Thomas Poinot

Marie-Claude Bartholin

Alexandre Govin
email: govin@emse.fr

Philippe Grosseau

Influence of the polysaccharide addition method on the properties of fresh mortars

Keywords: Polysaccharide (D), Admixture (D), Water retention (C), Rheology (C)

This study focused on comparison of polysaccharide addition methods, either in powder form, or as a solute in the mixing water. The influence of the methods was assessed by measuring water retention and rheological properties with one cellulose ether and two guar ethers.

Polysaccharides were more efficient to enhance water retention and rheological properties when they are pre-dissolved in the mixing water. This is related to differences in polymer concentration in the pore solution of mortar. These differences are not stemming from a difference in dissolution kinetics, but from a difference in adsorption on growing hydrates.

Being immediately available when it is pre-dissolved, the admixture slows down the nucleation and growth of hydrates limiting in turn the surface area for further adsorption.

Consequently, more molecules are left in the interstitial solution and a lower dosage is required to achieve the overlapping of polymer coils, responsible for the effectiveness of polysaccharides.

Introduction

Polysaccharides, natural or derivatives, are commonly used as admixtures in modern factorymade mortars. They are able to improve the water retention capacity of cement-based mortars at fresh state [START_REF] Desbrieres | Cement cake properties in static filtration. Influence of polymeric additives on cement filter cake permeability[END_REF][START_REF] Pourchez | Some aspects of cellulose ethers influence on water transport and porous structure of cement-based materials[END_REF][START_REF] Patural | Cellulose ethers influence on water retention and consistency in cement-based mortars[END_REF][START_REF] Bülichen | Working mechanism of methyl hydroxyethyl cellulose (MHEC) as water retention agent[END_REF][START_REF] Marliere | How water retention in porous media with cellulose ethers works[END_REF][START_REF] Lasheras-Zubiate | Effect of the addition of chitosan ethers on the fresh state properties of cement mortars[END_REF]. Limiting the absorption of mixing water by the substrate allows enhancing mechanical and adhesive properties of the mortar [START_REF] Bertrand | Wedge Splitting Test: A test to measure the polysaccharide influence on adhesion of mortar on its substrate[END_REF][START_REF] Jenni | Influence of polymers on microstructure and adhesive strength of cementitious tile adhesive mortars[END_REF]. Due to their thickening properties, polysaccharides improve also the mortars rheological properties since their use results in a highly shear thinning material [START_REF] Khayat | Viscosity-enhancing admixtures for cement-based materials -An overview[END_REF]. This particular rheological behavior induced by polysaccharides ensures a high apparent viscosity at low shear rate in order to ensure sagging and sedimentation resistance, while maintaining a high fluidity because of low viscosity at high shear rate [START_REF] Khayat | Effect of Welan Gum-High-Range Water Reducer Combinations on Rheology of Cement Grout[END_REF][START_REF] Rols | Effects of different viscosity agents on the properties of self-leveling concrete[END_REF][START_REF] Lachemi | Selfconsolidating concrete incorporating new viscosity modifying admixtures[END_REF][START_REF] Paiva | Effects of a water-retaining agent on the rheological behaviour of a single-coat render mortar[END_REF][START_REF] Sonebi | Rheological properties of grouts with viscosity modifying agents as diutan gum and welan gum incorporating pulverised fly ash[END_REF][START_REF] Leemann | The effect of viscosity modifying agents on mortar and concrete[END_REF][START_REF] Cappellari | Influence of organic thickening admixtures on the rheological properties of mortars: relationship with water-retention[END_REF]. The major drawback of the use of polysaccharide in cement-based materials is the induced delay of cement hydration [START_REF] Peschard | Effect of polysaccharides on the hydration of cement paste at early ages[END_REF][START_REF] Ridi | Hydration process of cement in the presence of a cellulosic additive. A calorimetric investigation[END_REF][START_REF] Silva | The influence of polymers on the hydration of portland cement phases analyzed by soft X-ray transmission microscopy[END_REF][START_REF] Pourchez | HPMC and HEMC influence on cement hydration[END_REF][START_REF] Pourchez | Current understanding of cellulose ethers impact on the hydration of C3A and C3A-sulphate systems[END_REF][START_REF] Knapen | Cement hydration and microstructure formation in the presence of water-soluble polymers[END_REF].

Most studies are devoted to the influence of cellulose derivatives since they represent the most widely industrially used polysaccharidic admixtures. Nevertheless, the use of hydroxypropylguars (HPGs) is of interest since the HPG manufacturing is less pollutant than cellulose ethers [START_REF] Biasotti | Highly substituted hydroxypropylguar: a strong contribution to construction chemistry[END_REF]. HPG is now well-established in the construction industry as water retention agent for mortars [START_REF] Biasotti | Highly substituted hydroxypropylguar: a strong contribution to construction chemistry[END_REF]. In previous studies, the influence of HPG on water retention capacity [START_REF] Poinot | Importance of coil-overlapping for the effectiveness of hydroxypropylguars as water retention agent[END_REF] and rheological properties [START_REF] Poinot | Influence of hydroxypropylguars on rheolocial behavior of cement-based mortars[END_REF] of cement-based mortars was investigated. In agreement with other authors [START_REF] Desbrieres | Cement cake properties in static filtration. Influence of polymeric additives on cement filter cake permeability[END_REF][START_REF] Bülichen | Working mechanism of methyl hydroxyethyl cellulose (MHEC) as water retention agent[END_REF][START_REF] Marliere | How water retention in porous media with cellulose ethers works[END_REF], the importance of polymer coil overlapping for the efficiency of HPG as admixture was highlighted.

The influence of HPG on the early age hydration of cement has been also investigated [START_REF] Poinot | Impact of hydroxypropylguars on the early age hydration of Portland cement[END_REF]. It was assumed that the mechanism responsible for the hydration delay is a decrease in the hydrates growth rate because of HPG adsorption on hydrated phases via polar interactions.

The influence of the HPG pre-dissolution in the liquid phase has been studied too. A higher hydration delay was noticed after pre-dissolution, especially for HPG with low substitution degree.

Method of chemical admixtures addition, and in particular the delayed addition, has been often investigated by researchers in order to improve the knowledge about the working mechanism of these molecules in the cement-based materials. Delayed addition of retarders such as sucrose, EDTA, calcium ligno-sulphonate, oxalic acid or organic acid has been studied [START_REF] Bruere | Importance of Mixing Sequence when using Set-Retarding Agents with Portland cement[END_REF][START_REF] Jennings | Interpretation of the effects of retarding admixtures on pastes of C3S, C3A plus gypsum and Portland cement[END_REF][START_REF] Luke | Effect of sucrose on retardation of Portland cement[END_REF]. It was found for example that delayed addition of sucrose leads to a greater percentage of sugar remaining in solution because less retarder is consumed in the initial reaction [START_REF] Luke | Effect of sucrose on retardation of Portland cement[END_REF]. Therefore, sucrose retards further hydration when its addition is delayed. It is also well know that the fluidity and the fluidity loss of fresh cement-based materials are affected by the time of superplasticizers addition [START_REF] Uchikawa | Influence of kind and added timing of organic admixture on the composition, structure and property of fresh cement paste[END_REF][START_REF] Hanehara | Interaction between cement and chemical admixture from the point of cement hydration, absorption behaviour of admixture, and paste rheology[END_REF][START_REF] Aiad | Effect of delaying addition of some concrete admixtures on the rheological properties of cement pastes[END_REF][START_REF] Aiad | Influence of time addition of superplasticizers on the rheological properties of fresh cement pastes[END_REF]. Flatt and Houst [START_REF] Flatt | A simplified view on chemical effects perturbing the action of superplasticizers[END_REF] have proposed a simplified view on the effects of superplasticizers in concrete. It appears that superplasticizers interact with the ongoing chemical reactions and hence these molecules can be consumed in an organo-mineral phase formed around cement particles. The delayed superplasticizer addition allowed confirming this hypothesis since the admixture is more effective to contribute to the dispersion because the polymer consumption is reduced.

The polysaccharide pre-dissolution in mixing water was useful to better understand the interaction between HPG and cement and its impact on cement hydration kinetics [START_REF] Poinot | Impact of hydroxypropylguars on the early age hydration of Portland cement[END_REF]. The aim of the current paper is to reuse this simple method of investigation in order to examine the key properties of freshly-mixed mortars induced by polysaccharides: water retention capacity and rheological behavior.

These two properties will thus be characterized on mortars prepared with two methods of addition: (i) "dry addition", the common way where the polymer is added as dry powder and homogenized with all the solid phases before being put into contact with water and (ii) "predissolved", where the polymer is first dissolved in the mixing water before being mixed with the dry mixture composed of sand and cement. The characterizations of dissolution kinetics and adsorption ability of polysaccharides will be useful to interpret the experimental data.

Finally, a schematic representation of the interaction between polysaccharide and cement will be presented and its impact on mortar macroscopic properties will be discussed.

Materials

Cement

This study was conducted using a CEM I 52.5 R CE CP2 NF type cement according to the EN 197-1 and NF P 15-318 standards. Chemical and phase compositions of the cement used are presented in Table 1. Oxide composition was determined by X-ray fluorescence spectroscopy using a Bruker-AXS SRS3400 instrument. Phase composition was obtained by XRD using a Siemens D5000 instrument. Siroquant V2.5 software was employed to quantify the amounts of individual phases present in the cement by following Rietveld's method of refinement.

Organic admixtures

The description and comparison of the cellulose and guar chemistry were detailed in [START_REF] Poinot | Use of ultrasonic degradation to study the molecular weight influence of polymeric admixtures for mortars[END_REF].

Guar gum is a polysaccharide extracted from the seed endosperm of Cyamopsis tetragonolobus, a native plant from India. This is a galactomannan consisting of a (1-4)linked β-D-mannopyranose backbone, with random branchpoints of galactose via an α-(

linkage. The ratio of mannose to galactose is about 1.8. HPG are obtained from the native guar gum via an irreversible nucleophilic substitution, using propylene oxide in the presence of an alkaline catalyst. Cellulose is a polysaccharide composed of individual anhydroglucose units linked through β-(1-4) glycosidic bonds. Because of strong intermolecular hydrogen bridging bonds, cellulose is not soluble in water. Thereby, cellulose ethers are obtained by pretreating cellulose with base (alkali cellulose) in order to break hydrogen bonds and to make accessible the active groups for etherifying agents. In the present work, two HPG and one HMPC were studied. Table 2 presents the qualitative substitution degrees (provided by the manufacturer), the weight-average molecular mass (determined by size-exclusion chromatography, analyses were carried out on a Water apparatus) and the parameters characterizing the concentration dependence of zero-shear viscosity of admixtures dissolved in 20 mM lime solution (b 1 and b 2 ) as explained in section 3.2.

