Assistant Professor, Christel De Lassus
email: christel.delassus@univ-mlv.fr

Maria Mercanti-Guérin
email: maria.mercanti_guerin@cnam.fr

I buy your product when I feel I know you: using blog disclosure to influence consumers

Keywords: blog, private life, perceived disclosure of private life, confidence, routes to persuasion

Whilst confidence in certain companies has fallen as a result of the feeling amongst consumers that their private life has been violated, it would seem that at the same time, consumers are very eager to know more about the private life of the bloggers they follow. In return, bloggers are revealing more and more about themselves and displaying their private lives on their blogs. We show that the role of disclosure is a key determinant in consumer persuasion and that the exposure by bloggers of their private lives has a positive influence on their visitors. A quantitative study made of fashion and beauty blog enabled us to assess the impact of such disclosure on confidence in the blog, attitude towards the blog and the brand, and on the various routes to persuasion observed. The managerial implications of this research are presented in conclusion to help managers choose relevant blogs.

1

Introduction

The phenomenon of blogs, and in particular, those concerned with fashion and beauty, has developed dramatically and the power of these blogs has been taken on board by companies: recruitment of certain bloggers by publishing and press companies, the development of advertising, the recourse to sponsored articles and the sending of free products to influential bloggers, etc. As a result, blogs are now entering into serious competition for audiences, competition that is reinforced by the appearance of measurement and classification tools such as Ebuzzing. 1 In this ceaseless race for visibility, bloggers have turned the disclosure of their private lives into a deliberate strategy for attracting and winning the loyalty of readers. This research contributes to understanding how the capacity of blogs for commercial persuasion is fuelled, with the private life of the blogger serving as an element of personalization and confidence. In 2009, Shankar and Batra emphasized the growing influence of online communications and this is particularly true of blogs, which are increasingly influencing sales (Dhar and Chang, 2009). The private life variable is very influential where online media is concerned (Peltier, Milne and Phelps, 2009), hence the development by bloggers of strategies that attract and persuade their visitors by intentionally revealing elements of their private life.

Although the literature has dealt with the reasons why bloggers are led to reveal their private lives, very little research has been done to measure the impact of such disclosure on consumers. In the first section, we present the literature relating to private life and Internet. We have centered this presentation on the particular case of the voluntary disclosure of private life with the aim of persuasion. In the second section, we establish a model of the influence of disclosure of the blogger's private life on confidence and persuasion. This model, presented in the third section, was tested on a sample made up of 300 consumers. It culminates in an analysis of the routes to persuasion taken by the bloggers and of the influence of the disclosure of the writer's private life on attitudes towards the blog and intentions to buy the featured product. In conclusion, the managerial implications are commented on and analyzed.

Contextual and Theoretical Background

The disclosure of private life on Internet: from search for gratification to inclination to disclosure

Two strands of research deal with the implications of self-disclosure online. The first endeavors to define the potential threats to the personal safety of the Internet user as a result of revealing private information online [START_REF] Andrade | Self-Disclosure on the Web: The Impact of Privacy Policy, Reward, and Company Reputation[END_REF]; [START_REF] Phelps | Antecedents and consequences of consumer privacy concerns[END_REF]) and the influence of such threats on the behavior of the Internet user [START_REF] Dinev | Privacy concerns and levels of information exchange: An empirical investigation of intended e-services use[END_REF]Hart 2005, Lee and[START_REF] Muratore | Teenagers, blogs and socialization: a case study of young French bloggers[END_REF].

The second strand is centered on the use that brands can make of this type of information, that is to say, the personalization of messages [START_REF] Blattberg | Interactive Marketing: Exploiting the Age of Addressability[END_REF], the influence on survey methodologies [START_REF] Tourangeau | Sensitive questions in surveys[END_REF] and consumers' resistance to intrusive communications (White, 2004). These research strands draw on Uses and Gratification Theory (Katz, Blumer and Gurevitch, 1974) to explain the motivations that lead individuals to self-disclosure on Internet. The disclosure of private life represents a form of exchange between that which is received and that which is given. Nonetheless, this theory only explains a small part of the motivations for self-disclosure on the Net. A paradox exists based on the following observations: individuals agree to self-disclosure with no firm assurance of real gratification. Therefore, disclosures of private life are a situational variable that cannot be explained wholly by the desire to receive gratifications. Acquisti, John and Loewenstein (2012) show that receiving private information from one's Internet contacts increases one's personal inclination for disclosure. This reciprocal disclosure is related to social imitation [START_REF] Moon | Intimate Exchanges: Using Computers to Elicit Self-Disclosure from Consumers[END_REF], since individuals are influenced by the behaviors of the Internet user with whom they are in contact.

These observations do not call into question Uses and Gratifications Theory, but they extend the sphere of application of gratifications, which may be monetary but also social. Lastly, the idea of inclination to disclosure must be understood in the light of the various presences on Internet. Balague and de Valck (2013) studied the effect of questioning. Although the idea of reciprocal disclosure is very important on social networking sites such as Facebook, it is much less so on blogs, which are a social media within which the transmitter (blogger) is the main actor.

Motivations for revealing one's private life: the specific case of bloggers

Blogs are characterized by a considerable degree of disclosure of private life [START_REF] Viegas | Bloggers' expectations of privacy and accountability: An initial survey[END_REF]. [START_REF] Suler | The online disinhibition effect[END_REF] explains this by the relative anonymity and asynchronicity of the information given. A certain number of research papers have shown that the phenomenon of blogs and personal sites is developing all the more rapidly since such sites "represent a recreational space for post-modern personalities and allow individuals to create and develop their identities" [START_REF] Marcus | Personality in Cyberspace: Personal Web Sites as Media for Personality Expressions and Impressions[END_REF]). These characteristics are in line with research on private life and Internet. Bloggers are seeking to generate authenticity as well as placing themselves in a setting that will be attractive to their visitors [START_REF] Kretz | Pixelize Me! : A Semiotic Approach of Self-digitalization in Fashion Blogs[END_REF]. Amongst the individual variables, gender seems to be an essential element in explaining this.

Women are more inclined to online revelations. A study carried out on female British bloggers (Pederson and Macaffee, 2007) shows that they are more interested in the social aspect of blogging. Moreover, the content of blogs plays a vital aspect in disclosure. Blogs centered on the presentation of general, rather than personal content are far less likely to reveal the private life of their authors.

However, the latter only represent half of all bloggers, with the other half made up of bloggers who write for themselves as though in a private diary and without really taking their readers into account [START_REF] Lenhart | Bloggers: A portrait of the internet's new storytellers[END_REF].

Motivations for blogging and influence on the disclosure of private life:

The motivations for blogging have a relatively weak influence on the voluntary revelation of a blogger's private life. Hollenbaugh (2010) constructed a scale for measuring the motivations for blogging. This comprised seven factors (sharing feelings, desire to inform, desire for entertainment, desire to become well-known, desire to archive and organize information, desire to improve one's image, desire to obtain feedback on posts). The author studied the links between these constructs and disclosure of private life. It would seem that only the motivation relating to the wish to archive and organize information exercises a significant influence on selfdisclosure. On the other hand, gender and propensity to reveal one's private life (which is a permanent psychological variable) have a strong influence on disclosure of private life. These results lead to a certain number of observations. Bloggers do not reveal their private life for commercial ends. "Professionalism" (importance for career or image) or "Feedback" (obtaining feedback and comments on the posts)

does not seem to be antecedents of disclosure. It is individual characteristics (being a woman and the degree of propensity to reveal details of private life) that would seem to explain disclosure. Nonetheless, these results need qualification. The bloggers questioned kept blogs that we would qualify as personal online diaries rather than content-driven blogs. Self-disclosure in a more commercial context remains to be studied.

Type of blog and measurement of perceived disclosure; two research fields yet to be explored

Taking account of the type of blog would seem to be essential to an understanding of the links that exist between self-disclosure and the motivations for blogging. [START_REF] Lenhart | Bloggers: A portrait of the internet's new storytellers[END_REF] showed that the type of audience and the target are antecedents of disclosure. Lastly, the degree of private life disclosure merits clarification. The degree of private life disclosure should be differentiated from the propensity to make private life disclosures. The latter may be defined as a tendency to reveal elements of private life whatever the context. [START_REF] Wheeless | A follow-up study of the relationships among trust, disclosure and interpersonal solidarity[END_REF] drew up a measuring scale comprising seven items (" I tend to talk about myself relatively often", "I like talking about myself" etc.) that was taken and adapted to the online context (Stefanove and Jang, 2007). As for the degree of disclosure of private life, this is based on a two-dimensional scale (quantity of information disclosed and depth of intimacy of the information disclosed) that has been tested in numerous research projects including [START_REF] Hollenbaugh | Personal journal bloggers: Profiles of disclosiveness[END_REF]. To our knowledge, however, no scale exists for measuring readers' perceptions of the blogger's disclosure of her private life.

