Sébastien Dalgalarrondo

Tristan Fournier
email: tristan.fournier@ehess.fr

Optimization as morality, or the routes of the self 1

The promise of self-optimization has colonized our everyday life. Individuals are now exhorted to optimize their body, their nutrition, their sexuality, their sleep, their physiological and cognitive performance, their biological and social life. In recent years this imperative towards maximization has made deep inroads into marketing discourse, public health programmes, personal development manuals and theories of how to age well. Transhumanist thinking, with its hyperbolic discourse on the inevitable transcendence of human nature, has emerged as one of the main centres of production and dissemination of an ethics of optimization.

]. Thus it is suggested that the normality of everyday experience of a 'healthy' body has to be constructed through a set of activities of self-monitoring, self-control, and selfoptimization.

The genealogy of a fluid concept

The concept of optimization was originally applied in the field of economic calculation. Rational choice theory and its model of optimality have been subject to much criticism from within economics [START_REF] Simon | Theories of decision-making in economics and behavioral science[END_REF] and in other fields, including anthropology [START_REF] Sahlins | Economic anthropology and anthropological economics[END_REF], sociology [START_REF] Kiser | The debate on historical sociology: Rational choice theory and its critics[END_REF][START_REF] Boudon | Beyond rational choice theory[END_REF] and political science [START_REF] Green | Pathologies of Rational Choice Theory: A Critique of Applications in Political Science[END_REF]. The development of psychoergonomics in the 1920s and 1930s was a key moment in the history of the inexorable convergence of the principle of optimization and the body of the individual. But it was in the field of psychology, during the 1950s, that the concept of optimization was reworked into the form this issue focuses on, becoming no longer an explanatory model, but a daily process and a moral frame of reference. It was Abraham [START_REF] Maslow | Motivation and Personality[END_REF] who articulated the aim of humanistic psychology as being to allow every individual to achieve self-actualization, through the identification and constant improvement of her/his capacities, and thus opened up the field of 'health psychology' [START_REF] Maslow | Toward a Psychology of Being[END_REF], and more generally that of 'personal development'. Some decades later, this positive psychology was to find fertile ground in normative theories of aging. The theory of 'successful aging' developed by Paul and Margret [START_REF] Baltes | Successful Aging: Perspectives from the Behavioural Sciences[END_REF], for example, is seen as a process of optimization that takes advantage of the plasticity of the human body.

'Optimization means that choices made in terms of projects and goals will be committed to in such a way as to get maximum benefit from them, in terms of both quality and quantity' [Hummel, 2009: 47].

This moral imperative was also highlighted by early studies on biomedicalization: 'In the biomedicalization era, the focus is no longer on illness, disability, and disease as matters of fate, but on health as a matter of ongoing moral selftransformation' [Clarke et al., 2003: 172]. Optimality has definitively lost its role as a model, becoming instead a vitalist morality, in which the aim is not only to prevent illness but also to produce more life: 'our contemporary biopolitics is not defined by health and illness, or even by the parameters of sexuality and procreation. It is a space of problems concerning the optimization of life itself' [Rose, 2007: 82]. In Nikolas Rose's view, the contemporary imperative toward optimization corresponds to one of the five great shifts which form the basis for his cartography of contemporary biopolitics. Rose emphasizes the normative aspect of the concept, and its close interrelation with neoliberalism. His choice of terminology is dictated by his aim of going beyond the binary opposition that structures both bioethics and social sciences, between the therapeutic field and that of enhancement. Céline Lafontaine, in her writing on the commodification of the body, reveals the breadth and diversity of a bioeconomics whose 'only perspective is the optimization of the productive potentialities of life itself […], the final stage of globalized capital' [Lafontaine, 2014: 122]. Anti-aging medicine, with its use of hormones [START_REF] Dalgalarrondo | Les économies de la promesse anti-âge. Le cas de la DHEA[END_REF] and its offer of holistic care, epitomizes this medicine of the optimal, centred on ensuring one's future wellbeing [START_REF] Mykytyn | Medicalizing the optimal: Anti-aging medicine and the quandary of intervention[END_REF]. Sociological studies in the arena of medication, and specifically the issue of cognitive enhancement [Coveney, Gabe and Williams, 2001;[START_REF] Maturo | The medicalization of education: ADHD, human enhancement and academic performance[END_REF], highlight the effects of the pathologization of this promise, and the practices it gives rise to. By naturalizing physiological states previously considered artificial, the process of optimization deconstructs the normal [START_REF] Collin | On social plasticity: The transformative power of pharmaceuticals on health, nature and identity[END_REF].

These multiple separate shifts of boundaries, identities and normalities also have the effect of altering the relationship of meaning between the pursuit of health and the pursuit of well-being. Marquis' work [2014] on the consumption of personal development manuals shows that readers seek first of all to determine the space of possibility, to construct their own position in the face of contingency. Thus these initiatory texts invite readers to turn major ruptures in their lives to their advantage, making them a way of trying out new expectations, new viewpoints, new paths. Contingency becomes the springboard for potential change, a trigger event, an opportunity. Above all, the success of these books reveals how the issue of personal autonomy, presented in the guise of an adaptive potential that is to be developed and realised, is now central to our evaluation of our behaviours and our lives.

Finally, the recently published Lost in Perfection: Impacts of Optimisation on Culture and Pysche [King, Gerisch and Rosa, 2018] clearly identifies the various elements implicitly mobilized in the concept of optimization. First there is maximization, which draws on a logic of accountancy. In these authors' interpretation, the notion of optimization also refers to a methodological process, in which ends and means are to be rationalized and placed in relation to one another in order to approach maximum efficiency. But as the title of their book suggests, this rationalization may equally take an aesthetic form, coming close to or even melding with a search for perfection. The authors distinguish two operational modes of this perfectionism: the first relates to a benchmark horizon that as it were guides the individual through an ascetic practice. The second takes the more specific form of a desire for enhancement, and in this sense aligns with contemporary transhumanist philosophy (non-adapted/suboptimal body). In making the body central, self-optimization reveals a particular understanding of health, which is seen as a potential to be expressed. Here we are once again in the realm of Canguilhem's 'free health' [2012: 49] and his metaphor of the athlete.

Yet it seems to us that this social scientific analysis of optimization misses its processual nature, an aspect that is central to the conceptualization we propose.

The collection of articles presented in this issue helps, in our view, to explain the fact that the first effect of self-optimization for those who practise it is one of detachment. We thus consider the processual dimension to be primordial, for it allows us to examine the effect of reflexivity inherent in it. The process is by definition non-linear: it is a construction in progress. Like a stream that finds its course by flowing with the topography, the process is adaptive, meandering and built up from contingencies. Because it involves introspection, a work of incorporation, it alters the way in which the individual is affected. Thus there is in the notion of process the possibility of slippage, a chance discovery, the establishment of a new relationship to society and its ideologies, to one's body and one's sensations.

