the rules that preside over the construction of a new house in order to establish harmonious relationships between a site and those who will live there, and the funeral practices of some of the castes of the region, they shed light on an intricate life-and-death cycle binding together people with their place and with the surrounding lands that provide them their sustenance. These findings accord well with previous anthropological works which stress the importance of humoral transactions in defining social identities in India (McKim Marriott, Daniel). They suggest, in addition, a possible specificity of Kerala in this matter, where it seems that a particular stress is given on the extremely intimate bonds that such transactions create between places and the life and identity of the people born or living there. Expressed in the specific language of transactionalist theory, this question is akin to the already much debated one about the relations between kinship and territory, to which many authors have answered by suggesting the primacy of kinship. This discussion is taken up again in the first chapter of part 3, along a different theoretical line of analysis.

The second part, then, provides three examples of how places and people are said to determine each others in India, be it in the case of ancient regional stereotypes, or of the learned theories and practices of geomancy among contemporary urban Brahmans, or of the vital exchanges that are said to occur between specific places and their inhabitants in today's Kerala. Soil, identities and events are intimately intertwined. There is a perception of an 'inequality' of places (so to say) linked to personal or social inequalities, and eventually a strong sense of rooting in the land, a 'sense of belonging' (Lovell) to well-defined places.

RELIGIOUS AND POLITICAL TERRITORIES

While such a 'sense of belonging' points to a personal or social identity expressed in terms of place, it does not necessarily entail identification with a territory, as already underlined; conversely, one may belong to a territory without developing any specific 'sense of belonging' to it, as is often the case with administrative circumscriptions, for instance. However, and without any necessary connection with the model of the modern nation-state, complex and multiple interplays between places and territories, between identities and jurisdictions, do often happen and they structure social groupings in depth. The last set of four chapters investigates such varying social and political dimensions of territories, understood as spatial divisions determined by the exercise of rights and power.

Gérard Toffin (Chapter 6) analyses the conception of territory among the Newars in the Kathmandu Valley of Nepal. Territory, there, is defined through various divine jurisdictions at the level of the whole village or of sections of it, through ritual marks at the boundary of villages, and through funerary associations whose membership relies on both lineage and residence, and whose elders are the effective chiefs of the village. Territory and kinship are particularly tightly bound together, so much so that the author speaks of 'territorial parentages', in which territory relegates to a secondary level the importance of blood relationships in the constitution of social groupings. Symbolic territories, imbued with a deep sense of belonging and local identities, are thus also in this case effective, well delimited judicial and political territories, in which the full control of the social life of the inhabitants is exercised.

The next two chapters are case studies of religious territories, with a very precise delimitation of their boundaries and an effective political import in the control of land and people. Such territories, which answer the strictest definition of the term, do not depend on the model of the nation-state, and appear to have been widely prevalent in India. Historically, they did -and sometimes continue to-interact with the political organization of the former kingdoms, of the colonial power, or of the contemporary Indian nation-state.

Gilles Tarabout (Chapter 7) develops a case study of a long-lasting dispute which opposed the former kingdoms of Cochin and of Travancore over the territory of a temple. The case exemplifies the multiple forms of territory that once structured power relationships in Kerala, and the changes in their conception that occurred between the end of the seventeenth and the end of the nineteenth century. From a multiplicity of fragmented, embedded territories of different natures and importance, there is a progressive change to the notion of a unified territory that is characteristic of the modern nation-state. Thus, far from a lack of territory in pre-colonial India, it could be said that there was an excess of them. But these territories were multiple, sometimes discontinuous, and regularly overlapping, as very different rights applied to a same tract of land. At a broader level of observation this might give the impression of 'fuzzy' boundaries, while they were in fact very precise and well delimited at the micro level. The specific autonomy that was granted to some temple jurisdictions led in some cases to legal battles between growing state powers, which provide an exceptional opportunity for reconstructing what ultimately led to the establishment of modern bureaucratic states in the region. This evolution corresponds to a simplification, standardization, and political centralization of previous territories, but definitely not to the invention of the notion. Daniela Berti's study of divine jurisdictions in Himachal Pradesh (Chapter 8) analyses the territorial aspects of the cults of village deities. These deities have specific and welldelimited jurisdictions, and the corresponding territories are examined in relation to the different political systems that have successively controlled the region -Hindu kingdoms, British colonial administration, and the democratic system of contemporary India. The author uses various sources, oral stories, manuscripts of former British administrators, and contemporary observation in order to demonstrate the extent to which local deities were, and still are, at the core of local perceptions of territory. Not only do they still function as ritual units, and as instances of arbitrage for ordinary litigation, but they have been the source for defining the limits of colonial and post-colonial administrative divisions, tax assessment units, and electoral circumscriptions. In this case, religious territories centred on village deities appear to have been the mould for economic administration and political dynamics, while retaining their relevance in the current religious life of the people.