With respect to the literature, a certain number of questions therefore continue to arise. How is the disclosure of private life by bloggers perceived by their readers?

How can this perception be measured? Does the perceived disclosure of the blogger's private life have an influence on the process of consumer persuasion in relation to blogs concerned with consumer topics such as fashion and beauty?

Presentation and bjectives of the study

The objectives of the quantitative study were to examine the possible link between a blogger's disclosure of her private life and persuasion, and to assess the effectiveness of such disclosure on attitudes to the blog, the brand featured in the blog, and purchasing intentions.

Perceived disclosure of private life

The disclosure of private life was studied from the point of view of perception and from the point of view of the measurement and detection of self-disclosure signals [START_REF] Brodin | Le développement d'un index d'exposition de soi dans les médias sociaux : phase exploratoire d'identification des indicateurs constitutifs[END_REF]. With regard to the detection of self-disclosure signals,

what the authors term "extimity" was assessed in relation to social media networks.

It was therefore possible to clarify the various indicators of the disclosure on Internet of private life: the formalization of status, public presence (open networks), free expression of the social role, quantitative production of signs linked to the self, etc. Another thread in the literature is concerned with measuring self-disclosure by approaching it as a perceptual construct. For these authors, it is more important to assess the force of the impression that others receive of an individual's selfdisclosure. [START_REF] Leung | Loneliness, Self-Disclosure, and ICQ ("I Seek You") Use[END_REF] defines the concept of self-disclosure as the way individuals reveal themselves to others, which includes their experiences and feelings. Self-disclosure is therefore measured in relation to others. It corresponds to all messages about oneself that a person communicates to others and to the perception of the degree of intimacy that the latter have of this. It is a multidimensional concept based on the following aspects: depth of revelation, honesty, and intentionality.

The various routes to persuasion that the readership of a blog can follow

In order to anchor our study in the literature dealing with advertising persuasion, we formulated our research proposals and hypotheses on the basis of MacKenzie, Lutz and Belch's persuasion model (1986). They identified four routes to persuasion, which are described in the following Table.

Hypothesis of affective transfer

The consumer transfers the feelings he experienced during his exposure to the message onto the brand. This route may be assimilated into the peripheral persuasion route of Petty and Cacioppo's Elaboration Likelihood Model (1981Model ( , 1986)).

Hypothesis of dual mediation

The consumer is influenced both by the beliefs he holds with regard to the advertisement and his beliefs with regard to the brand. Moreover, an interaction exists between attitudes and beliefs. The central and peripheral routes are interdependent rather than mutually exclusive.

Hypothesis of reciprocal mediation

The consumer seeks to maintain a balance between his attitude towards the advertisement and his attitude towards the brand by liking both the advertisement and the brand or by rejecting both of them.

Hypothesis of independent influence

No relationship is observed between the attitude to the advertisement and the attitude towards the brand.

Source: adapted from MacKenzie, Lutz and Belch ( 1986)

Presentation of the model and methodology

Our quantitative study is based on two levels of analysis. The first is centered on the link that may exist between the perceived disclosure of private life and the confidence generated by the blog. The second lies in the description of the routes to persuasion followed by the reader depending on the type of blog (impersonal blog with no disclosure of the blogger's private life or blog in which the blogger reveals details of her private life).

Analysis 1: This level of analysis (Figure 1) requires the construction of a scale to measure the perceived disclosure of the blogger's private life, the use of the measure of confidence scale [START_REF] Gurviez | Proposition d'une échelle de mesure multidimensionnelle de la confiance dans la marque[END_REF], the cleaning of items, and a study of the links between constructs using SPSS and Amos 16 software.

Analysis 2:

The second level of analysis is presented in Figure 2. This consisted in checking whether the type of blog (impersonal or disclosing the private life of the blogger) moderates the routes to persuasion followed by the reader. The analyses were based on pre-tests of all the scales of variables that constituted the model and a multi-group analysis using Amos 16 in order to check the moderating nature of the type of blog. Stage 2: a questionnaire that took all the items adopted was presented to two paired samples. The first sample read a blog in which the blogger revealed her private life. The second sample was shown a completely impersonal blog (with no information about the blogger).

Structure of the sample: the sample of interviewees was made up of 305 people (students on initial or further training courses). The average age was 22.9 years and the median age was 23. Women represent 61% of the sample. 53% of the sample, that is to say 162 people, were shown the blog disclosing details of the private life of the blogger.

Test material: the two blogs selected were fashion and beauty blogs. An identical brand of make-up featured in both blogs. The selection of these two blogs was made from a pre-selection of blogs listed in E-Buzzing in the Beauty category. A private life disclosure grid was drawn up using items identified in the qualitative study. Each item on each pre-selected blog was given a mark from 1 to 5 ("highly visible" item versus "not very" visible item) by a convenience sample made up of twenty people. The blog with the highest average mark for the items overall (blog disclosing private life) and the blog with the lowest average mark (impersonal blog)

were retained.

The blog containing disclosures of private life had the following characteristics:

scene-setting (blogger shown with products), confidences on her private life

The impersonal blog presents the following characteristics: minimalist introduction of blogger, very few confidences on her life apart from those corresponding to purchasing occasions.

Structure of the questionnaire: the structure of the questionnaire lists all the variables for the model: opinion on the brand and the blog, affective reactions triggered by the blog, questions linked to the measure of confidence generated by the blog, beliefs regarding the message delivered by the blog and its execution, items linked to perceived disclosure of the blogger's private life, purchasing intention, beliefs regarding the brand.

Results

Perceived disclosure of private life, antecedent of the confidence regarding the blog: a partial influence

The first part of our results consisted in estimating the antecedent nature of the perceived disclosure of private life on confidence in the blog (Figure 1). To do this, we:

1. Checked the validity and reliability of our measuring instruments, that is, the scale of perceived disclosure of the blogger's private life and the confidence scale.

2. Checked to see if a significant link existed between the perceived disclosure of the blogger's private life and the confidence generated by the blog.

The following Table summarizes the results of Leung's scale for measuring perception of disclosure of the blogger's life (2002) used in this research.

2 After cleaning (submitted to a sample of 290 individuals), it appears that perceived disclosure of private life is composed of two dimensions, one dimension founded on the impression of the blogger's honesty, sincerity and accessibility and the other centered on the blogger's intentions, that is to show herself to advantage and attract people to her blog. We called the first dimension the "honesty" dimension and the second, the "intentionality" dimension. Component 2: 37.8%

The confidence measurement scale we adopted (Bartokowski, Chandon and Müller, 2002) revealed three dimensions (credibility, integrity and benevolence). A complete review of the literature on confidence scales and research centered on confidence in online sites shows that two opposing opinions exist. The first considers that confidence should be taken globally [START_REF] Geykens | Generalizations about Trust in Marketing Channel Relationships using Meta-Analysis[END_REF]. The second insists on the multi-dimensional aspect of confidence as a personality, belief, state, personality trait, etc. Lastly, the object of confidence can be an institution or person representing the brand (interpersonal confidence). In the case of blogs, it would appear that there exists certain confusion between the institution and the person. The blogger does not represent the brand, but embodies the institution that is communicating. He or she is both an interpersonal and institutional source of confidence. Therefore the credibility of the blogger, her honesty towards her readers, and her desire to improve her recommendations are part of the same construct, that of a global perception of confidence. According to our results, it would seem that "honesty" is the sole antecedent of confidence in the blog. Moreover, the items linked to the credibility of the blog are particularly influenced by this dimension. Sig .000

To conclude, we would repeat that we detected two constitutive dimensions of the perceived disclosure of private life. The "honesty" dimension corresponds to the positive vision of the disclosure of private life, that is to say, transparency, accessibility, and a close relationship with the readership. The "intentionality" dimension corresponds to the objectives of this disclosure as felt by the blog readers. Disclosures of private life would not appear to be gratuitous but made with two precise aims: to appear to advantage and to attract readers by revealing elements of private life. Readers, therefore, are attracted but at the same time irritated by this method of capturing the attention of a readership; attracted because the exposure of these elements creates empathy with the blogger (honesty dimension) and irritated because they are aware that even if the private life that is revealed is a "real" life, the reasons it is revealed are not gratuitous (intentionality dimension) and correspond to a wish to appear to advantage or even to a degree of exhibitionism, a retention and audience-winning strategy.

So the question of the influence of the disclosure of private life on confidence then arises. Our results show that only the "honesty" dimension has a significant influence on confidence. Moreover, confidence in a blog seems one-dimensional.

For example, the authentic nature of private life disclosures can generate confidence and credibility. Bloggers that reveal their private life have a more effective power of recommendation than bloggers who reveal no personal facts at all. Nonetheless, the revelation must be made with spontaneity and no apparent signs of any commercial objective. It must, however, be noted that the taking into account of the intentional nature of private life disclosure by the consumer does not generate distrust of the blog (the intentionality-confidence relationship is not significant but not negative).