From imperative to appropriation

What is being optimized, how, and to what ends? Through these questions, we seek to highlight and to investigate the multiple ideologies that can be harnessed to the quest for optimization. We have seen that it operates as a moral frame of reference, as a normative injunction to maximize the use of the self in order to secure better performance, health, or well-being. In linking the fields of therapy and enhancement, the concept of optimization points to an original field of investigation. Optimization, to quote Deleuze, is a journey without a predetermined trajectory, a lived experience. While the concept of enhancement is associated with the idea of frontier, that of optimization retains a link with the normal. The contemporary promise of optimization thus slides easily along the continuum between the normal and the pathological, and depending on the terms used, shifts between the registers of care, enhancement, prevention and wellbeing. This flexibility, while it represents a challenge for research, allows commercial interests, public authorities, and all those who might make use of this moral frame of reference to adapt their products and their discourses to the diversity of demand, to regulatory concerns, and to the current state of the bioethics debate.

If this permanent injunction to strive for optimality is redrawing the boundaries of the normal, it begs another question: what is it doing to individuals? The quest for 'better', which can be interpreted as the product of a society saturated with discourses of competition that force each of us to strive for maximum performance and to outdo ourselves [START_REF] Ehrenberg | Calmann-Lévy. Foucault, Michel[END_REF], has obvious links with eugenicist thinking, which in its contemporary manifestations places the individual at the centre of the system and invites him/her to engage in 'intense self-exploitation' [Rosental, 2016: 62]. This exploitation is facilitated by techniques and technology, which are presented as life-saving and hold out a promise of empowerment [START_REF] Fournier | Se nourrir de promesses. Enjeux et critiques de l'introduction de deux innovations dans le domaine alimentaire: test nutri-génétique et viande in vitro[END_REF]. A responsible individual, then, who, through rational and daily honing of her/his body and her/his feelings, manages to fit her/himself appropriately to our society, its values and its norms [START_REF] Bröckling | The Entrepreneurial Self: Fabricating a New Type of Subject[END_REF]. As we have pointed out, through its reflexive effects the imperative toward optimality opens up a potential space for play, for lines of flight, for deviant and potentially critical explorations. Beyond the imperative itself, therefore, we need to examine the work of appropriation of the discourse of optimization, which can manifest in the form of ideological positions (critical distance, forms of engagement) and daily practices (resistance, negotiation, experimentation). We therefore feel it is important to reflect on optimization as a technology of the self -from a Foucauldian perspective [Martin, 1998] -which contains at its heart a bricolage of norms and possibilities, injunctions and preferences. This process can also take the form of a political discourse of liberation when it is presented as a way of taking back control over one's body and one's daily life, in order to achieve an 'authentic' way of life [START_REF] Macé | Styles. Critique de nos formes de vie[END_REF]. The issue of technologies of the self emerges as a site of friction between a normative space (and its technologies of domination) and the possibilities of resistance and emancipation. Because they are processual, these technologies of the self make it possible to discover and adopt different styles, optimalities that challenge, and which by their very existence reveal, in incarnate form, the possibility of a different life, with all that this implies politically [START_REF] Hauray | Incarnation and the dynamics of medical promises: DHEA as a fountain of youth hormone[END_REF]. One of the tasks of the social sciences is to identify and understand the individual situations in which the incorporation of the social operates. The articles in this issue demonstrate the benefits of paying attention to the equally individual forms taken by compromises and resistances to the quest for optimality. This collection brings together a unique repertoire of essays toward displaced, deviant and personalised optimalities that, in the view of those practising them, open a space where they may constitute their own moral subjectivity.

On the advantages of working from the everyday

Set within the context of a critical reading of the neoliberal logic of performance, our concern in this issue is above all to reveal the 'other side' of optimization.

Observing individuals close-up, we aim to determine how they appropriate the promises of enhancement, adopt or reject the moral imperatives of the market in performance, health and well-being, and organize individually and collectively to construct experiments on the self. It is in fact in this oft-neglected sphere of daily life that new relationships with the body and new ways of taking responsibility emerge, and that the boundaries between the normal and the pathological quietly evolve, beneath the constant stream of scientific marketing [START_REF] Gaudillière | The Development of Scientific Marketing in the Twentieth Century: Research for Sales in the Pharmaceutical Industry[END_REF]. It is also in this realm of the ordinary and the everyday that alternative uses, diversions, misappropriations and incongruities, at once discreet and instructive, are forged, in the privacy of personal experience and the discovery of new potentialities. The everyday thus becomes an ideal vantage point for observing possibilities, since daily repeated events such as eating are loaded with significance despite their apparent ordinariness. While the everyday has been subjected to critical analysis in the social sciences -for example in the work of Henri Lefebvre [1997] who, taking a Marxist approach, saw it as the site of human weakness, individual powerlessness and passivity -it also constitutes, in Lefebvre's view, that space-time that reveals the damaging effects of consumer society, in the face of which it is vital not to lose one's own skills and capacities.

Lefebvre thus aimed to reveal '[the] power concealed in everyday life's apparent banality, [the] depth beneath its triviality, something extraordinary in its very ordinariness ' [2002: 37].

For the everyday is eminently political! In the first volume of The Practice of Everyday Life, Michel de Certeau writes: 'it is always good to remind ourselves that we mustn't take people for fools ' [1988: 175]. To be sure, the everyday can be interpreted as a site of passivity in which neoliberal ideology is deployed, but de Certeau elsewhere reveals the forms and possibilities of critical reappropriation of the imperatives that go along with it. On the basis of very concrete situationswork, eating -he shows how individuals 'poach' the social and cultural order through 'ruses', micro-resistances enacted in the everyday that constitute spaces of creativity and freedom, possibilities of emancipation. Doing one's own private work in the factory, or the gift of food between generations [ de Certeau et al., 1994] are examples that testify to a 'truant freedom of practices'. These tactics, which according to de Certeau are to be distinguished from strategies,2 represent forms of politicisation by way of the everyday and from below. Entering by way of the everyday gives us access behind the scenes of power relations, the spaces where the 'hidden discourses' of subaltern groups can be identified, and on which these subaltern groups draw to assert their ideas of social justice [Scott, 2009].

These discourses, produced unbeknownst and away from the scrutiny of dominant groups, represent acts of resistance. Scott [2009] shows that even the most disadvantaged individuals possess a knowledge of the rules of the social game and are capable of putting on a 'good face' and yet not being duped behind the scenes. It is precisely in this space that what he calls 'infrapolitical resistance' is forged and revealed, the everyday thus emerging as a domain of discreet political struggle. Thinking along these lines, optimality is to be sought not so much in the more or less successful adoption of the imperative to maximize the use of the self as in the capacity of individuals to appropriate it, to find a satisfactory compromise, generated through bricolage in the everyday.

