Alain Kondjoyan

Samuel S Oillic

Stéphane S Portanguen

Eric Lemoine

Jean-Bernard B Gros

The use of models to monitor cooking processes

come   L'archive ouverte pluridisciplinaire

Cooking processes cannot be monitor using the data available in literature as these data remain fragmented and highly dependent on the specific equipment and the cooking conditions used in papers. Heat-water transfer modelling combined with other quality modules represents a powerful conceptual tool for quantifying the phenomena at work, downscaling the number of trials to be run, and to predict the effect of numerous changes in existing and non-existing cooking equipments.

Different models have been developed during the prosafebeef project: a combined heat-juice model, and kinetics models to predict HA and color formations during cooking. The heat-juice model was proved to predict average cooking losses in various types of beef meat pieces and different types of cooking conditions. Local water content inside the meat was also predicted by the model. First-order kinetics model used in literature to predict HA formation in juice were adapted to solid samples to predict the evolution of HA concentration in meat under different roasting and grilling conditions. Another first order kinetic model was used to predict the variation of colour during the cooking of beef meat.

Thanks to the heat-juice model abacus can be determined to improve yield control during cooking in existing equipments. Interest of the use of Abacus for meat industry, catering industry and consumer information is presently tested. Simulations can also help manufacturers in developing new control tools or to design new equipments.

Corresponding author: UR370 Qualité des Produits Animaux, INRA, 63122 Saint Genès Champanelle, France, Tel: +33 (0)4 73 62 44 92 -Fax: +33 (0)4 73 62 40 89, email: alain.kondjoyan@inra.clermont.fr


Michel Carail

Anne-Sylvie Fabiano-Tixier

Farid Chemat

Catherine Caris-Veyrat

Catherine Caris

High Power ultrasound Effects on all-β-Carotene

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.

Material & Methods: Experiments were performed using a thermostated

Ultrasonic reactor

Preliminary tests:

-Carotene concentration decreases significantly in all reactor equipped with a stirrer and an ultrasound probe.

three solvents under air and argon atmosphere. Highest degradation was found in aqueous medium under air.

Solvent and gas effects on -carotene stability. Left: air.

Right: Argon.

Experimental design: Air and water were chosen as experimental conditions to perform a Central Composite Design (CCD) face-centered, in which three parameters were studied : ultrasound power, temperature and sonication time.

Results:

Most influent variables are ultrasound power and time. Degradation decreases when temperature increases, due to more effectiveness of ultrasound at low temperature.

  aim of this work was to study the influence of ultrasound treatment on the stability of -carotene.


domain: sdv shs

text:
Spatial panel multinomial logit models for large samples : An application to land use change models

Abdourahmane Diallo, Ghislain Geniaux

GMM

The strutural model : Suppose that unobserved components are independently identically distributed across individuals and time-periods and drawn from the type I extreme value distribution, then the choice probability for the individual i to select an alternative j at period t is:

y * jt = α jt l n + λ t Wy * jt + X t β jt + jt (1) y ijt =    1 if y * ijt ≥ y * ikt k = j ∈ A 0 otherwise
P ijt = exp X * it β j + W * it α jt 1 + k∈A -exp X * it β k + W * it α jt
The previous model implies both heteroskedasticity and autocorrelation =⇒ multinomial panel logit estimation method is inconsistent. Let us denote θ = [β = (β 1 , ..., β J ), λ = (λ 1 , ..., λ T ), α = (α 11 , ..., α JT )] ∈ Θ, where Θ is the parameter open space.

Q(θ) = S nT (θ)Σ nT S nT (θ)
where S nT (θ) = 1 nT Z ũ , Σ nT some positive denite matrix and Z is a matrix of instruments Z

=        Z 1 0 . . 0 0 Z 2 . . . . . . . 0 0 . . 0 Z T       
.

Where Z t = X t , WX t , W 2 X t , W 3 X t ], t = 1, 2, ..., T .

Diallo Spatial Panel Multinomial Logit Models for large samples :

(G α j ) it = p ijt (1 -p ijt )((I -λ t W ) -1 l n ) i (G β j ) it = p ijt (1 -p ijt )X * it (G λt ) it = p ijt k∈A p ikt H it (β j -β k ) - X * it (β j -β k )Λ ii σ 2 i + k∈A p ikt H * it (α jt -α kt ) - (W * l n ) it (α jt -α kt )Λ ii σ 2 i Where H t = (I -λ t W ) -1 WX * t , H * t = (I -λ t W ) -1 WW *
t and Λ is a the digonal matrix of the following matrix

(I -λ t W ) -1 W (I -λ t W ) -1 (I -λ t W ) -1 .

Diallo

Spatial Panel Multinomial Logit Models for large samples :

It is important to note that, when λ t = 0 and α jt = 0,

G α j = p j (1 -p j )[I t ⊗ l n ] G β j = p j (1 -p j )X G λt = p j k∈A p k WX t (β j -β k ) X =     X 1 . X T    
As [START_REF] Klier | Clustering of auto supplier plants in the united states[END_REF] and [START_REF] Diallo | Spatial multinomial logit model for large samples: An application for land use model[END_REF], we develop a linearized version of our GMM Diallo Spatial Panel Multinomial Logit Models for large samples :

to propose a full GMM for spatial panel multinomial choice model,

We propose, like in [START_REF] Pinkse | Contracting in space: An application of spatial statistics to discrete-choice models[END_REF], [START_REF] Klier | Clustering of auto supplier plants in the united states[END_REF] and [START_REF] Diallo | Spatial multinomial logit model for large samples: An application for land use model[END_REF], a GMM estimator based on the moment conditions implied by the likelihood function for a spatial panel multinomial logit model. LGMM

where G(.) is a gradient term

where θ 0 = (β SMNlogit , λ = 0, α = 0) . We estimate β SMNlogit by standard multinomial logit estimation method with λ = 0 and α = 0 1 and we calculate u(β SMNplogit , 0, 0) , we obtain the following gradient terms: We present the results of Monte Carlo analysis to evaluate the performance of full GMM and linearized multinomial logit GMM estimators with a spatial panel data framework.

we generate the data according to:

MC settings

The xed time-varying preferential eects are genarated as

The exogenous spatial weight matrix for the experiments is created as follows: rstly we draw two random numbers from the uniform distribution U(0, 1) for each observation. These numbers are used to specify the coordinates of each observation in the [0, 1] × [0, 1] plane. To work in large samples, we use the following

and we suppose that each location have two neighbors.

.