What routes to persuasion are followed in the case of private life disclosure by the blogger?

In order to determine the different routes to persuasion followed in the case of reading a blog in which considerable revelations of private life are made, we 1. Cleaned the different scales of the variables we adopted 2. Carried out a multi-group analysis (blog exposing the private life of the blogger versus impersonal blog) in order to confirm the moderating nature of the disclosure of the blogger's private life on the persuasion of her readers. .

805

.62

Theoretical Implications

The routes to persuasion followed by readers exposed to a blog revealing the blogger's private life highlights the importance of beliefs relating to the message and positive affective reactions. In this case, persuasion is both cognitive and affective. Moreover, negative affective reactions have a significant negative influence on beliefs surrounding the brand, which would tend to show that the reader has an ambivalent attitude towards private life disclosures. It is an important factor of persuasion since it improves attitudes towards the blog. Nonetheless, this persuasion is peripheral since at the same time negative affective reactions damage beliefs surrounding the brand. It would seem that the blog benefits from private life disclosure but that this disclosure is made to the detriment of the brand it is intended to promote.

The routes to persuasion followed by the reader exposed to an impersonal blog display two strong significant links: the link between attitude towards the blog and attitude towards the brand and the link between positive affective reactions and attitude towards the blog. Whilst in the case of private life disclosure, persuasion is dual (both cognitive and affective), in the case of an impersonal blog, persuasion would seem to be purely peripheral. Moreover, it is worth noting that where beliefs are concerned, only beliefs regarding execution of the blog have an influence on attitude towards the brand. This would tend to show that:

 Blogs are a specific media in which the elements of execution (form of the blog, ergonomy of the blog, good presentation of images and videos)

occupy an important place. In the case of impersonal blogs, with a reading contract only tenuously based on content (form is more important than the message), the reader gains little vital information on the brand. Moreover, affective reactions occupy little space in persuasion. So an impersonal blog will not trigger a great deal of attachment and affect.

 On the other hand, disclosure of the blogger's private life enhances the message to the detriment of the form. The latter becomes an important element of persuasion since it generates confidence and makes visitors want to read what it says about the product.

The visualisation of the different routes to persuasion is detailed in the following Tables: It should be noted that overall differences in means is significant. Nonetheless, it would seem that the biggest mean deviation concerns purchasing intention. The fact that the blogger personalizes her experiences with the product by inserting them into her life may be the source of a stronger wish to buy the product. At the same time, the attitude towards the blog is most favorable when the blogger's private life is revealed. This confirms our previous results on the routes to persuasion. In the case of an impersonal blog, the attitude towards the blog is less positive than the attitude towards the brand (deficit of attachment and affective reactions towards a media perceived as cold).

Managerial Implications

Unlike other fields, where Internet would seem to threaten the private life of Internet user, personal revelations are an important element of persuasion. The results underline the importance of specific elements that construct legitimacy and credibility, based on private life. Therefore, the perceived exposure of private life is a variable that generates confidence in the blog and is a moderator of the different routes to persuasion. Blog visitors are appreciative of this type of self-disclosure by the blogger and will assimilate the message concerning the brand at both cognitive and affective level. Lastly, this type of blog encourages more favorable attitudes towards the brand and the blog and increases intentions to purchase the product.

Disclosure may constitute a real commercial strategy for the blogger. Nonetheless, a certain number of precautions are essential. The honesty of the disclosure is central in this strategy. This dimension should not be clouded by overly visible commercial intentions. In that case, the perceived intentionality will affect the special relationship a blogger can have with her audience. This research therefore gives us a better understanding of the stake blogs now represent and over and above this, new forms of brand presence. This may lead to greater effectiveness in

Conclusions

The above research gives us a better understanding of the reactions of blog visitors to disclosure and of the relationships between visitors and bloggers. At managerial level, these results offer media-planning keys to the rapidly developing, complex and multi-form world that is the blogosphere. In practical terms, it enables the selection of supports and type of brand presence to be used.

The limits of our research work lie in the audience of young adults chosen. Indeed, the literature on self-disclosure shows that young people are less embarrassed than older populations by intimate revelations. These young adults are, however, the main audience for blogs. Another limit is linked to the fact that we have chosen to examine women bloggers. It would be interesting to carry out the same type of research with reference to male bloggers. This is an avenue to be explored in the future. The disclosure of a man's private life is a hitherto unexploited field of research.

Figure 1 First

 1 Figure 1First level of analysis, the perceived disclosure of private life as an antecedent of the confidence generated by the blog

Table 1 Description of MacKenzie Lutz and Belch's four potential persuasion mechanisms (1986)

 1

Table 3 -

 3 Scale for Measuring perceived disclosure of the blogger's private life

	Main indicators of		Items		Representat	Matrix of	Matrix of	Standard	T
	the adequacy of		retained		iveness	the	the	ized co-
	the measurement		after	first		compone	compone	efficient
	model		cleaning			nts 1	nts 2
	Chi-two	39.29 She seems	.859	.924		0.92	2
			sincere when
			talking about
			herself
	ddl	7	She seems	.854	.925		0.91	1
		(.000)	sincere when
			revealing her
			feelings
	GFI	970	She seems	.803	.888		0.806	1
			close	and
			accessible
	AGFI	0.845 She is not	.818	.904		0.892	1
			being
			hypocritical
			when	she
			reveals her
			feelings and
			emotions
	NFI	983	She makes	.793	.876		0.78	1
			you want to
			be her friend
	RMR	0.066 She presents	.822		.901	0.522	8
			herself	to
			advantage
	Cronbach's Alpha	.903	In her blog,	.864		.929	0.659	1
			she only talks
	3 Associated Student Test T

Table 4 -

 4 Confidence measurement scale after cleaning

	Items on the confidence measurement	Representativeness
	scale relating to a blog
	The advice given in this blog is good 0.880

Table 5 -

 5 Influence of the perceived disclosure of the blogger's life on confidence in

	the blog
	Perceived disclosure of the blogger's	Associated Student T -links between
	private life	private life and confidence
	"Honesty" dimension	18.8
	"Intentionality" dimension	NS
	Lastly, the mean tests effected on the level of confidence generated by an
	impersonal blog versus a blog that reveals the blogger's private life show a
	significant mean difference between the two types of blog. The same is true if we
	take the level of credibility generated by the two types of blog.

Table 6 -

 6 Mean difference, confidence and credibility generated by impersonal blogs versus blogs that disclose the blogger's private life

	Confidence mean Impersonal blog	Blog disclosing	Significance test
			private life
		1.94	3.64	F 45.931
				Sig .000
	Credibility mean	Impersonal blog	Blog disclosing	Significance test
			private life
		1.65	3.35	F 53.956

Table 7 -Summary of the measurement scales used in this research Variable Adaptation of the scale used Items after cleaning Matrix of the components Community Variance percentage explained

 7

	
	Cronbac
	Jöresko
	
	
	Fornell
	and
	Larcker'

Table 8 -

 8 Significant links between variables in the case of a blog that reveals

	private life
	Main significant links between variables	Standardised coefficients (Student T)
	Beliefs surrounding message -beliefs	1.146 (23.297)
	surrounding execution
	Beliefs surrounding message -positive	0.823 (9.351)
	affective reactions
	Links	between	positive	affective	0.689 (11.482)
	reactions-attitude towards the blog
	Links between attitude towards the blog-	0.540 (6.803)
	attitude towards the brand
	Links	between	positive	affective	0.442 (7.546)
	reactions-beliefs surrounding the brand
	Links between negative affective -0.265 (-4.815)

Table 9 -

 9 Significant links between variables in the case of an impersonal blog

	Main significant links between variables	Standardised coefficients (Student T)
	Links between attitude towards the blog-	0.555 (6.984)
	attitude towards the brand
	Links between beliefs surrounding	0.948 (16.324)
	execution of blog -att
	The following Table confirms the moderating nature of the type of blog on the routes
	to persuasion.

Table 10 -

 10 Moderating effect of the type of blog on the process of persuasion

	Adjustment indicators	Model resulting from the	Restricted model	Key values
		multi-groups analysis
	Chi-two	148.135	385.6
	ddl	18	30
	Chi-Two difference	237 difference for 12		Difference
		degrees of freedom > 46.08		greater than 3.84
		for an associated probability		for one degree o
		of 0.05		freedom
	To conclude, we wished to evaluate the effectiveness of a message based on
	private life disclosure by comparing the different means of the following variables:
	attitude towards the blog, attitude towards the brand, purchasing intentions.

Table 11 -

 11 Analysis of means, blog exposing private life versus impersonal blog

		Mean:	Blog	Mean:	F	Sig
		disclosing		Impersonal blog
		private life
	Attitude	3.648		3.02	38.377	.000
	towards	the
	brand

Ebuzzing is a monitoring and audience measurement platform for blogs but also an advertising agency specialising in social media.

