Sonia Rezk
email: rezksonia@yahoo.fr

Cédric Join

Sadok El Asmi

Mohamed Dogui

Mohamed Hédi Bedoui

Frequency Change-Point Detection in physiological Signals : an Algebraic Approach

Keywords: Abrupt change, differential algebra, non-commutative algebra, operational calculus, EEG, epileptic seizure, ECG, QRS complex

This paper considers the problem of change-point detection for noisy data. Estimation of signal frequency content relies on differential algebra and non-commutative algebra together with operational calculus. We adapt this approach to the study of changes that may be observed in EEG signal dynamics during epileptic seizure and in ECG signal during the occurrence of a QRS complex. The correlation with frequency change is what this idea is based on. The interest of our estimator is firstly illustrated according to several academic examples. Then, the method is applied on real physiological signals to detect abrupt frequency changes.

Introduction

For some years, the techniques of automatic, control, estimation together with diagnosis have always been applied more frequently in biology as well in medicine. In these fields, it is either a question of facilitating the decision-making of the specialist by highlighting particular phenomena or by assuring a control constantly. In this paper, we are interested in the problem relying on automatic detection of changes that occur in physiological signals such as the epileptic seizure in EEG signal and the occurrence of QRS complex in ECG signal. In the analysis of epileptic seizures, it has long been noted that the frequency content often changes during seizures. 'In the most fundamental terms, electrographic seizure activity is manifested by a sequential change in frequency and amplitude that is distinct from non-seizure activity and in most instances it is also distinct from artifacts'(Gabor et al. [START_REF] Aj | Automated seizures detection using a self-organizing neural network[END_REF]). The two main aspects to consider are the following: -the frequency aspect, -sequential change 1 . Nowadays, the major part of the proposed solutions is inherent to representations and time-frequency studies of signal [START_REF] Adeli | Analysis of records in an epileptic patient using wavelet transform[END_REF][START_REF] Senhadji | Epileptic transient detection: wavelets and time-frequency approches[END_REF][START_REF] Tafti | Analyse numérique du sommeil[END_REF][START_REF] Yamaguchi | Fourier and wavelet analyses of normal and epileptic electroencephalogram (EEG)[END_REF]. The independent components analysis is also a recent method applied to the epileptic EEG [START_REF] Hoeve | Detecting epileptic seizure activity in the EEG by Independent Component Analysis[END_REF][START_REF] Jing | A Novel Constrained Topographic Independent Component Analysis for Separation of Epileptic Seizure Signals[END_REF]. In the electrocardiogram (ECG), the most relevant tasks are the detection and the characterization of the QRS complex. As a result much information about the current state of the heart can be obtained. QRS detection is difficult not only because of the physiological variability of the QRS complexes but also due to the various types of noise that can be presented in ECG signal. Many QRS detection schemata are described in the literature [START_REF] Pan | A real-time QRS detection algorithm[END_REF] and are still being proposed [START_REF] Burke | Wavelet based analysis and characterization of ECG signal[END_REF]. Many practical problems arising from signal processing can be modeled with the aid of parametric models in which the parameters are subject to abrupt changes at unknown time instances. By abrupt changes, we mean changes in characteristics that occur very fast with respect to the sampling period, if not instantaneously. The detection of abrupt changes refers to tools that help us decide whether such change occurred in characteristics of considered object [START_REF] Basseville | Detection of Abrupt Changes: Theory and Application[END_REF]. The detection of abrupt changes in a signal is also the subject of an abundant literature [START_REF] Basseville | Detection of Abrupt Changes: Theory and Application[END_REF][START_REF] Brodsky | Nonparametric Methods in Change-Point Problems[END_REF][START_REF] Brodsky | Non-parametric statistical diagnosis: Problems and Methods[END_REF][START_REF] Csörgö | Limit Theorems in Change-Point Analysis[END_REF][START_REF] Mboup | A delay estimation aproach to change-point detection[END_REF] 2 . In addition, identifying a signal frequency in continuous time is a very hard challenge using classical linear analysis. That is why we choose to use a new tool that is based on differential algebra, non commutative algebra and Mikusiński operational calculus [START_REF] Mikusiński | Operational Calculus[END_REF][START_REF] Mikusiński | Operational Calculus[END_REF]. Our algebraic approach for the abrupt frequency estimation changes had never been used in the analysis of the physiological signals. As a contribution, we suggest to improve the detection of abrupt changes in physiological signals by following-up the changes which reflect their appearance. The Work presented in this article aims at epileptic seizure detection in EEG and QRS complexes detection in ECG thanks to an estimation in continuous time of the signal frequency. Thus, a change-point or abrupt variation of the estimated frequency will translate a seizure occurrence in EEG or a QRS complex occurrence in ECG. This paper is organized as follows: the algebraic setting for linear identifiability is tackled in the next section. In section 3, the method is tested on academic signals built from scenarios which is elaborated with an expert describing an abrupt frequency changes. Then, the method is validated on real physiological signals recorded. A brief conclusion evokes some future perspectives.

An algebraic setting for linear identifiability

In this section we recall the recent results obtained in estimation. For further details, the reader would be referred to the following articles [9,[START_REF] Fliess | Questioning some paradigms of signal processing via concrete examples[END_REF][START_REF] Fliess | Compression différentielle de transitoires bruités[END_REF][START_REF] Fliess | Une autre vision de l'identification de signaux et systèmes[END_REF][START_REF] Fliess | Analyse et représentation de signaux transitoires: application à la compression, au débruitage et à la détection de ruptures[END_REF][START_REF] Fliess | Non-linear estimation is easy[END_REF][START_REF] Mboup | New algebraic estimation techniques in signal processing and control[END_REF][START_REF] Mboup | A revised look at numerical differentiation with an application to nonlinear feed back control[END_REF][START_REF] Mboup | Parameter estimation via differentiel algebra and operationnel calculus[END_REF].

Differential algebra

A differential ring3 , or more precisely, an ordinary differential ring, R is a commutative ring which is equipped with a single derivation, written here d ds , i.e., a map R → R such that, ∀ a, b ∈ R,

-d ds (a + b) = da ds + db ds , -d ds (ab) = da ds b + a db ds .
A differential field, or more precisely, an ordinary differential field, is a differential ring which is a field4 . A constant c ∈ R is such that d ds (c) = 0. A differential ring (resp. field) of constants is a differential ring (resp. field) whose elements are constants. A differential field extension L/R is given by two differential fields R, L, such that:

-R ⊆ L, -the restriction to R of the derivation of L is the restriction of R.

Note that R S , S ⊂ L, the differential subfield of L generated by R and S. Assume that L/R finitely generated, i.e., L = R S , where S is finite. An element ξ ∈ L is said to be differentially algebraic over R if, and only if, ξ satisfies an algebraic differential equation P (ξ, . . . , ξ (n) ) = 0, where P is polynomial over R in n + 1 indeterminate. The extension L/R is said to be differentially algebraic if, and only if, any element of L is differentially algebraic over R. The following result plays an important role: the extension L/R is differentially algebraic if, and only if, its transcendence degree is finite [START_REF] Mboup | A revised look at numerical differentiation with an application to nonlinear feed back control[END_REF]. An element of L which is not differentially algebraic over R is said to be differentially transcendental. A differentially transcendental extension L/R is an extension which is not differentially algebraic. A set {ξ ι ∈ L | ι ∈ I} is said to be differentially algebraically independent over R if, and only if, no trivial relation exists over R: Q(ξ (νι) ι ) = 0, where Q is a polynomial over R, imply: Q ≡ 0. An independent set which is maximal with respect to inclusion is called a differential transcendence basis. The cardinalities, i.e., the numbers of elements, to such bases are equal. This cardinality is the differential transcendence degree of the extension L/R. Note that this degree is 0 if, and only if, L/R is differentially algebraic.

Linear identifiability

Let k 0 be a given ground field, which is assumed to be a differential field of constants. Let k be a finite algebraic extension of k 0 (θ) where θ = (θ 1 , • • • , θ r ) is a finite set of unknown parameters. Thus, the transcendence degree of the extension k/k 0 is ≤ r. Moreover, we give to k a canonical structure of the differential field of constants. Let K/k(s) be a finitely generated differentially algebraic extension. A signal x is an element ok K.

Remark 1. The Mikusiński M, generated by Mikusiński's operators [START_REF] Mikusiński | Operational Calculus[END_REF][START_REF] Mikusiński | Operational Calculus[END_REF][START_REF] Van Der Pol | Operational Calculus Based on the Two-Sided Laplace Integral[END_REF] is a differential field with respect to the derivation d ds which corresponds to multiplication by -t. Its subfield of constants is C.

The set of linear differential operators of the form

f ini a α d α ds α , a α ∈ k 0 (s), is a commutative ring, principal left and right; it is written k 0 (s)[ d ds ].
A differential operator is said to be proper (resp. strictly proper) if, and only if, the coefficients are proper (resp. strictly proper) rational functions (we remind that rational functions are said to be (strictly) proper if, and only if, the degree of numerator is (strictly) less than the degree of denominator). It is said to be polynomial in

1 s if, and only if, a α ∈ k 0 [ 1 s ].
The parameters θ are said to be linearly identifiable5 with respect to x ∈ K if, and only if,

P    θ 1 . . . θ r    = Q (1)
where the entries of the r × r square matrix P , and the r × 1 vector Q, belong to span k0(s)[ d ds ] (1, x), and det(P) = 0.

