domain: math info sdv

text:
Jean-Pierre Gauchi
email: pierre.gauchi@jouy.inra.fr

Keywords: sensitivity indices, PLS regression, D-optimal design, aeronautics, InfraRed Signature

A novel practical method to conduct a Global Sensitivity Analysis (GSA) for computer models is proposed in this article. It is based on Partial Least Squares polynomial regression metamodeling, used in conjunction with a D-optimal computer experiment design. This practical method is particularly well adapted to the following four situations: (i) when the cost of a single computer simulation run is very high (long computing time), limiting computation to just hundreds of simulation runs, whereas the usual GSA methods (typically, those based on Latin Hypercube Samplings or Sobol sequences) require thousands or tens of thousands of simulation runs; (ii) when the inputs are not independent because some of them are stochastically linked (correlated) or deterministically (functionally) linked; (iii) when some inputs are of a qualitative (categorical) nature; and (iv) when the outputs are multivariate. This practical method, proposed in a deterministic simulation framework, is useful for moderately nonlinear computer models. It makes it possible to define and compute novel sensitivity indices, referred to here under the general term of SIVIP, not to be confused with Sobol indices defined for independent inputs. We have called our new method the SIVIP method. It is applied here to the aeronautics field, in particular, for the estimation of detection performances of infrared sensors and, more precisely, for the computation of aircraft InfraRed Signatures (IRS).

Introduction

Global Sensitivity Analysis (GSA) is de…ned as the study of how the output uncertainty of a computer model can be allocated to di¤erent sources of uncertainty in the model inputs [START_REF] Saltelli | Sensitivity Analysis for Importance Assessment[END_REF]. GSA leads to a quanti…cation and a ranking of the input in ‡uences. A major …nal objective is the simpli…cation of the model, enabling us to obtain a parsimonious model in the end. GSA based on variance methods has undergone considerable development since the 1990s, with many applications in several scienti…c areas such as applied physics and, more recently, in the biological sciences [START_REF] Ellouze | Sensitivity analyses applied to an exposure model of Listeria monocytogenes in smoked cold salmon[END_REF]. Several books provide a good overview of the techniques used in GSA [START_REF]Sensitivity analysis[END_REF][START_REF] Saltelli | Sensitivity analysis in practice -A guide to assessing scienti…c models[END_REF]. Sobol' Sensitivity Indices (SSI ) [START_REF] Sobol | Sensitivity estimates for nonlinear mathematical models[END_REF] are intended to represent the sensitivities for general (nonlinear) models. Almost all of the published methods are based on Monte Carlo simulations [START_REF] Saltelli | Making best use of model evaluations to compute sensitivity indices[END_REF][START_REF] Sobol | Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[END_REF] and require thousands or even tens of thousands of simulation runs for computing accurate estimations of the SSI. This is typically the case of the methods based on space-…lling designs [START_REF] Fang | Design and modelling for computer experiments[END_REF]. Moreover, these classical methods only work correctly if the random inputs of the computer model are continuous and independent because the SSI are rigorously de…ned only in this situation [START_REF] Sobol | Sensitivity estimates for nonlinear mathematical models[END_REF]. Thus, the need for a large number of simulation runs and the necessity for the inputs to be continuous and independent constitute three major constraints for SSI estimation.

To address the …rst of these constraints, i.e., the large number of simulations to be carried out with Monte Carlo methods, some authors [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF][START_REF] Blatman | Adaptive sparse polynomial chaos expansion based on Least Angle Regression[END_REF] have proposed a completely di¤erent approach for computing the SSI, mainly based on sparse polynomial chaos expansions. This latter approach leads to a large decrease in the number of simulation runs to be performed. This major advantage makes it possible to obtain the SSI, even for huge computer models where a single simulation run requires several minutes or hours and where it is obvious that none of the classical methods based on Monte Carlo simulations can be used. However, even the methods [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF][START_REF] Blatman | Adaptive sparse polynomial chaos expansion based on Least Angle Regression[END_REF] cannot take account of the correlations among some (or all) of the quantitative inputs, or of linear functional relationships between them (typically, bounded linear combinations of inputs), and the presence of qualitative (categorical) inputs. In [START_REF] Jacques | Sensitivity analysis in presence of model uncertainty and correlated inputs[END_REF][START_REF] Rabitz | Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs[END_REF][START_REF] Mara | Variance-based sensitivity indices for models with dependent inputs[END_REF][START_REF] Kucherenko | Estimation of global sensitivity indices for models with dependent variables[END_REF], the authors focus on correlated inputs, but these inputs must be quantitative and cannot be either strictly functionally linked or qualitative.

