C Manuel Carlevaro

Luis A Pugnaloni

Arches and contact forces in a granular pile

come

The study of mechanically stable granular beds has become a major point of interest in granular physics. Studies range from analysis of force network properties [1][2][3][4] to structural characterization [5][6][7] to thermodynamic and statistical descriptions [8][9][10][11][12]. A recurrent question in the subject is related to the existence or not of a relation between force chains and arches [13,[START_REF] Mehta | Granular Physics[END_REF].

Arches are multiparticle structures where all grains are mutually stable [13,[START_REF] Pugnaloni | [END_REF][16][17], i.e. fixing the positions of all other particles in the assembly the removal of any particle in the arch leads to the collapse of the other particles in it. For an arch to be formed, it is necessary (although not sufficient) that two or more falling particles be in contact at the time they reach equilibrium in order to create mutually stabilizing structures [18]. Like arches in architecture, granular arches are assumed to sustain the weight of grains above.

Highly stressed grains in static deposits are generally found to form linear structures: the so-called force chains. A correlation as been pointed out [13,[START_REF] Pugnaloni | [END_REF]19] between the distribution of horizontal span of arches in a granular pile and the distribution of normal forces at the grain contacts. Therefore, it is assumed that a strong correlation has to be present between arches and highly stressed grains in a granular deposit. In this paper we assess this general belief in the frame of a simulation of granular packings prepared by tapping.

We used a velocity Verlet algorithm to integrate the Newton equations for 512 monosized disks in a rectangular box. The disk-disk and disk-wall contact interaction comprises a linear spring-dashpot in the normal direction and a tangential friction force that implements the Coulomb criterion to switch between dynamic and static friction. Units are reduced with the diameter of the disks, d, the disk mass, m, and the acceleration of gravity, g. Details on the force equations and the interaction parameters can be found elsewhere [18,20]. Tapping is simulated by moving the confining box in the * Electronic address: manuel@iflysib.unlp.edu.ar † Electronic address: luis@iflysib.unlp.edu.ar vertical direction following a half sine wave trajectory of frequency ν = π/2(g/d) 1/2 . The intensity of the excitation is controlled through the amplitude, A, of the sinusoidal trajectory; and it is characterized by the parameter Γ = A(2πν) 2 /g. A new tap is applied after the system has come to mechanical equilibrium defined via the stability of each particle-particle contact [18]. After many taps, the system reaches a steady state where the properties of the static configurations generated have well defined mean values and fluctuations. Averages were taken over 500 taps (configurations) in the steady state corresponding to each value of Γ. Details on the algorithms used to identify arches can be found in previous works [START_REF] Pugnaloni | [END_REF]16,18]. Briefly, we need first to identify the supporting grains of each particle in the packing. In 2D, there are two disks that support any given grain. Two grains in contact with a given particle are able to provide support if the segment defined by the contact points lies below the center of mass of the particle. Some of these supporting contacts may be provided by the walls of the container. Then, we find all mutually stable particles. Two grains A and B are mutually stable if A supports B and B supports A. Arches are defined as sets of particles connected through these mutually stabilizing contacts (MSC). The fact that the supporting particles of each grain have to be known implies that contacts, and the chronological order in which they form, have to be clearly defined in the model. In the case of MD simulations, an algorithm that tracks the contacts that support each particle has been designed [18]. We use this scheme in the present work. We measure the stress tensor σ for grain i as:

σ αβ i = 1 π(d/2) 2 Nc j=1 f α ij r β ij , (1)
where, f ij is the force exerted by grain j on grain i and r ij is the branch vector that goes from the center of grain i to the contact point with grain j. The sum runs over the N c particles in contact with particle i.

Figure 1 shows some examples of the distribution of pressures and arches inside a granular pile. As it is to be expected, particles are subjected to higher pressures, in average, in the lower part of the pile as compared with the upper layers. The mean pressure grows continuously with the tapping intensity Γ [12,22]. This contrasts with the appearance of a minimum packing fraction, φ, at intermediate Γ [see Fig. 2(a)] as previously observed in various models [20,21] and experiments [12,22]. This minimum in φ is related with the existence of a maximum in the number of grains involved in arches [see Fig.

2(b)] [20].

It is worth mentioning that the system does not display force chains that span the system from top to bottom as is commonly seen in many experiments and simulations. This is due to the fact that the system is in mechanical equilibrium under its own weight; no external compression is applied to the sample in any direction. It can be observed from Fig. 1 that, at any depth into the pile, grains can present high and low stress irrespective of whether they belong to an arch or not. For a more quantitative analysis we plot in Fig. 3 the mean value of the contact forces (normal and tangential to the contact). MSC and non-MSC have been separated in the analysis. The mean normal contact force increases with Γ in agreement with the increasing mean pressure reported elsewhere [12,22]. It is clear that MSC (i.e., contacts within arches) have, in average, larger normal and tangential forces. However, Fig. 4 shows that the distribution of contact forces for MSC and non-MSC are rather similar. The exponential tail for contact forces adobe the mean contact force characteristic of granular packs subjected to external compression [2,3,23] or stable under their own weight [24] is also present in our systems. The behavior for forces below the mean resembles the weak divergence found for packings without external compression when bulk contacts (as opposed to contacts made between the grains and the container) are considered [23]. The different mean values observed in Fig. 3 for MSC and non-MSC are only due to a somewhat lower preponderance of large forces for the non-MSC and not to a clear separation of the two population of contacts. Deciding if a given contact is or not mutually stabilizing based on the strength of the forces involved is in fact impossible.

In Fig. 5, we show the results of a similar analysis but now the stress tensor on each particle, as defined in Eq. ( 1), is considered. The stress tensor accounts for both MSC and non-MSC on each grain. We separate in-arch grains from out-of-arch grains in the analysis. As observed in previous studies [12,22], Tr(σ) increases monotonically with Γ, which is in correspondence with the increasing normal contact forces [see Fig. 3(a)]. In-arch grains support, in average, pressures about 30% higher than off-arch grains. In contrast, the shear stress, σ xy , seems to be rather similar for both types of grains. These results indicate that in-arch grains are essentially subjected to larger compressive stresses. However, the stress tensor distributions do not show any peculiar difference between in-arch and off-arch grains. Figure 6 displays the characteristic exponential decays for both compressive and shear stresses distributions. While important differences in mean stress between in-arch and out-ofarch grains are observed in the compressive terms [see Fig. 5(a)], the stress distributions are hardly distinguishable for large Tr(σ). In contrast, the shear component, σ xy , for the in-arch grains present longer tails in comparison with out-of-arch grains even though their means are similar. Once again, the differences found between in-arch and out-of-arch grains are not the cause of a bimodal character of the stress distribution and particles with high and low stresses are likely to be found forming arches.

It is important to comment on some effects that might cause the lack of a clear separation of the two grain classes (i.e., in-arch or out-of-arch grains) in the contact force distribution. On the one hand, arches can always exist in the structure that sustain little weight since they are shielded by other arches above. This leads to the preponderance of small forces in the distributions for MSC. On the other hand, force chains can also develop without the need of arches. A deposit carefully built by sequential deposition of grains contains no arches in the structure, yet it will present force chains and the ubiquitous exponential PDF of contact forces. An interesting conclusion drawn in Ref. [17] -were the term bridge is used in the same sense we use arch-is directly connected with our results: "...bridges can be neither load-bearing nor load-induced... Bridges thus characterize the load-bearing ability, not necessarily the actual degree of load-bearing, of a packing." Such conclusions came from the fact that arch size distributions proved to be independent of gravity. Here, we went one step further and showed that in a single packing the weight is not born by the arches much more than by the rest of the grains.

In summary, we have shown that MSC, which define arches, present higher normal and tangential components of the contact forces as compared with non-MSC contacts. Grains belonging to arches are generally subjected to larger pressures but similar shear. However, the PDF of contact forces and particle stresses present similar exponential decays for in-arch and out-of-arch grains. A clear separation of the two populations of grains cannot be made. Future research in this respect should look into the effect that applied external loads can make to the force distributions for in-arch and out-of-arch grains.

LAP thanks fruitful discussions with Gary C. Barker and Anita Mehta. This work was supported by CON-ICET (Argentina).

FIG. 1 :

 1 FIG. 1: (Color online). Sample images of the simulated granular columns for different Γ: (a) Γ = 2.2, (b) Γ = 4.93 and (c) Γ = 15.4. The color code indicates the trace, Tr(σ), of the stress tensor for each particle. The joining segments indicate the arches detected in the system.

FIG. 2 :

 2 FIG. 2: (a) The mean packing fraction, φ, as a function of tapping intensity Γ. (b) Fraction of in-arch grains as a function of Γ.

FIG. 3 :

 3 FIG. 3: (Color online). The mean value of the contact force for mutually stabilizing contacts (black circles) and nonmutually stabilizing contacts (red-squares). (a) Normal contact forces, and (b) tangential contact forces..

FIG. 4 :

 4 FIG. 4: (Color online). The PDF of contact forces for MSC (black circles) and non-MSC (red-squares) for Γ = 2.2. (a) Normal contact forces, and (b) tangential contact forces.

FIG. 5 :

 5 FIG. 5: (Color online). Stress tensor for in-arch (black circles) and out-of-arch (red squares) grains. (a) The trace Tr(σ) of the stress, and (b) the off diagonal component σxy of the stress.