Linear estimators

Let N/k 0 (s) be a differential field extension such that K and N are linearly disjoint over k 0 (s). A noise n, or a perturbation, is an element of N . It is said to be structured if, and only if, it is annihilated by π ∈ k 0 (s)[ d ds ], π ∈ k 0 (s): πn = 0, π = 0. If not, the noise is said to be unstructured. A signal with an additive noise is a sum x+w, where x ∈ K and w ∈ N a noise. Let y = (y 1 , . . . , y κ ), where y ı = x ı + w ı be a finite set of such noisy signal depending upon the parameters θ. If the parameters θ are linearly identifiable, then (1) becomes

P    θ 1 . . . θ r    = Q + Q ′ (2)
where the matrices P and Q are obtained from (1) by substituting y to x. The entries of the (r ×1)-vector

Q ′ belong to span k ′ (s)[ d ds ] (w),
where k ′ is the quotient field of k ⊗ ko k 1 , and w = (w 1 , . . . , w κ ).

Remark 2. In practice we will assume that an unstructured perturbation corresponds to a rapidly oscillating time-function, i.e., a high frequency signal, which may be attenuated by a low pass filter.

Assume that the components of w are structured. Multiplying both sides of (2) by △ ∈ k 0 (s)[ d ds ], leads to the following estimator:

△P    θ 1 . . . θ r    = △Q (3)
This result derives from the fact that k 0 (s)[ d ds ] is the left ideal annihilator's entries of Q ′ . Equation (3), which is independent of the noises, is called a linear estimator of unknown parameters if, and only if, det(∆P ) = 0. The estimator is said to be proper (resp. strictly proper) if, and only if, the entries of △P and △Q are (resp. strictly) proper differential operators. Multiplying both sides of (3) by a suitable proper element of k 0 (s) yields the Proposition 1. Any linear estimator may be replaced by a proper (resp. strictly proper) one.

Simple example of estimation

In order to explain the used approach, let us start with an example with a first order linear input-output system :

ẏ(t) = ay(t) + n(t) (4)
for t ≥ 0, where a is an unknown parameter to estimate and n(t) a noise corruption. This noise may be decomposed as : n(t) = n 0 (t) + γ, i.e., the sum of a constant γ representing its mean (average) value and zero-mean term n 0 (t).

Translated into the operational domain, this differential equation reads as:

sy(s) = ay(s) + y(0) + γ s + n 0 (s) (5)
where, due to the output noise, the initial condition y(0) is not necessarily well known [START_REF] Fliess | Correcteurs proportionnels-intégraux généralisés[END_REF]. The constant γ is considered as undesired perturbation, like the initial condition y(0). Note that these perturbations are easily annihilated by multiplying both sides of (5) by s and after 2 derivations with respect to s. This amounts to applying the linear differential operator:

Π = d 2 ds 2 s = s d 2 ds 2 + 2 d ds (6)
to both sides of (5). The resulting equation, given by : Figure1: First order system with online identification shows that the constant γ and the initial condition y(0) will have no effect on the estimation result.

Remark 3. Recall that : multiplication by s in operational domain, in turn, corresponds to derivation in time domain.

Implementing the linear estimator [START_REF] Csörgö | Limit Theorems in Change-Point Analysis[END_REF] in its present form is therefore not convenient : derivation amplifies the high frequency components and consequently, the noise contribution. A simple solution is obtained by making the estimator (strictly) proper. So, it satisfies to multiply both sides of ( 7) by s ν , where ν is an integer greater than or equal to the highest power of s in [START_REF] Csörgö | Limit Theorems in Change-Point Analysis[END_REF]. Here, the operators deduced from [START_REF] Csörgö | Limit Theorems in Change-Point Analysis[END_REF] are strictly proper for ν ≥ 3. Thus, we obtain the following estimator:

s -2 d 2 y ds 2 + 2s -3 dy ds a = s -1 d 2 y ds 2 + 4s -2 dy ds + 2s -3 y (8)
To obtain numerical estimate of the parameter a, it needs to express equation [START_REF] Fliess | Correcteurs proportionnels-intégraux généralisés[END_REF] in time domain, using the classical rules of operational calculus. Recall that:

the derivation d α ds α with respect to s, α ≥ 0, translates into the multiplication by (-1) α t α , -1 s α is replaced by the α th iterated time integration

t 0 tα-1 0 • • • t1 0 x(τ )dτ dt 1 • • • dt α-1
which, thanks to Cauchy rule, equals

1 (α -1)! t 0 (t -τ ) α-1 x(τ )dτ
the unstructured noises are viewed as highly fluctuating phenomena. They are attenuated by the iterated time integrals, which are simple examples of low pass filters 6 .

Finally, the estimation of the parameter a is given, as time-function by the explicit formula:

a e (t) = t 0 τ 2 -4(t -τ )τ + (t -τ ) 2 y(τ )dτ t 0 (t -τ )τ 2 -(t -τ ) 2 τ ) y(τ )dτ (9)
In Both figures 1-(b) and (d), the evaluation of the estimator is shown. The abscissa axis is graduated in number of samples and the initial condition y(0) = 0.2. In the free-noise case (n 0 (t) = 0), the estimation is practically perfect. It remains very good in the noisy case. The purpose of this paper is not to compare these results to those using classical techniques (the interested reader can always be referred to the publications previously mentioned) nevertheless, we insist, as well, on the poverty of the excitation signal.

Application to physiological signals

In order to fit our approach to physiological signals, we choose to represent these signals according to a very simple model:

y(t) = sin(ϕ 0 + ϕ 1 t) + n(t) (10)
where ϕ 1 is the angular frequency of the signal (proportional to the frequency) and ϕ 0 the phase, n(t) an unstructured perturbation. The use of such a model is justified because it doesn't represent the signal only during a very short lapse of time. The variation of the frequency content is translated by the variation of ϕ 1 . Therefore, we are interested in estimating it quickly and online. The algebraic techniques are all indicated. Keeping the continuous-time nature of the signal we readily observe that the noise-free signal x(t) = y(t) -n(t) satisfies the following linear differential equation with constant coefficient:

ẍ(t) + ϕ 2 1 x(t) = 0 (11)
In translating this equation to operational domain, we obtain :

s 2 x(s) -sx(0) -ẋ(0) + ϕ 2 1 x(s) = 0 (12)
or also in calculating initial condition

(s 2 + ϕ 2 1 ) x(s) = ϕ 1 cos ϕ 0 + s sin ϕ 0 ( 13
)
the parameter ϕ 2 1 is then linearly identifiable7 and its estimation is now described.

Taking derivative, twice, with respect to s permits to ignore structured perturbations, here are the initial conditions 2x + 4s dx ds + (s 2 + ϕ 2 1 )

d 2 x ds 2 = 0 (14)
After that, we multiply both sides by s -2 to avoid derivations with respect to time (positive power of s)

2s -3 x + 4s -2 dx ds + (s -1 + s -3 ϕ 2 1 ) d 2 x ds 2 = 0 (15)
The well-known rule of operational calculus yields to the following on-line estimator of ϕ 2 1 , i.e., a time-domain representation with no derivative but only integrations with respect to time:

ϕ 2 1e (t) = -2 t t-T ((T -τ ) 2 -4(T -τ )τ + τ 2 )x(τ )dτ t t-T (T -τ ) 2 τ 2 x(τ )dτ (16)
Let us note that the multiple integrals are transformed in simple integrals with the help of Cauchy formula. Besides, T indicates the size of sliding estimation window.

Academic example

We The second signal is distinguished from the first one from the introduction of an abrupt change in its frequency. The signal's angular frequency is defined in [0, T f ] 8 as follows:

ϕ 1 (t) = 6Π si T f 3 < t < 2T f 3 24Π otherwise
These signals are shown in figure 2.

For convenient implementation of our estimator, we introduce a sliding window in which we suppose that the model ( 10) describes the signal well. For each estimation window, we get the numerical estimation of ϕ 2 1 . Their variations on the whole length of the signal are depicted in figure 3 with T = 500 samples. In all subsequent numerical simulations the integrals are computed via the classical trapezoidal rule. Besides, the numeric estimations of the angular frequencies are Figure2: Academic signals initialized to zero at t = 0. To avoid zero-crossing of the denominator in the equation ( 16), a threshold is fixed at 10 -4 . The performance of our estimator is based on a compromise during the choice of estimation window. Indeed, the more the window is important the better the free noise is but more signal model is questionable. Figure 3 depicts angular frequency evolution of the two academic signals according to the time. We note that the estimator ( 16) has excellent capacities to estimate and pursue the frequency evolution even in the presence of noise. It also appears that the noise characteristics do not have a significant effect on the estimation. Figure3: estimated frequency of the two academic signals

EEG signals

In this section, we depict the result of using our method on EEG recording for which the clinical signs of an epileptic activity have been observed. The sampling rate is of 64 Hz. Figure 4-(a) shows one of the recordings (the measured voltage is function of the number of samples). The data contains a total of 1 minute with pre-seizure, the seizure and some of post-seizure activity. Based on the visual inspection of experimented neurologist, the seizure which translates an anomaly in the EEG signal and substitutes from the normal activity, occurs from the 5 th seconde and lasts 35 seconds. Here, the frequency estimation is used to analyze EEG signal with epileptic seizure. The aim is to find the relationship between frequency content variation of EEG signals and the pre-seizure, seizure and post seizure to detect a brain disorder such as an epilepsy. Figure 4-(b) shows the frequency variation of the EEG portion by using the estimator [START_REF] Aj | Automated seizures detection using a self-organizing neural network[END_REF]. To remove peaks which result from the zero-crossing of the estimator's denominator, the threshold is fixed at 10 -4 . Based on the hypothesis that signal's angular frequency is weak out of the critical phase, any abrupt deviation translates a seizure. In order to limit the noise effect again, we make an average of the estimated frequency value in each point in short durations segments. In figure 4-(b), the curve in solid line shows the average variations of the estimated frequency. It is also possible to filter the previous estimation with a filter of cut-off frequency w c = 0.01Hz (dotted line figure 4-(b)). However, this latter smooths the frank variations. In the set of the obtained curves, the estimator ensures the frequency changes detection translating the seizure appearance in EEG signal. Indeed, the three different stages : pre-seizure, seizure and post-seizure, could be observed by using the curves. While supervising this estimation, it is possible to localize the seizure onset and offset. Besides, this detection coincides with the expert interpretations.

