Anđela Davidović

Yves Coudière

Thomas Desplantez

Clair Poignard

Andjela Davidović

Microscopic Modelling of the Non-Linear Gap Junction Channels

The usual way to model the propagation of the action potential through the cardiac tissue is to assume passive diffusive intracellular and extracellular domains, and ion channel dynamics on the cells' membrane. Gap junctions (GJ) are localised clusters of gap junction channels (GJCs) that connects electrically adjacent cells. The importance of GJCs and their modifications in the signal propagation has been demonstrated in the experimental studies (e.g. Beauchamp et al 2012). But, in the current mathematical models the behaviour of the GJCs is either neglected or assumed to be passive, i.e the conductance of GJCs is taken as a steady constant. On the other hand, the experimental results, obtained by the dual-voltage clamp technique, show that GJCs are time and voltage dependent. Here we focus on describing ventricular GJCs made of connexin Cx43 and Cx45. We use the Hodgkin-Huxley formalism to describe GJC conductance via one gating variable. We incorporate the non-linear GJC voltage dependence into the microscopic model of the tissue as a new boundary condition on specific parts of the cells' membranes.

Introduction

We are interested in mathematical models of the electrical propagation in the cardiac tissue. The main parameters that define the shape and speed of propagation are ionic properties of the cardiac cells, the geometric structure and the gap junction conductance between the adjacent cells.

We can approach the modelling of the signal propagation from two points of view. The more common one is to treat the cardiac tissue as the continuous domain, and write the model that is not dependent on the size of the single cardiac cell. These standard bidomain and monodomain models are convenient for the large scale numerical experiments (thousands of cells) as one can use the coarse meshes on the single domain.

The other way to model the signal propagation, that we will use here, is to look into the propagation of the signal on the scale of a few cardiac cells. Such models are numerically very challenging, and they should not be used for the simulations on the larger scales. But they provide closer insight into the contributions of different parameters of the model. More specifically, we are interested in understanding the non-static electrical properties of gap junctions. Additionally, we should note that the standard continuous models are derived from the microscopic models using the multi scale homogenisation techniques (Neu-Krassowska 1992).

The cardiac cells are surrounded by an extracellular matrix and neighbouring cells are electrically connected via gap junctions (GJ). Gap junctions are clusters of gap junction channels (GJCs) that are mainly localised on the longitudinal ends of the cells, where they compose the intercalated disks. These channels play a role of resistance pathways for electrical propagation, by providing the direct passage of molecules and ions from one cell to another.

Each gap junction channel is formed by two end-to-end hexameric structures called hemichannels or connexons, each of which is inserted in the membrane of adjacent cells. The hemichannels are composed of connexins, currently believed to be a protein family of approximately 20 isoforms (Harris 2001). The different isoforms compose channels that have diverse electrical properties (e.g. Desplantez et al, 2004).

Three different connexins, Cx43, Cx40, and Cx45, are expressed in heart. Cx43, the most abundant connexin, is found in ventricular and atrial myocardium. Cardiac diseases that lead to arrhythmias are associated with gap junction remodelling (Beauchamp et all 2004(Beauchamp et all , 2012)). Additionally, it has been observed in the experimental settings that the action potential (AP) propagation in the engineered strand of cells is highly dependent on the level of expression of Cx43, and the speed of propagation can be decreased to 7% of normal in knock-out Cx43 transgenic mouse model.

In the usual continuous models for the electrical propagation, the GJCs are tiny channels between cells which interior domains extend the intra-cellular domain, e.g. sim- In this ongoing work, we propose a 2D discrete microscopic mathematical model that takes into account the nonlinear behaviour of GJCs. We use non-standard geometrical setting for the tissue micro structure, where we abandon the physical connection between adjacent cells (Figure 4). We keep the functional relation between the intracellular potentials between the adjacent cells via boundary conditions. Using this setting and the data on GJCs from Desplantez et al 2004, we would like to observe the decrease in propagation velocity due to different GJC, imitating the experiment in Beauchamp et al 2012.

1.

0-D Non-linear GJ model 1.1.

Dual voltage clamp experiment data

The technique used to perform the dual voltage clamp experiment is described in del Corso et al 2006. It is a technique used to assess the behaviour of GJCs between a single pair of adjacent cells. The patch clamp electrodes are inserted in each cell and a constant transjunctional voltage V j is applied, which provides the insight into the time evolution of the transjunctional current I j , and junctional conductance G j = V j /I j .

The behaviour of GJCs is described with the following parameters: g j,0 represents the maximal junctional coupling between cells and g j,inst represents the instantaneous junctional conductance. Due to limitations of the experimental setup, these two are not necessarily the same. We use g j,0 as a reference value for the maximal conductance that can be achieved in alive tissue. The dynamics is described by normalised g j,∞ that represents the steady state junctional conductance and τ j,∞ that describes the time rate at which the GJCs go from the instantaneous to the steady state. g j,inst , g j,∞ and τ j,∞ are measured with respect to transjunctional voltage, V j .

All parameters depend on type of connexins that form GJCs. In healthy ventricular myocytes the most expressed connexin is Cx43, and in much smaller amount Cx45. Hence we will be interested in GJCs formed by these two connexins. The experimental data (Desplantez et al. 2004(Desplantez et al. , 2007(Desplantez et al. , 2011)), shown in Figure 1, suggest that the conductance of homomeric homotypic Cx43 (Cx45) GJCs is roughly symmetric with respect to V j . While we know that GJCs can express significantly different behaviour in case of heteromeric or heterotypic GJCs, for the modelling purposes we will focus only on these two types of the GJCs.

Data fitting into non-linear GJ model

Even though the behaviour of GJCs has long been observed and described as non-linear (Harris 1981), currently the common way to model GJCs in the tissue is to assume passive behaviour. This means that the electrical current for a given transjunctional voltage V j ,

I j = G j V j , (1)
is assumed to be linear, i.e the junctional conductance G j is assumed to be constant. This simplification is useful and in the healthy tissue it is a good approximation, due to the very different time scales for GJCs (order 3s) compared to ionic channels (order 20-300ms). As we are interested in the pathological cases we want to observe the importance of the dynamical behaviour of GJCs. Hence, we use non-linear functions to fit the experimental data presented above.

We assume that GJCs behave as gates and the data are used to specify the nature and behaviour of the gating variables. The gates have three known states but we use only two, open and closed, for sake of simplicity. The rates at which the gates open or close depend on the transjunctional voltage. We write the conductance as follows

G j (t, V j ) = g j,0 g j (t, V j ), (2)
where g j,0 is the above mentioned maximal junctional coupling, and g j represents the gating variable, that takes values between 0 and 1. The dynamics of the gating variable is described by a simple ODE

dg j dt = g j,∞ (V j ) -g j τ j,∞ (V j ) . (3)
where g j,∞ and τ j,∞ are fitted to the experimental data (Figures 1 and2). These data are taken from the work of Desplantez et al 2004Desplantez et al , 2007Desplantez et al and 2011. We fit the relationship between g j,∞ and V j to a two-state Bolzmann equation (Cristiane del Corso 2006)

g j,∞ (V j ) = 1 -g j,min 1 + e A(Vj -Vj,0) + g j,min , (4)
where V j,0 is the voltage at which the conductance is halfminimal, g j,min is a normalised voltage-insensitive residual conductance and A is a parameter defining the steepness of voltage sensitivity. We know that τ j,∞ depends on the opening and closing rates, and these depend on V j in an exponential way (Harris 1980). It is easy then to derive the simple relationship between τ j,∞ and V j used for data fitting:

τ j,∞ (V j ) = ae -bVj . (5)
The parameters obtained from the data fitting in the case of homotypic Cx43 and Cx45 GJCs are presented in Table 1.