In our view the concept of bricolage is particularly apt as a way to understand what individuals do with the moral precepts of optimization. Claude Lévi-Strauss extols this practice in his introductory chapter to The Savage Mind [1966]. Lévi-Strauss points out that in its old sense the verb 'bricoler' was always used 'with reference to some extraneous movement: a ball rebounding, a dog straying or a horse swerving from its direct course to avoid an obstacle. And in our own time the "bricoleur" is still someone who works with his hands and uses devious means compared to those of a craftsman […] The rules of his game are always to make do with "whatever is at hand"' [Lévi-Strauss, 1966: 16-17]. 'Bricolage', then, refers to the act of recuperating materials and diverting them from their primary use. Here we are close to de Certeau's sense of tactics [1990], that is, the capacity of individuals to react and adapt. To be sure, the bricolaged object often has, as Yves Deforge puts it in his afterword to the French edition of Gilbert Simondon's On the Mode of Existence of Technical Objects, 'an air of compromise'. Deforge continues: 'this compromise between desire and ability, between the plan and the means whereby it is realised, is perceived by the bricoleur as a triumph over difficulty… and by the outside observer as an excessive expenditure of energy for a questionable result.' But, he explains, this is beside the point, for the true purpose of the bricolage lies in '[the bricoleur's] creative power, his capacity for dialogue with recalcitrant material, his need to invest in a personal project' [Deforge 2001: 330]. Bricolage, on a metaphorical level, is thus more of a deviation than a project in itself, and this deviation carries meaning; it can be liberating, at least for those who have the capacity and are permitted to engage in it [START_REF] Altglas | Exotisme religieux et bricolage[END_REF]. While it may at first sight appear non-optimal given the amount of time it takes and the unsatisfactory ratio of energy expended to result obtained, bricolage perfectly encapsulates the way we understand self-optimization: it is not that it is itself a form of optimality, but rather that it can produce optimality in the sense that it can lead to a satisfactory compromise between norms and possibilities, between injunctions and preferences.

The principal aim of this issue is therefore to go beyond the normativity of the concept of optimization by examining the games, the stratagems, the negotiations, the resistances and the bricolages brought to bear by individuals faced with their inequalities of skill and knowledge.

Forms and registers of optimization

We have chosen to group the articles in this issue around three main axes of investigation, which in our view help to make clear the discursive foundation and the ideological bulwarks supporting the promises of self-optimization [START_REF] Dalgalarrondo | Un transhumanisme "à mains nues". Sociologie de la promesse du jeûne[END_REF]]: these are asceticism, self-exploration and politics.

Asceticism as process

In his book You Must Change Your Life, Peter Sloterdijk [2013] suggests that we take the athlete as the most complete and most accessible contemporary "incarnation" of the overcoming of the self through rational optimization.

Sloterdijk's hypothesis is that there is a powerful return to the practice of asceticism in our secularized societies. He posits 'modernity' as a new anthropotechnic regime that 'secularized and collectivized the practising life by breaking the longstanding ascesticisms out of their spiritual contexts and dissolving them in the fluid of modern societies of training, education and work' [Sloterdijk 2013: 331]. He argues thus that what we are seeing is a vast process of 'massification of asceticism' -and the ideology of the optimal human is just one version of this. Sport, that laboratory of the superhuman, of victory over the self and of risk-taking [START_REF] Dalgalarrondo | Les dispositifs de prise de risques dans le rugby professionel[END_REF], in which physiotherapists, doctors and engineers from new technology companies work together to explore the limits of the human [START_REF] Dalgalarrondo | Surveiller et guérir le corps optimal. Big Data et performance sportive[END_REF], is part of this process of massification of asceticism, disseminating a moral imperative toward self-optimization. This laboratory of the optimal human and its experimental context thus corresponds to the great media gymnasion of anthropotechics, 'the methods of mental and physical practising by which humans from the most diverse cultures have attempted to optimize their cosmic and immunological status in the face of vague risks of living and acute certainties of death' [Sloterdijk, 2013: 10]. The sportsperson, secularized embodiment of the ascetic and his/her 'exploits', demonstrates the possibility, available to any scrupulous practitioner, of producing him/herself: 'the gymnasion, the place where physical exercises were practiced, was the same place where philosophy lessons were given; in other words, it was also the place for training in spiritual gymnastics' [Hadot, 1995: 102].

Finally, asceticism is closely linked to the concept of pleasure, the pleasure of exercise for its own sake, since it generates a heightened feeling of control, the pathological reverse of which has been extensively documented in research on anorexia [START_REF] Darmon | Devenir anorexique[END_REF].

In this section of the issue, Scarlett Salman analyses a key figure in this injunction to take exercise for its own sake, the business coach. She shows firstly that management techniques are one of the routes of dissemination of the ideologies underlying the quest for self-optimization: 'self-actualization' (and its pragmatic mode, 'the entrepreneur of the self') and 'interpersonal skills' (with its idealtypical form, the 'manager as coach'). Her genealogical approach reveals the links forged between psychology of work and coaching techniques, and the advantages of setting the pathological and health apart from one another in this way. Coaching is inscribed in the apolitical dynamics of personal development, offering individuals techniques for optimizing 'life itself'. In particular, this genealogy reveals how technologies of the self have gradually shifted their focus, from the group and its dynamics to the individual/manager and her/his potential.

Coaching is a practice of 'bringing-into-being' centred on 'personal development', where the manager's introspection is facilitated by her/his adherence to the ethos of self-actualization and to rational exploration of her/his potential, her/his authenticity. Salman makes clear that the depoliticization of the practice is partly linked to this discourse on self-actualization, which makes the subject responsible for her/his own quest to adapt socially: 'Coaching fosters the idea that problems of communication or tensions at work are attributable to the individual and her/his "personality", thus removing from the company any need to reflect on its modes of work organization and shifting the responsibility for resolving them onto the individual.' Yan Dalla Pria's article focuses on the use of sport as a technique of selfoptimization in the workplace, offering a prime example of the massification of asceticism and the role that physical activity -here presented as a simple pedagogical tool -can play in disseminating an ethos of transformative asceticism.

Here too, as with coaching, the practitioner subjected to the injunction toward self-optimization is constrained by her/his position as an employee. Analysis of training seminars shows how sports practice and personal development are brought together in an exercise so as to subject individuals to 'an alignment of all elements of human life to the logic of the market'. A quest for social fitness that works through the enlistment of bodies, constituted as biocapital, and now turns to the promise of neuroscience to legitimize a holistic approach. Exercise becomes a 'machine' for marginalizing the least productive, 'fragmenting teams' and 'ranking individuals on the basis of their economic potential'. Although apathy emerges as a possible mode of resistance in the face of this type of managerial injunction, these practices nevertheless help to support the dissemination of an ideology of 'self-shaping' by employees that seems to escape any politicization and that exerts a symbolic violence on even the most critical.

Ascetic practice can also be discerned in the quest for physical well-being and aesthetic ideals. Camille Couvry and Marion Braizaz present an ethnography of beauty pageants, showing us that these competitions can be transformed into a space of contestation, giving certain participants an opportunity to make a public statement of their individuality. Thus, through the display of different bodies and the expression of alternative values and norms the competition can, in its small way, become a political moment that invites reflection among those who witness it. It is thus possible for some contestants to avoid the 'tortured performance' by taking the route of 'destigmatization'. Couvry and Braizaz further point out that the most conventionally beautiful participants, those who might initially appear to reap the greatest benefits from subjecting their bodies (and personalities) to an ascetic regime and to competition, may find it difficult to assert the value of this experience in other social spaces: 'Aesthetic self-optimization as an end in itself or for the explicit ends of personal social advancement is seen as illegitimate and immoral'. Finally, Couvry and Braizaz' analysis of the how these very popular contests are organized, and of the work of socialization involved, reveals the personal triggers for these young women's compliance, and helps us understand the conditions in which these practices of beauty constitute techniques of selfoptimization.