In this article, we consider dependent inputs: either correlated quantitative inputs or inputs linked by some linear combinations of the general form min 1 X 1 + ::: + K X K max , where K p, p the total input number, and min , 1 , :::, K , max are real numbers. Qualitative inputs can also be present in the form of their (0/1)-indicator variables. Hence, if we are in a situation where we have to simultaneously deal with the following three speci…c constraints -(1) Constraint A: a number of simulation runs that must be small or moderate (relative to the 1 number in Monte Carlo simulations); (2) Constraint B: quantitative inputs that are correlated or deterministically linked by relationships of the previously mentioned general form; and (3) Constraint C: presence of qualitative inputs -we then propose a novel practical approach in this paper for conducting a GSA. Moreover, this approach also enables us to deal with multivariate outputs. Our approach is jointly based on a Partial Least Squares Regression (PLSR) for a polynomial metamodeling and on a D-Optimal Computer Experiment Design (DOCED) strategy. Consequently, the new sensitivity indices we propose here, referred to under the general term of SIVIP (not to be confused with the SSI that are only correctly de…ned for independent inputs), are based on a metamodeling approach. Concerning the DOCED, it should be stressed that we are in a deterministic simulation framework, i.e., the inputs are controlled (as in standard factorial designs) and take the values determined by the DOCED. Note that some types of SIVIP proposed in this paper were brie ‡y presented and partially de…ned in [START_REF] Ellouze | Sensitivity analyses applied to an exposure model of Listeria monocytogenes in smoked cold salmon[END_REF][START_REF] Gauchi | Optimal Sensitivity Analysis under Constraints: Application to Fisheries[END_REF][START_REF] Gauchi | PLS-based global sensitivity analysis for numerical models: an application to aircraft infrared signatures[END_REF][START_REF] Lefebvre | Multidimensional Global Sensitivity Analysis for Aircraft Infrared Signature Models with Dependent Inputs[END_REF], but were not statistically and mathematically justi…ed.

Other computer experiment modeling strategies obviously already exist, typically, those based on Gaussian Process (GP) models, beginning with the work of Sacks et al. [START_REF] Sacks | Design for computer experiments[END_REF] (for detailed discussions of such models, see [START_REF] Santner | The Design and Analysis of Computer Experiments[END_REF][START_REF] Fang | Design and modelling for computer experiments[END_REF]), but they only perform for continuous inputs and univariate outputs. A relevant article [START_REF] Qian | Gaussian process models for computer experiments with qualitative and quantitative factors[END_REF], however, does exist, which also proposes taking the qualitative inputs into account with the construction of correlation functions. Lastly, the approach of [START_REF] Lamboni | Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models[END_REF][START_REF] Marrel | Global sensitivity analysis for models with spatially dependent outputs[END_REF] for multivariate outputs should also be mentioned, but no optimal computer experiment strategy is given.

Our approach is simpler than [START_REF] Qian | Gaussian process models for computer experiments with qualitative and quantitative factors[END_REF]. It can be seen as a practical alternative method, very di¤erent from [START_REF] Qian | Gaussian process models for computer experiments with qualitative and quantitative factors[END_REF][START_REF] Lamboni | Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models[END_REF][START_REF] Marrel | Global sensitivity analysis for models with spatially dependent outputs[END_REF], particularly well adapted if the computer model nonlinearity is moderate, and useful with multivariate outputs as well.

The rest of the article is organized as follows. Section 2 presents the novel approach. Section 3 gives statistical justi…cations of this approach. Section 4 illustrates this novel approach with a case study in aeronautics, in particular, for the estimation of detection performances of infrared sensors and, more precisely, for the computation of aircraft InfraRed Signatures (IRS), revealing the e¤ectiveness of this methodology. Section 5 is the conclusion. The Appendix provides some background on PLSR.