Table 1: Parameters obtained from the experiments and the data fitting. The units in the table are the following: g j,0 in nS, V j,0 in mV , A and b in mV -1 and a in ms. We perform 0D simulation for the GJ current (1) with the non-linear model for the GJ conductance (2) - (5). In Figure 3 we plot the current w.r.t. time, for each fixed V j . The numerical results correspond to the experimental observations (Desplantez et al 2004).

2.

Tissue model with non-linear GJCs

Experimental results on the strand

The main reference in this section will be Beauchamp et al 2012. In the study they quantify the relation between the degree of heterogeneity in Cx43 expression and disturbances in electric propagation. The full details of the experiment can be found in their paper. They engineered patterns of murine strands (4-5 mm in length and 50, 100 or 200 µm in width) from various mixtures of Cx43 and Cx43KO cells (knockout of Cx43, i.e. cells that do not express Cx43).

The propagation velocity was measured from the time difference in average activation and the distance between 2 regions of interest in the various cell mixtures. The original velocity of 30.5 cm/s in the strands with only Cx43 cells, dropped to 76%, 55% and 19% of the original velocity when the ratios of Cx43 and Cx43KO cells were 80%:20%, 50%:50% and 20%:80% respectively. Finally it drops to 2.1 cm/s for the strands with only Cx43KO cells.

For the modelling purposes we assume that Cx43KO cells behave as homotypic Cx45 cells.

2-D Discrete mathematical model

In order to reproduce the results of the previously described experiment, we write a microscopic mathematical model for the signal propagation in the tissue. We use a non-standard geometrical setting for the tissue micro structure. Namely, we represent each myocyte as a separate rectangular domain, where the boundary represents the cell membrane. (Figure 4). Furthermore, we split the boundary into "ionic" and "junctional" boundaries and we apply the ionic model on the former and the previous non-linear GJ model on the latter. In this way, even if we do not have the physical connection, as is the case in the standard settings, we keep the functional relation between adjacent cells via boundary conditions.

Ω e Γ gr Γ app Ω i Ω i Γ j Γ j Γ ion Ω e
Figure 4: Geometric settings for 2D mathematical model. Ω i , Ωe -intra and extracellular domains, Γ ion -"ionic" boundary, Γ j -"junctional" boundary.

The governing equations for the potentials in both intra and extracellular spaces are Laplace equations.

σ i ∆u i =0, in Ω i , σ e ∆u e =0,
in Ω e ,

The ionic properties of the membrane are taken into account as the boundary conditions on the "ionic boundary".

∂ t V m + I ion (V m , h) = -σ i ∇u i • n, ∂ t V m + I ion (V m , h) = -σ e ∇u e • n, ∂ t h = f ion (V m , h),    on Γ ion .
Here, V m = u i -u e is transmembrane potential, σ i and σ e are intra and extracellular conductivities and h is a vector of variables in the ionic model. For this study we choose Beeler Reuter ionic model (Beeler Reuter 1977).

The non-linear gap junctions are taken into account as a boundary condition on the "junctional boundary".

G j (V j ) • V j = -σ i ∇u i • n, ∂ t g j = (g j,∞ (V j ) -g j )/τ j,∞ (V j ). on Γ j .
Here, V j represents the transjunctional jump of potential in the adjacent cells, G j is given as 2, g j,∞ is 4 and τ j,∞ is 5. We assume that the system is isolated, i.e. we have the homogeneous Neumann boundary conditions on the external boundary and Γ j .

σ e ∇u e • n =0, on ∂Ω e \ Γ ion ,
We set initial conditions such that the system is in the steady state. In order to observe the signal propagation we need to provide a stimulus. This is done as follows: on one side we keep the "ground" and on the other we apply the difference of potential, V stim , that can trigger AP in the first cells that are affected.

Numerical analysis and test case

To perform the numerical simulation we use the finite element approach with semi-implicit time discretisation scheme. Additionally, we decouple intracellular and extracellular problems and use the iterative scheme for each time step. As we expected, this problem is numerically very challenging. Even for a very small number of cells (4-10) the CPU time to simulate 10 -20ms is of order of 10hrs.

The first thing we were interested in was to investigate the behaviour of our model by assuming that there are no gap junctions, i.e. we would apply the ionic model on both Γ ion and Γ j . The size of the myocytes used in simulations are 100µm×20µm. This correspond to the average length and width of human ventricular myocytes. The space between adjacent cells is taken to be 1µm. The mesh step is 1µm and the time step in the simulation is 0.02ms.

In the first numerical experiments we used only one myocyte embedded in the extracellular space. By stimulating extracellular space we were able to trigger the AP in the cell and observe its propagation as expected. We observed all four phases of the AP in a single cell simulation.

On the other hand in two-cell experiments we were not able to observe the propagation of AP from one cell to another using only ionic model. Although, our current numerical experiments are very limited, GJ coupling seems necessary for the AP propagation. There are some possible explanations that we still need to test, i.e. smaller mesh step or the distance between the cells.

In this moment we do not have conclusive results from the simulations with gap junctions.

Discussion

Gap junctions play an important role for signal propagation in cardiac tissue. They have a non-linear dynamics that is neglected in the current mathematical models. There are experimental evidences that alternations in the expressions of their connexins affect the propagation velocity. In this project we use the experimental data to fit the non-linear 0D model for homotypic Cx43 and Cx45 GJCs. Finally, we propose a discrete spatial model for studying effects of non-linear GJCs in the tissue. In on going work we perform some 2D numerical test.

  ple linear electrical conductors. However, the voltage clamp experiments (e.g. Harris 1981, Cristiane del Corso et al 2006, Desplantez et al 2004) have shown that GJCs exhibit a non-linear voltage and time dependence on the difference of membrane potential between adjacent cells.

Figure 1 :Figure 2 :

 12 Figure 1: Dependence of the normalised gap junction conductance g j,∞ (lower curves) and g j,inst (upper curves) on junctional potential Vj for homotypic Cx43 and Cx45 channels.

Figure 3 :

 3 Figure 3: Transjunctional current simulated with the parameters obtained from the experiments and the data fitting.

  In other words, during the stimulation time t ∈ [t 0 , t 0 + t stim ], where t 0 is the beginning of stimulation, we solve the system with Dirichlet boundary conditions

	u e =0,	on Γ gr ,
	u e =V stim ,	on Γ stim ,
	and we keep the homogeneous Neumann boundary condi-
	tions on the rest of the external boundary. Using the vari-
	ational formulation of the problem and the standard tech-
	niques of functional analysis we can prove that the problem
	is well posed.


Anđela Davidović

Yves Coudière

Clair Poignard

The effects of the diffusive inclusions in the bidomain model: theoretical and numerical study. Application to the rat heart

∂ t h + g(v m , h) = 0 ∂ t v m + I ion (v m , h) = ∇ • (σ i ∇u i ) ∂ t v m + I ion (v m , h) = -∇ • (σ e ∇u e )

Main Factors

• Nonlinear ionic currents

METHOD: HOMOGENISATION OF THE MESOSCALE MODEL

∂ t h ε + g(v ε , h ε ) =0, in Ω B ε , ∂ t v ε + I ion (v ε , h ε ) =∇ • (σ i ε ∇u i ε ), in Ω B ε , ∂ t v ε + I ion (v ε , h ε ) = -∇ • (σ e ε ∇u e ε ), in Ω B ε . ∇ • (σ d ε ∇u d ε ) = 0, in Ω D ε . ε Ω Ω B ε Ω D ε Σ ε ∂Ω Y Y D Y B Γ 1

Assumptions

• Periodic inclusions of size ε.

• Isotropic conductivity in the inclusions.

• No cells in the inclusions -passive conductors.

Theoretical Result: MODIFIED BIDOMAIN MODEL

• Limit macroscale model σ d ,w).