ECG signals

ECG signals that we use were excerpted from the MIT-BIH Arrhythmia Database [START_REF] Mark | MIT-BIH arrythmia database directory[END_REF]. In order to depict the contribution of our approach, we choose two examples of ECG portions which cause a problem in the QRS complex detection by their forms and by the noise dominance. The first example is illustrated by the record 200. The choice of this record is based on the fact that it presents a very particular morphology which is difficult to extract the QRS complex by the existing methods. We can notice that in figure 5-(a) this recording presents on the one hand, a QRS complex reversed and an S wave completely flooded in the T wave, on the other hand, the amplitude of the T wave is superior to that of the QRS complex which makes the QRS complex detection difficult. But, the results obtained by the proposed estimator as shown in figure 5-(b) show that we can detect the occurrence of QRS complex in the ECG signal. The study of this signal through the draw of the frequency variation offers us the possibility of indicating the locations of a particular frequency in time. For example, the peaks in the curve of frequency coincide with those corresponding with the occurrence of a QRS complex in the original cardiac signal. The second exam- Figure5: ECG data with particular morphology ple is illustrated by the noise-contaminated recording 118 (figure 6-(b)). The signal-to-noise ratio of this recording is SN R = 24dB. This clinical additive noise was extracted from the MIT-BIH Noise Stress Database [START_REF] Moody | A noise stress test for arrythmia detectors[END_REF]. The noise recordings from the latter base were made using physically active volunteers and standard ECG recorders, leads, and electrodes in positions where the subjects' ECG were not visible. Three noise records were generated by selecting intervals that contained predominantly baseline wander, muscle (EMG) artifact, and electrode motion artifact. Electrode motion artifact is generally considered the most troublesome which cannot be removed easily by simple filters, as noise of other types can do. We choose to display the result obtained for the noisy signal (figure 6-(c)). The estimator ( 16) is able to detect correctly the location of the assumed QRS candidates even in the presence of noise. It seems that the noise has no effect on the estimation result. We based all judgments of correctness upon the annotations in the database. Each annotation in the locations and the morphology of a beat was determined by arbitration between two cardiologists.

These latters had to be in agreement to obtain the computer-readable reference annotations for each beatt included in the database.

Conclusion

Our work tackles the problem of the physiological signals analysis, markers of abrupt changes such as an epileptic activity in EEG and QRS complex occurrence in ECG, with new mathematical tool of estimation. This tool is based on a combination of differential algebra and operational calculus. We suggest an estimator of the "instantaneous" 9 angular frequency with the help of a simple local model ensuring a physiological signal representation during a short lapse of time. By applying this method to the EEG recordings of patients recovering from an epileptic activity, we are able to detect the seizure. Our approach shows also satisfactory results in ECG signal by detecting QRS complex occurrence in a severe context. This opens a promising research field in biomedical for this new estimation theory. Among several possible applications, we will consider the problem of the ECG modeling.

  ae(t) (-) a (--) ae(t) (-) a (--), SNR=25dB

  focus our attention on two types of test signals corrupted by a gaussian white noise. The noise level, measured by the signal to noise ratio in dB, i.e, SN R = 10 lg 10 |y(ti)| 2 |n(ti)| 2 , corresponds to SN R = 25dB. The size of the signals is L = 10000 samples. The first is a sinusoid signal which frequency is a constant function of time. The value of the angular frequency is ϕ 1 = 12Πrad.s -1 .

8 T

 8 f is the length of the signal

  estimated (-) et real (--) ϕ 2 1

  Figure4: EEG data

  Figure6: Noisy ECG data

These sequential changes are generally abrupt. They will be considered as changepoints.

[START_REF] Basseville | Detection of Abrupt Changes: Theory and Application[END_REF] These lists are not exhaustive otherwise the reader will be able to find other references there.

See[START_REF] Chambert-Loir | A Field Guide to Algebra[END_REF][START_REF] Kolchin | Differential Algebra and Algebraic Groups[END_REF] for more details

see[START_REF] Chambert-Loir | A Field Guide to Algebra[END_REF][START_REF] Kolchin | Differential Algebra and Algebraic Groups[END_REF] for more details. All fields are assumed to be of characteristic 0.

This definition is borrowed from[9,[START_REF] Fliess | Questioning some paradigms of signal processing via concrete examples[END_REF][START_REF] Fliess | Compression différentielle de transitoires bruités[END_REF][START_REF] Fliess | Une autre vision de l'identification de signaux et systèmes[END_REF].

In[START_REF] Fliess | Analyse non standard du bruit[END_REF], the reader will find all the theoretical justifications.

Let's note that to estimate ϕ 2 1 rather than ϕ 1 is enough to translate the frequency change-point.


Martin Grandjean

Comparing the Relational Structure of the Gospels Network Analysis as a Tool for Biblical Sciences

Introduction: character network analysis

Network analysis allows the literary scholar to take a step back from a given text, by providing both an overview to approach the object differently, and a new structural and mathematical angle. With this paper, we wish to present a process, some elements of which lay the basis of an approach that we think biblical studies should seize. This paper is divided into four main parts: after a short introduction, it addresses, both generally and technically, the stakes of network analysis for narratology. Secondly, it presents the results provided by a network analysis of characters in the four Gospels. Then, a third part examines several levels of analysis: visual, quantitative and mathematical. Before a conclusion, a fourth section discusses the benefits of scaling in network analysis, focusing on particular groups within the narrative field. While character network analysis and visualization has evolved considerably over the past ten years, it remains a stammering field. This contribution can be seen as a continuation of the debate launched by Cohen (2007) which questions some uses of network analysis and visualization in literary studies. Commenting on Wattenberg and Viégas (2007) promoting Many Eyes, the new IBM online data visualization service, he rightly shows the limits of the example chosen to prove the merits of this tool: an analysis of the New Testament presenting a so-called "social network of the New Testament" based on the cooccurrences of characters in chapters. Cohen's criticism is directed to the wonder of researchers towards a tool merely highlighting what anyone could have established: the centrality of the person of Christ in the New Testament. He concludes "Make sure your visualizations expose something new, hidden, non-obvious". In fact, the authors of this questionable visualization do not draw such conclusion since they keep to the technical exercise. But it shows very well that data visualization -and network visualization in particular -should not be limited to a nice visual result. Our goal here is to bring other elements to this discussion and to show that the centrality of the Christ in the Gospel can be questioned through network analysis. The narrative situation is not as simple as it appears, especially since Jesus is not only present through the occurrences of his own name. We will firstly show how such a simple automated distant reading is not sufficient, and secondly that the visual aspect of a network isn't by far its only reading key. It is also to show that in the world of network graphics, the interest is sometimes actually in the details rather than in what is immediately obvious, at the center of the graph.

A text is a network

Characters analysis and narratology

The shape of a given narrative influences its analysis. More specifically, the point of view of the narrator (see the typology in Abrams 1999:231-236) determines the axis of the quantitative study based on the characters in a novel. Various studies, following Barthes' (1975:238) advice not to be reluctant to structural analysis inspired by experimental sciences have focused on the interactions between characters (e.g. [START_REF] Batagelj | Network Analysis of Texts[END_REF][START_REF] Stiller | Weak Links and Scene Cliques Within the Small World of Shakespeare[END_REF][START_REF] Elson | Extracting Social Networks from Literary Fiction[END_REF][START_REF] Sack | Character Networks for Narrative Generation: Structural Balance Theory and the Emergence of Proto-Narratives[END_REF]. This allows the partial reconstruction and visualization of the latter's social network, although it is limited by the gaze of a more or less omniscient narrator. There is no "social" network in our study, because our goal is to avoid these social approaches by analyzing the simultaneous presence of characters in the scenes of the story. Such an analysis is made possible in the Gospels by the omniscient narrator's position. It is therefore not a mapping of social interactions but a comprehensive and interpretative vision of the facts that are told, a focus on the content of the narrative and not its form. Thus, by mapping the presence of the characters, we analyze the space created by the narration, we reconstruct a fictional space based on character appearance metadata. In this respect, it is interesting to recall how Rimmon-Kenan (1983:29-42 cited by Hunt et al. 2013:5) describes the difference between the "level of the story" and the "level of the text". Analyses that automate terms, nouns and pronouns indexing (e.g. [START_REF] Keim | Visual Analytics: Combining Automated Discovery with Interactive Visualizations[END_REF][START_REF] Mott | Probabilistic goal recognition in interactive narrative environments[END_REF], seem to forget that characters are built by the reader, as Chatman (1978:121-130) defends. It is not enough to identify their strict occurrences; one must also focus on their implicit appearances (in a group, in the background of an action, etc.). Note also that the analysis of co-occurrences of characters (their identification in a common scene) is one of six aspects of Finnerrn (2010:162-164) methodology for the study of Biblical characters, without forgetting that "the guiding principle behind literary network analysis is that narratives are not merely depictions of individual experience in language but are also artificial societies whose imaginary social forms can be quantified and analysed" (Sack 2013:185).