2 The novel approach proposed 2.1 Postulation of a polynomial metamodel and its estimation

Let M be the computer model of the "black box" type. Assume that for x i = (X i1 ; : : : ; X ip ), a point in the p-dimensional space of the p X j inputs, j = 1; : : : ; p, the simulation run result of the univariate Y output is y i = M (x i ). Note that p can be large in practical applications (frequently as high as 30).

We assume that the Y output can be approximated by a (full or not) polynomial metamodel (surrogate model) of degree d, referred to as M d , built from the p inputs (the categorical inputs are coded with their (0/1)-indicator variables). For one simulation run, we can write

y i = M (x i ) = M d (x i )+ i and M d (x i ) = M (x i )+" i
where i is a deterministic model error because M d is a deterministic polynomial approximation of M, and all of the x i form a deterministic design. Moreover, " i is a residual due to the estimation method chosen.

With several y i obtained from M at several x i , the estimation of the vector of the M d coe¢ cients is computed by PLSR (see Appendix for details on this regression method), leading to the estimated metamodel, Md;PLS , that will be simply referred to as M in the text. Therefore, we obtain M = X ^ P LS as the estimation of M, where X is the design model matrix of M d . The value of d and the monomials present in M d are chosen beforehand by the user. For practical applications of moderate nonlinearity, a value of 2 or 3 for d is generally used.

Building strategy of an e¢ cient DOCED

Our basic idea for determining an optimal computer experiment design is inspired by the theory of optimal design of real (non-computer) experiments for linear models (see the book by Atkinson and Donev [START_REF] Atkinson | Optimum experimental designs[END_REF] for a very clear introduction to this theory).

We now explain how to determine a small-size computer experiment design formed by computer experiments selected from a large candidate computer experiment set that we will refer to as the X C set. This selection is made according to the D-optimality criterion [START_REF] Fedorov | Theory of optimal experiments[END_REF]. A DOCED is associated with a model, M d in this case. The following two steps are therefore required to determine a DOCED*. This DOCED* will be considered as a deterministic design.

Step 1: Construction of the X C candidate set This construction depends on the (quantitative or qualitative) nature of the p inputs, as well as on the constraint types (correlations or linear combinations).

Let p 1 be the quantitative input number and p 2 be the qualitative input number, with p = p 1 + p 2 .

If we want to correlate the p 1 inputs, a convenient and simple method is to start from a space-…lling design, SFD, based on a large N 0 row number (typically N 0 = 1000 p), e.g., a Latin Hypercube Sampling (LHS) [START_REF] Mckay | A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[END_REF], and then use the Iman and Conover method [START_REF] Iman | A distribution-free approach to inducing rank correlation among input variables[END_REF] to (approximately) obtain the desired correlations among the concerned inputs. Another possible method is to use copulas [START_REF] Nelsen | An Introduction to Copula 2nd Ed[END_REF][START_REF] Joe | Multivariate Models and Dependance Concepts[END_REF] for correlating the p 1 inputs, which is the case for the application detailed in Section 4. In another situation, if the p 1 inputs are linked by a linear combination (see Introduction section), then only the rows among the N 0 original rows that satisfy this combination are selected to form a new (smaller) constrained SFD. Hence, the number of rows of this latter SFD can be considerably decreased. The resulting SFD remains acceptable if its row number is greater than or equal to 100 p. Note that this problem of functional (or structural) constraints is encountered in the constrained optimization …eld as well. The reader may refer to the relevant approach [START_REF] Kleijnen | Constrained optimization in expensive simulation: Novel approach[END_REF] to deal with this situation.

Let N C be the row number of this constrained SFD. Moreover, if p 2 qualitative inputs are present, then their levels are repeated and randomized until N C values are obtained for each of the p 2 inputs. Finally, we obtain a constrained SFD of N C rows and p columns, which will be referred to as SFD* in the text.

Step 2: Construction of a sequence of several DOCED and choice of a DOCED* Firstly, using SFD*, a design model matrix is built depending on d and the chosen monomials. The modalities of the p 2 inputs are replaced by their (0/1)indicator variables, and the construction of eventual interactions are then performed with some quantitative inputs. Let X be this design model matrix of N C and P columns, where P corresponds to the number of chosen monomials in M d , i.e., main e¤ects of the quantitative inputs, indicator variables of the qualitative inputs, interaction terms, quadratic terms, and cubic terms, if necessary.