Where Z t = X t , WX t , W 2 X t , W 3 X t ], t = 1, 2, ..., T .


Dr Laurent Saint-André

Dr Gael Sola

Dr Matieu Henry

Nicolas Picard

Training on tree allometric equations, December 10-14th 2012, Lusaka, Zambia Use and prediction •

The variance of errors of the given compartment regarding the whole system of equation z X ˆThe weighting function Confidence intervals for the predictions û

Using a biomass/volume equation

Range of calibration û

Confidence intervals for the predictions

û Linear regression Ä ∑ - - + ± - i i X X X X n t X Y 2 2 2 / 1 ) ( ) ( 1 ) ( σ α
Confidence interval for the mean

∑ - - + + ± - i i X X X X n n t X Y 2 2 2 / 1 ) ( ) ( 1 ) ( σ α
Confidence interval for an individual prediction

Using a biomass/volume equation

General case for linear and non linear regression, utilization of the delta-method (Serfling, 1980)

Ä 2 ) 2 / 1 ( . ) ( y S t X Y α - ± with :
Confidence interval for the mean

        ∂ ∂ ∑         ∂ ∂ = β β β Y Y S y . . ' 2 z c c y X S t X Y , 2 2 ) 2 / 1 ( . . . ) ( σ σ α + ± -

Confidence interval for an individual prediction

The variance for Y From the tree to the stand, Monte-Carlo simulations û

        ∂ ∂ β Y The

Using a biomass/volume equation

From the tree to the stand, Monte-Carlo simulations Step 1 : analysis of the bar chart

Using a biomass/volume equation

Behind the single estimation of biomass, the understanding of the ecosystem functioning û

Step 3 : decomposition of the fertilization effect on a per hectare basis

  /2000 09/01/2001 19/04/2001 28/07/2001 05/11/2001 13/02/2002 24/05/2002 01/09/2002 /2000 09/01/2001 19/04/2001 28/07/2001 05/11/2001 13/02/2002 24/05/2002 01/09/2002 128 ± 1.9 t/ha Above-Ground = 104 ± 1.8 t/ha Below-ground = 24 ± 1 t/haFrom the tree to the stand, Monte-Carlo simulations û simulations can be applied also to ratios (rootshoot, wood density, etc.)

  al. 2005 (accepted in Trees, Structure and Function). Fertilization effect on Spruce and Douglas fir Behind the single estimation of biomass, the understanding of the ecosystem functioning û

G3C 49 to 61 2001 12/01/2001 11/01/2002 9.6  1.9 G3C 61 to 74 2002 11/01/2002 31/01/2003 15.3  2.4 G3D 74 to 86 2001 13/01/2001 11/01/2002 14.7  2.9 G3D 86 to 99 2002 11/01/2002 31/01/2003 10.9  2.8 Standard errors where relatively large (from 7 to 25 % of the biomass increment) For

	û	Biomass increments
		Plot	Age (months)	Year	Start date	End date	Total biomass
							increment (t/ha)
		G3A	9 to 22	2001	23/03/2001	23/03/2002	19.5  1.6
		G3A	22 to 34	2002	23/03/2002	02/04/2003	25.6  3.3
		G3B	26 to 38	2001	08/01/2001	27/12/2001	12.0  0.9
		G3B	38 to 49	2002	27/12/2001	28/11/2002	12.9  1.0

the eddy-correlation site, ∆ biomass2002 = 12.9  1.0 t/

ha/year Using a biomass/volume equation

Example Sicard et al. 2005 (accepted in Trees, Structure and Function). Fertilization effect on Spruce and Douglas fir

Training on tree allometric equations, December 10-14th 2012, Lusaka, Zambia

Additional Resources

The complexity of tree growth 17


Irène Gabriel

Barbara B Konsak

Sandrine Mignon-Grasteau

Genetic selection of poultry based on

come


domain: math info sdv sdv.bv

text:
Mapper

with multiple hits but not at their original position

  Dealing with multiple hits is a strong difference point Choice of software depend of the biological question Tuning of parameters is important Similar trends for the bacterial datasets.Two software, BWA and Bowtie seem a little ahead

	Failures for multiple matches
	n s h g p p p g g n s h n s h Each software has specific heuristics that leads to different n s h h g p p p g p p w n + s h m g p BWA novoalign bowtie SOAP2 SSAHA2 MPscan GASSST PerM s g g h g w n + s h m g p BWA novoalign bowtie SOAP2 SSAHA2 MPscan GASSST PerM Reads Number of reads (log10 scale) 0 1 2 3 4 5 6 n s h Benchmark h n h s results, even at H 0	n h g p p g p g n h h n
	w n + s m g w n + m w n + s m	w + w + w +	w + w + w + p	w + w + w +
	H0 H0	H1 H1	H2 H2	H3 H3
	Sophie Schbath (INRA -MIG)	A benchmark for mapping tools	RADIANT, January 2013	15 / 18

hits or more between 2 and 10 hits

Acknowledgments People involved in this work Véronique Martin Matthias Zytnicki Julien Fayolle Valentin Loux Jean-François Gibrat Pierre Nicolas Jérôme Compain Computational ressources Funding ANR CBME : Computational Biology for Metagenomics Experiments Mapping Reads on a Genomic Sequence : An Algorithmic Overwiew and a Practical Comparative Analysis Journal of Computational Biology 2012 vol. 19, pp. 796-813. http://genome.jouy.inra.fr/ngs/mapping


Jean-Pierre Huiban
email: jean-pierre.huiban@ivry.inra.fr.

Antonio Musolesi

Augmenting the production function with knowledge capital to test the Porter hypothesis: the case of French food industries*

Keywords: productivity, environmental investment, R&D, knowledge capital, food industries JEL-Codes: C23, D24, L25, Q55

We investigate the impact of pollution abatement effort on the economic performances by exploiting a rich panel data set composed of French food industry firms, observed over the 1993-2007 period. We test the Porter hypothesis, assuming that pollution abatement effort has a positive effect on the firm performance by triggering innovation. This is done by estimating a production function augmented with knowledge capital, such a capital being produced by both pollution abatement and R&D investments. Using different estimation methods, including structural semi-parametric ones, we first show than the so-called Porter assumption cannot be rejected when focusing on the full population of French food industry firms since the estimations indicate a positive and significant (though rather small) contribution of the pollution abatement capital to the firm productivity. Then, we consider a more restrictive sample of (potentially) innovative firms, actually engaging both RD and pollution abatement investments. Henceforth, the contribution of pollution abatement capital becomes not significant in regard to the R&D's one. These results do not support the sometimes invoked hypothesis according to which the positive effect of pollution abatements efforts on firms' performances is linked to the induced increased innovation. At the same time, the standard hypothesis, assuming that pollution abatement effort significantly decreases the firm performance is always rejected.

