M.D.; Pierre Roupsard
email: pierre.roupsard@irsn.fr

PhD; Muriel Amielh
email: amielh@irphe.univ-mrs.fr

Didier Maro

Professor; Alexis Coppalle
email: alexis.coppalle@coria.fr

PhD; Hubert Branger
email: branger@irphe.univ-mrs.fr

PhD Olivier Connan
email: olivier.connan@irsn.fr

PhD; Didier Hébert Philippe Laguionie
email: philippe.laguionie@irsn.fr

D Hébert

PhD Martine Talbaut
email: martine.talbaut@coria.fr

M.D. Mr Pierre Roupsard

Professor; Denis Maro
email: denis.maro@irsn.fr

D Maro

Measurement in a wind tunnel of dry deposition velocities of submicron aerosol with associated turbulence onto rough and smooth urban surfaces

Keywords: dry deposition, deposition velocity, submicron aerosol, urban surfaces, wind tunnel

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

Text

Click here to view linked References results of two models for dry deposition. The dry deposition velocity of the fluorescein aerosol increases with the intensity of the turbulence. This highlights the importance of the turbulent processes of impaction and interception in deposition. However, the ratio of dry deposition velocity to friction velocity depends on the surface type. It depends on the turbulence conditions in the boundary layer. These turbulent dry deposition processes thus vary in importance depending on the studied surface. Finally, settling represents a significant part of the deposition for low wind speeds and for smooth surfaces. This wind tunnel study permits the study of the deposition as a function of turbulent processes. It should be supplemented by in situ experiments to take into account all the physical processes involved under real conditions. KEYWORDS: Dry Deposition, Deposition Velocity, Submicron Aerosol, Urban Surfaces, Wind Tunnel.

I. Introduction

In a polluted atmosphere or during transit of a plume containing stable or radioactive pollutants, and in the absence of rainfall events, dry deposition is the only transfer pathway from the air to the surface for particles and pollutants. At present, this dry deposition has been studied especially on natural surfaces representing the first link in the human food chain, but very little in the urban environment [START_REF] Kelly | The importance of the urban environments for accident consequences[END_REF][START_REF] Fowler | Atmospheric composition change: Ecosystems-Atmosphere interactions[END_REF]. However, a significant portion of the human population is concentrated in the urban environment, and in the case of passage of a radioactive plume, the quantity of radionuclides deposited by aerosols must be taken into account in estimating the dose rates received by the population [START_REF] Kelly | The importance of the urban environments for accident consequences[END_REF]. Precise assessment of the transfer of pollutants by dry deposition of aerosols can thus be very important, and the lack of significant data for the urban environment is now acknowledged. Dry deposition of aerosols depends on the aerosol diameter, the deposition surface (the roughness and temperature, for example) and the turbulence conditions [START_REF] Sehmel | Particle and gas dry deposition: a Review[END_REF]. Therefore aerosols do not deposit homogeneously in the urban environment. In the case of radioactive pollutants, this deposition must be studied for various surfaces, on a wall or street level, and not for an urban canopy, on a neighbourhood or city level, because the distribution of the deposits must be known precisely to assess the doses received by the residents. The dry deposition velocity is the coefficient used to quantify the transfer of aerosol particles by dry deposition in the environment. Most of the measurements of dry deposition velocities on urban surfaces in urban environments were conducted by [START_REF] Roed | Deposition velocity of caesium-137 on vertical building surfaces[END_REF][START_REF] Roed | Dry deposition of urban surfaces[END_REF][START_REF] Roed | Dry deposition in rural and in urban areas in Denmark[END_REF] as a result of the fallout from nuclear tests and the Chernobyl accident, and by [START_REF] Pesava | Dry deposition of particles to building surfaces and soiling[END_REF] and [START_REF] Maro | Quantification of the dry deposition of aerosols in an urban environment: towards a new methodology[END_REF] with a tracer aerosol generated in situ. However, these deposition velocities are not associated with precise measurements of turbulence or local meteorology. Presently, there are very few experimental data related to turbulent parameters for urban environments and surfaces. As a result there are significant uncertainties in the use of predictive models of deposition for this environment [START_REF] Fowler | Atmospheric composition change: Ecosystems-Atmosphere interactions[END_REF].

Urban environments are complex and heterogeneous from the point of view of the turbulence and measurements under simple conditions should aid in understanding the deposition processes and quantifying deposition velocities on urban surfaces. The wind tunnel is an advantageous tool. It can be used as an initial approach to quantifying dry deposition velocities as a function of a restricted number of controlled parameters and reproducible experiments can be conducted. Dry deposition has already been the subject of wind tunnel studies, on natural surfaces [START_REF] Chamberlain | Transport of Lycopodium spores and other small particles to rough surfaces[END_REF] or on smooth and rough substrates [START_REF] Liu | Experimental observation of aerosol deposition in turbulent flow[END_REF][START_REF] Horvath | Technique for measuring the deposition velocity of particulate matter to building surfaces[END_REF][START_REF] Toprak | The soiling of materials under simulated atmospheric conditions in a wind tunnel[END_REF][START_REF] Dai | Wind tunnel studies of particles transport and deposition in turbulent boundary flows[END_REF], but rather for micron particles. However, the accumulation mode of the atmospheric aerosol (0.1 µm ≤ d p ≤ 1 µm) is the mode that is the primary vector for chemical pollutants and radionuclides. It is the mode on which the surface distribution of the atmospheric aerosol is centred [START_REF] Gründel | Differences between the activity size distributions of the different natural radionuclide aerosols in outdoor air[END_REF][START_REF] Van Dingenen | A European aerosol phenomenology -1: physical characteristics of particulate matter at kerbside, urban, rural and background sites in Europe[END_REF][START_REF] Papastefanou | Radioactivity in the Environment[END_REF]. Moreover, it transports these pollutants over large distances from a source to the urban environments, due to a relatively long residence time in the atmosphere [START_REF] Jaenicke | Aerosol physics and chemistry[END_REF][START_REF] Papastefanou | Residence time of tropospheric aerosols in association with radioactive nuclides[END_REF]. While the deposition of particles greater than a micrometre most often studied is strongly affected by sedimentation, deposition of submicron aerosols, which are less studied, results from the contribution of several physical processes (Brownian diffusion, impaction, interception). The main objective of this study is to quantify dry deposition velocities of a submicron aerosol on horizontal and vertical urban surfaces, for several wind speeds and under isothermal conditions in the wind tunnel. Various turbulent boundary layer conditions are thus encountered. These turbulence conditions associated with the dry deposition velocities are quantified by hot wire anemometer measurements and focus especially on determination of the friction velocities. Finally, the data from this study are compared to data in the literature and to operational models, solved analytically, developed for smooth surfaces [START_REF] Lai | Modeling indoor particle deposition from turbulent flow onto smooth surfaces[END_REF] and natural canopies [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF].

II. Experimental setup

II.1 The wind tunnel and the studied surfaces

The experiments were conducted in a recirculating wind tunnel of the IRPHE (University of Aix-Marseille, campus of Luminy, Marseille, France). The experimental test section is a glass channel with a stainless steel base 8650 mm long and a cross-section 280 mm high and 640 mm width. Airflow speeds between 0.5 and 19 m s -1 can be generated. Deposition was studied on horizontal conventional glass surfaces, cement facing and synthetic grass in a first experimental campaign (Fig. 1.a), then on vertical conventional glass and cement facing surfaces in a second campaign (Fig. 1.b). The commercial names of the materials and the roughness parameters of the cement facing [START_REF] Flori | Salissures de façades (SALIFA), Programme PRIMEQUAL[END_REF] and synthetic grass are listed in Table 1. The roughness parameters of the cement facing measured by laser roughness measurements are the arithmetic mean deviation of the profile Ra, the standard deviation of the profile Rq, the valley depth of the profile Rv and the peak height of the profile Rp. The synthetic grass is composed of primary straight blades grouped into tufts, and thinner and shorter curly blades included in the canopy to make it denser. The parameters characterising the synthetic grass were determined by the authors for the primary straight blades and are the average canopy height h c , the length of the straight blades l b , the width of these blades w b , the number of tufts per square metre n t and the number of straight blades per square metre n b . During the experiments on horizontal surfaces, the bottom of the test section was successively completely covered by each type of surface to develop the boundary layers and turbulence conditions characteristic of each surface. In the same way, a vertical wall of the test section was successively covered with conventional glass and cement facing, to measure deposition on a vertical wall. It should be noted that glass cover the walls in the form of a pavement of square plates 200 mm on a side, while the cement facing and synthetic grass covered the wind tunnel homogeneously and continuously. To study deposition over a broad range of wind speeds that can be encountered in the urban environments, airflows of speeds u ref of 1.3, 5.0 and 9.9 m s -1 were generated in the test section. The turbulence was quantified above all the horizontal surfaces.

II.2 Quantification of the dry deposition velocity V d

The dry deposition velocity V d (m s -1

) of an aerosol is defined by [START_REF] Chamberlain | Transport of Lycopodium spores and other small particles to rough surfaces[END_REF]Chadwick (1953, in Sehmel, 1980) as the ratio of the surface flux of dry deposition F (kg m -2 s -1

; by convention a deposition flux is negative) by the average concentration of the aerosol in the air C (kg m

-3

) at a given height (1).