The DOCED sequence to be constructed is referred to as ( D n P , n = P (= n 0 ); P + 1; :::; N C 1), where each DOCED, D n P , is a (n P ) matrix. Every D n P is optimal in the sense of the D-optimality criterion [START_REF] Fedorov | Theory of optimal experiments[END_REF], i.e., among all n size designs drawn from SFD* forming the so-called n set it is the one with the largest normalized determinant n = det(X T n X n ) =n P where X T n X n is the so-called information matrix. It was generally found that n is very small compared to N C , which is the major advantage of the method, therefore satisfying constraint A. Several speci…c (discrete) algorithms exist for …nding a D n . The well-known Fedorov [START_REF] Fedorov | Theory of optimal experiments[END_REF] and Mitchell [START_REF] Mitchell | An algorithm for the construction of D-optimum experimental designs[END_REF] exchange algorithms can be used, and they can be easily and e¢ ciently put into practice by means of [START_REF]QC module, Optex procedure, Version 9[END_REF].

An important remark must be made here about …nding a D-optimal design with algorithms of [START_REF] Fedorov | Theory of optimal experiments[END_REF]. These algorithms require the inversion of the information matrices. However, strong correlations between quantitative inputs and/or the presence of all of the indicator variables (resulting from the qualitative inputs) lead to the non-invertibility of these information matrices. Before using these algorithms, we propose, in this case, to replace the X matrix by the orthogonal matrix formed by its principal components (obtained from a Principal Component Analysis), by retaining a number of components corresponding to at least 99% of the explained inertia. This prior transformation was achieved for the application in Section 4. Finally, on the graph of the normalized determinants (or their logarithms) versus n, we can detect a good compromise between a high level of the D-optimality criterion and a reasonable value of n (see Figure 1 in the Application section). Let n be this optimal value of n. The DOCED*, D n P , is therefore found.

The novel Sensitivity Indices

These new sensitivity indices, which we refer to under the general term of SIV IP in this article, are based on the V IP statistics obtained in PLSR outputs. The V IP statistics are de…ned by formula [START_REF] Kucherenko | Estimation of global sensitivity indices for models with dependent variables[END_REF] given in the Appendix. We propose two types of SIV IP :

the Individual Sensitivity Index de…ned for each k monomial term among the P monomial terms of M d , for univariate and multivariate output, by:

ISIV IP k = V IP 2 k =P (1)
If the output is multivariate, we refer to it as the Generalized Individual Sensitivity Index in this case, or GISIV IP k .

the Total d order Sensitivity Index de…ned for each of the p original inputs, for univariate and multivariate output, by:

T d SIV IP j = J X u=1 ISIV IP ju ( 2
)
where ju is the uth index set where a j index appears, J is the total number of these ju , and ISIV IP ju is the corresponding monomial individual sensitivity index. For example, with three inputs, X 1 , X 2 , X 3 , and d = 2, the Total 2 order Sensitivity Index for X 1 is expressed as

T 2 SIV IP (X 1 ) = ISIV IP (X 1 ) + ISIV IP (X 2 1 ) + ISIV IP (X 1 X 2 ) + ISIV IP (X 1 X 3 )
. If the output is multivariate, we refer to it as the Generalized Total d order Sensitivity Index in this case, or GT d SIV IP j .

We emphasize here that the GISIV IP k and the GT d SIV IP j are particularly useful from a practical point of view. Indeed, they can reveal several strong or weak inputs for all the outputs studied simultaneously, which is especially useful when the multivariate output is a spectrum, e.g., infra-red spectrum.

3 Justi…cations of the novel approach proposed

Justi…cation of the PLSR choice

Firstly, we can observe that the PLSR metamodel deals with partial covariances for constructing its t h components, h = 1; :::; H. This aspect is clear if we examine the developped vectorial structure of a t h component given in formula (9) of the Appendix. Indeed, the term cov (F h 1 ; E h 1;j ) is a covariance between the F h 1 residual matrix and the E h 1;j residual vector and is therefore a partial covariance by de…nition. Formula (9) thus explains why the multicolinearity among the monomials can be correctly taken into account. Moreover, PLSR leads to the approximation F0 = P H h=1 t h r T h , and we therefore obtain for the Y l univariate output:

var( Ŷl ) = var(Y l ) H X h=1 r 2 lh var(t h ); l = 1; :::; L (3)
which is an empirical orthogonal decomposition of the total variance of Ŷl . Moreover, since Y l Ŷl , formula (3) gives an approximation of an empirical orthogonal decomposition of the Y l output. We can then see with formula (9) that the decomposition (3) is linked to the partial covariances between the Y l output and the monomial inputs.