Leung's original self-disclosure scale (2002) had five dimensions: depth, accuracy, intention, frequency, valency.

Seeding consists of sending a new product to influential bloggers and waiting for the media results. The abuses this has led to (systematically positive remarks in exchange for money) have led to specific legislation being drafted in the United States.


Nomos alpha. Remarks on performance

Introduction: chtonic vs cosmic performance

Nomos alpha (1965-66) is one of Xenakis's most 'formalised' pieces. Dating from the time of his research on 'outside-time' structures, the piece is calculated down to the last detail, as we can see in the composer's own analysis in his article 'Towards a philosophy of music', of which there are several versions 1 . This is no doubt why his compositional processes have been the subject of several different analyses by musicologists, some of which are very thorough. 2 For the critic Antoine Goléa, Nomos alpha was 'the ugliest thing he had ever heard ' (in: Xenakis 1988, 136).

What a distance we've come since its premiere by Siegfried Palm in Bremen in May 1966! Today, it is greeted with loud applause each time it is performed. However, the piece remains 'difficult' for the listener: it is submerged in the torrent of 144 micro-events, an extreme fragmentation accentuated by the presence of many silences and tempered only by a few fuller gestures. Its immediate success is no doubt due to its particularly virtuoso instrumental writing, which means that each performance establishes a particular relationship between the musician on stage and his/her audience. A 'unique and integral work in the cello repertoire' (Meunier 1981, 254-255), Nomos alpha was (after Herma) the second manifestation of virtuosity Xenakis would put before players. As a result they shied from it 'for many years until a younger generation of cellists took up the challenge' (Matossian 1981, 226). If it has not yet been fully incorporated into the contemporary cello repertoire, this is because it remains particularly difficult to playbut more and more musicians are now taking it on. This article will focus on the performance of the piece, a subject, which has still been little investigated (see Meunier 1981, Monighetti 1981, Peck 2003, Uitti 2010, Nakipbekova forthcoming). We can divide the musicians having taken up the challenge into three generations.

The first includes Palm, who recorded it in 1974 (Palm 1975) and Pierre Penassou who was the first to perform Nomos alpha in France and had already recorded it in 1968 (Penassou 1968). We could also place Rohan de Saram in the same generation, with a certain lag (see his recording: Saram 1992). Saram, had the opportunity of playing the piece several times in front of Xenakiswho, as we know, gave very limited instructions to players. In the second generation, we might place Pierre Strauch (1992), the cellist of the Ensemble InterContemporain, French cellist Christophe Roy and the Belgian Arne Deforce. Finally, there's no shortage of names when it comes to the third generation: Martina Schucan, Moritz Müllenbach (a Roy's pupil) and Alfia Nakipbekova to name but three.

Here, I would like to compare the recorded versions made by Christophe Roy and Arne Deforce, sometimes making reference to a few other recordings, in order to illustrate certain points.

Interviews carried out with our two main musicians will sometimes be quoted from. Born in 1960, Christophe Roy, a contemporary music specialist and co-founder of the Aleph ensemble and the Nomos ensemble, worked at length on the piece before performing it in a concert setting note that beforehand he played Charisma, an equally difficult but less virtuoso piece for cello and clarinet 3 . During his first meeting with Xenakis he asked him few questions, 4 but found beneficial Xenakis's remarks on the 'poetry of harmonics', in which he requested that the grain, the substance of the sound be made audible rather than the sinusoidal sound. He recorded it in 1998. Born in 1962, Arne Deforce did not meet Xenakis. In his interview, he insists that he produced an intuitive version of the piece, without, for example, using a metronome. 5 He adds that he 'sings' it from beginning to end (as with other pieces he plays) and he compares it to the research on multiple vocal and theatrical articulations in Berio's Sequenza III. 6 Coming in 2011, it was part of a complete collected recording of Xenakis's cello pieces (Deforce 2011).

3 "From Xenakis, I started by working on Charisma, with Dominique Clément, a piece that allowed me to enter Xenakis' universe head on. We sweated on this work, which lasts 4 minutes and in which there are only twenty sounds to play, for a whole year before getting what we wanted! This was in 1975, shortly after the composition of the piece, at a time when we were very young, still students... Throughout this time, for several years, I kept Nomos Alpha on a stand -I was doing a lot other stuff in parallel." (Christophe Roy). 4 "I was twenty-five years old at the time and I was very intimidated. I had not had a real discussion with Xenakis as perhaps Siegfried Palm or others had had before." (Christophe Roy). 5 "When I did this version, I did it purely artistically, even intuitively, obviously respecting the score; for example, I never worked with metronomes when I recorded -at first I did, of course, yes." (Arne Deforce). 6 "I have a fairly "vocal" approach to contemporary cello. In Nomos Alpha, for example, I can sing the piece from beginning to end. I do this for many pieces I play. It's a way of giving body to the music for me, even the most abstract or noisy sequences. It's a way of playing this music more in an organic rather than an analytical way. So ... As we will see later, Deleuze emphasises the cosmic character of modernity, which is something that could be attributed to Deforce's recording. We could say that Christophe Roy's version, however, comes from the bottom of the earth, that it is somehow Chthonian.

[he hums the beginning of the piece], it's almost like Sequenza III by Berio. I try to internalise everything corporally and vocally. I see Nomos alpha as an abstract song contained within the cello's multiple voices." (Arne Deforce).

Tempos, difficulties, getting inside the sound, final section

Tempos, difficulties, getting inside the sound

To start with, an easy comparison: the overall length of each recording. Here, Roy and Deforce have something in common: they give us long versions, 18'50" and 19'05" respectively. The Palm version only lasts 14'39" and Saram's is only 15'20". On initial analysis, our firstgeneration players are right to produce short versions7 . On the score, Xenakis specifies the piece as lasting about 15'. As the tempo (and therefore the overall duration of the piece) is one of the formalised parameters of Nomos alpha (it has three values, whose alternations follow the rotations of a group consisting of a triangle), it ought to be followed. But the task is impossible, for the two reasons that will be set out below. Xenakis himself was probably fully aware of this impossibility. Indeed, when we calculate how long the piece should last, we end up with 10'26"!8

One might suppose that he specifies 15' to account for the time taken with the scordatura that takes place during the piece (in four passages, including the final passage, the bass string must be tuned very low, which means therefore that it needs to be re-tuned three times). However, far less time is needed for the scordatura than the additional 4'34". Unless one assumes a miscalculation, then, it might be hypothesised that the inclusion of this additional period of time was Xenakis's way of taking the utopian nature of his requirements into account.

Utopian nature: the first reason why the second generation of performers takes longer to play Nomos alpha is obvious. They try to play everything or at least play as much as possible, the piece being of an extreme virtuosity. As Deforce explains, in the Palm and Saram versions, many details are lost and, as a result, tension is also lowered. 9 Roy emphasises the fact that Xenakis considers the cello as a set of possibilities that tend towards the infinite (which is also where the idea of the low scordatura comes in). 10 He adds that everything is playable, that is to say, in the temporality of the written score that we can only move towards by playing the piece more slowly.

A typical example is the pizzicato from the very beginning (see Example 1). The string is supposed to be plucked 20 times within 2". Saram plays slightly faster, but he only plucks 10 times. Roy does pluck 20 times, but to do this, he is forced to take 3.5". Note that Deforce makes this passage last as long as Roy, but plucks twice as many times. This is because, having been a guitarist, he kept a long fingernail on his thumb, which he uses as a plectrum. The second reason for the slower tempo adopted by Roy and Deforce stems from an apparent paradox: the piece is made up of micro-events (except for the slower 'path 2' sequences), but it 9 "In Siegfried Palm's version, and also in Rohan de Saram'sthese are the first versionssometimes I tend to lose some tension [because of the rapid tempo that stops you from playing everything]. In Nomos alpha, I take certain liberties regarding the formalised aspects of the composition and I approach the question of tempo as a way of taking time to get inside the sound, to bring out the sound event, so that we can capture the energetic sensations of sound: to 'make audible' as Deleuze said." (Arne Deforce). 10 "You see immediately that Xenakis has a vision of the cello as a set of gigantic notes, in a space that tends towards infinity." (Christophe Roy). [START_REF] Roy | Translation from the French: Jack Sims Bibliography Interviews with Christophe Roy and Arne Deforce carried out in September[END_REF] "At the time when I played the guitar, I had the classical guitarist's nail, which I kept, and which works a little like a plectrum. This gives a tremolo-pizzicato that I love. It's a technique I've developed, and that I've used with other composers such as Richard Barrett, Raphael Cendo and Hèctor Parra." (Arne Deforce).