Introduction

« Physically, pollution occurs because it is virtually impossible to have a productive process that involves no waste; economically, pollution occurs, because polluting is less expensive than operating cleanly » (Helfand et al., 2005, p. 249).

According to the conventional wisdom, firms produce pollution as a fatal by-product and moreover they would not voluntarily expense some money in order to produce cleanly. Consequently, environmental regulation may be a necessary instrument to force firms to reduce their pollution.

Following a standard view, pollution abatement effort due to environmental regulation may be benefic for environmental performance but would negatively affect the firms' competitiveness. At the contrary, the so called Porter hypothesis [START_REF] Porter | America's green strategy[END_REF] assumes that environmental regulation could have a positive effect on the firm competitiveness. One reason would be that such regulation would stimulate firms and produce "innovation offsets" [START_REF] Porter | Toward a New Conception of the Environment-Competitiveness Relationship[END_REF]. A large number of empirical studies have investigated the Porter hypothesis, obtaining rather mixed results even if there is increasing evidence supporting such a hypothesis [START_REF] Ambec | The Porter Hypothesis at 20: Can Environmental Regulation Enhance Innovation and Competitiveness? Discussion Papers 11-01[END_REF].

This study contributes to this empirical literature in four ways. First, as many other studies, we include the pollution abatement (PA hereafter) effort within a production function but we also include the Research and Development (RD hereafter) effort in the same function. This is done because it assumed along the paper that knowledge is obtained not only from the R&D activity but also from the firms' efforts to reduce pollution. Second, we use a panel dataset which provides a consistent measurement of both RD and PA investments at the firm level, while many previous studies adopted rougher proxies for PA efforts. Third, we focus on the French Food Industry which is a field of particular interest for this question. Finally, we propose a distinction between two kinds of populations, which are called as the "reference" and the "innovative" populations of firms and we show that the results differ significantly depending on population which is analysed.

A lot of studies test the Porter hypothesis by using a production function augmented with a measurement of antipollution effort (Shabedgian and [START_REF] Shadbedgian | Pollution abatement expenditures and plant-level productivity: a production function approach[END_REF]. We extend such an approach by incorporating it into the quite standard framework used to explore the relationship between innovation and firm efficiency, namely the production function augmented with "knowledge capital" [START_REF] Griliches | Issues in assessing the contribution of research and development to productivity growth[END_REF]. We shall assume that knowledge capital is the fruit of several inputs. First, RD activity is considered as the main observable innovation input and has been traditionally incorporated into standard production functions as an additional separable factor of production [START_REF] Hall | Measuring the Returns to R&D[END_REF], for a survey). When extending such an approach in order to test the Porter hypothesis, we also introduce the pollution abatement effort and we thus consider a production function augmented with both RD and PA as inputs.

Second, we propose a consistent measurement of these two inputs at the firm level. To do this, we use a unique large data base concerning a thousand of firms and covering the period 1993-2007. This dataset provide a measurement of both RD and PA annual investment, from which we can build the corresponding stock of RD and PA capital stocks. These inputs are then included in the production function together with the traditional inputs, namely labour and capital stock.

Third, our population is composed of firms from the French Food Industries, a field which is particularly relevant for such a kind of analysis. The Food industry is not only relevant in terms of size, representing in France à large part of manufacturing, (about 550,000 employees in 2011, i.e. 18% of manufacturing employment), but is also relevant because it is both very polluting and more and more innovative. With respect to pollution, it has been documented that the food sector is one of the most polluting sector with respect to several indicators in many European economies, especially when looking the effects of total final consumption of the produced goods. This has been shown by several studies. [START_REF] Marin | Linking NAMEA and Input output for 'consumption vs. production perspective' analyses. Evidence on emission efficiency and aggregation biases using the Italian and Spanish accounts[END_REF] using the NAMEA data show that food and especially animal-based food productions have a dominant role in the total environmental impact by consumption. [START_REF] Vieux | Greenhouse gas emissions of self-selected individual diets in France: Changing the diet structure or consuming less?[END_REF] note that the contribution from the food sector to the total green house gas emission range from 15 to 31%. In terms of innovation, many authors have stressed that despite that food industries have been for long time considered as low-tech, they are becoming more and more technology intensive as a result of an increasing demand for research (Trail and Meulenberg, 2002). As an example, when looking at the French fourth wave of the Community Innovation Survey, it can be noticed that in the food sector, the share of firms introducing product or process innovation (37% and 35% , respectively) is higher than when looking at the total French economy (26% for both product and process innovation). These figures are confirmed when looking at the expenditures for R&D and for other kinds of knowledge. The relevance of such a sector is also attested by the number of studies, based on this empirical field, testing the Porter hypothesis such as [START_REF] Galdeano-Gomez | Environmental spillover effects on firm productivity and efficiency: An analysis of agri-food business in Southeast Spain[END_REF] or [START_REF] Alpay | Productivity Growth and Environmental Regulation in Mexican and U.S. Food manufacturing[END_REF]. Finally, when considering the survey statistics, PA and RD efforts offer very different patterns. PA investment concerns a large (more than 50%) and growing overtime share of firms, but with a low average investment amount (representing only 2% of the physical capital stock). At the opposite, RD investment only concerns less than 20% of firms, such a share being almost stable during the observed period. But firms engaging RD activities provide a relevant effort in doing so since the RD capital stock represents, in average, more than 13% of the stock of physical capital. This may suggest that the AP effort is conducted by some constraints, particularly regulatory constraints, while RD effort is the result of an active firm's strategy in terms of innovation. To make such a distinction clearer, we build two different samples. The first one, called the "Reference population" concerns a large part of the firms of French industry, i.e. 999 firms. The second one, called the "Innovative population", is composed of the 197 firms, extracted from the first population, which are actually engaged in both RD and PA and thus are supposed to be (potentially) innovative. Our assumption is that the second population is the right one to consider when speaking of innovation, while the first one is generally considered in the literature.

As surveyed by [START_REF] Ackerberg | Econometric Tools for Analyzing Market Outcomes[END_REF] endogeneity problems arise when estimating a production function because of both simultaneity and unobserved heterogeneity. Because of this, we use the structural semi-parametric estimator proposed by [START_REF] Levinsohn | Estimating production functions using inputs to control for unobservables[END_REF]. Our results are as follows.

