From MEMS to NEMS : Modelling and characterization of the non linear dynamics of resonators, a way to enhance the dynamic range

Abstract :

The resonant sensing technique is highly sensitive, has the potential for large dynamic range, good linearity, low noise and potentially low power. The detection principle is based on frequency change that is induced by rigidity changes in the resonator.

In order to compensate the loss of performances when scaling sensors down to NEMS, it proves convenient to find physical conditions in order to maximise the signal variations and to push the limits of the linear behavior. To do so, a comprehensive model including the main sources of nonlinearities is needed. In the present paper, a process, characterization methods and above all an original analytical model are presented.

Mots clefs : MEMS, NEMS, Resonator, non linear dynamics, dynamic range, characterization

Introduction

The permanent quest for cost cuts has led to the use of potential "In-IC" compatible thin SOI-based technologies, which imposes drastic size reduction of the sensors. Combined with the need for in-plane actuation for fabrication and design simplicity, this implies a large reduction in detectability. Moreover nonlinearities [START_REF] Roessig | Integrated MEMS tuning fork oscillators for sensor applications[END_REF] occur sooner for small structures which reduces their dynamic range.

On the way from MEMS to NEMS, a "small" MEMS resonant accelerometer [START_REF] Seshia | A vacuum packaged surface micromachined resonant accelerometer[END_REF] has been fabricated. The sensor structure has been designed in order to validate process and characterization choices. This paper deals with the design of the sensitive element : the resonator. Many studies have presented models on the dynamic behavior of MEMS resonators. Some of them are purely analytical [START_REF] Tilmans | Electrostatically driven vacuum-encapsulated polysilicon resonators part ii. theory and performance[END_REF][START_REF] Gui | Nonlinearity and hysteresis of resonant strain gauges[END_REF] but they include coarse assumptions concerning nonlinearities. Other models [START_REF] Najar | Dynamic analysis of variable-geometry electrostatic microactuators[END_REF][START_REF] Nayfeh | Dynamic pull-in phenomenon in mems resonators[END_REF] are more complicated and use numerical simulations which makes them less interesting for MEMS designers. In the present paper, a compact and analytical model including the main sources of nonlinearities is presented and validated thanks to the characterization of the accelerometer sensing element, an electrostatically driven clamped-clamped beam.

Model

A clamped-clamped microbeam is considered (Figure 1) subject to a viscous damping with coefficient c per unit length and actuated by an electric load v(t) = V dc + V ac cos( Ωt ), where V dc is the DC polarization voltage, V ac is the amplitude of the applied AC voltage, and Ω is the excitation frequency.

FIG. 1 -Schema of an electrically actuated microbeam

Equation of motion

The equation of motion that governs the transverse deflection w(x, t) is written as :

EI ∂ 4 w(x, t) ∂ x4 + ρbh ∂ 2 w(x, t) ∂ t2 + c ∂ w(x, t) ∂ t = Ñ + Ebh 2l l 0 ∂ w(x, t) ∂ x 2 dx ∂ 2 w(x, t) ∂ x2 + 1 2 ε 0 bC n V dc + V ac cos( Ωt ) 2 (g -w(x, t)) 2 (1)
where x is the position along the microbeam length, E and I are the Young's modulus and moment of inertia of the cross section. Ñ is the applied tensile axial force due to the residual stress on the silicon or the effect of the measurand, t is time, ρ is the material density, h is the microbeam thickness, g is the capacitor gap width, and ε 0 is the dielectric constant of the gap medium. The last term in Equation ( 1) represents an approximation of the electric force assuming a complete overlap of the area of the microbeam and the stationary electrode including the edge effects by the coefficient C n [START_REF] Nishiyama | Capacitance of a strip capacitor[END_REF]. The boundary conditions are :

w(0, t) = w(l, t) = ∂ w ∂ x (0, t) = ∂ w ∂ x (l, t) = 0 (2)

Normalization

For convenience and equations simplicity , we introduce the nondimensional variables : 1) and ( 2), we obtain :

w = w g , x = x l , t = t τ (3) Where τ = 2l 2 h 3ρ E . Substituting Equation (3) into Equations (
∂ 4 w ∂x 4 + ∂ 2 w ∂t 2 + c ∂w ∂t -α 2 [V dc + V ac cos(Ωt)] 2 (1 -w)) 2 = N + α 1 1 0 ∂w ∂x 2 dx ∂ 2 w ∂x 2 w(0, t) = w(1, t) = ∂w ∂x (0, t) = ∂w ∂x (1, t) = 0 (4)
The parameters appearing in Equations ( 4) are :

c = cl 4 EIτ , N = Ñ l 2 EI , α 1 = 6 g h 2 , α 2 = 6 ε 0 l 4 Eh 3 g 3 , Ω = Ωτ (5)