Self-exploration

The morality of asceticism, as a process of transformation, cannot be reduced simply to the application of a regime or the adoption of a moral-aesthetic position.

Asceticism is an exploratory process in the sense that the individual seeks to experience a transformation of the self through practice. On this level, the techniques of optimization can be understood more prosaically as a journey. The technologies of the self associated with this concept are mainly introspective processes, an invitation to an interior journey, a practice of the self aimed at increasing one's capacity for self-government. A liberating journey towards the self that compels the individual to establish a new dialogue with her/his body, her/his sensations and her/his emotions. Taken to a deeper level, this dynamic of the journey can become an exploration of one's limits and one's capacities for adaptation.

This experience of the self is at issue in Milana Aronov's article. Aronov presents an original analysis of social use of LSD by individuals in good health who seek an enhancement in and of their everyday life. She establishes a genealogy of the 'pyschedelic experience' that highlights the development of the concept of 'enhancement', its emergence within the American counter-culture of the 1960s, and its current redeployment in the promises claimed for 'psychedelic microdosing'. She thus shows how a promise of enhancement circulates between the individual's everyday personal life, where it takes the form of a care for the self and a quest for well-being, and organizational thinking where the potentials in terms of efficiency and creativity at work are presented as central to the process of production and innovation: 'My interest in the case of such "psychedelic" drug use has lain in exploring how an economic understanding of the "matter" meets an embodied understanding of individuals' identity. In doing so, my aim was more broadly to think through contemporary problematizations of "neuroenhancement".' This interwoven history of theories of management and the 'psychedelic experience' reveals how the quest for efficiency has, over the course of its history, produced a highly original assemblage in which Zen techniques, neuroscience, theories of management, psychology and pharmacology meet and mingle.

Éric Dagiral's article on the practices of personal quantification deals with another facet of this work of self-exploration. Here the exploration takes the form of expressing one's life, one's behaviours, one's shortcomings and one's goals in numbers. Dagiral shows that these particular forms of attention to the self can lead to a feeling of confusion for those who engage in them: 'we have shown that there is a danger that the means come to substitute for the ends, in as much as the latter are difficult to grasp (i.e. 'happiness'), despite the considerable efforts made to slice up the ingredients of a successful and satisfying life into singular objectives.' Converting one's life into a series of equations can in fact result in a daily practice of optimization whose extreme complexity hides the fact that one is simply 'spinning one's wheels'. Indeed, it is difficult to set a 'social optimum' in advance, to determine the ideal balance between family life and work, without experiencing burnout. The intensive practice of self-quantification can thus result principally in the revelation of the complexity of our social life and the need to take other routes, adopt other technologies of the self, other ways to go around, in order to grasp the issue of the optimal life. The failure of the strategy of self-optimization via quantification returns the individual to the broader question of the quality of our lives and the impossibility of breaking it down into independent variables: 'we have described a relationship to optimization that does not appear to achieve the optimum sought, yet continues to guide these individuals' research into their objectives. In this sense, if perfection is by its very nature unachievable, but remains as an unattainable individual goal, optimization represents its contemporary culmination, in terms of a self-control that may be required both by organizations and by individuals of themselves.' Self-exploration coupled with the quest for moral perfection may also emerge out of a restrictive situation. Virginie Wolff's study of people following a gluten-free diet takes an original approach to show how, in a deft reversal of stigma, the 'sensitive' body moves from the status of constraint to that of ally in this journey of introspection. The various bodily manifestations of people who are glutenintolerant -stomach pain, bloating, digestive problems or even chronic diarrhea -are initially experienced as permanent and disabling reminders that can arouse disgust [START_REF] Memmi | Introduction du numéro: La fabrication du dégoût[END_REF] and hence turn the 'sensitive' body into an abnormal body that is difficult to manage in public. Yet this vulnerability leads to an intimate self-knowledge, opening the way to exploration and experiment and thus becoming a technology of the self: the bodily signs reported by survey respondents gradually become understood as pointers offered by a body which, by resisting gluten, is attempting to guide them toward a different way of life. This shift in interpretation can then lead to a new ethical stance and enable the individual to feel justified in challenging moral authorities, particularly with regard to the mainstream world of eating. 'The sensitive or hypersensitive body […] thus becomes a tool for expressing an ethical commitment, while the choice to deprive oneself of a foodstuff, initially justified on the basis of its effect on the body, acquires a political value.'

The idea that attention to one's own body arises especially when the body makes itself manifest through pain, injury or disease is also the focus of Nicoletta Diasio and Vulca Fidolini's article in this section. Their study looks at men aged between 40 and 60, an age bracket little studied by the social sciences, which nevertheless offers a rich field of observation in considering ways of achieving a 'body project' [Shilling, 1993]. These men have to come to terms with the first marks of time on their bodies: putting on weight, problems with cholesterol, etc. Food thus emerges as a primary site of surveillance, reflection and work on the self. But Diasio and Fidolini suggest that when such attention to nutrition becomes necessary, it implies a reconfiguration of models of masculinity. For food, whether in terms of consumption, domestic labour or relationship to the body, is a powerful weapon for maintaining and reproducing gender roles [START_REF] Fournier | L'alimentation: arme du genre[END_REF]. Here it becomes a 'field of play and experimentation on the self, where control over time, maintaining health and preserving one's life are all brought into play', and where, in addition, models of masculinity may be interrogated, hybridized and refined. This mechanism recalls the 'moral perfectionism' [Laugier, 2010] that arises from the realization of human fallibility and subsequently works toward improvement; in this article, this perfectionism is enacted through experimentation, trial and error, and bricolages of sometimes clashing normativities.

Politics

The various different techniques and situations of optimization analysed in this issue share an eminently political dimension, both in the content of the promises described and in the practices themselves. Thus we discover the multiple and polymorphous frictions between domination techniques and techniques of the self. We observe how the capacity for deviation sometimes consists simply of a gap that allows for the establishment of a new power relationship in the interstices between mechanisms of domination, a relation in which it is possible to express one's agency, a different view of the world. This liberating deviation may first take the form, as John Coveney and Lee Thompson suggest, of a critical detachment. Coveney and Thompson's highly original article is set out as a dialogue, a reflexive look back at their own professional careers, which are notable for the fact that they first worked as health professionals, and then moved into the academic context of social sciences.

Through the lens of what might even be described as a 'coming out', they describe how the moral imperative of optimization at work in relations of care is based on the injunction to take individual responsibility, an injunction that substantially informed their professional and personal behaviour, and from which they have gradually learned to detach themselves: 'we examine the ways in which our experiences as learners, or "docile bodies" [Foucault, 1995], embodied various forms of optimisation, whether this was for our patients, clients, or ourselves.' As noted above, optimization here gives rise, beyond the injunction, to a process of introspection. To take up the Foucauldian concept of subjectivation, it is primarily reflexivity that allows for critique, empowerment, and finally emancipation. Thus in Foucault's view [1990], critical distance is allied to virtue, and can then constitute an ethical and political attitude that emerges as the first stage in the process of appropriating promises of optimization. This attitude is also at the base of more clearly asserted forms of resistance which, when they become collective and organized, may build into political movements.