The history of how India as a nation-state has come into being has been told at length in numerous scholarly publications, and is not repeated here. The social and historical processes leading to the conception of India as a bounded whole has, for instance, been brought to light by [START_REF] Goswami | From Swadeshi to Swaraj: Nation, Economy, Territory in Colonial South Asia, 1870 to 1907[END_REF][START_REF] Goswami | Producing India: From Colonial Economy to National Space[END_REF]. The present volume concludes with a study by Christiane Brosius about the ways in which religious nationalism has developed in recent years (Chapter 9). Brosius explores particularly the relationships between the religious construction of territories and electoral politics at the time of the pan-Indian processions organized by the Hindu right at the end of the 1980s and the beginning of the 1990s. 21 The analysis focuses on some videos that were made about these so-called patriotic pilgrimages, which relied on an explicitly religious imagination and rhetoric so as to develop a 'mysticism of the territory', to use Jaffrelot's expression (Jaffrelot 1996: 92). For Jaffrelot, the ideology propagated by the RSS leads to a devaluation of administrative frontiers in favour of cultural ones. To the territorial nationalism it opposes an 'ethnic conception of the nation that structures the "Indian land" by exclusive reference to elements that are relevant in terms of cultural roots. Points of reference in the landscape are especially given a national value through a reinterpretation of the signification they may possess in the Hindu tradition' (Jaffrelot 1999: 93, our translation). Such a traditional sacred geography was particularly studied by D. [START_REF] Eck | India's Tirthas: "Crossings" in Sacred Geography[END_REF][START_REF] Eck | The Imagined Landscape: Patterns in the Construction of Hindu Sacred Geography[END_REF], who has shown how ritual processions and pilgrimages are instrumental in the elaboration of Hindu visions of 'an "imagined landscape" in which networks of pilgrimage places have generated a powerful sense of land and location' (Eck 1998: 166). The author goes on to suggest that 'in a range of Hindu traditions, map-making has been the domain of both the cosmologists and mythmakers, and it is arguable that the imagined landscape they have created is far more culturally powerful than that displayed on the Bartholomew's map' (ibid.: 169).

As Christiane Brosius demonstrates in her contribution, this imagined landscape has been the support on which the Hindu right has tried to politically mobilize the electorate. The videos that are analysed here reveal the constant use of evocations of an impending menace collectively threatening a united Hindu people. This is expressed at the mythical level (the loss of a Hindu Golden Age), at the level of (a revised) history, and at the level of biological metaphors (the nation as a kindred family), all concurring in producing an imagined and diversified landscape for a claimed 'Hindu territory'. In this, we find a process of trying to redefine a political frame in terms of a religious and ethnicized territory. Militants identify the whole of India with a national soil (sometimes blurring the limits of international borders), towards which a sense of belonging is exclusively equated with Hinduness.

Soil and identities, divine and administrative jurisdictions, landmarks and territorial boundaries, all these ways in which relations to the land concur in the formation of social groupings are present and intertwined in this last case, as they were in the different other chapters of this volume. But they appear in a radically new configuration and organize the State at an unprecedented level in a typically nationalistic, nativistic way. 'Nation' in this understanding -and not the existence of territories -is the recent product of 'modernity'. It is thus a comparison with other societies that these studies eventually invite, but a comparison based on the recognition of the historicity and plurality of territorial organizations that are at the core of human relationships. NOTES 20. Moreover, it is necessary to distinguish between territorial gods, installed in shrines but often said to have come from 'outside', and the deities and various invisible powers of more or less dangerous character who inhabit places in the landscape -trees, waters, mountains. This opposition has sometimes been arbitrarily interpreted in terms of a contrast between 'Aryan gods' and so-called autochtonous 'Dravidian gods' (Shulman 1980: 134). 21. See also her recent book on the question, [START_REF] Brosius | Empowering Visions: The Politics of Representation in Hindu Nationalism[END_REF].

Acknowledgments: The essays in this volume are part of a collection originally published in Italian in 2003, as a special number of Etnosistemi, Processi e dinamiche culturali (n°10, 'Terra, territorio e società nel mondo indiano'). We thank the publisher, CISU, Roma, for kindly authorizing their publication in English. The contributions have been revised, and the introduction entirely rewritten for the present edition -we are grateful to the anonymous reader for her/his insightful and stimulating comments.