In the case of the Reference population including most French food firms, the PA capital exhibits a significantly positive estimate which is even higher than the RD coefficient. However, the results change when considering the innovative population: the estimated RD coefficient becomes significant with a magnitude in line with the related literature [START_REF] Hall | Measuring the Returns to R&D[END_REF], while the PA capital' estimate is no more significant. Indeed, when compared with the returns to RD capital, and when considering the adequate population, it clearly appears that PA capital has no effect on productivity. On the other hand, the standard hypothesis, assuming that PA effort significantly lower the firm performance is always rejected.

The remainder of the paper is as follows. Section 2 describes the model. Data and our sample are presented in Section 3. In Section 4 we provide the estimation results. Section 5 concludes.

The model

Pollution in the economic process: Standard versus Porter hypothesis

Pollution clearly appears as an undesirable output of production [START_REF] Ball | Productivity of the US Agricultural Sector: The Case of Undesirable Outputs[END_REF]. Because producing cleanly is more expensive than polluting, environmental regulation may be necessary to reduce pollution and pursue a sustainable process of economic growth. But, the standard view among economists is that environmental regulation aiming at reducing pollution is a detriment factor for firms' competitiveness and productivity. Indeed, according to this view, environmental regulation forces firms to allocate the usual production inputs labor and capital to pollution reduction, which push them away from the optimal production choices. This in turn could lead firms to delay their investments [START_REF] Viscusi | Frameworks for analyzing the effects of risk and environmental regulation on productivity[END_REF] or relocate their activities in countries imposing less stringent pollution regulations [START_REF] Greenstone | The impacts of environmental regulations on industrial activity: evidence from the 1970 and 1977 clean air act amendments and the census of manufactures[END_REF]. At the national level, pollution regulation may hamper economic growth: [START_REF] Jorgenson | Environmental Regulation and U.S. Economic Growth[END_REF] suggest that environmental regulation (combined with the increase of world petroleum prices) may explain the sharp decline in the rate of economic growth during the 1970's and 1980's.

From the early nineties, however, this traditional view has been challenged by what has become known as the "Porter hypothesis" [START_REF] Porter | America's green strategy[END_REF]. Porter and Van der Linde (1995, p. 98) assume that:

"Strict environmental regulation can trigger innovation (broadly defined) that may partially or more than fully offset the traditional costs of regulation". This citation first suggests a result: not only firm's environmental performance, but also firm's economic performances, may be positively affected by environmental regulation. It also suggests that innovation can be the channel to explain this result.

On the applied perspective, some authors have proposed a distinction. The statement that a welldesigned antipollution regulation may trigger innovation has been labeled the "weak" version of the Porter hypothesis whereas the idea that this induced innovation may more than offset regulatory costs enhancing productivity has been called the "strong" version of the Porter assumption. To date, there is a certain evidence supporting the existence of a positive link between environmental regulation and innovation [START_REF] Jaffe | Environmental Regulation and Innovation: A Panel Data Study[END_REF][START_REF] Arimura | An Empirical Study of Environmental R&D: What Encourages Facilities to be Environmentally-Innovative[END_REF][START_REF] Brunnermeier | Determinants of Environmental Innovation in US Manufacturing Industries[END_REF] whereas much more mixed results have been achieved by looking at the link between regulation and productivity [START_REF] Jaffe | Environmental Regulation and Innovation: A Panel Data Study[END_REF][START_REF] Berman | Environmental Regulation and Productivity: Evidence from Oil Refineries[END_REF]Bui, 2001, Alpay et al. 2002;Shadbegian and Gray, 2005;[START_REF] Lanoie | Environmental Regulation and Productivity: NewFindings on the Porter Hypothesis[END_REF]Lanoie et al., , 2012;;[START_REF] Gray | The Cost of Regulation: OSHA, EPA and the Productivity Slowdown[END_REF]. A large review of the literature can be found in [START_REF] Ambec | The Porter Hypothesis at 20: Can Environmental Regulation Enhance Innovation and Competitiveness? Discussion Papers 11-01[END_REF].

Augmenting the production function with knowledge capital to test the Porter hypothesis

The production function framework provides a tractable way to test the strong version of the Porter hypothesis and consequently some studies have focused on the estimation of a function which can be expressed as: ( ,,, )

it it it it it Q f L C PAE U = (1)
Where it Q is a measure of production, it L and it C are the standard labor and physical capital inputs, it PAE measures the Pollution Abatement efforts of the firm and it U stands for all other unobserved determinants of output. Different solutions may be used to measure the variable it PAE in the production function. Some works introduce dummies for the existence of constraining environmental regulations: [START_REF] Alpay | Productivity Growth and Environmental Regulation in Mexican and U.S. Food manufacturing[END_REF] use "The frequency of reported inspections (concerning environmental laws) as a proxy for abatement expenditures" (p. 892), or environmental devices (as "environmental management systems" used by [START_REF] Albornoz | In Search of Environmental Spillovers[END_REF]. Finally some studies use a direct measurement of the expenses and/or investments engaged by the firms. Studies using the US PACE (Pollution Abatement Costs and Expenditures) are an example [START_REF] Keller | Pollution Abatement costs and Foreign Direct Investment Flows in the USA[END_REF], Shadbegian et al., 2005). Such approach deserves some few comments. The first one concerns the conceptual argument underlying the use of the production function. The Porter main arguments explaining a rather counterintuitive positive impact of PA effort on firms' performances are twice: the "green products" and the triggering of innovation. If the success of green products may be indeed a way to improve the commercial performances of a firm, it is not straightforward to understand how it should affect the productive efficiency. Analyzing the relation between environmental regulation and firms' financial performances [START_REF] Yang | Environmental Compliance and Firm Performance: Evidence from China[END_REF][START_REF] Konar | Does the Market Value Environmental Performance?[END_REF]) is a consistent way to test whether the (profitable) demand for "green" products is a possible explanation for the Porter hypothesis.

However, using the analytical framework of a production function may be appropriate if the triggering of innovation is the main argument to support the Porter hypothesis. Indeed, augmenting the production function with "knowledge capital" is the usual approach to test the impact of innovation on firm productivity (see [START_REF] Griliches | Issues in assessing the contribution of research and development to productivity growth[END_REF][START_REF] Hall | Innovation and Productivity[END_REF], for a recent survey). A general specification can be written as:

( , , , )

it it it it it Q f L C K U = (2)
Where it K is the knowledge (intangible) capital. As this knowledge capital is not directly observed, most studies use some proxies, especially the Research and Development (R&D) expenditures. Obviously, R&D contributes to innovation and, by this, may increase the productivity level of the firm. Other relevant determinants of knowledge and innovation are more difficult to observe such as experience, conducting to learning by doing, while other factors may contribute to the firms' stock of knowledge by improving their "absorption capacity" [START_REF] Cohen | Innovation and Learning: the two faces of R&D[END_REF]. Finally, and as specific focus of this paper, following the Porter hypothesis, PAE can enter such a specification because it will stimulate the innovation process. According to this, R&D and PA efforts can be viewed as two observable measures for the knowledge capital, both representing an input of innovation.