Resolution

A reduced-order model is generated by modal decomposition transforming Equations ( 4) into a finite-degreeof-freedom system consisting of ordinary differential equations in time. We use the undamped linear mode shapes of the straight microbeam as basis functions in the Galerkin procedure. To this end, we express the deflection as :

w(x, t) = n k=1 a k (t)φ k (x) (6)
Where a k (t) is the k th generalized coordinate and φ k (x) is the k th linear undamped mode shape of the straight microbeam, normalized such that 1 0 φ k φ j = 0 for k = p and governed by :

d 4 φ k (x) dx 4 = λ 2 k φ k (x) (7)
φ k (0) = φ k (1) = φ k (0) = φ k (1) (8)
Here, λ k is the k th natural frequency of the microbeam. We multiply Equations ( 4) by φ k (x)(1 -w) 2 , substitute Equation ( 6) into the resulting equation, use Equation ( 7) to eliminate d 4 φ k (x) dx 4 , integrate the outcome from x = 0 to 1, and obtain :

äk + c k ȧk + λ 2 k a k -2 n j=1 λ 2 j a j 2 + c j a j ȧj + a j äj 1 0 φ k φ j 2 dx -α 2 [V dc + V ac cos(Ωt)] 2 1 0 φ k dx + n j=1 λ 2 j a j 3 + c j a j 2 ȧj + a j 2 äj 1 0 φ k φ j 3 dx - n j=1 N a j + α 1 a j 3 1 0 φ j 2 dx 1 0 φ k φ j dx +2 n j=1 α 1 a j 4 1 0 φ j 2 dx + N a j 2 1 0 φ k φ j φ j dx - n j=1 α 1 a j 5 1 0 φ j 2 dx + N a j 3 1 0 φ k φ j 2 φ j dx = 0 (9)
Noting that the first mode should be the dominant mode of the system and the other modes are neglected, so it suffices to consider the case n = 1. Equation (9) becomes :

ä1 + (500.564 + 12.3N )a 1 + (1330.9 + 38.3N )a 1 2 + (927

+ 28N + 151α 1 ) a 1 3 + 471α 1 a 1 4 +347α 1 a 1 5 + c 1 ȧ1 + 2.66c 1 a 1 ȧ1 + 1.85c 1 a 1 2 ȧ1 + 2.66a 1 ä1 +1.85a 1 2 ä1 = - 8 3π α 2 [V dc + V ac cos(Ωt)] 2 (10)
To analyse the Equation of motion (10), it proves convenient to invoke perturbation techniques which work well with the assumptions of "small" excitation and damping, typically valid in MEMS resonators. To facilitate the perturbation approach, in this case the method of averaging [START_REF] Nayfeh | Introduction to perturbation techniques[END_REF], a standard constrained coordinate transformation is introduced, as given by :

       a 1 = A(t) cos [Ωt + β(t)] ȧ1 = -A(t)Ω sin [Ωt + β(t)] ä1 = -A(t)Ω 2 cos [Ωt + β(t)] (11)
In addition, since near-resonant behavior is the principal operating regime of the proposed system, a detuning parameter, σ is introduced, as given by :

Ω = ω n + εσ (12)
Separating the resulting equations and averaging them over the period 2π Ω in the t-domain results in the system's averaged equations, in terms of amplitude and phase, which are given by :

Ȧ = -1 2 ξ 0 A -1 8 ξ 2 A 3 -1 2 κ ω n sin β + O(ε 2 ) A β = Aσ -3 8 χ 3 ωn A 3 -5 16 χ 5 ωn A 5 + 7 10 ω n A 3 + 1 2 κ ωn cos β + O(ε 2 ) (13)
Where ω n = √ 500.564 + 12.3N , ξ 0 = c 1 , ξ 2 = 1.85c 1 , χ 3 = 927 + 28N + 151α 1 , χ 5 = 347α 1 and κ = 16 3π α 2 V acV dc. The steady-state motions occur when Ȧ = β = 0, which corresponds to the singular points of Equation (13). Thus, the frequency-response equation can be writen in its implicit form as :

3 4ω n χ 3 A 2 + 5 8ω n χ 5 A 4 - 7ω n 5 A 2 -2σ 2 = κ Aω n 2 -ξ 0 + 1 4 ξ 2 A 2 2 ( 14
)
The normalized displacement W max with respect to the gap in the middle of the beam and the drive frequency Ω can be expressed in function of the phase β. Thus, the frequency response curve can be plotted parametrically as shown in Figure 2 for a typical resonator with the following dimensions :

l = 200µm, b = 4µm, h = 2µm.
The numerical simulations were carried out for an AC voltage V ac = 5mV .

FIG. 2 -Predicted forced frequency responses

This analytical model enables the capture of all the non linear phenomena in the resonator dynamics and describes the competition between the hardening and the softening behaviors. Specific parameters combination permits the compensation of the nonlinearities in order to enhance the dynamic range of the resonator, i.e. its detectability by obtaining a linear behavior (black curve).

Motional current

Since the system driving electrode/air/resonator constitutes a capacitor (CMEMS), any mechanical motion of the resonator directly translates into an electrical signal. The total capacitive current generated by this system can be expressed as :

I cap = -ω n V ac sin [ω n t] 1 0 bC n 0 1 -a 1 (t)φ 1 (x) dx+ (V dc + V ac cos [ω n t]) 1 0 bC n 0 φ 1 (x)a 1 (t) (1 -a 1 (t)φ 1 (x)) 2 dx
(15) The total capacitive current was calculated analytically using the results of the reduced order model in displacement and a Taylor series expansion of the capacitance.