1. For instance in France, Lévy 1991; Géographie et Cultures n°20;Di Méo 2000. 2. Also Geertz (1996).


Hélène Collavizza
email: helene.collavizza@univ-cotedazur.fr

TotemBioNet User Manual

Introduction

This manual is a short user manual for TotemBionet users. TotemBionet is a tool dedicated to parameter identication for Biological Regulatory Networks (BRN), using the discrete formalism of René Thomas [START_REF] Thomas | Biological feedback[END_REF]. Given a BRN and some properties on the dynamics of the system, TotemBionet outputs all the parameterizations which satisfy these dynamic properties.

TotemBionet exploits the complementarity of two approaches : temporal logic and Genetically Modied Hoare Logic, see [BCK + 19]. The benet is twofold. 1 On the one hand, the power of expression is reinforced. For the same case study, reachability properties such as multi-stationarity or homeostasis can be expressed by temporal logic, as well as path properties by Hoare logic. On the other hand, performance is improved because the weakest precondition calculated by Hoare logic is used to reduce the search space. This document is organized as follows. We rst recall the main principles of the René Thomas discrete formalization of BRN and state the parameter identication problem. Then we give an overview of TotemBionet framework.

Then we detail syntax, commands, and other functionalities provided by the platform. We do not enter into the details of the Genetically Modied Hoare Logic, the reader is invited to refer to [BCK + 19].

René Thomas descrete formalization of BRN

The logical modeling dened in [START_REF] Thomas | Biological feedback[END_REF] to describe and analyze the biological regulation networks, relies on a representation of the system in terms of graphs. The static description of the system is dened by an inuence graph while the dynamic behaviour of the system is a transition graph.

Inuence graph

The inuence graph describes the individual inuence of one gene to the others.

Inuence graph The vertices of the inuence graph are the genes. An edge between v 1 and v 2 means that v 1 has an inuence on v 2 : in a certain state, that is to say when the value of v 1 has exceeded a certain threshold, v 1 inuences the state of v 2 .

The domains of the variables are discrete domains 0, b v 1 with b v d + (v) where d + (v) is the outgoing degree of v.

Inuence graph with multiplexe An inuence graph with multiplexe is dened by Σ = (V ∪ M, A) where V ∪ M is the set of vertices and A is the set of edges , with :

V , the set of variables v of discrete domains 0, b V , M , the set of multiplexes m with associated multiplexe formulas ϕ m . ϕ m are recursively dened as follows. Atoms are identiers of M and atomic formulas of the form (v n) with v ∈ V and n ∈ 0, b v . Formulas are ¬ϕ, ϕ 1 ϕ 2 where ϕ, ϕ 1 and ϕ 2 are multiplexe formulas and is either ∧, ∨ or ⇒.

A ⊂ (M × V ), the set of edges. 1. a, b = {n ∈ N | a n ≤ b}.
Parameters The parameters associated with the variable v are denoted K v,ω where ω is a subset of the predecessors of v (i.e. ω ⊆ Σ -1 (v) with Σ -1 (v) the set of predecessors of v in the inuence graph).

Parameters allow to represent a combination of inuences for a variable v. For example, when v has two predecessors m 1 and m 2 , K v represents the case where v is not inuenced at all, K v,m1 the case where v is inuenced by m 1 , K v,m2 the case where v is inuenced by m 2 , and K v,m1,m2 the case where v is inuenced both by m 1 and m 2 .

Asynchronous transition graph

In the R. Thomas modelization, the dynamics of the system is dened by an asynchronous transition graph which denes the next state for each state of the system. The graph is asynchronous in the sense that when two transitions are possible, only one is non-deterministically selected to eect the state transition.

State A state η of an inuence graph is an interpretation which associates with each variable v of V a value in 0, b v . We denote ζ the set of states of the system, and η v the value of v for the interpretation η.

Regulatory network

A regulatory network (Σ, K) is the couple Σ associated with the parameter family K = {K v,ω |v ∈ V and ω ⊆ Σ -1 (v)}.
Applicable parameter Let η ∈ ζ be a state of an inuence graph Σ and v a variable in V . The applicable parameter of v on state η is the only parameter K v,ω where ω is the set of variables m i such as each formula ϕ mi associated with edge (m i , v), m i ∈ ω is true in state η 2 . The applicable parameter gives the next state of the variable v in the state η. It is the value towards which v tends, and is sometimes called the focal value of v.

Transition graph A transition graph associated with the regulation network (Σ, K) is dened as follows :

The set of vertices is the set of possible states ζ

The transitions between a state η = (η v1 , η v2 , . . . , η vn ) and the next state η = (η v1 , η v2 , . . . , η vn ) are such that :

1. There is a unique i such as η vi = η vi , 2. Let v i such that η vi = η vi , and K vi,ω the applicable parameter of v i on η. We have

K vi,ω = η vi and if K vi,ω > η vi then η vi = η vi + 1, if K vi,ω < η vi then η vi = η vi -1.
The rst point expresses that a single variable changes its state at each transition. The second point that the changes are made in steps of one, getting closer to the value of the applicable parameter.