But several points should be addressed. The definition of the variable it PAE , namely the PA effort, in the production function is a first important one. We argue that the measurement of it PAE should be consistent with the definition of a production input, thus favoring the studies which use a direct measurement of the expenses and/or investments engaged by the firms, as the one using the US PACE [START_REF] Keller | Pollution Abatement costs and Foreign Direct Investment Flows in the USA[END_REF], Shadbegian et al., 2005). Consequently, we will measure both R&D and PA efforts as stocks of capital, which are calculated by using a perpetual inventory approach, as a sum of the current investment and the past stock of capital which depreciates with a specific rate, as we do for the physical capital C:

1 (1 ) t k t t C C I δ - = - + (3) 1 (1 ) t rd t t KRD KRD RD δ - = - + (4) 1 (1 ) t e t t KPA KPA PA - = -δ + (5)
It is important to use the stock of the different capitals instead of the annual flows of investments because the innovation process is impacted by the contemporaneous but also by the lagged level (at period t-1, t-2…) of investments. Indeed, both RD [START_REF] Griliches | Issues in assessing the contribution of research and development to productivity growth[END_REF] and PA [START_REF] Lanoie | Environmental Regulation and Productivity: NewFindings on the Porter Hypothesis[END_REF][START_REF] Ambec | The Porter Hypothesis at 20: Can Environmental Regulation Enhance Innovation and Competitiveness? Discussion Papers 11-01[END_REF]) may take time to become productive. Moreover, past RD and PA investments depreciate and become obsolete. Using such formula allows handling both issues. 2008) study the case of Agri-food business in Southeast Spain and find evidence of the links between environmental practices (firm internal practices but also spillover effect) and economic performance. [START_REF] Alpay | Productivity Growth and Environmental Regulation in Mexican and U.S. Food manufacturing[END_REF] study the relationship between the local environmental regulation and the firm performances, comparing the Mexican and U.S. food manufacturing contexts. Finally, it also worth to note that the food industry, despite that it has been for long time considered as low-tech, it is becoming more and more technology intensive as a result of an increasing demand for research (Trail and Meulenberg, 2002) and thus studying the relation between productivity and knowledge capital in such an industry is more and more relevant.

Data and summary statistics

The Antipol survey

The Antipol survey is a plant-level annual survey devoted to French Food Industries, conducted by the indicator is aggregated at the firm-level, by summing the investments amounts of the different plants which compose the firm. Then, we build a corresponding PA capital stock using the perpetual inventory approach with a commonly used depreciation rate of 15%, and name this variable KPA15. We finally obtain an unbalanced panel dataset of 8260 observations, concerning 999 firms and covering the 1993-2007 years.

The RD survey

The "Moyens de la recherché" survey is a firm-level annual survey conducted by the Research Ministry and concerns all the French firms which actually perform RD activity. It provides a measurement for both the RD performed by the firm itself (defined as internal expenses) and the RD subtracted by the firm to other firms, or private/public research units (defined as external expenses). We first extract the population concerning food industry and build an unbalanced panel data covering the years 1993-2007, as for the previous Antipol survey. We build an aggregated indicator DRD, summing internal and external RD expenditures engaged by the firm. As for physical and PA investment, we build a stock of RD capital using the perpetual inventory approach with a depreciation rate of 15%, and then we obtain the variable KRD15. An important point is that RD survey has a particular selection rule: it only concerns firms which actually perform RD. It is worth to know that this represents only a small part of the entire population (namely 1/200 for the French economy, according to the survey presentation). This leads to a small panel data which is composed of 2608 observations concerning 755 firms during the 1993-2007 periods with no "0" value for the variable of interest KRD15.

Our sample design: two populations

In order to estimate the production function defined in section 2, we have to merge three files: the two previous surveys (Antipol and RD) and the Annual Business Survey ("Enquête Annuelle d'Entreprise").

This last one is the French survey which provides relevant information about the economic performances and structure of the firm: namely in our case, value-added, number of employees, physical investment and the stock of capital, plus a certain number of control variable as the industry location. It is an exhaustive survey at least for the category of firms considered by other surveys (firms with plants of up than 100 employees and firms which actually perform RD). Because of this, one can suppose that there is no attrition due to a merge with EAE Survey. As mentioned before, the Antipol survey is a sample composed of 999 firms and 8260 observations. It is supposed to be exhaustive when considering plants of 100 employees and more. The RD survey is also supposed to be exhaustive for this population but with a very hard selection rule: it only includes firms which actually perform R&D. Then, we are faced to three sub-populations:

1. The firms both surveyed in Antipol and RD, with full information on both RD and PA investment;

2. The firms surveyed in Antipol but not in RD: because of the selection rule of RD survey, we can affect the value '0' to the RD investment of such firms;

3. The firms surveyed in RD but not in Antipol. In this case we are not allowed to say anything about the PA investments of such firms: it may equals to 0 as well as being positive. Those firms cannot be used for the estimations.

According to this, when merging the surveys we obtain the populations presented in Table 1.

(Table 1)

One can observe that almost all firms with a strictly positive RD capital stock also exhibit a strictly positive PA capital stock (197 firms on 203). The opposite is not true: 889 firms have a positive PA capital stock but 692 firms have both positive PA capital stock and zero RD capital stock. This is a first important result: RD investment is much more concentrated than PA investment: 20% of the observed firms against around 80% 3

3 Such values differ of those from section 3.2 and 3.3 because we are considering here the stock and not the investment: a firm which invests one year has a positive stock during the period even if it does not invest after.

. According to this, we consider two samples of interest for our estimation.

The first one is composed of all the 999 food industry firms which are surveyed in PA survey and completed by the information from RD survey, which we could call the "Reference population". This first population can be considered as a representative sample of the greatest firms from French food industries (i.e. including at least a plant with 100 employees or more), whatever such firms are concerned or not by innovation. Thus, within this population we extract a second interesting sample, composed of the 197 firms which both invest in PA and RD. These firms are engaged both in RD and PA efforts and try to innovate by using the innovation inputs. They compose what we may call the (potentially4 ) "Innovative population".