Justi…cation of the D-optimality choice

If we use Ordinary Least Squares Regression (OLSR) for estimating the P 1 coe¢ cient vector of M d with n real data, the variance of the OLS estimator, ^ OLS , has the following well-known form:

var ^ OLS = 2 X T n X n 1 ( 4
)
where 2 is a constant, unknown, experimental variance. On the basis of (4), we can see that in order to minimize the variances and covariances of the ^ OLS vector components, which we always want to do, a D-optimal design, D n P , is a good choice because

D n P = Arg max n P n det X T n X n = Arg min n P n [det X T n X n 1 ] (5)
regardless of the value of the unknown 2 .

In the computer experiment framework, if the metamodel is …xed, then 2 is based on the " i residuals (see Section 2.1), and formula (4) can then makes sense as well.

Now, if we want to prove that it is also relevant to use D-optimal designs in the PLSR context strictly de…ned in the framework of OLSR then it might be proven that the determinant of an approximation (no exact formula exists) of the ^ P LS variance will be decreased if X n was based on a D-optimal design instead of on just any design. This is an open problem at that time. Only some numerical studies show an advantage of using D-optimal designs in the PLS context.

Lastly, it should be emphasized here that the choice of the D-optimality criterion is appropriate only if the postulated model is correct. It is for this reason that we assumed a moderate nonlinearity for the computer model and, therefore, a polynomial approximation with d 3.

Justi…cation of the VIP-based Sensitivity Indices choice

A …rst justi…cation of the V IP -based Sensitivity Indices, instead of a choice based on ^ P LS , for example, can be warranted by the fact that it has been observed for many years and in many studies that the V IP remains much more stable than ^ P LS when h increases. Moreover, the following two important arguments can be given in favor of this choice.

Deriving the SSI

It is possible to directly derive the SSI in the case of independent inputs in some particular situations. If the computer design is orthogonal, Q 2 G = 1, and L = 1 (one univariate output Y l is considered), then only one PLS component will be extracted. Its corresponding vectorial form will then be t 1 = E 01 w 11 + + E 0P w 1P , and formula (8) becomes F 0l = w 11 + + w 1P because the r vector becomes the scalar r = 1 and var(E 0j ) = 1; j = 1; ::: ; P . These w 2 1j are equal to cor 2 (F 0l ; E 0j ) = cor 2 (Y l ; Z j ). In this case, we can prove that w 2 1j is the SSI for the input Z j . For an input Z j , we have:

ISIV IP j = V IP 2 j =P = P 1 P cor 2 (Y l ; t 1 ) 1 cor 2 (Y l ; t 1 ) w 2 1j = w 2 1j (6) = cor 2 (Y l ; Z j ) = V (E(Y l jZ j ))=V (Y l ) = SSI j

Summation of the ISIV IP j

As a result of the property given in the Appendix, in the general case (univariate or multivariate outputs), for dependent or independent inputs, we have P P j=1 ISIV IP j = 1, which is a very convenient formula from a practical point of view if we wish to compare the ISIV IP j to each other. It is analog to the Sobol' theoretical summation [START_REF] Sobol | Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[END_REF] for independent inputs P Q j=1 SSI j = 1, where Q = 2 p 1:

Illustration of the SIVIP method for the Ishigami function

In GSA, this function is a very well known test function with three independent inputs [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF]. Even if the SIVIP method is speci…cally designed for dependent inputs, it can be relevant to apply it in this situation. Therefore, with a DOCED* of only 32 computer experiments (sampled in a 64-Legendre orthogonal array) and several (not full) M 3 polynomial metamodels, we obtained accurate estimations of the three analytical total sensitivity indices (ATSI). For example, with a polynomial metamodel formed by the 11 monomials X 1 ; X 3 ; X 1 X 2 ; X 1 X 3 ; X 2 X 3 ; X 3 1 ; X 2 1 X 2 ; X 1 X 2 2 ; X 3 2 ; X 2 X 2 3 and X However, we do not have any e¢ cient algorithm for …nding these correct monomials at this time. Only an exhaustive analysis enabled us to …nd them here. In any case, it is not the aim of the SIVIP method to compute sensitivity indices in the situation of independent inputs.

