Pr. SIC Fabienne Martin-Juchat

The Lyon Parc Auto Case Study : A Polysensorial Approach

Keywords: practices, sociology, semiotics, art, emotion, design, communication, parking's identity relooking

For over fifteen years, Lyon Parc Auto has been building parking buildings which are designed as services to male and female motorists, and not only as simple car storage towers.

These car parks, designed by pluri-disciplinary teams (structural architects, interior architects, artists, graphic designerssignposting specialists, environmental designers), with a polysensorial approach, are visited today by specialists from the world over, have been awarded the "grand Prix Européen du Design" (European Design Award), and are used as an example in the "D.Day, design today" exposition at the Georges Pompidou Centre in Paris.

The objective of this communication is twofold: to present the reasons behind the success of these innovative projects and to deconstruct the model of reception and of the user that these projects implicitly integrate. The theoretical contributions will essentially come from the sociology of practices which integrate a methodology stemming from sociosemiotics.

Introduction

Innovative practices require that we, researchers, question ourselves as to our ability to analyse and understand them. The main objective of this article is to give an account of an exchange between a communication professional and a researcher in Sciences of Information and Communication, in order to analyse the reasons behind the success of a communication project which integrates design.

The redefinition of the identity of parking buildings in the city of Lyon (semi-public company Lyon Parc Auto : LPA) through design enabled the transformation of the type of relationship that is usually established between users and this type of place. Traditionally, carparks are considered, throughout the world, as anxiety-causing and not very appealing, ordinary but unsightly. The objective of LPA's project, by rethinking these spaces, was to not only transform the emotions evoked by them, but also and as a result, transform the very image of this urban function incarnated by the LPA company.

An analysis of the environmental design and of the signposting of the LPA car parks will be carried out by crossing the main theories stemming from the sociology of users with the methodological tools used in sociosemiotics. In this way, we will be able to clearly measure the changes which have taken place in the relationship with car parks, thanks to work on the visual identity and the design of the LPA environment. It should be noted that this work on the physical aspects of the car parks was accompanied by training measures for the staff in customer relations and regular information to the press, to inhabitants of the area and to opinion leaders.

Case study

At the beginning of the 90's, the city of Lyon decided to entrust LPA with the construction of new parking buildings. The Communiquez group (specialised in public communication, identity and design) thus carried out an ethnographic field survey to observe the way in which motorists felt about the existing car parks, and to understand "the reasons" behind the car parks' mediocre image. The results of this study assisted the elaboration of a guiding document setting out the requirements from which would be designed a new generation of car parks (treatment of spaces for pedestrian and vehicle circulation, signposting, light, welcome and security,…), for which Georges Verney-Carron (President of Art/Entreprise, a company within Communiquez group) would be in charge of the artistic leadership.

The principle of the work was to form pluri-disciplinary teams, bringing together, alongside structural architects, an interior architect -Jean-Michel Wilmotte -and a graphic designersignpost specialist -Yan D. Pennor's -, who would design together the graphic charter outlining the common identity for all the car parks, and a guest artist invited to work on a car park by car park basis, for "in situ" work (like Daniel Buren, Joseph Kosuth, Mat Mullican, François Morellet, Marin Kasimir…) As this team worked together on the interior scenography from the beginning stages of each project, the design and artistic dimensions of these carp arks were not simply a fleeting lick of polish on the surface but, on the contrary, totally interwoven into the durable work of the structural architects.

With this work bringing together art, architecture and design, LPA opened the way for the car parks to be experienced in a different way, designed as real entrance ways in a human-sized city.

(see photos -series A -in the Annex)

In the context of this communication, we are going to focus our analysis on the elements of LPA's design and signposting so as to highlight their roles in the redefinition of the representations that individuals might have concerning:

 car parking buildings,  their use (which is to say the thoughts and emotions resulting from immersion in a car park or, more precisely, the different actions and interactions taking place in a car park.)

 the image that LPA receives in return, or in other terms, the image of the user according to LPA.

The basis of LPA identity through design:

Wilmotte's interior architecture, Pennor's' signposting Jean Michel Wilmotte, architect, town planner, designer, is internationally renowned and works all over the world. His agency has developed the concept of "interior architecture within cities", a new approach to the treatment of urban spaces which concerns surface coating (floors, walls and facades), planting, lighting, urban furniture and transport.

According to Jean-Michel Wilmotte, "People, the city, the movement in the streets, the swaying of a tree, the space explored to the rhythm of walking: this is the first task, the work site to discover, whether it be New York, Paris, Le Puy-en-Velay, Beyrouth, Tokyo, Seoul. For an architect it's always the same essential frame: the space to decipher" 1 . 1 Quote from Jean-Michel Wilmotte, on the Internet home page of his agency : http://www.wilmotte.com/pge/homepage/ For LPA, "Jean-Michel Wilmotte's scenography deliberately played the harmony and softness card, without being completely free of a certain rigorousness. The indirect lighting, the transparency of the walls are accentuated by the geometry of the structures treated in black and by the dull grey of the dividing walls. Here, the glass, the metal, the bare concrete come together to carry the image of modernity of Lyon Parc Auto through their own contemporary resonance. He brings back the memory of these places, by drawing for example the arches of the interior helix of the Celestins echoing Italian style theatre"2 .

(see photos -series B -in the Annex)

F. Dagonet rightly reminds us of the lexical closeness of the term "design" with the French term "dessein", which means "project" or "programme". Design is indeed at the service of a company project whose mission is to propose a new scenario of use to its clients. Furthermore, the term « design » also refers to « dessin » [drawing] which, according to Dagonet, "gives importance to the reshaping and the distribution of elements" (Dagonet, 2005 : 46). Moreover, the visual identity of LPA (which is essentially expressed through signposting applications) was reworked by the graphic designer Yan D. Pennor's.

Yan D. Pennor's claims to be a meticulous craftsman. He became internationally known as a typographer for renowned companies and institutions such as Sofitel and Larousse. He also designs objects, furniture and luxury product lines. He has worked for Laguiole, Pierre Hermé, Fauchon and many others.

Yan D Pennor's reshapes and redistributes elements which carry meaning, the meaning which will be attributed to the company. In this respect, it is indeed "the combination of invented and retrieved signs, born from a stroke and/or colour which best characterise the work of Pennor's" (Heilbrunn, 2005 : 86).

For LPA, "deliberately minimal, the sign markings designed by Yan D. Pennor's is free of all superfluous signs. It is content to accompany a path which is already coherent by its design.

Carriers of image for Lyon Parc Auto, elegance and rigorousness mark the signs and the typography. Information is presented in two ways: in yellow on a black background for motorists, in black on a yellow background for pedestrians"3 .

(see photos -series C -in the Annex) Theoretical issues

The values for use are the fruit of an immersion in a pluri-semiotic space, which will generate emotions then representations [START_REF] Blandin | La construction du social par les objets[END_REF]. The sense attributed to a place, arising from an activity, here that of parking, is deeply embodied in a practice. This type of acknowledgement is rich in theoretical consequences as it deconstructs the cybernetics notion of the interpretation process. Representations are the fruit of an activity which not only involves cognition but also the emotions and physical actions produced in an environment.

In the continuation of cybernetics, such as is developed by cognitivism, representations are abstract and logical units that it is possible to extract from their context of production.

Representations are made up of symbols, defined as formal elements which refer to the real world by a relationship of equivalence. Cognition amounts to an activity of treating these symbols. Interpretation is the activity of finding the middle ground between the representations of objects in the world and their references. Cognition is an activity of treating the information from the representations. Cognition is a mental and reasonable activity.

Finally, reception can be reduced to a simple activity of treating a space of symbolic representation.

Indeed, recent research in neurosciences [START_REF] Petit | La constitution par le mouvement : Hurssel à la lumière des données neurobiologiques récentes / Constitution by movement : Hurssel in light of recent neurobiological findings[END_REF][START_REF] Petitot | Introduction du numéro d'Intellectica : repenser le corps[END_REF][START_REF] Berthoz | Le sens du mouvement[END_REF] and in semiotics [START_REF] Landowski | Passions sans nom[END_REF][START_REF] Fontanille | Soma et Séma[END_REF]) reintegrated into the sociology of uses [START_REF] Blandin | La construction du social par les objets[END_REF] allows us to revisit these post-cybernetic notions of the way in which things make sense to us. Any symbolic interpretation activity of a space or pluri-semiotic action is fundamentally embodied in a practice which appeals to emotions. Any activity of appropriating artefacts (machines, instruments, etc.) is carried out in and by their use. Any activity of receiving a place, a space, is immersive in the sense where it involves a user in his/her entirety (physical and mental).

Meaning, as a system of values attributed by a place, is the product of a real-life experience which is both cognitive (thoughts), physical (the movement generated by the use) and above all emotional (all the positive and negative emotions which result from this use). These emotions give meaning to a theatrical space, giving it value. Moreover, the emotions experienced during the visit generate an overall feeling of identity which will be attributed to the place.

More precisely, from the entrance to the exit of a car park, the user will repeat scenarios of action which will appeal to him/her in a polysensorial manner (look, move, smell, listen, etc.).