(Table 2)

Table 2 presents summary statistics for all the variables used in the analysis recalling their definitions. The "Reference population" is composed only of firms with plants of 100 employees and more, which is the threshold used in the Antipol survey. Therefore, a large part of food industry firms, especially small firms are not taken into account in this study. But the gap is still larger between this Reference Population and the firms actually (or potentially) engaged in an innovation process, present in the Innovative Population. The second ones are larger (almost twice), their value-added as well as capital being more than twice as large. Such results are consistent with the literature, suggesting a positive relationship between the size and the innovation propensity of the firm (see [START_REF] Mansfield | Size of Firm, Market Structure, and Innovation[END_REF].

A special attention should be paid to our two variables of interest, namely PA and RD investments and capital stocks. It is worth to recall that the investment average amount has two components: the number of firms which actually invest and the average amount engaged by these investing units. The respective cases of PA and RD investment appear to be very different, as shown by Graph 1 which represents the part of firms which actually invest in RD and PA.

(Graph1)

First, the average level is significantly higher in the case of PA investment: the rate of firms which actually invest is almost up than 50%, while it never attains 20% in the case of RD. RD concerns a minority of firms while the majority of firms invest to abate pollution. The respective trends also differ.

In the case of RD, the rate of investing firms first declines (16.76% in 1994) until 2000 (9.86%), then grows until the end of observed period (16.55%). The rate of PA investing firms globally rises during the observed period, from 44.97% in 1994 to 65.70% in 2007. When considering the period, it appears that the average amount by plant increase because of this growing share of plants which actually invest whereas the average amount by investing plant does not significantly augment. This average amount represents only 3% of the total investment. AP investment concern now a majority of food industry firms (at least those with plants of 100 employees and more), but each firm contribution still remains low.

An important point is the relationship between the environmental regulation and the actual AP investment. It is extremely difficult to define regulation and moreover to provide a synthetic indicator of regulation stringency, because regulation has different forms and applies differently according to the industry, the size, the location…But, it is sometimes possible to identify a temporal shock, as the one which happened in 2000, when the European Union promulgated a directive devoted to the use of water by firms. Because water is an important dimension of pollution, especially in the case of food industry, because such a directive has important implications and assuming that the year 2000 was not affected by any other substantial exogenous shock, it is thus possible to assume that the significant leap, from 53.46% in 2000 to 69.04% in 2001 reveals the impact of environmental regulation on PA investment.

Once the share of firm population which actually invests has been studied, we consider the corresponding average investment amounts. The average amount of PA investments is low for populations, conducting to a PA capital stock which represents less than 2% of the stock of physical capital. The case of RD investment is different. Because it concerns few firms, the average amount is apparently low in the reference population, with a RD capital stock around 5% of the stock of physical capital, which is however higher than PA capital stock. But, when considering the firms actually engaged in RD investment, the amount of such an investment attains 13.84% of the amount of physical investment and represents more than seven times the amount of PA capital stock.

Such differences are significant: PA and RD efforts are different. The first one concerns a lot of firms with a low average intensity while the second one greatly matters but for a reduced part of firms.

One should need additional information in order to explain this difference, but it could be suggested that PA effort is merely conducted by some constraints, particularly regulatory constraints, while RD effort is the fruit of an active strategy. The first one concerns automatically all firms of a given category (of a plant size category, for instance) while the second is issued from firms for which innovation is a necessary but also an attainable goal.

Results

Econometric model and estimation methods

In order to estimate an empirical specification we make some assumptions:

1. As in [START_REF] Griliches | Issues in assessing the contribution of research and development to productivity growth[END_REF], the production is a function of standard inputs labor and physical capital, knowledge capital and others unobservable variables:

( , , , )

it it it it it Q f L C K U = (6)
2. The knowledge capital is a function of both R&D and PA capital stocks.

The unobservable term it

U can be decomposed in two distinct terms:

exp(

)

it it it U ω ε = + (7)
where it ω represents productivity shocks potentially linked to firms' input decisions while it ε indicates shocks that are not related to input choices and refers to the standard econometric error term.

4. The technology of the firms can be represented using the Cobb-Douglas formulation where both observable and unobservable determinants enter multiplicatively. This gives:

it l it c it krd it kpa it it it q l c krd kpa β β β β ω ε = + + + + + (8)
Minuscule letters indicate the log transformation of the variables. The estimation of such a production function leads to some well-known problems, namely endogeneity due to simultaneity and unobserved heterogeneity. Simultaneity occurs because in the profit maximization program of the firm, the levels of inputs are jointly determined and depend on the level of output. Unobserved heterogeneity occurs because some variables, as manager ability, environmental conditions…may affect the resulting level of output, for a given level of inputs. In order to solve such problems, some methods are proposed, which take advantage of the use of panel data. The standard panel data methods provide alternative way to introduce the key term it ω which is supposed to affect the input choices and is known by the producers but is not known by the econometrician. In the standard panel data approaches, it is assumed that the term it ω can be written as a sum of a firm specific firm effect and a common time effect, i.e. it i t ω α λ = + . By taking natural logarithms we obtain the standard specification:

it l it c it krd it kpa it i t it q l c krd kpa β β β β α λ ε = + + + + + + (9)
Such a model can be estimated assuming either that the individual and time effects are fixed or that they are random variables. Both specifications are imperfect. The random model supposes that the individual effects are drawn from a normal distribution and uncorrelated with the explanatory variables [START_REF] Hsiao | Analysis of Panel Data[END_REF]. Such an exogeneity assumption, stating that there is no correlation between the effects the explanatory variables, seems to be unrealistic in the framework of a firm level production function. The individual effect reflects the unobserved heterogeneity which may be linked to some variables, as manager ability, environmental conditions: such variables may be correlated to the explanatory variables introduced in the production function, as labour, capital or the two RD and PA capital stock that we define. As an example a more "efficient" manager may have a higher propensity to invest in RD and in PA.

The assumption of no correlation between the individual effects and the explanatory variables is no more necessary when applying the Within estimator to the Fixed-Effect model. But it still imposes an additive structure to the unobservable:

it i t ω α λ = + (10)
Such a structure is very restrictive because it does not allow considering unobserved time varying firm individual effects. Consequently, some authors, following [START_REF] Olley | The Dynamics of Productivity in the Telecommunications Equipment Industry[END_REF] have proposed some methods, which improve the previous ones, to several extents. Such methods are directly derived from a theoretical model of industry dynamics [START_REF] Ericson | Markov-Perfect Industry Dynamics: A Framework for Empirical Work[END_REF] and are based on several assumptions.