2. True is understood here with the interpretation η for variables and the usual meaning of in N.

Parameter identication

Since the values of variables depend on the value of K, there is not a unique transition graph for a given regulatory network, but as many graphs as correct interpretations of the K. A correct interpretation of K v assigns to K v a value less or equal to b v .

The parameter identication problem consists to nd all parameterizations (i.e. correct interpretations of the K) such that some dynamic properties are veried on the associated transition graph. This is the aim of the TotemBionet tool.

TotemBioNet Overview

TotemBionet is the successor to SMBionet, written by Adrien Richard [START_REF] Khalis | The SMBioNet method for discovering models of gene regulatory networks[END_REF]. SMBionet has been used to model and identify parameters for many case studies. For example, the production of mucus in Pseudomonas aeruginosa [START_REF] Pérès | Contribution of computational tree logic to biological regulatory networks : example from pseudomonas aeruginosa[END_REF], the control of immunity of bacteriophage lambda [START_REF] Richard | Modern Formal Methods and Applications, chapter Formal Methods for Modeling Biological Regulatory Networks[END_REF], the analysis of the apoptosis and tail growth of tadpole [START_REF] Khalis | The SMBioNet method for discovering models of gene regulatory networks[END_REF], and more recently to support the biologist's expertise in the identication of parameters of a model of energy metabolism regulation [START_REF] Khoodeeram | An Ockham Razor model of energy metabolism, chapter Book chapter in[END_REF].

TotemBionet integrates Hoare-fol written by Maxime Folshette, see [START_REF] Folschette | The Hoare-fol Tool[END_REF] and le doc/Hoare-folTool.pdf. Hoare-fol implements the calculus of the weakest precondition of the Genetically Modied Hoare Logic (GMHL for short). Inference rules of GMHL are applied to calculate the weakest precondition.

Then, if a precondition is provided, it is propagated to simplify the weakest precondition using formal simplication rules such as a ∧ F alse ⇒ F alse.

Properties on the dynamics of the system

Properties on the dynamics of the system may be : information on parameters (known values or domains), CTL properties, FAIRCTL properties. A FAIRCTL property is a CTL property on innite fair paths. A fair path is such that if a vertex v occurs innitely often in p, then all the edges starting from v occur innitely often in p. For more details, see the note by Adrien Richard in doc directory. a Hoare triple {P } trace {Q}, where P is an initial operable state, trace is an observation trace and Q is a nal obervable state. TotemBionet uses these dynamic properties in the following way :

Information on parameter values are used to reduce the domain of parameters, potentially to only one value, When no property is given, all possible parameterizations are computed, When many properties are provided, the conjunction of the properties is used, When a Hoare triple is provided, the weakest pre-conditon is computed and simplied. If this simplied pre-condition swp only contains condi-tons on parameters, it is used to reduce the state space. Three cases can occur :

1. swp has been reduced to F alse. The triplet is inconsistent and there is no model, 2. swp is a conjunction of atomic formulas of the form K s where is a comparison operator and 0 ≤ s ≤ K b with K b the maximum bound of parameter K. In the GMHL, such a formula characterizes the settings whose dynamics are consistent with the observed triple.

In that case, the Hoare formulas are used to reduce the parameter domains, 3. swp is a disjunction of formulas. In the GMHL, such formulas are obtained when the trace contains existential quantiers or conditions.

In that case, the formulas are evaluated on the y during the enumeration process : only the parameterizations which satisfy the Hoare formulas are generated.

TotemBionet core

The initialization step builds the internal data structure from a SMB le.

A SMB le contains some blocks to dene the BRN and some optional blocks with dynamic properties (see 4). In SMB format, the inuence graph is dened as a set of variables and a set of regulations. A regulation is an edge from a multiplexe to a variable.

One important point is that the set of parameter variables is deduced from the set of regulations. Let v a variable which is the target of the regulations R = {reg 1 , reg 2 , ..., reg n }. Then the set of parameters K v for v is the set {K v:ω s.t. ω ⊆ P(R)} where P(R) the set of parts of R. In the SMB syntax, regulations are separated with the symbol :. Possible parameters for v are for example K v , K v:reg1 , K v:reg1:reg3 . For the sake of eciency, only eective parameters are generated. A parameter is eective if there is at least a state where the multiplexe of the regulation is valid 3 . If a Hoare block exists, Hoare-fol is called to compute the simplied weakest precondition swp. If swp is a conjunction of atomic formulas (see 2 in subsection 3.1), then domains of parameters are reduced. If not, the ag dynHoare is set to indicates that the enumeration process must check the swp.

The main loop of TotemBionet consists in enumerating all possible parameterizations compatible with the BRN and known information on parameters.