Each action which makes up the use of the car park and its artefacts (take the ticket at the entrance, find a space for the vehicle, park, continue on foot, look for the lift, go up the stairs, go out, then, later on, pay the car park attendants or at an automatic machine, find the car, drive to the exit, go out) will thus generate thoughts and emotions which will either add to or not the image of the car parks, those of LPA company, and especially the image that the user has according to LPA.

It is therefore a matter of understanding how, by reworking the design of a place, it is possible to change the values and the emotions generally attributed to this type of place. From a semiotic point of view, it is a question of developing a semiotic of the mark. The places touch the users, leaving impressions which are mental, emotional and sensorial. This process constructs the meaning which will be attributed to the place. From a methodological point of view, this implies describing in detail the characteristics on an expression level of the theatrical measure and of the signposting in order to understand in a heuristic manner what they can generate on a contents level (in the form of thoughts or emotions).

Methodology

Methodology of analysing the signposting

The visual identity of an institution or of a brand is structured most of the time on three levels4 :  The level of discursive expression, where the manner in which the visual identity presents itself in a certain form to the client/user shows itself and will be analysed.

This level takes into consideration the visual codes of the time, the production techniques of the image and the constraints or advantages of the representation supports. Colours, shapes, their topology and their vectorialisation make up this level of expression.

 The content level, where the meaning that will be attributed to the institution by the means of the expression of its visual identity is thought out. This meaning will be reconstructed by the receiver by the act of reception including the emotions which will be associated. By interpreting the expression, the receiver builds him/herself a representation of the institution and above all of the manner that it conceives relationships. The visual identity thus implies a conception of the client, a model of the user: his/her personality, cognitive especially emotional structure, style of relationships with the institution and its services.

 The axiological level, where the values of the institution in a system of oppositions and complementarities (often represented as a semiotic square) can be revealed. This level allows the main principles, which feed the institution's action towards its clients via the act of buying services, to be highlighted. This level can be summarised in the form of promises of added value, values promising to be acquired through the act of consuming (Baudrillard, 1968). This three level model only has a heuristic and explicative value. It doesn't claim to describe the path of elaboration followed by the designers, nor the real interpretative path of the users/clients.

Methodology of analysing the environmental design

As far as the theatrical design or environment design are concerned, it is the different actions or interactions (manipulate, see, hear, move, find bearings, smell, etc.) with or without a car, in the LPA car parks which will provide the user with a new image of a car parking building, of its use, of LPA and above all of the image that LPA has of its clients. Moreover, the environment design provides an embodied identity, an identity in relation, in action and in emotion for LPA.

Beyond the design conceived to facilitate the different processes of action and interaction carried out in a car parking building, the scenography work for these car parks clearly had the objective of transforming the representations and especially the emotions usually associated with this type of place and its practices [START_REF] Thomas | Environmental Design -An Introduction for Architects and Engineers[END_REF]. Leaving the not very reassuring, anxiety-causing, unsightly dimension behind, the new car parks would have to generate feelings of attractiveness, well-being, confidence, and harmony so as to render their use more pleasant and efficient.

Indeed, the postulate is that the energy lost in difficult manoeuvres or complicated actions (during the different phases which characterise the use of a car parking building), in the negative emotions resulting from an anxiety-causing atmosphere, disturb the use of a car park and as a consequence deteriorate the image of the company which manages it.

The objective was thus for the designers to facilitate and to improve the different actions and interactions taking place in the car park (circulate, find bearings, wander, park) but also the emotions generated from the sensorial appeals in this place (odours, sounds, lights, …) and thus to not only make this activity ergonomic but also more harmonious, giving the image of a place which is respected by the users.

Better again, the feeling of well-being and of harmony is the product of the balance between thoughts, emotions and actions generated by the use of the place, of an artefact, of an instrument [START_REF] Berthoz | Le sens du mouvement[END_REF]. If there are too many emotions, the thoughts and actions risk being disturbed. If there is too much physical effort (to park) or intellectual effort (for example orientation or memorisation) required, the action will be hindered. The purpose of a car park's use is to allow the user to free his/her thoughts so that (s)he can dedicate his/her time to the reasons why (s)he came to park in this area (shopping or business for example).

All actions will be more efficient if they are made « routine » by an accompaniment throughout the client's course (the role of signposting), and if his/her thoughts are not disturbed by negative emotions (the role of lighting and the attractiveness of the place) or too complex manoeuvres (the role of ergonomics). The objective of the design of the car parks is to avoid losing energy in the manoeuvres and long and difficult actions, time consuming and likely to trigger stress and annoyance: take a ticket, find a lift, park the car, find it again, etc…

Analysis

In this last part, our intention is to analyse the graphic and environmental identity of the new LPA car parks. It is a matter of artificially deconstructing the interpretation process as it was thought out by the project team, while resorting to a methodology stemming from the semiotics of impression (Fontanille, Landowski) and of the sociology of uses. In other terms, our aim is to understand the reasons for which the signposting combined with the design of the Lyon car parking buildings allowed the image of LPA to be transformed through work on modifying the thoughts, emotions and actions which are normally generated in this type of place.

A. Yann D Pennor's' signposting

To analyse the added value of Yann D Pennor's' signpostings we have compared his propositions with classic examples from the highway code. We are going to successively analyse the expression level (colours, shapes, topology, vectorialisation) then the content level (of which the guiding principles, the main values define LPA's identity).

Conclusion

In a slightly artificial manner, we separated for the analysis the signposting and design work although the two elements were thought out as completely interconnected. The design is at the signposting's service, indeed is even, at times, signposting, in the sense that it indicates a direction, a path, or even a drawing, a life project within the car park. For example, the accentuated lighting at the pedestrian exits compared to that at the parking spaces naturally orientates, without cognitive overloading or anxiety, the user towards the exits. The angled parking spaces intrinsically dictate the direction of the circulation and reduce the amount of signposting.

A conception methodology placing the user and his/her parking practices at the heart of preoccupations was applied upstream with success by the actors of a project of rethinking of Lyon car parks. The design work combined with the signposting made the latter less visible lighter but more intuitive. This considerably modified the emotions and representations usually associated with this type of urban function. Freeing thoughts by facilitating the actions carried out in a car parking building; generating a feeling of balance and harmony by combining more pleasant auditory, olfactory, visual and corporal sensations than in a classic "car park", participate in a feeling of respect for the user. LPA, by expressing this respect, induces an ethic model of the user which could only have direct consequences on its own company image. In this way, LPA built, by combining ethics and aesthetics, an identity, that of an institution which places human values at the heart of its preoccupations. Emotions and aesthetic feelings, considered in most projects to be pointless as not very profitable, have completely found their place here to show that profitability can also occur through clients' physical, psychic and emotional comfort.

http://www.lyon-parc-auto.com/fr/sensible/sb.html

http://www.lyon-parc-auto.com/fr/sensible/sb.html.

We will use, in this article, a simplified version of the analysis model of visual identity, put together from the writing of semioticiens such as R. Barthes, U. Eco, J.M. Floch, L. Hjemslev, F. Saint-Martin, reappropriated by Heilbrunn and Hetzel in Sciences de Gestion/Marketing.


Denise Vella-Chemla

Goldbach's Conjecture, chip-firing game, 2 × 2 matrices and infinite descent

published or not. The documents may come

Introduction

We propose here another attempt to demonstrate Goldbach's conjecture.

In the following, we focus on even integers n decompositions of the form p + (n -p) in sum of two odd numbers greater than 3 and for what p is a prime number smaller than or equal to n/2.

Our proposition is based on the following elements :

-a two letters language L based on the alphabet A = {a, b}. The letter a codes decompositions of the form p + (n -p) such that n -p is a prime number ; the letter b codes decompositions of the form p + (n -p) such that n -p is compound ; -transition 2×2 matrices with integer coefficients * ; each matrix integrates in its coefficients some knowledge on n's decompositions as well as some knowledge on n + 2's decompositions, we will see how ; -chip-firing game notion [START_REF] Björner | Chip-firing games on graphs[END_REF] : we won't use here results from this notion theory, but it has been useful for its suggestive potential from one part, and also, it will permit to understand easily how takes place the passage between the matrix associated to even number n to the one associated to even number n + 2.

Examples

To fix ideas, let us begin by studying two examples :

-to the even number 30 is associated matrix

M 30 = 1 2 1 1 . * . See for instance A.
Connes, Noncommutative geometry year 2000, http://alainconnes.org/docs/2000.pdf, [START_REF] Connes | Noncommutative geometry year[END_REF], p.8, to find matrices such that f ab (n) = f ba (n) but in this context, matrices are operators. This idea has been of a great suggestive potential for us.

1

-to the even number 32 is associated matrix M 32 = 1 1 2 1 .

To think the transition between M 30 and M 32 in terms of chip-firing game consists to tell oneself that the 2 at right top of M 30 "has given" 1 (chip) to the 1 at left bottom of M 30 , and this has made this element at left bottom pass from 1 to 2, and has made itself at right top pass from 2 to 1.

Let

Modelisation

As we can see in those examples, each matrix integrates in its coefficients a certain knowledge on n's decompositions (in left letters of couples of letters that its coefficients count) as well as a certain knowledge on n + 2's decompositions (in right letters of couples of letters that its coefficient count).