Manufacturing

The fabrication starts with 200mm SOI wafers (4µm Si, 1µm SiO2). The use of DUV lithography combined with deep RIE process has allowed 500nm wide gaps and lines. Some low stiffness beams have been designed, so FH-vapor technique had to be improved to enable the release and protection against in-plane sticking. Main steps are shown in Figure 3.

FIG. 3 -Simplified process flow 4 Experimental characterisation

For a start, only the resonant beams were released. The fabricated resonators are electrostatically actuated in-plane. Considering the low capacitance variations and the high motional resistance combined with the important parasitic capacitances, tracking the resonance peak purely electrically is rather awkward. An original SEM set-up was developed, coupled with a real-time in-situ electrical measurement, using an external low noise lock-in amplifier (Figure 4). This set-up allows the simultaneous visualization of the resonance by SEM imaging and the motional current frequency response. Figure 5 shows some non-linear frequency responses. The residual stress ( Ñ bh = 15M P a) and the edge effects coefficient (C n = 1.8) have been measured experimentally and the quality factor is identified for every DC voltage from a linear peak. In addition to these 3 experimental parameters, all what we need to compare the experimental and the model results are the geometric and the electric parameters of the resonator (dimensions : 200µm × 2µm × 4µm, gap = 750nm, V ac and V dc). First comparisons are in good agreement with model results.

Conclusions

As detailed throughout this work, in-plane MEMS resonators was fabricated and electrically characterized thanks to an original SEM-setup. An analytical model including all the sources of nonlinearities was done in order to predict the resonator behaviors. This analytical model based on a reduced order model obtained with Galerkin procedure and solved via the averaging method, has the advantages to be simple and easy to be implemented for MEMS designers. Moreover, using this model, the dynamic range improvement of MEMS resonators is realizable by compensating the hardening and the softening behaviors. In a future work, the whole sensor will be released and characterized under ac acceleration, so its overall dynamic behavior will be studied. Experimental and model results will be compared, which will complete the model validation.

FIG. 4 -

 4 FIG. 4 -(4a) : Connection layout for the electrical characterization. (4b) : Block diagram of a lock-in amplifier.

FIG. 5 -

 5 FIG. 5 -Measured and predicted frequency responses

Références

  N. KACEM a,c , S. HENTZ b , S. BAGUET c , R. DUFOUR c

	a. CEA/LETI /3DSI/DIHS/LCMS, 17 rue des Martyrs 38054 Grenoble, France b. CEA/LETI /3DSI/D2NT/LSCDP, 17 rue des Martyrs 38054 Grenoble, France c. LaMCoS, INSA-Lyon, CNRS UMR5259, F69621, France
	Résumé :

Le mode de détection fréquentielle a pour avantages d'être extrêmement sensible, a le potentiel d'avoir une large gamme dynamique, peu sensible au bruit, une large gamme de linéarité et une faible consommation électrique. Le principe de détection est basé sur le changement de la fréquence de résonance induit par une modification de la raideur du résonateur. Afin de compenser la détérioration des performances lorsqu'on réduit les tailles des résonateurs des MEMS au NEMS, il s'avère important de trouver des conditions physiques permettant de maximiser le signal de détection et pousser les limites du comportement linéaire. Pour cela, un modèle complet qui prend en compte toutes les sources principales des nonlinéarités est nécessaire. Dans ce papier, un modèle analytique sur la dynamique non linéaire de micro et nanorésonateurs ainsi qu'une validation expérimentale sont présentés.


Guillaume Gadek
email: guillaume.gadek@litislab.eu

Alexandre Pauchet

Stéphan Brunessaux

Khaled Khelif

Bruno Grilhères

AI techniques to analyse a

Keywords: Deep Web, Social network analysis, User profiling, Group discovery, Graph analysis

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Web 2.0 and the social media have introduced a new paradigm in the informational space. Its specificities as a broadcast media enable anyone to be a new source of information, entertainment, or propaganda, at will. It gives power to the consumer, signalling defects on products ; it gives the opportunity to the citizen to directly chat with his/her representatives ; overall, the social web enables the user to be more connected and informed. However, the presence of threats on Twitter and other social platforms is attested : the jihadist group Daesh is said to benefit from the support of 100,000 accounts on Twitter [START_REF] Bertolin | Digital Hydra : Security Implications of False Information Online[END_REF] ; Russia is suspected by the FBI of interferences in the 2016 US election ; in almost every election, worldwide, the intensive use of deception has been widely observed during the last years. Automation enables any party to produce and diffuse content quite effectively, if we consider the appearance of malicious accounts in the classic media a victory. The diversity of threats implies a multiplicity of the tools to tackle all of the aspects of the problem. The quantity of messages exchanged in an Online Social Network can be astounding, with almost 500 million new tweets each day. As is possible the automation of their publishing, it is also possible to automate the reading. Opinion mining and topic detection enable the analyst to grasp the trend on a mass of texts, providing a classification along various keywords and characteristics.