Of course, the analysis and visualization of the actors in a text is only one way among others to understand the content of a narrative, often studied through its succession of topics (e.g. Jacquemin 1997, [START_REF] Budanitsky | Semantic distance in wordnet: An experimental, application-oriented evaluation of five measures[END_REF][START_REF] Plaisant | Exploring erotics in Emily Dickinson's correspondence with text mining and visual interface[END_REF][START_REF] Cui | Textflow: Towards better understanding of evolving topics in text[END_REF][START_REF] Kim | Word-Bridge: Using Composite Tag Clouds in Node-Link Diagrams for Visualizing Content and Relations in Text Corpora[END_REF], language specifications (Rydberg-Cox 2011) or simply words themselves [START_REF] Burrows | Textual analysis[END_REF][START_REF] Vuillemot | What's being said near 'Martha'? Exploring name entities in literary text collections[END_REF], not to mention traditional qualitative analyzes [START_REF] Hamon | Le personnel du roman: le système des personnages dans les Rougon-Macquart d'Emile Zola[END_REF][START_REF] Bennema | Encountering Jesus: Character Studies in the Gospel of John[END_REF].

Watching a text as a network

To extract a network out of a text, we must first divide the text into parts. Compared to many literary works that do not have a well-defined structure, the biblical texts1 are particularly easy to divide due to their very precise and studied internal organization, although the choice of the unit is large. We have chosen a division into sections of several verses, the pericopes. It has the great advantage of being a coherent thematic, temporal and spatial unit. In less structured texts, researchers rely on other types of divisions: ten-words frame in Sack (2013:186) on Cervantes, Dickens, Woolf or page by page in [START_REF] Rochat | A social network analysis of Rousseau's autobiography Les Confessions[END_REF] on Rousseau, but these approaches only consider the mentioned characters, not the characters present in the scene without being cited (which of course would be impossible for many novels). Analysis by ten-words frames or pages postulates that spatial proximity of proper names in a text means a relationship between them (this measure is still expertly weighted to minimize the effect of page turning). Analysis by unity of action -as the text sections we have chosen, but also scenes in a theatre play or a movie script -ensures that meaning. Taking the section as a unit goes against traditional practices, for this division is not dependent on the original text (which raises the question of what an original Biblical text is) but rather on the given edition. We will see how this division is in fact unproblematic (it does not bias the analysis, especially since this division is interpretative and still respects the unity of place) but also that it allows the analyst to leave the textual reality and focus solely on the content and action reality, which is beneficial for our characters analysis. The advantage of focusing on the presence and not the mere naming of a character is to leave a blind automated distant reading for an interpretative qualitative approach. Obviously, this requires a very careful reading of the text and a meticulous tracking of all "presences"; something which is made easy, in the case of the Gospels, by a small, well studied corpus. One must first identify all the actors in the section, i.e. those involved in the action which takes place. Those cited as references (the Lord, Moses, Isaiah, etc.) and the crowd 2 are therefore excluded. Furthermore, one can extrapolate the presence of specific characters from global references (the twelve disciples become Peter, John, James, etc.). In our first example from John 21 (the miraculous catch), randomly selected for its diversity, we consider three sections: Jesus meets seven disciples (21A), then speaks with Peter (21B), then with Peter in the presence of John (21C). We can represent the situation in a simple graph (fig. 1): eight characters are listed in the first subdivision, two are present in the second, and three are present in the third.

Here, an edge connects each character to the fragment(s) of text in which he appears. This is visually interesting for such a short excerpt. However, this type of bipartite graph complicates the analysis if the volume of data to visualize increases. The data is therefore visualized as a projected graph (fig. 2), where an edge materializes the presence of the two characters in the same section, eliminating the "references" nodes to keep only the "characters" nodes. As all the characters were present in the first section, there is an edge between each of them. Some edges are thicker because of several (two or three) co-occurrences. We see a denser group consisting of Jesus, John and Peter, leaving the other disciples after the miraculous catch.

Figure 3. Gospel of Matthew

Four Gospels Matthew Fig. 3 shows the result of this procedure for the Gospel of Matthew. The size of the nodes and their color varies according to their degree centrality [START_REF] Koschützki | Centrality Indices[END_REF], the number of connections that link them to other characters (we always speak about co-occurrences in the sections/pericopes). Their spatial distribution is obtained using a force-directed algorithm that moves nodes in the manner of magnets seeking to reject others but being attracted to those they are connected with.3 Jesus logically occupies the central place, here in white. 4Secondly, one can clearly see the twelve disciples, which are densely intertwined to each other as they often appear simultaneously. In this graph, Jesus is connected to every single other character, except the two servants because of whom Peter denied him. We can differentiate the characters connected both to Jesus and the disciples (above right) and those who appear in events where only Jesus is present (left). At first glance, we also clearly distinguish identified groups such as the cluster composed by Mary, Mary Magdalene, the guards and the angel of the tomb scene. Another cluster represents a paralytic who met Jesus alone. By zooming in on the image, we observe that the situation is not as obvious as it first appears: the twelve disciples are not all equally connected with the rest of the entourage of Christ. We will focus on

Mark

As can be expected, the network created from the Gospel of Mark (fig. 4) is very similar to that of Matthew's, with a few more characters. One can clearly observe the ministry above the graph and the "Easter" cluster at the bottom. A very small cluster (left) composed by the paralytic and his 4 carriers (plus the scribes criticizing Jesus) can also be found on the left.

Luke

Because of its high number of characters, the Luke graph (fig. 5) is particularly interesting. One can clearly see all the peripheral scenes and actions. It's also the only graph where some characters are disconnected from the whole network. These are Luke and Theophilus, because of the very first verse in which the evangelist addresses the recipient of the Gospel. Since this situation fundamentally changes the graph's properties, we shall ignore these 2 people for the sheer sake of our analysis. According to their meta status, they do not partake in the narrative as the other characters do.

John

Because it is entirely different from the three synoptic Gospels on a narrative level, this Gospel's graph is also visually very dissimilar (fig. 6). The twelve apostles are less closely interwoven, and the side stories are less visible (on the left) in a graph where everything seems to be part of a unique big cluster. Even though it is not possible to make a precise analysis of the differences in these four networks, a global panorama such as this already provides a fresh outlook and interrogate our assumptions. Indeed, using the same spatialization algorithm highlights the structural differences.

Figure 6. Gospel of John

Three levels of analysis

Graphs and visual aspects

The first level of analysis is the visual one. It should not be depreciated because of its simplicity. In the analysis of very large corpora, it is sometimes very informative for the researcher to look at global patterns (e.g. [START_REF] Ryan | Diagramming narrative[END_REF]). Seeing the object from up close provides a global outlook which can then feed into a more precise analysis. In our case, we can already see that the visual comparison of the four graphs obtained above allows us to make some assumptions.

General properties

The second level of analysis is the quantitative aspect of the corpus: the number of chapters (fig. 7) is an obvious information, as is the number of sections (fig. 8) or words (fig. 9). The number of characters (fig. 10) however, along with that of relations between those characters (fig. 11) are not trivial and give insights about the network graphs. Unsurprisingly, the number of relations seems to be proportional to the number of characters. But this proportionality is not always observed: for instance, the number of relations is very high in Mark, considering its length (few text sections, so fewer possibilities to contain relations). This is a first quantitative indicator of a qualitative aspect of the text, that is, the fact that it perhaps contains more action and dialogue scenes and less teaching and descriptive scenes than other Gospels. Thus, to derive information through a quantitative approach restores the qualitative aspect of the object, as Moretti argues when he writes, speaking about the number of significant characters present in a narrative space, that "the difference between five and fifteen is not just a matter of quantity, here: it's a qualitative, morphological one" (Moretti 1999:68). This also puts qualitative information in an intelligible context (Moretti 1999:149).

Network properties

The third level of analysis concerns the network mathematical properties themselves. Indeed, the humanities and social sciences can take advantage of network analysis, for it provides them with many useful metrics to categorize graph properties and well-described algorithms. The analysis of these metrics differs from visual analysis: the results do not need to be subjectively interpreted to be usable (the visual result of a network analysis may be displayed differently depending on the spatial algorithm selected).