Let us write formally what the 4 elements of each 2 × 2 matrix count :

M n f aa (n) f ab (n) f ba (n) f bb (n) with : -f aa (n) = #{(p + q = n) ∧ (p prime) ∧ (3 ≤ p ≤ n/2) ∧ (q prime) ∧ (((n + 2) -p) prime)} ; -f ab (n) = #{(p + q = n) ∧ (p prime) ∧ (3 ≤ p ≤ n/2) ∧ (q prime) ∧ (((n + 2) -p) compound)} ; -f ba (n) = #{(p+q = n) ∧ (p prime) ∧ (3 ≤ p ≤ n/2) ∧ (q compound) ∧ (((n + 2) -p) prime)} ; -f bb (n) = #{(p+ q = n) ∧ (p prime) ∧ (3 ≤ p ≤ n/2) ∧ (q compound) ∧ (((n + 2) -p) compound)}.
It can be easily understood that the sum

f ba (n) + f bb (n) counts the couples (x, x + 2) such that x ≥ n/2 et n -x is prime.
Sum of the 4 elements of matrices is equal to π(n/2) -1 (with π(x) the usual notation for the number of prime numbers smaller than or equal to x), since we focus only on even numbers'decompositions that are "based" on a small sommant that is a prime number.

This sum is increased by 1 at each even number that is twice a prime.

We provide in annex matrices associated to even numbers between 10 and 100.

Infinite descent

The number of n's Goldbach decompositions is equal to f aa (n) + f ab (n). Demonstrating Goldbach's conjecture is the same as demonstrating that f aa (n) + f ab (n) > 0 is always true.

Let us try now to break down the process that is at work during the passing from the even number n to the following even number n + 2 in terms of each element of matrix M n associated to n taken separately.

Let us refer to examples matrices M 30 and M 32 observing the column containing the couples of letters at the right of decompositions.

If a number would have no Goldbach's decomposition, we should have f aa (n) = f ab (n) = 0. Only f ba (n) and f bb (n) would be different from zero. Then, there would be, at right of the matrix M n , only couples of lettres ba and bb. But we saw that left letters of couples of letters of n + 2 and right letters of couples of letters of n are the same (since those letters code the same decompositions).

Let us specify now the chips circulation, in terms of chip-firing game, we have that (or are inclusive or ) :

-ba spills in aa or in ab ; -bb spills in ba or in bb ; -aa spills in aa or in ab ; -ab spills in ba or in bb.

We can represent this chips circulation on the diagram below :

aa ba ab bb
Observing the way "chips circulate" in the diagram, we understand that the only way to obtain a matrix M n such that f aa (n) and f ab (n) are both equal to zero consists in going from a matrix M n-2 such that f aa (n -2) and f ab (n -2) are also both equal to zero.

The contradiction † comes from a kind of reasoning called Fermat infinite descent : we saw that if Goldbach's conjecture wasn't verified by an even number, it wouldn't be verified no more by the even number just before. However, there is no infinitely decreasing sequence of positive integers that verify simultaneously a same property (here for an even number to decompose itself in a sum of two odd prime numbers, such a property for which we recall that it is true for all even numbers between 6 and 100). The set N of positive natural numbers and all its not empty proper parts have a remarkable property : they admit a smallest element. We made a reductio ad absurdum reasoning : supposing that the matrix associated to n is such that f aa (n) = f ab (n) = 0, we saw it was necessary that the matrix associated to n -2 should be also such that f aa (n -2) = f ab (n -2) = 0. But n -2 < n. So we are led to a contradiction by infinite descent and such a reasoning should ensure that Goldbach's conjecture is true.

By the only game of letters manipulations, one has effectively the sensation of something that turns, that is to say something that is as circulating in time.

Annex 1 : 2 × 2 matrices associated to even numbers between 10 and 100 We would have wished initially to establish the contradiction from the fact that, since the overall sum of the 4 elements of each matrix is equal to π(n/2) -1, and since we have seen that the sum f ba (n) + f bb (n) counts couples (x, x + 2) such that nx is prime, if only f ba (n) and f bb (n) were equal to zero, it would significate that there are as many primes between 3 and n/2 that there are primes between n/2 and n, that would be impossible, the number of primes going decreasing on two successive intervals of the same length. But we didn't find in literature a result demonstrating that π(n) -π(n/2) < π(n/2).

return False

  ab = 0 ; ba = 0 ; bb = 0 ; 3 for x in range(3,n/2+1,2): 4 if (prime(x)): 5 if ((prime(n-x)) and (not(prime((n+2)-x)))): 6 ab=ab+1 7 elif ((prime(n-x)) and (prime((n+2)-x))): 8 aa=aa+1 9 elif ((not(prime(n-x))) and (prime((n+2)-x))): 10 ba=ba+1 11 elif ((not(prime(n-x))) and (not(prime((n+2)-x)))): )+' '+str(ab) 16 print(s) 17 s=str(ba)+' '+str(bb) 18

  us explain to what correspond the 4 elements of M 30 matrix and the 4 elements of M 32 matrix.

		p n -p (n + 2) -p doublon
		3	27	29	ba
	n = 30	5 7	25 23	27 25	bb ab	aa 1 ab 2 ba 1 bb 1
		11	19	21	ab
		13	17	19	aa
		p n -p (n + 2) -p doublon
		3	29	31	aa
	n = 32	5 7	27 25	29 27	ba bb	aa 1 ab 1 ba 2 bb 1
		11	21	23	ba
		13	19	21	ab

print(s)

Bibliography


To cite this version:

Sabrina Mervin, "The Clerics of Jabal 'Âmil and the Reform of Religious Teaching in Najaf Since the Beginning of the 20th Century", in The Twelver Shia in Modern Times. Religious Culture and Political History, Werner Ende and Rainer Brunner (eds.), Leiden, Brill, 2001, pp. 79-93. The Clerics of Jabal 'Âmil And the Reform of Religious Teaching in Najaf Since the Beginning of the 20th Century

The rationalisation of higher religious studies, which is at the centre of the reformist project had, and has today, fundamental and problematic implications for the Shii clergy. What is at stake for the clergy is not just its adherence to the ethics of the century but the saving of its independence and that of the marja'iyya vis-à-vis the State. This question will be treated here through the participation of the clerics of Jabal 'Âmil to the reform of the teaching system in Najaf. But before we get to Jabal 'Âmil, it is necessary to remind the reader of the main characteristics of the teaching system in Najaf and other holy shiite cities which constituted the hub of knowledge in the Shii world at the beginning of the 20th century.

The teaching was scattered among several independent schools, each directed by a mujtahid whose knowledge and charisma attracted a certain number of students. The schools called hawzât were the more flexible since no organisation headed or regrouped them: hence, there was no bureaucratisation. In addition, these schools had no program to follow but certain customs that were in use to monitor the progress of the students in each discipline. Nevertheless, the students were entirely free to choose the courses they would attend and there was no exam at the end to sanction their curriculum: the best students and those better prepared would get to ijtihâd while others would remain at a more mediocre level. It is thus that the religious aristocracy insured its reproduction and continuity. The absence of bureaucratisation in the system, its independence vis-àvis the State and the fact that it was entirely based on the mujtahid made it difficult to reform. 1 1 On the subject, see Yitzhak Nakash, The Shi'is of Iraq, Princeton, Princeton University Press, 1994, chap. 9; Meir Litvak, Shi'i Scholars of nineteenth-century Iraq. The 'Ulama' of Najaf and Karbala', Cambridge, Cambridge University Press, 1998, chap. 3 et 4; Sabrina Mervin, « La quête du savoir à Nagaf. Les études religieuses chez les chi'ites imâmites de la fin du XIXe siècle à 1960 », Studia Islamica, 81 (1995), p. 165-185. In Jabal 'Âmil, religious schools had become more popular after the 1880s, due to the efforts made by a few mujtahid that we will call the "protoreformists". These clerics who had been educated in Najaf by the disciples of Murtadâ al-Ansârî, revived the local teaching tradition by opening schools in small towns and villages. Thus, the movement of students going to finish their studies in Iraq was intensified and the links between the 'Âmilî clerics and the religious milieus in Najaf became stronger.

Simultaneously, in Jamal 'Âmil, certain 'ulamâ' and intellectuals started to entertain reformist ideas especially on the question of education. As of 1909, they were able to express and broadcast them through the channel of the Shiite magazine al-'Irfân that was edited in Saïda.

From the end of 1909 al-'Irfân started publishing a first call to the reform of higher religious schools. The article was signed by the initials of Sadr al-Dîn al-Sadr: it is true that he was not a 'Âmili cleric, but he had family ties linked with the Sharaf al-Dîn family, on the greatest buyût al-'ilm in Jabal 'Âmil; his son Mûsâ was to come to South-Lebanon at the end of the 1950s to follow up the work of 'Abd al-Husayn Sharaf al-Dîn.

Sadr al-Dîn al-Sadr's article2 already had in it the elements of a debate that would last the entire century : he criticised mainly the lack of organisation of the curriculum and the absence of a program. He found the number of students too important and thought the state should participate in their selection. The author also blamed the clerics who would compete in public. Hence, Sadr al-Dîn al-Sadr not only called for an organisation and a rationalisation of the studies, but he also accepted, for that reason, an interference of the State in the affairs of religious schools. In addition, through his talk on the competition between the clergy, he did not hesitate to criticise the mode of selection of the marja', who had to stand out in the circles of mujtahid to "emerge" as the more learned among them.