FIG. 6 :

 6 FIG. 6: (Color online). The PDF of the stress tensor for inarch (black circles) and out-of-arch (red-squares) for Γ = 2.2. (a) The trace, Tr(σ), of the stress tensor, and (b) the shear component, σxy of the stress.


Liliane Jean

François Bordas
email: francois.bordas@unilim.fr

Jean-Claude Bollinger

Chromium and nickel mobilization from a contaminated soil using chelants

Keywords: contaminated soil, chromium, nickel, chelant, mobilization Capsule: Chelant-induced dissolution of soil mineral matrix which controls metal solubilization

The mobilization of chromium and nickel from an industrial soil was investigated using two biodegradable chelants (citric acid and histidine), compared with a persistent one (ethylenediaminetetraacetic acid). Successive metal mobilizations were carried out in batch experiments. The main reactions involved were estimated by modelling the system with MINEQL+.

For a single mobilization, citric acid was the most effective for Cr mobilization and EDTA for Ni.

Their effectiveness could be explained by their ability to solubilize the mineral matrix and by the competition for the surfaces sites to desorb Cr(VI). Before and after the mobilizations, the distribution of metals was determined by a sequential extraction procedure. Only slight modifications were observed due to the low percentage of solubilized metal. A concentration of 0.05 mol.L -1 (citric acid and EDTA) allows a good compromise between metal mobilization and preservation of the soil mineral integrity.

Introduction

Metal contaminated soils are a serious environmental problem with implications for human health. The presence of metals in soil has two main origins: the alteration of the bedrock and human activities, the latter being the major cause of high levels of metals in soils (metallurgical industries, surface treatment industries, sewage sludge amendment...). The risks are related to the mobility and the bioavailability of the metals and consequently to their speciation in soil. Even when immobilized in the less mobile fractions, metals remain harmful and constitute pollutant stores, which can be removed if environmental conditions such as pH and Eh change [START_REF] Stumm | The cycling of iron in natural environments: considerations based on laboratory studies of heterogeneous redox processes[END_REF][START_REF] Bourg | Mobilization of heavy metals as affected by pH and by redox conditions[END_REF].

Various remediation methods, in-situ or ex-situ, are available. The conventional methods are solidification/stabilization, biochemical processes, phytoremediation, soil washing [START_REF] Mulligan | Remediation technologies for metal-contaminated soils and groundwater: an evaluation[END_REF]. Among ex-situ techniques, soil washing using chelating agents is an effective technique [START_REF] Peters | Chelant extraction of heavy metals from contaminated soils[END_REF].

Many studies have been carried out on metal extraction with chelants such as ethylenediaminetetraacetic acid -EDTA, citric acid, nitrilotriacetic acid -NTA, [S,S]ethylenediaminedisuccinic acid -EDDS [START_REF] Wasay | Organic acids for the in situ remediation of soils polluted by heavy metals: soil flushing in columns[END_REF][START_REF] Kim | Factors affecting EDTA extraction of lead from leadcontaminated soils[END_REF][START_REF] Tandy | Extraction of heavy metals from soils using biodegradable chelating agents[END_REF][START_REF] Luo | Enhanced phytoextraction of Cu, Pb, Zn and Cd with EDTA and EDDS[END_REF][START_REF] Palma | Copper leaching from a sandy soil: mechanism and parameters affecting EDTA extraction[END_REF][START_REF] Leštan | Soil washing using a biodegradable chelator[END_REF]. These chelants have a high affinity for many metals. Several parameters must be taken into account, the choice of the ratio of chelant to metals being important. Consequently, chelant concentration must be higher than trace metal concentration to obtain maximum extraction. But in the soil, there are also major elements such as Fe, Al, Mn, Mg and Ca which can be simultaneously solubilized by the chelants [START_REF] Kim | Factors affecting EDTA extraction of lead from leadcontaminated soils[END_REF][START_REF] Tandy | Extraction of heavy metals from soils using biodegradable chelating agents[END_REF]. Whereas many papers have been published about metal extraction with chelants, only few studies have been carried out about Ni and especially Cr extraction. Extractions of Cr and/or Ni using chelants were mainly studied with the purpose of phytoextraction [START_REF] Turgut | The effect of EDTA and citric acid on phytoremediation of Cd, Cr and Ni from soil using Helianthus annuus[END_REF][START_REF] Meers | Comparison of EDTA and EDDS as potential soil amendments for enhanced phytoextraction of heavy metals[END_REF][START_REF] Do Nascimento | Comparison of natural organic acids and synthetic chelates at enhancing phytoextraction of metals from a multi-metal contaminated soil[END_REF]. Indeed, chelating agents increase the solubility of heavy metals for plant uptake during phytoremediation [START_REF] Brooks | Plants that hyperaccumulate heavy metals[END_REF][START_REF] Salt | Phytoremediation[END_REF]. It is of course important to know the degree of biodegradability of the chelants. EDTA is persistent in the environment [START_REF] Bucheli-Witschel | Environmental fate and microbial degradation of aminopolycarboxylic acids[END_REF] and its presence in soil can lead to uncontrolled leaching of metals (Bordas and Bourg, 1998b), thus limiting its use for phytoextraction [START_REF] Alkorta | Chelate-enhanced phytoremediation of soils polluted with heavy metals[END_REF]. Citric acid and histidine are natural organic molecules that are easily biodegradable, their half-lives, in a soil suspension, being a few days (Brynhildsen and Rosswald, 1997;[START_REF] Römkens | Potentials and drawbacks of chelateenhanced phytoremediation of soils[END_REF].

The aim of this study is to compare the ability of two natural and biodegradable chelants (citric acid and histidine) with a persistent one (EDTA) to solubilise metals from an industrial soil contaminated mainly by nickel and chromium.

Materials and methods

All reagents used to prepare the solutions were with an analytical grade. High purity deionized water (Milli-Q system: resistivity 18.2 MΩ.cm, TOC < 10 µg.L -1 ) was used for all experiments.

Soil sampling and characterization

The studied soil came from a metallurgical site where special steels, superalloys, aluminium and titanium alloys are produced. The pollution was due to long time refuse storage on the bare ground. Before sampling, a superficial layer of soil (0-5 cm) containing refuse and the main part of the litter was discarded. The 5-10 cm layer of the soil was then sampled manually near the storage zone. This thickness was selected due to its contamination rate. The soil was air-dried and sieved (< 2 mm) [START_REF] Afnor | Qualité des sols[END_REF]. Soil properties: pH H2O (6.3 ± 0.1), pH KCl (5.3 ± 0.1), organic carbon (2.90 ± 0.08 g.kg -1 ), cation exchange capacity (12.3 ± 0.1 meq/100 g) were determined by standard methods [START_REF] Afnor | Evaluation de la qualité des sols[END_REF]. The granulometry was determined by the standard method, NF X 31-107 [START_REF] Afnor | Evaluation de la qualité des sols[END_REF]. Bulk powder X-ray diffraction (XRD) was used for mineralogical characterization of the soil sample (INEL CPS 120° Curved Position Sensitive Detector, CuKα1).

The total metal content was determined in the sample after a microwave-assisted digestion with aqua regia (microwave oven: MARCH 5, CEM). A recent study [START_REF] Larner | Comparative study of optimized BCR sequential extraction scheme and acid leaching of elements in the Certified Reference Material NIST 2711[END_REF] proved the correctness of this method by comparison with HF digestion.

The chemical distribution of metals in the soil was quantified by the BCR sequential extractions procedure [START_REF] Ure | Improvements in the determination of extractable contents of trace metals in soil and sediment prior to certification[END_REF] accelerated by ultrasound [START_REF] Pérez-Cid | Speeding up of a three-stage sequential extraction method for metal speciation using focused ultrasound[END_REF] (Table 1). The sonication was done with a 60W probe (Bandelin, model HD 70). After centrifugation (3000 g), the supernatant was filtered through 0.45 µm cellulose nitrate filter (Sartorius).

The fractionation of Fe was determined by oxalate [START_REF] Schwertmann | Differenzierung der Eisenoxide des Bodens durch Extraktion mit Ammoniumoxalat-Lösung[END_REF] and pyrophosphate extraction [START_REF] Mckeague | An evaluation of 0.1 M pyrophosphate and pyrophosphate-dithionite in comparison to oxalate as extractants of the accumulation products in podzols and some other soils[END_REF]. Oxalate extracts the poorly crystalline Fe oxides and the organically bound Fe and pyrophosphate extracts organically bound Fe.

To determine the speciation of Cr, an alkaline digestion was applied (0.5 mol.L -1 NaOH + 0.28 mol.L -1 Na 2 CO 3 ) and the quantification of Cr(VI) was carried out using the colorimetric method with diphenylcarbazide (Centre d'expertise en analyse environnementale du Québec, 2003). Cr(III) is calculated by subtracting Cr(VI) from total Cr.

Batch mobilization with chelating agent

Metal mobilizations were carried out in batch experiments at room temperature (20  2°C).

The solid:solution ratio was 1:10 with 50 mL of EDTA, citric acid or histidine solutions. Na 2 -EDTA salt, citric acid and L-histidine were used. Three replicates were made.

An optimum contact time was determined by a preliminary experiment. For this, each chelating agent was applied at 0.01 mol.L -1 and the suspension pH was established with no adjustment (variation of pH were 3.2-5.2, 4.7-5.7, 7.2-7.9 respectively for citric acid, EDTA and histidine). The suspensions were shaken on an orbital shaker (IKA Labortechnik KS501 digital model -150 rpm). At various time intervals (1, 4, 16, 24, 48, 72, 96, 144 h), sacrificial samples were analyzed for metal content.