The user accounts can be classified according to various taxonomies. In this article we distinguish the profile (who the user claims to be), and the behaviour (how s/he performs actions). Unsupervised machine learning helps here to cluster the users along similar types, and enables the analyst to recognise similar situations. The never ending list of "friendship" connections, as well as the list of interactions between user accounts, is fertile to grow graphs. This kind of graphs can be used to easily compute social influence scores [START_REF] Noordhuis | Mining twitter in the cloud : A case study[END_REF], and to detect one of the most interesting features of a social network : people naturally gather in groups, where there is more continuous interaction. To detect these groups from graphs, we rely on community detection algorithms [START_REF] Blondel | Fast unfolding of communities in large networks[END_REF] ; specific measures help the analyst to characterise the impact and the pertinence of such groups with regard to his preoccupations [START_REF] Gadek | Measures for topical cohesion of user communities on twitter[END_REF]. Galaxy2, on Tor, is a strange place. Created in 2015 to replace a predecessor social network (simply called Galaxy), it has been branded as the most frequented social network on Tor. In this article, we show the added value of a variety of tools to scan this very peculiar social network, analyse the topics of discussion during Galaxy2's uptime, detect its key-actors, and discover and characterise its communities. Finally, using all this information, we perform a case study, showing the interest of dedicated tools for social network analysis. This paper is organised as follows : Section 2 presents the website and the context of TOR, Section 3 presents the tools used, Section 4 shows the case study ; Section 5 proposes a discussion about our results and concludes this article.

Presentation of Galaxy2

The TOR network

Partly developed through DARPA funding in the 90s, Tor, The Onion Router, has been launched in 2002. Aiming to bring anonymity to the data flow, it relies on an encryption and routing protocol, named onion, to hide the content of the packets to the transiting servers. Tor is used either to anonymously access the clear web, as well as to access the so-called darknet : some websites are only accessible through the onion protocol, protecting the host. Well-known examples include a Wikileaks portal, and a disrupted illegal marketplace, the silk road. As anyone can use the Tor network and enjoy the increased privacy, it helps to breach censorship and can be used by journalists, political activists or anyone else. Unfortunately, Tor is also used to host illegal content, such as hacker forums, drug marketplaces, dark forums, porn and pedo-pornography 1 .

https

://www.fbi.gov/news/stories/playpen-creator-However, due to the perceived complexity of use and the strong incentive to link one's Internet profile with his real life (shopping, all kinds of services...), the global usage of Tor is not very high. Moreover, some countries deploy firewalls, laws and rules to prohibit this kind of tools.

Galaxy2 : history and main features

Founded in 2015 after the disruption of a previous Torhosted social network ("Galaxy"), Galaxy2 is based on an open source framework named elgg, enabling to build small social websites. According to its anonymous founder, Lameth, "The server broke down and your terrible host here (me, not the current host, mind you !) hadn't been keeping regular backups off the server." The service is shut down since end of October 2017 2 . The main features of Galaxy2 include The Wire, a space for microblogging posts ; blogs, polls and pages ; image and file sharing. Because of the anonymity introduced by the Tor network, the users are less keen to use their real names, and do not expose personal data. Thus, only the private direct messages are kept private, and it was possible to consult all the posts, friendship connections, images and comments performed by the users over the almost three years of uptime. The collection of our corpus covers a time range from Galaxy2 creation, on 9 th of January, 2015 to the 22 nd of September, 2017. It includes all traces of activity logged and then publicly available, but does not consists of personal profiles nor photos, excluded of the collect.

3 Tools for social media analysis

Focused on text processing

The first axis of analysis deals with text processing. The tremendous amount of new messages emitted through the Online Social Networks pushed the development of machine text understanding and summary. Moreover, as users often express their feelings and opinions about products, facts and events, one of the most necessary tasks is opinion mining, which can briefly be explained as the automatic computation of a couple (topic, sentiment) matching a message [START_REF] Pang | Thumbs up ? : sentiment classification using machine learning techniques[END_REF].

The sentiment, or polarity, enables the evaluation of the support or reject of an entity by the author of a message. It can be either computed specifically with a topic, using a learning corpus, or generically using linguistic resources. Such a resource, SentiWordNet [START_REF] Baccianella | Sentiwordnet 3.0 : An enhanced lexical resource for sentiment analysis and opinion mining[END_REF], associates polarities with sets of synonyms, sometimes considering contextual associations to modify the polarities according to the surrounding sentence. An anasentenced-to-30-years 2. https ://socialmediaalternatives.org/archive/collections/show/10 lyser, Vader [START_REF] Hutto | Vader : A parsimonious rule-based model for sentiment analysis of social media text[END_REF], has been made available as an open source module, and compiles various resources and a classifier to compute sentiment scores, at document level. Topic detection can be performed either through a supervised or an unsupervised method. An analyst can describe a topic using a few keywords, or rely on text clustering to let an algorithm cluster similar texts together, based on the semantics. Instead of matching pre-established categories, this approach adapts well to new corpora, enabling the analyst to grasp the topic distribution. Often cited as a reference for text clustering, LDA (Latent Dirichlet Allocation) [START_REF] Blei | Latent dirichlet allocation[END_REF] can briefly be resumed as a dimensionality reduction applied on a matrix where each line consists of the tf*idf representation of a text of the training corpus. It is said adapted to short text topic classification and can be associated with a module of visualisation of the detected topics, to better depict their distribution [START_REF] Sievert | Ldavis : A method for visualizing and interpreting topics[END_REF].