These critiques brought up two fundamental questions: the rationalisation of the system and the interference of the State.

These two themes will later on be taken up again. But it was not until the end of the 1920s that the reformist clerics formulated again a systematic criticism of the higher religious education that was given in the schools of Najaf and other holy cities. Two 'Âmilî clerics called for the reform: one was a famous mujtahid who lived in Damascus, Muhsin al-Amîn (1867-1952); the other was a young cleric finishing his studies in Najaf, Muhsin Sahrâra (1901-1946).

Muhsin al-Amîn enclosed this call to the reform of the schools in a dense work tackling varied topics, a sort of kashkûl, which appeared in 1929. 3 But his reflections on the schools had matured for several years. They were the product of his own experience in Najaf, where he had studied for ten years. He reused these remarks in the autobiography he wrote in 1951, just before his death. 4 As any good reformist, he fought against the disorder (fawdâ) created by the total liberty the students had in their choice of professors, subjects, timetable and level of courses. He wanted to rationalise the teaching in establishing a regulation for the schools. As an experienced pedagogue, he advised a change of the manuals, suggesting books that were more accessible to the students and adapted to their needs. This call did not entail any reactions in the clerical milieu. By contrast, a few months before, Muhsin Sharâra had triggered the anger of the conservatives in Najaf, to the point where he was declared an "infidel" by some mujtahid. Muhsin Sharâra belonged to a group of young clerics issued from the great families of science in Jabal 'Âmil who were achieving their studies in the religious schools of Najaf. In 1925 they were joined by Iraqis 5 in an association called al-Shabîba al-'âmiliyya alnajafiyya ('Âmilî-najafî youth). Among these young clerics, we can name 'Alî al-Zayn, Hâshim al-Amîn, Muhammad and Muhsin Sharâra. These young clerics called for a renewal of literature and in general, professed modern ideas. Several among them will later on drop the turban and embrace communism. 6 That was not the case for Muhsin Sharâra.

In 1928, he had already a reputation in Najaf: literary circles discussing "avantgarde" ideas were meeting at his place; he had also followed English and mathematics courses in parallel to his religious curriculum. Moreover, he supported the reforms of the rituals of 'Âshûrâ' called for by Muhsin al-Amîn in Damascus and Mahdî al-Qazwînî (d 1939) in Basra. 7 During the summer of 1928, he published a series of three articles in al-'Irfân where he called for a recast of the teaching system and the coming of a shiite Muhammad 'Abduh to start it. 8 In brief, it was also a call for rationalising teaching and adapting it to the modern times: thus the necessity to introduce modern sciences like sociology, psychology, foreign languages and the comparative study of religions.

The religious circles of Najaf were divided: certain accused Muhsin Sharâra, others defended him and started arguing for the same cause. At the beginning of the 1930s, a debate started: the Iraqi Ja'far al-Khalîlî expressed himself in the magazine al-Hâtif, in addition to 'Âmilî clerics such as Husayn Muruwwa, Muhammad Sharâra, or Muhammad Hasan al-Sûrî. Then it was 'Alî al-Zayn who, in South-Lebanon, called for a reform of the schools in Najaf: first, in 1937, in a Cairo magazine 9 , then in 1939, in al- 'Irfân. [START_REF]Bawâdir al-islâh fî jâmi'at al-Najaf aw nahdat Kâshif al-Ghitâ[END_REF] In it he elaborated on the experience of the school founded by Muhammad Husayn Âl Kashif al-Ghitâ' who constituted the first step towards the necessary reform. For 'Alî al-Zayn, this reform went through a total reorganisation of the studies, the religious institutions and the cultural life in Najaf. His project, well-thought and plausible, remained on paper. But it did not trigger the outcry Muhsin Sharâra's project had unleashed ten years before. The mentalities had started to change.

In that same year, 1939, al-'Irfân published a letter written by Muhammad Ridâ al-Muzaffar, the founder of the association Muntadâ al-nashr. [START_REF]Letter from Muhammad Ridâ al-Muzaffar[END_REF] After fifteen years of procastinatings, Muhammad Ridâ al-Muzaffar had estimated that it was possible to open a "reformed" religious school (with programs, time-tables, classes, etc.) that taught the students until the end of the cycle traditionally known as al-sutûh. It had 150 students, amongst whom the sons of a good number of Najaf 'ulamâ' but also the sons of 'ulamâ' of Jabal 'Âmil such as Muhammad Husayn Fadl Allâh. Today Fadl Allâh says he does not remember why he left the school of Muntadâ al-nashr before the end of his schooling. 12 It is in fact because the school had closed down. The founder attempted other experiences and opened other schools clashing with the conservatives for twenty or so years.

Finally, in 1958, the association Muntadâ al-nashr opened a higher religious teaching institution, Kulliyyat al-fiqh, the diploma of which was recognised by the Iraqi State. Its functioning was copied on that of a university. Later on, Kulliyyat al-fiqh was linked to the Iraqi University as of 1974 and that until 1991, when it was abolished by the government. To the traditional religious sciences, the school added other courses such as literary criticism, English, sociology and psychology. It also gave courses of comparative usûl al-fiqh: it was the field of its first Dean, Muhammad Taqî al-Hakîm, and that of Lebanese clerics teaching there, the brothers Muhammad Mahdî and Muhammad Ja'far Shams al-Dîn. [START_REF] Al-Wâ'ilî | Hawla muntadâ al-nashr[END_REF] Kulliyyat al-fiqh was the only religious Shiite school integrated in the State educating system. In fact, as of the end of the 1950s, other religious schools opened in Najaf: they were reformed schools but contrarily to the Kulliyyat al-fiqh, they remained in the model of the hawza. They only asked for recognition from the State allowing their students to be exempted from the obligatory military service. Thus, for example, the Madrasat al-Najaf, founded in 1957 by 'Izz al-Dîn al-Jazâ'irî 14 and the Madrasat al-'ulûm al-islâmiyya, founded in 1963 in Najaf by the marja This school had 13 professors, 3 Iranians, 5 Iraqis, and 5 Lebanese, amongst who was 'Alî Makkî, who is today the spiritual leader of the shi'a in Syria (who is officially called marja' but, in fact, he is the agent of 'Alî al-Sistânî).

The purpose of these schools was mainly to renovate the contents of the curriculum: in Muhsin al-Hakîm's school they taught, for example, economy and philosophy through the works of Muhammad Bâqir al-Sadr, but also Qoranic sciences (in the tafsîr of Abû al-Qâsim al-Khû'î). 16 They wanted then to introduce at the same time modern sciences susceptible to open the students to the world and make out of them clerics capable of confronting the century, and to revive the so-called secondary sciences taught in the past at Najaf and abandoned nowadays such as astronomy, geography or medicine. In addition, without copying their functioning on profane institutions as the Kulliyyat al-fiqh, had done, these "renovated" hawzât tried to organise the teaching and to guide the students. Those were not free anymore to choose their courses as they were in the traditional system.

Even though the Kulliyyat al-fiqh and other new schools existed in the hawza, strong resistance was still opposed to this type of project. Whatever lead to an organisation and a rationalisation of the teaching was often rejected. Ever since the first attempts of Muntadâ al-nashr the detractors of reform had often summarised their position in a motto which said: If science organises itself, it disperses and if sciences disperses, it organises itself. al-'ilm idhâ taba'thara inta˙ama wa idhâ inta˙ama taba'thara. 17 In other words, organisation is here considered ad harmful to science. This meant that the detractors of the reform saw in the organisation projects of the teaching system a threat to what constituted the specificity of Najaf: the freedom of the students and the independence of the teaching system vis-à-vis the State. In 1957 when the marja' Burujurdî organised an exam for the students to compete for a scholarship, only one student came to take the test. Muhammad Jawâd Mughniyya told the anecdote in al-'Irfân after having been informed of it by this student, a Lebanese. Not only there was no other candidate but the mujtahid had countered the endeavour accusing it of being a renovation (tajaddud), or even a blameable innovation (bid'a)! 18 Finally, it was the conservative trend which prevailed on the renovating current. Schools, like that of Muhsin al-Hakîm which closed in 1977, disappeared. After the Shii 14 On this school, see Muhsin Muhammad Muhsin, Min al-tanzîm al-dirâsî fî al-Najaf alashraf. ibid., This formula is a topos often mentioned in the texts on the reform of religious schools. 'Alî al-Khâqânî attributes it to the marja' Abû al-Hasan al-Isfahânî, but it is not certain that the expression is his. Cf. Shu'arâ' al-Gharî, vol. XII, Najaf, 1956, p. 459. 18 « Al-Najaf wa al-imtihân », al-'Irfân, vol. ILV, 1, pp. 22-24 (1957); see also 'Alî al-Khâqânî, Shu'arâ' al-Gharî, vol. XII, p. 484. uprising of 1991, other schools, traditional or reformist, were closed down or destroyed by the Iraqi government. Kulliyyat al-fiqh was literally confiscated: it constituted an easy prey to neutralise as it was inserted in the State apparatus. As for traditional schools, more flexible because of their organisation, they could reconstitute themselves elsewhere: that is why hawzât have increased in number around the mausoleum of Sayyida Zaynab, near Damascus.