The effect of chelating agent concentration was studied in the range 10 -3 to 1 mol.L -1 during 140 h. The initial pH of the solutions was adjusted with HNO 3 or NaOH to the soil pH H2O value (6.3). During these experiments, no adjustment of pH was made; the variations were: 6. 3-7.7, 6.3-6.3, 6.3-7.3 respectively for citric acid, EDTA and histidine. At the end of the experiment, after centrifugation and filtration, the soil was recovered, rinsed with 50 mL of de-ionized water and then air-dried at room temperature. This technique limits modifications in the metals' distribution (Bordas and Bourg, 1998a). The distribution of residual metals was determined by the sequential extractions procedure.

Respirometric tests

A respirometric BOD OxiTop® (WTW, Germany) method was used to monitor the biodegradation of citric acid. Respirometric tests were carried out in the designated measuring bottles: four replicates with citric acid solution at 0.05 mol.L -1 and two controls with de-ionized water. A ratio of 9.7 g of soil in 97 mL of solution was used. No inoculums or inhibitors were added. The suspensions of soil were stirred at 20 ± 1°C, in a thermostated room (WTW, Germany), in the dark for 15 days.

Chemical analysis and modeling

For all experiments, the metals were analyzed after sample centrifugation (3000 g -Bioblock Scientific, Sigma 2-15) and filtration (0.45 µm cellulose nitrate filter-Sartorius).

Depending on the concentration, flame atomic absorption spectrometer (Varian SpectrAA 220) or graphite furnace atomic absorption spectrometer (Varian SpectrAA 800) was used.

To estimate the main reactions involved in the extracting solutions, the system was modelled with MINEQL+, considering:

• the main solubilized elements: Al, Fe, Mg, Ca, Mn, Zn, Cu, Pb, Co, Cr(III) and Ni;

• the constants used come from MINEQL and other databases: [START_REF] Schecher | MINEQL+: A Chemical Equilibrium Modeling System, Version 4.5 for Windows[END_REF], [START_REF] Pettit | IUPAC stability constants database[END_REF];

• the calculation was done at 20°C, the ionic strength and the pH were calculated by MINEQL+.

Results and discussion

Metals speciation in the soil

The studied soil was a sandy, acid soil, with a low organic carbon content and with moderate levels in Cu, Co, Pb (Table 2). In this study, we focused mainly on Cr and Ni because they were present in relatively large proportions, have an environmental impact and are rarely studied (especially Cr) under such conditions. Table 3 shows the distribution of Cr and Ni in different soil fractions ("control"): 105 ± 34% of total Cr and 87 ± 12% of total Ni were recovered.

Cr and Ni were present mainly in the "residual" fraction, 101 ± 34% for Cr and 75 ± 5% for Ni.

Only minor amounts of Cr and Ni were found in the "acid extractable" fraction. Although such a distribution and recovery have been observed in industrial soils [START_REF] Mcgrath | Application of single and sequential extraction procedures to polluted and unpolluted soils[END_REF][START_REF] Davidson | A critical evaluation of the three-stage BCR sequential extraction procedure to assess the potential mobility and toxicity of heavy metals in industrially-contaminated land[END_REF], it is possible that the R2 fraction ("reducible" fraction) was under-estimated. In our studied soil, crystalline Fe (Fe T -F oxa ) is 81 ± 2 %; XRD diagrams (data not shown) showed the presence of maghémite (-Fe 2 O 3 ). According to the literature, crystalline Fe is known to be only slightly solubilised by hydroxylammonium chloride (Xiao-Quan and Bin, 1993;[START_REF] Force | Solid-phase iron characterization during common selective sequential extractions[END_REF][START_REF] Davidson | Should acid ammonium oxalate replace hydroxylammonium chloride in step 2 of the revised BCR sequential extraction protocol for soil and sediment?[END_REF][START_REF] Neaman | Improved methods for selective dissolution of manganese oxides from soils and rocks[END_REF]).

In the environment, chromium is present in two stable forms Cr(VI) and Cr(III). The chromium speciation experiment allows to estimate the content in Cr(VI) (28  3 mg.kg -1 ) representing 25  3% of the total Cr.

Kinetics of metal mobilization in the presence of chelants

Figure 1 indicates two steps in metal mobilization: a fast step (<1 h) followed by a slower one. This has already been observed by many authors (Bordas and Bourg, 1998b;[START_REF] Bermond | A kinetic approach to predict soil trace metal bioavailability: preliminary results[END_REF]. The fast step corresponds to the solubilization of accessible metals (exchangeable and slightly adsorbed). During this fast step, the mobilization is greater for Ni than for Cr. This result is consistent with the fractionation of the metals in the soil (Table 3) which showed more Ni in the R1 fraction (acid extractable) than Cr. The slower step may correspond to the solubilization of less mobile and less accessible metals, those bound to oxides, which requires a partial dissolution of the matrix. This step is important for the Ni extraction with EDTA, which can be explained by the amount of Ni in the "reducible fraction" fraction compared to Cr (Table 3) [START_REF] Nowack | Environmental chemistry of aminopolycarboxylate chelating agents[END_REF][START_REF] Dubbin | Influence of organic ligands on Cr desorption from hydroxy-Cr intercalated montmorillonite[END_REF].

As over a contact time of 140 h, the major part of the mobilizable metals is extracted; this was considered to be appropriate for the present study. "True equilibrium" would be reached after longer extraction times; it depends on the chelants and the mineral matrix considered (Bordas and Bourg, 1998b;Fangueiro et al., 2002).

The respirometric test (BOD OxiTop® method), showed an increase in microbial activity in the presence of citric acid after 168 h (data not shown), thus only a slight degradation of citric acid by microbial activity would be expected for a contact time of 140 h. A limited and slow biodegradation of the nickel-citrate complex in the presence of a selected citrate-metabolizing bacterium has indeed been evidenced by [START_REF] Francis | Biodegradation of metal citrate complexes and implications for toxic-metal mobility[END_REF].

Effect of the chelating agents on metals mobilization

For these experiments, the initial pH of the chelating agent solutions was adjusted to the soil pH and monitored throughout the experiment. At the end of the experiments the pHs were respectively 7.7, 6.3 and 7.3 with citric acid, EDTA and histidine. The percentage of Cr extracted was calculated from total Cr content. The main reactions involved in the metals' complexation by chelants were estimated by modelling the system for the pH range 5-8 using MINEQL+ [START_REF] Schecher | MINEQL+: A Chemical Equilibrium Modeling System, Version 4.5 for Windows[END_REF].

The percentage of Cr and Ni extracted increased with the chelating agent concentration up to a maximal value (Figure 2). Effectiveness of the reagents for Cr mobilization can be classified as: citric acid > EDTA >> histidine. For 0.1 mol.L -1 citric acid, 7.7  0.1% of Cr was extracted, beyond 0.1 mol.L -1 the effectiveness of citric acid was similar. Within pH range of the experiments, Cr was totally complexed with EDTA and citrate, as Cr(EDTA) -and Cr(citrate) 0 respectively. [START_REF] Quiros | Crystal structure and EPR spectrum of bispyridinium bis(citrato)chromium(III) tetrahydrate[END_REF] and [START_REF] Hamada | Potentiometric and UV-Vis spectroscopy studies of citrate with the hexaquo Fe 3+ and Cr 3+ metal ions[END_REF] described only discrete Cr(citrate) 2 3-units; these authors did not quote formation constants. Thus, in the absence of data, the Cr(citrate) 2 3-complex was not taken into account. In the absence of data on complexation constants, the Cr(histidine) 2+ complexes were not taken into account. For Ni, a maximum of 12.8  0.8 % was extracted with 0.1 mol.L -1 EDTA.

The The effectiveness of the chelants ability to solubilize Cr and Ni, observed during our experiments, is not directly related to their complexation constants (Table 4). For example, Cr was better solubilized by citrate than by EDTA whereas logK(Cr(EDTA -)) is greater than log K(Cr(citrate) 0 ). This order cannot be justified by the differences in pH conditions. For all experiments, chelants were in large excess compared to total Cr and Ni. Ca, Fe, Mn, Al, and Mg, were simultaneously solubilized by chelants (Table 5) corresponding to a partial dissolution of the mineral matrix. According to our modeling, the totality of the solubilized metals was complexed with chelants; however because of their excess, 70 to 80% of the chelants were always present as uncomplexed species. Consequently, the differences in the order of efficiency can not be explained totally by the chelant speciation.

For a chelant concentration of 0.05 mol.L -1 , the amounts of Cr(III) and Cr(VI), present in the extraction solution after 140 h, were determined (Table 6). Cr(VI) is more mobilized in presence of citric acid (1.6  0.3 %) than with EDTA (0.6  0.1 %) or histidine (0.1  0.3 %). The chelating agents do not bind Cr(VI) but could desorb it by competition for surface sites as well known for phosphates with ascorbate, citrate and EDTA [START_REF] Nowack | Adsorption of EDTA and metal-EDTA complexes onto goethite[END_REF][START_REF] Geelhoed | Competitive interaction between phosphate and citrate on goethite[END_REF][START_REF] Hu | Effect of several organic acids on phosphate adsorption by variable charge soils of central China[END_REF]. Then, citric acid could be more potent in desorbing Cr(VI) than EDTA or histidine, in complement of the mobilization of Cr(III) by complexation.