User profiling

One of the main tasks of social network analysis, or social listening, aims to spot the key actors, i.e. the most important users of the network. The focus is commonly directed either towards the influence [START_REF] Kwak | What is twitter, a social network or a news media ?[END_REF][START_REF] Rao | Klout score : Measuring influence across multiple social networks[END_REF], defined as the ability of a user to trigger actions from other users, or towards community detection [START_REF] Java | Why we twitter : understanding microblogging usage and communities[END_REF][START_REF] Aynaud | Static community detection algorithms for evolving networks[END_REF].

Influence is commonly defined as the ability to engage, i.e. to make the other users do something (typically, sending a message or clicking on a URL). A complete method has been exposed to build a social graph from Twitter follow links [START_REF] Noordhuis | Mining twitter in the cloud : A case study[END_REF]. This enables the computation of a daily PageRank, as a score of influence. However, using the public free API, a very long time (counted in months) is needed to obtain the complete social graph. To evaluate influence, various indicators have been compared, among which the number of retweets, number of followers and PageRank computed on a graph of friendship links [START_REF] Kwak | What is twitter, a social network or a news media ?[END_REF][START_REF] Lee | Finding influentials based on the temporal order of information adoption in twitter[END_REF]. Sometimes, the focus is not set on the most influential accounts, but on a general profiling to help the analyst understand "who" is a given account : what its typical behaviour is. Machine learning tools can answer this question using numeric features, through clustering or classification. When the data represent a graph, specific algorithms, such as RolX [START_REF] Henderson | Rolx : structural role extraction & mining in large graphs[END_REF], enable a tagging of the nodes based on their graph features.

Group detection

Studies in psychology highlight the power of the "group" as a structure, and the variety of its impacts on individual behaviour [START_REF] Milgram | Group pressure and action against a person[END_REF][START_REF] Cohen | Party over policy : The dominating impact of group influence on political beliefs[END_REF]. In computer science, a study on polarisation of the attitudes on online debates concludes similarly : groups can be considered as influencers, too [START_REF] Yardi | Dynamic debates : An analysis of group polarization over time on twitter[END_REF]. Detection. To detect these groups, the main approach relies on community detection from friendship relation graphs. A community is a set of nodes, in a graph, more densely linked than a random graph. An intuitive way to discover groups is to look for communities in a graph built from the social network data. However it has been pointed out that the social graph ("follow" graph) does not illustrate user interaction [START_REF] Lim | An interaction-based approach to detecting highly interactive twitter communities using tweeting links[END_REF]. As a response, random walks community detection have been applied on a graph of interactions between Twitter users (retweets and mentions) [START_REF] Tyshchuk | The nature of communications and emerging communities on twitter following the 2013 syria sarin gas attacks[END_REF]. To help choosing the best community detection method, a comparison of various state-of-the-art algorithms [START_REF] Cazabet | Simulate to detect : a multi-agent system for community detection[END_REF] on large networks (around 400k nodes) has been performed between FastGreedy [START_REF] Clauset | Finding community structure in very large networks[END_REF], InfoMap [START_REF] Rosvall | Maps of information flow reveal community structure in complex networks[END_REF] and Louvain/Blondel [START_REF] Blondel | Fast unfolding of communities in large networks[END_REF]. In this experiment, the Louvain method seems to be, by far, the fastest, for similar results in terms of quality.

Characterising the strength of the groups. Topological graph features such as the modularity value or the density of the detected groups can be considered to evaluate a community detection algorithm. A comprehensive review of scoring functions for community evaluation details the following measures [START_REF] Yang | Defining and evaluating network communities based on ground-truth[END_REF]. Internal density (d) follows the intuition that communities are more dense than a random set of nodes. However, for large, non-complete communities, its value may be very low. On the other side, the smallest possible communities (pairs of nodes) have an internal density of 1. Triad participation ratio (TPR) evaluates the number of nodes belonging to triads, or triangles, in community S. A value of 1 means that the group is strongly internally linked. Communities should include numerous triangles, showing interaction between the members. Conductance (c), evaluates the quantity of edges linked with the other communities [START_REF] Shi | Normalized cuts and image segmentation[END_REF]. It illustrates the community behaviour, ranging from 0 (not linked towards the exterior) to 1 (strongly connected to other groups). Modularity (Q) focuses on the number of internal edges (which link members of a community), compared to a "normal" quantity if the graph was random. Introduced by [START_REF] Newman | Modularity and community structure in networks[END_REF], a high modularity Q, close to 1, denotes a good partitioning at the graph level. These topological metrics enable the analyst to check whether a community is sufficiently connected internally and/or with its boundaries : internal interaction and reach towards the exterior are measured.