A case study in aeronautics 4.1 Presentation of the problem

This methodology has been applied to aircraft InfraRed Signature (IRS) analysis, within the framework of detection performances of infrared sensor estimation [START_REF] Lefebvre | A methodological approach for statistical evaluation of aircraft infrared signature[END_REF]. For an aircraft in a given atmospheric environment, the …rst order e¤ects on the IRS are related to the spectral range, the presentation geometry, the aircraft speed and the engine power setting. Several sources of variability lead to a dispersion of the values likely to be observed: weather, aircraft aspect angles, aircraft type and optical properties. These uncertainties in the input data are propagated through the computer model to the output data. Therefore, the simulated result is an interval of possible IRS that should include the IRS measured at a given moment. Note that a single run with the computer model takes approximately 3 minutes (on a 64 bit Sun Fire workstation with four Intel Xeon processors).

Since many of the input factors of our IRS simulation were uncertain, we used a GSA to identify the most important ones. We considered a daylight air-to-ground full-frontal approach in France by a generic aircraft ‡ying at low altitude (800-1200 ft). The infrared sensor was located on the ground, at a distance of 20 kilometers from the aircraft, in the ‡ight direction. The aircraft was assumed to be spatially unresolved by the sensor.

De…nition of inputs and outputs

Sixteen uncertain original inputs were analyzed. Eight were related to ‡ight conditions and IR optical properties of aircraft surfaces: altitude (ALTI), Mach number (MACH), engine power setting (POWERS), emissivity of air intake (EAI), and to aspect angles of the aircraft: cap (CAP), yaw (YAW), roll (ROLL) and pitch angles (PITCH). Eight were related to atmospheric conditions: visibility (VIS), relative humidity (RH), ground air temperature (TA), atmospheric model (MODEL), aerosol model (IHAZE), cloud presence (CLOUDS), base altitude of the cloud layer (HBASE), and hour to compute solar position (HOUR). The three inputs, MODEL, IHAZE and CLOUDS, were qualitative, with two, three and two levels, respectively. The three aerosol models are the modalities of the IHAZE qualitative input: urban (IHAZE1), maritime (IHAZE2) and rural (IHAZE3). By using the three indicator variables of IHAZE, we had a total of 18 inputs. The modalities of MODEL and CLOUDS were coded as 0/1.

The outputs analyzed were the sensor di¤erential irradiances between the target and the background, and we focused both on: (i) the 3-5 m spectrally integrated target intensity, which corresponds to typical infrared sensor spectral ranges, designated as IRStot hereafter; and (ii) a multispectral intensity, integrated on 14 spectral bands equally spaced in the wave-number domain. The usefulness of multispectral or hyperspectral sensors for remote sensing assignments has been proven [START_REF] Ho¤ | Enhanced Classi…cation Performance from Multiband Infrared Imagery[END_REF][START_REF] Chang | Anomaly detection and Classi…cation for Hyperspectral Imagery[END_REF][START_REF] Amato | Statistical cloud detection from SEVIRI multispectral images[END_REF], and some studies [START_REF] Karlholm | Wavelength band selection method for multispectral target detection[END_REF][START_REF] Ahlberg | Multi and Hyperspectral Target and Anomaly Detection[END_REF][START_REF] Manolakis | Detection algorithms for hyperspectral imaging applications[END_REF] emphasize their potential for target detection.

We are currently working on the speci…cation of a multispectral sensor for di¤erent missions such as aircraft detection or classi…cation, and being able to perform a sensitivity analysis on a multispectral infrared signature is therefore of the utmost importance.

Construction of the dependent candidate set

We started by building a type of SFD by sampling 20,000 candidate experiments using the estimated distribution of variables related to atmospheric conditions, except for HOUR, and a Sobol low discrepancy sequence for the nine other variables: ALTI, MACH, POWERS, EAI, CAP, YAW, ROLL, PITCH and HOUR, as explained in [START_REF]Sensitivity analysis[END_REF][START_REF] Fang | Design and modelling for computer experiments[END_REF].