The molar substitution ratio (MS HP ) is defined as the number of hydroxypropyl groups per anhydroglucose units and is less than 3 for our molecules. The degree of substitution, noted DS M , represents the amount of substituent methoxyl groups on the anhydroglucose units of cellulose and is about 1.8 for HPMC 2 according to the manufacturer. The weight-average molecular mass is noted as Mw and the critical overlap concentration of polymer coils is noted as C*. These three polysaccharidic admixtures were chosen since they exhibit strong (HPG 1), medium (HPG 3) and slight (HPMC 2) pre-dissolution effect regarding cement hydration kinetics [START_REF] Poinot | Impact of hydroxypropylguars on the early age hydration of Portland cement[END_REF].

Methods

All tests were carried out at controlled temperature because fresh mortar properties and dissolution kinetics are temperature-dependent. All the rheological measurements were carried out with Anton-Paar Rheometer MCR 302.

Freshly-mixed mortars properties

For a given formulation (i.e. kind and dosage of admixture), freshly-mixed mortars properties (i.e. water retention and rheological properties) and pore solution viscosity were determined on the same mortar which have been divided into three parts. Each test was repeated in order to ensure the reproducibility of the results. Moreover, the same procedure was performed with a mortar without admixture as a control test.

Preparation of mortars

In the case of pre-dissolved addition, admixtures were previously dissolved in deionized water. Complete dissolution of all polymers was obtained after strong stirring for 24h by means of a magnetic stirrer. Polymer dosages in mortars varying from 0.1 to 0.66% by weight of cement (bwoc) by preparing polymer solutions of concentrations ranging from 1 to 6.66 g.L -1 .

Mortars were then prepared according to the following mixture proportions: Dry mixture (i.e. cement, sand, filler, and polymer in the case of dry addition) was homogenized in a shaker (Turbula, Wab) for 15 min. Deionized water or admixture solution, according to the method of polymer introduction, was then added to the dry mixture in order to obtain a water to cement ratio W/C = 1. Mortars were mixed (MIx40, CAD Instruments) in accordance with EN 196-1 [START_REF]Methods of testing cement -Part 1: Determination of strength[END_REF].

It is worth mentioning that the mortar formulation with high W/C was adapted from the CEReM (European consortium for study and research on mortars) mixture design [START_REF] Pourchez | Some aspects of cellulose ethers influence on water transport and porous structure of cement-based materials[END_REF][START_REF] Patural | Cellulose ethers influence on water retention and consistency in cement-based mortars[END_REF]. This work is indeed a part of a larger study that focuses on the influence of HPG on overall mortar properties at the fresh state. Moreover, regarding water retention, high W/C ratio corresponds to extreme conditions which are useful to highlight the effectiveness of HPG as water retention agent.

Water retention measurements

Different tests, based on a measurement of the removed water after suction or depression, allow measuring the water retention capacity of freshly-mixed mortar [START_REF] Patural | Cellulose ethers influence on water retention and consistency in cement-based mortars[END_REF]. The test specified in the ASTM C1506-09 standard [START_REF]Standard test Method of Water Retention of Hydraulic Cement-Based Mortars and Plasters[END_REF] was performed 15 min after mixing in order to measure the water loss of mortar under depression. The standardized apparatus was submitted to a vacuum of 50 mm of mercury for 15 min. Then, water retention capacity, noted WR, was calculated using the following equation: W 0 represents the initial mass of mixing water; W 1 is the loss of water mass after aspiration.

100 (%) 0 1 0 × - = W W W WR (1)

Mortars rheological properties

The method used to investigate the fresh mortar rheological properties was well detailed in a previous study [START_REF] Poinot | Influence of hydroxypropylguars on rheolocial behavior of cement-based mortars[END_REF]. Briefly, a vane-cylinder geometry was employed with the gap thickness, distance between the periphery of the vane tool and the outer cylinder, of 8.5 mm. The calibration was performed with glycerol, following the Couette analogy [START_REF] Ait-Kadi | Quantitative analysis of mixer-type rheometers using the Couette analogy[END_REF][START_REF] Choplin | La rhéologie systémique ou une rhéologie au service d'un génie des procédés et des produits[END_REF].

The mortar was introduced into the measurement system at the end of the mixing. The suspension was then held at rest for 6 min. Ten minutes after the contact between cement and water, the mortar was pre-sheared for 30 s at 100 s -1 in order to re-homogenize the sample and to clear its flow history. After a period of rest of 4.5 min, the rheological measurements were started, i.e. at the age of 15 min.

Imposed shear rate was decreased by step from 300 to 0.06 s -1 . At each shear rate, the measuring time was adjusted in order to obtain a steady state whatever the formulation [START_REF] Pourchet | Effect of the repartition of the PEG side chains on the adsorption and dispersion behaviors of PCP in presence of sulfate[END_REF][START_REF] Geiker | The effect of measuring procedure on the apparent rheological properties of self-compacting concrete[END_REF]. Nevertheless, because of sedimentation risk due to high W/C ratio, the samples were systematically sheared at 100 s -1 for 20 s before each imposed shear rate in order to put back in suspension particles of the mortar. This resuspension procedure was validated in [START_REF] Patural | Cellulose ethers influence on water retention and consistency in cement-based mortars[END_REF] and [START_REF] Poinot | Influence of hydroxypropylguars on rheolocial behavior of cement-based mortars[END_REF]. Finally, the measurement procedure took about 17 min for 16 steps.

The results can be expressed as shear stress τ according to shear rate γ& . Experimental data were fitted well with the Herschel-Bulkley (HB) model [START_REF] Herschel | Measurements of consistency as applied to rubber-benzene solutions[END_REF], which is often used to describe mortars rheological behavior (see Fig. 2a):

n Kγ τ τ & + = 0 (2)
where 0 τ is the yield stress, K the consistency coefficient and n the fluidity index which characterizes how shear-thinning the mortar is. In the following, the three HB parameters were thus chosen to compare admixtures to each other.

Pore solution viscosity

At 15 min (i.e. similar to water retention and mortars rheological measurements), a large volume of mortar, in order to have a representative sample, was centrifuged (Thermo Scientific, Sorvall Legend XF) for 10 min at 4,500 rpm. Then, the supernatant was collected and centrifuged again (Eppendrof, MiniSpin Plus) at higher speed (14,500 rpm) for 5 min which allows removing residual particles.

The steady shear flow of final supernatant, representing pore solution, has been investigated using decreasing logarithmic ramps in the 10 3 -1 s -1 range with cone and plate geometry (2° cone angle, 50 mm diameter). Flow curves

) (γ η & f =
exhibited typical shear thinning behavior with a Newtonian region in the low shear rate range [START_REF] Morris | Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions[END_REF][START_REF] Risica | Rheological properties of guar and its methyl, hydroxypropyl and hydroxypropyl-methyl derivatives in semidilute and concentrated aqueous solutions[END_REF]. Experimental data were well correlated with the Cross model [START_REF] Cross | Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems[END_REF] (see Fig. 2b):

) ( 1 ) ( 0 n γ α η η η γ η & & + - + = ∞ ∞ (3)
where η 0 is the zero-shear rate viscosity, η ∞ the infinite rate viscosity, α a relaxation time and n a non-dimensional exponent. Among Cross parameters, the zero-shear rate viscosity represents the constant viscosity in the Newtonian plateau region at low shear rate and was chosen to characterize pore solution viscosity.

Dissolution kinetics

The dissolution process was monitored by viscosity measurements. The procedure was the following, adapted from Wang et al. [START_REF] Wang | Dissolution kinetics of guar gum powders. I. Methods for commercial polydisperse samples[END_REF]: HPG was introduced (final concentration: 6.66 g.L - 1 ) through a sieve in 1L of 20 mM lime solution. The dispersion through a sieve allows having a good dispersion of the sample into the vortex created by the mechanic stirrer and thus minimizing the aggregation of particles and producing a homogeneous polymer solution. The experiment was done in a sealed reactor, thermostated at 20°C, under continuous flow of nitrogen in order to avoid carbonation of lime.

At different times, an aliquot of approximately 5 mL was taken from the batch solution and centrifuged by means of a micro-centrifuge (Eppendorf MiniSpin Plus, 14500 rpm) for 5 min in order to remove undissolved particles. The supernatant was collected and homogenized by vortex-stirring. The viscosity measurements were then performed exactly in the same way than for the pore solution. Finally, the concentration at a given time was calculated from calibration curves.

The concentration dependence of zero-shear viscosity is well known and can be described by 2.

Adsorption measurements

A High TOC II apparatus (Elementar, Hanau, Germany) equipped with a CO2 detector was used to quantify the amount of polymer adsorbed on cement. As to determine the pore solution viscosity, a large volume of mortar was centrifuged at 15 min. The alkaline pore solution containing the non-adsorbed polymer was diluted with 0.1 M HCl at a ratio of 1:10 (vol/vol) in order to obtain a final pH of about 1.0 [START_REF] Bülichen | Working mechanism of methyl hydroxyethyl cellulose (MHEC) as water retention agent[END_REF] and then tested with the TOC analyzer.

The TOC analyzer was first calibrated with pore solution of a control mortar without admixture and with solutions of admixture of known concentration. Thus the adsorbed amount was calculated from the difference in concentrations of polymer present in pore solution and in solution without contact with cement, taking into account the amount of organic carbon in cement.

Results

Fresh state properties of mortar

Water retention capacity

The effect of method of polysaccharide introduction on WR of admixed mortars according to the dosage is presented Fig. 3.

The control test performed with a mortar without admixture exhibits a low WR value of 58.5 ± 0.8 %. Then, as expected, WR is dosage dependent. The WR is improved as a result of increased amount of admixture until reaching very high WR values. Nevertheless, whatever the polymer, the increase in WR is not linear. Below a threshold dosage, the increase in WR is slight. The increase in WR is much more important above this critical dosage.

Fig. 3: Impact of pre-dissolution on water retention (WR) capacities of fresh mortars according to the dosage and kind of admixture.

Regarding the impact of the method of introduction, the effectiveness of HPMC 2 as water retention agent seems not to be affected by the pre-dissolution.