must nevertheless be possible to get inside the sound. Our two musicians agree on this point. 12 Getting inside the sound: although, on paper, a piece composed of notes and parametric in its conception, Nomos alpha is, like any other work by Xenakis, a music-of-sounda piece of composed sound, to be precise (see Solomos 2013, 352-361). However, whether composed (Xenakis) or exposed (Cage or Scelsi), sound needs time, both physically and mentally, and as much for the listener as for the performer. In Nomos alpha, beats, which are a literal way of 'entering the sound', are characteristic of this. The 'beats', Xenakis instructs the musician, are achieved by: 'slightly raising or lowering (respectively) the note thus marked so that it 'beats' against the second note, at a rhythm indicated by the figure, which expresses beats per second' (Xenakis 1967b). For Example 2, Saram manages to play much of what is written, but as he plays in the tempo of the score and even a little faster (3" instead of 3.5"), the ear struggles to follow. To conclude on tempo and the overall lengths of recordings, we note a difference between our two musicians. Roy tends to respect the proportions; he slows down in a uniform way. Deforce however slows down certain events so as to enlarge the spectrum and to make audible certain energetic dimensions of the piece. 13 12 "I have to divide up the tempo proposed by Xenakis in a major way, which makes it possible to get into the sound in a more in-depth way -I think it's Flaubert who said: if we want to find something beautiful, we need to look at it for a long time! [laughs]" Christophe Roy."In some places, I would like to take some time to bring in effects that are written and prescribed in the score. For example, the beat effect. If you do it in the given tempo, sometimes you can't bring in these beats, or give them to the ear either." (Arne Deforce). 13 "A very special case in the piece, where I take a lot of time, comes in the three sections where sensational sounds are created with the bass string in scordatura." (Arne Deforce).

The final section

Special mention needs to be made of the last section of the piece. The final sequence of Nomos alpha, bars 365-386 (Example 3), conclude both path 2 and the entire work. As a result, they are treated as a composition in the composition, in the manner of the final 'tourniquet' (Batigne 1981, 181) in Persephassa. Thus they are not governed by any possible systematisation of path 2 and constitute a supreme gesture of compositional freedom. This is perhaps why such extreme virtuosity is solicited. In this passage, there's a scale of 96 pitches spread over 8.5 octaves, consisting of three movements: a whole tone scale ascending or descending; a three-quarter tone scale ascending or descending; a one and one quarter tone scale ascending only. The development is very complex result, as shown in the graph for Example 4. Moreover, another complex development is superimposed over this one of pitches; that of intensities (Example 5). It is absolutely impossible to play what is written. Some performers use a second cellist, hidden behind the scenes. Others pre-record a part, either at the performance or during the recording: this is so for Deforce. 14 To my knowledge, Roy is one of the few to play it as it is, using a very particular harmonic 14 "How to play the final section depends on the type of concert (with or without electronics). I can play with a prerecorded tape, in mono and with a speaker half-hidden behind my chair, creating a deus ex machina effect, bearing in mind that the passage ends very quickly before the audience realises what is really happening. There is a certain Greek theatre heroism, if you will, in hearing and seeing someone play the impossible. Several times after a concert people have come up to me to ask how I was able to play these two lines at the same time. Where the pre-recorded option isn't available, I try to survive by exhausting the possible in what is written. It's horrendous, but wonderful at the same time." (Arne Deforce).

technique. 15 The result is striking: besides the significant slowing down and the transformation of the timbre, this technique produces a rather peculiar fragility, which contrasts with the energetic power of the other parts of the piece. Let us now turn to some specifically Xenakian aspects, including the question of sound, which has just been mentioned. For Roy, sound and sonority are fundamental elements when he plays Xenakis. 16 His way of playing accentuates the ruggedness that characterises the Xenakis sound, a perfectly controlled ruggedness, in which each detail finds its place. This aspect is, of course, related to the other very Xenakian characteristic that Roy accentuates with particular enthusiasm: energy. Finally, energy is related to the third very Xenakian element: the gestureenergy is linked to the body in its totality, it is gestural. It is as if everything came from 'down below', from the ground -hence the term 'chthonian'giving the sound the power of a tree with deep roots. In the last section, however, Roy brings out the fragility we have mentioned, as if all the energy accumulated had evaporated into thin air. For Deforce, sound is also a decisive 16 "When I first heard Pierre Penassou playing Nomos alpha in Royan -I was very young, I had not started the cello yetwhat struck me very intensely was the sound, which was something I had never heard before or even experienced. I say 'experienced' because I was 1.5 meters away from him, just under a platform. [...] For me, the most important thing in Xenakis is the energetic power, the spell of the sound." (Christophe Roy).

element, but apprehended differently. Even if stemming from gesture, it somehow presents itself as autonomous. This undoubtedly comes about because the energy applied is 'cosmic', as analysed by Deleuze: in the modern age, the forces "to be captured are no longer those of the earth, which still constitute a great expressive Form, but the forces of an immaterial, nonformal, and energetic Cosmos. […] This is the postromantic turning point: the essential thing is no longer forms and matters, or themes, but forces, densities, intensities." (Deleuze and Guattari 1987, 341-342).

This may be why the result is less harsh than in Royyou might even say there are 'beautiful' sounds in Deforce's interpretation. However, this is not to say that the energy invested by the Belgian musician is abstract. It is just as physical. 17 To search, to elaborate, to sculpt the sound till the point that its energy becomes an authentic sensorial experience, such is the goal.

This difference between our two musicians is accentuated in the recording. Deforce gives us a very elaborate result: almost an electroacoustic work. This reinforces the autonomous nature of the sound, as if it had no cause. Hence, perhaps, the tendency towards a 'beautiful' sound. 18 The Belgian cellist indicates that he carried out extensive editing, sometimes going as far as to edit isolated notes. For him, the result given by the recording is an end in itself, an autonomous work of art, that one apprehends for itself, independently of live performance. 19 It is not insignificant that he appreciates the electroacoustic music of Xenakis and he believes that players of Xenakis's work should be inspired by it. 20 In Roy, the recording is less sophisticated. It is conceived as an image of the performance. The cellist explains that Joël Perrot, the sound engineer, was interested in the living energy and the continuity, wanting to capture the singular character of the moment 17 "For me, the energy comes very naturally. It's very corporal. I tend to play contemporary music in a very physical way. This energetic aspect is a kind of commitment where everything comes together in a 'sound-becoming': the mind, the body, the gesture, the mental or the emotional, the psychic and the physical." (Arne Deforce).

"Another dimension of the 'beautiful' that helped me greatly in approaching the problem of the virtuosity of Nomos alpha comes from meditations on the concept of athletics of the ancient Greeks (I'm thinking, for example, of the famous bronze statues like the Poseidon of the Temple of Artemis at Ephesus). This led me to develop a very refined and elaborate muscular technique, accentuating victory over matter that gives glory to the corporal and beauty to the cello sound body." (Arne Deforce).

19 "The recording took me three hours. We did five versions of the piece, in large parts: the first three pages, then two more pages, and so on. Afterwards, we worked and edited, sometimes even taking better notes from a different version. For me, you don't record a CD in the image of a concert. Rather it's about offering something distinct. As Glenn Gould said, a recording is a work of art in itself." (Arne Deforce). 20 "I love Xenakis's electronic music. If I gave a class to a cellist who wanted to play Nomos alpha, I would tell him that you not only have to listen to the orchestral works, but also the electronic works. It's a matter of immersing yourself in electronics and then returning to the cello. The speed with which we play a pizzicato or a Bartók pizzicato can contain something reminiscent of electronic music: a kind of nervousness, as if the fingers and the bow had been electrified while playing this piece." (Arne Deforce).

of performance. However there has been some editing on the long passagesand, of course, the moments of scordatura are cut.

Some other aspects

Pitch

The question of pitch is always delicate in this builder of sound that is Xenakis. At the time of the composition of Nomos alpha, he attached great importance to it. As has been mentioned, this was the time of his research on 'outside-time' structures, in which pitch constitutes the best model.

After setting out the structures of pitch in Greek antiquity and Byzantine music at length, his article 'Towards a Metamusic' (Xenakis 1967b) introduces the theory of pitch 'sieves' -which is to say, scales. And we know that he spent a lot of time on sieve-construction for Nomos alpha.

Pitch, then, is a crucial element in Nomos alpha.

Nevertheless, we are tempted to relativise this aspect. First of all, it is now understood that Xenakis is a musician of sound. This does not mean he was a musician of 'timbre' (in the manner of a certain French tradition), but a composer who put all the 'parameters' of sound at the service of an overall conception of music, synonymous, in this sense, with 'sound': timbre of course, but also space, rhythm and, just as importantly, pitchthese elements can be thought of as serving sound. And it is obvious that the parameter of 'sound complexes' is more important than the pitch sieves in Nomos alpha. Next, those who have analysed them know that there are many 'gaps' between the theoretical sieves (those built by Xenakis) and the practical ones (the notes found in the score), differences that come from calculation errors or theoretical errors (see Solomos 1997).