∂ t h + g(v m , h) =0, |Y B |(∂ t v m + I ion (v m , h)) =∇ • (σ i ∇u i ), σi = σ i |Y B | + A i (σ i , w i ), |Y B |(∂ t v m + I ion (v m , h)) = -∇ • (σ e ∇u), σe = σ e |Y B | + σ d |Y D | + A(σ e ,
• A i , A matrices obtained by solving the cell problems on Y for w i and w.

• UPDATED CONDUCTIVITIES -depend on the volume fraction AND geometry.

Numerical results: study of the effects in 2D

  = -I ion (v m , h) -I stim dh dt = -g(v m , h) v m = u i -u eTISSUE SCALE -Bidomain model

Figure :

 : Figure :The infarct border zone.(Rutherford, 2012)

  (a) Shape 1: effects on the values of the conductivity tensors and on the anisotropy ratio. (b) Shape 2: effect on the eigenvalues of the conductivity tensors and on the anisotropy ratios. (c) Simulation of the circular wave propagation. Upstandard model, center -modified model with inclusion of the shape 1, down -modified model with inclusion of the shape 2. We observe the difference in speed and alternation in the principle direction of the propagation. Application of the model to the real HD-MRI of the rat heart.

  from Giblert et al. (2012), provided by Bordeaux. The size of the image 256 × 256 × 512. Image analysis steps to obtain the required parameters for the simulation. Software used: SEG3D, SCIRun, MATLAB, Perl.

Figure :

 : Figure : Simulation on the slab of the rat heart, up -standard model, down -modified model. Times: 20ms, 40ms, 60ms.

Acknowledgements: This work has been done with help of Yves Bourgault, Univ. Ottawa, Canada and Stephen H. Gilbert Max Delbruck Center, Berlin, Germany. Supported by ANR HR-CEM project: ANR-13-MONU-0004.


domain: stat scco math info

text:
Magalie Ochs
email: magalie.ochs@telecom-paristech.fr

Edwin Diday
email: diday@ceremade.dauphine.fr

Filipe Afonso
email: afonso@syrokko.com

From the symbolic analysis of virtual faces to a smiles machine

Keywords: Smiles, Symbolic data processing, Virtual characters, Graphical tool

In this paper, we present an application of symbolic data processing for the design of virtual character's smiling facial expressions. A collected database of virtual character's smiles directly created by users has been explored using symbolic data analysis methods. An unsupervised analysis has enabled us to identify the morphological and dynamic characteristics of different types of smiles as well as of combinations of smiles. Based on the symbolic data analysis, to generate different smiling faces, we have developed procedures to automatically reconstitute smiling virtual faces from a point in a multidimensional space corresponding to a Principal Component Analysis (PCA) plane.

I. INTRODUCTION

Nowadays, computers are more and more used to endow roles typically embodied by humans, such as a tutor in a virtual learning class or an assistant for a virtual task realization. Such roles are often embodied by animated cartoons or human like virtual characters, called Embodied Conversational Agent (ECA) [START_REF] Cassell | More than just another pretty face: Embodied conversational interface agents[END_REF], able to communicate through verbal and non-verbal behavior with the user. Research has shown that when people are involved in an interaction with such virtual characters, they tend to react naturally and socially as they would do with another person [START_REF] Krämer | Social effects of virtual assistants. a review of empirical results with regard to communication[END_REF].

One important social cue during social interactions is a smile [START_REF] Knapp | Nonverbal Communication in Human Interaction[END_REF]. Smiles may enhance the global perception of a person [START_REF] Lau | The effect of smiling on person perception[END_REF]. Moreover, a smiling virtual character enhances the human-machine interaction, for instance the perception of the task, of the agent, and the motivation and enthusiasm of the user [START_REF] Krumhuber | Effects of Dynamic Attributes of Smiles in Human and Synthetic Faces: A Simulated Job Interview Setting[END_REF], [START_REF] Theonas | Employing Virtual Lecturers' Facial Expressions in Virtual Educational Environments[END_REF].

A smile is one of the simplest and most easily recognized facial expressions. To create a smile, the two muscles zygomatic majors, on either side of the face, have to be activated. However, others muscles may be implied in an expression of a smile. Moreover, a smile may have several meanings -such as amusement and politeness -depending on subtle differences in the characteristics of the smile itself and of other elements of the face that are displayed with the smile.

In this paper, we present research work that is aimed at creating a repertoire of smiles to give the capability to an embodied conversational agent to express different types of smiles during an interaction with a user. The existing methods to construct repertoires of virtual characters' facial expressions are presented in the next section (Section II). In our approach, to identify the facial expressions associated with different smiles, a corpus of virtual character's smiles directly created by users (presented in Section III) has been analyzed with descriptive methods of symbolic analysis (Section IV). An unsupervised analysis of the data has enabled us to identify types and combinations of smiles (Section V). Based on this analysis, procedures have been proposed to automatically generate different smiles continuously in a Principal Component Analysis (PCA) plane (Section VI). We conclude with Section VII.

II. STATE OF ART

Symbolic data processing has been used in several application domains. Indeed, people are not only interested in the study of individuals but also in the identification of classes of individuals. Symbolic data analysis has been used for instance for recommendations in marketing [START_REF] Dantas Bezerra | Symbolic data analysis tools for recommendation systems[END_REF], for medical applications [START_REF] Quantin | Classification and regression trees on aggregate data modeling: An application in acute myocardial infarction[END_REF], in biology to study pigs illnesses [START_REF] Fablet | Classification of Hierarchical-Structured Data with Symbolic Analysis. Application to Veterinary Epidemiology[END_REF], in text mining [START_REF] Haddad | Approche symbolique pour l'extraction de thmatiques: Application un corpus issu d'appels tlphoniques[END_REF], etc. However, as far as we know, symbolic data analysis methods have never been explored for virtual character's facial expressions synthesis.

In the domain of virtual characters, several computational models have been proposed to give the capability to virtual characters to display emotions or feelings, in particular through their facial expressions [START_REF] Albrecht | Mixed feelings : expression of non-basic emotions in a muscle-based talking head[END_REF], [START_REF] Bui | Emotions And Facial Expressions For Embodied Agents[END_REF]. Indeed, evaluation studies have shown that virtual characters expressing emotions enhance human-machine interaction [START_REF] Maldonado | We learn better together: enhancing elearning with emotional characters[END_REF], [START_REF] Beale | Affective interaction: How emotional agents affect users[END_REF].

A facial expression arises from muscular contractions. To animate the facial expression of a virtual character, both the morphological and dynamic characteristics of the virtual face should be considered. To give the capability to a virtual character to express through its face particular emotional states and communicative intentions, the latter should be endowed with a lexicon, i.e., a dictionary of facial expressions linking morphological and dynamic characteristics of the face to specific meanings. To create a repertoire of a virtual character's facial expressions, the method that is commonly used consists of exploiting the empirical and theoretical studies in psychology that have highlighted the morphological and dynamic characteristics of human's facial expressions. In particular, most of the computational models are based on the "Big six" theory of Ekman and Friesen [START_REF] Ekman | Unmasking the Face. A guide to recognizing emotions from facial clues[END_REF] describing the facial expressions associated with six emotions (happy, fear, anger, surprise, disgust, and sadness). To allow virtual characters to display a large number of emotional expressions, a dimensional approach was also proposed [START_REF] Ruttkay | Emotion disc and emotion squares: tools to explore the facial expression face[END_REF]. In the dimensional models, a new expression is often created by applying some arithmetical operations, such as linear interpolation, on numerical definitions of discrete emotions placed in a multidimensional space.