On the contrary, the effectiveness of HPG, and especially HPG 1, as water retention agents is significantly influenced by the method of introduction. Indeed, the water retention capacity is slightly better when the polymer is added dry at low dosage. As the dosage increases, the effectiveness of HPG as water retention becomes better when HPG is pre-dissolved in mixing water. It is strongly significant for HPG 1. At a dosage of 0.5% bwoc, the water retention capacity of mortar admixed with pre-dissolved HPG 1 is 24% higher than the mortar admixed with dry HPG 1. For HPG 3, a maximum difference of 10% is noticed for a dosage of 0.4% bwoc.

Nevertheless, the curves of water retention as a function of the dosage exhibit similar shape.

The critical dosage above which the WR increases strongly with the dosage is just shifted towards higher dosage, when the admixture is added according to the dry way.

Rheological properties

The rheological properties of admixed mortars at fresh state were characterized with the parameters of the Herschel-Bulkley model used to fit the experimental data.

The evolution of mortar consistency according to the dosage and the method of introduction of the admixture is shown in Fig. 4. An increase in polymer dosage leads to an increase in the consistency coefficient.

Once again, no impact of HPMC 2 pre-dissolution is evidenced, while HPG 3 and especially HPG 1 is much more efficient to increase the consistency when they are previously dissolved in the mixing water, mostly at high dosage. For example, for a polymer dosage of 0.66% bwoc, the HPG 1 pre-dissolution leads to an increase in the consistency coefficient, from 1.8 to 5.8 Pa.s n .

Fig. 4: Impact of pre-dissolution on consistency coefficient (K) of fresh mortars according to the dosage and kind of admixture.

Regarding the yield stress, as expected [START_REF] Poinot | Influence of hydroxypropylguars on rheolocial behavior of cement-based mortars[END_REF] τ 0 was found to decrease with dosage in the case of HPMC 2, while it remains stable in case of HPG (Fig. 5). Nevertheless, a strong difference according to the method of introduction is observed. Indeed, when the HPG is pre-dissolved, the yield stress value is about 5 Pa, and much higher than 10 Pa when the HPG is added dry.

Fig. 5:

Impact of pre-dissolution on yield stress (τ 0 ) of fresh mortars according to the dosage and kind of admixture.

Fig. 6 gives the impact of pre-dissolution on fluidity index of fresh mortars. As described in previous study [START_REF] Poinot | Influence of hydroxypropylguars on rheolocial behavior of cement-based mortars[END_REF], the fluidity index remains almost stable around 1.0 until a threshold dosage. Above this dosage, the fluidity index decreases. This overall evolution of the fluidity index as a function of the polymer dosage is the same whatever the method of introduction.

Nevertheless, as in the case of water retention (Fig. 3), the regime change occurs at higher dosage when the polymer is added dry. Moreover, it is worth noting that for the dry method of addition, the fluidity index is below than 1.0 at low dosage. The impact of pre-dissolution is not significant in the case of HPMC 2. To sum up, a strong impact of pre-dissolution on macroscopic properties was found for HPGadmixed mortars. Indeed, when the polymer is pre-dissolved in mixing water, the water retention capacity and the consistency of the mortar is significantly higher, while the yield stress is lower. The differences are stronger in the case of HPG 1 than for HPG 3. On the contrary, the method of admixture addition does not affect the macroscopic properties of HPMC-admixed mortars.

Pore solution viscosity

The effect of pre-dissolution on pore solution viscosity was investigated. By means of centrifugation, the pore solution was extracted. Then its viscosity was determined and characterized by the zero-shear viscosity. Fig. 7 shows the pore solution viscosity of mortars admixed with dry and pre-dissolved admixture at three polymer dosages (0.3, 0.5 and 0.66% bwoc). For a dosage equivalent to 0.66% bwoc (i.e. 6.66 g.L -1 ), polymers were also dissolved in real pore solution extracted from the control mortar. The viscosity is represented as a diamond in the Fig. 7.

Fig. 7:

Impact of pre-dissolution on pore solution viscosity as a function of polymer dosage.

As expected, the pore solution viscosity increases with the dosage. It appears that the pore solution viscosities of HPMC 2-admixed mortars are not affected by the method of introduction. The pore solution viscosity is slightly lower when HPG 3 is added dry than when it is pre-dissolved in the mixing water. For HPG 1, the pore solution viscosity is strongly different according to the method of introduction. For a dosage of 0.66% bwoc for example, η 0 is about 8.10 -3 Pa.s for the dry addition, and about 36.10 -3 Pa.s for the predissolved addition. With the same polymer, dissolved in the same media, a difference of viscosity reflects a difference of polymer concentration. This result means therefore that there are clearly more polymers remaining into the pore solution when HPG 1 is added predissolved.

Dissolution kinetics of polysaccharides

In order to explain the results exhibited above, the admixture dissolution kinetics was investigated. On the one hand, the dissolution kinetics was characterized in nearly saturated lime solution, which may represent a very simplified pore solution model. On the other hand, the polymer dissolution after mixing was determined by means of viscosity measurements. To overcome the potential effect of cement-polysaccharide interaction, this experiment was carried out only in 100% sand system.

In lime solution

The dissolution kinetics of the admixtures studied was determined in 20 mM lime solution.

Concentration was calculated from viscosity measurements thanks to parameters C*, b 1 and b 2 (see Table 2) obtained from calibration curves.

The final concentration expected is 6.66 g.L -1 . This concentration is reached quickly for the two HPG, while HPMC 2 is still partially dissolved after 24h (Fig. 8a). Nevertheless, by focusing on the first two hours of dissolution (Fig. 8b), it appears that the dissolution kinetics of HPG 3 is faster than HPG 1. After 10 min, 90% of HPG 3 is dissolved while 73% of HPG 1 is actually in solution. At the same time, only 8% of HPMC 2 is dissolved.

After mortar mixing without cement

For this experiment, all the solid phases of the mortar were substituted by sand. The dry admixture was first added to the sand and the dry mixture was homogenised. The amount of polymer was the same than for dosage of 0.66% bwoc in mortars. Then, deionized water was added, keeping a liquid to solid ratio of 0.3 (i.e. similar to the mortars L/S ratio). This mixture of sand, polymer and water were mixed for 4 min in accordance with EN 196-1 [START_REF]Methods of testing cement -Part 1: Determination of strength[END_REF], as mortars.

At 5 min (i.e. 1 min after the end of the mixing), the mixture was centrifuged and the viscosity of the supernatant was determined, as described in section 3.1.4. The same procedure was repeated 15 and 30 min after the beginning of the mixing.

Whatever the admixture, no evolution of the interstitial solution viscosity over time is observed, suggesting that after mixing with water, the total dissolution of each polymer occurs within the first 5 min (Fig. 9).

Adsorption of polysaccharide on cement

The adsorption ability of the admixtures studied on cement was also investigated since it reflects in some way the admixture-cement interaction. The amount of polymer adsorbed on cement in the mortar (polymer dosage of 0.66% bwoc) was determined from TOC analyses.

Measurements were carried out 15 min after the contact between cement and water. The results are shown in Fig. 10. Whatever the method of introduction, HPMC 2 is the admixture that adsorbs less on cement.

The adsorption ability of HPG 1 is higher than HPG 3. In the case of the dry method of addition for example, 58% of HPG 1, 30% of HPG 3 and 13% of HPMC 2 is adsorbed on the cement. The same ranking is obtained for the pre-dissolved method of addition.

Moreover, the amount of polymer adsorbed is higher in the case of dry addition than in case of pre-dissolved addition whatever the polymer. It is worth noting that in the case of HPMC 2, high standard deviations were obtained. Therefore the difference in adsorption ability according to the method of addition is not significant.

Discussion

The polymer concentration is a parameter of primary importance in controlling rheological properties of polysaccharide solutions [START_REF] Morris | Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions[END_REF]. At low polymer concentration, i.e. dilute solution state, individual polymer molecules are present as isolated coils. As the concentration of polymer is increased, the coils begin to bring into contact with one another leading to the formation of polymer aggregates. In this semi-dilute solution state, the polysaccharide solutions exhibit shear-thinning behaviors and their zero-shear viscosity increase highly with the dosage.

Previous studies highlighted the importance of the polysaccharide solution state on macroscopic mortar properties. Aggregates of HPG [START_REF] Poinot | Importance of coil-overlapping for the effectiveness of hydroxypropylguars as water retention agent[END_REF] and cellulose derivatives [START_REF] Bülichen | Working mechanism of methyl hydroxyethyl cellulose (MHEC) as water retention agent[END_REF][START_REF] Marliere | How water retention in porous media with cellulose ethers works[END_REF],

present in the pore solution because of polymer coils overlapping in the semi-dilute solution state, were found to be responsible of the increase in WR by plugging the porous network.

Moreover, for a polysaccharide dosage corresponding to the dilute solution state, mortar exhibits a Binghamian rheological behavior (i.e. fluidity index equal to 1.0) and the increase in consistency is slight [START_REF] Poinot | Influence of hydroxypropylguars on rheolocial behavior of cement-based mortars[END_REF]. Above the critical dosage, the pore solution and so the mortar becomes shear-thinning and the consistency increases strongly with the dosage.

The impact of method of polysaccharide addition on pore solution viscosity was investigated in the current paper (Fig. 7). It appears clearly that, for a given dosage, the pore solution viscosity is lower when the polymer is added dry than when it is pre-dissolved. This suggests that the amount of polymer in the pore solution is lower in the case of dry addition. A higher dosage is therefore necessary in order to reach the critical concentration and thus to improve macroscopic mortar properties.

In the case of HPG 1 previously dissolved in the mixing water, above a threshold dosage of 0.3% bwoc, the WR (Fig. 3) and the consistency (Fig. 4) of the admixed mortar increase suddenly, while the fluidity index starts to decrease (Fig. 6) meaning that the mortar becomes shear-thinning. The same behavior is observed when HPG 1 is added dry, but for a higher dosage of 0.5% bwoc (+ 0.2% bwoc). In the same way, the critical polymer dosages of HPG 3 are 0.3% and 0.4% bwoc, for dry and pre-dissolved addition respectively (+ 0.1% bwoc).

There is no difference for HPMC 2 which exhibits a critical polymer dosage of 0.1% bwoc whatever the method of addition. These observations are consistent with the impact of method of polysaccharide addition on pore solution viscosity, which is strong for HPG 1, medium for HPG 3 and non-existent for HPMC 2 (Fig. 7).

Therefore the method of addition influences the amount of polymer present in pore solution which shifts the boundary between dilute and semi-dilute solution states and so the improvement of mortar properties. Two hypotheses can be considered to explain this phenomenon: polymer dissolution kinetics or adsorption ability.