For those who the word 'error' frightens, it should be remembered that at the time Xenakis calculated his sieves using constructions on graph paper, which easily generates errors, whether at the time of the construction of the sieve or, more often, during transcription onto staffs, without even going into the errors resulting from the concrete choice of a pitch during the composition of a precise passage using the sieve in question. Moreover, because of the multiplication of parameters calculated separately in Nomos alpha, contradictions can often be found. For example, there is also a parameter 'register' specifying that, in such and such a passage, only a particular register should be used. However, it may happen that the sieve used has no pitches in this register. Finally, it may be useful to remember that the Nomos alpha sieves are often very complex (their mode of repetition is not the octave) and too little repeated for the listener to memorise them. In short, for the listener, they do not have the same preponderance as the sound complexes. It is, therefore, justified that many performers today play Nomos alpha with more attention to sound than pitch. Nevertheless we must not go too far in this interpretation. Thus, the temptation to treat the quarter-tones in the passage in Example 6 as a bisbigliando (a particular timbre)a temptation to which Strauch (1992) yields, which produces a kind of insect hummust, it seems to me, be avoided. I think the time has come to reconcile Xenakis the sculptor-ofsound with Xenakis the theorist, who wants to rebuild the pitch cosmos. A passage like the one just quoted has a real melodic intention. Such passages, where the melodic intention is obvious, can be found in Oresteia, composed during the same period as Nomos alpha (see Example 7).

Roy's recording is particularly successful on this point: he reaches that delicate compromise between the realm of pitch and the emphasis on sound. 21 As for Deforce, because of the tendency to think of sound as autonomous, he is rather of the school of those who consider pitch as secondary.

Example 6. Nomos alpha, page 1, system 4, last 2 bars.

Silence and continuity

A word on the silences. At first, Xenakis probably intended to treat them as a formalised, calculated parameter. In Vandenbogaerde's analysis, which is reproduced in one of the versions of 'Towards a philosophy of music' (Xenakis 1971a, 111-118), mention is made of the fact that the silences are calculated using a kinematic diagram, as is the register parameter. However, Xenakis's own analysis does not mention them, which suggests that being too occupied with the other parameters, he ended up treating the silences in an intuitive way. Whatever the case may be, in Nomos alpha, silences play a vital role. They contribute to the extreme fragmentation of the piece.

Roy explains that when he met Xenakis, he seemed somewhat troubled by this fragmentation. This is why he abbreviates the silences within the sections slightly when he plays the piece. He thus tends towards greater continuity, which is reinforced by his tendency to interpret certain pitch passages melodically. However, in his recording, this continuity is contradicted by the fact that little processing is introduced (in particular, no reverberation) and that, consequently, the silences tend to be felt more strongly. Deforce, however, also seems to abbreviate the silences inside the sections slightly. This results, in the recording, in a continuity that is reinforced by the (moderate) use of reverberation. When it comes to the silences between the sections, Roy accentuates them, thus accentuating the separation between the sections.

Relationship to Xenakis's theory

The compositional system and the score One last question: what relationship do our two musicians have with the theoretical system developed by Xenakis for Nomos alpha? In interviewing them, I asked them if they wished to transmit this theoretical system to the listener, and, in particular, the idea that the piece is built on the model of the rotations of a cube, proposing the transfer of a geometrical and spatial model to the sonic and temporal universe of music. Both said they wanted to do this. How to proceed with this transmission remains of course a delicate question: Roy mentions the play on dynamics able to create a space sensation, which serve as a figure for the cube rotations. As for Deforce, adopting Deleuzian language, we could say that he tends towards a 'cube-becoming' when he plays the piece. 22 Both musicians also enlarge the score, which is a reproduction of the We would "conclude from this that in this method of working every opportunity is given to the personality of the musician to come out." (Barraud 1968, 185).

This is certainly true: Xenakis often makes choices that, in highly formalised works, can blow the theoretical system and its calculations apart. However, it is important to add that, often, the gaps largely come from errors, as we remarked previously regarding the calculation of pitch sieves (errors generated by their transcription on staffs or the choice of pitches in a sieve to compose a passage).

To give an example: a manifest error is highlighted in a manuscript provided by Xenakis in the 1992 edition of Formalized Music (see Example 8). The error concerns the construction of sieve Λ (11, 13). The analysis -the comparison between the theoretical sieve and the notes found in the scoreshows a gap of more than 50%. Obviously such a gap does not arise out of choice. As the handwritten annotations of Xenakis in Greek attest, an error was made. On the left, it reads: 'αλλάζει. Γιατί;' (this changes, why?). In fact, Xenakis got it wrong when he wrote one of the sieve modules, shifting it, which, in the final calculation, produces wrong pitches, hence the huge gap. Recognising this error, but unwilling or unable to reconstruct the sieve (the music had To conclude

This article sketches out a preliminary analysis of the performance of Nomos alpha, comparing, in particular, two versions, given by two 'second generation' musicians playing

Xenakis. The analysis needs to be continued, both to refine the comparison and to introduce other versions as well. To limit ourselves to our two cellists, I would like to add in conclusionbut also in an assertion that should not be taken too seriously -that their respective chthonic and cosmic characters are also revealed in the photos given in Example 11.

11

 11

Example 1 :

 1 Nomos alpha: bars 1-2. ©Copyright 1967 by Boosey & Hawkes Music Publishers Ltd. Reproduced by permission of Boosey & Hawkes Music Publishers Ltd.

  Roy and Deforce play the passage much more slowly (6" and 7.5" respectively), thus allowing the listener to enter more deeply into the vibration. Example 2: Nomos alpha: page 1, system 3, bars 5-7. ©Copyright 1967 by Boosey & Hawkes Music Publishers Ltd. Reproduced by permission of Boosey & Hawkes Music Publishers Ltd.

Example 3 :

 3 Nomos alpha: final section of the piece. ©Copyright 1967 by Boosey & Hawkes Music Publishers Ltd. Reproduced by permission of Boosey & Hawkes Music Publishers Ltd.

Example 4 .

 4 Nomos alpha: graph of the pitches in the final section. (realised by the author) Example 5. Nomos alpha: graph of the intensities in the final section. (realised by the author) Specifically Xenakian aspects: sound, energy, gestuality

  probably already been composed and published), he tried to legitimise it by indicating at the top of the manuscript: 'από το μηδέν ισχύει μόνο για τα C. Το A+B έχουν O' (as of zero this only applies to the Cs. The A+Bs are O), an arrow referring this indication to a particular place that is the 'origin' (O) of the module A+B of the sieve. It is obvious that having two origins in a sieve does not make sense! Example 8. Xenakis 1992, 234. When I questioned the two cellists about the gaps, they did not seem to be aware of this issue. Maybe, in the future, with the help of a critical edition of the score, musicians might raise it? This does not mean that they should necessarily 'correct' all 'errors' because they are part of the music…There is, however, one particularly obvious error that many musicians have tried to correct. It is located between systems 5 and 6 on page 1 of the score (see Example 9). It reads D-A, a perfect fifth that is very explosive in the context of Nomos alpha. Palm or Saram play it. Since then, in Roy and in the third generation, musicians have often played a sustained A. It is likely that this correction comes from the extract of the score reproduced in one of the versions of 'Towards a philosophy of music' (see Example 10). However this is not the right correction! In terms of the theoretical sieve, the musician should play a sustained D with the error rather being a wrong key indication: there should be an F at the beginning of system 6 of the score. Deforce is one of the few to play this D. 23 Example 9. Nomos alpha: page 1, systems 5-6. ©Copyright 1967 by Boosey & Hawkes Music Publishers Ltd. Reproduced by permission of Boosey & Hawkes Music Publishers Ltd.Example 10.Xenakis 1971 a, 116.

  When we compare what we play from the score with the 'sound complexes' we are supposed to play, we realise that we did not necessarily guess the type of sound that Xenakis wanted. It's interesting, because it makes us see the sound we're playing in a different way.[...] For example, he talks about 'ionized atoms' for the beats. This enables us to see that, what interests him, is hearing the inner pulsation. The cube rotations, for example, are indicated on the score by letters. We must be aware of this. When I play, I think about this a lot.[...] With the cube, Xenakis has a 3D vision, which must be heard. The whole dynamic of the piece (the nuances) is translated into distance and proximity. For me, it is important to conceive of the pitches vertically (an infinite space in this direction) and then nuances in the other direction: sound exists in a curved space. The cello makes this happen. For example, you can be playing extreme nuances and, at the same time, a limit is reached very quickly. You end up designing a sound sculpture in this space." (Christophe Roy). "I was very interested in the analyses of the pieceeven if they are too composer's manuscript, in order to play more comfortably. But, while Deforce finds it to be very well written and says he likes working with the handwriting of the composer, Roy finds it difficult to read and would like a new edition.As has been mentioned, every Xenakis analyst knows that there are many discrepancies between the composer's calculations and what is found in the score. A certain mythology is in circulation concerning this. In the past, to moderate the image of the composer-mathematician, a cold calculator, and especially when he made use of computers for the first time (ST program), it was said that Xenakis "keeps what needs to be held kept, changes what he feels should be changed, grafting his own choices (where his taste and sensitivity can be introduced) onto the choice of the machine [...]".