In the present work, we adopt a dimensional approach to create a repertoire of virtual character's expressions. However, the proposed method differs from existing models on different points. First of all, in the existing dimensional models, each facial expression is represented by a vector of continuous values. In our work, we represent a facial expression by discrete variables. Indeed, in the literature in human and social sciences [START_REF] Ekman | Unmasking the Face. A guide to recognizing emotions from facial clues[END_REF], [START_REF] Ekman | Telling Lies: Clues to Deceit in the Marketplace[END_REF], [START_REF] Krumhuber | Can Duchenne smiles be feigned? New evidence on felt and false smiles[END_REF], [START_REF] Ambadar | All Smiles are Not Created Equal: Morphology and Timing of Smiles Perceived as Amused, Polite, and Embarrassed/Nervous[END_REF], the characteristics of emotional facial expressions, and in particular of smiling facial expressions, are not generally described with precise intensity of the muscles contractions. Consequently, in our model, the facial expressions are represented by discrete variables (with values such as "high", "low"). In this context, the symbolic data analysis offers methods particularly suitable to such data. Moreover, contrary to most of computational models, we do not focus on emotions but on the specific signal of smiles.

Last but not least, to collect data, we adopt a particular method in which the users directly created the virtual character's smiles. This method has several advantages. First, it considers directly the user's perception of the virtual character instead of replicating findings of human's non-verbal behavior on virtual characters. Moreover, a corpus of virtual character's facial expressions avoids the problem of acted human's expressions (not necessarily similar to spontaneous expressions) or the difficulty to collect spontaneous expressions (i.e. , to induce the emotional state to the actor). Secondly, this method may generate one-to-many correspondences between socioemotional states and facial expressions: the virtual characters have not one unique smile but may display several smiles to express a same state. The platform to collect the virtual agent's smiles is described in more detail in the next section.

III. A VIRTUAL SMILING FACES DATABASE

To construct a database of smiling virtual faces, a first problem consists of identifying how to represent the different smiles and their characteristics.

The most common type of smile is the amused smile (also called felt or Duchenne smile). Another type, which is often thought of as the amused smile's opposite is the polite smile (also called non-Duchenne, false, social smile). A specific smile appears in the facial expression of embarrassment [START_REF] Ekman | Telling Lies: Clues to Deceit in the Marketplace[END_REF]. In this paper, we focus on the smiles of amusement, politeness and embarrassment. These smiles have the advantage to have been explored in the human and social sciences literature both from the encoder point of view (from the point of view of the person who smiles) [START_REF] Ekman | Telling Lies: Clues to Deceit in the Marketplace[END_REF], [START_REF] Krumhuber | Can Duchenne smiles be feigned? New evidence on felt and false smiles[END_REF] and from the decoder point of view (from the point of view of the one who perceived the smile) [START_REF] Ambadar | All Smiles are Not Created Equal: Morphology and Timing of Smiles Perceived as Amused, Polite, and Embarrassed/Nervous[END_REF].

The amused, polite and embarrassed smiles are distinguishable by their distinct morphological and dynamic characteristics. Although no consensus exists on the morphological and dynamic characteristics of these smiles, the researchers in human and social sciences generally agree on the characteristics to consider to describe the different smiles: the amplitude of the smile, its duration, the openness of the mouth, the symmetry of the lip corner, the tension of the lips, the velocity of the onset and offset of the smile, and the cheek raising [START_REF] Ekman | Telling Lies: Clues to Deceit in the Marketplace[END_REF], [START_REF] Krumhuber | Can Duchenne smiles be feigned? New evidence on felt and false smiles[END_REF].

In order to identify the morphological and dynamic characteristics of the amused, polite, and embarrassed smiles of a virtual character, we have proposed a user-perceptive approach: we have created a web application that enables a user to easily create different types of smiles on a virtual character's face (Figure 1). Through radio buttons on an interface, the user could generate any smile by choosing a combination of seven parameters (amplitude of smile, duration of the smile, mouth opening, symmetry of the lip corner, lip press, the velocity of the onset and offset of the smile, and cheek raising). We have considered two or three discrete values for each of these parameters (for instance, small or large for the amplitude of the smile). When the user changes the value of one of the parameters, the corresponding video of a virtual character smiling is automatically played. The user was instructed to create one animation for each type of smile. The user had to indicate his satisfaction related to the smile he has created (through a Likert scale of 7 points). As described in the following, this value of satisfaction has been used to oversample the data.

Three hundred and forty eight participants (with 195 females) with a mean age of 30 years have created smiles. We then collected 1044 descriptions of smiles: 348 descriptions for each smile type (amused, polite and embarrassed). On average, the participants were satisfied by the created smiles (5.28 on a Likert scale of 7 points) 1 (for more details on the collected smiles, see [START_REF] Ochs | Smiling virtual agent in social context[END_REF]).

The user indicated a level of satisfaction for each created smile (a level that varied between 1 and 7). The level of satisfaction was used to oversample the data with the assumption that smiles with a high level of satisfaction were more reliable than smiles with a low level. To give a higher weight to the smiles with a high level of satisfaction, we did oversampling2 such as: each created smile was duplicated n times, where n is the level of satisfaction associated with this smile. So, a smile with a level of satisfaction of 7 is duplicated 7 times whereas a smile with a level of satisfaction of 1 is not duplicated. The resulting data set is composed of 5517 descriptions of smiles: 2057 amused smiles, 1675 polite smiles, and 1785 embarrassed smiles.

Finally, in the database, each created smile is represented by 9 variables:

• an identification number (ID ∈ [1, 5517]),
• a smile type (TYPE ∈ {amused, polite, embarrassed}),

• the size of the smile (SMILE SIZE ∈ {small, large}),

• the openness of the mouth (MOUTH OPEN ∈ {open, close}), • the symmetry of the smile (SMILE SYMETRIE ∈ {sym., asym}), • the lips tension (LIPS TENSION ∈ {notension, tension}),

• the cheek raising (SMILE AU6 ∈ {no -AU 6, AU 6}),

• the onset and offset of the smile (SMILE ONOFFSET ∈ {short, medium, long}), • the total duration of the smile (SMILE DURATION ∈ {short, long}). The discrete values of the variables correspond to those indicated by the user in the application of smile creation (Figure 1).

To analyze the data, the variables have been handled as symbolic variables corresponding to diagram of frequencies of the discrete values (i.e. the modalities). In the next section, we describe more precisely the database with symbolic analysis methods.

IV. SYMBOLIC ANALYSIS OF POLITE, EMBARRASSED AND AMUSED SMILES

A symbolic analysis [START_REF] Diday | Symbolic Data Analysis : Conceptual statistics and data Mining[END_REF], [START_REF] Diday | Handbook of categorization in cognitive science[END_REF], [START_REF] Noirhomme-Fraiture | Symbolic Data Analysis and the SODAS Software[END_REF], [START_REF] Cohen | Handbook of Categorization in Cognitive Science[END_REF] is based on a characterization of each class by the variations of the variables describing the class. For qualitative variables, the variation is represented through a diagram of the frequencies, corresponding to "symbolic data". In our context, the symbolic data are represented by the diagram of frequencies of the values of each variable describing a smile (the smile type, the openness of the smile, its size, the symmetry of the smile, the lips tension, the cheek raising, the onset and offset of the smile, and the total duration of the smile). In the next paragraph, we describe the symbolic data.

A. Frequencies of the smiles' characteristics

To illustrate the frequency of each discrete value of the variables for each type of smile, a graphic representation with a 3D star has been used (Figure 2). This graphical representation has been generated with the SOE method [START_REF] Noirhomme-Fraiture | Analysis of Symbolic Data[END_REF] implemented in the freeware SODAS. An European consortium of 15 universities and companies has produced this academic freeware SODAS 3 . The module SOE of this software is for graphical visualization of symbolic data.