Today in the clerical milieu, the outcome of the Kulliyyat al-fiqh experience is often seen as negative and that for several reasons. First, it is compared, explicitly or not, to the model of the traditional hawza which has proved itself. It is then clearly compared to the training that the marja' Abû al-Qâsim al-Khû'î had on his own insured: a majority of the great clerics of the Shii world today were at one time his disciples. In addition, the level of the studies is criticized. And last, the opening up to profane sciences is seen as quite relative: it is said that they were introductory conferences more than real courses.

Even the more ardent defenders of reform go back on their words. For example, Muhammad Taqî al-Hakîm who was one of the founders of Kulliyyat al-fiqh and who taught then in Baghdad at the Kulliyyat al-Dîn has declared that between the system of the traditional hawza characterised by freedom and the reformed system, characterised by modern methodology, he would adopt a median position. He based his position on his attachment to the freedom in the traditional model. 19 Other clerics of Lebanese origins have given me similar opinions.

True, freedom (hurriyya) leads to anarchy (fawdâ), so much criticised by the reformists. It is clear that I have to justify my translation of (fawdâ) by anarchy. The word, in Arabic, belongs in fact almost to the same semantic field as anarchy. In both cases, for the common meaning anarchy-fawdâ is first disorder but etymologically speaking, it is the lack of command. This etymology leads us to the militant understanding of the concept of anarchy, summarised in the well-known slogan: anarchy is order without power. In addition, in Shii clerical milieus, they speak of organised anarchy, al-fawdâ al-munazzamma, i.e. a willed disorder. This is not surprising since it is the guarantee of several components of the specificity of higher Shii religious education, among which elitism, meritocracy, and independence vis-à-vis the State. The debate goes then beyond the antagonism between old and new or renewed and between tradition and modernity. Nevertheless, there are clerics who refuse to be duped by this apologetic discourse on freedom and disorder. Hence, Hânî Fahs believes it is a primary freedom (bidâ'iyya) which necessitates being elaborated and civilised (tahdîr); for this cleric, an understanding of the democracy of education is a must. 20 The debate is not yet ended, even if we witness a tendency to go back to the traditional model of the hawza but the model has more or less been reformed as far the content of the teaching and the organisation of the studies.

In Lebanon, two mujtahid share the politico-religious leadership: Muhammad Mahdî Shams al-Dîn, president of the Supreme Shi'a Council and Muhammad Husayn Fadl Allâh, who is seen as a marja' by some believers. The two clerics project a modernist image and defend their own conceptions of tajdîd. Each runs or supervises hawzât of the traditional type in Lebanon and in al-Sayyida Zaynab. Muhammad Mahdî Shams al-Dîn, a partisan of tajdîd, seems to have encountered resistance, from his entourage, to introduce it in religious schools. However he founded a university in Beirut, al-Jâmi'a al-islâmiyya, where diverse disciplines are taught.

Muhammad Husayn Fadl Allâh says he is very attached to the hawza system and to its "spirit of ijtihâd". According to him, the hawza should not be transformed into a university but it should be renovated by introducing modern sciences and by organising it without damaging the spirit of liberty which prevails in it. He explains: « There is a trend which considers that the method of the hawza, which leaves the student free, to be as far as pedagogy is concerned, the most modern method. »21 In other words, Muhammad Husayn Fadl Allâh suggests that on these questions, Islamic tradition has anticipated the development of modernity.

4

  Muhsin al-Amîn, Autobiographie d'un clerc chiite du Jabal 'Âmil, translation and annotations by Sabrina Mervin and Haïtham al-Amin, Damascus, IFEAD, p. 110-111. 5 'Abd al-Razzâq Muhyî al-Dîn, Sâlih al-Ja'farî Âl Kâshif al-Ghitâ', Muhammad Sâlih Bahr al-'Ulûm. 6 Cf. Sabrina Mervin, Un réformisme chiite, chapter V. 7 Cf. Werner Ende, « From Revolt to Resignation: The Life of Shaykh Muhsin Sharâra », pp. 68-69; Sabrina Mervin, ibid.8 "Bayna al-fawdâ wa al-ta'lîm al-sahîh" (Between the disorder and the correct teaching), al-'Irfân, vol. XVI, 1, « Al-ijtihâd lâ yazkû ma'a al-fawdâ », al-Risâla (Cairo), 25/10/1937, p. 1 734.

« Nazra fî al-madâris al-dîniyya » (A point of view on religious schools), al-'Irfân, vol. I, pp. 587-591. Sadr al-Dîn al-Sadr (1882-1953) regularly sent articles to al-'Irfân from Karbalâ', where he resided; this one was signed S. N.

Muhsin al-Amîn, « Islâh al-madâris », Ma'âdin al-jawâhir, vol. I, 1929, pp. 33-39.

Muhsin Muhammad Muhsin,

Correspondence of sayyid Hânî Fahs, an answer to a questionnaire I had submitted in Beirut, in April 1999.


Ruohao Zhang

Jean-Philippe Condomines

Nicolas Larrieu

Riad Chemali

Network intrusion detection system for drone fleet using both spectral analysis and robust controller / observer

Keywords: UAV, Intrusion Detection System, Robust Estimator, Spectral Analysis, Drone Ad Hoc Network

This paper proposes an hybrid method based on both a spectral traffic analysis and a robust controller / observer for anomaly estimation inside UAV networks. This method is based on both Lyapunov Krasovskii functional and dynamic behavior of Transmission Control Protocol (TCP) and User Datagram Protocol (UDP). The proposed hybrid method considers, as a preliminary step, a statistical signature of the traffic exchanged in the network. By looking up this signature in a bank of signatures, it is possible to characterize the different anomalies that can be observed in UAV networks. Consequently, the different signatures that we can process, based on the different types of intrusion we generate in the network, are used to select the accurate model for robust control estimation. This selection is conducted by choosing a specific controller / observer among a dedicated bank of models. The first statistical signature extraction of the analyzed traffic is done with a multi-fractal analysis. This solution based on wavelet analysis has been selected because it offers a wide spectral characterization of the entire traffic process. The wavelet-based analysis methodology has been widely used for the last decade for Internet traffic characterization but this is the first time that this tool has been used on a UAV ad hoc network traffic. Moreover, several research studies on network anomaly estimation have been carried out using automatic control techniques. These studies provide methods for designing both observer and command laws dedicated to time delay problems while estimating the anomaly or intrusion in the system. As a first result, the spectral analysis tool has provided clearly distinguishable signatures between the traffics with and without anomalies. Then, the designed controller / observer system has been successfully applied to some relevant practical problems such as ad hoc networks for aerial vehicles and its effectiveness is illustrated by using real traffic traces including Distributed Denial of Service (DDoS) attacks. Our first results show promising perspectives for Intrusion Detection System (IDS) in a fleet of UAVs. Indeed, different types of anomaly have been considered and they are all accurately detected by the intrusion detection process we propose in this paper.

I. INTRODUCTION

The number and diversity of applications involving Unmanned Aerial Vehicles (UAVs) are growing every year. The need to use a fleet of versatile UAVs has led to an increased interest from the network community to design algorithms for Anomaly Detection Systems (ADS) or Intrusion Detection Systems (IDS) based on TCP network. Among abnormal patterns in TCP networks [START_REF] Lakhina | Diagnosing network-wide traffic anomalies[END_REF]- [START_REF] Chandola | Anomaly detection: A survey[END_REF] such as overload, flash crowds, worms, port scans, flash crowds have the worst impact on the fleet of UAVs because they create congestion and reduce significantly the Quality of Service (QoS) of the entire network. This is the worst-case scenario for UAV certification and integration into civil airspace. Consequently, malicious anomaly detection is an important issue nowadays. In [START_REF] Chandola | Anomaly detection: A survey[END_REF] an overview is provided reviewing multiple research areas and application domains.