A lower amount of polymer dissolved in the pore solution without pre-dissolution than with pre-dissolution may be due to slow dissolution kinetics. In the aim to test this hypothesis, the dissolution kinetics of the three admixtures was investigated in nearly saturated lime solution (which represents a very simple model for pore solution with high alkalinity and strong concentrations of calcium ions) for a final concentration of 6.66 g.L -1 (which represents the highest amount of polymer, i.e. a dosage of 0.66% bwoc). Effectively, HPG 1 exhibits slower dissolution kinetics than HPG 3 (Fig. 8). According to Cheng et al. [START_REF] Cheng | homme, Characterization and Intermolecular Interactions of Hydroxypropyl Guar Solutions[END_REF], the increase in MS HP leads to a decrease in the intermolecular interactions of HPG. Therefore the dissolution of HPG 3 (high MS HP ) is easier than the dissolution of HPG 1 (low MS HP ). Nevertheless, HPMC 2 exhibits by far the slowest dissolution rate while there is no difference in pore solution viscosity with or without pre-dissolution (Fig. 7). This measurement thus characterizes well the dissolution kinetics but not what is really happen in the mixer. Indeed, the results from Fig. 7 suggest that, although a very slow dissolution rate, HPMC 2 is completely dissolved at the end of the mixing.

In order to focus on dissolution kinetics during the mixing and to overcome the likely adsorption of polymer on cement, all the solid phases were substituted by sand. It appears that whatever the admixture, the polymer is completely dissolved at the end of the mixing since the pore solution viscosities are exactly the same at 5, 15 and 30 min after the mixing with water (Fig. 9). The strong shear forces induce in the mixer and the friction with the granular media allow therefore the complete dissolution of polysaccharide, even of cellulose derivatives known for their slow dissolution rate. Thus dissolution kinetics cannot be responsible for the impact of pre-dissolution.

A second hypothesis would be a difference in the amount of adsorbed polymer according to the method of addition. To test this assumption, the adsorption ability of the three admixtures was investigated by means of TOC analyses. Effectively, it appears that the amount of polymer adsorbed is higher in the case of dry addition than in case of pre-dissolved addition (Fig. 10). Moreover, the adsorption ability of HPG 1 is the greatest. These results are in good agreement with the measurements of pore solution viscosity where a large loss of viscosity was obtained for HPG 1 between the two methods of addition (Fig. 7). For a given polymer dosage, a loss of viscosity was also observed between the "reference" (polymer dissolved in the pore solution of un-admixed mortar) and the real pore solution (extracted from the admixed mortar). The same trend can be observed for HPG 3 but with slighter differences.

The viscosity loss can be attributed also to a loss of polymer in solution because of adsorption.

It is worth mentioning that according to Bülichen et al. [START_REF] Bülichen | Working mechanism of methyl hydroxyethyl cellulose (MHEC) as water retention agent[END_REF], adsorption of anionic polysaccharides on cement should be excluded. The TOC measurements would reflect the amount of polymer retained as agglomerates plugged in the porous network rather than the adsorbed amount.

We are certainly in agreement that at such polymer dosage (0.66% bwoc), agglomerates are present in the pore solution. Nevertheless, if TOC measurements reflect only a physical retention of polymer agglomerates, and based upon the water retention mechanism which is linked to presence of agglomerates, higher is the "retained amount", higher should be the water retention capacity. Our experimental results are contradictory since values of retained polymer (obtained from TOC) are higher for the dry addition than for the polymer predissolved in mixing water (Fig. 10) but the water retention capacity is lower (Fig. 3).

Moreover, pore solution extracted by centrifugation exhibit a shear-thinning behavior which is characteristic of polymer coils overlapping. We therefore believe that the high speed centrifugation would be able to extract some agglomerates but not to trap all of them in the pellet.

Furthermore, it was previously assumed that the mechanism responsible for the cement hydration delay induced by HPG [START_REF] Poinot | Impact of hydroxypropylguars on the early age hydration of Portland cement[END_REF] is the adsorption of these molecules on the hydrated cement phases. Indeed, HPG are molecules which contain a lot of polar functional groups (-OH). Therefore, interactions through Van der Waals forces and hydrogen-bonding can occur between polysaccharides and the highly polar hydrated phases [START_REF] Jolicoeur | Chemical admixture-cement interactions: phenomenology and physico-chemical concepts[END_REF]. Moreover, the hydrated cement phases exhibit a high surface charge density [START_REF] Barret | Filter dissolution of C3S as a function of the lime concentration in a limited amount of lime water[END_REF]. The ionization of the hydroxyl groups of HPG in the alkaline pore solution [START_REF] Barret | Mechanism of C3S dissolution and problem of the congruency in the very initial period and later on[END_REF] would enhance the adsorption through strong electrostatic forces.

The adsorption ability of polysaccharide at the surface on the cement grains is therefore matter of debate but in our mind and for the specific case of HPG, this is the only valid theory to explain all the experimental results of the influence of HPG on mortars properties. Since adsorption is measured by depletion method, our results not allow confirming or invalidating the incorporation of the admixture in an organo-mineral phase during the early age hydration of the cement as suggested by Flat and Houst [START_REF] Flatt | A simplified view on chemical effects perturbing the action of superplasticizers[END_REF] regarding the superplasticizers.

Nevertheless, if this occurs, this should accentuate the consumption of polymer when it is added as dry powder.

Fig. 11 is a schematic representation of the polysaccharide-cement interaction. On the abscissa, the time at early age is arbitrary represented. The two cases, dry and pre-dissolved addition, are also shown. Once the cement is in contact with water, the anhydrous cement grains dissolve rapidly in the first seconds after wetting [START_REF] Barret | Filter dissolution of C3S as a function of the lime concentration in a limited amount of lime water[END_REF][START_REF] Barret | Mechanism of C3S dissolution and problem of the congruency in the very initial period and later on[END_REF] and nucleation of the first hydrates occurs at very early times, close to the time of mixing [START_REF] Bullard | Mechanisms of cement hydration[END_REF]. The dissolution of cement leads to a strong increase of calcium hydroxide concentration in the pore solution [START_REF] Garrault-Gauffinet | Experimental investigation of calcium silicate hydrate (C-S-H) nucleation[END_REF][START_REF] Damidot | Kinetics of Tricalcium Silicate Hydration in Diluted Suspensions by Microcalorimetric Measurements[END_REF] and thus the ionization of hydroxyl groups of polysaccharide. In the case where polymer is previously dissolved, the polysaccharide is able to adsorb rapidly on the first hydrates and to constrain their growth. The slowdown of hydrates growth rate in presence of polysaccharides has been highlighted in the past [START_REF] Peschard | Effect of polysaccharides on the hydration of cement paste at early ages[END_REF][START_REF] Pourchez | HPMC and HEMC influence on cement hydration[END_REF][START_REF] Poinot | Impact of hydroxypropylguars on the early age hydration of Portland cement[END_REF][START_REF] Weyer | Time-resolved monitoring of cement hydration: Influence of cellulose ethers on hydration kinetics[END_REF][START_REF] Peschard | Effect of polysaccharides on the hydration of cement suspension[END_REF][START_REF] Pourchez | Changes in C3S hydration in the presence of cellulose ethers[END_REF]. Nevertheless, when the polymer is added as dry powder, it has to dissolve first before to be able to adsorb on hydrates. Therefore the hydrates have more time to grow and the surface area available for adsorption is higher. Once dissolved, more polymers can be adsorbed or consumed leading to less polymer in solution in comparison with the pre-dissolution state. Ultimately, it has been shown in a previous paper that pre-dissolution of HPG leads to a greater hydration delay than when admixture is introduced as a powder in the dry-mix [START_REF] Poinot | Impact of hydroxypropylguars on the early age hydration of Portland cement[END_REF]. The adsorption ability of polysaccharide is linked to the substitution degree. Lower the substitution degree is, higher the content of hydroxyls is and thus stronger the adsorption ability is. This can explain the difference between HPG 1 and HPG 3. The adsorption ability of HPG 1 (low MS HP ) is so high that the difference induced by the method of addition is amplified.

The yield stress values (Fig. 5) are consistent with this theory. Indeed, because of its very long chains, the same HPG molecule can adsorb on separate cement particles and bound them together. This phenomenon is well known as polymer bridging flocculation [START_REF] Dickinson | Particle flocculation by adsorbing polymers[END_REF][START_REF] Lafuma | Bridging of Colloidal Particles Through Adsorbed Polymers[END_REF][START_REF] Swenson | Structure of bridging polymers[END_REF].

According to some authors [START_REF] Khayat | Viscosity-enhancing admixtures for cement-based materials -An overview[END_REF][START_REF] Collepardi | Self-Compacting Concrete: what is new?[END_REF][START_REF] Brumaud | Cellulose ethers and yield stress of cement pastes[END_REF], this bridging effect between cement particles would be one of the cause responsible for the cement-based materials yield stress induced by polysaccharide. A linear correlation between the amount of adsorbed polymer and the yield stress was even established [START_REF] Brumaud | Cellulose ethers and yield stress of cement pastes[END_REF]. This allows understanding the lower yield stress values when the polymer is pre-dissolved (Fig. 5) since the pre-dissolution reduces the amount of adsorbed polymers (Fig. 11).

At low dosage, i.e. without entanglement and formation of agglomerates, the mortars admixed with dry HPG exhibit better WR (Fig. 3) and higher consistency (Fig. 4) than mortars admixed with pre-dissolved admixture. Moreover, in the case of dry addition, the mortars present a strong shear-thinning behavior (Fig. 6) meaning a high viscosity at low shear rate. Thus, it can be assumed that the enhancement of bridging effect leads to improve yield stress, but also slightly the water retention ability, the consistency and the shear-thinning behavior of the admixed mortars.

Conclusions

Based upon this study, it appears that the method of addition of polysaccharidic admixtures may influence their impact on the fresh state properties of mortars. It is obvious for HPG 1 which has a low degree of substitution. This pre-dissolution effect is due to a difference of the amount of polymer in the pore solution regarding the method of addition. Indeed, a greater amount of polymer in solution was noticed when the polymer is pre-dissolved in the mixing water rather than when the polymer is added as dry powder to the other solid phases of the mortar as usual.

The pre-dissolution of the polymer may accelerate the adsorption on hydrated cement phases.