C F V d   (1)
A common approach to measure dry deposition velocities is to use a stable or radioactive chemical tracer for the studied aerosol. This method has the advantage of directly measuring a quantity of tracer, and thus of particles, in number or in mass. The deposition flux F is calculated according to (2), M substrate (kg) is the mass of tracer, A substrate (m 2 ) is the total surface of the substrate sample, and t (s) is the duration of the experiment.

t A M F substra te substra te   (2)
The average concentration C is calculated according to (3), with M filter (kg) the mass of tracer collected on the filter with an airflow rate Q filter (m 3 s -1

) over the same duration t. ) generated with a pneumatic generator is used as a tracer. The operating principle of this generator is described in French standard NF X 44-011. A fluorescein solution is nebulised, the produced droplets are sorted by centripetal filters, then entrained and dried by a dry air flow to obtain a dry solid fluorescein aerosol. The granulometric mass distribution of this aerosol was measured by three samplings with a Dekati (LPI) low pressure cascade impactor (separation of the particles over 12 stages of cutoff diameters between 24 nm and 9.55 µm) and gave on average an aerodynamic mass median diameter d amm of 0.27 ± 0.07 µm with a geometric standard deviation of 2.06 ± 0.23 (Fig. 2). The air recirculation in the wind tunnel allows to generate particles only for the first two minutes of the experiment and to let the concentration to decrease with time until the end of the experiment. Substrate samples are removed at the end of the fifteen minutes of the experiment. The generated aerosol is introduced at the outlet of the test section to be mixed with air in the recirculation section of the wind tunnel so that its concentration will be homogeneous over the test section inlet. It is injected at the centre of the cross-section with a horizontal copper injection nozzle regularly pierced along a line oriented toward the outlet duct with an airflow rate of 10.8 m 3 h -1 . Finally, the air in the test section is renewed between experiments by extracting air towards the exterior. The dry deposition fluxes are measured by exposure of samples (square plates 200 mm on a side composed of the studied substrates) to the fluorescein aerosols for a the experiment time. Samples are used for several experiments. After they are rinsed with distilled water and dried at room temperature, the substrates are placed in the test section with great care so as not to pollute them with fluorescein deposited on the walls of the test section. The static electrical charge is consistently removed from the synthetic grass samples by spraying the blades with denatured ethanol.

The charge state of these specimens is then checked with a fieldmeter (Eltex EMF 58). During the experiments on horizontal substrates, three rows of three samples placed across the width of the test section are incorporated into the substrate studied at various distances from the test section inlet. These distances from the inlet are also called "fetch" (m). The edges of these specimens adjoin the substrate surfaces covering the base of the test section. The leading edges of each row of samples are located at 1.0, 5.0 and 6.8 m from the inlet. Each type of substrate is studied separately, as the base of the section is completely covered by a single type of substrate. To measure dry deposition velocities on vertical surfaces, the vertical wall used is covered in the same way with the studied substrate, from the test section inlet to 6 m inside the test section. Three samples are intercalated lengthwise into this vertical wall, with leading edges at 4.8, 5.0 and 5.2 m, to measure the dry deposition fluxes. These specimens are centred in height, 40 mm from the base of the test section. In parallel, samples are taken on cellulose filters (Whatman 1440-047) throughout the exposure time of the specimens to the aerosol in order to quantify its concentration in the air of the test section. Bent copper sampling tubes with a 10 mm inside diameter are introduced from the top of the section so as not to perturb the flow above the studied surfaces and connected to filter holders with 500 mm long fluoroelastomer tubing. During the experiments on horizontal substrates, three samples are taken on filters 10 mm above the surface halfway across the test section, downstream of the specimens, with the inlet of the tube just behind each row of samples (fetch = 1.2, 5.2 and 7.0 m) so as not to perturb the flow over the specimens and thus not to perturb deposition. Likewise, for the experiments on vertical substrates, a sample is taken on a filter just behind the third specimen, 10 mm from the wall, halfway up the test section. In each experiment, a sample is taken on a filter at the centre of the test section, 5.2 m from its entrance, to control a posteriori the homogeneity of the particle concentration in the air in the section during the experiment. Collection flow rates are between 7.6 and 8.6 L min -1 and are checked with a TSI 4000 Series mass flowmeter. The samples and filters are carefully removed, wrapped in aluminium foil to avoid any pollution, and then treated for measurement. Fluorescein is hydrophilic, thus the deposited particles are dissolved simply by rinsing the surface with a pH 9 solution of ammonia water using a syringe (with successive rinsings with the same solution for the glass and cement facing) or directly by soaking (synthetic grass). The filters are immersed directly in the ammonia water to dissolve the filtered fluorescein particles. These solutions are measured with a fluorescence spectrometer (Jobin Yvon Horiba FluoroMax-3) to determine M substrate and M filter . The background fluorescence of each type of surface is subtracted from the measurement result.

Experiments are conducted at least twice to ensure their repeatability.

II.3 Estimation of the turbulent parameters

In the wind tunnel, in the absence of heat exchange on the studied surface, the turbulent parameter mainly associated with V d is the friction velocity u * (m s -1

) because it quantify mechanical turbulence that enhance the aerosol deposition. Also, it is one of the parameters necessary in modelling V d in confined environments [START_REF] Lai | Modeling indoor particle deposition from turbulent flow onto smooth surfaces[END_REF] or in situ [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF]. It quantifies the turbulence generated by shear of a flow over a surface and is used as a reference velocity near the wall. The friction velocity is estimated with (4) by measuring p (kg m -1 s -2

), the frictional or shear stress at the wall, with (kg m -3

) the fluid density.

  p u  * (4)
It can also be estimated with (5) using velocity profile measurements above the surface.

  0 * ln 1 z d z u z u    (5)   B k d z u z u s    ln 1 *  (6) In (5), u(z) (m s -1
) is the mean velocity in the flow direction measured at the vertical position z (m), and then the parameters to be fitted. The aerodynamic roughness height is flow-dependent for dynamically smooth flows and depends on roughness geometry for fully rough flows [START_REF] Raupach | Rough-wall turbulent boundary layers[END_REF]. For synthetic grass, z 0 is equal to 0.13h c (Tanner and Pelton, 1960, Stanhill, 1969[START_REF] Raupach | Rough-wall turbulent boundary layers[END_REF].

For cement facing, z 0 , is determined from ( 5) and ( 6

III. Results and discussions

III.1 Dry deposition velocities V d

The measured concentrations of aerosols in the air show no significant difference between the sample in the centre of the test section and samples 10 mm from the walls during the experiments (median deviation of 6.6%) and show homogenisation of the aerosol concentration in the air recirculation circuit of the wind tunnel. The average dry deposition velocities on each type of horizontal surface are calculated from the deposition fluxes at 1.0, 5.0 and 6.8 m from the test section inlet and the associated concentrations for each flow speed. They show neither variation with the fetch, nor a notable difference between the specimens at the centre of the row and those on the sides. The average dry deposition velocities calculated for each type of surface, horizontal and vertical, and for each airflow speed u ref are

shown in Table 2 andFig . Thus there is a factor of over two orders of magnitude between the lowest and highest values measured on these urban surfaces. Those measured on vertical surfaces vary from 1.1 10 -5 m s -1 on conventional glass for u ref = 5.0 m s -1 to 8.0 10 -5 m s -1 on cement facing for u ref = 9.9 m s -1

. The dry deposition velocity V d could not be measured on vertical conventional glass for u ref = 1.3 m s -1 during the experimental campaign.

III.2 Turbulent parameters

Aerodynamic parameters determined by hot wire measurements are listed in Table 3. All the developed boundary layers are turbulent at fetches of 1.1, 5.1 and 6.9 m, with a transition zone to the logarithmic profile (Fig. 4). The friction velocities are determined by fitting the logarithmic relation ( 5) to the mean velocity profiles. The estimated friction velocities decrease for an increasing fetch. This variation is consistent with the reduction in the stress at the wall p upon development of a completely turbulent boundary layer [START_REF] Antonia | The response of a turbulent boundary layer to a step change in surface roughness, part 1. Smooth to rough[END_REF]. The representation of the profiles in terms of dimensionless velocity (u + u)+ and dimensionless vertical position (z + d)+ (u+ = u / u * ; z+ = z u * / , with the kinematic viscosity of air) and the mean velocity shifts values u, with u = lnz 0 + + C (C = 5), show the different rough regimes of the flows generated by each surface type at each u ref [START_REF] Krogstad | Surface roughness effects in turbulent boundary layers[END_REF].

The profiles of I u and I w were calculated using (7.a) and (7.b), and profiles of I w are shown in Fig. 5. All the profiles over u and w have the same shape, with a maximum I wmax in the immediate vicinity of the surface.

The calculated values are shown in Table 3. For equal u ref , the values of I umax and I wmax are higher for synthetic grass than for cement facing, and higher for cement facing than for glass, with I umax greater than I wmax . These observations are consistent with the observations of [START_REF] Antonia | The response of a turbulent boundary layer to a step change in surface roughness, part 1. Smooth to rough[END_REF] for a boundary layer on a rough surface. Unlike the friction velocities, these relative turbulence intensities show no notable decrease as a function of the fetch but are essentially constant at each fetch for the same surface at the same flow speed.