In Figure 2, each axis represents a variable characterizing smiles: tension of the lips (LIPS TENSION), the cheek raising (SMILE AU6) duration of the onset and offset (SMILE ONOFFSET), total duration of the smile (SMILE DURATION), smile size (SMILE SIZE), openness of the mouth (MOUTH OPEN) and the symmetry of the smile (SMILE SYMETRIE). The star (Figure 2) regroups the data for each concept, i.e., for each smile type (amused, polite, embarrassed) represented by a particular color.

This graphical representation shows that the amused smiles are mainly characterized by an absence of lips tension (92.2%), a long duration (84.4%), a large size (83.6%), an openess of the mouth (85.6%) and a cheek raising (78.4%). Even though the difference is less significant, the amused smiles seem more often described with a symmetry (59.9%). The embarrassed smiles are characterized by a lips tension (74.6%), a small size (73.1%), a closed mouth (81.8%), an assymmetry of the smile (59.1%) and an absence of cheek raising (59%). The duration of these smiles seems more frequently long (56.4%). The smiles of politeness have both the characteristics of the amused smiles and of the embarrassed smiles. Indeed, they are characterized by an absence of lips tension (69.4%), a small size (67.7%), a close mouth (76%), a symmetry of the smile (67.1%) and the absence of cheek raising (58.9%). The three smiles with the predominant characteristics are illustrated in Figure 3.

B. The discriminant variables of smiles

In order to identify the relevant variables to distinguish the types of smiles, a ranking of the variables ordered by their discriminant power (by ascending order, Figure 4) for each type of smile has been generated with the module TABSYR of the software SYR 4 .

The openness of the mouth (MOUTH OPEN) appears as the most discriminant variable among the 7 variables describing the smiles. This variable discriminates in particular the smiles of amusement compared to the smiles of politeness and embarrassment. The variable of the lips tension (LIPS TENSION) is also important to distinguish between the amused and polite smiles and the embarrassed smiles. The less discriminant variables, i.e., the size of the smile (SMILE SIZE) and the cheek raising (SMILE AU6), make it possible to distinguish between the amused smiles and the polite and embarrassed smiles. Even if the symmetry of the smile (SMILE SYMETRIE) has smaller discriminant power, it discriminates the embarrassed smiles compared to the polite and amused smiles. The variable describing the onset and the offset (SMILE ONOFFSET) does not appear as essential to distinguish the three types of smiles.

V. UNSUPERVISED SYMBOLIC ANALYSIS OF SMILES

In the previous section, we made the assumption that only three types of smiles appear in the database: the smile of amusement, politeness, and embarrassment. In this section, our objective is to explore, with an unsupervised symbolic analysis, the different types of smiles that can be distinguished without the assumption of the existence a priori of three types of smiles. For this purpose, we have used a dynamic clustering algorithm with the module NETSYR of the software SYR. This software enables the computation of the PCA of a symbolic data table in which the rows represent each class and the columns are the modalities of the histogram. In other words, the symbolic data table is considered as a numeric data table in which each cell contains the frequency of the modality of one symbolic variable for a given class.

We have studied the partitions of 3 to 15 classes. The choice of the number of classes has been done empirically by testing the partition until 15 classes. The curve of the inertias is illustrated in Figure 5.

There are different mathematical criteria to choose the appropriate number of classes. For example, in [START_REF] Milligan | An examination of procedures for determining the number of clusters in a data set[END_REF], 30 procedures are compared by Monte Carlo simulation. In [START_REF] Diday | Validation of Clustering Structure: Determination of the Number of Clusters[END_REF], the authors compare the Calinsky and Harabasz, I-index, Cindex, Gamma Index, the Beale Test and others based on the Poisson law. They give an extension of some criteria to symbolic data. The conclusion is that the indexes give different results as they express different aspects of the cluster. In this paper, we have used the sum of the intra-cluster inertia. Of course, there is not one unique solution. Consequently, the choice of the best mathematical criterion may be subjective. In our context, the choice, of 15 classes, is based on the decision of the expert on virtual smiles. This choice is supported by the curve of inertias (Figure 5) showing an inflexion between the partitions of 14 and 17 classes. We present in the following section B, the partition in 15 classes.

A. Typology of smiles in three classes

The first unsupervised classification in 3 classes enables us to analyze if, in fact, the 3 classes of smile predefined a priori (amusement, politeness and embarrassment) exist for the considered variables describing smiles (Figure 2). Regarding this unsupervised analysis, we have considered all the variables describing the smiles, except the variable corresponding to the type of smile (SMILE TYPE) to avoid a presupposition on the existence a priori of the 3 smile types. The partition is illustrated in Figure 6.

Regarding the types of smiles (SMILE TYPE), this typology in 3 classes shows that the class C3 is of type 1 (amused smile), the class C2 is of type 3 (polite smile) and the class C1 is of type 2 (embarrassed smile). Whereas the class C3 is mainly composed of amused smiles, the classes C2 and C1 correspond more particularly to a combination of polite and embarrassed smiles. Finally, this typology with 3 classes does not correspond exactly to the typology defined a priori. Indeed, there is no class only composed of embarrassed or polite smiles. These two smiles seem to be mixed. Consequently, two new classes appear in the typology corresponding to a combination of polite and embarrassed smiles with a predominance of one of the two types.

The optimized criterion for this classification is the inertia rate. The inertia rate for the classification in 3 classes following the 3 modalities of SMILE TYPE (supervised classification) is 16 051. The inertia rate for the classification in 3 classes presented above (unsupervised classification) is 13 235. This unsupervised classification contains classes more homogeneous than in the supervised classification.

B. Typology of smiles in 3 to 15 classes

To refine this typology of smiles, we have studied the partitions of 3 to 15 classes. In order to consider all the classes resulting from the partitions of 3 to 15 classes, we have computed a PCA on the prototypes associated with the classes of all the partitions of 3 to 15 classes, i.e., we have considered the prototypes of the 117 classes. The prototypes are the means of the histograms of the class. Then, we have represented the 15 classes, themselves clustered in 5 classes. Figure 7 illustrates the partition on 15 classes by the representation of the 15 associated prototypes and by the representation of a partition in 5 classes of these 15 prototypes obtained by the same algorithm (i.e., dynamic clustering).

This unsupervised analysis shows partitions with a high frequency of prototypic smiles: the class named "Amused", "Embarrassed", and "Polite" (Figure 7) that have the main characteristics of the prototypic smiles described in Section IV (Figure 1). The other classes highlight different types of combinations of smiles: the class named "Embarrassed-Polite" and "Amused-Polite". The smiles of politeness appear often in combination with other smiles (embarrassed or amused). In contrast, the smiles of embarrassment are rarely combined with the smiles of amusement. These results are coherent with the meanings conveyed by these smiles, embarrassment and amusement being relatively opposed since it is difficult to feel amusement and embarrassment at the same time.

VI. SMILES MACHINE: AUTOMATIC GENERATION OF VIRTUAL SMILING FACES

Based on the unsupervised symbolic analysis, we have developed procedures to automatically reconstitute a virtual smiling face given a point in a PCA plane. In Section A, we first present the procedure to automatically compute the characteristics of a virtual smiling face (i.e., the histogram of frequencies of the variables describing the smiles) from a PCA point in the plan. Then, in Section B, we present a procedure to generate the smiling virtual face from these characteristics.

A. Reconstitution of virtual smile's characteristics from a PCA point

Let u j be the unit vector of the j th factor among R of a PCA class of smiles such that u T j = (u j1 , ..., u j R ) where R = p l=1 m l where m l is the number of modalities (i.e., possible discrete values) of the variable l among the p symbolic variables. For more technical details on this PCA , see [START_REF] Diday | Principal component analysis for bar charts and metabins tables[END_REF]. We have by definition u T j u j = 1. It is known that: where 1 R is the identity matrix of R dimension.