Characterising the topical cohesion and relevance of the groups. To measure each of the obtained groups based on the topics expressed by the users, two topical metrics ξ and ρ, inspired from machine learning (ML) precision and recall, have been proposed [START_REF] Gadek | Measures for topical cohesion of user communities on twitter[END_REF]. These two ML inspired topical measures, which enable to better attribute a weight of the importance of a community on a given topic (ρ), and to evaluate the internal cohesion of a group (ξ), make the link between the graph and the semantic of the texts. Another measure (θf.igf ) [START_REF] Gadek | Measures for topical cohesion of user communities on twitter[END_REF], similar to the natural language processing domain tf * idf , evaluates the specificity and the importance of a topic in a group. The analysis of these scores yields interesting insights on a social and textual corpus. For marketing purposes, one can identify then target a customer group, helping to induce a positive opinion about a new product.

Discussion and contribution

Although much work has been done to tackle specific challenges in the domain of Online Social Networks, only a few systems and frameworks propose a complete analysis of a website. Most of the platforms focus on the graph and miss the texts, such as UCINET, Net-Draw, Pajek and ORA, presented in [START_REF] Everton | Disrupting dark networks[END_REF], or a work on graph characterisation [START_REF] Ediger | Massive social network analysis : Mining twitter for social good[END_REF]. As in a mirror, a set of efficient textual analysis tools is available, enabling specific platforms for news monitoring [START_REF] Sankaranarayanan | Twitterstand : news in tweets[END_REF] or for disaster management and evaluation [START_REF] Toriumi | Real-time tweet classification in disaster situation[END_REF]. However they lack of user profiling features and social graph exploration and analysis. In this paper, we propose a full-stack processing pipeline, integrating various open-source modules and providing our own model for specific aspects. We perform the textual analysis on the text, model the users and propose an influence ranking, and conclude with exploration through graph analysis and community detection and characterisation.

Case study

In this section, the Galaxy2 network is exposed through the explanation of the collected data type. Then, results are proposed to analyse the texts, the user accounts and the groups, which are an emerging social feature.

Types of actions logged

Fortunately for the privacy, not every action can be retrieved. In the collected data, actions are regrouped to better grasp their diversity : first are the comments. Users can add some words to react to the other's actions : publication of photos, files, new pages or polls, and of course blog posts. A total of 4032 comments on blog posts are stored ; much less (375) on photos. A second kind of actions gathers the upload of files and images : those are deemed to be shared, and frequently include pictures from the Anonymous. As Tor and Galaxy2 philosophies are not based on personal holidays pictures publication, the quantity of images is quite low (around 600 pictures, in total). Creation of pages, groups and polls and their modification (new topics of discussion) are seen as an aspect of the network life. This step of page creation is to be linked with the cluster of votes, replies and publication on said pages/groups. Overall, 1944 blog posts have been emitted, and 548 groups created. Blogging or "micro"-blogging features were the predominant ones, with 29,000 posts on The Wire, the message feed. Message size was not limited, though frequently short. Finally, the last cluster includes some connection information : account creation notifications (19233 "joined the site"), link establishment between a user and a page, a group or another user (61027 friendship links).

Text : topic and sentiment repartition

LDA for topic detection. LDA is commonly used with a high number of topics ; a number of 200-500 is usually recommended as a first try3 . This method clusters documents with similar tf.idf representations, resulting in a predetermined number of emerging topics, seen simultaneously as sets of documents and as tf.idf vectors. As a trade-off between computation time and representativeness of the topics, a number of 40 topics is chosen. Compared to other values, this choice results in a distribution of the documents over the topics, also limiting the number of too-close topics.

Figure 1 -Visualisation of the topics

Figure 1 shows a tool, proposed by [START_REF] Sievert | Ldavis : A method for visualizing and interpreting topics[END_REF], which enables to navigate along the 40 detected topics through the word frequencies in a given topic (in red), compared to word frequencies over the whole corpus (in blue), in the right panel. A principal component analysis (PCA) is performed to place the topics in a 2D-space, in the left of the diagram. The area of the circles is proportional to the quantity of documents clustered in the topics. Thanks to this tool, the analyst can visualise the topic distribution of, here, more than 30,000 docu-ments, while having the ability to see which words are more frequent or more relevant in each of the topics.

Sentiment exploitation. Each text is also analysed with regard to the sentiment, representing the overall polarity of a text, as perceived by a reader. The implementation relies on the Vader module [START_REF] Hutto | Vader : A parsimonious rule-based model for sentiment analysis of social media text[END_REF]. Even if some of the sentiment predictions may be inaccurate, it results in a global view. For instance, Figure 2 proposes to compare the polarity of the texts containing some keywords : onion, Tor, Snowden, Trump and Syria 4 . Instead of an average value, and as one message is enough to set either a max or min sentiment value, we represent it as a boxplot, showing the statistical distribution. Onion is globally well perceived, with positive messages. Edward Snowden seems to enjoy a good reputation, while Galaxy2 members are more mitigated about Donald Trump. Finally, the polarity is more negative about Syria, because these messages are susceptible to mention the current conflict. The sentiment view can also be exploited to characterise a user activity. As an example, Figures 3 and4 expose the sentiment repartition of the messages of two active authors : XL33t and Fenris. On both figures, an artefact, for a sentiment of 0.0, exists, representing the messages where no polarity could be extracted by the analyser (no known sentimental word). However, the repartition shows some signals. On the first figure, XL33t seems to mostly emit very positive messages. The second author, Fenris, covers the whole range of sentiment, avoiding to publish too positive messages. This view let the analyst grasp one aspect of a user behaviour, as well as to estimate his activity 5 .