Moreover, the mineral fraction of the soil was more solubilized with citric acid than with EDTA or histidine (Table 5) which could explain also the greater mobilization of Cr. Then, it is possible that Ni is included in different minerals that citric acid does not solubilize, or only slightly. The effectiveness of chelants in mobilizing Cr and Ni could result of these two phenomena.

Successive extractions with the selected concentration

For the two most effective chelants (citric acid and EDTA), a concentration of 0.05 mol.L -1 seems to be a good compromise between the mobilization of Cr and Ni and the solubilization of the mineral matrix of the soil. Different authors have shown the importance of the mineral matrix. [START_REF] Papassiopi | Removal of heavy metals from calcareous contaminated soils by EDTA leaching[END_REF] worked on a calcareous contaminated soil (Pb, Zn and Cd) from past mining and smelting activities. They showed that a limited percentage (less than 10%) of the available EDTA was used for the removal of metals while 90% was consumed by the dissolution of calcite. This was also noted by [START_REF] Lim | Process evaluation for optimization of EDTA use and recovery for heavy metal removal from a contaminated soil[END_REF] who examined EDTA in the removal of metals from a laboratory-contaminated soil (Pb, Cd, Ni). As suggested by these authors, a low concentration of chelants was favourable to the mobilization of metal while preserving the original soil mineral composition.

A concentration of citric acid 0.05 mol.L -1 , extracted, respectively, 20.9  0.3 % Co, 2.0  0.1 % Cu, 7.7  0.2 % Zn, 2.4  0.1 % Pb. At the same concentration EDTA extracted 22.0  0.4 %, 30  3 %, 6.20  0.02 %, 27.9  0.2 % of these metals. Only Zn is in the same proportion as Cr and Ni.

Zn was better extracted than Cr, by citric acid and EDTA, and was solubilized in the same proportion as Ni. Taking into account their amounts in the soil, Co was better extracted than Cu, Pb with citric acid; and with EDTA, they were mobilized in the same proportion.

Successive mobilizations were carried out, during 140 h, to check if the metals potentially mobilizable could be solubilized, under our experimental conditions (Figure 3). Whatever the chelant considered, the percentage of Cr extracted during the first and the second mobilization was similar and decreased for the third. For Ni, the decrease was observed from the second mobilization on. EDTA and citrate mobilized a large amount of the major elements, hence the great mobilization of Cr and Ni in the first mobilization (Table 5). In the second and the third mobilization, major elements were mobilized at low concentrations (data not shown), which led to the decrease after these mobilizations. In the presence of chelants, the metals were extracted from a store of mobilizable metals operationally defined by the experimental conditions used. For Cr, this store is exhausted after the second extraction and for Ni it was exhausted after the first one.

Distribution of metals in soil after treatment with chelating agents

Table 3 shows the distribution of chromium and nickel in the soil fractions before and after the mobilization with 0.05 mol.L -1 of chelants. After the first treatment, Cr and Ni remained mainly in the "residual" fraction (R4). The amount of Ni in the first three fractions (R1 + R2 + R3) decreased from 10 ± 1% (before treatment) to 5.1 ± 0.8%, whatever the chelant. Ni was extracted mainly from the "acid extractable" fraction (R1), as it is easily accessible to the chelating agents, but it was also extracted from the fractions R2 and R3.

In the case of Cr, the results show that the sum of metal contained in the first three fractions (R1 + R2 + R3) decreased slightly from 3.7 ± 0.1% (before treatment) to 3.2 ± 0.3%, whatever the chelant. The amount of Cr decreased in the fraction R3, but increased in the fractions R1 and R2 after the treatment. It seems that Cr was extracted from the fractions R3 and R4 and was redistributed in both fractions, R1 and R2. In sequential extractions, the reagents used are rarely totally phase-specific. Even if the use of hydroxylammonium chloride is more generally applicable, this reagent does not bring about a complete dissolution of the iron-oxides (Xiao-Quan and Bin, 1993; La [START_REF] Force | Solid-phase iron characterization during common selective sequential extractions[END_REF][START_REF] Davidson | Should acid ammonium oxalate replace hydroxylammonium chloride in step 2 of the revised BCR sequential extraction protocol for soil and sediment?[END_REF][START_REF] Neaman | Improved methods for selective dissolution of manganese oxides from soils and rocks[END_REF]. During the sequential extractions, Cr bound to the iron oxides might not be extracted effectively from the fraction R2, and thus it can be extracted with the last fraction R4, but also in fraction R3. This part of Cr can thus be redistributed in the fractions R1 and R2, during the mobilization with chelants.

In the studied case, the modifications in metal speciation from the second and the third extraction could not be evaluated because of: (i) the low quantities of extracted metals, (ii) the changes in soil composition during the extractions in presence of chelants (partial dissolution of the mineral phases), (iii) the lack of selectivity of reagents used in the sequential extractions procedure and (iv) the possible of readsorption during the protocol.

Conclusions

The results of this study, as regards the comparison between the ability of two natural and biodegradable chelants with a persistent one to solubilize chromium and nickel from a contaminated soil, can be summarized as follows:

• EDTA and citric acid appear to offer the greatest potential as chelating agents, histidine was ineffective in mobilizing Cr and Ni from the soil.

• Effectiveness of the chelants for Cr extraction can be classified as: citric acid > EDTA >> histidine.

• For Ni, the effectiveness order was: EDTA > citric acid > histidine.

• The effectiveness of the chelants, to solubilize Cr and Ni, observed during our experiments is not directly related to their complexation constants. It could be explained by: (i) their ability to solubilize the mineral matrix containing the metals (Al, Ca, Mn, Mg and Fe were removed simultaneously with Cr and Ni by the chelants); (ii) by the competition of the chelating agents with Cr(VI) on the surface sites.

• In the studied case, a concentration of 0.05 mol.L -1 allows having a good compromise between metals mobilization and preservation the soil mineral integrity.

• After a single extraction with 0.05 mol.L -1 of chelant, a potentially remobilizable store of metals could remain available. The percentage of Cr extracted during the first and the second mobilizations was similar but decreased for the third. For Ni, the decrease was observed from the second mobilization on.

• A sequential extraction procedure, carried out before and after the metal extractions showed only slight modifications due to the low percentage of solubilized metals.

Xiao-Quan, S., Bin, C., 1993. Evaluation of sequential extraction for speciation of trace metals in 1 model soil containing natural minerals and humic acid. Analytical Chemistry 65, 802-807. 2

Table captions

Table1: Sequential extractions procedure for 0.5 g of air-dried soil Table2: Main physical and chemical properties of the soil

  effectiveness of the reagents for Ni mobilization can be classified as: EDTA > citric acid > histidine. Within pH range of our experiments, Ni was totally complexed with chelants. Ni(EDTA) 2- and Ni(histidine) + were the only complexes formed with these two chelants whereas for citrate, there was a mixture of three Ni complexes: Ni(citrate) -(10 %), NiH(citrate) 2 3-(35 %) and Ni(citrate) 2 4-(55 %).

Figure 1 :

 1 Figure captions

Figure 2 :

 2 Figure 2: Cr and Ni extracted vs. chelating agent concentration after a single extraction (% Cr was

Figure 3 :

 3 Figure 3: Successive extractions of Cr and Ni (E1: first extraction, E2: second extraction, E3: third extraction); % Cr was based on total Cr content; chelant concentrations 0.05 mol.L -1 . Error bars

Fig. 1 .Fig. 2 .

 12 Fig. 1. Extraction of Cr (a) and Ni (b) vs. contact time (chelant concentration 0.01 mol.L -1 ; 5 g of

Table 3 :

 3 Cr in the soil fractions before and after treatments with chelants

Table 4 :

 4 Ni in the soil fractions before and after treatments with chelants

Table 5 :

 5 Chelant acidity constants (pKa) and complexation constants (LogK ML ) with Cr 3+ and Ni 2+

Table 6 :

 6 Speciation of solubilized Cr after a single extraction

Table 1

 1 Sequential extractions procedure for 0.5 g of air-dried soil

		Operationally defined fractions	Reagents	Time and sonication power
	R1	"acid extractable"	20 mL AcOH 0.11 mol.L -1	7 min-20W
	R2	"reducible"	0.1mol.L -1 , 20 mL NH 2 OH-HCl	7 min-20W
			reagent adjusted to pH=2
			with HNO 3
	R3	"oxidizable"	10 mL H 2 O 2 30% 25 mL AcONH 4 1 mol.L -1 ,	2 min-20W 6 min-20W
			reagent adjusted to pH=2
			with HNO 3
	R4	"residual"	7.5 mL HNO 3 69% +	microwave-
			2.5 mL HCl 37%	assisted digestion

Table 2

 2 Main physical and chemical properties of the soilCr and Ni in the soil fractions (mg.kg -1 ) before and after treatments with chelants

	Parameters		Values
	Clay (< 2 µm)		177
	Fine silt (2/20 µm)		161
	Coarse silt (20/50 µm)		63
	Fine sand (50/200µm)		119
	Coarse sand (200/2000 µm)	g.kg -1	480
	Al		43.1 ± 0.9
	Fe		33.6 ± 0.8
	Mg		2.6 ± 0.1
	Ca		2.2 ± 0.1
	Mn		921 ± 36
	Zn		138 ± 4
	Cu		29 ± 2
	Pb	mg.kg -1	87 ± 3
	Co		40 ± 2
	Cr		113 ± 10
	Ni		280 ± 20

b from

Smith and Martell, 1974, 1982;

c from

[START_REF] Pettit | IUPAC stability constants database[END_REF]

Table 6

 6 Speciation of solubilized Cr after a single extraction (140 h) by the chelants (chelant concentration 0.05 mol.L -1 )

	Chelant	Cr T after 140 h (µg.L -1 )	Cr(VI) after 140 h (µg.L -1 )	%/Cr a	Cr(III) (µg.L -1 )	%/Cr a
	Citric acid	738 ± 67	186 ± 40	1.6 ± 0.3	552	4.9 ± 0.3
	EDTA	442 ± 16	64 ± 10	0.56 ± 0.09	378	3.34 ± 0.09
	Histidine	70.4± 0,9	15 ± 3	0.1 ± 0.03	55	0.49 ± 0.03
	Water	17 ± 1	ND b	-	-	-
	a: % Cr was based on total Cr content in soil
	b: not detected

Acknowledgments

The authors thank the anonymous reviewers for their constructive comments. This work was partially supported by the Regional Council of Limousin, the "Contrat de Plan Etat-Région" and "Plan Massif Central".