Therefore the growth of hydrates is rapidly constrained leading to a reduction of the surface area available to the adsorption. Contrariwise, the common addition of polymer as dry powder leads to a greater amount of polymer adsorbed.

By consuming polymer on the surface of cement grains, this common addition requires a greater dosage in order to achieve the overlapping of polymer coils. At equivalent dosage, in comparison with the pre-dissolved addition, the dry addition leads thus to mortars with lower water retention capacity and lower consistency but higher yield stress value and weaker cement hydration delay.

This study of method of addition allows highlighting the importance of cementpolysaccharide interaction on macroscopic properties of admixed mortars. Moreover, this paper confirms the fundamental influence of coil overlapping on polysaccharides effectiveness as admixtures for cement-based materials.

Fig. 1 :

 1 Fig. 1: Particle size distribution of the mineral phases.

Fig. 2 :

 2 Fig. 2: (a) Mortar shear stress and (b) pore solution viscosity versus shear rate according to the dosage -example of pre-dissolved HPG 1 -markers represent experimental data and lines represent calculated values according to (a) Herschel-Bulkley model (Eq 2) and (b) Cross model (Eq 3).

  two power-law type correlations (η 0 = aC b ) where the exponent b differs depending on the regime considered[START_REF] Morris | Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions[END_REF]. At low concentrations, the zero-shear viscosity increases slightly with the concentration (the exponent b 1 ranges from 1 to 1.5). Above a threshold concentration, socalled critical coil-overlap concentration C*, the polymer coils begin to bring into contact with one another. Therefore a dramatic change in flow behavior occurs which results in a sudden increase in the concentration-dependence of zero-shear rate viscosity (the exponent b 2 varies from 3.5 to 5)[START_REF] Morris | Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions[END_REF][START_REF] Graessley | The entanglement concept in polymer rheology[END_REF][START_REF] Robinson | Viscosity-molecular weight relationships, intrinsic chain flexibility, and dynamic solution properties of guar galactomannan[END_REF]. The critical coil-overlap concentration can be established from a double logarithmic plot of η 0 versus the concentration. It corresponds to the intersection of the two straight lines. For each admixture, the zero-shear viscosities of 20 solutions, with known concentrations from 0.5 to 20 g.L -1 obtained after complete dissolution of polymers, were determined. It was thus possible to obtain the power-law correlations (characterized by C*, b 1 and b 2 ) which were used as calibration curves. The data are given in Table

Fig. 6 :

 6 Fig. 6: Impact of pre-dissolution on fluidity index (n) of fresh mortars according to the dosage and kind of admixture.

Fig. 8 :

 8 Fig. 8: Dissolution kinetics of admixture in lime solution ([Ca(OH) 2 =20mM).

Fig. 9 :

 9 Fig. 9: Pore solution viscosity 5, 15 and 30 min after mixing, reflecting the dissolution kinetics of admixtures added dry in granular media.

Fig. 10 :

 10 Fig. 10: Impact of pre-dissolution on the amount of admixture adsorbed on cement.

Fig. 11 :

 11 Fig. 11: Schematic representation of the polysaccharide-cement interaction regarding the method of addition.

Table 1 :

 1 Chemical and phase compositions of the investigated cement.

		Chemical composition (% wt)		Phase composition (% wt)
	Oxides	XRF	Oxides	XRF	Phases	XRD (Rietveld)	Phases	XRD (Rietveld)
	CaO	66.1 ± 1.2	TiO 2	0.24 ± 0.01	C 3 S	73.0 ± 0.53	Gypsum	1.7 ± 0.15
	SiO 2	20.2 ± 0.4	P 2 O 5	0.05 ± 0.01	C 2 S	12.7 ± 0.50	Anhydrite	2.3 ± 0.28
	Al 2 O 3	4.8 ± 0.1	MnO	0.04 ± 0.00	C 3 A	4.2 ± 0.18 Hemi-hydrate 0.8 ± 0.30
	SO 3	3.5 ± 0.2	K 2 O	0.01 ± 0.01	C 4 AF	6.1 ± 0.22	Free CaO	0.5 ± 0.13
	Fe 2 O 3	2.9 ± 0.1	LOI	2.2 ± 0.2
	MgO	1.11 ± 0.02

Table 2 :

 2 Description of the admixtures used.

		MS HP	DS M	Mw (10 3 g.mol -1 )	C*	b 1	b 2
	HPG 1	Low	-	1700 ± 80	3.7	1.4	4.1
	HPG 3	High	-	1800 ± 50	3.2	1.2	4.0
	HPMC 2 Very Low Very High	950 ± 50	2.3	1.5	3.9

Acknowledgments

The authors would like to acknowledge Lamberti S.p.A. for the provided products. Also, the authors are grateful to Professor Johann Plank and all the people of the Chair of Construction


Mathieu Génois
email: genois@cpt.univ-mrs.fr

Christian L Vestergaard

Julie Fournet

André Panisson

Isabelle Bonmarin

Alain Barrat

Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers

Keywords: Complex networks, Temporal networks, Sociophysics, Epidemiology. ZU064-05-FPR

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Data-driven models of disease propagation are essential tools for the prediction and prevention of epidemic outbreaks. Thanks to important increases in data availability and computer power, highly detailed agent-based models have in particular become widely used to describe epidemic spread at very different scales, from small communities to a whole country or continent [START_REF] Davey | Effective, robust design of community mitigation for pandemic influenza: A systematic examination of proposed US guidance[END_REF][START_REF] Ajelli | Comparing large-scale computational approaches to epidemic modeling: Agent-based versus structured metapopulation models[END_REF][START_REF] Ajelli | The role of different social contexts in shaping influenza transmission during the 2009 pandemic[END_REF]Merler & Ajelli, 2010). One of the interests of such approaches comes from the level of detail they entail in the description of a disease propagation, from the amount of information they provide on the risk supported by each population category and on the probabilities of occurrence of transmission events in different circumstances. Moreover, the range of modeling possibilities is very large, and many different assumptions can be tested on how individuals come in contact, how a disease is transmitted and how such transmission can be contained. The drawback of this freedom in the model design lies in a certain arbitrariness in modeling choices. In order to alleviate this arbitrariness, models need to be fed with information and data concerning population statistics and individual behavior. In this respect, a crucial point regards the way in which people interact in their day-to-day life, and how these interactions affect disease propagation [START_REF] Mossong | Social contacts and mixing patterns relevant to the spread of infectious diseases[END_REF][START_REF] Read | Close encounters of the infectious kind: methods to measure social mixing behaviour[END_REF]. The collection of detailed data sets of human interactions is highly needed, as well as the extraction of the most relevant stylized characteristics and statistical features of these interactions (Stehlé et al., 2011b;[START_REF] Blower | The importance of including dynamic social networks when modeling epidemics of airborne infections: does increasing complexity increase accuracy[END_REF][START_REF] Machens | An infectious disease model on empirical networks of human contact: bridging the gap between dynamic network data and contact matrices[END_REF][START_REF] Barrat | Empirical temporal networks of face-to-face human interactions[END_REF][START_REF] Barrat | Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases[END_REF]. Understanding which features of human contact patterns are most salient can also help design low-cost methods based on limited information for targeted intervention strategies [START_REF] Lee | Exploiting temporal network structures of human interaction to effectively immunize populations[END_REF][START_REF] Smieszek | A low-cost method to assess the epidemiological importance of individuals in controlling infectious disease outbreaks[END_REF][START_REF] Chowell | A practical method to target individuals for outbreak detection and control[END_REF][START_REF] Gemmetto | Mitigation of infectious disease at school: targeted class closure vs school closure[END_REF].

In order to develop our knowledge and understanding of human interactions, novel techniques based on sensors using Wi-Fi, Bluetooth or RFID have emerged in the last decade and have provided important new insights [START_REF] Zhang | Towards a temporal network analysis of interactive WiFi users[END_REF][START_REF] Vu | Joint Bluetooth/Wifi scanning framework for characterizing and leveraging people movement in University campus[END_REF][START_REF] Eagle | Inferring friendship network structure by using mobile phone data[END_REF][START_REF] Stopczynski | Measuring large-scale social networks with high resolution[END_REF][START_REF] Cattuto | Dynamics of person-to-person interactions from distributed RFID sensor networks[END_REF][START_REF] Barrat | Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases[END_REF]Salathé et al., 2010). In the present article, we consider data on face-to-face contacts collected using wearable sensors [START_REF] Cattuto | Dynamics of person-to-person interactions from distributed RFID sensor networks[END_REF][START_REF] Barrat | Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases[END_REF]. The corresponding infrastructure, developed by the SocioPatterns collaboration (www.sociopatterns.org), allows obtaining time-resolved data on close face-to-face proximity events between individuals, yielding information not only on the overall network formed by these contacts, but also on the dynamics of these interactions. Previous works have shown that many properties of these dynamics -contact times, inter-contact times, number of contacts per link, etc -have broad statistical distributions and display robust features across several contexts: schools (Salathé et al., 2010;Stehlé et al., 2011a;[START_REF] Fournet | Contact patterns among high school students[END_REF], hospitals (Isella et al., 2011a;[START_REF] Vanhems | Estimating potential infection transmission routes in hospital wards using wearable proximity sensors[END_REF], museums (Isella et al., 2011b) or conferences (Isella et al., 2011b;[START_REF] Barrat | Empirical temporal networks of face-to-face human interactions[END_REF]Stehlé et al., 2011b). On the other hand, the contact networks also exhibit different high-level structures in each specific context, which can influence the way epidemics spread (Isella et al., 2011b;[START_REF] Machens | An infectious disease model on empirical networks of human contact: bridging the gap between dynamic network data and contact matrices[END_REF][START_REF] Gauvin | Activity clocks: spreading dynamics on temporal networks of human contact[END_REF][START_REF] Gauvin | Detecting the community structure and activity patterns of temporal networks: A non-negative tensor factorization approach[END_REF]. Here we consider the contact patterns between adults at work, which have been less studied in an epidemiological perspective, even if the influence of office spatial layouts on social interactions has been considered from a sociological and architectural perspective [START_REF] Penn | The space of innovation: interaction and communication in the work environment[END_REF][START_REF] Sailer | Social networks and spatial configurationhow office layouts drive social interaction[END_REF][START_REF] Brown | Tracking serendipitous interactions: How individual cultures shape the office[END_REF]Brown et al., 2014a). A priori, the workplace is one of the locations where adults spend most of their time and, as such, may represent an important spot for transmission of diseases between adults [START_REF] Ajelli | Comparing large-scale computational approaches to epidemic modeling: Agent-based versus structured metapopulation models[END_REF]. We therefore present an analysis of the human contact network in such a place, namely a building of the Institut de veille sanitaire (InVS, French Institute for Public Health Surveillance). We first discuss how the organization of Face-to-face contacts in an office building 3 the offices in departments determine the structure of the contact network and the dynamics of the contacts, and how these features affect epidemic spreading. We then focus on a new way to determine important nodes in such a contact network, based on the fraction of links each individual has with other individuals in the same department and in other departments, and present numerical simulations of an agent-based model of disease spread in order to discuss the efficiency of vaccination strategies based on this criterion.