By default, the parameterizations respect the Snoussi monotonicity property :

∀v ∈ V, ∀ω ⊆ Σ -1 (v), ∀ω ⊆ Σ -1 (v), ω ⊆ ω ⇒ K v,ω ≤ K v,ω
The user can indicate that it doesn't want to use the Snoussi condition on a variable (see 4).

For each parameterization K, (which satises swp when ag dynHoare is on), a non deterministic automatom is built. This automatom is a translation 3. Option -paras displays eective and non eective parameters of a network, see 7.

Behavioural properties

Selection of dynamics which satisfy the CTL/fair-path-CTL formula (NuSMV)

Reassessment Reassessment

Hoare Logic

Construction of contraints C

G ≥ 1

¬(P C≥1 ∧ ¬(L≥1))
of parameterizations Enumerator R. Thomas' modeling framework yes K. This automatom and some CTL formulas are provided to the model-checker NuSMV [START_REF]NuSMV Home page[END_REF]. If the CTL property is valid, then the parameterization K is a model. The global TotemBionet process is illustrated in Figure 1.

M i |= C M i contraints simple (M i |= Φ)

Running example : mucus production of P. aeruginosa

This example is fully described in [START_REF] Bernot | Logical Modeling of Biological Systems, chapter Formal methods applied to gene network modelling[END_REF], we encourage the reader to refer to it for more details. An operon activates several genes : AlgU , M ucB and some other ones that participate to mucus production. The protein of AlgU is a transcription factor that activates the operon, so the operon activates itself.

Inuence graph : We consider the simple inuence graph with two variables, Operon to represent the operon and M ucuB to represent the production of mucus (see gure 2). The multiplex alg represents the production of alginate AlgU by the operon at the threshold 2. The edge between Operon and M ucuB represents the production of M ucB by the operon at the threshold 1. The multiplex f ree represents the absence of the inhibition induced by M ucuB at the threshold 1. By convention, we denote v ≥ s (or +s) an activation of variable v at threshold s and !(v ≥ s) (or -s) an inhibition of variable v at threshold s.

Property on the dynamics of the system : 4 It has been established that P.

aeruginosa exhibits two attraction basins. The rst one produces mucus and the second does not. The production of mucus takes place at a level of operon greater than some unknown threshold. So, necessarily, the system produces mucus if the expression level of operon is equal to its maximal value 2 and it does not if it is equal to 0. We can express the two possible behaviours by the following CTL formulae :

4. This paragraph is a copy/paste of [BCS14] page 21.

TotemBionet syntax

TotemBionet uses text les in SMB syntax. Using text les is very light, and allows to use system facilities such as di, grep, ... However, the user can dene the BRN using the yEd graphical editor. The TotemBionet platform provides a facility for translating .graphml format to SMB format (see 6).

We describe here step by step the several parts of the grammar using the running example 5

: ctl IMPL ctl # ctl_impl | ctl BOOL_OP ctl # ctl_bool_op | '(' ctl ')' # ctl_brackets | CTL_PREFIX_1 '(' ctl ')' # ctl_temp_op1 | CTL_PREFIX_2 '(' ctl 'U' ctl')' # ctl_temp_op2 | NEG ctl # ctl_neg_op | ID (COMP|EQ|SEUIL) NUM # ctl_atome CTL_PREFIX_1: ('EX'|'AX'|'EF'|'AF'|'EG'|'AG'); CTL_PREFIX_2: ('E'|'A');
5 NEW Operations on sets of parameterizations using MDDs

For a same inuence graph, there could be dierent dynamic properties depending on the environnement. These properties can be sumarized in property matrices, as presented in [START_REF] Gibart | Totembionet enrichment methodology : Application to the qualitative regulatory network of the cell metabolism[END_REF]. In that case, it could be interesting to compute the set of models that satisfy the whole set of properties, which amounts to compute their intersection.

Multi-valued Decision Diagrams (MDDs) [START_REF] Kam | Multi-valued decision diagrams : Theory and applications[END_REF] are an extension of well-known BDDs, to represent set of multi-valued variables. MDDs provide an ecient data structure to store set of datas, avoiding redundancy. They also provide useful combination operations : the negation (set of elements not in the set), the conjunction (intersection of the sets) and disjunction (union of the sets).

MDDs may be used to represent sets of parameterizations which validate some dynamic properties of the network (see gure 3. TotemBionet uses the MDDs library https://github.com/colomoto/mddlib developped by Adrien

Naldi in order to study the dynamics of regulatory networks, in particular to study circuits and stable states [START_REF] Naldi | Decision diagrams for the representation and analysis of logical models of genetic networks[END_REF]. MDDs are used for two purposes :

to compute intersection or union of sets of parameterizations from the outputs of TotemBionet (from .csv les), to output a compact .csv le, where variables that doesn't matter for one conguration are abstracted by their domains (see gure 4). In that case, correct parameterizations are stored in MDDs to obtain an abstract representation which are written in a compact format.