III.3 Discussions

The average deposition velocities for each type of surface and each u ref (Table 2) have been compared to the data of the literature (Fig. 6). The deposition velocities measured in this study are of the same order of magnitude as those in the literature for smooth surfaces and grass. The absence of data on the geometry of the surface roughnesses studied by [START_REF] Toprak | The soiling of materials under simulated atmospheric conditions in a wind tunnel[END_REF] These results show the importance of turbulent processes of interception and impaction for this size range of particles, dependent respectively on the sizes of the aerosol and the obstacle, and on the Stokes number (itself dependent on the relaxation time of the aerosol, the flow speed and the size of the obstacle). Moreover, the measured differences in deposition velocities between horizontal and vertical walls, conventional glass and cement facing are on the order of the sedimentation velocity for the fluorescein aerosol calculated with (7) from the distribution of Fig 2.

       s m m gC d V ni i ui pi s   (7)
Here, g is the gravitational acceleration (9.81 m s -2

), is the density of the particles (1000 kg m -3 for aerodynamic diameters determined with a cascade impactor,) C ui is the Cunningham correctional factor for the aerosol of diameter d pi (geometric diameter of stage i of the cascade impactor), is the kinematic viscosity of air (1.5 10 -5 m 2 s -1

) and m ni is the fluorescein mass on stage i normalised to the total mass of fluorescein collected on the 12 stages. For low wind speeds, the contribution of sedimentation to deposition of this fluorescein aerosol is therefore non-negligible, contrary to what is usually believed for submicron aerosols. It can double the deposition velocity between a vertical wall and a horizontal wall, or even represent the entire deposit on a smooth horizontal wall for a low wind speed, as for glass with

u ref = 1.3 m s -1
. It should also be noted that deposition velocities on horizontal and vertical cement facing are approximately equal at u ref = 9.9 m s -1

. As the deposition flux depends on the vertical wind speed and its fluctuations, the deposition velocity V d is shown in Fig. 7 as a function of the maximum relative turbulence intensity over w, I wmax . An increase in deposition flux with turbulence intensity was already observed by [START_REF] Dai | Wind tunnel studies of particles transport and deposition in turbulent boundary flows[END_REF] for a smooth surface. Our graph shows a variation in V d as a function of I wmax independent of a particular type of surface. This observation is of interest as it represents V d as a function of a single turbulent parameter for several surface types.

The parameter usually related to V d is the friction velocity u * , as it quantifies the turbulence in a boundary layer. It is one of the main parameters used in the deposition models developed for inside and outside environments. The calculated deposition velocities for the polydispersed fluorescein aerosol with the models of [START_REF] Lai | Modeling indoor particle deposition from turbulent flow onto smooth surfaces[END_REF] and of [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF] (with zero aerodynamic resistance, because the concentration above the surface is consistent with that measured in the centre of the test section),

and the data of this study are shown as a function of u * in Fig. 8. The friction velocities of the vertical surfaces associated with the V d are those estimated for the same horizontal surfaces and same u ref at the fetch 5.0 m. The model of [START_REF] Lai | Modeling indoor particle deposition from turbulent flow onto smooth surfaces[END_REF] correctly estimates the deposition velocities on glass for u * greater than 0.2 m s -1

, but seems to overestimate them below this for horizontal glass.

On the other hand, [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF] systematically overestimate V d on grass by more than a factor of 5. This resistive model uses Brownian diffusion as the principal deposition process for a submicron aerosol deposition on grass and underestimates interception and impaction processes. By comparison, the recent mechanistic model of [START_REF] Petroff | Aerosol dry deposition on vegetative canopies. Part II: a new modelling approach and applications[END_REF] accords more importance to interception for this aerosol size range. It is in a better agreement with [START_REF] Chamberlain | Transport of Lycopodium spores and other small particles to rough surfaces[END_REF] data on grass in a wind tunnel for micron and submicron aerosols than [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF]. This shows the limits of the operational model of [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF] in assessing V d on grass precisely, and the need to either improve consideration of turbulent processes in deposition on grass, or to estimate V d from mechanistic models like that of [START_REF] Petroff | Aerosol dry deposition on vegetative canopies. Part II: a new modelling approach and applications[END_REF] that better account for these turbulent processes.

In the literature, dry deposition velocities measured in situ are generally normalised to u * . In this case, the sedimentation velocity V s (7), a non-turbulent deposition process, must be subtracted from V d . In recent studies of transfers in natural environments, the ratio of V d and u * was found to be independent of the various surfaces studied under neutral and stable conditions and approximately equal to 2.10 -3 [START_REF] Damay | Détermination expérimentale de la vitesse de dépôt sec des aérosols submicroniques en milieu naturel: influence de la granulométrie, des paramètres micrométéorologiques et du couvert[END_REF][START_REF] Donateo | Similarities and differences in dry deposition velocity normalized to friction velocity over maize, grass, bare soil and ice measured with different instruments[END_REF]. On the contrary, in this study, this ratio depends on the type of surface (Fig. 9) and thus on the flow conditions and the structure of the boundary layer. It is therefore determined by the importance of interception and impaction in the deposition process. The ratio is 5.3 ± 4.1 10 -5 for conventional glass, 1.5 ± 0.6 10 -4 for cement facing, and 1.3 ± 0.3 10 -3 for synthetic grass. The experimental results are close to the estimate of the model of [START_REF] Lai | Modeling indoor particle deposition from turbulent flow onto smooth surfaces[END_REF] for glass

(5.0 ± 0.1 10 -5

) and the in situ values of [START_REF] Damay | Détermination expérimentale de la vitesse de dépôt sec des aérosols submicroniques en milieu naturel: influence de la granulométrie, des paramètres micrométéorologiques et du couvert[END_REF] on a grassland, 0.8 10 -3 and 1.6 10 -3 respectively for d p = 0.20 and 0.32 µm, for synthetic grass.

In the urban canopy, in the urban sub-layer of the atmospheric boundary layer, measurable friction velocity u * in the boundary layers of the surfaces is not obvious. Use of u * alone as a turbulent parameter seems thus to be limited in modelling deposition on heterogeneous urban surfaces. As an initial approach, in the context of operational models to give quick estimates of deposition velocities, wind speed in the streets could turn out to be a good parameter, as it is easily measurable or modelled.

Empirical parameterisation of V d as a linear function of u ref for each type of surface according to the data of Table 2 could be a good first approximation.

IV. Conclusions

Presently, there is little experimental data on dry deposition velocities for the urban environment. This Vertical glass [START_REF] Liu | Experimental observation of aerosol deposition in turbulent flow[END_REF]; Glass [START_REF] Horvath | Technique for measuring the deposition velocity of particulate matter to building surfaces[END_REF]; horizontal sticky rough glass [START_REF] Chamberlain | Transport of Lycopodium spores and other small particles to rough surfaces[END_REF]; Cement [START_REF] Toprak | The soiling of materials under simulated atmospheric conditions in a wind tunnel[END_REF]; Sticky artificial grass, Real grass [START_REF] Chamberlain | Transport of Lycopodium spores and other small particles to rough surfaces[END_REF];

This study: Horizontal conventional glass; Vertical conventional glass;

Horizontal cement facing; Vertical cement facing; Synthetic grass. ---Horizontal smooth wall, ---Vertical smooth wall [START_REF] Lai | Modeling indoor particle deposition from turbulent flow onto smooth surfaces[END_REF]; --Grass [START_REF] Zhang | A size-segregated particle dry deposition scheme for an atmospheric aerosol module[END_REF];

This study: Horizontal conventional glass; Vertical conventional glass;

Horizontal cement facing; Vertical cement facing; Synthetic grass. ; u ref = 9.9 m s -1

; x mean on all u ref for each surface.

  monomodal submicron dry fluorescein aerosol (uranine, = 1500 kg m -3

  (0.4), d (m) and z 0 (m) are respectively the Von Karman constant, the displacement height and the aerodynamic roughness height. The friction velocity can be estimated by fitting this relation in the logarithmic overlap area of the velocity profile of a developed turbulent boundary layer; u * , d and z 0 are

  ), and equal to k s exp(-B ) (B = 8.5;[START_REF] Schlichting | Boundary-Layer Theory[END_REF]), with k s = Rv + Rp. For glass, d is equal to zero and z 0 can vary. The relative turbulence intensity I (%) is another dimensionless magnitude that quantifies the turbulent agitation (u', w') of a flow by comparison to the average motion ( u ) at a distance z from the wall. The relative turbulence intensities for the components u and w (I u and I w ) can be calculated according to (7.a) and (7.b). , turbulence can be classified into three categories: low (1%), medium (10%) and high (20% and more). The turbulent parameters were estimated in absence of aerosol injection for horizontal surfaces using hot-wire anemometry operating at high frequency. The system used is a probe with two crossed hot wires (type 55P61) combined with a Streamline anemometry system (Dantec Dynamics). It measures u, the horizontal component of velocity in the flow direction, and w, the vertical component, at high frequencies (2.5 kHz for u ref = 1.3 m s -1 and 10 kHz for u ref = 5.0 and 9.9 m s -1 , u ref measured at the center of the test section of the wind tunnel) with a 50 seconds acquisition duration in each position. These turbulence measurements were conducted above each surface type for each u ref and for each fetch above the centre of the central substrate sample, by vertical profiles of 40 points between z = 2.5 mm and z = 200 mm above the roughnesses of the surfaces.

  . 3. The dry deposition velocities measured on horizontal surfaces vary from 1

  makes it impossible to understand the differences in the measured V d . The dry deposition velocities vary with the mean air flow speed, the surface type and the orientation of the surface. On horizontal surfaces, V d varies on average by a factor of 1.7 and 23.7 respectively between conventional glass and cement facing and between conventional glass and synthetic grass, and by a factor of 1.9 and 3.6 between u ref = 1.3 m s -1 and u ref = 5.0 m s -1 and between u ref = 1.3 m s -1 and u ref = 9.9 m s -1 respectively.