First, the inputs levels are fixed at different periods: labour, considered as a totally flexible factor, is fixed at the considered period, while capital is fixed at the previous period, avoiding simultaneity problems.

Second, the unobserved heterogeneity is taken into account under a single variable it ω . This variable is unobserved by the econometrician, but known by the firm and may be estimated with the help of proxies, namely investment [START_REF] Olley | The Dynamics of Productivity in the Telecommunications Equipment Industry[END_REF] or materials [START_REF] Levinsohn | Estimating production functions using inputs to control for unobservables[END_REF]. When using the Levinsohn and Petrin approach, m being the materials, this leads to the following model:

it l it c it krd it kpa it it it q l c krd kpa β β β β ω ε = + + + + + (11) ( , , , ) it it it it it m c krd kpa ω =  (12)
A detailed technical discussion of such an approach can be found in [START_REF] Ackerberg | Econometric Tools for Analyzing Market Outcomes[END_REF] and an empirical use applied to environmental economics in Coles (2007).

Estimation results

As discussed in the previous section we estimate the production function of equation ( 11) by using the Levinsohn-Petrin estimator. Table 3 presents the results of the estimations successively on the Reference population and on the Innovative population.

(Table 3)

It may be first noted that, whatever the population considered, the physical capital and labor estimates exhibit standard values, which are a little bit higher (resp. lower) in the case of capital (resp. labour) than those generally obtained when using the standard panel estimators (Within or FGLS).

If we first consider the Reference population, we obtain a significant and positive estimate for kap β , which equals 0.0124. The Porter hypothesis is thus not rejected when considering the full population of French Food firms. Such a result is consistent with some previous studies [START_REF] Berman | Environmental Regulation and Productivity: Evidence from Oil Refineries[END_REF]Bui, 2001, Alpay et al. 2002;Shadbegian and Gray, 2005;[START_REF] Lanoie | Environmental Regulation and Productivity: NewFindings on the Porter Hypothesis[END_REF]. When considering krd β a significant and positive estimate of 0.0070 is obtained. The value is lower than those found in the literature, whose magnitude is often between 0.10 and 0.20 (see the survey by [START_REF] Hall | Measuring the Returns to R&D[END_REF]. Most of these studies, however, do not analyze the entire population of firms, but only focus on the firms engaged into RD activities, or in some cases use the predicted RD obtained from a selection equation instead of the observed RD (Griffith et al., 2006). This should explain why higher estimates are obtained for the RD coefficient.

The results obtained in the case of the Innovative population are significantly different from the previous ones. In this case, the RD's coefficient is positive, significant and much higher than in the previous case. The value equals 0.200 being in line with previous studies. Also the results concerning physical capital and labor are changed presenting a lower value for the labor's coefficient estimate and a higher value for the physical capital estimate. This is consistent with the respective composition of the two populations: innovative firms are significantly more capital-intensive than the others. But the most relevant result concerns the PA capital's coefficient which is no more significant in the case of such innovative population. Thus, while the Porter hypothesis is not rejected in the case of the population of all food firms, this is no more the case when considering specifically the population of innovative firms.

Our results suggest that when considering the complete population of firms in the French food industry, the Porter hypothesis cannot be rejected since whatever the estimator used, we obtain a small, but always significant and positive estimate for the coefficient associated to PA capital. But, when focusing on the innovative population, the results dramatically change. To our point of view, it does not reject the possibility of a "Porter effect", but it does not favor the assumption that such an effect could be explained by innovation. Indeed when considering the consistent population, in terms of innovation, and when compared to the "natural" input of innovation, namely RD capital, the PA capital does not appear to have any significant influence (positive or negative) on the firm performance. One should also note that in both cases (reference and innovative populations) the standard hypothesis of a negative and significant effect of PA on firm performances is decisively rejected.

Conclusions

This paper provides an econometric investigation of the relation between pollution abatement efforts and firms' performance for the French food industry by exploiting a rich panel data set covering the period 1993-2007.

We analyse a production function augmented with knowledge capital and combine the literature of the Economics of innovation and technological change with the framework used in the empirical tests of the Porter hypothesis. We indeed assume that both the PA and RD capital stocks are inputs of knowledge capital and consequently estimate a production function augmented with both RD and PA capital stocks.

Different estimations methods are used, including the standard panel data methods and the Levinsohn and Petrin's estimator. A first look to summary statistics reveals that PA and RD investments are different. PA concerns a majority of firms with a low amount of investment. RD is concentrated on a more reduced population, but represents a much greater effort in the case of the firms which are actually concerned. Our estimation results suggest that for the French food sector the Porter hypothesis cannot be rejected since whatever the estimator used, we obtain a small, but always significant and positive estimate for the coefficient associate to PA capital. However, the often invoked argumentation, based on the fact that PA efforts will affect productivity via the induced innovation does not seem validated. Indeed, when the analysis is constrained to a consistent population, those of firms which are actually concerned by innovation, the comparison of the returns to PA with the returns to RD, clearly shows that PA capital has not effects on firms' performances while RD' estimated elasticity is positive and significant. . 8 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 year IAP RD

  Ministry of Agriculture. Since 2006 it concerns productive units which employ at least 20 persons. From 1993 to 2005, only plants with at least 100 employees were concerned. Three kinds of indicators are used to describe pollution abatement investments 2 -investments specifically devoted to pollution abatement; : -general process investment inducing some effects in terms of pollution abatement; -Studies devoted to pollution abatement.Investments specifically devoted to pollution abatement concern different fields: water, wastes, air, noises, floor/ground, and landscape. In 2007, water still represents the main domain with 56.4 % of specific investments, but this part decreases: it was 61.1 % in 2004 and 76.4 % in 2001. The general process investments inducing some effects in terms of pollution abatement are measured along two ways: the total amount of investment and the part which is devoted to pollution abatement. This part is selfevaluated by the firm. One has to keep in mind that the specific investments still represent the main part of PA investments:80.5 % in 2007, 79.6 % in 2004, and 80.8 % in 2001. Several steps are necessary to provide a measurement of PA investment consistent with our approach. First, we build a global indicator, named INVANTIPOL which equals the sum of the specific investment plus the part of global investment devoted to pollution abatement plus the amount of investment devoted to studies. Second, we only keep the plant which employ 100 employees and more, in order to have a sufficiently long period (namely from 1993 to 2007). Third this plant-level observed