For intersection (or union), the sets of parameterizations can come from properties checked in dierent environments (use of ENV_VAR variables). In that case, some parameters can be eective for some environments and not eective for some others. The intersection is thus calculated for the whole set of parameters, and then the parameters which are not useful in the intersection (i.e. don't care values) are removed.

6 Translation from yEd to SMB format TotemBionet does not provide a proper graphical user interface but it provides facilities to use yEd graph editor (.graphml format) to design the BRN. -csv : Generate also the output in a CSV le <input>.csv (or <name>.csv if option -o is used). NEW When combined with verbosity level 2, <input>-MDD.csv is also output, with the compact vision computed from its MDD representation.

-from <parameterSet>.csv NEW Enumerate the possible parameterizations from OK models in <parameterSet>.csv. <parameter-Set>.csv must be in compatible format which means that it must contains valid parameters in the rst line and their domains in the second line (thus it can be the output of a previous call to TotemBionet ).

-from <parameterSet>.csv KO does the enumeration from KO models in <parameterSet>.csv When combined with option -csv, the enumeration uses the OK models in <parameterSet>.csv and outputs the checked models in <input>from.csv where<input>.smb is the input le of TotemBionet . Nota: TotemBionet has been tested and developed under Ubuntu platform. Some problems have been found under linux on Mac (le names with uppercase and lowercase). The installation procedure has been updated in consequence. If there remains any problem, please contact Helene.COLLAVIZZA@univ-cotedazur.fr.

  x+;y-;... {Post} (fair path) CTL formula

Figure 1

 1 Figure 1 TotemBionet processing ow

Figure 2

 2 Figure 2 Running example : mucus production

  CTL op1 = ((operon = 0) -> AG(!(operon = 2))); op2 = ((operon = 2) -> AG(!(operon = 0))); END /** Case with two inconsistent Hoare triples **/ # Hoare triples HOARE triple_1= PRE : {mucuB=0,operon=1} TRACE : mucuB+;operon-; POST : {mucuB=1,operon=0} triple_2= PRE : {mucuB=0,operon=0} TRACE : mucuB+;operon+;operon-; POST : {mucuB=1,operon=0} /** Result of TotemBioNet **/ *** Using Hoare formulas to reduce parameter domains... Triple triple_1, set of formulas: [(K_operon<1), (K_mucuB:prod>0)] Domains have been successfully reduced. Triple triple_2, set of formulas: [(K_operon<1), (K_operon>0), (K_mucuB>0)] Hoare constraint (K_operon>0) is inconsitent with current value of parameter Koperon. Intervals for K_operon : [0] *** Hoare failure Operators We use the notations below for logical operators. The temporal operators follow the usual syntax of CTL logic. A name can be associated with a CTL formula. In that case, this name is used to give an explanation of the error for parameterizations which do not satisfy the property. This is particulary useful when there are many temporal properties (use verbosity level 2 to print this error explanation in the output le). **** CTL ********/ ctl_block : KCTL ctl_decl+ ctl_decl : (ID '=')? ctl SEMI ctl

  The command .\totembionet -yed input.graphml translates the le input.graphml in SMB format into the le inputFromYed.smb. This functionnality is a very beta version. It requires many restrictions when editing the yEd le, only yEd les which follow these conventions are translated. Warning : few error messages are provided.

Figure 3

 3 Figure 3 Example of a MDD that represents a set of OK and KO parameterizations.

Figure 4

 4 Figure 4 Example of a compact representation of OK and KO parameterizations.

  Variables Variables can be either system variables (e.g. genes) or environment variables. An environment variable is used to freeze the value of some input, to enforce some particular conditions on the environmenent. Environment variables can't be used as target of regulations, thus no parameters are associated with environment variables. As a consequence, the state space explored to enumerate the parameters is reduced. Domains of variables are intervals denoted min..max. The domain of an environment variable is reduced to only one value. The key word (NS) idicates that the enumeration process will not use Snoussi conditions for parameters of It can be used to give the initial conditions of model-checking. These conditions are written in the INIT block of NuSMV le. When there is an INIT block, NuSMV checks if the CTL formula is true only for states which satisfy the initial conditions. On the contrary, when there is no INIT block, NuSMV checks if the CTL formula is true for all possible initial states.