Henri Luc

Valentin Arnal

Anne-Lise Wyart

Giraud

Luc H Arnal

Valentin Wyart

Anne-Lise Giraud

Transitions in neural oscillations reflect prediction errors generated in audiovisual speech

Introduction

Predictive coding and other models of perception based upon hierarchical Bayesian inference [START_REF] Friston | A theory of cortical responses[END_REF][START_REF] Mumford | On the computational architecture of the neocortex. II. The role of cortico-cortical loops[END_REF][START_REF] Rao | Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects[END_REF] assume that neural representations are optimized to reduce "prediction error". This error is classically defined as the difference between the representations (neuronal activity) at each cortical level and the "predictions" or expectations arising from the level above, or cascading back from higher cognitive levels. Hence, the better the prediction, the smaller the prediction error. This reciprocal relationship between predictions and prediction errors is overtly or covertly exploited by several experimental paradigms (e.g., oddball, violation and adaptation paradigms) that rely on the contrast between neural responses to anticipated and unexpected stimuli, and report stronger responses to stimuli that are not or incorrectly anticipated.

There is also growing evidence that perception involves coordinated slow and fast brain oscillations, typically theta/gamma nesting [START_REF] Buzsaki | Neuronal oscillations in cortical networks[END_REF][START_REF] Canolty | High gamma power is phase-locked to theta oscillations in human neocortex[END_REF][START_REF] Lakatos | An oscillatory hierarchy controlling neuronal excitability and stimulus processing in the auditory cortex[END_REF] , and novel hypotheses suggest that bottom-up information could be propagated forward on a gamma frequency channel from superficial cortical layers, whereas top-down information would use backward propagation on a beta frequency channel from deep cortical layers [START_REF] Wang | Neurophysiological and computational principles of cortical rhythms in cognition[END_REF] . How the coding of cognitive content and properties of electrical signaling articulate with each other is unclear. Here, we set out to experimentally address whether the rate and distribution of neural activity depends on correct or incorrect anticipation of the stimulus, and whether sensory predictions and prediction errors are conveyed using different frequency channels.

Audio-visual speech provides an ideal setting in which to test these hypotheses [START_REF] Van Wassenhove | Visual speech speeds up the neural processing of auditory speech[END_REF] . Our experimental paradigm capitalizes on a natural ~150 ms temporal lag between the onset of facial movements and vocal chord vibration that naturally occurs when we speak [START_REF] Chandrasekaran | The natural statistics of audiovisual speech[END_REF] . This lag allows the observer to synthesize phonological predictions prior to auditory onset on the basis of visual information. This also gives the experimenter the opportunity to temporally distinguish the neural effects related to these visually induced predictions and the prediction errors that emerge during audio-visual integration if predictions are invalidated. Here, sensory prediction errors were induced experimentally by violating the congruence between visual and auditory information. We also exploited the specificity with which visual input predicts auditory input in order to create a gradient of perceived incongruence [START_REF] Van Wassenhove | Visual speech speeds up the neural processing of auditory speech[END_REF][START_REF] Chandrasekaran | The natural statistics of audiovisual speech[END_REF][START_REF] Arnal | Dual neural routing of visual facilitation in speech processing[END_REF] . We thus induced graded prediction errors by varying audio-visual congruence, and expected them to be manifest at the neural level in the interaction between the amount of predictive information conveyed by the visual input (predictability) and the validity of this information with respect to incoming auditory input (audio-visual congruence). We quantified this "predictability-by-validity" interaction on neuromagnetic event-related fields (ERFs) measured with magnetoencephalography (MEG), and determined the oscillatory processes underlying prediction error using time-frequency analyses of the MEG data. We report qualitative differences in neural dynamics as a function of the validity of visual predictions, i.e. the amount of prediction errors.

Our central hypothesis was that there should be a fundamental and qualitative change in neuronal message-passing when sensory predictions are invalidated. In particular, audiovisual mismatch detection should enhance coordinated beta and gamma activities associated with the propagation of revised predictions and the redeployment of new prediction errors, respectively. While we observed distributed slow delta activity in higherlevel cortical areas during the perception of congruent stimuli, faster local cortical activity replaced these slow interactions when predictions from visual modality were invalidated by auditory inputs. In agreement with our hypothesis, beta activity appeared in regions where visual and auditory information converged, i.e. where multisensory predictions were generated, whereas gamma activity was seen in lower sensory cortices where prediction errors emerged and were propagated forward.

Results

We presented 15 subjects with stimuli in one of three conditions: videos (audio-visual: AV condition) of a speaker pronouncing different syllables, /pa/, /3a/, /la/, /ta/, /ga/ and /fa/, an auditory track of these videos combined with a still face (auditory: A condition), or a mute visual track (visual: V condition). The videos could be either natural or a random combination of auditory and visual tracks, entailing a condition where auditory and visual tracks were congruent (AVc condition) and one where they were incongruent (AVi condition; see Methods and Supplementary Fig. 1). Incongruent combinations yielding combination of fusion illusory percepts, i.e. McGurk stimuli, were excluded [START_REF] Van Wassenhove | Visual speech speeds up the neural processing of auditory speech[END_REF][START_REF] Mcgurk | Hearing lips and seeing voices[END_REF] . Subjects performed an unrelated target detection task on the syllable /fa/ that was presented in A, V or AVc form in 13% of the trials (97% correct detection). These trials were subsequently excluded from the analyses. The five other syllables were chosen because they yielded graded recognition accuracy when presented visually (Fig. 1a), resulting from an increasing predictability [START_REF] Arnal | Dual neural routing of visual facilitation in speech processing[END_REF] . The phonological prediction conveyed by mouth movements (visemes), varies in specificity depending on the pronounced syllable. Typically, syllables beginning with a consonant that is formed at the front of the mouth (/p/, /m/) convey a more specific prediction than those formed at the back (/g/, /k/, /r/, /l/) [START_REF] Van Wassenhove | Visual speech speeds up the neural processing of auditory speech[END_REF] . Our second experimental factor pertained to the validity of the visual prediction with respect to the auditory input. Physically, the audio-visual stimuli could be either congruent (valid prediction) or incongruent (invalid prediction), while perceptually, the level of incongruence varied gradually as a function of visual predictability, e.g. the strongest perceived incongruence was reported for the most predictable visemes in incongruent stimuli (see Supplementary Data).

Predictability-by-validity interaction was tested in a number of different data features to establish when and where in the brain prediction errors were expressed. We used the amplitude of event related fields over auditory regions to produce statistics as a function of predictability and validity across the peristimulus timecourse (Supplementary Fig. 2a). This indicates when ERFs are modulated by i) visual prediction validity (main effect of audiovisual congruence), ii) visual predictability separately under valid and invalid conditions, and iii) when prediction errors emerged (predictability-by-validity interaction). We went on to characterize the specific time-frequency patterns underlying ERF amplitude variations reflecting prediction error, by exploring time-frequency data in a way that is constrained by the time course of ERFs. This original methodological approach exploits inter-individualstimulus ERF variability to specifically probe time-frequency phase-locking and power effects that are sensitive to the experimental factors (Supplementary Fig. 2b). This method thus enhances the temporal sensitivity of the time-frequency analysis by revealing stimulusinduced and/or phase-locked oscillatory patterns underlying ERF modulations (see [START_REF] Shah | Neural dynamics and the fundamental mechanisms of event-related brain potentials[END_REF] , Methods and Supplementary Fig. 2b). This finally permits us to precisely identify the key frequencies, phase-locking and nesting principles that specifically underlie the expression of prediction error. Finally, to establish the regional specificity of these findings, we broadened the correlations between neuromagnetic indices of prediction error and time-frequency responses to all MEG channels.