R j=1 u j u T j = 1 R (1)
Let v be a point defined by the vector W = (w 1 , ..., w R ) in the initial normalized (i.e, centered and reduced) space. The projection of v in the factor space is defined by V a vector such as V T = (v 1 , ..., v R ) where v j is the coordinate of the projection of v on the factor axis u j . Therefore, we have: 1), we obtain W T = p j=1 v j u T j , which can be written:

W T u j = v j which implies W T u j u T j = v j u T j . From (
W T = ( p j=1 v j u j1 , ..., p j=1 v j u jR ). (2)
In order to reconstitute the smile corresponding to the v point, we denote its coordinates in the initial space by X T = (x 1 , ..., x R ). The link between V and X is given by:

W T = ((x 1 -µ 1 )/σ 1 , ..., (x R -µ R )/σ R ) (3)
where µ k and σ k are, respectively, the mean and the mean square of the j th variable in the case of a PCA of single smile and the mean and mean square of frequencies of categories in the case of a PCA of classes of smiles. It follows from ( 2) and (3) that:

(x k -µ k )/σ k = R j=1 v j u T jk .
Therefore, we can reconstitute the coordinates of the smile associated with the point v of the factorial plane by:

x k = µ k + σ k R j=1 v j u T jk . (4)
In practice, in the graph of the principal components, we can imagine the user clicking on a point in the graph and moving in the first plane defined by the two axis of the largest eigen value. An approximation of the smile reconstitution can be obtained by taking care on only the two first (or more) factorial axes of largest eigen value by replacing R by 2 (or more), in the formula (4). The user can improve the smile (reconstituted by its coordinates defined by (4) or its approximation), by using other factorial planes, for example the third and following axes crossed with the first axis, until he get the desired smiling face The procedure presented in this section enables us to easily obtained from a point in the PCA plane the histogram of each variable describing the smile corresponding to this point. We use these data to reconstitute the virtual smiling face. We present the procedure in the next section.

B. Reconstitution of a virtual smiling face

Based on the histograms resulting from the procedure presented above, we have developed a procedure to automatically reconstitute a smiling virtual face corresponding to a point in the PCA plane. The procedure is based on a deformation of the prototypical expressions of amused, polite and embarrassed smiles (Figure 3). These prototypical smiling faces have been designed manually by manipulating facial muscles. The deformations of the facial muscles are represented with a set of values corresponding to facial animation parameters (FAPs) of the MPEG-4 standard [START_REF] Ostermann | Face animation in mpeg-4[END_REF]). Given the facial muscles implied in an expression of a smile, each prototypical smiling face is represented by 25 values of FAPS, corresponding to the deformation of 25 facial muscles.

To reconstitute a smiling virtual face of a particular point of the PCA plane, we consider the histograms of the 7 variables of this point (openness of the mouth, lips tension, smile size, symmetry of the smile, cheek raising, duration of the onset and offset and total duration of the smile). These histograms are obtained following the procedure described in the previous section (Section A).

The procedure to reconstitute the smiling face from these histograms is based on a weighting of the values of the FAPS with the frequencies of the histograms of the variables. The variables corresponding to the openness of the mouth, the lips tension, the smile size, the symmetry of the smile, and the cheek raising are described with particular values of FAPS. For instance, the cheek raising (SMILE AU6) is characterized by the FAPS 21, 22, 39, 40, 41, and 42. Consequently, with each modality of these variables can be associated a set of values of FAPS. For instance, the FAPS values for the modalities AU6 and no AU6 of the variable SMILE AU6 are described in Table I The problem is that some modalities have FAPS in common. For instance, the lips tension is described by 19 FAPS among which 13 are also used to describe the openness of the mouth. Consequently, we cannot apply a simple weighting of the FAPS of the modality with the highest frequency of the histogram. To overcome this problem, we have considered two types of variables: the variables that define the value of the FAPS (i.e., MOUTH OPEN and SMILE SIZE) and the variables that modulate these values (i.e., SMILE SYM and LIPS TENSION). Based on the analysis of the FAPS of the prototypical smiles, we have defined vectors of values of FAPS corresponding to the following modalities: small open mouth, large open mouth, small size, large size, AU6 and no-AU6. Moreover, we have defined the deformation that the asymmetry and the tension of the lips generate on the FAPS by weights for each FAPS implied for these variables. For instance, the asymmetry may be modeled by a vector of 5 weights corresponding to the weighting to perform on the 5 FAPS to simulate asymmetry 5 . Finally, given the histograms of a class as input, the following procedure is performed:

1) for each variable MOUTH OPEN and SMILE SIZE: select the modality of the variable with the highest frequency in the histogram; 2) select the corresponding values of FAPS; 3) weight the values of the FAPS related to MOUTH OPEN and SMILE SIZE with the corresponding frequency extracted from the histogram of the variable; 4) weight the values of the FAPS related to SMILE SYM and LIPS TENSION using the weights themselves weighted by the frequency of the lips tension and asymmetry modalities described in the histogram. This procedure enables us to generate different combinations of smiles. We illustrate the results of the procedure on the partition in Figure 8. Note that this PCA differs from the PCA in Figure 7 since we have added 2 partitions of 3 classes 6 and we have considered the TYPE SMILE variable additionally to the 7 variables. In Figure 8, the smiling virtual faces of the classes have been generated using the procedures presented above. The correlation circles corresponding to this PCA are represented in Figure 9. On the correlation circles, the modalities of the variable SMILE TYPE highlight the characteristics of the three smiles (amused, embarrassed and polite) and their position in the plane 8. The correlation circle shows that the axis can correspond to a "smile multidimensional space" going from the smiles the most embarrassed (lower left part) to the smiles the most amused (right part), the polite smiles being rather at the top.

VII. CONCLUSION

In conclusion, in this paper, we have presented a method to automatically generate smiling virtual faces. This method 5 For the lips tension, given that the deformation of the FAPS resulting from the tension of the lips depends on the size and openness of the mouth, we have defined vectors of weights for the following combinations of modalities: large size open mouth, large size close mouth, small size open mouth and small size close mouth. is based on an unsupervised symbolic analysis of a corpus of virtual smiling faces directly created by users. The method makes it possible to generate different types of smiles of amusement, politeness and embarrassment but also combinations of these smiles by simply selecting a point (or a class) in a multidimensional space (PCA plane).

The originality of the proposed method comes from different aspects. First of all, most of the virtual characters express one or at most two different smiles during an interaction with a user. In this paper, we present a method to increase considerably the repertoire of a virtual character's smiling expressions. Moreover, the approach generally used for the synthesis of facial expressions is based on empirical and theoretical research in human and social sciences describing the characteristics of human facial expressions. In this article, the synthesis of facial expressions is based on a corpus of virtual smiling faces directly created by the users. Secondly, some previous research works have proposed models to generate automatically facial expressions from a point in a dimensional space. However, the latter are generally based on classical numerical data analysis and do not enable the generation of combinations of different types of smiles.

In the next step of this work, we aim at analyzing the perception of the users of the generating smiling faces to evaluate if the combinations of meanings are perceived through the smile expressions.

Fig. 1 .

 1 Fig. 1. Screenshot of the web application to create smiles.

Fig. 3 .

 3 Fig. 3. Images of the three smiles (at the apex) with the most frequent characteristics identified in the database (from the left to the right) : amused smile, embarrassed smile and polite smile.

Fig. 2 .

 2 Fig. 2. ZOOM star of the morphological and dynamic characteristics of the amused, embarrassed and polite smile.

Fig. 4 .

 4 Fig. 4. Descriptives variables of the smiles ordered by the discriminant power (ascending order).

Fig. 5 .

 5 Fig. 5. Curve of the inertias for the partitions from 2 to 25 classes.

Fig. 6 .