Such is the case with the practice of voluntary sterilization studied by Emma Tillich in this section. In her ethnographic study of childless women who decide to become sterilized, sometimes at a young age, sterilization emerges as an optimal form of contraception but also -and herein lies its creative originality -as a way of achieving full self-actualization. Like fasting [START_REF] Dalgalarrondo | Un transhumanisme "à mains nues". Sociologie de la promesse du jeûne[END_REF], this permanent contraception in some way allows them to do more with less. Moreover, in the most radical versions, those involved in the 'childfree' movement are not content with improving their own life conditions and liberating themselves from the norm of parenthood which they find suffocating and even debilitating, but also promote 'a scale of values that establishes a hierarchy of levels of personal development'. In a neo-Malthusian approach, procreation sits at the bottom of this scale, and voluntary sterility at the top. 'Thus optimization here takes the form of a subversive culture of refusing to reproduce, accompanied by a discourse that preaches liberation and the achievement of full self-actualization.' Optimization via restriction is also the focus of Sébastien Mouret's article in this section, which focuses on veganism. The ambition of followers of this movement is to improve human nature by ending the consumption of animal products -meat, dairy produce, honey, leather etc. But this approach is not merely ethical, it is also concerned with health, and it is political. It is concerned with health because a dietary adaptation [START_REF] Fournier | Entre médicalisation et migrations, les enjeux de l'adaptation alimentaire[END_REF] is required, since a vegan diet leads to a lack of vitamin B12, an organic compound essential to the functioning of the human body that is not found in plants. Vegans' moral labour therefore entails a work of arbitrating between concern for the self and concern for others: between taking a supplement, which makes this diet viable but involves a relation to artifice, and refusal to supplement, which may be claimed as a political act or tried as experiment, but puts the movement itself at risk. For 'the issue is to create a healthy vegan body, in other words an exemplary vegan body, which is thus a political tool.' Each vegan is in effect the embodiment of the movement she/he promotes, a movement that cannot be defended with a body that is too puny or feeble. It seems indeed that this incarnation, in the sense used by [START_REF] Hauray | Incarnation and the dynamics of medical promises: DHEA as a fountain of youth hormone[END_REF], constitutes one of the political aspects of self-optimization.

The range of promises of self-optimization analysed in this issue helps us to comprehend the diversity of assemblages mobilized by those who promote them and by those who embark on these routes of the self. A number of articles thus reveal, in line with the thinking of Ivan Illich [START_REF] Paquot | Ivan Illich. Pour une ascèse volontaire et conviviale[END_REF], a triangulation between asceticism, self-exploration and political claims. These assemblages [Ong and Collier, 2008] or aggregations [START_REF] Lepiller | La place des médias dans la reliance de la critique de l'alimentation industrielle: Le Nouvel Observateur et l'alimentation après la "vache folle[END_REF] operate like a tiled roof, where each tile/argument partially overlaps the one beneath, and thus reinforces, by continuity or contrast, the attractiveness of the promise of optimization. The performativity of these promises is closely linked to the way they are put together out of a heterogeneous multiplicity. The disparate elements that make them updiscourses, representations, techniques and technologies, visions of the futurework together and offer new zones of exchange [Deleuze and Guattari, 1980] to discover and experiment with. These assemblages take the form of functional entities [START_REF] Patton | Metamorphic logic: Bodies and powers in A Thousand Plateaus[END_REF] and open new horizons, new ways of and reasons for acting on the self. It is here, in this play between norms and possibilities, that the work of appropriation occurs: individuals "bricolage" and assemble, in order ultimately to move towards a satisfactory compromise that enables them to make a change, however minimal, and to hold onto it.

According to de Certeau, tactics are more implicit, going unsaid and evidence of a capacity to react, while strategies are more explicit and declared, established as a line of action.

Acknowledgements

Our warm thanks to the contributors of the articles and reviews for the quality of their writing, and to the editorial team at Ethnologie Française for supporting us through this project. Special thanks to Jean-Pierre Hassoun for his reading and his astute advice.

Translated by Rachel Gomme.


Riks Kup

Julien Trébosc

Barbara Perrone

Olivier Lafon

Jean-Paul Amoureux
email: jean-paul.amoureux@univ-lille1.fr

C Quat

Recording 13 C-15 N HMQC 2D sparse spectra in solids in 30 sec

Keywords: D-HMQC, Hadamard encoding, solid-state NMR, 2D spectra, 13 C-15 N HETCOR

We propose a dipolar HMQC Hadamard-encoded (D-HMQC-H n ) experiment for fast 2D correlations of abundant nuclei in solids. The main limitation of the Hadamard methods resides in the length of the encoding pulses, which results from a compromise between the selectivity and the sensitivity due to losses. For this reason, these methods should mainly be used with sparse spectra, and they profit from the increased separation of the resonances at high magnetic fields. In the case of the D-HMQC-H n experiments, we give a simple rule that allows directly setting the optimum length of the selective pulses, versus the minimum separation of the resonances in the indirect dimension. The demonstration has been performed on a fully 13 C, 15 N labelled f-MLF sample, and it allowed recording the build-up curves of the 13 C-15 N cross-peaks within 10 min. However, the method could also be used in the case of less sensitive samples, but with more accumulations.

I.