Data collection

In order to collect data on the contacts between individuals, we used the sensing platform developed by the SocioPatterns1 collaboration, based on wearable sensors that exchange ultra-low power radio packets in order to detect close proximity of individuals wearing them [START_REF] Cattuto | Dynamics of person-to-person interactions from distributed RFID sensor networks[END_REF][START_REF] Barrat | Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases[END_REF]. Each individual that accepted to participate in the study was asked to wear a sensor on his/her chest. As described elsewhere [START_REF] Cattuto | Dynamics of person-to-person interactions from distributed RFID sensor networks[END_REF][START_REF] Barrat | Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases[END_REF], the body acts as a shield at the radio frequencies used by the sensors, so that the sensors of two individuals can only exchange radio packets when the persons are facing each other at close range ( 1.5 m). Signal detection is set so that any contact that lasts at least 20 seconds is recorded with a probability higher than 99 % [START_REF] Cattuto | Dynamics of person-to-person interactions from distributed RFID sensor networks[END_REF]. This defines the time resolution of the setup.

The study took place in one of the two office buildings of the InVS, located in Saint Maurice near Paris, France, and lasted two weeks. The building hosts three scientific departments -the Direction Scientifique et de la Qualité (DISQ, Scientific Direction), the Département des Maladies Chroniques et des Traumatismes (DMCT, Department of Chronic Diseases and Traumatisms) and the Département Santé et Environnement (DSE, Department of Health and Environment) -along with Human Resources (SRH) and Logistics (SFLE). DSE and DMCT are the largest departments, with more than 30 persons each, DISQ and SRH consist of around 15 persons, and finally logistics consists of only 5 persons (Table 1). DISQ, DMCT and SFLE share the ground floor, while DSE and SRH are located on the first floor.

Two thirds of the total staff agreed to participate to the data collection. The coverage ranges from 63 % (DSE, the largest scientific department) to 87 % (human resources) (see Table 1). A signed informed consent was obtained for each participating individual and the French national bodies responsible for ethics and privacy, the Commission Nationale de l'Informatique et des Libertés (CNIL, http://www.cnil.fr) was notified of the study. Data were treated anonymously, and the only information associated with the unique identifier of each sensor was the department of the individual wearing it.

Contact dynamics

Aggregated and temporal contact networks

We build the global contact network, shown in Fig. 1, by aggregating the contact data over the two weeks of the experiment. Each node represents an individual, and a link is drawn between two nodes if the corresponding individuals have been in contact at least once during the study. Each link carries a weight calculated as the total duration of the contacts between the two individuals. The resulting distributions of node degrees (the degree of an individual gives the total number of distinct other individuals with whom (s)he has been in contact during the study) and link weights are shown in Fig. 2a&b. Moreover, we take advantage of the fact that the data is time-resolved to treat the contact network as a temporal network [START_REF] Holme | Temporal networks[END_REF] and compute the distributions of contact durations and of the times between successive contacts of an individual (Fig. 2c&d).

In addition to the statistics of the present data set, Figure 2 also displays the properties of networks of face-to-face contacts collected in two other settings, namely a conference (Stehlé et al., 2011b) and a high-school [START_REF] Fournet | Contact patterns among high school students[END_REF]. Although the contexts are very different, the distributions are extremely similar. In particular we find broad distributions with an approximate power-law shape for weights, contact and inter-contact times, which are typical of the heterogeneous behavior often found in human activities [START_REF] Barabàsi | The origin of bursts and heavy tails in human dynamics[END_REF].

Sparsity of the contacts and consequences for the potential spread of infectious diseases

One of the main specific features of the present data set is the sparseness of the contacts: although the study lasted two weeks, the average degree in the aggregated network is only around 15, meaning that each individual met only ∼ 15% of the office population participating to the study over the course of these two weeks. The contact network is thus very far from a fully connected structure, with immediate consequences on possible dynamical processes taking place on such a network, such as the propagation of an infectious disease. To explore this issue, we perform numerical simulations of the spread of a Susceptible-Infected-Recovered (SIR) epidemic model in the population under study. In this model, Susceptible nodes (S) are infected with rate β when they are in contact with an infected node (I): for each small time step dt, an S node in contact with n I nodes becomes infected with probability nβ dt. Infected nodes (I) recover from the infection with rate µ and enter the Recovered (R) compartment. Recovered nodes cannot be infected again. Our goal here is not to explore the whole phase diagram of the spreading process but rather to illustrate the influence of the contact patterns and of the interplay between the time-scales of the contacts and of the spreading process. We therefore consider two different values of the ratio β /µ and vary the speed of the epidemics by changing β . We vary β in order to explore a wide range of time-scales: β ∈ [0.0004; 0.02], which correspond to a typical time of 2500] seconds;For β /µ = 100,70] hours Face-to-face contacts in an office building 7 and for β /µ = 1000, µ -1 ∈ [14; 700] hours. The duration of the spread depends on the value of β and ranges from 10 5 to 10 7 seconds.

Each simulation starts with a single, randomly chosen, infected node ("seed"). We use the time-resolved data set to recreate in-silico the contacts between individuals (including the periods of inactivity, i.e. nights and week-end, during which individuals are considered isolated) and thereby the possibility of the infection to spread. We run each simulation until no infected individual remains (nodes are thus either still S or have been infected and have then recovered (R)). We define the duration T of an epidemic as the time needed to reach this state, and the final size N of an epidemic as the number of nodes that have been affected by the spread, i.e. the number of R nodes at the end of the epidemic. As T might be longer than the duration of the data set, we repeat the two-weeks sequence of contacts in the simulation if needed (Stehlé et al., 2011b). For each realization we randomly choose both the seed and the moment when the spreading process starts. We compute the statistics of the final epidemic size over 1000 realizations for each value of the parameters.

Figure 3 displays the resulting distributions (i.e., the probability that the spread affects N individuals). For β /µ = 100, no large outbreaks are obtained (Fig. 3a). Even for the longest values of the infectious period (lowest values of µ), the sparsity of contacts makes the propagation of infection difficult. Indeed, at the fastest time scale, i.e. the time resolution of 20 seconds, nodes have an average instantaneous degree of 0.013, and overall only 0.66 links exist on average in the whole network: very few transmission opportunities exist at each time. Epidemics spread only if the ratio β /µ is increased enough to compensate for this very low contact rate (e.g., if, at fixed β , the recovery rate is strongly decreased). An example is given in Fig. 3b where we use β /µ = 1000. Even in this case, many realizations lead to epidemics of small size, but epidemics affecting a large fraction of the population are also obtained.

Interestingly, Fig. 3b also illustrates the role of the interplay between the timescale of the disease spread and of the contact network (Isella et al., 2011b;[START_REF] Barrat | Empirical temporal networks of face-to-face human interactions[END_REF]. At fixed β /µ indeed, a mode of the distribution corresponding to large epidemics is present for small values of β and µ. Larger values of β and µ corresponding to faster processes, with high spreading probability at each contact but also fast recovery and thus shorter infectious periods, lead to smaller probabilities of large epidemics: as β is increased, the mode of the distribution corresponding to large epidemics tends to be suppressed. This phenomenon is related to the temporal constraints and correlations inherent in temporal networks that can slow down and hamper the propagation of rapidly spreading processes [START_REF] Karsai | Small but slow world: How network topology and burstiness slow down spreading[END_REF]Isella et al., 2011b;[START_REF] Pfitzner | Betweenness preference: Quantifying correlations in the topological dynamics of temporal networks[END_REF][START_REF] Scholtes | Causality-driven slow-down and speed-up of diffusion in non-markovian temporal networks[END_REF]: for instance, if A meets B who is infectious, and then C, the infection can spread from B to C through A. If instead A meets first C then B, A cannot be an intermediary for the spread to C. Slowly spreading processes -with slow recovery-on the other hand are "less constrained" as the infectious period is longer and contacts with more individuals or repeated contacts with the same individual can occur during this period, effectively creating more possible paths of transmission between individuals (Stehlé et al., 2011b;[START_REF] Holme | Temporal networks[END_REF][START_REF] Barrat | Empirical temporal networks of face-to-face human interactions[END_REF]. To make the role of the contact chronology and of temporal constraints more explicit, we compare in the Supplementary Material the outcome of spreading processes simulated either on the temporally resolved contact data or on aggregated versions of the data, in which the information about the order in which different contacts occur is lost. Spreading processes with fixed β /µ values unfolding on a purely static contact structure would lead to exactly the same distribution of final epidemic sizes for different values of β . In our case, we still take into account the fact that nodes are isolated during nights and weekends. As a result, larger values of β lead to slightly larger epidemics, because faster spreading processes unfold over less inactivity periods (and inactivity periods, during which nodes can recover but cannot transmit, tend to hinder the spread). Overall, we thus have an opposite trend on temporal and static networks, at fixed β /µ: on static networks, increasing β tends to increase the final epidemic size and, in particular, the mode at large final sizes is kept, while if the whole temporal resolution is considered, such an increase tends to suppress the large epidemics.

Organization in departments

The offices are organized in five departments, on two floors. DISQ, DMCT and SFLE (logistics) are on the ground floor, along with a cafeteria and conference rooms. The remaining departments -SRH (human resources) and the DSE department -are on the first floor. As found in literature linked to social sciences and architecture, the spatial organization is expected to have an impact on the interactions between office workers [START_REF] Penn | The space of innovation: interaction and communication in the work environment[END_REF][START_REF] Sailer | Social networks and spatial configurationhow office layouts drive social interaction[END_REF][START_REF] Brown | Tracking serendipitous interactions: How individual cultures shape the office[END_REF]Brown et al., 2014a).

A detailed investigation of this issue is beyond the scope of our work, in particular as, due to anonymity of the participants, we do not have access to the office location of each participant. As shown in Fig. 1 the collected data show nonetheless a clear impact of the structure in departments, while the separation in two different floors is less apparent, at least at this resolution. As we will see in the next sections and as discussed for instance in (Salathé & Jones, 2010;[START_REF] Hébert-Dufresne | Global efficiency of local immunization on complex networks[END_REF], the fact that departments seem to correspond to communities in the network structure shown in Fig. 1 has consequences for the possibility to define mitigation strategies against the spread of epidemics.