Late ERF oscillatory regime reflects prediction errors

Our first analysis step was to correlate the amplitude of ERFs (AV-A, i.e. audio-visual integration index, see Methods) in response to each of the five syllables with their corresponding predictability value, i.e., the recognition level they yielded when presented as visemes (Fig. 1a), over the whole peristimulus timecourse (-100 to 600 ms relative to auditory onset; Supplementary Fig. 2a). The first two ERF components evoked by audiovisual syllables on the sensors that responded best to auditory stimuli correspond to feedforward visual and auditory responses [START_REF] Garrido | Dynamic causal modelling of evoked potentials: a reproducibility study[END_REF] . We refer to these components as M170V and M100A, respectively. Reflecting the natural delay between visual and auditory onsets, M170V and M100A were separated by approximately 100 ms. A main effect of visual prediction validity (audio-visual congruence) was detected after M100A peak in 4 distinct ~20 ms time-windows (Fig. 1b). Critically, we detected an effect of predictability (p < 0.01, shaded windows in Fig. 1b andc) on the M170V preceding auditory onset (Window 1) and on M100A (Window 2) in both AVc and AVi conditions (Fig. 1c). The parametric effect on M100A responses confirms that the independently assessed behavioral gradient is recovered by early physiological signals despite an un-related task instruction. A further late predictability effect was observed in AVi stimuli only, at around 350-500 ms (solid line in Fig. 1c, Window 3). Accordingly, the predictability-by-validity interaction emerged within this third window (Fig. 1c, interaction: p < 0.001). These data confirm that prediction errors only occurred late, after cross-modal prediction had emerged at cortical levels higher than auditory cortex, presumably at the superior temporal sulcus (STS) level, and possibly above.

We addressed a potential divergence in neural dynamics between the processing of correctly and incorrectly anticipated stimuli by comparing the time-frequency structure of evoked responses in valid and invalid conditions (see Methods). Consistent with the ERF data, timefrequency correlation maps (Fig. 2a) show that while AVc and AVi conditions evoked similar early (-100 to 300 ms) phase-locking increases in the delta-theta band (2-9 Hz), diverging patterns occurred during the latest time-window (350-550 ms). When visual prediction was valid, the amplitude of late ERFs correlated with an increase in slow delta (3-4 Hz) phaselocking (Fig. 2a andb, left panel, 350-500 ms, p < 0.001, interaction: p = 0.04), and a decrease in theta phase-locking. Conversely, when the prediction was invalidated by auditory input (Fig. 2a andb, right panel), ERF variations were associated with an increase in phaselocking factor (PLF) in a low-beta band (14-15 Hz, 400-550 ms, p = 0.045, interaction: p = 0.13), and a PLF decrease in the theta range (5-6 Hz, 350-500 ms, p = 0.018, interaction: p = 0.05). That predictability-dependent phase-locking departed from the theta band to either adopt a lower rate regime when predictions were valid, or a higher one when they were not, supports our hypothesis that visual prediction validity determines a transition in neural dynamics.

Beta and delta regimes show distinct spatial dynamics

To check whether these two distinct phase-locking modes were implemented through spatially distinct neural networks, we broadened the analysis to the whole scalp surface while focusing on the two time-frequency clusters reflecting the difference between valid and invalid conditions (black arrows, in Fig. 2a). We computed Pearson correlations at each sensor, between their PLF values in these time-frequency windows and the ERF amplitude of auditory sensors (Supplementary Fig. 2b). Scalp topographies of correlation values show diverging spatial patterns of stimulus phase-locked oscillatory activity depending on the validity of visual prediction (Fig. 2c). When prediction was valid, phase-locked delta activity (3-4 Hz) emerged across regions usually involved in high-order language processing, i.e., the ventral temporal cortex and the angular gyrus [START_REF] Hickok | The cortical organization of speech processing[END_REF] (Fig. 2c, left).

When visual prediction was invalid, the phase-locked pattern in the beta band (14-15 Hz) remained confined to the posterior middle temporal region (Fig. 2c, right), presumably the STS that is often described as a convergence point of visual and auditory (speech) inputs 15- 17 . The location of this effect strongly converges with fMRI results obtained in an independent study in which we also probed predictability-by-validity interaction using a similar experimental design (Supplementary data and Supplementary Fig. 3 and4). The transition in frequency regime when predictions were invalidated was thus associated with a drastic change in response topography, presumably reflecting a change in message-passing mode emphasizing top-down processing.

Prediction invalidation increases beta PLF and gamma power

An important implication of predictive coding [START_REF] Friston | A theory of cortical responses[END_REF][START_REF] Rao | Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects[END_REF] is that the brain dedicates more resources to unexpected than to anticipated events. As high-frequency oscillations are energetically more demanding than slow oscillations [START_REF] Koch | Stimulus-induced and state-dependent sustained gamma activity is tightly coupled to the hemodynamic response in humans[END_REF][START_REF] Mukamel | Coupling between neuronal firing, field potentials, and FMRI in human auditory cortex[END_REF][START_REF] Niessing | Hemodynamic signals correlate tightly with synchronized gamma oscillations[END_REF] , we checked whether oscillations in the gamma range could explain late ERF amplitude modulations associated with prediction errors (Window 3 in Fig. 1b andc). This analysis hence focused on late prediction error effects, i.e. 350 ms after auditory onset. We performed the same correlation analysis as above, using the sensors (n=10) that showed the strongest validity effect at the group level. These sensors were situated over posterior superior and middle temporal regions. Whereas low-frequency (< 30 Hz) phase-locking and power correlation maps showed the same patterns for these sensors as for "auditory" sensors, we detected several clusters showing significant correlations between ERF amplitude and high-frequency power. The largest effect occurred in the AVi condition between 350 and 500 ms in the 70-90 Hz range (Fig. 3a, black arrow in right panel, p < 0.001, interaction: p = 0.01). Prediction invalidation hence increased late gamma power.

We further tested for a possible coordinated activity (see Methods) between low-frequency phase-locking and high-frequency gamma power (Fig. 3b). When prediction was invalid (AVi), late (350-500 ms) mid-and high gamma power distinctly correlated with the two lowfrequency phase-locking patterns shown in the right panels in Figures 2a andb. Prediction error resulted in i) a joint increase in mid-gamma (60-70 Hz) power and PLF in low beta frequencies (14-15 Hz) suggestive of oscillation hierarchical coupling (nesting) [START_REF] Buzsaki | Neuronal oscillations in cortical networks[END_REF][START_REF] Canolty | High gamma power is phase-locked to theta oscillations in human neocortex[END_REF][START_REF] Lakatos | An oscillatory hierarchy controlling neuronal excitability and stimulus processing in the auditory cortex[END_REF] , and ii) an increase in high-gamma (70-90 Hz) power with a PLF decrease in the theta band (5-6Hz) (Fig. 3b). The transition to a beta phase-locked mode likely gated an increase in mid-gamma oscillation power, while the increase in high gamma power was accompanied with a dissolution of phase-locked oscillations in the theta band.

Finally, to address whether high gamma power modulations in the AVi condition reflected the level of prediction error, and in such a case where this occurred at the scalp level, we averaged power values in the time-frequency window defined by the interaction above (350-500ms; 70-90 Hz; Fig. 3a, black arrow in right panel) and computed Pearson correlations with visual predictability at each sensor. As shown in Figure 3c, the highest correlation values were visible over the left occipital and temporal sensors, mainly distributed between early visual areas, auditory areas and the STS. When visual prediction was both strong and invalid, high-gamma power increased in low-level sensory regions. The increase in beta phase-locking in the STS was seen conjointly with an increase in gamma activity locally and in lower-tier sensory areas. This supports the proposal that the beta range is involved in inter-areal coupling [START_REF] Kayser | Directed Interactions Between Auditory and Superior Temporal Cortices and their Role in Sensory Integration[END_REF][START_REF] Engel | Beta-band oscillations--signalling the status quo?[END_REF][START_REF] Von Stein | Top-down processing mediated by interareal synchronization[END_REF][START_REF] Womelsdorf | Modulation of neuronal interactions through neuronal synchronization[END_REF] , and more specifically used in feedback projections [START_REF] Sejnowski | Network oscillations: emerging computational principles[END_REF][START_REF] Wrobel | Beta activity: a carrier for visual attention[END_REF] , and further suggests that the gamma range serves to propagate prediction error forward.

Discussion

Our results support theoretical models assuming that the brain uses prediction estimation procedures to construct percepts [START_REF] Friston | A theory of cortical responses[END_REF][START_REF] Rao | Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects[END_REF][START_REF] Neisser | Cognitive psychology[END_REF][START_REF] Poeppel | Speech perception at the interface of neurobiology and linguistics[END_REF][START_REF] Stevens | Remarks on analysis by synthesis and distinctive features[END_REF] and control action [START_REF] Wolpert | An internal model for sensorimotor integration[END_REF] . In sensory perception, the general idea is that the brain continuously uses available information to update internal estimates that are used to predict the subsequent input. In this view, the information that is propagated forward reflects the difference between incoming input and expectation (i.e., what remains to be explained), whereas predictions are propagated backward. In our experimental setting, the temporal precedence of visual signals allows for the generation of predictions that are then confronted with incoming auditory signals [START_REF] Van Wassenhove | Visual speech speeds up the neural processing of auditory speech[END_REF] . Consistent with predictive models, detectable correlates of prediction error were confined to late responses (~350 ms). This is because they are most strongly manifest after auditory and visual signals have converged on the STS, where phonological predictions generated on the basis of the visual input are effective (see Supplementary Data).