Introduction

Presently, nearly all the two-dimensional (2D) spectra observed in Nuclear Magnetic Resonance (NMR) are recorded with the same principle: the acquisition during a time, t 2 , of a series of signals (free induction decays or FIDs) for numerous evolution times, t 1 , during which the spin system is subject to a selected interaction. After a 2D Fourier Transform (FT), the frequency (F1, F2) 2D spectrum is then observed and analyzed. Most of the time, the step for the evolution time, t 1 , is kept constant. Along F1, the resolution and the spectral width, SW1, are then the inverse of the maximum evolution time, t 1,max , and of t 1 , respectively. As a result, when the resonances are narrow and when they span over a large frequency range, the number of required t 1 steps, m = t 1,max / t 1 , is large, and hence also the experimental time, T exp . Provided the sensitivity is sufficient to observe the signals of interest in a few scans, the situation is commonly described as sampling limited. For example, this is the case when 13 C spectra of well crystallized compounds are recorded under magic angle spinning (MAS) to enhance the resolution, especially at high magnetic fields because of the proportionality between the frequency range and the field. One way to decrease T exp is to use non-linear sampling of the evolution time, and on average the typical gain in time with respect to the linear t 1 sampling is of ca. 2. [START_REF] Sibisi | Maximum entropy signal processing in practical NMR spectroscopy[END_REF] In the case of homo-nuclear correlation (HOMCOR) spectra, the m value can be decreased, and hence also T exp , by using along F1 the prior knowledge provided by the directly detected signal along F2; this is known as the Covariance scheme. [START_REF] Zhang | Spectral deconvolution of chemical mixtures by Covariance NMR[END_REF] This method has been used in solid-state NMR with either linear or non-linear sampling. [START_REF] Hu | Solid-state NMR covariance of homonuclear correlation spectra[END_REF] The prior knowledge is also used in the Hadamard spectroscopy to dramatically reduce T exp in sparse spectra. In this case the time saving is achieved by excluding empty spectral regions that contain no useful information. Indeed, when dealing with sparse spectra, two particular ways can be used to reduce T exp . Both methods use selective excitations of the N species indirectly detected along F1, and hence they both require a previous acquisition of the 1D spectrum of this nucleus to know its resonance frequencies. In the first method, each of the N resonances is excited selectively, and the corresponding N FIDs are recorded separately. In the second method, n FIDs are observed, each related to a multi-selective simultaneous excitation of the N resonances encoded according to a Hadamard matrix, [H n ], [START_REF] Kup E | Frequency-domain Hadamard spectroscopy[END_REF] where the size of this matrix, n, is either a power of 2 or a multiple of 4 larger than or equal to N. After a Hadamard decoding processing, the N individual FIDs can be retrieved and used to reconstruct the 2D spectrum of interest. It can be shown that using the Hadamard encoding-decoding process, instead of N consecutive single excitations, allows gaining a factor of up to n for T exp to achieve the same signal-to-noise ratio (S/N). In both cases, the 2D spectrum of interest can be reconstructed from the individual traces. As a result, the 2D spectrum is obtained with only n steps, instead of m = t 1,max / t 1 in case of the conventional way. Unlike the Fourier matrix, the Hadamard matrix is real rather than complex, which considerably simplifies the Hadamard transform. More importantly, it reduces the number of Hadamard encoding steps by a factor of two. For the same reason, it improves the S/N of the experiment by a factor 2 as compared to that obtained with a classical FT of a similar selective frequency encoding experiment. 4c,d The main limitation of these two methods is to obtain a selective excitation for each resonance. Indeed, when two resonances are separated by , their selective excitation requires a pulse of minimum duration in the order of 1/ . Therefore, when on a spectrum the minimum separation between two close resonances, min , is very small, the selective excitation of each of these two resonances requires very long pulse lengths, in the order of sel 1/ min . These long excitations may lead to a large signal decrease due to losses occurring during sel , particularly in solids where the T 2 values are often in the ms range. One way to increase the S/N may appear to be reducing the length of the Hadamard encoding pulses. However, when doing this the two closest resonances are not separately excited, and their signals are weighted mixtures of the responses of the two species. This is still more difficult with two partly overlapping resonances, and in this case only a common response of the two sites can be observed.

In two previous works, [START_REF] Ashida | Hadamard NMR spectroscopy in solids[END_REF] we have demonstrated in solids on 13 C labeled amino-acids the validity of multi-selective Hadamard excitations in the cases of 13 C-13 C correlations based either on throughbond 5b or through-space 5a recouplings, and of 13 C-1 H CPMAS hetero-nuclear correlations (HETCORs). 5a

In this communication, we would like to extend the Hadamard scheme to the case of 13 C-15 N D-HMQC (Dipolar Hetero-nuclear Multiple-Quantum Correlation) indirect detection 2D method. Indeed, it has been shown that this through-space HETCOR method is very simple and very robust in the case of high abundance nuclei. [START_REF] Gan | 13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling[END_REF] As a test sample, we have chosen the fully 13 C and 15 N labeled f-MLF tri-peptide, N-formyl-Met-Leu-Phe. The molecule and the 1D CPMAS 13 C and 15 N spectra are shown in Fig. 1, together with the 13 C and 15 N assignments and their isotropic chemical shifts given in Table 1. [START_REF] Mao | Directly and indirectly detected through-bond hetero-nuclear correlation solidstate NMR spectroscopy under fast MAS[END_REF] The three 15 N resonances are well separated, whereas the 13 C spectrum is more crowded due to the presence of 19 different resonances. It must be noted that in Fig. 1c, most of the 13 C resonances are broadened by the 1c because it is not labelled in our sample. Because of 1 J13C-13C couplings, L 1 and L overlap in Fig. 1c, whereas they are discernible with unlabeled samples. [START_REF] Mao | Directly and indirectly detected through-bond hetero-nuclear correlation solidstate NMR spectroscopy under fast MAS[END_REF] Ar carbons (F , F and F ) are broadened by 180° flips of the phenyl ring and hence they cannot be cleanly separated. At B0 = 14.1 T ( 0,13C = 150.9 & 0,15N = 60.8 MHz), R = 13 kHz corresponds to 86 ppm. Therefore, the three small resonances at ca. 88 ppm are spinning sidebands of the three C peaks at ca. 174 ppm, whereas those at ca. 218 ppm are sidebands related to Ar carbons at ca. 132 ppm. The 13 C shifts are referenced with respect to TMS, and the 15 N ones to ammonia.

II. Pulse sequence

The D-HMQC sequence has been derived from the scalar J-HMQC scheme used with liquid samples, 8 by introducing two symmetrical dipolar recoupling parts. [START_REF] Gan | 13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling[END_REF] As a result, instead of the through-bond correlations achieved in liquids, the D-HMQC sequence allows performing throughspace analyses in solids. Most of the time, dipolar interactions are much larger than scalar couplings, and therefore, D-HMQC allows using much shorter recoupling times than J-HMQC, which decreases the large losses encountered in solids.

When observing protons, the SR4 2 1 recoupling scheme is often used because: (i) it eliminates the 1 H-1 H interactions, at least to the first-order, which limits the signal losses during rec , (ii) it is amplitude-modulated and hence robust to rf-field inhomogeneities, (iii) it is unaffected by dipolar truncation, hence allowing the observation of distant nuclei, and (iv) it requires a low rf-field ( 1 = 2 R ). [START_REF] Brinkmann | Proton-selective 17 O-1 H distance measurements in fast magicangle-spinning solid-state NMR spectroscopy for the determination of hydrogen bond lengths[END_REF] However, when the homo-nuclear dipolar interactions of the two involved nuclei are much smaller than R , they are mostly canceled by MAS. Then one of the most efficient dipolar recoupling scheme is SFAM (Simultaneous Frequency and Amplitude Modulations), 10 because it is very robust with respect to offset and its dipolar scaling factor is 2 larger than that of SR4 [START_REF] Zhang | Spectral deconvolution of chemical mixtures by Covariance NMR[END_REF] 1 , hence decreasing the losses. The hetero-nuclear dipolar interaction has two time-dependent terms under MAS: one with R frequency and the other with 2 R . Therefore, SFAM recoupling is composed of two modulations, one for the amplitude, 1 (t), and the other for the change of frequency with respect to the carrier one, 0 (t):

1 (t) = 1,max sin(2 R t) and 0 (t) = 0,max cos(2 R t) (1)
We have recently made a detailed analysis of the SFAM efficiency versus the two maximum modulations, 1,max and 0,max . 10b We have analyzed the trajectories of the spin magnetization starting from B 0 during the basic element of SFAM irradiation, which lasts T R . This analysis has shown that SFAM is only efficient when its basic element is cyclic, which means that the spin magnetization comes back to its initial orientation along B 0 every T R . Practically, largest SFAM efficiencies are hence observed when rf-parameters are under certain regimes:

( 1,max / R , 0,max / R ) (1.5, 0.5), (2.5, 3.5) and (2n + 1, 2n + 1) (n 2)

(2) We have used SFAM for the dipolar recoupling between 13 C and 15 N in this communication, and after an initial train of saturation pulses, the experiments always started with a ramped CPMAS transfer from 1 H to increase the S/N.