RH, TA and HBASE were correlated, and their distribution was estimated on the basis of 3200 measured data using a non-parametric kernel reconstruction of marginal distributions, coupled with a dependence modeling based on a Normal copula [START_REF] Nelsen | An Introduction to Copula 2nd Ed[END_REF][START_REF] Joe | Multivariate Models and Dependance Concepts[END_REF]. This modeling was performed using the scienti…c library Open-TURNS (http://www.openturns.org/).

We also obtained a non-parametric reconstruction for the distribution of VIS and CLOUDS. A discrete uniform distribution was associated with the qualitative MODEL. The three aerosol models, IHAZE1, IHAZE2 and IHAZE3, are not equally probable in France, and we considered a {0.45; 0.1; 0.45} probability law.

At this stage, the SFD* was obtained. With these 18 inputs, we built the design model matrix, X, from this SFD*, by postulating an incomplete M d of 158 monomials: the 13 original continuous inputs, their 13 squared terms, their 13 cubic terms, and the 114 two-input and three-input interaction terms speci…ed by the infrared signature expert. Therefore, the dimensions of X were 20,000 rows and 158 (= P ) columns.

Construction of the DOCED*

Firstly, since the information matrices, X T n X n , built with X n selected in the preceding X, were generally not invertible, this X matrix was replaced by the Z matrix formed by the …rst 50 principal components of a principal component analysis (these 50 components represented 99% of inertia). A DOCED sequence was extracted from the SFD*, from n = n 0 = 50 to n = 1000. A good compromise was obtained in 180 experiments between the maximization of the (log) normalized determinant (see Step 2 in Section 2.2) and the number of runs, if we observe Figure 1. The DOCED*, D n =180;P =158 , was then formed with n = 180.

Results and discussion

We focused here on the total indices, the T 3 SIV IP and the GT 3 SIV IP , since it was quite di¢ cult to analyze all of the 158 monomial ISIVIP. However, it should be noted that the 20 largest ISIVIP and GISIVIP were associated with terms involving VIS or IHAZE2, and that the largest one-degree monomials were also associated with VIS and IHAZE2. The bar plot of Figure 2 presents the T 3 SIV IP (in %) associated with the 18 variables. The total IHAZE input contribution can be computed by summing the T 3 SIV IP corresponding to the IHAZE1, IHAZE2 and IHAZE3 indicator variables. The T 3 SIV IP associated with IHAZE is then 10.65, corresponding to the second highest T 3 SIV IP in comparison with the others. Thus, two variables are particularly predominant: VIS and IHAZE and, more precisely, the maritime model of aerosol If we now focus on the multispectral infrared signature, the bar plot of Figure 3 presents the GT 3 SIV IP (in %) associated with the 18 variables. As previously mentioned, the GT 3 SIV associated with the total IHAZE contribution is computed by summing the GT 3 SIV IP corresponding to the IHAZE1, IHAZE2 and IHAZE3 indicator variables. Their sum is 10.8 and corresponds to the second highest GT 3 SIV IP in comparison with the others. Hence, as in the IRStot case, the two predominant variables are VIS and IHAZE. The three additional variables that also have an important impact on IRS variability are unchanged: RH, TA and HOUR. The main di¤erence with IRStot stems from the higher indices corresponding to the three angles: PITCH, which extends from rank 13 up to rank 8, and, to a lesser extent, YAW and ROLL, which remain without in ‡uence. A possible explanation is that some of the 14 bands signi…cantly emphasize the impact of phenomena that vary with aspect angles, such as the plume emission contribution or the airframe re ‡ected light from the surrounding background. Finally, only …ve variables among the whole set actually in ‡uence the spectrally integrated and the multispectral infrared signature variability for the scenario considered, and they are all atmosphere-related factors. If we want to reduce the IRS uncertainty, we can thus combine the optics sensor with some detectors that can measure these atmospheric data. By virtue of the scenario chosen, a full frontal approach, large variations in IRS due to changes in aircraft aspect angle are excluded. The variations in aspect may dominate the rest of the variables. Hence, by essentially …xing the aspect to focus on, the variability of the meteorological phenomena may be given more importance in the overall IRS than if viewed from a di¤erent angle. Secondly, the low aircraft altitude and the long path between the sensor and the aircraft lead to an optical path that crosses the lowest atmospheric layers.