In our example, we'll have a look at three of them, and use them to conduct a comparison of the characteristics of Luke and John. The path length (fig. 13) is a value obtained by testing the distance between all pairs of nodes. Adjacent nodes have a graph distance of 1. The average of all these paths provides information about the structure of the network. Although John was the most dense graph, its average path length is very high, which is not obvious at first. This is due to the position of Jesus. While he is connected to almost all characters in the synoptic Gospels, it is not the case with John (take, for example, the position of this blind man, connected with Pharisees and his parents, who are themselves not connected with Jesus). If Jesus had been connected to everyone, then the path length would always be 2 because everybody could go through Jesus to reach another character. In this hypothetical case, the value would obviously be less than 2, because of the connections between the characters themselves.

Figure 14. Average clustering coefficient

The clustering coefficient (fig. 14) is a way of measuring the nodes' tendency to appear as groups of various sizes. It indicates how densely connected the neighborhood is. A very heterogeneous network will have a high coefficient. It appears that John doesn't contain as many little communities as Luke and the other synoptic Gospels (this is a confirmation of the "visual" analysis, shown above). One can also observe that the disciples cluster is less interconnected than in the other texts: the disciples appear less united in John.

Changing scale

Focusing on a structured group: the Apostles Until now, we have tried to obtain a global view of the network, but the most interesting observations are generally possible when focusing on specific parts of networks. This explains why the "magical" heuristic overviews of the data visualization should not be sought at any price: the most important is to clearly define the area to be analyzed. One way to problematize this approach is to focus on an already formed group, such as the twelve disciples. In the Gospel of Mark, four disciples stand out: the two sons of Zebedee, along with Peter and Andrew. As they appear earlier in the text, they are more often cited along with other characters, giving them a degree (number of connections) above average. Peter also has a higher degree than the three others. In the three Synoptic Gospels, the first followers of Jesus have a superior degree to the others. They are four in Matthew and Mark, and three in Luke. Although Judas appear in the lower middle in the Synoptics (above all because of his leaving the group after the Last Supper), he holds an important position in John.

In John, the most connected disciples exceed by far the number of connections of the other disciples, which is quite remarkable and shows that the passages where the disciples are all together are very occasional in this text. These charts, and therefore the data behind them can become signatures of the networks underlying the four texts. Their four distinguishable properties make them instantly recognizable to the reader able to decipher them.

Focusing on an isolated core network

Another way of trying to develop a graph signature is to isolate a nucleus of well-defined characters. Consider Jesus, Mary, Mary Magdalene, Judas, Peter, Pilate and John the Baptist, and focus on the internal connections of this small group. The strong relationship between Jesus and his disciples is represented by thick edges in fig. 19-22 because they very often appear in the same sections of the text. Less involved in this core network, Mary, Pilate and Mary Magdalene are connected because of their appearance in the section in which Joseph of Arimathea asks for permission to take Jesus down from the cross. In a very visual way, we see four new signings. Again, it is not worth looking at the position of Jesus, but at the secondary characters. It is to be noted for example that John the Baptist changes "partners" in each Gospels: he only is with Jesus in Matthew (fig. 19) at the baptism. He is with Peter in Mark (fig. 20), because his capture is placed in the same section as the first calling of the disciples. He is connected to Mary in Luke (fig. 21), as he is concretely present when Mary visits Elizabeth. Finally, he stands with Peter in John (fig. 22), as Peter is one of the two disciples of John the Baptist who begin to follow Jesus. Again, beyond the visual aspect, the degree centrality of the characters is an element that allows recognizing patterns. Without forgetting that a pattern is not only to be found in regular forms: the lack of regularity is also meaningful. Similarly, we should note that network analysis is not the only way to search for patterns in such a text, as evidenced by [START_REF] Oelke | Fingerprint Matrices: Uncovering the dynamics of social networks in prose literature[END_REF] about fingerprint matrices, or [START_REF] Don | Discovering interesting usage patterns in text collections: integrating text mining with visualization[END_REF].

Perspectives

In this study, we showed that network analysis and visualization can lead to a new understanding of an already well studied object. We can easily distinguish the four Gospels in the three selected observation levels. Visually, John is very different from the three Synoptics. Quantitatively, although much shorter than the other three, Mark has a very high density of relationships. Finally, in terms of network properties, John is the most fragmented. This article also shows that focusing on small selections of characters, makes it possible to distinguish four patterns, four different signatures.

Definitely, network analysis carries interesting potential for biblical studies. When applied to this kind of textual corpus, it complements the research on authorship attributionalthough the latter does not always need this kind of visual aspect, e.g. the "Delta" proposed by [START_REF] Burrows | Delta: A Measure of Stylistic Difference and a Guide to Likely Authorship[END_REF] -since it can be used both syntactically and semantically. Without revolutionizing the discipline, this tool illustrates and provides additional insight to the question of the synoptic problem. In particular, opportunities exist in the "horizontal" comparison of the texts, which can also be extended to all the apocryphal manuscripts. This method can also be of great interest in the "vertical" comparison of the many versions of the same text, mapping syntactic units instead of characters. In both cases, horizontal and vertical, these means do not replace the expert eye of the researcher but speed up the process. They also allow the systematic comparing of information, offering a new look at this well explored object. This approach can be completed by a dynamic analysis (see [START_REF] Van De Bunt | Friendship networks through time: An actor-oriented dynamic statistical network model[END_REF][START_REF] Brandes | Visual Unrolling of Network Evolution and the Analysis of Dynamic Discourse[END_REF][START_REF]Dynamic network analysis[END_REF][START_REF] Berger-Wolf | A frame-work for analysis of dynamic social networks[END_REF][START_REF] Goldenberg | Exporatory study of a new model for evolving networks[END_REF][START_REF] Stein | Pixel-Oriented Visualization of Change in Social Networks[END_REF] to compensate for the fact that the display of a comprehensive network does not describe all aspects of the narrative, thus avoiding some characters that appear very infrequently, but in a context where there are many stakeholders, taking center stage. Very important people may be thrown to the periphery of the graph if their presence is irregular, or if they are only present along, and overshadowed by the main heroes (the opposite is also true: according to Agarwal et al. 2012:94 the Mouse in Alice in Wonderland is very central in the complete graph despite appearing only once in a crowded chapter). However, a dynamic network is sometimes hard to read, especially because it involves the risk for the reader of losing track of the "mental map", when facing a graph whose points change space, colour or size too drastically [START_REF] Purchase | How Important is the 'Mental Map'? -an Empirical Investigation of a Dynamic Graph Layout Algorithm[END_REF]. This problem can be partially offset by an adjacent matrix visualization [START_REF] Stein | Pixel-Oriented Visualization of Change in Social Networks[END_REF]), yet the latter raises further issues of large datasets.

Figure 1 .

 1 Figure 1. John 21 is divided into three sections A, B and C (sets of verses that forms coherent units).

Figure 2 .

 2 Figure 2. Co-presence graph (projection of fig.1).

Figure 4 .Figure 5 .

 45 Figure 4. Gospel of Mark

Figure 7 .Figure 8 .Figure 9 .Figure 11 .

 78911 Figure 7. Number of chapters

Figure 12 .

 12 Figure 12. Graph density

Figure 13 .

 13 Figure 13. Average path length

Figures 15 and 16 .

 16 Figures 15 and 16. Degree centrality of the 12 Apostles in Matthew and Mark.

Figures 17 and 18 .

 18 Figures 17 and 18. Degree centrality of the 12 Apostles in Luke and John.

Figures 19 -

 19 Figures 19-22. 'Core network' around the same set of characters. The number that appears next to the name indicates the degree centrality of the character.

Figure 23 .

 23 Figure 23. Comparison of the degree of the main characters in the four texts.

In this paper, the division of the Gospels into chapters, sections (pericopes) and verses is taken from the Nouvelle Bible Segond (NBS

2002) in French.2 The crowd can rightly be considered as a "character", but the fact that this group changes composition in every scene is problematic.

Network graphs produced using Gephi[START_REF] Bastian | Gephi: an open source software for exploring and manipulating networks[END_REF]).these differences in the last section of this paper, but we can already see how character network analysis does not only produce quantitative output but also structural information about the characters' involvement in the plot.

As in the graph commented by Cohen (2007), yet that graph depicted the whole New Testament divided into chapters.


Yasser Wahyuddin

Governing the smart city: How Lyon Metropolis managed to steer a heterogeneous ensemble of public and private actors towards sustainable climate-energy policies

Keywords: Smart city, governance, city branding, smart, sustainable

In 2012, Electricité de France (EDF) launched one of the biggest smart meter experiment in the Greater Lyon Metropolis. The innovation project constructed a consortium named Smart Electric Lyon (SEL). SEL was established as a pilot project in France to scale out new smart meter device in the city level. SEL hybrids the funding from national government, EDF and dozens of private enterprises that latterly acknowledged as 'smart city' for Lyon Metropolis.

In the meantime, Lyon Metropolis is reshaping their institutional governance to catch up with smart city program promoted by its private partners. The metropolis itself have experienced its territory as fertile ground for private investment on smart city innovation project. As for SEL, Lyon Metropolis seems to harness its presence as part of the city campaign to leverage the new city branding of attractiveness as 'smart and sustainable'. Thus, such reconfiguration disclosed the opportunity to investigate unprecedented effect of smart city in different cities particularly the governance model. An in-depth interview with dozens of Lyon Metropolis actors and SEL initiators constituted as the mains sources of this work. The findings illustrate that Lyon govern a central role to steer private smart city program in favor of territorial attractiveness branding. It confesses the growing investment on smart city have driven the city to promote the label of "smart" and "sustainable" to congregate international benchmark indicators.