	KENV_VAR KVAR /** Example: BRN of mucus operon **/ : 'ENV_VAR'; : 'VAR'; /** The regulation named Operon_To_Mucus **/ | 'Exists' '(' hoare_trace (',' hoare_trace)* ')' Parameters The PARA block is optional. It can be used to give some information on parameters. Parameter identiers for variable v are denoted | 'Assert' '(' hoare_assert ')'
	KINIT KREG /** has automatically been generated from the .graphml file **/ : 'INIT'; : 'REG'; VAR | '(' hoare_trace ')' K_v :r1 :r2 :rn where r i are the identiers of regulations whose v is a target. hoare_term : (NUM|ID|KID)
	KPARA KCTL KHOARE KPRE Mucus = 0..1 ; Operon = 0..2 ; REG KID para_block | hoare_term OPER hoare_term : 'PARA'; : ('CTL'|'FAIRCTL'); : 'HOARE'; : 'PRE'; : 'K_'[a-zA-Z][a-zA-Z0-9_]*(':'[a-zA-Z][a-zA-Z0-9_]*)*; | '(' hoare_term ')' : KPARA para_decl* para_decl hoare_assert : hoare_term (EQ|COMP|SEUIL) hoare_term : KID '=' NUM ('..' NUM)? SEMI | '(' hoare_assert ')'
	KTRACE KPOST COMMENT Operon_To_Mucus [(Operon>=1)] => Mucus ; : 'TRACE'; : 'POST'; : '#' ~('\n')* alg [Operon>=2] => Operon ; | hoare_assert (BOOL_OP|IMPL) hoare_assert /** Example: BRN of mucus operon **/ | NEG hoare_assert /** With mucus as environment variable and a PARA block **/ free [!(Mucus>=1)] => Operon ; ENV_VAR Mucus = 0; NEW Many Hoare blocks can be used (and can be named). When there END are many Hoare blocks, they are handled in the following way :
	VAR if all the triplets contain some disjunction, the conjunction of the tri-NEW Initial conditions for model-checking The INIT block is optional. Operon = 0..2 ; plets are checked for each parameterization and if it is satised, then the
		REG NuSMV automatom is built and checked,
		alg [Operon>=2] => Operon ;
		free [!(Mucus>=1)] => Operon ;
		PARA
		K_Operon=0..1;
		this variable. K_Operon:alg=2;
	ID NS /** Example: BRN of mucus operon **/ : [a-zA-Z][a-zA-Z0-9_]*; */ : '(NS)'; /** no Snoussi **/ /** With exists Hoare block and CTL **/
	/** The regulation named Operon_To_Mucus **/ VAR env_var_block : KENV_VAR env_var_decl+ /** has automatically been generated from the .graphml file **/ operon = 0 .. 2 ; env_var_decl : ID EQ NUM SEMI var_block VAR mucuB = 0 .. 1 ; : KVAR var_decl+ var_decl Mucus = 0..1 ; : ID EQ NUM '..' NUM NS? SEMI /** Example: BRN of mucus operon **/ Operon = 0..2 ; REG WARNING : conditional statements and assertions have not been intensively prod [(operon>=1)] => mucuB;
	/** There are two variables **/ tested and used for the moment. free [!(mucuB>=1)] => operon; REG
	/** Parameters for Mucus will be enumerated **/ Operon_To_Mucus [(Operon>=1)] => Mucus ; alg [(operon>=2)] => operon;
	/** without the Snoussi monotonicity conditions **/ alg [Operon>=2] => Operon ; hoare_block : KHOARE hoare_decl+
	VAR free [!(Mucus>=1)] => Operon ; hoare_decl : (ID '=')? # Hoare triple
	HOARE	Mucus = 0..1 (NS) ;	hoare_pre_decl
	prog # initial conditions for model-checking Operon = 0..2 ; hoare_trace_decl PRE : {mucuB=0,operon=1} : env_var_block? INIT hoare_post_decl TRACE : Exists(mucuB+,mucuB-);operon-; var_block reg_block init_block? para_block? reg_expr : reg_expr BOOL_OP reg_expr | ID '-' 'END' reg_decl : ID '['reg_expr']' CIBLE ID+ SEMI pinit = AX(EX(!(operon = 2))); | ID '+' ctl_block* reg_block : KREG reg_decl+ # steady states for operon | ID ':=' NUM hoare_block* hoare_trace : 'Skip' used to dene another regulation. In that case, its multiplexe is used. # expr_bool_op CTL hoare_trace_decl: KTRACE ':' hoare_trace SEMI inside brackets, and one or many target variables. A regulation name can be hoare_post_decl : KPOST ':' '{' (hoare_assert (',')? )* '}' Regulations A regulation is dened with an identier, a multiplexe given operon=0; hoare_pre_decl : KPRE ':' '{' (ID EQ NUM (',')? )* '}' POST : {operon=0}
	| NEG reg_expr # pinit + INIT block is equivalent to p | hoare_trace SEMI hoare_trace /** Key words for SMB blocks **/ | '('reg_expr')' # p = ((operon = 0) -> AX(EX(!(operon = 2)))); | 'If' hoare_assert 'Then' hoare_trace ('Else' hoare_trace)? # expr_neg # expr_brackets
	| ID SEUIL NUM | 'While' hoare_assert 'With' hoare_assert 'Do' hoare_trace # expr_atome 5. The syntax for describing the grammar is usual : ? means optional, + means at least one and * means zero or many. | ID # expr_mux_name END | 'Forall' '(' hoare_trace (',' hoare_trace)* ')'