Network anomalies and security-related problems (such as Distributed Denial of Service (DDoS) attacks) are important issues for the detection of active security threats. A variety of tools for anomaly detection are principally based on data packet signature. This behavior is known to be very effective against well-known DDoS attacks. However, this mechanism is inefficient when a new type of attack is performed. For this reason, we outline in this paper a new type of IDS able to detect different types of DDoS. The proposed IDS is a two-step process (see Figure 1 for details). The first step is dedicated to traffic characterization. Its objective is to get a specific signature of the traffic we want to analyze. These different signatures are used to automatically select the different controller / observer models used in the second step of the intrusion detection process. This approach has the major advantage that it is not associated with a specific type of attack. Any attacks which do not follow the initial model can be analyzed, detected and managed. Consequently, the security and performances of the entire network can be improved. This traffic estimation is performed thanks to a statistical signature of the traffic exchanged in the network. This signature provides us an unique identification of the current traffic. By looking up this signature in a bank of signatures, it is possible to characterize the different anomalies that can be observed in UAV networks. Consequently, the different signatures that we can process, based on the different types of intrusion we generate in the network, are used to select the accurate model for robust control estimation. This selection is performed by choosing a specific controller / observer among a dedicated bank of models. The first statistical signature extraction of the analyzed traffic is done with a multi-fractal analysis. This solution, based on wavelet analysis, has been selected because it offers a wide spectral characterization of the entire traffic process. Moreover, this analysis methodology has been widely used for the last decade for Internet traffic characterization but this is the first time that this tool has been 1 used on a UAV ad hoc network traffic. The contribution of this paper is to propose a new hybrid method which is able to detect traffic anomalies (i.e. DDoS). This algorithm has been designed and tested in real traffic conditions. Indeed, the Simulink design of our new IDS process and its theoretical evaluation have been faced with real traffic traces. These traces have been generated using a hybrid UAV network simulator. Consequently, the validation of the theoretical estimator is improved by testing its performances faced with real DDoS attacks, real UAV trajectories, real UAV background traffic, and real UAV fleet topology. Guided by the Lyapunov theory, we propose a new design to define all correction terms associated with time delay linear statespace representation of TCP model. Initial results for Intrusion Detection System (IDS) in a fleet of UAVs are promising. Indeed, different types of anomaly have been considered and they are all accurately detected by the intrusion detection process we propose in this paper.

In the sequel, Section 2 presents the theoretical background of our proposed controller / observer system and the state of the art of characterization tools described in the literature to extract network traffic signatures. Section 3 presents the basics of the characterization and the modeling adopted to tackle the time delay linear estimation problem of determining the state vector components of a fluid-flow model fitted out with a TCP model. Section 3 also introduces the principles of our IDS methodology which combines spectral analysis and traffic reconstruction. Finally, Section 4 gathers all the results from the validation tests performed on both steps.

II. RELATED WORK

The intrusion detection methodology proposed in this paper is the result of a collaboration between two scientific areas. The first one is related to traffic characterization. It uses spectral analysis in order to generate a specific traffic signature depending on the type of attacks we want to detect. The second is related to automatic control methods applied for traffic reconstruction. It uses robust controller / observer methods to analyze the traffic and rebuild its characteristics and behavior.

In the next subsections, we will summarize the latest research for these two specific scientific fields.

A. Spectral analysis for traffic characterization

Several research studies have been conducted for traffic characterization using spectral analysis. One of the most consistent is [START_REF] Borgnat | Seven Years and One Day: Sketching the Evolution of Internet Traffic[END_REF]. The authors have demonstrated how Long Range Dependence (LRD) can be an efficient parameter to quantify the level of variability of Internet traffic. They have developed a specific method (including a Matlab toolbox) to process data traffic. This process uses wavelet analysis (see [START_REF] Abry | Long-range Dependence: Revisiting Aggregation with Wavelets[END_REF] for details) which is an efficient tool to obtain the variability level of any data series for different time scales and different moments of analysis. In this paper, we will use an enhanced version of the method introduced in [START_REF] Abry | Long-range Dependence: Revisiting Aggregation with Wavelets[END_REF] developed by H. Wendt more recently called Wavelet Leader Multi-fractal (WLM) analysis (see [START_REF] Wendt | Contributions of Wavelet Leaders and Bootstrap to Multifractal Analysis: Images, Estimation Performance, Dependence Structure and Vanishing Moments. Confidence Intervals and Hypothesis Tests[END_REF]- [START_REF] Wendt | Wavelet leaders and bootstrap for multifractal analysis of images[END_REF] for details).

B. Robust controller / observer for traffic reconstruction

Exploiting the capabilities of observers or estimators allows us, by generating consolidated signals, to extend the way malicious intrusion can be controlled while enhancing the intrinsic flight handling qualities of a fleet of UAVs. Among the non-linear methods [START_REF] Fliess | Advances in Communication Control Networks[END_REF] described in the literature, the Super-Twisting Algorithm (STA) [START_REF] Rahme | Sliding mode observer for anomaly detection in TCP/AQM networks[END_REF]- [START_REF] Rahme | Sliding Modes for Anomaly Observation in TCP Networks: From Theory to Practice[END_REF] is the most widely used for chattering avoidance while detecting anomalies. Its principles rely firstly on the non-linear fluid model applied on TCP dynamics and secondly on sliding modes [START_REF] Floquet | On sliding mode observers for systems with unknown inputs[END_REF] which are often used to design robust non-linear observers or control laws. Unfortunately, building upon this peculiar observer provides for bounded input-bounded state (BIBS), finite-time stability only [START_REF] Edwards | Advances in Variable Structure and Sliding Mode Control[END_REF]. Consequently, this statement restricts the application of this observer to the class of the systems for which the upper bound of the initial condition might be estimated in advance. Such an approach can be very nonsystematic for complex dynamic systems such as the TCP model for a fleet of UAVs.

Another relevant method proposed in the literature is based on time delay linear state estimation. Such an approach [START_REF] Ariba | Traffic monitoring in transmission control protocol/active queue management networks through a time-delay observer[END_REF] draws on both Lyapunov Krasovskii functional and dynamic behavior of TCP/AQM (Transmission Control protocol/ Active Queue Management) to use a Luenberger observer to cope with anomaly detection. An Active Queue Management consists of adjusting data flow rates sent by the UAV through the network. The principle consists of dropping (or marking when the ECN (Explicit Congestion Notification) [START_REF] Ramakrishnan | A proposal to add explicit congestion notifi-cation (ecn) to ip[END_REF] option is enabled) some packets before the buffer saturates. Consequently, the estimator must be associated with a robust AQM in order to perform its diagnosis. The study of congestion control in a time delay system framework is not new and has been successfully demonstrated in [START_REF] Chen | Design of robust active queue management controllers for a class of TCP communication networks[END_REF]- [START_REF] Kim | Design of feedback controls supporting TCP based on the state space approach[END_REF]. A relevant constructive algorithm [START_REF] Ariba | Design and performance evaluation of a state-space based AQM[END_REF] has been proposed.

III. INTRUSION DETECTION METHODOLOGY

Our methodology introduced in this section is a two-step process (as shown in Figure 1). The first step is dedicated to traffic characterization. Its objective is to get a specific signature of the traffic we want to analyze. We will see in Section IV that we are able to obtain two completely different attack signatures according to Wavelet Leader Multifractal analysis (WLM). These different signatures are used to automatically select the different controller / observer models used in the second step of the intrusion detection process.

A. Step 1: spectral analysis-based traffic characterization

The WLM analysis is used to quantify the variability of any time series (in this paper we focus on network traffic) we want to characterize. This method has the advantage of capturing the complexity of traffic for different time scales and different moments of analysis. This process produces a graphical result (called a spectral signature) which is used to find the difference between legitimate traffic and traffic which contains an attack.

Based on the WLM methodology we can quantify the variability of any time series according to two complementary parameters: the time scale and the moment of analysis. Time scale allows us to see any repetition in the process over time. Moment of analysis allows us to analyze traffic data in different spectral representations. This second metric quantifies the variation of the traffic according to, for instance, q = 1 (average), q = 2 (variance) and so on.

An example of spectral signature for regular traffic (i.e. not containing any attacks) is shown in Figure 2. This figure represents the spectral characteristics of the data according to the time scale of analysis (i.e. the granularity parameter) and the moment of observation. We will illustrate in section IV how this signature can be different according to the type of attack we wish to analyze and detect. There is an initial theoretical assumption to verify each time you want to use the WLM method on any specific time series. Indeed, any data series needs to verify scale invariance in order to justify the self-similarity feature. Computer network traffic naturally exhibits scale invariance property throughout different time scales as demonstrated in [START_REF] Fontugne | Scaling in Internet Traffic: A 14 Year and 3 Day Longitudinal Study, With Multiscale Analyses and Random Projections[END_REF]. Fig. 2. Example of spectral signature using WLM method These differences can be easily quantified and analyzed with analytic methods such as curve similarity score (an example of edge matching algorithm is given in Section IV). Furthermore, by comparing the observed signature with a bank of signatures of known traffics, we will then be able to automatically select the different controller / observer models used in the second step of the intrusion detection process. This is the topic of the next subsection where we will describe the automatic control modeling we have performed based on an controller / observer robust estimation.

B. Step 2: controller / observer-based robust estimation

In order to tackle a wide range of applications, various implementations of TCP models in terms of assumptions and numerical techniques [START_REF] Low | Internet Congestion Control[END_REF]- [START_REF] Tarbouriech | Advances in communication Control Networks[END_REF] exist. TCP network is commonly represented using a linearized fluid-flow model [START_REF] Low | Internet Congestion Control[END_REF] associated with our network topology. In this paper, the topology consists of N TCP sources, with the same propagation delay connected to a destination node through a router.

This simple topology is due to :

1) The high complexity behavior of a fleet of UAVs in which each UAV can be sender, receiver and router; 2) The difficulty for such systems to derive a reliable and representative network modeling from scratch.