Introduction

This article did not address to quantitatively measure how smart city could contribute to sustainable city. "Does smart mean green?" is not at the stake of article's core problematic. The principal ideas were to analyze the heterogenous approach carries out by local government around the world in which the conceptual models of smart city are evolving (Anthopoulos, Janssen, & Weerakkody, 2016a) It has been an interesting debate among the urban sociologist discipline that smart city is a challenging topic in urban studies. The 'intelligence of the city' is an ancient utopia that has taken on many faces over the ages, as historians offer us the perspective [START_REF] Picon | Smart Cities: A Spatialised Intelligence[END_REF]. In recent years, this utopia has been directly associated with the rise of "new information and communication technologies" (NICT) revolution, promoted notably by Cisco through Urban connected development program [START_REF] Gabrys | Programming environments: Environmentality and citizen sensing in the smart city[END_REF] and Smarter citiessmarter planet introduced by IBM in 2008 [START_REF] Townsend | Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia[END_REF]. The "American" passport of these technologies largely explains the English language in which this last episode developed. Around the world, the question for intelligent city has settled under the banner of the smart city. The phenomenon has been very rapid, as the absence of these words in a critical dictionary of fashionable urban words published only a few years ago [START_REF] Reigner | Nouvelles idéologies urbaines. Dictionnaire critique de la ville mobile, verte et sûre[END_REF]. In many cities all over the world, the concept of smart is thus used everywhere embedded on global urban agenda without, more often than not, the nature of the suggested 'smart' word being deeply explained [START_REF] Kaika | Don't call me resilient again!': the New Urban Agenda as immunology … or … what happens when communities refuse to be vaccinated with 'smart cities' and indicators[END_REF].

In practice smart city era bears with the shift toward a new perspective of the cities densified, rewired and networked with the architecture of digital information systems [START_REF] Offner | La smart city pour voir et concevoir autrement la ville contemporaine[END_REF]. The omnipresence of interconnected digital devices such as smartphone, smart watch, tablets, being integrated to the macro system of the whole cities could produce a 'responsive and real time city' thanks to its big data considered as principal materials in smart city ideas [START_REF] Batty | Smart cities, big data[END_REF][START_REF] Kitchin | Data-Driven, Networked Urbanism[END_REF] For example, the contemporary rapport between the city and its citizen are being defined through the influence of real-time data service such as geolocation, or an 'event near you' [START_REF] Picon | Smart Cities: A Spatialised Intelligence[END_REF]. The supply of information from apps and the rise of the alternative services from a platform provide the new form of governmentality role that troubling the established traditional publics services, that lately popular as 'uberization' of public action [START_REF] Teboul | L ' Uberisation , l ' automatisation[END_REF] such as the case of Waze platform in Paris [START_REF] Blok | Data Platforms and Cities[END_REF].

For many authors, the current digital transformation that pushed by the role of IT industry have deeply unveil the city and its ecosystem as digitally embedded. We might directly cite here how smart city since it first appearance in early 2000 is becoming more and more subject for critics from urban planning scholars such as industrial rhetoric [START_REF] Hollands | Critical interventions into the corporate smart city[END_REF][START_REF] Söderström | Smart cities as corporate storytelling[END_REF] or global marketing discourses [START_REF] Joss | The Smart City as Global Discourse: Storylines and Critical Junctures across 27 Cities[END_REF] that came to penetrate city as virgin terrain for such interested group [START_REF] Townsend | Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia[END_REF]. Thus, smart city in which the entry of global leader IT industry into the field of urban planning marks a new, inviting a polarize discussion among interdisciplinary fields of academics.

Despite the critical waves, pro and contra, smart city ideology has anchored firmly as new reference in the digital era that appear to surpass traditional doxa of urban planning [START_REF] Cowley | Smart city as anti-planning in the UK[END_REF]. As explained some authors, local government around the world have developed various approach in engaging smart city, notably as tools for a smarter government [START_REF] Anthopoulos | The Smart City in Practice BT -Understanding Smart Cities: A Tool for Smart Government or an Industrial Trick?[END_REF][START_REF] Anthopoulos | Comparing Smart Cities with different modeling approaches[END_REF]. Smart city ideas are upheld through different global agenda such as IBM smart city ranking [START_REF] Albino | Smart cities: Definitions, dimensions, performance, and initiatives[END_REF], IBM smart city grants dedicated to train city officials around the world to develop smart city programs [START_REF] Alizadeh | An investigation of IBM's Smarter Cites Challenge: What do participating cities want? Cities[END_REF] and through international urban organization such as the Un-habitat SDG's [START_REF] Kaika | Don't call me resilient again!': the New Urban Agenda as immunology … or … what happens when communities refuse to be vaccinated with 'smart cities' and indicators[END_REF] etc. Thus explained how the 'smart city mentality' are dispersed evenly around the world particularly among local stakeholders [START_REF] Vanolo | Smartmentality: The Smart City as Disciplinary Strategy[END_REF]. The local municipalities have in its disposal various institutionalized timetable to legitimate its action on smart city agenda and thus, perhaps, investigating particular local smart city policy would provide a novelty in this field. Now that this article has clarified the way it's intention to articulate the contextual understanding of the word 'smart city', it is necessary to present the fragmented approach of different discipline on smart city. As analyzed by numbers of authors, there existed no single definition of smart city among academic discipline [START_REF] Gabrys | Programming environments: Environmentality and citizen sensing in the smart city[END_REF]. Suggesting smart city as urban phenomenon, it holds in fact the interest of many academic disciplines: sociology (urban), geography (urban), urban planning (more applied), economics (urban) or even political science which, for its part, proposes the object of "urban governance". It should be noted that a very developed academic tradition around the world concerning the subject of the urban phenomenon, claims an interdisciplinary approach combining the aforementioned disciplines and takes the name of "urban studies". So thus, to avoid the bias of the actual debate among researchers due to fragmented interpretation on smart city, this article proposed to contextualize its regard on smart city under the concern of urban governance studies.

Urban governance came up as urban studies topic since late 80's. The rise of urban entrepreneurialism saw a transformation in which the growing interest to engage private investment in city services that unfold neoliberal ideology on city management [START_REF] Harvey | From Managerialism to Entrepreneurialism: The Transformation in Urban Governance in Late Capitalism[END_REF]. For some authors, such new form of urban governance related to the privatization were determinedly developed in urban policy during the Thatcherian era in Great Britain (Le [START_REF] Gales | Du gouvernement des villes à la gouvernance urbaine[END_REF][START_REF] Parkinson | The Thatcher government's urban policy, 1979-1989: a review[END_REF]. Urban governance then described as lesser hierarchy of public actors vis à vis of its private counterparts, erecting the new terms of "heterarchical" relation between the two [START_REF] Kooiman | Governing as governance[END_REF][START_REF] Mayntz | New challenges to governance theory[END_REF]. Urban governance latitudes has now progressed toward a complex array of urban studies analysis such as public private partnership [START_REF] Ysa | Governance forms in urban public-private partnerships[END_REF], urban governance through strategic infrastructure project [START_REF] Pinson | Urban Projects and Governance. The Pluralization of Political Spaces and Recomposition of the Capacity for Collective Action in European Cities[END_REF] etc. Some authors demonstrated urban governance as instrument that strategically explain specific approach exercised by city actors to address urbanization issues, socioenvironment and politico economics [START_REF] Mccann | Governing urbanism: Urban governance studies 1.0, 2.0 and beyond[END_REF]. Therefore, smart city should constitute contemporary topics faced by the local government. A preliminary research on smart city governance pointed out how smart city transcended technology issue to step on institutional transformation subject and political issues, interrogating in turn the governance model [START_REF] Meijer | Governing the smart city: a review of the literature on smart urban governance[END_REF]. Bearing with the latest, this article should provide a critical thinking and novelty at the same time in which smart city of EDF's Smart electric Lyon program are subjected of the governance model of Smart city in a city level. The Greater Lyon Metropolis benefited the presence of the project to redefine its "smart and sustainable" city branding. Accordingly, the urban governance perspective should be at the interplay of such phenomena.

The historic State company on "Smart City"

To ignite our discussion, we intended to elaborate our conception about the engagement of historical actors, such as EDF toward Smart City. Most of the studies in Social Science have defended the idea of the role of IBM, Microsoft, Siemens and Cisco as the pioneer to advocate the advent and the global campaign of Smart City [START_REF] Townsend | Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia[END_REF][START_REF] Picon | Smart Cities: A Spatialised Intelligence[END_REF][START_REF] Teboul | L ' Uberisation , l ' automatisation[END_REF]: Söderstorm, 2014). In the first place, the arrival of Smart City is challenging the traditional way of how cities are fabricated. On Smart City, we are bearing with the shift toward a new perspective of the cities that is being densified and networked by the flow of information systems [START_REF] Offner | La smart city pour voir et concevoir autrement la ville contemporaine[END_REF]. For example, the contemporary rapport between the city and its citizen are being defined through the influence of real-time data service such as geolocation, or an event near you [START_REF] Picon | Smart Cities: A Spatialised Intelligence[END_REF]. The supply of information from apps and the rise of the alternative services from a platform provide the new form of governmentality role that troubling the established traditional publics services, that lately popular as uberization of public action (Teboul, 2015) such as Waze in Paris [START_REF] Blok | Data Platforms and Cities[END_REF].