The conventional pulse sequence with 13 C detection, called 13 C-{ 15 N} D-HMQC, is shown in Fig. 2a. All /2 and -pulses are hard-pulses to excite simultaneously the two whole spectral widths. A 1 H and 13 C decouplings were applied to enhance the 15 N resolution and to decrease the losses. To avoid spinning sidebands along F1 and thus to increase the S/N, the t 1 step is often a multiple of the rotor period, T R .

The multi-selective version with [H n ] Hadamard encoding, called 13 C-{ 15 N} D-HMQC-H n in the following, is shown in Fig. 2b. It is derived from Fig. 2a by fixing t 1 = 0, and by replacing the two /2 15 N pulses with a multi-selective -pulse on/off irradiation. We have tried several types of selectivepulses, and the best results with the shortest pulse lengths, and hence with the smallest losses, were always observed with a simple Gaussian line-shape, truncated at 10% to minimize its length. The encoding in this type of Hadamard spectroscopy is line-selective and more sophisticated pulses (e.g. BURP series) that are band-selective are not needed and would be significantly longer, hence leading to larger losses. The efficiency of the selective -pulses, depends on the relaxation during the selective pulses as described in section III, but it was always very good, and higher than 90% in our experiments. The length of the selective excitation, sel , is on the order of several ms, and hence much longer than the hard -pulse on the observed channel. Therefore, to minimize the losses, we have introduced during sel a 13 C decoupling. The 13 C -pulse in the middle of the [H n ] encoding pulse serves as a refocusing pulse providing phase sensitive spectra. The pulse program is given in the SI.

III. Results

The experiments were performed at B 0 = 14.1 T with an AV-III-HD Bruker NMR spectrometer, equipped with a HCN Bruker MAS probe with a 1.9 mm rotor spinning at R = 13 kHz. The multiselective Hadamard encoded excitation was generated with the Wave-Maker (wvm) module available within the Topspin software. The same pulse length, sel , was used for all resonances, and its value was chosen to selectively excite the two closest ones. The amplitude of this multi-selective excitation was then fine-tuned directly on the spectra by maximizing the signal. It must be mentioned that Hadamard experiments require very linear rf-amplifiers in the low rf-regime to allow the simultaneous optimization of the selective -pulses for all resonances and all elements of the [H n ] Hadamard encoding matrix. All spectra were recorded with the same recycling delay, RD = 5 sec, and the number of scans, NS, was from 1 to 4, and is indicated in the captions.

The SFAM recoupling was obtained with amplitude and frequency maximum modulations of 1,max = 22 and 0,max = 15 kHz, respectively. The rf-field for the -pulse on the detected channel was of 67 and 43 kHz for 13 C and 15 N detection, respectively. The CPMAS Hartmann-Hahn initial transfer ( cp = 2 ms) was obtained with 1 H linearly ramped from 50 to 100 kHz with 13 C rf-amplitude set at 67 kHz. The 1 H decoupling was set to 100 kHz and the decoupling schemes were CW during the mixing period and SWF-TPPM during the acquisition and t 1 periods.

The 13 C-{ 15 N} D-HMQC and D-HMQC-H 4 2D spectra are shown in Fig. 3a andb, respectively. The conventional spectrum (left) was acquired in 22 minutes, but at least 1 hour would have been required to achieve an adequate resolution along F1. In comparison, the Hadamard spectrum, shown on the right, required only 30 sec. During the 15 N selective pulses, a hard 13 C -pulse removes the J CN couplings between the observed carbon and the nitrogen atoms that are not affected by the selective pulses, while J CN couplings are preserved for nitrogen atoms that are selectively inverted. However, this little affects the reconstruction of the Hadamard spectra because the J CN couplings are much smaller than the observed 15 N linewidths in solids. The 15 N-{ 13 C} D-HMQC and D-HMQC-H 8 2D spectra are shown in Fig. 4a andb, respectively. Because of the previous knowledge of the C-N proximities, 7 six 13 C encoding frequencies were selected: M , F , L the lower 15 N Larmor frequency, 15 N-{ 13 C} experiments are less sensitive than the 13 C-{ 15 N} ones. Nevertheless, 15 N-{ 13 C} experiments can be useful if 13 C resonances are better resolved than 15 N ones. In the case of f-MLF, the 13 C spectrum is more crowded than its 15 N counterpart. Therefore, it was important to keep sel of 15 N-{ 13 C} experiments as short as possible, not only for sensitivity reasons, but also to avoid multiple-quantum effects and 1 J 13C-13C evolution that occurs for pulse durations comparable to or larger than ca. 0.5/ 1 J 13C -13C , i.e. ca. 10 ms. [START_REF] Nuzillard | A new form of correlation spectroscopy[END_REF] The conventional spectrum (Fig. 3a) was acquired in 44 minutes, whereas its H 8 Hadamard version (Fig. 3b) required only 165 sec. In the four 2D spectra of Fig. 3 and4, the same five expected cross-peaks were observed: M -M N , F -F N , L -L N -L N -F N . The excited spectral ranges were calculated with the Wave-Maker module, and with sel = 3 and 4.5 ms they are equal to FWHM 6.5 and 1.7 ppm in Fig. 3b and4b, respectively. This means that all 15 N and 13 C narrow resonances observed in Fig. 1b andc were fully excited. Simultaneously, these spectral ranges were selective enough to only excite one resonance at a time, even the C quat which are the closest resonances in this sample (Fig. 1c). Moreover, it must be noted that even if the smallest C quat -C quat separation is of 1.2 ppm ( -), to a nitrogen, and hence the closest separation to be taken into account is of 3 ppm ( -) (Table.1). For C resonances, the separations are equal to 2.3 (M -F ) or 2.5 ppm (L -F ). Furthermore, a perfect selectiveness is not crucial as long as only the positive signal is taken into account (see below). It must be mentioned that the selective encoding approach has the flexibility to extract the information from a sub-system in a crowded spectrum. This is demonstrated in Fig. 5 were we have isolated the 15 N-{ 13 C} D-HMQC-H 4 response for the C region. Moreover, because the selected spin system had a smaller size than the total system, the size of the Hadamard matrix was decreased from 8 to 4, and hence T exp was reduced by a factor of 2 with respect to Fig. 4b. As pointed out earlier, the main of the Hadamard encoding experiments resides in the selective excitation of each indirectly detected resonance. We have analyzed this limitation in solids in more detail by recording four 2D 13 C-{ 15 N} D-HMQC-H 4 spectra for various sel values. The corresponding slices observed for F N at 15N 108 ppm, are shown in Fig. 6. As anticipated, the optimum length for the excitation is a compromise in between the selectiveness of the excitation and the loss of signal intensity. For the optimum excitation length, sel,opt 3 ms, the signal is maximum, and as expected only two cross-peaks are visible in this slice: F N -F and F N -When the duration of the selective pulse is decreased to 1.5 ms, it also excites the L N species and hence two new cross peaks become visible: L N -L and L N --resonance irradiation, the effective rffield is larger than on-resonance, and for this reason these peaks appear with a negative amplitude. M positive cross-peaks are not changed with respect to experiment with sel = 3 ms. This means that the selective pulse length does not require an accurate optimization if only positive signals are taken into account. With respect to the minimum peak separation along 15 N of 8 ppm (116 -108), which means ca. 500 Hz at 14.1 T, the useful range for HMQC-H n experiments can thus be expressed as: sel,opt * min 0.75-1.5