We hypothesized that prediction validity at the origin of prediction errors induces a qualitative shift in neural dynamics that determines the message-passing mode. As expected, in the case of visual prediction validation, we observed stimulus-locked slow neural activity in a large high-order integrative network. In contrast, visual prediction invalidation induced the dissolution of distributed low-frequency oscillations and the emergence of higher-frequency activity in the STS. Consistent with previous studies [START_REF] Mukamel | Coupling between neuronal firing, field potentials, and FMRI in human auditory cortex[END_REF][START_REF] Niessing | Hemodynamic signals correlate tightly with synchronized gamma oscillations[END_REF] , this increased high frequency activity co-localized with an increase in the BOLD signal (see Supplementary Fig. 4). The oscillatory pattern involved low beta and gamma activity locally in the STS and high gamma (70-90 Hz) activity in early auditory and visual processing systems. In other words, we observed a transition from a smooth distributed flow of information to a fast local processing, presumably aiming at i) resolving the conflict at the stage where audio-visual phonological incongruence is registered by forming new plausible sensory predictions, and ii) estimating these predictions in lower processing stages. Superficial layers of the cortex are the predominant source of gamma oscillations [START_REF] Roopun | Period concatenation underlies interactions between gamma and beta rhythms in neocortex[END_REF] and the notion that prediction error is indexed by increased gamma power in lower-tier sensory areas is therefore consistent with the proposal that superficial pyramidal cells, that originate forward projections in cortical hierarchies, report prediction error 1 (see Supplementary Fig. 5). That low beta activity increased in the STS, a higher hierarchical stage, also fits with the idea that deeper layer pyramidal cells, notionally representational units originating backward predictions [START_REF] Spratling | Reconciling predictive coding and biased competition models of cortical function[END_REF] , are associated with beta activity [START_REF] Wang | Neurophysiological and computational principles of cortical rhythms in cognition[END_REF][START_REF] Sejnowski | Network oscillations: emerging computational principles[END_REF][START_REF] Wrobel | Beta activity: a carrier for visual attention[END_REF][START_REF] Buschman | Top-down versus bottom-up control of attention in the prefrontal and posterior parietal cortices[END_REF] . Given that superficial pyramidal cells receive their input from layer IV and project back on deep layers [START_REF] George | Towards a mathematical theory of cortical micro-circuits[END_REF] , an increase in prediction error enhancing superficial gamma activity likely strengthens connections across superficial and deep cortical layers. This coupling between superficial and deep layers generates a low beta rhythm (15Hz) that changes the nature of message-passing [START_REF] Kopell | Are different rhythms good for different functions?[END_REF][START_REF] Kramer | Rhythm generation through period concatenation in rat somatosensory cortex[END_REF] . Functionally, the emergence of this common rhythm across superficial and deep layers could reflect i) the convergence of error and representation units on a new representational solution (prediction error minimization) and ii) top-down propagation of this solution to hierarchically lower regions. A slower frequency channel for top-down than for bottom-up signal propagation could reflect that top-down predictions result from the accumulation of bottom-up prediction errors. The emergence of low beta activity (14-15Hz) in the STS and increased high gamma activity locally and in lower-tier sensory areas could signal the redeployment of prediction errors due to alternative prediction testing operations (Supplementary Fig. 5).

While beta and high gamma (80Hz) activity (and BOLD response) indexed prediction error and its resolution, slower delta/theta oscillatory activity signaled further processing of correctly anticipated stimuli. Delta (3-4Hz) activity in our data localized to distributed lexicosemantic areas, suggesting that late slow stimulus-locked oscillatory activity reflects higher stages of speech processing [START_REF] Hagoort | Integration of word meaning and world knowledge in language comprehension[END_REF][START_REF] Hald | EEG theta and gamma responses to semantic violations in online sentence processing[END_REF] and stabilizes sensory representations [START_REF] Kayser | Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns[END_REF][START_REF] Schroeder | The gamma oscillation: master or slave?[END_REF] . It is unclear how slow activity precisely relates to perception. Perception is often thought to rely on synchronization of focal neuronal assemblies in the gamma range [START_REF] Engel | Dynamic predictions: oscillations and synchrony in top-down processing[END_REF][START_REF] Fries | Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry[END_REF][START_REF] Wyart | Neural dissociation between visual awareness and spatial attention[END_REF] . Delta/theta activity on the other hand has been suggested to shape gamma activity in superficial cortical layers [START_REF] Schroeder | Low-frequency neuronal oscillations as instruments of sensory selection[END_REF] that propagate information to the next hierarchical stage [START_REF] Rockland | Laminar origins and terminations of cortical connections of the occipital lobe in the rhesus monkey[END_REF] . Accordingly, we observed that gamma activity related to prediction error is accompanied by a decrease in theta phaselocking (Fig. 3b). The observation that mid and high gamma activity are related to the phaseconsistency of beta and theta activity, respectively, extends the idea that gamma frequency variations reflect information routing [START_REF] Buschman | Top-down versus bottom-up control of attention in the prefrontal and posterior parietal cortices[END_REF][START_REF] Kopell | Are different rhythms good for different functions?[END_REF][START_REF] Akam | Oscillations and filtering networks support flexible routing of information[END_REF][START_REF] Colgin | Frequency of gamma oscillations routes flow of information in the hippocampus[END_REF] , and that message-passing is indexed by specific hierarchical combinations of slow and high frequencies (low/high frequency ratio) [START_REF] Panzeri | Sensory neural codes using multiplexed temporal scales[END_REF] .

The current data demonstrate that violating intermodal expectations changes the neural dynamics of slow (delta/theta) brain activity, and increases the coordination between local low beta and high gamma oscillatory activity. Our data suggest that this transition occurs in brain regions where audio-visual predictions are likely updated (STS), and new prediction errors generated (auditory and visual cortices). These findings suggest a tight relationship between particular high-frequency modes of activity and prediction errors, and suggest that slow cortical activity contains a previously unappreciated wealth of information that reflects perceptual expectations. indicate the timeperiods where correlation is significant (signed r 2 ). Black horizontal lines delimit statistical threshold p < 0.01 (** p < 0.01, * p < 0.05). Window 1 indicates that the visually-evoked response increased with visual predictability but was not affected by prediction validity (interaction in window 1: p = 0.93). Window 2 indicates that the decrease in M100A was accelerated proportionally to visual predictability, confirming that visual input hence sped up [START_REF] Van Wassenhove | Visual speech speeds up the neural processing of auditory speech[END_REF][START_REF] Arnal | Dual neural routing of visual facilitation in speech processing[END_REF] and "sharpened" [START_REF] Grill-Spector | Repetition and the brain: neural models of stimulus-specific effects[END_REF] early auditory evoked responses proportionally to its informational value, yet without prediction error computation (non-significant interaction in window 2: p = 0.52). Prediction errors (visual predictability-by-validity interaction) emerged in the latest Window 3 (grey surfaces between dashed and solid lines in Window 3 delimit significant interaction, p < 0.001).

Figure 1 .

 1 Figure 1. Interaction between predictability and validity in ERFs. a. Predictability was assessed behaviorally as the recognition rate of syllables presented in the visual (V) condition. Normalized predictability of each syllable was then correlated with experimental measures. b. Main ERF components evoked on auditory sensors by the presentation of AVc (dashed line) and AVi (solid line) stimuli. Grey surfaces between dashed and solid lines delimit time periods showing a main effect of validity (** p < 0.01). c. Correlations between ERF (AV-A) amplitude and predictability were computed at each time bin, separately for AVc (dashed line) and AVi (solid line) conditions. ERFs and correlation lines are locked to visual onset on the left, and on auditory onset on the right of the vertical double bar, respectively (see Methods). Windows 1, 2 and 3 (shaded surfaces in b and c)

Figure 2 .

 2 Figure 2. Late low-frequency oscillatory patterns depend on the validity of inferences. a. Correlation strength (signed r 2 ) between ERF amplitude and PLF of low (2-20 Hz) frequency bands. Time is expressed relative to auditory stimulus onset. Contours delimits statistical threshold of p < 0.05, p < 0.01 and p < 0.001. Arrows indicate time-frequency effects of interest, subsequently used for topographical rendering (see c.). b. Significance of the correlation strength (cluster corrected for multiple comparisons) across time in selected frequency bands, in AVc condition (delta-theta [350-500ms; 3-4 Hz]), and in AVi condition (delta-theta [350-500ms; 5-6 Hz]; beta [400-550; 14-15 Hz]). Thick lines indicate p cluster < 0.05 across time (*** p < 0.001, * p < 0.05). Filled-in grey surfaces represent the mean and standard deviation of the corresponding null distributions across 1,000 permutations. c. Topographical renderings were obtained by computing Pearson correlations between amplitude of late ERFs (on auditory sensors) and PLF values of selected time-and frequency-windows of interest (see a. and b.) at each sensor for AVc (left topography) and AVi (right topography) conditions.

Figure 3 .

 3 Figure 3. Late high-frequency activity reflects prediction error computation. a. Correlation between ERF amplitude over sensors showing a significant effect of validity (located over the STS, see Methods section) and power of high (30-120 Hz) frequency bands for AVc (left panel) and AVi (right panel) stimuli. Black arrows indicate time-and frequency-windows of interest for subsequent analysis. Corrected r² for the frequency bands of clusters of interest are indicated below the right panel (AVi: high-gamma [350-500ms; 70-90 Hz], thick line indicates p cluster < 0.05, *** p < 0.001.) b. Correlation strength between high-frequency (30-120 Hz) power and low frequency (2-30 Hz) PLF for AVi stimuli (averaged across time between 350 and 500 ms). Contours delimit statistical thresholds of p < 0.05, p < 0.01 and p < 0.001. Significant theta/gamma and low beta/gamma correlations only occurred in the invalid condition. Corrected r² for the frequency bands of selected clusters of interest are indicated in right panel (theta 5-6 Hz and beta 14-15 Hz). Filled-in grey surfaces represent the mean and standard deviation of corresponding null distributions across 1,000 permutations (thick line indicates p cluster < 0.05, * p < 0.05). c. Scalp topography of power × predictability correlation strength for AVi condition. Correlation strength (signed r 2 ) between normalized predictability rates and power (averaged across time-[350-500 ms] and frequency-[70-90 Hz] windows) were computed at each sensor.