In order to better quantify the mixing within and between departments, we build contact matrices giving for each pair of departments the total time of contact between individuals belonging to these departments. Figure 4a shows that contacts occur much more often inside departments (internal contacts) than between them (external contacts), with the exception of the logistics department. Furthermore, it confirms that the structure of external contacts does not clearly follow the spatial organization in two floors, but that scientific departments form a moderately connected sub-structure, leaving human resources and logistics more isolated. This structure is also found in the contact matrix restricted to the conference rooms (Fig. 4b). Scientific departments are in fact almost the only ones using these rooms for inter-departments meetings. Contacts between individuals of different departments also occur independently of scheduled meetings, for instance during lunch, which takes place either in the cafeteria or in the canteen (located in a distinct building). The contacts taking place in the cafeteria at lunchtime (Fig. 4c) show the same structure as the global one, with many internal contacts for each department, and a substructure corresponding to the three scientific departments on the one hand and logistics and human resources on the other hand. Strikingly, the structure of contacts occurring in the canteen is rather different, with a mostly diagonal contact matrix: in this situation, individuals from specific schedules, as e.g. in schools or high schools (Stehlé et al., 2011a;[START_REF] Fournet | Contact patterns among high school students[END_REF], the resulting patterns are still very different from contexts such as conferences (Stehlé et al., 2011b), and in particular very far from a homogeneous mixing situation. This has clear consequences in the design of realistic agent-based models of workplaces.

For instance, as shown in the Electronic Supplementary Material, modeling the spread of a disease in such a context under a homogeneous mixing assumption would result in a lack of accuracy with respect to more realistic data representations which take into account the division in departments and the restricted mixing between departments.

Weak inter-department ties

We investigate in more detail how the network structure is shaped by the departments by computing, as suggested in [START_REF] Onnela | Analysis of a large-scale weighted network of one-to-one human communication[END_REF], the topological overlap O i j of the neighborhoods of each pair of connected nodes i and j:

O i j = n i j /((k i -1)+(k j -1)-n i j ),
where k i and k j are the respective degrees of i and j and n i j is the number of common neighbors of i and j. If O = 0 the two nodes do not share any neighbors, while if O = 1 the two nodes have exactly the same neighbors. The topological overlap thus quantifies whether a link joins two nodes from the same group or community in the network, or two nodes from different communities. Figure 5 shows, similarly to the results of [START_REF] Onnela | Analysis of a large-scale weighted network of one-to-one human communication[END_REF] concerning a communication network, that overlaps and weights are positively correlated (we recall that the weight of a link is the total contact time between the two linked individuals). Moreover, we measure for internal links an average overlap of 0.29±?, with an average weight of 328±? s, while links joining individuals from different departments have an average overlap of 0.13±? and an average weight of 134±? s. This indicates that internal links are strong, whereas external links tend to be the weak ties in agreement with the weak tie hypothesis of [START_REF] Granovetter | The strength of weak ties[END_REF]. 3.5 Daily contacts structure

Stability of the overall structure

In order to understand how well the structure of the globally aggregated contact network and of the contact matrices described in the previous paragraph reflect how contacts occur every day, we build contact matrices giving for each day the durations of contacts between individuals of different departments (shown in the Electronic Supplementary Material) and compare their properties. Table 2 presents the mean similarity between each daily contact matrix and the matrices of the other days. The high values obtained show that the structure of the contact matrix is largely conserved from one day to another. As the diagonal of the matrices contains the largest values, we also compute similarities restricted to the non-diagonal elements. We still obtain rather large values, showing that even secondary structures are stable across days.

Network evolution

Although the overall contact structure is rather stable from one day to the next, the specific contacts of each individual change. Indeed, Fig. 6a shows that the average degree (number of distinct individuals contacted) of individuals increases steadily when we consider contact networks aggregated over increasing time intervals, both within a department and for external contacts. In order to gain more insights into this issue, we compute similarities between daily aggregated contact networks: the similarity between two networks (1) and (2) is defined here as the cosine similarity between their weighted lists of links, ∑ i, j w i j,(1) w i j,(2) / ∑ i, j w 2 i j,(1) ∑ i, j w 2 i j,(2) where w i j,(a) is the weight of the link i j in network (a) (if there is no link, the weight is set equal to 0). The resulting values are given in Table 3a. Table 3. Daily networks similarities. For each day, we calculate the cosine similarity between the weighted link list of the corresponding network and the lists of all other days. We show here the mean and standard deviation of these similarities. Statistics for the null models are calculated over 1000 realizations. a) Empirical similarities. b) Complete random rewiring of links. c) Rewiring keeping each individual node degree fixed. d) Random redistribution of link weights on the fixed topological structure. e) Rewiring in each contact matrix compartment. f) Random redistribution of link weights in each contact matrix compartment. In order to understand if these values correspond to a weak or strong stability, we compare them with several null models obtained by link rewiring. If we consider networks with the same number of nodes and the same set of weights, but edges placed at random between nodes (Table 3b), similarities are much smaller than for the empirical data. This is also the case if links are reshuffled while conserving the degree of each node (Maslov & Sneppen, 2002) (Table 3c) and if weights are redistributed at random among the links while conserving the topology of the networks (Table 3d). Finally, even null models which respect the department structure, i.e. with rewiring or reshuffling procedures inside each compartment of the contact matrix, yield similarities smaller than the empirical ones (Table 3e

a) b) c) d) e) f) Day (×10 -3 ) (×10 -2 ) (×10 -2 ) (×10 -2 ) (×10 -
& f).
Overall, these results indicate on the one hand that the precise structure of the daily contact networks fluctuate significantly across days, even if the contact matrix structure is stable. On the other hand, the changes from one day to the next are much less important than what would be obtained by random chance, and even some degree of intra-department structure is kept across days. Such results should thus be taken into account in the development of agent-based models, as done e.g. in (Stehlé et al., 2011b), as the amount of repetition of contacts over different days impacts how dynamical processes such as epidemics unfold in a population [START_REF] Smieszek | Models of epidemics: when contact repetition and clustering should be included[END_REF].

Daily activity

As Fig. 6b shows, the total duration of contacts within and between departments grows steadily. Contacts however might a priori occur at specific times for specific departments 14 M. Génois, C. L. Vestergaard, J. Fournet, A. Panisson, I. Bonmarin and A. Barrat (due to breaks, meetings, etc...). We therefore examine in Fig. 7 the activity timelines averaged over different days. The global, averaged activity for the whole building (Fig. 7a) exhibits activity peaks around 10am and lunchtime, but no other clear feature emerges. This is most probably due to the fact that no strict schedule constraints exist (in contrast e.g. to schools (Stehlé et al., 2011a) and hospitals [START_REF] Vanhems | Estimating potential infection transmission routes in hospital wards using wearable proximity sensors[END_REF]). We also show for each department both internal and external contact activities for an average day (Fig. 7b to f). Four departments present the 10am peak of activity, which may be related to a common tendency to have a break around that time. During lunch (12am-2pm), DSE, DMCT and SFLE have many contacts, both within and outside the department, whereas SRH exhibits a decrease of activity, and DISQ shows an inversion between internal and external contacts. Finally, for the three scientific departments, external contacts are more present in the morning than in the afternoon.

4 Node behaviors

Residents, wanderers and linkers

In the context of spreading phenomena, links joining groups of individuals in a contact network play a crucial role [START_REF] Karsai | Small but slow world: How network topology and burstiness slow down spreading[END_REF][START_REF] Onnela | Analysis of a large-scale weighted network of one-to-one human communication[END_REF]Salathé & Jones, 2010;[START_REF] Hébert-Dufresne | Global efficiency of local immunization on complex networks[END_REF]. In the present case, the possibility for an infectious disease to spread in the whole population thus strongly depends on the structure of contacts along inter-departments links. In order to shed more light on the role of each node in linking communities, we consider the static aggregated network, and we compute in Fig. 8 for each node the fraction of its links with individuals of each department. We focus in particular on the fraction f of internal links (i.e., with nodes in the same department). Most nodes are "residents": the large majority of their links are internal. Some other nodes (such as individuals from the Logistics department, or node 105 from DMCT and node 253 from DISQ) are on the other hand mostly linked to nodes outside their own department: they are "wanderers".

In order to determine how these different types of behaviour could be exploited in the design of targeted vaccination strategies, we investigate in Fig. 9 the relation between the centrality of a node in the aggregated contact network, as measured by its betweenness centrality (BC), and its fraction f of internal links. We note here that different definitions of node centrality exist. They are often correlated but the precise ranking of nodes' centrality slightly depends on the specific centrality measure used, and various works have compared how different centrality measures perform in identifying individuals most at risk of infection or the most efficient spreaders for various models of epidemic spreading [START_REF] Christley | Infection in social networks: Using network analysis to identify high-risk individuals[END_REF][START_REF] Kitsak | Identification of influential spreaders in complex networks[END_REF][START_REF] Castellano | Competing activation mechanisms in epidemics on networks[END_REF]. In the context of targeted measures to mitigate the spread of diseases in particular, immunizing (i.e., removing) the nodes with highest degree or largest BC is known to be among the most efficient strategies [START_REF] Pastor-Satorras | Immunization of complex networks[END_REF][START_REF] Holme | Attack vulnerability of complex networks[END_REF][START_REF] Dall'asta | Vulnerability of weighted networks[END_REF]. We also note that BC can be defined both on the unweighted and weighted versions of the network [START_REF] Dall'asta | Vulnerability of weighted networks[END_REF][START_REF] Opsahl | Node centrality in weighted networks: Generalizing degree and shortest paths[END_REF]. We have considered both cases and found very similar results so we use for simplicity in Fig. 9 the unweighted BC. Residents have, as could be expected, low centrality. Wanderers, as nodes connecting to other departments, could be expected to be crucial in potential spreading paths. However, they turn out to have low centralities as well. The most central nodes correspond to a specific population, composed of nodes whose neighborhood is composed by approximately one half of internal links and one half of external links. We call them "linkers", as they are effectively responsible for the connectivity between the departments and act as bridges [START_REF] Wasserman | Social network analysis: Methods and applications[END_REF] between them.