(3) When the pulse-length is decreased to 1 ms, the excitation is much too broad and the spin dynamics is completely changed. When sel = 4.5 ms, there is no off-resonance effect, but the losses during the pulse are evident. When sel > 4.5 ms, the multiple-quantum interferences and significant losses become unacceptable. To finish this analysis, we have recorded a series of 2D 13 C-{ 15 N} D-HMQC-H 4 spectra with the aim to obtain the built-up curves of the five cross-peaks versus rec . These curves, shown in Fig. 7, required recording thirteen 2D spectra, which took only ca. 10 min of experiment time. Obtaining this information with conventional 2D methods is typically quite time consuming. In this example, all the build-up curves only depend on the C-N one-bond distances, and they thus all have similar relative evolutions. The classical C-N distance of ca. 1.46 Å corresponds to d 13C-15N = 980 Hz. Therefore, when taking into account the SFAM recoupling scaling factor, the maxima of the build-up curves should be observed at rec 960 s. [START_REF] Nagashima | Independent through-space hetero-nuclear correlation between spin-1/2 and quadrupolar nuclei in solids[END_REF] However, in Fig. 7, the maxima are observed in the range of rec 700-850 s. This decrease of the optimum recoupling time is related to the losses occurring during the two recoupling periods. The differences in between the actual distances and their experimental values emphasize the fact that a correct distance determination always requires a reference experiment that allows cancelling the effects resulting from the losses. This is the case when using optimized sequences either in between two spin-1/2 nuclei with REDOR, 13a or in between one spin-1/2 and one quadrupolar nucleus with RESPDOR 13b or FM-RESPDOR. 13c

IV. Conclusions

We have demonstrated significant advantages in experimental time obtained by using Hadamardencoded 13 C-15 N D-HMQC-H n experiments. This method is not designed to improve the sensitivity, but rather to reduce the experiment time, provided there is sufficient sensitivity. The main limitation of the Hadamard methods resides in the length of the encoding pulses, which results from a compromise between the selectivity and the sensitivity due to losses. For this reason, these methods should mainly be used with sparse spectra, and they profit from the increased separation of the resonances at high magnetic fields. In the case of the D-HMQC-H n experiment, we give a simple rule that allows directly setting the optimum length of the selective pulses, versus the minimum separation of the resonances in the indirect dimension.

The demonstration has been performed on a fully 13 C, 15 N labelled f-MLF sample, and it allowed recording the build-up curves of the 13 C-15 N cross-peaks within 10 min, which is very difficult with conventional methods. However, the method could also be used in the case of less sensitive samples, but with more accumulations. It must be noted that Hadamard methods would also benefit from paramagnetic relaxation agents.

It must be emphasized that the D-HMQC method is a very robust experiment that works perfectly when the indirectly detected nuclei have a large abundance. When this is not the case, e.g. with 13 C or 15 N without labelling, the 2D spectra often suffer from significant t 1 -noise . This effect cannot be directly observed in the Hadamard 2D spectra, but it may affect the amplitude of the cross-peaks. In the case of two spin-1/2 nuclei, if the indirectly detected one is dilute, the conventional CP-CP method is as efficient as the conventional D-HMQC experiment, but with much less t 1 -noise. [START_REF] Ishii | Sensitivity enhancement in solid state 15 N NMR by indirect detection with highspeed magic angle spinning[END_REF] Therefore, it should be possible to use a Hadamard-encoded version of CP-CP, e.g. to indirectly detect 13 C or 15 N nuclei on small unlabeled molecules. Actually, HMQC is only one of the possible applications of Hadamard encoding-decoding, but it is an easy experiment to start with. We are presently looking into other possible applications and correlation sequences.

Fig. 1 .Fig. 6 . 7 .

 167 f-MLF: (a) molecule, and 15 N (b) and 13 C (c) MAS spectra observed at 14.1 T with R = 13 kHz. The labelling and assignment of 13 C and 15 N resonances have been given in ref[7]. In(c), the * indicate spinning Fig.2. 13 C-{ 15 N} D-HMQC pulse sequences: (a) conventional, (b) selective Hadamard-encoded, (c) and (d) the Hadamard matrices [H 4 ] and [H 8 ] as used in this work. Fig.3. 13 C-{ 15 N} D-HMQC 2D spectra: (a) conventional with T exp = 22 min, (b) H 4 -encoded with sel = 3 ms NS = 1 and T exp = 30 sec. Data matrix 1k x 128 (45.45 x 6.4 kHz; 22.5 x 10 ms) or (1k x 4) for (a) or (b), respectively. Fig.4. 15 N-{ 13 C} D-HMQC 2D spectra: (a) conventional with T exp = 44 min, (b) H 8 -encoding of 6 peaks (3 in CO and 3 in C regions) with sel = 4.5 ms, NS = 4 and T exp = 165 sec. Data matrix 1k x 128 (21.3 x 26.0 kHz; 48 x 2.5 ms) or (1k x 8) for (a) or (b), respectively. Fig.5. 15 N-{ 13 C} D-HMQC H 4 -encoding of the three C peaks with sel = 4.5 ms, NS = 4 and T exp = 82 sec.The other experimental details are the same as in Fig.4. Traces at 15N = 108 ppm (F N ) from 13 C-{ 15 N} D-HMQC-H 4 2D spectra versus sel . They show that the best compromise between selective excitation and losses is observed at sel 3 ms, but that a shorter selective excitation can also be used down to sel 1.5 ms if only the positive signal is used. Fig.Top: build-up curves of the 13 C-{ 15 N} cross-peaks versus rec expressed in unit of rotor periods T R = 77 s ( R = 13 kHz) with NS = 2. Bottom: array of traces taken at 15N = 108 ppm. The data points for (dots), (rombs), C (triangles), Leu C (squares) and Met C (crosses) are colour coded in the electronic version of the manuscript.

Acknowledgments.

Recherche, Région Hauts-de-France, and FEDER are acknowledged for supporting and funding partially this work. Authors are also grateful for funding supported by contract ANR-14-CE07-0009. --------------------------------------------------------------------------------------------------------------------------------------