 6 Fig. 6. Variables of the 3 classes of smile obtained by an unsupervised classification.

  6 one reflecting the prototypical smiling faces: Part 3 C1, Part 3 C2, and Part 3 C3, and one corresponding to the unsupervised analysis in 3 classes illustrated in Figure 6: Part 3 C1 clust, Part 3 C2 clust, and Part 3 C3 clust.

ACKNOWLEDGMENT

  This research has been supported by the European Community Seventh Framework Program (FP7/2007-2013), under grant agreement no. 231287 (SSPNet).

Fig. 7 .

 7 Fig. 7. Typology in 5 classes based only on the type of smile variable (SMILE TYPE). Note that even if an overlap of the clusters appears in the figure, there is no overlap of the classes.

Fig. 8 .

 8 Fig. 8. Automatically generated smiling faces.

Fig. 9 .

 9 Fig. 9. Correlation circle of the symbolic variables (left) and of the modalities of the variables (right).

  .

	FAPS	AU6	no AU6
	21	100	-300
	22	100	-300
	39	-100	0
	40	-100	0
	41	400	-100
	42	400	-100
		TABLE I
	VALUES OF FAPS FOR THE SMILE AU6 VARIABLE

Globally, the users' satisfaction was similar for the three smiles (between 5.2 and 5.5)

Note that an undersampling could be also applied by not considering smiles with a low level of satisfaction. We have given priority to oversampling to have the maximum of smile descriptions to model the variability of smile expressions.

http://www.info.fundp.ac.be/asso/sodaslink.htm

This software is provided by SYROKKO company.


Ameni Kacem
email: ameni.kacem@gmail.com

Haithem Ghorbel

Rami Belkaroui
email: rami.belkaroui@gmail.com

Rim Faiz
email: rim.faiz@ihec.rnu.tn

Dhouha Jemal
email: dh.jemal@gmail.com

Ines Hammami Abid

Towards improving e-government services using social media-based citizen's profile investigation

Keywords: CCS Concepts, Information systems ➝ Information retrieval ➝ Users and interactive retrieval ➝ e-government, social media, big data, user profile, recommendation, open data

Governments are making considerable efforts in order to enhance citizens' participation in their decision-making and policy processes. In order to understand the citizens' needs, the decision makers need to know more about citizens' behaviors, preferences and ability to use e-government online services. Recently, social media represents a strategic opportunity that can help governments to become more transparent by providing citizens with better services and enhancing information's access in a way that makes them more involved.

In this paper, we propose a new conceptual framework that investigates users and communities' profiles based on social media. The aim of this paper is to explore the social citizens' profiles in order to improve and adapt public services, decision making, information sharing, transparency and collaboration enhancing...to the individual's current and relevant needs.

INTRODUCTION

E-government refers to the use of information and communication technologies (ICTs) to achieve citizens' satisfaction through more suitable services. Governments need to be more interactive and reach citizens where they are. Therefore, e-government is considered as one of the channels to enhance public trust in the government through increased accountability and empowerment of its citizens [START_REF] Demchak | Webbing governance: National differences in constructing the public face[END_REF]. Recently, social media services have become the main way of communication, content sharing and opinion expressing and is considered as an invaluable source that help collect all needed information about citizens and communities. In fact, governments can take advantage of the high capabilities and popularity of social media, in order to improve government's strategies and performance. The considerable massive interest and involvement on social networks use reveals that there is now serious potential for the enhancement of online participation. A plausible indicator of this potential is the rising number of those using one or more online government services, which has increased from 39% in 2005 to 57% in 2011 [START_REF] Dutton | Next generation users: the internet in Britain[END_REF]. Social media have already played seminal roles in political protests in various countries, including Tunisia, Iran, Egypt and others caught up in the Arab Spring revolutions. The Arab Spring is probably the most recent example when talking about social media abilities to impact government and shape political discourse. M oreover, social media represents a strategic opportunity that should be cautiously managed to better engage individuals, businesses and public organizations [START_REF] Hofmann | What makes local governments' online communications successful? Insights from a multi-method analysis of Facebook[END_REF]. It can help government to become more transparent by providing citizens with better services and information's access, opening an active communication channel, in a way that makes them more involved. In this paper, we address the following questions: How can egovernment systems exploit data provided by social media? And how those data contribute to improve efficiency of e-government services and government decision-making process? Thus, we propose a new conceptual framework that investigates users and communities' profiles based on social media. It allows a better delivery of services to citizens, an increased transparency and a greater convenience. The remainder of this paper is organized as follows: we begin by describing some related works. In section 3, we present our conceptual framework of citizens' profile investigation based on social media for e-government services improvement. Finally, we present a summary of our work and some future directions.

RELATED WORK

In this section, we review prior solutions in the e-government field using social media, user profiles and Big Data techniques. SAMPLE: Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

User profile and e-government

Personalization of Information Retrieval (IR) systems in the egovernment field is used in order to better satisfy citizens' needs, through providing personalized public services or helping citizens find relevant information within the huge rising amount of data. M ost of the prior work that address the user-profiling problem in e-government does not include activities of the user extracted from social media. They rather use the demographic information, user browsing history or feedback. However, the user's profile content can be extracted from his online activities on social media Web sites. In fact, recently IR systems take advantage of the emergence of user-created content such as blogs, microblogs and social networks [START_REF] Hussain | Social M edia as a Tool for Transparency and Good Governance in the Government of Gilgit-Baltistan, Pakistan[END_REF]. This kind of content is not commonly used in the e-government field.

M any prior works use the user profile explicitly extracted from his inputs when interacting or creating his/her account on public services platforms. For instance, in [START_REF] Zaoui | Towards a personalized e-government platform[END_REF], the authors propose a personalization platform that adapt proposed services to each user profile. After the creation of the user profile from multiple sources, they used two types of profiles: a long-term profile that contains static information about the user, and a short-term profile that considers only information extracted from the current session.

M ore recent works exploit social media as a source of government services' personalization such as the work proposed by [START_REF] Bista | The human touch of government services[END_REF] in which the authors explained the importance of having a human interface with citizens that can be obtained thanks to social media especially forums. The work of [START_REF] Reddick | Citizens and E-government: Evaluating Policy and Management[END_REF] highlighted that social media is bringing new elements to the electronic government such as the exploration of online communities, social networking and user generated content. They consider that the collaborative aspect is very important in the Web 2.0 because it integrates communication, interaction, content sharing and social networking.

E-Gove rnment between Open and Big Data

When combined with the power of social media, Open and Big Data offer substantial opportunity to foster civic engagement and social innovation. Open Data, also referred as open Public Sector Information (PSI), has received considerable attention in recent years in order to increase transparency, participation and government efficiency. In [START_REF] Janssen | Benefits, adoption barriers and myths of open data and open government[END_REF], the authors present Open Dat a as a recent phenomenon in an early stage of development. They analyzed the benefits and barriers of Open Data systems by synthesizing people's experiences with Open Data.

The promises and potential of Big Data in transforming digital government services, governments, and the interaction between governments, citizens, and the business sector, are substantial through increased efficiency and effectiveness in the delivery of services. As described in [START_REF] Kim | Big-Data Applications in the Government Sector[END_REF], the adoption and benefits of Big Data solutions in various government projects can support the government's decision-making processes for ushering in a new era of digital government services.

In [START_REF] Bertot | Big data and e-government: issues, policies, and recommendations[END_REF], the authors reviewed and analyzed the U.S. policy context regarding Big Data. They present some examples of Big Data initiatives that offer views of the promise of Big Data-driven application and research, such as a range of Big Data techniques in order to assess implications of climate change on the New York state, and provide strategies to deal with this issue in areas such as agriculture, public health, energy, and transportation. In this paper, we study how we can learn from the presented experiences, and create solutions that better meet citizens' needs using some of today's Big Data applications.