Fig. 1 :Fig. 2 :

 12 Fig. 1: illustrations of the wind tunnel configurations to study deposition on horizontal (a) and vertical (b) walls; the studied surface is grey; the substrates samples are the grey squares.

FiguresFig. 4 :Fig. 5 :

 45 Figures Click here to view linked References

Fig. 8 :

 8 Fig. 7: average V d as a function of I wmax for each type of surface. Conventional glass: u ref = 1.3 m s -1 ; u ref = 5.0 m s -1 ; u ref = 9.9 m s -1 ;

  Fig. 9:

Table 1 :

 1 characteristics of the studied surfaces.

		Conventional glass	Cement facing	Synthetic grass
	Commercial name	Planilux®, Saint-Gobain	Fema®-Therm-Mineralputz 5 mm	"Romana"
	Roughness parameters Glass thickness = 4 mm	Ra = 0.57 mm	hc = 34 ± 2 mm
			Rq = 0.74 mm	lb = 38.4 ± 1.9 mm
			Rv = 2.36 mm	wb = 1.2 ± 0.1 mm
			Rp = 1.86 mm	nt = 10364 m -2
				nb = 164675 m -2

Table 2 :

 2 average V d as a function of u ref .

uref (

m s -1 ) Vd (x 10 -5 m s -1 ) Glass Cement facing Synthetic grass

		Horizontal	Vertical	Horizontal	Vertical
	1.3	1.4 ± 0.4		2.2 ± 0.9	1.4 ± 0.3	28.1 ± 8.4
	5.0	2.3 ± 1.3	1.1 ± 0.4	4.8 ± 1.8	3.6 ± 0.7	54.6 ± 19.3
	9.9	4.5 ± 2.0	2.4 ± 0.3	7.2 ± 1.6	8.0 ± 2.0	124.7 ± 29.6

HIGHLIGHTS:

Submicron aerosol deposition on urban surfaces is studied in a wind tunnel. Associated turbulent parameters are measured or estimated with a hot wire anemometry.

Settling has an influence on deposition on smooth surface and at low wind speed.

Submicron aerosol deposition is dependent on turbulent deposition processes.


Philippe Thomas André
email: philippe.thomas@univ-lorraine.fr

One approach of data-mining for Product Driven Systems

Keywords: Product Driven Systems, Viable systems, Learning machines, Neural network, Data mining

The first objective of this paper is to highlight some new Product Driven Systems (PDS) issues. Effectively, several possibilities have been proposed to give to products or objects capacities to react to environment modifications (especially in manufacturing and logistics context here). In particular, bio-inspired approaches are now promising. All these new perspectives lead putting products in action according to collected information. That's why all technics leading to exploit and organize data are necessary. The main objective of the paper is addressed in a second part, where we highlight why learning machines could be seen as a new way to do that.

INTRODUCTION

After the second industrial revolution the main companies' objective has been productivity. Ford Motor Company has introduced the concept of mass production. Since then, many techniques have been introduced leading to process automation and optimization of planning and production control activities. Among Manufacturing Planning and Control Systems, MRP Systems emerged during the seventies in order to solve problems such as those related to delays of orders, to intermittent stock consumption or to forecasting of raw materials consumption. However, inertia facing unexpected events occurring on the shop-floor has been seen as a residual issue. In order to compensate for this drawback, a new MRP² generation has been proposed with a closed loop approach (Vollman et al., 1997). The main characteristic of these systems is the multi decision level horizons structuration. These horizons may be classified into long, medium, short and very short term. Considering them, four decision levels have been identified: strategic, tactical, operational and execution one. At the beginning of eighties, new management philosophies appeared which implied drastic changes in production management area. The main goals of these changes have been to improve the system reactivity and flexibility, on the one hand, and the service quality, on the other. These challenges are still valid today and have been mainly implemented by Just in Time (JiT) and Theory of Constraints (ToC) philosophies.

The main idea of JiT philosophy is based on the efficient use of productive resources. Various approaches have been proposed such as Lean manufacturing, Demand Flow Technology or Six Sigma. On production workshops, the main used tool to implement this philosophy to control physical/material flows is the kanban system. Lean manufacturing and, in particular, kanban system have implied a great revolution in production system management. The management functions, which is in MRP2 systems centralized and hierarchical, become, in lean philosophy, completely or partialy distributed. In spite of the results obtained with these decentralized approaches, Theory of Constraints (ToC) introduces a new point of view, different and complementary, based on a global optimum attainment which brings back to a centralized approach (Goldratt et Cox, 1992). ToC induces that organization has to be evaluated and controlled by using three indicators: profits generated by sales, operating costs and inventories. In ToC, a good bottleneck management is the key of the success. Finally, the existence of these three concurrent philosophies of production management have led to the proposition of many hybrid systems using techniques coming from MRP², JiT or ToC which were implemented in software such as ERP (Enterprise Resources Planning), APS (Advanced Planning Systems), SCM (Supply Chain Management Systems)... In the next section, a brief overview of intelligent manufacturing systems is recalled with their advantages and weaknesses. Section 3 presents a viable system model for product driven system. Section 4 focuses on the need of knowledge of these systems and the learning approaches used to design knowledge. An illustration of this approach is presented in section 5 before to conclude.

INTELLIGENT MANUFACTURING SYSTEMS

The development of production management systems has led to the "Computer Integrated Manufacturing" concept. The main goal of these systems is to interconnect all the information systems included in the production system. CIM systems have to supervise and control all company operations. At that time, the paradigm generally accepted was that the CIM system would be able to have a great flexibility when changes occur and would give the best solution to the problems encountered in production system. Nevertheless, implementations led to centralized and rigid structures unable to adapt quickly to changes. However, some flexible manufacturing systems were very productive. So, at the beginning of nineties, CIM systems were no longer considered as the solution of all problems of production companies [START_REF] Babiceanu | Developpement and applications of holonic manufacturing systems: a survey[END_REF].

Considering the bad results of integrated systems in terms of flexibility and reactivity, collaborations between research centers, universities and companies have been initiated in order to design and develop the production systems for the future. The most important of them was the "Intelligent Manufacturing Systems" Project (IMS) (Yoshikawa, 1995). The basic idea of IMS was the design and implementation of decentralized systems. Its main goal was system flexibility in order to deal quickly with disturbances inherent to the production processes. Before this function was allocated to men who monitored and changed the shop orders. The idea was to automate all or a part of this function by using new communications technologies (Auto-ID, Multi-Agent systems…). These new systems have to be robust, reconfigurable and reusable (Leitao, 2009).

Considering the centralization criterion, the production systems have been divided into four types [START_REF] Babiceanu | Developpement and applications of holonic manufacturing systems: a survey[END_REF]): centralized systems, hierarchical ones, modified hierarchical ones and heterarchical systems. Around the design of decentralized systems appeared different types of systems and concepts. The main decentralized production systems are bionic, fractal and holonic ones (HMS). This paper focuses on the last one.

HMS consortium has proposed holonic production systems based on the holon concept. A holon is an entity which may be included in other holons (Van Brussel et al., 1998) and are organized in holarchies. Holons have the abilities of autonomy and cooperation. Nevertheless, concepts of agent and holon are often confused. Although the holon may be viewed as an agent, the main difference is that the control part is associated to the physical part in a holon. In an agent (which is an abstract entity), a physical entity may be merged or modeled by an abstract entity. Product Driven Systems is an evolution of holonic system where interoperability and intelligence are improved. In PDS, products become the company resources controllers (Morel, et al. 2003). This leads to the intelligent product concept. It has been defined as an entity equipped with physical and informational representations, able to affect decisions which may affect the intelligent product itself (McFarlane et al., 2003). In practice, the Radio Frequency identification (RFID) is a technology able to link information and physical environment. The central idea is to move from a classical hierarchical and aggregated control to a distributed decision making where a part of the decision is made locally, all along the products life cycle. So, the needed information is reduced and locally processed. The PDS have been generally designed as a particular class of holonic systems. The main advantages of IMS approaches are feasibility, robustness, flexibility, reconfigurability and reusability.

Up to now, many methodologies have been proposed in order to model distributed approaches (PROSA, ADACOR, METAMORPH…). Despite this, no standardized criterion exists allowing model design. The modeling step may be performed by focusing on functional, physical or abstract aspects (Creput 2008). And yet, the tools choice, the criterions choices and the models choices remain linked to the abilities and preferences of designer. This lack of uniformity makes the evaluation and the comparison of different applications in the literature, difficult.

One of the most critical points for the heterarchical approaches (decentralized) comparatively to traditional ones (centralized) is the decision optimization. Heterarchical systems are not able to formally guarantee their performances in terms of quantifiable variables, and more particularly, of costs. Heterarchical systems are interested in classical criterions of cost, time or efficiency, but also to goals relating to flexibility, reconfigurability, reactivity, interoperability… These goals are not easily quantifiable, and so, the comparison and evaluation of benefits of such systems are difficult.