	The gaps and errors

22 "

Note that Strauch's version is even shorter: 12'40".

The piece contains: a) 188 bars at 4/4 with a tempo minim = 75 MM; b)

bars at 4/4 with a tempo minim = 84 MM; c) 9 bars at 4/4 with a tempo minim = 62 MM; d) a few incomplete measurements totalling 3'5".

"In this passage, the notation is incomplete. It is impossible to play the harmonics of a fourth written with a note held simultaneously. Beyond a few of the sounds, the fingering requested by Xenakis cannot be done. This implies that everyone does their own version.[...] The solution that I adopted is to replace the harmonics of a fourth by harmonics of an octave, fifth, fourth, third major and third minor, so that a gesture can be obtained that descends visually on the string and ascends for the ear. This has a magical side: we see the hand going down and we hear a sound going up![...] We thus manage to do enough to make the idea clear and perceptible. This pre-supposes a rather slow tempo to really control things and give this liquid aspect." (Christophe Roy).

"I always saw the note at the end of the fifth system as a legato note. Also, it seemed clear to me that it was in the wrong key and that it needed to be in F to make the related note logical. Just as the key of C is missing in the third measure of this system." (Arne Deforce).


T V Tran

F Schoefs

E Bastidas-Arteaga

G Villain

X Derobert

Optimization of Geo-positioning of NDT measurements for Modeling spatial field of defects: a two stages procedure

Keywords: Confidence interval, probability of interval, spatial variability, Karhunen-Loève, optimization of inspection

The localization of weak properties or bad behavior of a structure is still a very challenging task that concentrates the improvement of Non Destructive Testing (NDT) tools on more efficiency and higher structural coverage. In case of random loading or material properties, this challenge is arduous because of the limited number of measures and the quasi-infinite potential positions of local failures. The paper shows that the stationary property is useful to find the minimum quantity of NDT measurements and their position for a given quality assessment. It is shown that a two stages procedure allows us (i) to quantify the properties of the ergodic, stationary field (ii) to assess the distribution of the characteristics. The optimization is reached following a criterion based on confidence intervals of the statistics.

Introduction

Industrially developed countries face more and more the maintenance of existing infrastructures. This challenge began in the 80's with nuclear power stations or offshore oil and gas platforms for which safety requirements were very provided very early because of the high level of consequences of failure. Specific methods for Inspection Maintenance and Repair where devoted to each industrial field. However, their generalization to other assets is not immediate because of the required money and human resources. That is why methods based on visual inspection have been developed with a real potential [START_REF] Estes | Updating Bridge Reliability Based on Bridge Management Systems Visual Inspection Results[END_REF] and that new methods and techniques of monitoring, within Bridge Management Systems (BMS), are under development [START_REF] Okasha | Integration of structural health monitoring in a system performance based life-cycle bridge management framework[END_REF]. Various other assets than bridges assets are now under consideration: sewer networks [START_REF] Duchesne | A Survival Analysis Model for Sewer Pipe Structural Deterioration[END_REF], wharfs. In the probabilistic thinking, this question is addressed under the methods of "random variable updating" that have been widely addressed during the two last decades. Random variable updating is very useful when a prior distribution is known and data coming from inspections or monitored systems are collected for condition assessment and reliability updating [START_REF] Straub | Modelling dependency in inspection performance[END_REF]. Basically, the so-called RBI generalizes these approaches in the case of non-perfect inspections by linking inspection and decisions [START_REF] Faber | Risk Based Inspection: The Framework[END_REF].

Moreover, establishing a prior distribution for a whole set of material parameters of existing structures is a very difficult task and probabilistic updating must be applied with care. In parallel, it is more and more feasible and inexpensive to collect a huge quantity of data, by an operator or a new generation of remotely operating vehicles and robots devoted to Non Destructive Testing tools (interferometer robot for instance: [START_REF] Lu | Mechanical properties estimation of functionally graded materials using surface waves recorded with a laser interferometer[END_REF]). On the whole, the stochastic nature of material properties and deterioration processes as well as the factors that reduce the quality of the inspections that can be used to quantify them, trans-form the management of deteriorating systems in a major challenge for owners and operators. In the light of this, we suggest providing a flowchart for optimizing the number of inspections and provide the statistics of material characteristics on real structures with spatial dependency starting from five main assumptions about the inspection and the random field modeling one-dimensional.

The goal of the paper is to present and solve the optimization problem of the total number of measurements after the two stages. The paper first presents in the second part usual representation of spatial variability in civil engineering through stochastic field modeling and focuses on stationary stochastic fields: the Karhunen-Loève decomposition is reminded for modeling this spatial variability. Then the third part presents the twostage inspection strategy in view (i) to assess the correlation function and (ii) to get a set of fairly dependent measurements to compute statistics of the marginal distribution. A criterion of quality of the modeling after inspection is suggested. Original parameters are highlighted in view to represent the role of the distance between inspections. The paper ends in the fourth part with an application to an academic study case in view to illustrate the potential of the methodology and the suggested parameters.

2 Spatial random field modeling

Usual approaches for spatial field modeling

The stochastic field could take several forms more or less complicated. The most simple when the degradation can be considered as homogeneous is the stationary stochastic field that can be used, for instance, to model chloride distribution, concrete properties [START_REF] O'connor | Experimental Evaluation of the Scale of Fluctuation for Spatial Variability Modeling of Chloride-Induced Reinforced Concrete Corrosion[END_REF], or soil properties. In some cases, when a stochastic process is influenced by several phenomena that vary with time (sea wave for instance) or with space (concreting of a structure in several steps with heterogeneity of these steps), it can be modeled as piecewise stationary. This more sophisticated stochastic field can represent, for example, the variability of concreting materials by pieces or the corrosion of structures located in contiguous environments with different characteristics [START_REF] Boéro | Statistical analysis of corrosion process along French coast[END_REF]. In this case, a piecewise stationary stochastic field could be used to have a good representation of the loss of thickness.

Main assumptions for the stochastic modeling

Starting from the previous sections and to limit the study, we consider five main assumptions about the inspection and the random field modeling: (i) the stochastic field is statically homogeneous, and only few information on the marginal distribution is known: the type of the unique probability density distribution. In the following applications we consider a Gaussian field; (ii) a huge number (more than 100) of measurements can be performed; (iii) second order stationary stochastic field can piecewise or totally describe the spatial fields; (iv) inspections are regularly spaced for simplicity of the campaign planning; and (v) inspections are considered as perfect. Given a probability space (Ω, F , P), a stochastic field or process with state space Z is a collection of Zvalued random variables indexed respectively by a set s "space" or t "time". We consider here homogeneous fields only. This means that the marginal distribution of Z(x 1 , θ) does not depend on the location. A stochastic field is second order stationary if it follows three main properties: (i) expectation E[Z(x, θ)] does not depend on the location x -i.e., E[Z(x, θ)] = E[Z]; (ii) variance V[Z(x, θ)] does not depend on the location x -i.e., V[Z(x, θ)] = V[Z]; and (ii) spatial covariance COV[Z(x, θ), Z(x, θ)] depends only on the distance (xx'). Thus, the second order stationary is a property restricted to the two first probabilistic moments. It can be shown that geometries of welds for ships or the spatial distribution of chloride concentration in reinforced concrete structures can be represented by stationary stochastic fields. For instance, FIG. 1 presents the correlation function of the chloride diffusion coefficient as function of the distance between two points (duratiNet project: http://www.duratinet.org, following [START_REF] O'connor | Experimental Evaluation of the Scale of Fluctuation for Spatial Variability Modeling of Chloride-Induced Reinforced Concrete Corrosion[END_REF]. In this paper, we select a Karhunen-Loève expansion to represent the stochastic field of resistance of a structure Z(x, θ). This expansion represents a random field as a combination of orthogonal functions on a bounded interval [-a, a]:

Z(x,θ ) = µ Z +σ Z . λ i .ξ i (θ ). i=1 n ∑ f i (x) (1)
where, µ Z is the mean of the field Z, σ Z is the standard deviation of the statistically homogeneous field Z, n is number of terms in the expansion, ξ i is a set of centered Gaussian random variables and λ i and f i are, respectively, the eigenvalues and eigen functions of the correlation function ρ(Δx). It is possible to analytically determine the eigenvalues λ i and eigen functions f i for some correlation functions. For example, it can be determined if we assume that the field is second order stationary and we use an exponential correlation function:

ρ(Δx = x 1 -x 2 )=exp( - Δx b ); 0 < b (2)
where b is the correlation length and Δx ∈ [-a, a] : 3 Inspection strategy and goals

Concept of Inspection Distance Threshold

The two stages inspection we suggest should provide both the parameters of the spatial correlation function and independent events that characterize the marginal distribution of Z. We considerer in this paper a onedimensional spatial field and we will apply the methodology on a set of trajectories: these trajectories could be a set of 1D components (beams). In view to limit the inspection costs we first inspect a trajectory with a "sufficiently low distance L b " to assess the shape of the correlation function ( 2): for instance the shape parameter b. In view to sample independent events for Z, we need to inspect the trajectories with a "sufficiently high distance L c " to get fairly correlated events. These "sufficiently low and high distances" can be gathered

Assessment of the correlation function from discrete inspections

We assume that the stationary stochastic field can be characterized by an autocorrelation function (ACF) considered for spatial variability of structures with their parameter, called length of correlation b. A complete overview of the auto-correlation functions and their application is available in [START_REF] Lu | Mechanical properties estimation of functionally graded materials using surface waves recorded with a laser interferometer[END_REF]. Let us focus on the assessment of this function from experimental data (sensors or NDT tests). In the first procedure, reported by Li [START_REF] Okasha | Integration of structural health monitoring in a system performance based life-cycle bridge management framework[END_REF], the Maximum Likelihood Estimate method (MLE) is used in which different values for the model parameter of the proposed ACF model is assumed and the value that maximizes the corresponding MLE is taken as the model parameter. In the second procedure, proposed by Vanmarcke [START_REF] Vanmarcke | Random fields: analysis and synthesis[END_REF]. In this paper, we select an exponential ACF (see ( 2)) and we use the MLE for the estimation of b (4).

L h = 1 2π exp - ν i 2 2 " # $ % & ' " # $ % & ' i=1 k ∏ = 1 2π " # $ % & ' k exp - ν i 2 i=1 k ∑ 2 " # $ $ $ $ % & ' ' ' ' (4)
where ν i is the i th component of the vector of independent standard values.

Number of inspections to optimize in the two stages procedure

When focusing on a practical application, we will have to optimize the total number of discrete inspections N=Np*Ns*Nt where Np is the number of repetitive tests for reducing the error of inspection, Ns is the number of inspected sections and Nt the number of trajectories. Here the error of inspection is neglected and we inspect separately and firstly Ns 1 sections on the first trajectory to assess the spatial correlation function, thus N= Ns 1 + Ns*(Nt-1) (see FIG. 2).

FIG.2-Definition of the number of inspections.

Our objective is to optimize the number of inspections in view to reach a given quality of the result.

Definition of a reliability oriented measure of quality of inspection

The quality of a result of inspection can be expressed by several concepts. If we consider the error of measurement risk oriented measures have been developed: PoD, PFA, PoI, PGA and PWA. We select in this paper a confidence interval of both the mean µ and the standard deviation σ expressed as a percentage ε of µ and σ respectively. We carry out Monte-Carlo simulations to estimate the bounds of the confidence interval for a target probability for the inspection respectively P ti,µ and P ti,σ . In a reliability study, P ti will be provided by the requirements on the accuracy of the probability of failure assessment. Thus we focus on the two estimates:

[ ]

Z Z P P σ ε σ ε σ µ µ µ ) 1 ( ; ) 1 ( ( ˆ+ - ∈ = Z Z and P Ẑ σ = P(σ Ẑ ∈ (1-ε σ )σ Z ;(1+ε σ )σ Z [ ] (5)
Where if only a statistical error occurs (no effect of weak dependency between measurements), theory of confidence intervals gives:

ε µ =u 1-α 2 σ Z µ Z N and ε σ =u 1-α 2 1 2N (6)
With u 1-α/2 =1.96 for P ti =0.95 (α=0.05).

In the case of measurements on trajectories with a weak dependency between data, these values will be affected.

4 Application to a study case

Structure characteristics and inspection goals

We consider a structure for which L>>b that allows to assess b from theoretical point of view. The Gaussian stationary stochastic field is characterized by: b=1, µ Z = 100 and σ Z = 20 and the length of the structure is L=200. We aim to provide an inspection protocol that ensures: respectively P ti,µ = P ti,σ = 0.95.

Effect of SCT on confidence interval

We first analyze the effect of a weak correlation between measurements due to the spatial field on the quality of inspection according to ( 9) and [START_REF] Vanmarcke | Random fields: analysis and synthesis[END_REF]. For N=100, theoretical values deduced from (12) and ( 13) are: εµ = 3.9% and εσ = 13.85%. FIG. 3 plots the effect of SCT (from 0.1 to 0.9) on εµ and εσ respectively. The width of the confidence interval increases obviously with SCT and this effect is more pronounced for SCT higher than 0.4 for both µ and σ. In the following we fix SCT=0.4 and IDT is computer from [START_REF] O'connor | Experimental Evaluation of the Scale of Fluctuation for Spatial Variability Modeling of Chloride-Induced Reinforced Concrete Corrosion[END_REF]. We can also express the result in another way. The optimal number N opt is solution of equation [START_REF] Okasha | Integration of structural health monitoring in a system performance based life-cycle bridge management framework[END_REF]. Here N opt = 40 if 4 trajectories are available and N s =10.

N opt = argmin N max(N ε µ ; N ε σ ( ) (7)

Inspection methodology: first stage

According to section 3, the first stage of the inspection methodology is devoted to the assessment of b on a single trajectory according to 3.2. We propose

m b L b 7 . 0 ) 5 . 0 ln( . ≈ =
. Practically b can be deduced from expert judgment. Here it is fixed at is theoretical value: b=1. In [START_REF] Tran | Optimization of Geo-positioning of NDT measurements for Modeling spatial field of defects: a two stages procedure[END_REF] we plot the mean value µ B and the standard deviation σ B of B as a function of N s1 . The convergence of µ B is quick and the error is less than 0.1 for N s1 =38 but the convergence of σ B is very slow and the error remains high (more than 0.3) even for N s1 =100. That underlines the role of the choice of L b .

Inspection methodology: second stage and optimization

The uncertainty on the assessment of b will cause an uncertainty on Lc and will propagate this uncertainty when assessing statistics of Z ˆ. Let us fix for instance N s =23 and N t = 2 to reach εµ= 5% and εσ= 20%. FIG. 5 gives the effect of the choice of N s1 on εµ and εσ respectively, with L c =1.2 m (see section 4.3). That allows us to illustrate that exceeding 70 measurements N s1 for εµ and 50 for εσ doesn't decrease the confidence interval. Note that the values expected for confidence intervals that confirms the good selection of L b .

Conclusion

We propose in this paper an original two stage method for the optimization of the number of inspection of a Gaussian stationary stochastic field in view to (i) assess the shape of the correlation function (ii) deduce the statistics of the marginal distribution. The role of the distance between measurement for assessment of (i) and (ii) is highlighted and a probabilistic-oriented measure of quality is suggested in terms of confidence intervals of these quantities. That underlines the key role of a Spatial Correlation Threshold. The methodology relies on (1) the measurement of the correlation function on a first trajectory with a given number of inspections and (2) the assessment of statistics of the marginal distribution on a given set of trajectories, knowing (1). The paper ends with a practical applications and suggestions for the spacing between inspection in view to reach (1) and (2).

A

  journal paper will be published in 2015. Please cite this paper as: Schoefs F., " Tran T.V., Schoefs F., Bastidas-Arteaga E., Villain G., Derobert X., "Probabilistic Characterization of Uncertainties and Spatial Variability of Material Properties from NDT measurements", CFM'013, 21ème Congrès Français de Mécanique, S25 « Incertitudes, fiabilités et maitrise des risques » session 2, 26 au 29 août 2013, Bordeaux, 6 p., (2013)"

FIG. 1 -

 1 FIG.1-Spatial correlation of the chloride diffusion coefficient in concrete -data Trinity College of Dublin.

  under the generic term IDT for Inspection Distance Threshold. Thus L b and L c should satisfy: L b ∈ ]0, IDT[ ; L c ∈ ]IDT, L[ where L is the length of the trajectory. For illustrating the methodology, we consider in the following a set of 1D-components (beams) with infinite length L ~ ∞: we don't discuss the case of components with a limited size, especially those where L< L b for which it is quite impossible to characterize the spatial variability. The IDT is defined by assuming that after a given distance, the events measured from an inspection can be assumed as statistically independent. A Spatial Correlation Threshold SCT of the spatial correlation gives this weak correlation. For instance in FIG.1 (red line) for SCT=0.4, IDT=3 meters. It is linked with IDT by the relationship: IDT = b. ln(SCT )

FIG. 4 -

 4 FIG.3 -Effect of SCT on εµ and εσ

FIG. 5 -

 5 FIG.5-Effect of N s1 on εµ and εσ