. Other examples can be found in directory examples.The complete SMB grammar can be found in le TotemBioNet/src/front/smbParser /grammar/RRG.g4. SMB les structure. A SMB le contains an optional environment variable declaration bloc, a variable declaration block and a regulation block. These 3 blocks dene the BRN. The 4 next blocks are about dynamic properties and are all optional. The SMB le is ended by keyword END. The order of the blocks must be respected. In the next example, checking formula AG(!(operon = 2)) with INIT block containing operon=0; gives the same result as checking the formula ((operon = 0) -> AG(!(operon = 2))) with no INIT block. END Hoare The Hoare block allows to specify a Hoare triple. The pre-condition is a set of equality relations. The post-condition is a set of logical conditions. The trace may be an assignment, an increment (decrement), a conditional statement, a forall or exist quantier and an assertion (see [BCK + 19] for the details). if one of the triplet is a conjunction, then it is used to reduce the bounds of the parameter variables (and and by the way to optimize the enumeration process), if the bound reduction for one of the triplets is incoherent with the bounds obtained for a previous triplet, then the set of Hoare triplets is inconsitent, and there is no model. /** Example: BRN of mucus operon *

  Information on the BRN : ./totembionet <input>.smb -<options> By default, the MDD operation if on OK models. -<MDD-operation> KO allow to build the MDD-operation for KO models. Translation to json : ./totembionet <input>.smb -json Translate <input>.smb le into a JSON format in le <input>.json Translation from yEd ./totembionet <input>.graphml -yed Translate <input>.graphml into <input>FromYed.smb. <input>.graphml contains BRN information built from yEd according conventions listed in 6. This project is written in Java and Ocaml. The input le is parsed using antlr4, the CTL properties are checked with NuSMV. java : a JDK is required to install the project, at least version 9. Ocaml : at least version 4.03.0 is required see https ://ocaml.org/docs/install.html NuSMV : a zipped compatible version for linux is provided in `./lib/-NuSMV`. You need to unzip it. If you already use another version of NuSMV, you can give its path into the `Makele`le. antlr4 : jar les for antlr4 are provided in `./lib/antlr4TotemBioNet also provides a parser from .graphml to SMB format. You can download the yEd graphical tool here : https ://www.yworks.com/products/yed/download3. Compile the projectTo compile the project, just enter `make`in the root directory. Two scripts will be created `totembionet`which should be used to run TotemBioNet `ASTtreeViewer`to visualize the AST (Abstract Syntax Tree) of the Type `make install`(eventually preceded by a `sudo`) to install the project in the install directory. The install directory is dened at the top of the `Makele`in the `INSTALL_DIR`variable (defaults to `/usr/local/d.TotemBioNet`).Once installed, eventually update your `PATH`variable with something like `PATH=$PATH :<TotemBioNet install directory>`to give access to the command `totembionet`everywhere.

	8 Installation
	1. Clone or download the project
	`git clone https ://gitlab.com/totembionet/totembionet.git2
	. Install dependencies
	Option details
	-paras : Print the set of eective parameters
	-simu : To start simulation mode (this option calls an option of SM-BioNet which has not been upgraded, without Hoare, without en-vironment variables, not maintained, see SMBioNet user manual in the doc directory) You can test these programs with .smb le
	`./totembionet examples/mucusOperon/mucusOperon.smb`to run To-
	temBioNet `./ASTTreeViewer examples/mucusOperon/mucusOperon.smb`to view the AST of `mucusOperon.smbÒ ther examples are provided in the `examples`directory. NEW In par-ticular, benchmarks discussed in [BBCC20] and [GBCC21]. NEW MDD Management Help : ./totembionet -help 4. Install the project
	Print help guide.

: ./totembionet <path> -<MDD-operation> Path is a path to a directory that contains .csv les output from a previous run of TotemBionet on the same inuence graph, with dierent environment variables and properties to check. MDD-operation is either intersection or union. The intersection (resp. union) of the OK models in <path> are computed and written in <path>/intersection.csv (resp. <path>/union.csv). If verbosity level is 2, then the compact version is also computed in <path>/intersection-MDD.csv (resp. <path>/union-MDD.csv).