In conclusion, it can be noticed that the two great approaches of production planning and control have strengths and weaknesses. Actually, the conventional approaches (centralized) insure the efficiency of the global system but at the expense of flexibility and reactivity. At the opposite, the IMS approaches (distributed) insure flexibility and reactivity, but are not able to insure performance and consistency between decisions taken to different levels. So the search of global consistency of a system working, through the comportment of sub systems and their own goal is essential (Thomas, 2004). Verstraete et al. (2008) have proposed to associate a HMS to a hierarchical planning system. The function of HMS is to determine an alternative planning when disturbance occurs. Another way would be to design hybrid systems (centralized/distributed). Herrera (Herrera et al., 2011) highlights that to allow acceptable efficiency and consistency between different decision levels and to improve the flexibility and reactivity capabilities of the systems; "Viable Model" could be a good way to structure their architecture. Moreover these systems have to include a data acquisition system in order to collect data from the physical system to be controlled. These data must be filtered, analyzed, possibly aggregated… in order to become exploitable. This paper focuses now on this point.

VIABLE SYSTEM MODEL FOR PDS

Viable System Model (VSM)

The origins of VSM arise from the works of Beer [START_REF] Beer | The viable system model: Its provenance, development, methodology and pathology[END_REF] applied to the steel industry in the fifties. This research can be placed in the line of works of Norbert Wiener, Warran McCulloch and Ross Ashby. The main objective of the model was to identify and to explain how systems are viable. Although, VSM is a general model for the study of any viable system, the most concerned application areas has been human activity organizations, i.e., corporations, firms or governments. In this domain, VSM changes the view of the traditional management model based on command and control, in which a control system is designed as a pyramid and such decisions are disaggregated in a top-down manner at different structural levels. The main difference, inspired by the biological organization, consists in mapping this hierarchy into a structural recursion (Herrera et al., 2011). The premise of this change of perspective was inspired from the living beings composition (cells, organs, systems, etc.). Indeed, they have properties of autonomy, self-organization and self-regulation, allowing them to have an independent existence. The differentiation of their functions and the relationships between these elementary components produce more complex systems, without that subsystem essential properties would be lost. However, one of the most important properties of a viable system is their intrinsic recursion. In fact, any viable system contains and is contained by another viable system. Every subsystem maintains its autonomy towards its environment, but it also contributes to generate the viable system in which it is included. In that way, a viable system and its different subsystems have the same structural requirements. A viable system supports its objectives thanks to an overall cohesion and adapts itself by the autonomy of its subsystems. VSM was developed looking for invariances in organic systems. These invariances allow defining a homomorphism of their functions, organization and structure. Beer defines five elementary functions that any viable system must have: implementation, coordination, control, intelligence and policy.

VSM model of Manufacturing Planning and Control system

The model describes here (Fig. 1) has been proposed by Herrera et al. (2011). It is consistent with the five functions of the Manufacturing Planning and Control Systems which can be described as: Strategic Planning, Sales and Operations Planning (S&OP), Master Production Planning (MPS), scheduling and execution. Each of these functions corresponds to a level in the decision making process regarding to different horizons going from a longer to shorter one. In practice, these decisions are taken using a rolling horizon to take into account the frequent changes that occur in the data (demand, capacity, etc.). Thus, the strategic planning is revised once a year, the S&OP is computed monthly, the MPS is get per week, and the schedules are performed daily or more frequently depending on disturbances. Each function deals with a corresponding aggregation level of products respectively families, finished products and items (components). In this context, one of the major issues is to adapt decisions at each level when disturbances (internal or external) happen. The frequently resulting modifications in the decision making process lead to the so-called nervousness system which deteriorates the system performance (productivity and efficiency). One should notice that the shorter the horizon is, the more frequent are the changes. Thus, the performance is more deteriorated at the lower level (scheduling level). More precisely, this model is a generic model based on VSM dealing with production planning considering both MPS level and scheduling (lot-streaming).

In a PDS, the basic unit is the intelligent product, which is capable of i) acquiring and archiving data, ii) communicating with its environment and iii) interacting with and on it. So, intelligent products have autonomy, auto-organization and auto-regulation properties necessary to become the basic subsystem of a VSM model which is able to model all levels of a MRP2 system. The quadrant I shows the planning system which may be centralized or distributed. Its decomposition is based on four levels of aggregation of product entities (weekly production, manufacturing orders, lots and products). To each level, entities are modeled as agents. The product entities are agents with a specific control/autonomy level which allow to represent all the hybridization levels of the system from a pure centralized system (product agents transmit information to upper level where decision is made) to a pure heterachical system (agents communicate among themselves in order to make decision). The quadrant II is a conceptual representation of the instantiation phase. It shows the physical implementation and corresponds to the instancing of products in the form of holons, which load intelligence and the functions allowing them to interact with environment and to acquire the desired level of autonomy. The quadrant III shows the physical control in which product holons are able to make decisions according to events concerning their own evolution. The quadrant IV shows the virtual implementation and corresponds to the transformation process of data (coming from the shopfloor) to information allowing knowledge to emerge. It is this knowledge which must be loaded by agents in quadrant I in order to improve their adaptation abilities to events with the principle of experience feedback. The question that needs to be answered is "How perform this experience feedback"?

DATA MINING AND PDS

As previously said, in the concept of product driven system (PDS), product must take decisions and interact with its environment thanks to acquired knowledge and information.

The synchronization of physical and informational flows inherent to PDS implies that many data may be exploited in order to create this knowledge and this information. These data may be related to product himself, or to the production process. So, the question becomes: how to exploit these data?

Considering figure 1, green arrows (thick) connect the elements of quadrant IV to elements of quadrant I. These connections represent the knowledge loaded in agents. So, the first task is to determine which knowledge is needed by different levels agents. Obviously, a product agent doesn't need the same knowledge than a manufacturing order agent. So it is necessary to define precisely these needs in order to be able to answer them. When this is done, it remains to determine how to build this knowledge. For this, the recursion of the VSM model may be useful. A first level may be defined which includes the two physical quadrants (II and III) and the product layer of the two virtual quadrants (I and IV). This level is surrounded by dotted line. The second level (Lots) includes the first level and adds the lots layer of quadrants I and IV. It is surrounded by short dashed line. The third level (Manufacturing Order level) includes Lots level and adds the fabrication order layer of the quadrants I and IV.

It is surrounded by long dashed line. At last, the fourth and last level (weekly production level) includes fabrication order level and adds the weekly production layer of the two virtual quadrants (I and IV). It is surrounded by solid line. This decomposition is comparable to the concepts of systems and sub-systems of the system engineering which may be used in order to define interfaces between levels. To each level, the knowledge manufacturing process is performed in several steps: 1. Determination of witch knowledge must be loaded in agent. As explained previously, this need is different according to agent level. 2. Determination and collect of information available in order to produce knowledge. This point will be detailed afterwards. 3. The structure of the model (here multilayer perceptron) has to be determined. 4. At last, learning and validation phase must be performed. The failure of the learning process implies a feedback on the second or third points.

Let us focus on the product level. In quadrant IV, the knowledge to load in the agent has to be built. The main particularity of this level is that the entries of knowledge manufacturing process are only data collected on the workshop. This process is then a classical process of knowledge extraction from data. The main difficulty is to know which data is necessary. It can be noticed that these data may be of continuous or discrete nature, determinist or stochastic one, and the knowledge design process must take into account the hybrid nature of this data.

When the next level is considered, the entries of knowledge manufacturing process may be data (aggregated or not) collected on the workshop, but also information and knowledge built at the product level. So the double challenge is:

-To determine which data, but also which information and which knowledge at the product level are necessary in order to built the knowledge to be loaded in agent at the lot level, -To define a tool allowing to aggregate entities of different nature (data, information, knowledge) in order to built the desired knowledge.

The desired knowledge to be loaded in agents of upper levels will be built with a recursive approach by using the preceding procedure. This paper highlights knowledge manufacturing process at the product level in order to point out the main difficulties encountered and to propose solutions.

ILLUSTRATION

Let us consider a simple production process constituted of sequential work centers presented by figure 2. One of these work centers is a bottleneck. The only knowledge which must be loaded in product agents is the lead time between the release of manufacturing order and the products arrival into input queue of bottleneck. The knowledge manufacturing process must be highly automated. So, the data loaded by holons (quadrants II and III) are collected and exploited by using multilayer perceptron which uses supervised learning. Its structure is given by:

0 1 2 1 0 1 1 1 . . n n i ih h i i h z w g w x b b = = 1 2 = + + 3 4 5 6
7 7

(1)

where 0 h x are the n 0 inputs of the network, 1 ih w are the weights connecting the input layer to the hidden layer, 1 i b are the biases of the hidden neurons, g(.) is the activation function of the hidden neurons (here, the hyperbolic tangent), 2 i w are the weights connecting the hidden neurons to the output one, b is the bias of the output neuron and z is the network output.

The weights and biases are determined by using a supervised learning which can be performed in two steps (Thomas et al. 2011): i) initialization step; this initialization may be randomly performed or by using more complex algorithms. This step is crucial in order to avoid local optimum trapping. ii) learning step; many learning algorithms exist. One of them is the Levenberg-Marquardt algorithm. It works as a hessian algorithm when solution is distant and as a gradient algorithm when solution is near.

This neural network must model the lead time between the release of manufacturing order and the products arrival into input queue of bottleneck. This lead time is a continuous notion. A first step is to fetch the lead time and all the explanatory variables collected by each product holons. These explanatory variables will become the neural network inputs. They may be continuous, as utilization rates, queues size… or discrete, as routing choice, machine choice… The question that needs to be answered is "How to take into account this discrete data"? Previous works have shown that some discrete variables may be used without particular precautions but other variables may not (Thomas et al., 2011). In order to solve this problem, two approaches may be used. The first approach is similar to the multi model philosophy. In fact, if learning cannot take into account some discrete variables, this is due to the system comportment changes when these variables change of state. So, these discrete variables define different operating areas of the system, and so, it is necessary to design one neural model for each operating area. As example, if two discrete variables X1 and X2 may take 3 and 2 states respectively, the considered system can be found into 2*3=6 operating areas and so, it needs 6 neural models to learn (figure 3). The advantages of this approach are that the neural networks have only continuous inputs and so, the learning is much simpler. Moreover, the structures of the networks include less input and hidden neurons and so the computational time decreases during the learning and exploitation steps. However, the main drawbacks are the number of neural networks to learn and the need to design a models selection system in function of states of discrete variables (Thomas et al., 2011).