The bottleneck link is shared by N flows and TCP applies the congestion avoidance algorithm described in [START_REF] Jacobson | Congestion avoidance and control[END_REF]. To implement an Intrusion Detection System (IDS) according to the network topology presented previously, it is necessary to use, if possible, additional instruments (e.g. probability of packet, queue of the router buffer) and linear / non-linear estimation algorithms. The estimation algorithm makes use of the queue at the router buffer which delivers a scalar q. Assuming a continuous flow, the behavior of our topology network can be represented mathematically as follows:

M s      Ẇ (t) = 1 τ(t) -W (t)W (t-τ(t)) 2τ(t-τ(t)) p(t -τ(t)) q(t) = W (t) τ(t) N -C + d(t) (process) y(t) = q(t) (measurement) (1)
In the first differential equation, W (t) represents the TCP window size, τ(t) the round trip time (RTT) which can be modeled using parameters associated to the network configuration C, T p as τ = q/C + T p . The latter quantity C represents the transmission capacity of the router, T p the propagation delay and N the number of TCP sessions. The variable p(t) is the marking / dropping probability of a packet and can be seen as known measured input. This quantity relies on the explicit congestion notification to regulate the queue size of the router buffer. In the second differential equation, q(t) is the queue length of the router. The malicious anomalies are modeled by an additional signal d(t) mixed with the regular traffic passing through the router and filling the buffer.

The non-linear state space representation corresponding to M s can be described in a compact form such as: ẋ = f (x, u, d) and y = h(x, u) where: x = [W T , q T ] T , u = p and y = q are the state, input and output vectors respectively. Moreover, a linearization of M s was carried out in [START_REF] Misra | Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to red[END_REF] to allow the use of traditional control theory approaches. The fluid-flow model of TCP now becomes :

δ M s            δ Ẇ (t) = -N τ 2 0 C (δW (t) + δW (t -τ(t)) -1 τ 2 0 C (δ q(t) -δ q(t -τ(t)) -τ 0 C 2 2N 2 δ p(t -τ(t)) δ q(t) = N τ 0 δW (t) -1 τ 0 δ q(t) + d(t) (2)
where δW = W -W 0 , δ q = qq 0 , δ p = pp 0 are the perturbed variables around the operating point defined by:

       d(t) = 0 Ẇ (t) = 0 ⇒ W 2 0 p 0 = 2 q(t) = 0 ⇒ W 0 = τ 0 C N τ 0 = q 0 C + T p (3)
Inspired by the theory of time delay systems [START_REF] Ariba | Traffic monitoring in transmission control protocol/active queue management networks through a time-delay observer[END_REF], the dynamics of the queue and the congestion window are modeled to address delay issues. Indeed time delay is an intrinsic phenomenon in networks whose control should improve the precision of δ M s . The idea is to exploit the linearized TCP fluid-model within a time delay framework as follows where δ x(t) = [δW (t) δ q(t)] T is the state vector and δ u(t) = δ p(t) the input:

δ M s    δ ẋ(t) = Aδ x(t) + A d δ x(t -τ(t)) + Bδ u(t -τ(t)) + B d d(t) y(t) = 0 1 δ x(t) (4) with            A = -N τ 2 0 C 1 τ 2 0 C N τ 0 -1 τ 0 A d = -N τ 2 0 C -1 τ 2 0 C 0 0 (5)
and

         B = -C 2 τ 0 2N 2 0 B d = 0 1 (6)
Based on such a linearized model, formulated in the general form of a time delay system, it is possible to design both AQM and estimator by using the Lyapunov Krasovskii method [START_REF] Gu | Stability of Time-Delay Systems[END_REF] which is an extension of the traditional Lyapunov theory.

Various AQM mechanisms exist in the literature such as Random Early Detection [START_REF] Floyd | Random early detection gateways for congestion avoidance[END_REF] (RED), Random Early Marking [START_REF] Athuraliya | An enhanced random early marking algorithm for internet flow control[END_REF] (REM) and more recently using control theory (proportional and proportional integral controller [START_REF] Hollot | Analysis and design of controllers for AQM routers supporting TCP flows[END_REF] or state feedback controller [START_REF] Ariba | Congestion control of a single router with an active queue management[END_REF]). As shown in Figure 3 the control law stabilizes the TCP network (queue lengths and rates) to a desired equilibrium (W 0 , τ 0 , q 0 ) in spite of the presence of some non-responsive traffics, ensuring then a certain level of quality of service (QoS). A major issue in the certifying of a fleet of UAVs is to estimate the malicious intrusion while taking into account a level of QoS (i.e., the drop probability p(t)). This is why the non-modeled malicious traffic d(t) needs to be estimated. The estimator has to be designed in addition to an AQM. Thus, in [START_REF] Miquel | Design of a robust Controller/Observer for TCP/AQM network: First application to intrusion detection systems for drone fleet[END_REF] we proposed a robust controller / observer for IDS by solving an LMI criteria. In order to validate our new traffic estimator in real traffic conditions, we use a hybrid experimental system to take advantage of the low cost of a simulation while still obtaining the accuracy of a real protocol stack. We have been using virtual machine implementations to deal with the entire complexity of the Linux operating system. The traces used to generate UAV mobility patterns were extracted from real traces so that physical related factors could be as realistic as possible. The system we have been using to evaluate protocols is divided into several parts. It includes a set of tools that can deal with several scenarios: a hypervisor to run the virtual machines, measurement tools and a framework to allow virtual machines to communicate through a virtual wireless medium. We chose to use VirtualBox as a virtualisation tool because it is an easy-to-use and efficient hypervisor. The virtualized system is a 12.04 version Ubuntu, working with the 2.6.38 version of the Linux kernel. Our testbed architecture uses a Virtualmesh framework. It is a framework that interfaces a Linux-based system with an OMNeT++ simulation. OMNeT++ is a powerful network simulator which simulates several systems and normalized protocols. An illustration of this system is shown in Figure 4. In [START_REF] Maxa | Emulation-Based Performance Evaluation of Routing Protocols for Uaanets[END_REF], more details about this hybrid tool can be found.

IV. INTRUSION DETECTION SYSTEM VALIDATION

A. UAV ad hoc network hybrid platform

The main advantage of using such a hybrid simulator is to extract any characteristics from the simulation and to inject them into the Simulink design directly. The theoretical model is then used under real traffic conditions and not only theoretical stimulus. The advantage of such an evaluation is to take into account the huge variability and complexity of real traffic. Consequently, we have been able to generate DDoS between the different virtual machines by taking into account the exact UAV environment of the drone mission we have considered in this research. First, we captured the network traffic generated (both regular traffic and the DDoS traffic) and then, we injected this traffic into the Simulink design.

B. Traffic characterization results for intrusion detection system calibration

The objective of this analysis is to create a bank of signature, in order to extract a specific pattern for each type of intrusion and to analyze the differences between normal traffic without anomaly and traffic with anomaly. In order to obtain traffic signature in three dimensions (3D), we measured the scaling function with respect to the statistic moments (q), which can take positive or negative values, and also with respect to the granularity of the traffic. We now illustrate the results obtained by our multi-fractal analysis (WLM) method on the basis of the hybrid UAV network simulator. As we stated previously, the normal TCP traffic is generated by 5 TCP sources generating long-life TCP flows to a receiver through a router with a link capacity C = 1250 packets/s (which is equivalent to 3 Mbit/s), and T p = 30ms the propagation delay. We will analyze the traffic in the face of different DDoS (Distributed Denial of Service) attacks. Two types of DDoS attacks are considered: a Constant Flash-Crowd (CFC) and a Progressive Flash-Crowd (PFC) attack. These anomalies have been generated using the HPing3 tool. This software is run on the hacker node (see Figure 5 for details about the network topology which has been considered) and can run different types of attack but mainly flooding attacks for our experiments. Indeed, in our scenario, HPing3 exchanges thousands of small TCP flows in order to generate a SYN flood attack on the receiver node. The resulting malicious traffic is much more significant than the regular traffic. Figure 6 shows the features of the traffic which has been generated through the hybrid network simulation tool. This traffic includes 4 different CFCs of the same magnitude but with different durations and, consequently, different impacts for the UAV network.

1) Attack signature for traffic with Constant Flash-Crowd CFC: We consider in this section, the CFC attacks which have been generated. The objective is to obtain a dedicated spectral analysis for this specific type of DDoS attack. This spectral analysis (based on scaling function characterization) provides a specific attack signature for each type of network traffic. Consequently, in Figures 7 and8, a comparison of the signatures of the regular traffic and traffic including CFC attacks is illustrated. The obtained results show a large Fig. 5. Considered topology variation in the scaling function ζ (q), especially in the case of negative moments for traffic including attacks. We observe that the scaling function (for the negative moment q = -5) reaches values ζ (q) ≤ -19 for traffic including DDoS attacks while it does not exceed the value of ζ (q) ≤ -13 for normal traffic.

2) Attack signature for traffic with Progressive Flash-Crowd PFC: In a second time, the network is exposed to PFC attacks (see Figure 9 for details about the traffic profile of this DDoS). The comparison between traffic with and without attack shows that the variation of the scaling function ζ (q) is always visually noteworthy in negative statistic moments (here q = -5). Indeed, we can see in Figure 10 the value of the scale function is between ζ (q) ≥ -17 and ζ (q) ≤ 6 for regular traffic. On the contrary, in the case of traffic including PFC attack, the values ζ (q) are between -19 ≤ ζ (q) ≤ 5 (see Figure 11 for details).