No distinction has been made between uppercase and lowercase.

5. Thanks to the number of messages, indicated on the yaxis.

Influential users and types of behaviour

Top-5 key users. Influence can be measured through a variety of prisms. In a first glance on a social network, one can look for the key actors, detecting a "top5". Table 1 compares the most connected users (having the highest number of friends, noted #Friends) ; the most popular users (the most mentioned, noted #Mentions) ; the users of reference (a score based on the mentions graph, in the column Sc(Mentions), explained in the following paragraph) ; and the most active ones (performing the highest number of actions on Galaxy2). Inspired from the literature [START_REF] Kwak | What is twitter, a social network or a news media ?[END_REF][START_REF] Lee | Finding influentials based on the temporal order of information adoption in twitter[END_REF], a score of influence is computed from G M the graph of mentions. The intuition is the following : a mention gives some value, some social capital to the mentioned user ; this value is higher if the author of the mention already has some influence him/herself. The PageRank algorithm also follows this intuition and has been shown to empirically match this representation of influence. In consequence, ScoreMentions is the ranking resulting from the Pagerank scores of each user-node in G M . In a few words about Table 1 : XsyntaX outperforms every other account, with 7974 actions performed during the scope of the study ; the second, kheper, performed 1846 actions. Lameth is the founder of this social network ; as such he is often either for thankful messages for hosting, or for administration purposes. ChatTor provides a chat service through Tor ; this account promotes the service and publishes news and updates.

Although some names are present on every influence score Top5, they do not all indicate the same kind of influence. Lameth is mentioned a lot, due to his status of host. However, he did not intend to be the friend of everyone else, or to be the most active. Xl33t connected to many accounts, but is not mentioned as much as the other influential users. Influence and key-actors take many different forms, while only the symptoms can be measured.

Types of behaviour. The social network analyst cannot be expected to know who is every user on a platform. More precisely, the data of interest can be narrowed along a few aspects to grasp the essence of the behaviour. Biography contains the user identity : username, ID, date of creation and other available data. Style explains how the user writes : length of messages and quantity of punctuation usually make a difference, and can be combined with the main topic of interest and global sentiment polarity. The social aspect details the number of friends, of mentions, and the resulting influence of the user, both from the graph of friendship and the graph of mentions. Media groups the features explaining the type of actions and objects posted (be it photos, texts, etc). Finally, the temporal aspect covers the global rhythm of publication of the user : average number of posts on TheWire per day, and average number of actions per day. All these numerical features enable the repartition of the users along a few typical clusters, whose reduced number (commonly 4 to 6, depending of the data) enables the analyst to get used to this unsupervised labels.

Technically, this repartition is made in a few steps. First the data is cleaned, so as to avoid zero divisions and exponential distribution of the data : some features are converted to their log-values to reduce dis-persion, and normalised to follow a 0-mean, 1-standard deviation distribution. A PCA reduces the dimension of the problem, switching from 34 variables to 5 and still keeping most of the dataset variance. Finally, a k-means finds the groups ; a number of 4 groups is a good trade-off between dataset dispersion and cluster shape.

Quantity of user accounts

Figure 5 -of the user profiles Figure 5 shows the repartition of the users along the 4 types of profiles. The first type (0) is the most common, including more than 90% of the profiles : most of the accounts are created, perform one or two actions, and then are forgotten. A second type, profile (1), characterises the regularly active users, even though they are not the central users of the network. Finally, profile (2) and the sole user in profile (3) are the central users, very active, those who produce most of the contents on the network. A similar repartition had already been remarked on networks such as Twitter [START_REF] Kwak | What is twitter, a social network or a news media ?[END_REF].

To picture the shape of the profile clusters, Figure 6 represents each of the 19,177 Galaxy2 users along the first two dimensions of the PCA. These dimensions are linear combinations of the behavioural features, and consequently are quite abstract. However, positions near (0,0) are linked with very low levels of activities (the red cluster (0) being the most populated). In blue, cluster [START_REF] Bertolin | Digital Hydra : Security Implications of False Information Online[END_REF] shows the many different ways to be a standard active user. The green cluster (2) is very dispersed but matches high levels of publications, be it by posts, comments or creation of pages. Finally, the purple cluster (3) is constituted of only one account, Spooky, performing an average of 2.5 actions each day.

When the analyst reviews the posts, thanks to this step of profiling, he can quickly evaluate if the messages comes from well-established, influential users, or whether a given topic is dominated by usually inactive accounts, or show a unusual repartition.