Acknowledgements

This work was supported by the Centre National de la Recherche Scientifique (A.-L.G.) and the Fondation Fyssen (V.W.). We thank the staff of the Centre de Neuroimagerie de Recherche and the Magnetoencephalography Center (Hôpital de la Pitié-Salpêtrière), in particular Jean-Didier Lemarechal, Antoine Ducorps, and Denis Schwarz, and the colleagues who commented on this work: Virginie van Wassenhove, Benjamin Morillon, Alexandre Hyafil, Sophie Denève, Lucia Melloni, François Griffon, Andreas Kleinschmidt, Etienne Koechlin, Brian Fischer, Karl Friston and Catherine Tallon-Baudry.

Author Contributions

The author(s) have made the following declarations about their contributions: Conceived and designed the experiments: LHA, ALG. Performed the experiments: LHA. Analyzed the data: LHA, VW, ALG. Contributed to analysis tools: LHA, VW. Wrote the paper: LHA, VW, ALG.

Methods

Subjects

All subjects gave written informed consent to take part in these studies that were approved of

Experimental procedures.

Stimuli were excerpts from digital videos of a male speaker pronouncing consonant/vowel syllables (C/a/ syllables). Specific stimulus combinations and durations are provided in Supplementary Figure 1. Stimuli were presented using Presentation software (Neurobehavioral Systems). Two preliminary experiments served to i) establish a behavioral gradient of visual predictability, which was subsequently normalized and correlated with MEG signals (see statistical analysis section below) and ii) assess how visual predictability interacts with the subjective percept as a function of audio-visual congruence (see

Supplementary data).

During the MEG experiment, participants sat at a distance of 1 m from the monitor, the movie (720×576 pixels) subtending 10.5° (horizontal) and 8.5° (vertical) visual angles. To prevent eye movements, subjects were asked to fixate a cross and blink only after giving their motor response (after the video). Thus, only few trials (less than 5%) were contaminated by eye movement artifacts and were excluded. Each stimulus was presented 54 times in a pseudo-randomized order.

MEG recordings and data processing.

Continuous cerebral activity was recorded with a whole-head MEG system (Omega 151, CTF Systems), with 151 axial gradiometers over the scalp, at a sampling rate of 1250 Hz and low-pass filtered online at 300 Hz. Data preprocessing, analysis, and visualization were performed using both in-house software (http://cogimage.dsi.cnrs.fr/logiciels/) and programs written in MATLAB (The Mathworks, Natick, MA). Eye movements and blinks were monitored with four ocular electrodes (Viasys Healthcare) and automatically marked when they deviated by 2 standard deviations (SDs) from the mean. This technique, however, does not detect microsaccades. One supplementary electrode was used to monitor cardiac activity.

We rejected off-line trials that were contaminated by eye or head movement, muscle contractions, or electromagnetic artifacts. Artifacts related to cardiac activity were eliminated by using a heartbeat trace matched filter. Event-related fields (ERFs) and time-frequency signals (phase-locking factor and oscillatory power, see below) were analyzed on a 1200 ms interval centered on auditory onset (AO) (-600 to 600 ms) and baseline corrected (when appropriate) on the interval (-600 to -300 ms, i.e., during the presentation of a still face), to ensure that the correction occurred before mouth movement onset. High-pass (0.15 Hz) and low-pass (30 Hz) filters were applied before averaging epochs to obtain ERFs. All signals were smoothed across time using a 20 ms sliding-average window.

Time-frequency analyses.

Time-frequency wavelet transforms were applied to each trial at each MEG sensor using a family of complex Morlet wavelets (m = 8), resulting in estimates of Phase-Locking Factor [START_REF] Tallon-Baudry | Stimulus specificity of phase-locked and non-phase-locked 40 Hz visual responses in human[END_REF] at each time sample and at each frequency between 2 and 30 Hz (frequency step, 1 Hz), and of oscillatory power at each time sample and frequencies ranging from low (2-30 Hz; frequency step, 1 Hz) to high (30-120 Hz; frequency step, 2 Hz) frequency bands. Baselinecorrected power was defined at each time sample and frequency, as the increase of oscillatory power relative to baseline in logarithmic units. The log-transformed data were distributed normally, which allowed us to use standard parametric statistical tests (e.g., paired t tests, Pearson correlations).

Statistical analyses.

We first computed Pearson correlations between the magnitude of ERF amplitude and predictability (Fig. 1c). To measure the effect of predictability in early auditory regions, we extracted the time courses of ERFs from auditory sensors selected individually as the three sensors where M100A amplitude was maximal. Pearson correlations were computed across subjects between visual predictability and AV-A ERFs at each time bin of peristimulus time, and significance was assumed for p < 0.01 (a detailed description of the correlation method is illustrated in Supplementary Fig. 2a). To measure the interaction between validity and predictability on ERFs we computed two-sample t tests at each time bin of peristimulus time by using individual regression slopes of the predictability × ERF amplitude correlation (Fig. 1c, grey surface between dashed and solid lines, significance assumed for p < 0.05). To correct for slight latency differences between the onsets of visual mouth movements (MO) and auditory onsets depending on the syllable (see Supplementary Fig. 1 b), we separated the analysis in two parts: the first part (Fig. 1b andc, left of the double vertical bar) was synchronized on MO, and the second one (Fig. 1b andc, to the right of the bar) was synchronized on auditory onset. For each syllable, MO was detected by measuring the overall color change of pixels (comprised in a 321×151 pixels rectangle surrounding center of the mouth) between successive frames of the videos. MO was therefore defined as the timepoint where the average of pixel colors of a frame deviated significantly of 2 SDs from the previous frame. The M170V component, resulting from averaging neuromagnetic fields time-locked on MO, peaked 170 ms after MO. While the M170 response to faces is classically detected in the fusiform cortex, MO elicited a specific response in motion sensitive cortex, previously identified as MT/V5 [START_REF] Arnal | Dual neural routing of visual facilitation in speech processing[END_REF] . As there was a delay of about 25 ms between responses to visual input in MT/V5 and that in auditory regions, we conclude that the component measured by auditory sensors results from direct cross-modal (lateral) input to auditory cortex [START_REF] Arnal | Dual neural routing of visual facilitation in speech processing[END_REF] and not from volume conduction. Importantly, we assume that this component is specifically related to visual mouth movement as we used a static face as a baseline (see Supplementary Fig. 1).

Pearson correlations between ERF amplitude and time-frequency signals (power or PLF)

were computed after normalization across experimental conditions (i.e., zero mean and unit variance) at the single subject level to correct for a possible influence of outliers (a detailed illustration of the correlation method is provided in Supplementary Fig. 2b). To determine the oscillatory structure underlying modulations of ERF amplitude, we computed correlation maps (Fig. 2a) by correlating time-frequency signals (low-frequency [2-30 Hz] PLF and power, respectively) with the amplitude of ERFs on individually selected auditory sensors.

Because ERF-by-power and ERF-by-PLF maps did not qualitatively differ, and because there was no significant cluster above 20 Hz, we restricted the presented results to ERF-by-PLF maps between 2 and 20Hz. We then focused on window 3 to determine the spectral signature of the predictability-by-validity interaction. From AVc and AVi maps in Figure 2a, we selected two time-frequency windows overlapping with window 3 and showing significant positive correlation strengths during time periods exceeding 100 ms (Fig. 2a: AVc [350-500 ms; 3-4 Hz] and AVi [400-550 ms; 14-15 Hz]). In each of these time-frequency windows, we measured the interaction between predictability and validity by computing two-sample t tests using individual regression slopes between PLF values and predictability. Note that this interaction was not significant for the (14-15 Hz) cluster shown in Figure 2a (p = 0.13), but was significant when extending the frequency range to 12-15 Hz (p = 0.017), consistent with the spread of the beta-gamma 'nesting' cluster shown in Figure 3b. Scalp topographies in To assess the strength of the observed effects and correct for type-I errors potentially arising from multiple comparisons performed at single time points within each frequency band, we used non-parametric cluster statistics [START_REF] Maris | Nonparametric statistical testing of EEG-and MEG-data[END_REF] . This analysis consists in clustering adjacent time samples that exhibit similar modulations between conditions, or similar correlations with event-related fields. As a first step, we selected all time samples in a variable of interest (ERF amplitude or PLF or power in specific frequency bands) which r-square difference exceeded p < 0.05. Then, the selected samples were clustered in connected sets on the basis of temporal adjacency. Cluster selection criterion in Figure 3b was based on the extraction of contiguous samples in PLF frequency-bands of interest. A cluster-level statistic was then computed by taking the sum of the r-squares within a cluster.

Non-parametric statistics were computed by performing permutation tests. To assess the null distribution, the syllable labels were randomly intermixed within each subject and the rsquare difference was computed and a p < 0.05 threshold was applied. This procedure was repeated 1,000 times. For each of these permutations, the maximum cluster-level statistic was extracted. The non-parametric p-statistic was computed by comparing the null distribution of cluster-level statistics to the original cluster-level statistic. It is important to note that cluster-corrected p-statistics were computed with respect to the null distribution of the maximum cluster-level statistics: this statistical test hence controls the false alarm rate for all clusters. All reported results and p values were corrected at the cluster level following this procedure, and correlations maps in Figures 2 and3 only display clusters that reached a corrected p value < 0.05.