  Antipol" survey) and the French survey on the RD (named the "Moyens de la recherché" survey). As in many empirical French studies, the Annual Business Survey ("Enquête Annuelle d'Entreprise") is used as a complement to provide data on firm performances. These surveys cover the same field: food industry, defined as the transformation of agricultural materials and products, into food products 1 . Such a field is an interesting one for several reasons. First it represents a significant part of French Manufacturing firms (about 550,000 employees in 2011, i.e. 18% of manufacturing employment). Second, it is composed of many industries, namely 10 at the NACE2-3 digit level, and 41 at the 4-digit level, with various characteristics. Thus, a significant heterogeneity can be preserved within such a sample, in terms of performance, PA regulation, RD effort... Third, pollution regulation matters in such industries. On one hand food industries use large amounts of materials, as water, on the other hand provide consumers goods for which sanity/safety characteristics are crucial. As

3.1. The field: food industry

To our knowledge, this study is the first one to use simultaneously a direct measurement of RD and PA investments at the firm level. To do this, we employ the French survey on the PA investments (named the "an illustration, food industry was in 2007 the third French industry in terms of PA investment, with a total amount of 167 million €, only preceded by the Energy (437 million €) and Chemicals, Rubbers and plastics (204 million €). Undoubtedly, PA is a relevant issue for food industry. This is attested by the number of studies, based on this empirical field for testing the Porter hypothesis. For instance, Galdeano-Gomez et al. (

Table 1 :

 1 The sample design

		Firms with PAK = 0	Firms with PAK > 0	Total
	Firms with RDK = 0	104	692	796
	Firms with RDK > 0	6	197 (Innovative Sample)	203
	Total	110	889	999 (Total sample)

Table 3 :

 3 Estimates of the production function, food Industry: 1993-2007 Levinsohn-Petrin estimator

	Variables	Reference population	Innovative population
	L	0.601***	0.643***
		(0.000)	(0.000)
	K	0.274***	0.352***
		(0.000)	(0.000)
	KRD15	0.0070***	0.2005***
		(0.001)	(0.008)
	KAP15	0.0124***	-0.0149 ns
		(0.004)	(0.541)
	N	8260	1073
	Adj R-squared	0.7087	0.7568
	(Step 2)

P values are in parentheses: * p < 0.10, ** p < 0.05, *** p < 0.01 Time and industry (Nace3 level) dummies are included in regressions whose coefficients are not reported.

Such a definition excludes non transformed products (agriculture) or transformed products with non-alimentary use (bio-fuel).

This survey provides a precise distinction between investments and current expenses (as taxes, for instance, or the cost of maintaining or using currently anti-pollution equipment). Current expenses are not surveyed annually.

By using the term "potentially", we just mean that all firms using these inputs do not necessarily innovate, whereas, at the opposite, some firms may innovate without using its.

Acknowledgments:

We gratefully acknowledge funding from the ANR project ANR-11-ALID-0002 OCAD "Offrir et Consommer une Alimentation Durable".


Aude Watrelot

Mouhamadou Kebe

Catherine M G C Renard

Anne Imberty

Jean Francois Maingonnat

Carine Le Bourvellec

Retention of procyanidins by apple cell walls limits their diffusion ?

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.

Retention of procyanidins by apple cell walls limits their diffusion ?

Aude A. Watrelot ( 1)* , Mouhamadou Kebe (1) , Catherine M.G.C. Renard (1) , Anne Imberty (2) , Jean-François Maingonnat (1) , Carine Le Bourvellec (1) (1)

INRA, Université d'Avignon et des Pays du Vaucluse, UMR408 Sécurité et Qualité des Produits d'Origine Végétale, F-84000 Avignon, France

CERMAV-CNRS, B.P. 53, F-38041 Grenoble Cedex 9, France *Presenting author: aude.watrelot@avignon.inra.fr

Apples are rich in polyphenols and more precisely in procyanidins contained in vacuoles of cells. Cell walls are composed of a network of polysaccharides such as cellulose, hemicellulose and pectins which define the structure and the texture of cells. It has already been shown that procyanidins interact with polysaccharides and that the affinity of procyanidins for pectins is higher than for hemicelluloses when cells are ruptured [START_REF] Renard | Interactions between apple cell walls and native apple polyphenols: quantification and some consequences[END_REF]. The aim of this study is to understand the impact of leaching process on the fate of procyanidins in apple. We present here the influence of the osmotic pressure on removal of procyanidins from apple pieces and their associations with cells walls by binding isotherms and with commercial pectins by isothermal titration calorimetry.

Apple parenchyma (cv. Granny Smith) was immersed in water for 6h at room temperature and changes of osmotic pressure via different concentrations of mannitol (0 to 0.6M) in external medium were used. Samples were removed each hour and procyanidins content was analyzed by HPLC-DAD. For association analyses, procyanidins with intermediate degree of polymerization (DP 8) were extracted from freeze-dried pulps of apple (cv. Golden delicious) as described in [2]. Cell walls were isolated from fresh ripe apples (cv. Ariane) using the phenol: buffer method (PB) as described in [START_REF] Renard | Interactions between apple cell walls and native apple polyphenols: quantification and some consequences[END_REF]. For binding isotherms, procyanidins (5 g/L) were incubated for 1h with the cell wall suspension (PB) or commercial pectins (20 g/L), in citrate/phosphate buffer pH 3.8 [START_REF] Renard | Interactions between apple cell walls and native apple polyphenols: quantification and some consequences[END_REF]3]. After incubation the solution and the cell wall-polyphenol complexes were separated by filtration under vacuum. The binding isotherms were interpreted according to the Langmuir formula [3]. For isothermal titration calorimetry, commercial apple pectin (30 mM galacturonic acid equivalent) dissolved in citrate/phosphate buffer pH 3.8 was titrated by procyanidins (30 mM (-)-epicatechin equivalent) in VP-ITC instrument (Microcal®, GE Healtcare) [2].

The higher the mannitol concentration, the lower the diffusion of procyanidins: some procyanidins were lost from the apple tissue when there was a difference in osmotic pressure between parenchyma cells and outer medium, none when osmotic pressures were equilibrated. Therefore in living tissue loss of procyanidins was only possible when cells were ruptures. With cooked tissues, procyanidin loss was observed whatever the osmotic pressure but remained partial, in contrast to monomeric polyphenols. This could be explained by the association between cell walls and procyanidins as it showed by binding isotherms. From cell walls, pectins associated with procyanidins with an affinity on the order of 10 3 M -1 through hydrophobic interactions and hydrogen bonds.