From a specific perspective, we are noting the embeddedness of Smart City into the historical actors like urban utility services company are somehow escaping the attention of many researchers. In the case of EDF, Eiller (2013;2015) and Boulanguer and Yannick (2017) argue how Smart City has attracted the mobilization of historical actors as a new promoter of Smart City (Ibid, 2013). These phenomena have fueled the current debate in which Smart City is sort of an auto-claim [START_REF] Picon | Smart Cities: A Spatialised Intelligence[END_REF]. Despite the global common understanding of a big company like IBM as the role model, the multiplication and heterogeneity of actors that turn toward Smart City are all in search of their own form. The least certainty is that the topic of 'Smart City' is primarily at the core of discourses. Thus, it contributed to the growing fragmentation of Smart City's typology. The acculturation of the Smart City notion by EDF could probably be considered as a phenomenon of riding a similar prospective market like the one IBM has constructed. The involvement of such actor like EDF towards the subject of the Smart City testifies that the Smart City will no longer be a simple relationship between the cities and the TIC enterprise like IBM, but we are expecting the new aspiration of historical actor. This phenomenon stark the actual critics that state the TIC Company as the only legitimate actors of the Smart Cities. On the contrary, the notion of Smart City has been spreading ubiquitously and is being embedded into various fields of activities (Eiller, 2015).

Figure: Comparison of traditional actors of cities and the embeddedness of Smart City

"Linky Smart Meter": The digital electricity network modernization!

Since 2004, EDF Group through its affiliate company on electricity distribution networks, Enedis, has begun their program to modernize the electricity meters. A more digital architecture of the new devices was chosen to replace the traditional one. The leading digital device constructors such as Atos Origin, Landis+Gyr, Itron, and Iskraemeco comprised the appointed consortium to develop the new smart meter for EDF that was later named "Linky". The technical approach of the new device was to promote the flow of information more rapidly, real time, and to collect individual data consumption without human intervention. On the general plan of Smart Grid development, the "intelligent decision support systems" was dedicated to pedagogically attract more awareness for the consumers to associate to a more flexible and dynamic electricity pricing (Sianaki et al., 2010). Such "by design" capacities might be well framed into the Big data category [START_REF] Townsend | Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia[END_REF]Kitchin, 2014).

The discussion on big data has gone beyond its simple definition of triple V: Volume, velocity, and variety (Boyd & Crawford, 2013). The Social and Human Science discipline have started to take a role in contextualizing big data, which provides some critical element and at the same time suggests for a comprehensive understanding on big data and its surrounding features. In the era of big data, data and information production are becoming more and more decentralized on the individual level (Einav and Levin, 2013). These phenomena opposed the traditional method of data collection in which a centralized State administration such as census bureau registry, survey, and inquiry were the main legitimate resources of data (Desrosières, 2008). The hybrid of the individual and the internet of things are also a means of data production (Brown, Chui, and Manyika, 2011). Every aspect of life and daily activities are now being numbered significantly, which gave rise to the term of "datafication" (Cukier & Schonberger, 2013), "statistical individual" (Bouk 2015), "selfquantified" society or "the society consumer of data". Self-quantified explain how people and their personal gadgets control, measure, and probably govern their daily life activities (Lupton 2013). To a certain extent, the Linky smart meter are deploying these fundamental principles.

EDF Group announces that within the horizon of 2030, the objective was to replace the traditional electricity meter to Linky. As part of the socialization and democratization steps, Lyon Metropolis was the first city to experiment the Linky with 270,000 devices installed in the household and in the tertiary building categories during the 2008 and 2009. Almost in the same year, European Commission through the "Directorate General of Energy" established "The Task Force for Smart Grid (TFSG)" to push the development of Smart Grid throughout its country members. We analyzed the TFSG as the main indicator of political institutionalization process of Smart Grid within EU policy agenda. The TFSG itself consisted of the representation from national board of energy, environment and renewable energy of EU members and the industrial actors on European market. The experts brought down the conclusion to promote Smart Grid as tools to integrate the renewable resources to the existing grids that still largely depended on fossil fuels. Smart Grid are highly rated as a solution of the current debate that renewable resources could not be integrated to the grid due to its problem of being "intermittent" (Philibert, 2013). In addition, the experts also stated that Smart Grid could leverage the EU liberalized energy policy 1 .

As for the French side, Linky is registered as the symbol of a concrete commitment of EDF Group to be parallel with the EU policy. On the national level, Linky obtained an advantage momentum as the French Ministry of Sustainable Development in accordance of La CRE (Regulation Commission of Electricity) stamped the label of national innovation on Linky as a vector to the renewable resources, and to satisfy the new requirement of European regulation on electricity market.

Smart Electric Lyon: simulation of new market as well as a « Smart City » project

In the early 2012, EDF launched Smart Electric Lyon (SEL) experiment project as the extension of EDF's efforts to assess the social, economy and political aspects of Linky before its mass installation. The project is focusing on a profound research and development of Linky devices. The SEL is the largest in France in terms of investment. The amount of 69 M€ was granted from EDF and the subvention of l'Ademe through the program of future investment (PIA). The project scopes 270,000 units of Linky installed in the city of Lyon as experiment materials.

Table: Smart Grid projects in France (Think Smart Grid, 2012)

The SEL project was formalized by the creation of a consortium named after the project, the 'Consortium of Smart Electric Lyon'. Around twenty members of different actors from energy sector, home appliance producer, and home smart connected devices are invited to perform their programs or to test their latest products to connect to Linky. Our in-depth interview shows most of the consortium members are interested in experimenting how the individual behavior represented by the fine-grained data generated by Linky could produce the new insight into the further development of their products. For example, a smart box company tested to integrate the box with Linky. The product allows one stop interface control of daily energy consumption at home. It proposes to display the detailed data concerning the household appliances energy consumptions 2 . The device features a stimulating-awareness program for the family member in order to govern their habits by looking at maximizing the use of each appliance according to the needs and avoiding the peak hours. This form of activities has been part of a vocal critic from many associations and scientific. Linky as Smart Grid does not necessarily bring a direct significant contribution except more on empowering people (Lepretre, 2015). Number of researchers also criticized the kind of Smart meter as a sort of TIC as the intermediary to governing at a distance-the new model of the citizen's empowerment that corresponds to what Foucault defined as "the conduct of conduct" (Attour, 2014;[START_REF] Söderström | Smart cities as corporate storytelling[END_REF]. At the same time the smart meter can become an agent of neoliberalism that mirrors the individual activities (Levenda et al., 2015).

The choice of Lyon is our main problematic issue in this part. In many occasions such as seminars and public dialogs, the instigators of SEL claimed Lyon Metropolis as the favorable ecosystems for SEL 3 . To contextualize the so-called "favorable ecosystem", our findings show the choice of Lyon was fundamentally relying on two aspects: technical infrastructure due to the presence of Linky and the political choice within the internal 2 Interview with member of consortium SEL structure of EDF at the national level4 . For the first aspect, Lyon was the first to experience the democratization and the territorialization of Smart Grid project in France. According to the concept of "niches" coined by Bulkley et al. (2016), the Linky devices could be constituted as the element of technical infrastructure niche that paves the way for such innovation and experiment to be conducted.

For the second aspect, we investigated the role of the "efficient agent" (Bourdieu, 1997) within the high-level hierarchy of EDF that strongly pointed out Lyon. The actor himself was an "Executive Director in charge of the Innovation, Strategy and Programming Department", and member of the "Executive Committee" of the EDF Group that indisputably represents the symbolic capitals of "prise de position" as a determinant factor of negotiation on the exercise of power relation. As Bourdieu (1983) explained, "Prises de position" arise from the encounter between particular agents' dispositions (their habitus, shaped by their social trajectory) and their position in a field of positions which is defined by the distribution of a specific form of capital'. We later deeply examined that the actor has a privilege relation with Lyon both with EDF Regional and Lyon Metropolis where he started his career. On the occasion of Smart Grid projects and eventually through SEL, he intended to prompt a Smart City project in Lyon on the energy sector5 . He was convinced to promote SEL on a form of "Smart City" in order to make echo with the political orientation of Lyon Metropolis that envisioned the international attractiveness policy by positioning the city among the pioneers of Smart City network6 . Therefore, presenting SEL as a Smart City would be considered a proxy line for both parties to collaborate and to govern the project within Lyon's territory7 . As revealed by the director of SEL, his first mandate as director was to negotiate with the president of Lyon by proposing SEL and its Showroom as an attractive hi-tech site in Lyon.

At this stage, EDF seems to play an aggressive role not only as a pressing side (Cadiou, 2016) to render Lyon metropolis as an ideal ecosystem for their experimentation, but also to favor Lyon's international vision. From this point of view, we argue the label of "a favorable ecosystem" embedded to Lyon does not necessarily reflect the spatial context of Lyon as the most technically suitable for such Smart Grid project, especially SEL, but carrying the political discourses coming from the top level of EDF. The use of Smart City notion was solely a means as a leveraging element to align with the local politics, but it does not necessarily changed the content of the project by nature.