The second approach consists to transform the discrete variables into binary ones and to use these binary variables as inputs of the network. With the same example as above, five binary input variables must be created, each of them may take the states 0 and 1: "X2=1"; "X2=2"; "X1=1"; "X1=2"; "X1=3". The main advantage of this approach is that only one neural network models the entire system. However, this model includes more inputs and hidden neurons and so the computational times increase during the learning and exploitation steps (Thomas and Thomas, 2009). These two approaches are not paradoxical. An optimal solution may be to mix these two approaches in order to limit both, the growing number of neural models to learn and the size of each of these models.

Following the explicative variables are collected and defined. In a second step, the structure of the neural network must be designed. The works of Cybenko and Funahashi have proved that a multilayer perceptron with only one hidden layer (using a sigmoïdal activation function) and an output layer (using a linear activation function) can approximate all nonlinear function with any desired accuracy. However, nothing is said about the number of hidden neurons.

The simplest approach would be to choose a very great number of hidden neurons which permits to obtain the best accuracy. However, we are not in front of a regular approximation problem but in front of a function adjustment to a finite number of points [START_REF] Dreyfus | Réseaux de[END_REF]. The risk is to learn the noise and not the function. This risk is called overfitting. In order to avoid it, different techniques have been proposed as regularization methods, early stopping or penalty methods. However, the determination of the optimal structure of the network allows to avoid the overfitting and to optimize the calculation times. For this, two approaches exist. The first one is a constructive one where the hidden layer is iteratively built. Another way is to start from a structure including too many hidden neurons and to remove the spurious neurons. The main advantage of this approach is to allow to some algorithms to determine simultaneously the hidden neurons number and the feature selection (Engelbrecht, 2001;Hassibi et al., 1993;Setiono and Leow, 2000).

Three algorithms have been tested and compared on the lead time model in a sawmill (Thomas and Thomas, 2008). These three algorithms are OBS (Hassibi et al., 1993), N2PFA (Setiono andLeow, 2000) and the one proposed by Engelbrecht (Engelbrecht, 2001). The obtained results have shown that the association of two algorithms (an extension of Engelbrecht algorithm and N2PFA) gives the optimal structure of the network quickly. In fact, a first step of pruning with the fastest algorithm (extension of Engelbrecht) allows finding the number of hidden neurons. In a second step, the N2PFA algorithm works with a smaller structure than the initial one (less hidden neurons) allows to design the network structure by pruning the spurious inputs.

CONCLUSIONS

In this paper, in a first step, we have summarized the new advances in product driven system approach and a VSM model has been presented. In a second step, we have investigated the knowledge manufacturing process. In summary, we can say that data are essential sources of knowledge but they are often unclaimed treasure because their exploitation may become time consuming. However, some tools exist, as learning overall and neural network in particular, allowing automating this exploitation. Nevertheless, we need to be careful and to make sure to respond positively to the questions: i) all the necessary information is included in the data? ii) all the collected data is well necessary? iii) how associate data of different natures (continuous or discrete) in the same model?

If the learning fails, this implies that the answer to the first question is negative. In this case, in order to supplement database, the product holons must collect other variables which may require improving the instrumentation. For the two other questions, some tools and methods have been presented succinctly here.

The implementation of this approach has two sides. The learning phase of a neural model is a complex task which must be designed off line. However, the resulting model is a simple equation which may be loaded in an agent.

However, one open question remains to be addressed: How to perform the knowledge manufacturing process for upper levels? This point represents a double challenge: i) how to determine which data, but also which information and which knowledge at the lower level are necessary in order to perform this knowledge manufacturing process? ii) which tool allows to aggregate entities of different natures (data, information, knowledge)? iii) These challenges will be addressed in our future works.

  Fig. 1. VSM based product driven control system. Concerning the figure 1 above, we have made the hypothesis that products are instrumented with RFID technology which allows acquiring, archiving data and communicating and interacting with their environment. The products holarchy is designed in order to represent the decision levels of a MRP2 system. This resulting metamodel uses the holon concept. This figure is subdivided into four quadrants (I, II, III, and IV) in order to simplify the explanations. The horizontal axis distinguishes the physical world to the virtual one. The vertical axis distinguishes the design which is a representation of the system to the implementation which performs the decision making and the knowledge management. Red arrows (dashed) represent the data flows from the shop floor to the quadrant IV (Data Management System -DMS), when the green (bold) arrows represent informational or knowledge flows into the DMS. To avoid overloading the figure, only some examples of these flows are shown.

Fig. 2 .

 2 Fig. 2. Considered production system.

Fig. 3 .

 3 Fig. 3. Taken into account discrete variables -multi-model approach.

ACKNOWLEDGEMENTS

This paper is based on many works that have been achieved and supervised by authors. Many thanks to researchers that have worked with us on this subject. Particular thanks to Mr. C. Herrera for its contribution during its works of Ph.D. Moreover, the authors gratefully acknowledge the financial support of the CPER 2007-2013 Competitiveness Fibre Cluster (Structuration du Pôle Compétitivité Fibres Grand'Est), local (Conseil Général des Vosges), regional (Région Lorraine), national (DRRT and FNADT) and European (FEDER) funds.

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Shi Bai

Emmanuel Thom

Paul Zimmermann

FACTORISATION OF RSA-704 WITH CADO-NFS

We give details of the factorization of RSA-704 with CADO-NFS. This is a record computation with publicly available software tools. The aim of this experiment was to stress CADO-NFS -which was originally designed for 512-bit factorizations -for larger inputs, and to identify possible rooms of improvement.

We report on the factorization of RSA-704 (212 decimal digits), which is the 2nd largest integer factorization with the General Number Field Sieve (GNFS), after the factorization of RSA-768 (232 digits) in December 2009 [START_REF] Kleinjung | Factorization of a 768-bit rsa modulus[END_REF].

Polynomial Selection

Polynomial selection started end of April 2011. We used the following degree-6 polynomial:

f (x) = 10614120x 6 + 62813641710611x 5 + 1938361239259842311964x 4 + 931957113890545875115664715x 3 -11187228497714282733145127980606483x 2 + 275791344247583495761263211927712634450x + 631618785519411550157074523461307229101210175
with 4 real roots, skewness 2159616.00, Murphy's α = -9.46, and Murphy E-value 9.55 • 10 -16 , together with the linear polynomial

g(x) = 1701314346829200310007393599x -10040119372014939875708192394943108.
This polynomial pair was found using the CADO-NFS implementation of Kleinjung's 2008 algorithm [START_REF] Kleinjung | Polynomial selection[END_REF], and can be reproduced as follows:

$ ./polyselect2l -nq 800 -lq 7 -degree 6 -incr 60 -maxnorm 70 -admin 10614120 -admax 10614120 -N 740. The command-line above says that we are searching the leading coefficient of the linear polynomial g(x) of the form g 1 = p 1 p 2 • • • p 7 q 1 q 2 with P < q 1 , q 2 < 2P , P = 2000000, and p 1 , ..., p 7 are seven small primes.

We also looked for degree-5 polynomials, but we prefered to use a degree-6 polynomial since CADO-NFS had been less used -if any at all -with such a degree. The total time spent in polynomial selection was about 12 core years (about 2.2 for degree 5, and 9.9 for degree 6), using about 100 cores at ANU.

Sieving

Sieving started on June 20, 2011, using clusters both at ANU and Inria Nancy-Grand Est. We used as factor base bound 250, 000, 000 on the rational side, 500, 000, 000 on the algebraic side, 2 33 as large prime bound on both sides, with up to two large primes on the rational side and three on the algebraic side. Due to a limitation of the CADO-NFS lattice sieve, we had to use a sieving region of 2 29 only (I = 15) which was sub-optimal (I = 16 like for the factorization of RSA-768 would have been better). This limitation has been removed now in CADO-NFS, but we prefered to finish the experiments with I = 15 (in addition, I = 16 uses a lot of memory, which would not enable us to use all cores of the clusters we had access to).

Due to the sub-optimal sieving parameters, we had to sieve over a large range of special-q, namely from 500M to 10000M. This in turn caused lots of duplicate relations (see below). On February 26, 2012 we had collected a total of 1,313,935,004 relations. We estimate to 500 CPU years the total sieving time (most of the computers used for sieving were Intel Xeons L5420 running at 2.5Ghz).

Filtering

The 1,313,935,004 raw relations gave 832,908,644 unique relations (i.e., 36.6% of duplicates). After removing singletons, we had a matrix with about 650M rows, and an initial excess of about 98M. After the "clique removal" algorithm, it remained about 320M rows and columns with an excess of 160, and an average weight of 22.19 per row.

In the merge phase, we merged ideals of weight up to 50. The CADO-NFS code does not consider the heavy ideals in the merge phase (here 132 heavy ideals were "buried"). The final matrix had about 89M rows and columns, with 17720843456 non-zero coefficients (about 200 per row), and 16568894691 in the sparse part (about 187 per row), while the dense part consists of the 32 heaviest ideals. (The size of the sparse matrix is 67Gb in binary form.)