Interactive groups, their cohesion and structure

About the user mentions. A common practice on social networks consists to mention people, using an "@" sign before their usernames in the text of the messages. At first this was only a social behaviour without any technical feature in the code of the social platform ; nowadays most platforms recognise such mentions.

As Galaxy2 is based on the old-fashion social framework elgg, such a feature is not hard-coded, but is still used by some members. Following the intuition that this interaction (the mention) would bring us valuable information, a mention extraction module has parsed each of the publications in search for "@" signs followed by usernames.

From the set of mentions M associated with the authors A, a graph of mentions, G M = (V, E) is built.

V is the set of the union of the authors and the mentioned users ; edges e ∈ E links the author of a message to the eventual mentioned user. This graph G M is composed of 968 nodes, linked by 2342 edges 6 . The Louvain community detection [START_REF] Blondel | Fast unfolding of communities in large networks[END_REF] results on a set of 31 communities, amongst which only 11 contain more than 3 members. Figure 7 illustrates one of these communities. Red nodes are part of the detected community ; blue nodes are the only external contacts, the boundary of the community in the graph G M . A central user, Bishop, is the target of a few mentions, notably from an auda-6. there was a total of 5481 mentions : some accounts have been mentioned by a same user various times cious account, Nishikino_Maki 7 . In a glance, we see that this community is centred on Bishop, who is not the most active in terms of community life (he does not mention the other members of the group). This community view helps the analyst to see the relations between a user and the rest of the network, and can guide his exploration along the interaction between accounts. However, as this graph of mentions is built from a social usage (using "@" to mention a user), the tool probably missed some differently written mentions and thus may be incomplete 8 .

Bishop

The friendship graph. The most known feature of social networks is the friendship connection. On Ga-laxy2, one can claim his friendship with another user, which is considered reciprocal on Galaxy2. This action is part of the list of the collected activities, and enables to link users along these friendship relations. Let G F be the graph of friendship, where nodes are user accounts. Edges represent a claim of friendship. From this graph, communities emerge, using the Louvain algorithm to reveal them. These communities may vary in number, based on the algorithm used. Here, 32 communities were obtained, amongst which 11 include more than 3 users. Figure 8 shows the distribution of the communities along two topological measures : xaxis gives the size of the group while y-axis represents the conductance, that is the proportion of boundary edges, linking the community to its environment, showing both its influence or its isolation. On Figure 8, a group attracts the attention : with size=125 and conductance=0.74, this community is less tied to the rest of the network than it normally should. Its topical scores, based on [START_REF] Gadek | Measures for topical cohesion of user communities on twitter[END_REF], require some interpretation. ξ = 0.064 means that only 6,4% of its 7. He claimed to be "building a porn site cuz i can" 8. This graph G M is one of the graphs of interaction, not the only one. members, as a maximum, have been active about the same topic ; however, compared with the duration covered on the corpus, this situation is not surprising. In particular, this "main topic" clusters mainly around two sets of texts at different dates. The first refers to a small pornographic discussion group ; the second concerns the use of peer-to-peer mail through Tor. These topical measures may benefit from improvements on the topic detection part, notably covering the temporality of topics and their labelling. This would lead to a more usable topic modelling, and a more precise group characterisation for the analyst.

Conclusion

The emergence of modern social networks reveals the inherent complexity surrounding us. Although most of the analysis is focused on the most known Online Social Networks (OSN), such as Twitter or Facebook, other instances exist ; Galaxy2 is much smaller than Twitter, but big enough to turn its analysis tedious due to the amount of exchanged messages. We presented a whole system capable of analysing any type of OSN, showing its capabilities on a Tor-hosted social network. The functionalities include text analysis for topic and sentiment, user profiling and graph analysis, both on the friendship links as well as on the interaction between users. We showed that the tools, mostly developed for Twitter, can also be exploited for smaller networks. This approach has easily been adapted to the specific links and interactions of Galaxy2, as it could be for other platforms such as Reddit or Facebook. Future work will be oriented on real-time processing, to analyse a social network as it lives. We have the intuition that a stream of messages would better fit the requirements in scaling and response times. We also desire to publicly release the Galaxy2 corpus, as one of the first complete social network archives.

Figure 2 -

 2 Figure 2 -Sentiment distribution for some keywords

Figure 3 --Figure 4 -

 34 Figure 3 -Visualisation of the sentiment emitted by the user XL33t

Figure 6 -

 6 Figure 6 -Visualisation the clusters of users in a PCA space

Figure 7 -

 7 Figure 7 -Visualisation of a small community and its contacts through mentions

Figure 8 -

 8 Figure 8 -Visualisation of the topological features of the communities

Table 1 -

 1 Top5 of the users along three dimensions

	#Friends	#Mentions	Sc(Me.)	#Actions
	XsyntaX	8187	XsyntaX	514	Oxyy	XsyntaX	7974
	prozac	3182	Oxyy	164	XsyntaX	kheper	1846
	Spooky	3012	Lameth	121	Lameth	prozac	1783
	xl33t	2140	Fenris	119	ChatTor	ChatTor	1583
	kheper	1922	cpnnemo	96	MahaKali	Spooky	1569

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