THE PROPOSED CP-GOV FRAMEWORK

Aiming to improve and adapt public services, decision making, information sharing, transparency and collaboration with citizens, we propose a conceptual framework of citizens' profile investigation for e-government services improvement, called CP-Gov, as depicted in Figure 1. This framework is comprised of six main components assembled to offer the most relevant recommendations that meet citizens' requirements. It can be applied to various government departments, such as education, tourism, welfare, and healthcare dep artments. The CP-Gov framework offers two facets of relevant information for citizens and policy makers.

• For citizens: the personalized recommendations are offered to users according to their profiles to improve the quality of public service delivery.

• For policy makers: our framework offers citizens' needs based on profile investigation, in order to improve and adapt decision making, e-government strategies, transparency and collaboration.

In the following, we will give a general description of each main component focusing on conceptual functionality and technical details.

Personalized Citizens Interface and Data Collector

The personalized citizen interface ensures the interaction between citizens and the system. The login of each citizen in the governmental framework is ensured by providing his or her user name and password obtained upon registration. The citizen personal information is gathered explicitly when she makes registration such as their demographic data (name, age,..., personal interests and preferences towards e-government services). In fact, the user has the possibility to update regularly these information in database through her personal page. Implicitly, information related to context (personal and social) are . captured from citizens' social profile and activities on social media.

Social Media-Based Citizens Profiles Construction

The profiling process, in our CP-GOV, is composed of two main elements. The first one is the citizen profile creation using his activities in social media websites: Social Citizens Profile (SCP).

The second one called Social Citizens Interactions (SCI) resides in integrating citizens' interactions in the profile.

Social Citizens Profiles (SCP)

Considering the social media emergence, users in the social networking sites express freely their opinions, preferences and share content in which they are interested. In our approach, we first extract citizens' activities on social media specifically Facebook as it is the most popular social media used by citizens especially in Tunisia.

For user profiling construction, we use the keyword-based representation where the keywords can be explicitly provided from each user or implicitly extracted from his online activities on social media. Formally the user profile is presented as follows:

(

) 1
where: is the extracted term, is its corresponding weight and design the publication moment. After collecting terms that are used in our profiling approach, we assign in each day the normalized term frequency (nTF) score that gives an overview of the terms' frequency distribution. Thus, considering the relative frequency of a term in a publication moment compared to the frequencies of all terms , we obtain the following content feature:

(2)

Owing to the constantly changes in the users' preferences, we use the day as a temporal unit. We use the same weighting scheme as in [START_REF] Kacem | Timesensitive user profile for optimizing search personalization[END_REF] where we combine short-term and long-term profiles by integrating the Kernel Gaussian function in order to give fresh terms higher value: [START_REF] Bista | The human touch of government services[END_REF] where σ is the interpolation coefficient, is the current moment and is a prior moment of publishing a post on Facebook. Thus, the final score W is calculated according to the following formula: [START_REF] Demchak | Webbing governance: National differences in constructing the public face[END_REF] Where and design respectively Content-Feature and Temporal-Feature presented previously. Consequently, our weighting scheme supports both the frequency and the time distributions.

Social Citizens Interactions (SCI)

In order to enrich the created user profile, we propose to integrate social citizens' interactions. In order to efficiently integrate citizens' interactions, we first leverage the "hashtags" of Facebook status in order to extract the present entities. Specifically, we consider each hashtag in Facebook posts as a single entity. Then we retrieve a common set of conversation using our conversations trees detection system [START_REF] Belkaroui | Social users interactions detection based on conversational aspects[END_REF] that covers these entities. In the second step, we analyze all of the conversation for all of the discovered entities in a user's set of Facebook posts, and determine the set of categories that define that user's topic profile (e.g., the topics of interest). To generate topic profile, we rank each of the categories using a frequency ranking function. After that, we define topic profile as the top -K categories, ranked according to our ranking function. The output of this step is used to enrich the user and community profiles by boosting the interests and preferences that meet the top -K categories of topic profiles.

Community Profiling

Based on citizens' information collected from social media, user communities can be formed to represent groups of users who share common characteristics, interests and/or needs in a specific e-government domain. This component can be used to predict and recommend the most relevant services among the available ones. Relevant services will be generated for each citizen community as personalized output based on interests and needs determined from citizens' profiles, in order to increases citizens satisfaction levels.

Data Source Repository (DSR)

The role of the Data Source Repository component is to store all the data that is required as an input for the data analysis module. It comprises of:

 User Profile Database: It stores built citizens' profiles based on the implicit and explicit collected information. The purpose of storing the profiles is to make use of them as input for the next phase of analysis in order to capture the needs, goals, values, expectations and habits of users into well-defined user groups.  Open Data Governance Database: It contains data collected on the provision of open data initiatives. It includes all the public services that we aim to recommend as well as their features and rules. In fact, taking advantage for data available on national portals, can enabling more effective interactive and collaborative governance. The DSR component is expected to support huge volume of data: citizens' collected information from social media, citizens' input information and available government data. This requires reliable technology and solution to handle with the massive quantities of data. It is not just about storage of and access to data, it is necessary to think about data security, integrity and availability [START_REF] Faiz | What if mixing technologies for Big Data mining and queries optimization[END_REF]. In our framework, Hadoop has been chosen as the solution to answer our need for a powerful and trusted storage technology. Indeed, this solution can ensure our data security in the face of faults and failures in disks, nodes and networks.

Data Analysis Module

CP-GOV is based on the emergence of network access, citizens' personal information that become available especially on social media reflecting their needs, goals, values, expectations and habits. Due to the huge volume and the unstructured nature of those data, we use Hadoop and its data analysis system called M apReduce that is characterized by performing heavy processing on large structured and unstructured data volumes. In fact, when the data regarding user and communities profiles are loaded on the cluster, they are broken down into smaller blocks and distributed throughout the cluster in order to enable a Hadoop M apReduce system of processing many parts of them in parallel by executing map and reduce functions on smaller subsets.

Citizens Interaction Module

In order to increase citizen satisfaction levels, the Citizens Interaction M odule (CM I) consists on automatically recommending the most relevant services to a given citizen. We use a content-based filtering approach. First, each citizen's profile is analyzed as it contains his/her preferences and properties described in section 3.2. Second, the similarity between the user's profile and each service, which is also represented as a vector of weighted keywords, is measured. The user-service similarity can be obtained using the cosine measure for instance. Then, the recommendations are generated and presented through notification to citizens as a top -N list of services that have the most important similarity and consequently fit the best the users' profiles and needs. Finally, direct feedback from a citizen, in the form of a like or dislike button, can be used to assign higher or lower value to certain services and consequently contributes to maintain recommendation quality and consistency.

Policy Makers

Through our CP-Gov framework, we aim to help policy makers and government organizations improve their strategies. Thus, output reports are available using data mining techniques based on users and communities profiles, their preferences and demographic information. Those reports help not only to improve efficiency and effectiveness of services delivery, but also to define long-term strategies, to adjust policies and national projects development, and to welcome new ideas and ways of collaboration with citizens.

CONCLUSION

Conscious of social media opportunities and of the government need to enhance public transparency, interactivity and accountability, we find that it is important to develop solutions for this issue. In this context, a conceptual framework for boosting interaction government-citizens is proposed. The CP-Gov framework was designed in the aim of offering personalized egovernment services to citizens. For the government side, the framework might improve its decision-making process by means of better understanding citizens' needs and expectations. In future work, we will focus on evaluating and validating our CP-Gov framework in a particular field, and try to develop a functional system to provide the personalized e-government services to citizens.

Figure 1 .

 1 Figure 1. Our CP-Gov proposed framework.