Linkers and spreading processes

As the linker behavior seems to be associated with high node centralities in the aggregated contact network, we consider here the effect on a potential epidemic spread of a containment strategy targeting linkers. Although it is expected that the precise detection (and vaccination) of the nodes with the highest centrality would be more efficient, as the correlation between linkers and high centrality nodes is not perfect, the detection of linker behavior relies a priori on less information than the computation of betweenness centralities and might thus represent an interesting alternative. We show in Fig. 10 the result of simulated SIR processes on the temporal contact network when a fraction of nodes are vaccinated, i.e. considered immune to infection (they can neither be infected nor transmit the infection), according to different strategies. The figure shows that the targeted vaccination of linkers decreases the probability to observe a large outbreak, and, in the case of such an outbreak, limits its size. This strategy is much more efficient than random vaccination, and, for a vaccination rate of 20 %, performs almost as well as a strategy based on centrality, with a strongly decreased outbreak probability. For a small vaccination rate (5%), the outbreak probability is not much reduced, but, in case of outbreak, the resulting epidemic sizes are clearly smaller than for a random vaccination strategy.

f f f N N N β β β β β β a) b) c) d) e) f )
5% 10% 20% Fig. 10. Vaccination strategies. We simulate SIR epidemics on the time-resolved contact network, with β /µ = 1000, in order to test different vaccination strategies. In each case we perform 1000 realizations. a), c), e) Fraction f of epidemics that reach more than 10 individuals. b), d), f) Size distribution of these large epidemics. For each strategy we vaccinate nodes according to the following rules: highest betweenness centralities, best linkers (fraction of internal links closest to 0.5) and random choice. We also plot the case without vaccination as a reference.

Stability of the linker behavior

Linkers are defined as nodes with approximately 50 % external links, based on the network aggregated over the two weeks data set. If we perform the same analysis on data restricted to either of the weeks, we do not necessarily find the same nodes, as the fine structure of the networks fluctuates a lot from one day to another, as highlighted in the previous section. We investigate this point in Fig. 11 by plotting, for each node with a linker behavior in the global two weeks aggregated networks, its betweenness centrality versus its fraction of external links in each of the two networks aggregated over one week. Though some of these nodes would not be selected as linkers if we restricted the data to one week, their behavior can still be considered as linker-like, as the fraction of external links remains between 40 % and 60 % for most of them. Only two nodes (150 and 255) are insiders one week and linkers the other week. The linker behavior thus seem rather stable over time, and a one week data set may be enough to find linkers. To check this hypothesis, we perform simulations of an SIR model using data corresponding to one of the two weeks of the study, and use a vaccination strategy targeting the linkers defined using data from the other week. Figure 12 shows that, although this strategy performs less well than the strategy using linkers defined from the full two weeks data, it still largely outperforms random vaccination in reducing the risk of large outbreaks and the size of large epidemics. The reduced efficiency obtained when using data from one week to define a strategy applied in the other week is reminiscent of the results of [START_REF] Starnini | Immunization strategies for epidemic processes in time-varying contact networks[END_REF] showing a limit in the efficiency of vaccination strategies due to the fluctuations of contact networks.

Discussion

In this paper, we analyzed data describing the contacts between individuals in the context of an office building. Not all individuals participated in the study, which means that the data cover only a part of the real contact network. As the sampled fraction is quite high, and uniform among the departments, we assume that the behavior of the sampled population is representative of the whole. Under this caveat, we have shown that, in this situation, many statistical features of contacts are similar to the ones measured in different contexts, with some important specificities. First, contacts are very sparse, which for instance tends to hinder the spread of infectious diseases, especially rapidly spreading ones. Second, the contact network structured in communities that approximately match the organization in departments of the building. The connections between departments do not reflect their spatial organization in the building, but rather their roles: the three scientific departments form a cluster, whereas human resources and logistics are more isolated. The structure is thus very different from a homogeneous mixing hypothesis, with important consequences on the design of agentbased models of e.g. epidemic spreading processes.

The presence of a strong community structure linked to the organization in departments in the contact network has led us to define three node behaviors, depending on the fraction of links each node shares within its own department: residents, whose links are mostly internal; wanderers, whose links are mostly external; linkers, whose links are half internal, half external, and therefore connect departments, acting as bridges between communities [START_REF] Wasserman | Social network analysis: Methods and applications[END_REF]Salathé & Jones, 2010). Empirically, the most central nodes of the network turn out to be linkers. As a consequence, targeted vaccination strategies based on the linker criterion efficiently prevents epidemic outbreaks. This behavior is also stable enough on the scale of one week for such a strategy to remain efficient if based on fewer data.

The precise identification of linker behavior relies on the knowledge of the contact network. One could thus argue that it requires almost as much knowledge as the identification of the nodes with highest betweenness centrality. However, the linker behavior, contrary to the betweenness centrality criterion, may be more easily linked to recognizable human behavior or to individual attributes in the organizational chart, for instance in relation to professional grade or specific activities. In this case, one could a priori discern which individuals are more susceptible to be linkers and play an important role in the event of an outbreak, and therefore use such limited information to design an efficient vaccination strategy entailing only a low cost in terms of necessary information [START_REF] Smieszek | A low-cost method to assess the epidemiological importance of individuals in controlling infectious disease outbreaks[END_REF][START_REF] Chowell | A practical method to target individuals for outbreak detection and control[END_REF]. We final note that the linker behavior might also be identified from limited information in other social contexts with communities -schools, hospitals, etc -and provide an important ingredient in agent-based models of epidemic spreading phenomena, as such agents provide crucial gateways between communities. Moreover, in the perspective of modelling and studying epidemic processes in real, largescale systems, obtaining a complete data set of contacts between individuals in a large-scale Face-to-face contacts in an office building

Fig. 1 .

 1 Fig.1. Empirical network of contacts between individuals, aggregated over the two weeks of study. Each node represents an individual and the color-code corresponds to the different departments. Each link between two nodes indicates that the corresponding individuals have been in contact at least once during the data collection. Nodes are laid out using the Force Atlas algorithm (see Gephi software, http://www.gephi.org), which allows communities to be apparent in the visualization of the network.

Fig. 2 .

 2 Fig. 2. Main features of the contact data. For each distribution we compare the features of the present study (InVS) with two previous studies: a scientific conference (SFHH, cf. (Stehlé et al., 2011b)) and a high school (Thiers12, cf. (Fournet & Barrat, 2014)). a) Distributions of normalized degrees. Original mean degrees are: 15.1 (InVS), 47.5 (SFHH), 26.4 (Thiers12). b) Link weight distributions. c) Contact time distributions. d) Inter-contact time distributions.

Fig. 3 .

 3 Fig. 3. Distributions of the final size N of simulated epidemics. Simulations are performed for different values of the infection rate β (given in the legend), the recovery rate µ being determined by the fixed β /µ ratio. At given β /µ, larger values of β correspond to both faster spread and faster recovery. For each value of β , distributions are computed from 1000 simulations with initial conditions given by one single randomly chosen infected individual. a) β /µ = 100. b) β /µ = 1000.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Contact matrices. Each matrix element (at row X and column Y) gives the total time of contact between individuals from departments X and Y during the two weeks of the study, in different locations. a) Entire building. b) Conference room. c) Cafeteria, restricted to the interval between 12am and 2pm for each day. d) Canteen. This place is in a different building and is not taken into account in a).

Fig. 6 .Fig. 7 .

 67 Fig.6. Network aggregation. We compute the mean degree (number of distinct individuals contacted) a) and the mean node strength (total time in contact) b) as a function of time while aggregating the network over the two weeks of measurement, disregarding nights and the weekend. These are calculated globally (black), and restricted to internal links (blue) and external links (red).

Fig. 8 .Fig. 9 .

 89 Fig. 8. Proportion of links with individuals of each department, for each node. Values are calculated from the network aggregated over the two weeks.

Fig. 11 .

 11 Fig. 11. Stability of linker behavior during the two weeks. For each node defined as a linker from the two weeks of data, we plot its characteristics based on each week's data (squares). Circles show their positions according to the full two weeks of data.

Fig. 12 .

 12 Fig. 12. Efficiency of sampling over one week. We simulate SIR epidemics on the temporal contact network, with β /µ = 1000, over only one week of data, with vaccination strategies based on data from the other week. In each case 10 % of the population was vaccinated. The labels indicate on which week the vaccination strategies were defined.

  Génois, C. L. Vestergaard, J. Fournet, A. Panisson, I. Bonmarin and A. Barrat population seems beyond reach, so that this type of criterion could be a way to uncover the central elements who could be targeted for outbreak detection and control.

Table 1 .

 1 Departments of the InVS.

	ZU064-05-FPR	papier	3 December 2014	10:54
		4 M. Génois, C. L. Vestergaard, J. Fournet, A. Panisson, I. Bonmarin and A. Barrat
			Number of tags Number of persons Coverage Floor
			DISQ	15	19	79%	0
			DMCT	30	46	65%	0
			DSE	38	60	63%	1
			SRH	13	15	87%	1
			SFLE	4	5	80%	0
			Total	100	145	69%

Table 2 .

 2 Daily contact matrices similarities. For each day, we compute the cosine similarity between the list of elements of the contact matrix and the ones of the other days, both with and without the diagonal elements. We list in this table the mean value and the standard deviation of the similarities.

	ZU064-05-FPR	papier	3 December 2014	10:54
			Face-to-face contacts in an office building
			Day	full	w/o diagonal
			06/24 0.753 ± 0.103 0.563 ± 0.222
			06/25 0.843 ± 0.069 0.481 ± 0.087
			06/26 0.837 ± 0.046 0.400 ± 0.246
			06/27 0.870 ± 0.052 0.534 ± 0.108
			06/28 0.871 ± 0.075 0.426 ± 0.134
			07/01 0.821 ± 0.058 0.592 ± 0.152
			07/02 0.850 ± 0.087 0.579 ± 0.180
			07/03 0.858 ± 0.072 0.488 ± 0.262
			07/04 0.767 ± 0.058 0.317 ± 0.131
			07/05 0.795 ± 0.123 0.398 ± 0.199

http://www.sociopatterns.org/

December 2014 10:54

http://www.sociopatterns.org/

Acknowledgments

We thank the direction of the InVS for accepting to host this study in their facility, and all the participants to the study. We acknowledge the SocioPatterns 2 collaboration for providing the sensing platform that was used in the collection of the contact data. M.G., I.B. and A.B. are partially supported by the French ANR project HarMS-flu (ANR-12-MONU-0018); C.L.V. and A.B. are partially supported by the EU FET project Multiplex 317532.