After the merge phase, we tried the cycle optimization method from Denny and Müller [START_REF] Denny | On the reduction of composed relations from the number field sieve[END_REF], which is implemented in msieve too. We tried this method in two ways: firstly to reduce the number of relations in the matrix, secondly to reduce the number of ideals. In both cases we started with 319879050 relation-sets, and an initial weight of 1029799871 relations (11.63 on average per relation-set). If we use this method to reduce the number of relations in the merged matrix, we save only about 0.03% of the total number of relations, which in turn reduced by about 0.02% the total weight of the matrix. If we use this method to reduce the number of ideals (instead of relations) in the merged matrix, we gain only a little more in the total weight of the matrix. We conclude that the cycle optimization method from Denny and Müller is not interesting with modern merge algorithm using Markowitz pivoting.

Linear Algebra

The linear algebra was started on March 19, 2012. The block Wiedemann algorithm has been used, using only one sequence of 64-bit vectors (in other words, blocking parameters m = n = 64 have been used for the algorithm). The first phase (krylov) ended on May 11. The second phase (lingen) started on May 13, although the full run, taking 10 days, completed only on June 12, due to successive power outages. The last phase (mksol) started on June 13 and ended on June 29, 2012, producing a kernel of dimension 61.

All krylov and mksol jobs within this project were carried on the french Grid'5000 computer grid. The article [START_REF] Kleinjung | Using a grid platform for solving large sparse linear systems over GF(2)[END_REF] indicates how the block Wiedemann algorithm may be split into small jobs in order to be used on a grid. Overall, 1800h of wall-clock time have been spent on these krylov and mksol tasks, on clusters of varying sizes (clusters have been used in an opportunistic manner, depending on resource availability). Noteworthy is the fact that all of these jobs have been setup as "best-effort" jobs, allowing any competing job submission to immediately kill our job, without any notice. This setup has obviously led to jobs spending time in their start-up phase (importing data to the cluster nodes), yet not being able to do much useful work later on. The overhead cost of this sometimes useless I/O time on the previously indicated timing is roughly 800h. This large overhead could have been lowered considerably if we had been able to replicate our storage points on several nodes, as we did previously for the RSA-768 computation.

Characters and Square Root

The characters program gave 10 dependencies. We had 64 dependencies from the linear algebra, minus 32 since we skipped the 32 heaviest columns, thus 22 dependencies were "killed" by the characters, which is larger than the usual value of 10-15; we have to investigate why.

Conclusion

The factorization of RSA-704 is n = p • q where p = 90912135295978188784406583026004374858926083103283587204285121689 60411528640933367824950788367956756806141 q = 81438592591100452657278091262844293358778990021676278832009141724 29324360133004116702003240828777970252499 have both 106 digits. The prime factors of p ± 1 and q ± 1 are:

p -1 = 2 2 • 5 • 17 • 7759 • 248701 • 3311937667 • 1669783862489 • 1880450644642000493838449 • p49 p + 1 = 2 • 3 2 • 43 • 71 • 157 • 2630713 • 1850017111 • 1040072485315298476627 • 2023909737931501893269845781 • p36 q -1 = 2 • 19 • 149 • 233 • 426163 • 34302641 • 415283201 • p79 q + 1 = 2 2 • 3 2 • 5 4 • 8753 • 27539 • 962945197 • p85

Acknowledgements. The computation was done with CADO-NFS, a free software whose main developpers are Pierrick Gaudry, Alexander Kruppa, François Morain and the three authors (see http://cado-nfs.gforge.inria.fr/). Lionel Muller helped distributing jobs in the sieving phase. The orac cluster in the Mathematical Sciences Institute of the Australian National University was used for polynomial selection and sieving. The TALC cluster of Inria Nancy-Grand Est was used for the sieving phase, and Grid 5000 was used for the linear algebra phase. Grid'5000 is an experimental testbed, being developed under the INRIA ALADDIN development action with support from CNRS, RENATER and several Universities as well as other funding bodies (see https://www.grid5000.fr).


Simon Labarthe

Yves Coudiere

Jacques Henry

Hubert Cochet

A Semi-Automatic Method To Construct Atrial Fibre Structures : a Tool for Atrial Simulations

Fibre structure and anisotropy is a determinant issue to provide accurate simulations of the electrical activity of atrial tissue. Though, atrial fibre architecture remains unreachable to standard imagery techniques on patients. A method to construct models of the fibre architecture on patient-specific geometries is then a key for numerical simulations of atrial tissues. Such a method is proposed. Pathological and non pathological patient specific surface models of the left atria (LA) are defined. Hence, a pathological scenario is explored : a mechanism of microreentry in the left superior pulmonary vein (LSPV) and its interaction with the sinus rhythm (SR).

Introduction

The propagation of the action potential in the heart tissue is very anisotropic. In the different mathematical models of the cardiac electrical activity, this characteristic is modelled by an anisotropic diffusion tensor field based on the underlying fibre structure of the tissue. The introduction of this anisotropy is essential to simulate accurately the activation maps and the action potential duration repartition which are key information especially for arrhythmogenic dynamics modelling [START_REF] Zhao | An image-based model of atrial muscular architecture / clinical perspective[END_REF].

However, imaging the fibre orientation is still challenging. If an accurate fibre structure on the atria can be imaged on ex-vivo hearts [START_REF] Zhao | An image-based model of atrial muscular architecture / clinical perspective[END_REF], fibres imaging tools such as DTMRI remain inefficient on in-vivo atria, owing to the weak thickness of atrial tissues. Then, constructing an a priori fibre structure from histological description [START_REF] Ho | Anatomy of the left atrium: implications for radiofrequency ablation of atrial fibrillation[END_REF] on a patient specific geometry is an acceptable trade-off toward patient specific simulations. We present here a new semiautomatic method that gives such an anisotropy characterisation in a semi-automatic way. A left atrium (LA) model is constructed, and a pathological fibre orientation scenario in the left superior pulmonary vein (LSPV) is tested.

Method

Histological descriptions [START_REF] Ho | Anatomy of the left atrium: implications for radiofrequency ablation of atrial fibrillation[END_REF] of the fibre structure of the LA present two main features : [START_REF] Zhao | An image-based model of atrial muscular architecture / clinical perspective[END_REF] The LA can be divided in basic cylinder-like structures with circumferential fibre orientation. (2) The variation of the fibre direction from a cylinder-like element to another is continuous.

Our method aims to mimic those main physiological characteristics using three steps. A surface mesh is extracted from a MR image of the LA. It is manually decomposed in cylinder-like elements which local circumferential structure is semi-automatically constructed. An in-painting algorithm extends continuously the fibre direction on the whole atrium, taking the local orientation in the basic elements as a constraint.

2.1.

Imaging the LA LA geometry was acquired in-vivo using ECG-gated contrast-enhanced multi-detector computed tomography (MDCT) in a patient with history of paroxysmal atrial fibrillation. Imaging was performed using a 64-slice CT scanner (SOMATOM Definition, Siemens Medical Solutions, Forchheim, Germany) during the intravenous injection of a 120 mL bolus of iodinated contrast agent at the rate of 4 mL/s. ECG-gating was set for acquisition window to occur at end-systole, when LA motion is minimal. Acquisition parameters were: slice thickness 0.5 mm, tube Voltage 120 kV, maximum tube current 850 mAs, and gantry rotation time 330 ms. An imaging volume comprising the whole LA was reconstructed with a voxel size of 0.5×0.4×0.4 mm. Trans-axial images were imported in DICOM format in a local database of the software OsiriX 3.6.1 (OsiriX foundation, Geneva, Switzerland). The endocardial surface was segmented automatically using region growth segmentation. Volume rendering reconstructions were used to remove non atrial structures from the segmentation. Pulmonary veins (PV) were cut several cen-timetres from their ostia. The resulting segmentation was used to compute a 3D mesh in vtk format using the software CardioviZ3D (INRIA Asclepios, Sophia Antipolis, France). The mesh was smoothed with weighted laplacian smoothing and optimized with freeYams [START_REF] Frey | About surface remeshing[END_REF] to get a mesh suitable for calculation.

Circumferential fibres

We call Ω h the mesh representing the descretisation of Ω the endocardial surface of the imaged LA.

We identify manually using MeshLab (3D-CoForm Project, Italy) the following cylinder-like elements in Ω h : dome, vestibule, insertions of the dome in the vestibule, PVs, auricle fingers and auricle. Some of this basic structures are clearly tubular, such as the PVs. Others can be identified as a portion of cylinder, such as the atrial dome.

After this identification, we have Ω = Ω c ∪Ω i where Ω c is the set of all the circumferentially distributed cylinderlike zones of the LA, and Ω i is the area to be completed by the in-painting method. Let η be the outward unit normal vector field and u be a unit vector field modelling the fibre orientation on Ω. We want u(X) to be tangent to the surface for all X ∈ Ω. To impose this characteristic, we compute the vectorial product u = u * ∧ η where u * is an adjoint vector field that is to construct.

To construct circumferential fibres on a given cylinderlike basic element ω of Ω c , we need to obtain the vector field u * |ω which should be closed to the "axis" of ω. In that goal, an usual method in vascular imaging [START_REF] Hernandez-Hoyos | Segmentation anisotrope 3D pour la quantification en imagerie vasculaire par résonance magnétique[END_REF] is performed : we search for the rotation axis that minimizes the inertia momentum of the structure by a spectral analysis of the inertia matrix.