From Smart City project to Energetic transition tools

From the point of view of urban marxism, the cities are envisaged as reticular capitalism thanks to its role as a market pool and as an ecosystem that directly or indirectly contributed to create the supply and demand and the flow of production (Vanier, 2015). In the era of Smart City, numbers of critics have singled out the city as the victim of the new technology and information market in which the overflow of industrial interests are occurring (Deltour et al., 2016). The ideas of Smart City are then noted as an avatar of neoliberalism [START_REF] Townsend | Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia[END_REF][START_REF] Söderström | Smart cities as corporate storytelling[END_REF]. In the extension of the hypothesis on the new urban governance, there is a confidence that the cities should play a vital role to orchestrate a new form of governance, to negotiate and to collaborate with any level of actors (Le [START_REF] Gales | Du gouvernement des villes à la gouvernance urbaine[END_REF]Kooiman, 1998;Le gales and Lorrain, 2003;Gaudin, 2002;Le Galez and Borraz, 2010). All of the authors have provided an insightful reading in which the cities, especially the metropolis that are the emerging actors, have even surpassed the central power of the state (Chevallier, 2003). Specifically, through the debates on urban sustainable development issue, numbers of scholars have proposed a paradigm concerning the term of sustainable cities or cities that contribute to 'sustainable cities' (Satterthwaite, 1997). The discussion arose following the hypothesis of certain authors such as Craig Johnson, Noah Toly, and Heike Schroeder (2015) that the cities are not the object of the "sustainable cities" campaign but more likely the pivotal actors of such campaign through its political bargaining powers. Hence, in a more specific topic, the authors outline a stimulating question to rethink the role of cities as lobbying parties in global climate-energy governance.

Regarding the problematic issue above, we underlined the awareness of many scholars, in which they question whether the arrival of smart city would become a big challenge for the cities notably in climate-energy governance. Herewith, some simple questions are worth to be preserved, to what extent the climate-energy are going to propel on Smart Cities? Additionally, to echo Robert Dahl (2005) eventually 'who governs?'.

Through the case of SEL, we figured out a phenomenon of overlapping subjects in which SEL that was initially presented as a Smart City was forced to associate with the climate-energy theme8 . It is not by chance at all that it is turned towards climate-energy since the governance of Lyon Metropolis Smart City program are attached to the division of expert staff of Lyon metropolis President: "Smart innovation and Urban Sustainable Development". We identified the form of contemporary agency in which Smart City agenda are entrusted to the sustainable issues. It gives certain political weight of the governance of Lyon's Smart City ecosystems, especially when it comes to the configuration of multi-level stakeholders that defend their own interests and values (see. Bevir 2010; Faure 2005, 2017 on urban governance).

Lyon is among the first cities in France to launch a smart city program on its agenda setting and become the national reference9 . Thus, the political agenda of Lyon on the governance model of Smart City was also revealed. Even though SEL has generated a large portion of support from all level of actors, European, national government, as well as infranational actor such as la CRE, we argue that the metropolitan level clutches its proper political standards. Lyon situated itself with strong commitment to environmental concerns. In Lyon, the elaboration of climate and energy has been formed in several public action such as Plan Climat Energie territorial (PCET) (Rocher, 2016).

Within two years of the appearance of SEL, its instigator needed to change certain aspects on the activities of the project in order to aspire the climate-energy plan of Lyon. During 2013-2014 the SEL was then declared as Smart City as well as a part of an energetic transition instrument development. Bearing with this transformation, the instigator of SEL propose a fundamental discourse by affirming Smart Meter Linky as the basic ingredient to for climate-energy plan. Thus, the company insisted the interplay of so-called big data generated by Linky which could largely contributes to the energetic transition by providing the control of energy demand.

Figure: The benefits of Data-Linky as energetic transition tools for local government (l'Ademe, 2013)

In some discourses delivered by the SEL instigators, big data from Linky could perform as the new model of climate-energy quantification by replacing the old model. We confess under the radar of such self-declaration, most of the stakeholders and eventually the scholars are on a big debate. As explained by Garnier and Lecler (2015), the tools (Linky) are the designed by product that could only induce certain changes of consumerism performances without sharing other variety of significance on energy sobriety. After all, Linky were originally meant to be the supporting tools to consumers awareness. Hence, how Linky could quantitatively contributed to reduce energy consumption or to be a sustainable one needed to be assessed carefully in the future research. It seems too premature to cage the power of big data since very few scientific discussions have approved on how it comes to play.

The construction of climate-energy quantification scenario is always the fruit of negotiation between multi-dimensional stakeholders: Scientifics, politics, international organizations, economics actors, etc. (Dalmedico, 2007). From Rio convention to Kyoto Protocol, the investment on mathematics models is the most common tools across the globe in which the tools are expected to represent the hybridization between politics and Scientific's dynamics. It is important to note the fact that the case of SEL led us acknowledge the introduction of big data by EDF as tools to climate energy quantification. How it came to join the dynamics on the 'negotiation table' as Dalmedico explained, the big data could have triggered a new debate.

In order to frame big data as a new form of climate-energy quantification instrument, we propose to overlay the approach of "commensuration" analysis (Espeland and Stevens, 1998). Commensuration was introduced as a cultural technic that anticipates the transformation of different qualities into a common metric. In one part, commensuration identifies the ensemble of elements associated to the dynamism of power, value and interest, sometimes cognitive, or even political symbols that prefigure the tools of quantifying processes toward the objects. In other parts, it reveals a critic of the possible divergence perspectives between the parties. For this reason, how EDF came to promote and establish big data as common tools to energy-climate Lyon Metropolis level does not appear yet as an object in the scientific discussion roadmap. We argue that, it is part of a new belief in big data programs, as if big data has achieved great economic success for GAFAM actors (Google, Amazon, Facebook, Apple, and Microsoft) (Faghmous & Kumar, 2014). But, will the same tools be able to give the same success with regard to the subject of energy and climate? Thus we see the multifaceted approach of big data that being mobilized by different actors to address the different topics (Horban, 2016).

The transformation of the form of SEL to embed energetic transition has once again displayed the political weight of a city as the local actor among the multilevel governance of climate-energy. We also figured out that EDF was forced to approach the local political supports and change some content of the project in order to apply the financial grant of PIA from l'Ademe. We assessed through our interview, the support of the local authorities of Lyon metropolis president was essential for l'Ademe's to validate the feasibility of the project as well as to formalize the grant 10 . Thus, an addition element that confirms the proliferation influences of city's environmental politics has an extensive impact to encourage economic actors to grasp the environmental issues on their activities.

In terms of Lyon as experiment site, for now the city still played an important role as an enabler of industrial innovation, hence to contribute to a new market development under the banner of the Smart City (Vilajosana et,al. 2013) that represents a measure for the market potential available to and from the city itself (Caragliu, 2008). The SEL invites us to observe the typology of Smart City model constructed by the historical actor, EDF. We need to underline, however, that EDF is initially a non-Smart City player that became a Smart City promotor. The notion of Smart City has produced the unprecedented effects on new economic transformation of various actors (Boulenguer and Yannick, 2017). This event principally opposes the early model of Smart City in which the primary advocates such as IBM, Microsoft, and Cisco teamed up directly with the municipality to create the Smart City [START_REF] Townsend | Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia[END_REF]. At this stage, despite the consideration of climate-energy on Smart City, we still encounter the fact that Smart City gave a new dialect to the city-metropolitan that proactively contribute to the needs of industrial development.

Conclusion

As the result of our investigation through the Smart City program promoted by EDF, we would like to invite the readers to reposition the city at the center of the stage in promoting climate-energy policy. The example of SEL finally illuminates a determinant role of cities in the governance of climate-energy eventually under the penetration of Smart City.

Our analysis also demonstrates that climate-energy politics that are being embedded on Smart Grid are not merely a matter of international negotiation such as European Commission through TFSG, national climate-energy strategy, or even the negotiation of the industrial actors, but cities are also taking an important place to mobilize global issue. However, we noted that the governance on the local level was not conducted on a direct and clear structure of governance, but the fruit of power relations instead. The hybridization of Smart City and the sustainable development in Lyon allow for the creation of new domains of authority that are important as the instruments for Lyon to govern both Smart City and their Climate-energy policies.

Figure :

 : Figure:Identification on the typology of "Smart City" cities(Boulenguer and Yannick (2017)

Figure :

 : Figure:Lyon as the first metropolis to demonstrate Linky in2008 -2009 (l'Ademe, 2013) )

Interview with the Top Management of EDF Regional Auvergen-Rhone Alpes and the Director of Smart Electric Lyon

Interview with Top Management of EDF Regional -Lyon Metropolis

Interview with the expert staff of Lyon Metropolis president

Interview with the Director of Smart Electric Lyon.

Interview with the expert staff of Lyon Metropolis president

See the rapport Luc Belot for the Prime Ministry «De la smart city au territoire d'intelligence(s) -l'avenir de la smart city » (2017) and three consecutives « Prix Le monde de Smart City » since 2015 to 2018.

Acknowledgement

This paper is part of PhD researches that fully funded by Indonesia Endowment Fund for Education (LPDP) https://www.lpdp.kemenkeu.go.id/