3) Discussion on traffic signature characterization: These characterization results show that it is possible to extract dedicated signature for traffic with and without anomalies. Moreover, the spectral analysis provides different signatures for each type of DDoS. Indeed, the scaling function is not the same for DDoS CFC and PFC. Consequently, we can build a selector according to each specific spectral signature which will be able to select automatically a specific controller / observer for the IDS tool. However, this automation process is not completely performed at this time by our intrusion detection system algorithm. Indeed, these two steps (characterization and anomaly reconstruction) are performed separately. It is worth noting that the whole process is considered as a workin-progress task. However, in the next section, we present some preliminary results for WLM signature comparison. We used a edge matching algorithm to be able to quantitatively find a difference between two different signatures generated with and without DDoS attacks.

C. WLM signature comparison results

Before the acquisition of the aforementioned bank of signatures, it is important to tune the WLM method's variables including moments and time scale to obtain the optimum sensitivity. One way to quantify the sensitivity is to measure how much difference there is between signatures with and without different attacks. In order to compare signatures one by one, we need to use a reliable and performant algorithm for solving equivalence problems. Among fundamental methods, three-dimensional edge matching method introduced in [START_REF] Grim | Automatic Reassembly of Three-Dimensional Jigsaw Puzzles[END_REF] appears to be the most suitable signal processing methodology for classifying 3D curves.

This method, which was designed to help solving 3D Jigsaw Puzzle problems, allows to compare two curves in a three dimensional space and returns a value normalized between 0 and 1 called "similarity score". Let C and C two discretized curves. A "similarity score" is defined as p(C , C ) ∈ [0, 1], such that if C and C are congruent then p = 0 , and the closer p gets to 1 the more C and C are different. In our case of having multiple signature curves at different moments of analysis, we simply connect the curves end-to-end and consider it as one three-dimensional curve and perform the similarity score calculation. This method has been tested and validated with signatures acquired from our UAV ad hoc network hybrid platform generating communications from one drone to one host PC acting as Ground Control Station (GCS). This experimental scenario was a two-step process. In the first step, we generated only regular drone-to-GCS traffic, and in the second step, we generated regular drone-to-GCS traffic plus CFC flooding attack to GCS.

We took some samples of the resulted signatures during the test and plot them all together as shown in Figure 12 and 13. As noticed in the previous section, it can be observed that the signatures are visually very different when the GCS is attacked by CFC flooding attacks. With this specific CFC flooding attack only on the GCS the shape of the signature is also modified compared to the original CFC flooding attack (see Figure 9 for details). As shown in Figure 14, the curve similarity score has clearly distinguished the differences in the signatures when each of the 6 attacks happened during our test.

Although it can be observed in Figure 14, that during the 3 rd , 4 th and 5 th attack, the similarity score experienced two peaks and form a valley shape waveform during the attack as if there are two attacks. This is caused by prolonged attacks which saturated the reception buffer of this experimental IDS design.

In this case, because the buffer is saturated, the IDS does not see any difference in the incoming traffic and therefore resulted in signature which resembles a normal traffic with only small variations that are not significant in terms similarity score analysis. Therefore we have successfully demonstrated that how the first step of our newly purposed IDS can distinguish network traffic with and without CFC flooding, and how the variation of some parameters such as the test duration, which translates into the size of reception buffer, will influence the performance of this implementation. With an addition of an analytical method such as the curve similarity score method mention W 0 15 packets q 0 37.5 packets/s p 0 0.0089 R 0 0.06 s TABLE I EQUILIBRIUM POINT in this section, it is possible to achieve an automatic detection of anomalies. But the curve similarity score method has work exceptionally well in our test case, which has led us to think we can actually implement a similar mechanism in our IDS. Because an actual pattern recognition algorithm is expensive in terms of computation power, it is less efficient to perform such calculation on all signatures we obtained in a drone network. Consequently, a simple and algorithmic efficient curve matching method can be implemented on individual nodes in a distributed drone network, and it can act as an alarm and a trigger to the command center/ground station to notify the operators about the anomalies. Then, decisions can be made on, whether or not, to further investigate the anomalies with more powerful tools such as pattern recognition and anomaly reconstruction.

In the next section, we are going to present additional results related to the second step of this process: anomaly reconstruction and detection using robust controller / observer.

D. Anomaly reconstruction results

We now illustrate the performances reached by the developed controller / observer on the basis of our hybrid UAV network simulator. To conduct such a task, we define in Table I the values of the congestion window size and the router queue length at the equilibrium point of the system: W 0 and q 0 . They have been selected by considering the mean value for N sessions around which W (t) and q(t) oscillate respectively. The proposed observer has been tested with the state feedback AQM in [START_REF] Ariba | Traffic monitoring in transmission control protocol/active queue management networks through a time-delay observer[END_REF] and observer gains are L = [1.2338538, 5.2445906, 2.24 * e + 3, 1.94 * e + 2]. This observer is synthesized to construct the state of CFC and PFC attacks.

1) Attack reconstruction for traffic with constant flashcrowd (CFC): Figures 15, 16 and 17 illustrate a typical realization of traffic including CFC attack which can be detected by our time-delay linear observer. This CFC attack generated by our hybrid UAV network simulator has been injected into Simulink to compare our IDS model to the real traffic traces. This is depicted in Figure 17 where regular traffic is around 30 pkt/s when, for the malicious traffic, the throughput is increased to 150 pkt/s. Moreover, the real traffic (blue) and estimated intrusion (red) are plotted on the same figure for comparison purposes. Figure 16 shows the time response of the estimation queue q(t) calculated by the time-delay linear observer method. As expected, the queue is stabilized above the desired level and the intrusion does not affect the different steady states of the system. Figure 15 shows the time response of the TCP congestion windows W (t). As expected, the TCP congestion window evolution is reconstructed with great accuracy. 2) Attack reconstruction for traffic with progressive flashcrowd (PFC): In this section, we consider the PFC attack generated by our hybrid UAV network simulator. As previously mentioned, these attacks have been injected into Simulink to compare our IDS model with the real traffic traces. This is depicted in Figure 20 where regular traffic is around 40 pkt/s; while for the malicious traffic, the throughput is increased slowly to reach values close to 140 pkt/s. We can observe that the estimator is able to reproduce the shape of the anomaly quickly and make an accurate distinction between the normal traffic and the intrusion traffic (see Figure 20 for details). In addition to this, our controller / observer is able to estimate the states of system W (t) and q(t) with accuracy (see Figures 18 and19 for details). 3) Discussion on traffic reconstruction performances: These results look promising given that the estimator simulated with Matlab Simulink is able to detect the different intrusions rapidly and with an accurate threshold. The delay in the detection is negligible and the estimator can make an accurate distinction between legitimate traffic and traffic with intrusions. Consequently, this is a first promising result for intrusion detection system design applied to drone fleet network. In this paper, we have explained how a new hybrid method can improve intrusion detection systems in the specific context of drone fleet. We have combined the use of a linear controller / observer and spectral analysis of the traffic. Based on a wavelet analysis, this traffic characterization process provides a preliminary level of knowledge about which type of intrusion is performed in the network. Based on this information, our linear controller / observer can be tuned and can perform traffic reconstruction in order to estimate accurately the level of attack observed in the network. Consequently, our design methodology provides a simple way to construct and instantiate our gain matrices for both the AQM controller and the observer. This approach has given us promising results with a simple topology within a time-delay framework. Indeed, two different types of anomaly have been considered in this paper (constant and progressive flash-crowds) and they are both accurately detected by the intrusion detection process proposed in Section 3 and validated in Section 4.

In our future work, we intend to identify several research perspectives. First of all, we plan to propose an evolution of the modeling in the drone fleet network. This should include different types of traffic (UDP and TCP for instance) and also take into account network mobility. Moreover, we plan to analyze different types of attack: not only DDoS but also intrusion where the traffic generated in the network is significantly lower and therefore, more difficult to detect. A proposed solution would be to consider one bank of models in order to detect, with different signatures, DDoS and other types of attack. Finally, we plan to investigate a way to implement and test this new generation intrusion detection system operating in a real environment. To address this last objective, we would like to consider real experiments with real UAVs. Each UAV could embed this specific bank of models. By conducting a collaborative mission, in the context of one UAV fleet, we will be able to test and validate the theoretical estimators which, until now, have only been studied in simulation. We plan to perform this part of the research in the near future in the recently constructed UAV flight arena in ENAC, Toulouse, France.

Fig. 1 .

 1 Fig. 1. General framework of the proposed IDS system

Fig. 3 .

 3 Fig. 3. IDS design

Fig. 4 .

 4 Fig. 4. Testbed implementation

Fig. 6 .Fig. 7 .

 67 Fig. 6. Real UAV traffic profile with DDoS attacks (CFC)

Fig. 13 .Fig. 14 .

 1314 Fig. 13. Scaling function for traffic with CFC anomaly

Fig. 15 .

 15 Fig. 15. TCP congestion window W(t) -CFC attack

Fig. 18 .

 18 Fig. 18. TCP congestion window W(t) -PFC attack

Fig. 20 .

 20 Fig. 20. Estimation with real traffic replay -PFC attack V. CONCLUSION AND FUTURE WORK