Let ω h be the mesh resulting from the discretization of ω and ∆ a line through the origin O. ω h is considered as a non-deformable homogeneous geometry with a uniform surface mass of 1. The inertia momentum I ∆ (ω h ) of ω h respectively to a rotation around the axis ∆ supported by a unit vector e ∆ can be written :

I ∆ (ω h ) = pi∈ω h R 2 pi
where R pi is the distance between the point p i ∈ ω h and ∆.

For all p i ∈ ω h , R 2 pi can be calculated with the formula

R 2 i = (e ∆ ∧ P i ).(e ∆ ∧ P i )
where P i = (x i , y i , z i ) is the coordinates vector of the point p i . I ∆ (ω h ) can be rewritten as follows

I ∆ (ω h ) = e ∆ .I(ω h )e ∆ with I(ω h ) = i y 2 i + z 2 i i x i y i i x i z i i x i y i i x 2 i + z 2 i y i z i i x i z i i y i z i i x 2 i + y 2 i
the inertia matrix of ω h . I(ω h ) is a real symmetric matrix. Let α(ω h ) be the smallest eigenvalue of I(ω h ) and e α (ω h ) a corresponding unit eigenvector. Then, e α(ω h ) is the direction of the axis α(ω h ) that minimizes the inertia momentum of the rotation of Ω h . For a cylinder C, e α(C) corresponds to the axis of C.

We set u * |ω h = e α(ω h ) and we construct u |ω h = u * |ω h ∧ η |ω h . A result of this step can be seen in figure 1.

If the the shape of the initial component is too far from a cylinder, this method may not give acceptable results : a manual correction must be performed using linear combination of the three eigenvectors.

Completion using an in-painting method

The second step of the method consists in completing continuously the fibre structure u outside the basic cylindrical elements.

Inpainting PDE methods usually recursively perform a smoothing procedure on an initial distribution on the whole domain Ω until a convergence criteria is reached -see [START_REF] Rousseau | Geometrical Modeling of the Heart[END_REF] for a short review of in-painting methods adapted to fibre reconstruction. We use here an adaptation of the laplacian smoothing algorithm which is easier to implement and compute than more sophisticated algorithms such as Sobolev or total variation smoothing. In counterpart, we don't have here the optimal regularity guaranteed by those algorithms.

We perform the inpainting algorithm on the adjoint vector field u * which may be more regular than the fibre vector field. Let Ω i,h the discretization of Ω i and U * |Ωi the discrete version of the adjoint vector field u * |Ωi that we want to construct. This vector has dimension N T , where N T is the number of triangles in Ω i,h .

We define U * 0 the matrix of dimension N T ×3 such that U * 0 j = (1, 0, 0) for all j ∈ [1, N T ]. We construct recur-sively a family of vector fields with the following process :

∀n > 0, ∀j ∈ [1, N T ], U * n j = 3 k=1 U * n-1 ϕ(j,k) || 3 k=1 U * n-1 ϕ(j,k) || + ǫ 0
where ǫ 0 is a small regularisation parameter that prevents an indetermination when || 3 k=1 U * n-1 ϕ(j,k) || vanishes. ϕ(j, k) is the index in Ω i,h of the k th of the three triangles sharing an edge with the j th triangle of Ω i,h . If the j th triangle is on the boundary of Ω i,h , some of this neighbour triangles are not included in Ω i,h but in Ω c,h . Then, ϕ(i, j) is the index in Ω c,h of such a triangle, and

U * n-1 ϕ(i,j)
is the value of the adjoint vector field already defined in the previous step of the method. This algorithm is stopped when

||(||U * n j -U * n-1 j || l 2 ) j∈[1,N T ] || l ∞ < ǫ
A result of the fibre organisation given by this method in the whole LA can be seen in figure 2.

A tool for simulations

This model of LA is used to perform simulation of a pathological situation. We study the interaction between several beats of sinus rhythm and a micro-reentry in LSPV triggered by a fibre direction heterogeneity.

Simulation method

We solve the monodomain equation with a P1 finite element method using an implicit Euler scheme. We set the surface capacity of the cells to 1 µF.cm -2 and the cell surface to volume ratio to 250 cm -1 to ensure propagation speed comparable to [START_REF] Harrild | A computer model of normal conduction in the human atria[END_REF].

Fibres orientation : we use the atrial fibre orientation model previously defined with a specific fibre structure in the LSPV inspired of a scenario presented in [START_REF] Zemlin | Spontaneous onset of atrial fibrillation[END_REF] : the fibre orientation is circumferential in the distal part of the vein, whereas it's tangential in the ostial part, with an abrupt change of fibre direction between those structures, excepted in a transition zone -figure 3. This complex structure is constructed by adapting our method : the spectral analysis is used in the ostial and distal part, while inpainting is computed for the transition zone. Conductivity : We set the longitudinal conductivity to 1.5 mS.cm -1 in the whole LA and the transverse conductivity to 0.24 mS.cm -1 , except for the pectinate muscles of the appendage that are set to 0.6 mS.cm -2 to model a more isotropic area triggered by the less regular fibre structure. The LSPV is given a longitudinal and transverse conductivity of respectively 1.6 mS.cm -1 and 0.02mS.cm -1 to ensure a conduction block at the fibre heterogeneity.

Electrophysiology :

We use the the Courtemanche-Ramirez-Nattel (CRN) model to simulate the atrial electrophysiology. We apply multiplicative factors on g N a , g Kl , g to and g Ca,l , with a value of respectively 1.1, 1.9, 0.74 and 0.85 in the LA and 0.42, 2.7, 0.6, 0.85 in the LSPV. Those factors shorten the action potential (AP) and increase the spreading velocity in the LA whereas they give a triangular shape to the AP and decrease the velocity in the LSPV.

Initial stimulations : we simulate the main inter-atrial connexions. We apply a stimulation current in, successively, the Bachmann's bundle insertion (BBI), in the coronary sinus (CS) and in the fossa ovalis (FO) that model the sinus wave spreading in the LA. Activation of CS and FO is delayed of respectively 21ms [START_REF] Harrild | A computer model of normal conduction in the human atria[END_REF] and 5ms, comparatively to the BBI which is stimulated with a period of 400ms. Two ectopic beats are applied in the distal part of the LSPV 113ms before and 64 ms after the BBI.

Simulation results

The front of the sinus wave is distorted by the anisotropy of the conductivity field so that preferential paths are taken: from the BB and CS to the vestibule and the roof of the LA, in a very comparable way than [START_REF] Zhao | An image-based model of atrial muscular architecture / clinical perspective[END_REF][START_REF] Krueger | Modeling atrial fiber orientation in patientspecific geometries: A semi-automatic rule-based approach[END_REF]. The ectopic wave front is extremely slowed by the characteristic set in the LSPV, so that the sinus wave and the ectopic wave meet together in the ostial part of the LSPV. A micro-reentry is triggered in the LSPV by the second ectopic beat (figure 4) : the ectopic wave is stopped distally by the fibre discontinuity zone, invades the proximal part through the transition zone and goes back in the distal part when the tissue has recovered. The micro-reentry perturbs the sinus wave during the next beats.

Discussion and conclusion

We presented a new method to characterise the anisotropy on patient-specific LA surface models. This method is able to reproduce in an interactive and semiautomatic way the main structures of fibre direction in LA as described in [START_REF] Ho | Anatomy of the left atrium: implications for radiofrequency ablation of atrial fibrillation[END_REF]. However, this fibre structure is not patient dependant : it's a priori defined from a description of the mean fibre direction in the LA. This method is still time-demanding, mainly because of the multiple software that were used : a more integrated tool could be designed. Nevertheless, it may be a more flexible tool than the previous method proposed in [START_REF] Krueger | Modeling atrial fiber orientation in patientspecific geometries: A semi-automatic rule-based approach[END_REF] : in particular, it can create complex local fibre structures in a straightforward manner. One scenario was implemented : it triggered microreentries in the LSPV that perturbed the sinus rhythm.

Figure 1 .

 1 Figure 1. Result of the fibre construction on the base of the left superior pulmonary vein.

Figure 2 .

 2 Figure 2. Result of the fibre direction construction process on the LA. Postero-inferior view.

Figure 3 .

 3 Figure 3. Pathological fibre structure in the LSPV. Acircumferential orientation in the distal zone. B -steep transition zone. C -smooth transition zone. D -tangential orientation in the ostial zone.

Figure 4 .

 4 Figure 4. Potential maps in a posterior view of LA. Dark blue : resting potential. Light-beige : depolarisation front. A, 156 ms: the first ectopic wave in the LSPV invades the transition zone to meet the sinus wave coming from BB (top) and CS (bottom). B, 340 ms : the second ectopic wave is coming into the repolarising ostial part through the transition zone. C, 460 ms : the first loop of the micro-reentry anchored in the discontinuity zone of the LSPV gets into the repolarising tissue of the last ectopic wave. The loop period of the micro-reentry is about 163 ms. D, 982 ms : the micro-reentry wave collides with the sinus wave from BB (top), surrounds the ostium of the left inferior pulmonary vein and meets the sinus wave from CS.

Acknowledgements

This work was partially supported by an ANR grant part of "Investissements d'Avenir" program reference ANR-10-IAHU-04.


Nicolas Maillet

Claire Lemaitre

Rayan Chikhi

Dominique Lavenier

Pierre Peterlongo

Pierre Peterlongo Compareads

Compareads: comparing huge metagenomic experiments

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