Consequently, the infrared transmission between sensor and aircraft and the atmospheric radiance, which both have a strong impact on the sensor di¤erential irradiance, are themselves in ‡uenced by the quantity and type of low altitude atmospheric aerosols. Even if the sensitivity analyses of the multispectral and the spectrally integrated IRS lead to rather similar results for our scenario, it is especially interesting to be able to perform a sensitivity analysis in dozens of spectral bands simultaneously. We can thereby consider di¤erent selections and mergings of bands in order to perform the speci…cation of a multispectral sensor.

Conclusions

Application aspects

Thanks to the methodology proposed in this paper, we were able to identify …ve variables that have a strong impact on integrated and multispectral IRS variability for the chosen scenario with only 180 simulations, and we can now proceed to the next step, the establishment of an IRS simulation metamodel, in order to be able to estimate IRS dispersion. Since these …rst results are quite promising, it would be interesting to extend this model to other scenarios with more uncertain variables, and to other military objects.

Methodological aspects

Our method, designated the SIVIP method, is based on two very well-established theories (PLS regression and D-optimal designs), and it is very simple and very easy to put into practice by means of an SAS/IML procedure or an R-language procedure, both available upon request to the corresponding author (the SIVIP Rpackage will soon be available on the CRAN). To our knowledge, no other practical method exists to simultaneously manage the A, B and C constraints, notably with multivariate outputs and, therefore, no realistic comparison of our method can be made today with an alternative method. Only scienti…c experts in the …eld are quali…ed to validate the results at this time. This has been done in the real application problem presented in Section 4, as well as in the application presented in [START_REF] Gauchi | Optimal Sensitivity Analysis under Constraints: Application to Fisheries[END_REF] with success. We hope that new competitive methods will be developed in the near future, which will then make it possible for the researchers involved to test our dataset using their own methods. It should also be noted that even with independent inputs, this method can be useful in the frequently encountered situation of costly simulations, even if the SIVIP will generally be di¤erent from the SSI (even in this particular situation of independent inputs).

The SIVIP method works correctly in the situation where the user can postulate that the nonlinearity of the computer model is reasonable, i.e., if d 3. Many real applications fall within this framework. However, if no prior knowledge is available about the nonlinearity, then neither the value of d nor the structure of the polynomial metamodel can be assumed (no previously chosen monomials are possible). In this situation, giving a large value to d can be a dangerous choice because of the well-known poor behavior of high-degree polynomials in terms of approximations. To address this di¢ culty, we propose an adaptive -and therefore parsimonious, in terms of the total simulation run number -version of the method for strong nonlinear computer models, which is currently being developed.

Figure 1 :

 1 Figure 1: Evolution of the normalized determinant logarithm versus the number of experiments n.

Figure 2 :

 2 Figure 2: The 18 T 3 SIV IP (in %) corresponding to the 18 inputs for the IRStot univariate output.

Figure 3 :

 3 Figure 3: The 18 GT 3 SIV IP (in %) corresponding to the 18 inputs for the multivariate output.

Acknowledgments: We would like to thank Gail Wagman, a professional English language translator, who corrected the English, and Régis Lebrun, from EADS Innovation Works, who performed the dependence modeling based on copulas.

Appendix: PLSR background

A brief overview of PLSR

PLSR is a bilinear method for relating inputs to outputs, and that is very popular in the chemometrics …eld [START_REF] Martens | Multivariate calibration[END_REF][START_REF] Tenenhaus | Régression PLS et Applications[END_REF][START_REF] Tenenhaus | Régression PLS -théorie et pratique[END_REF][START_REF] Wold | PLS Regression: a basic tool of chemometrics[END_REF]. It is very di¤erent (particularly from the algorithm point of view) from the familiar Ordinary Least Squares Regression (OLSR) in that no matrix inversion is needed. For the sake of clarity, we use input notations in this Appendix that are di¤erent from those used in the other sections of this paper. Bold characters are used for vectors and matrices, but standard characters are used when a general meaning is assumed, e.g., a PLS component is designated as t h , whereas in its vectorial form, it is designated as t h .

The general goal of PLSR is to model, via linear combinations, the link between R explanatory (input) variables j , j = 1; : : : ; R, and L (> 1) responses (outputs) Y l , l = 1; : : : ; L, both observed on the same N objects. We can represent the PLSR model by using the multivariate model form:

where Y N L is the observed multivariate ouput matrix, N R is the input matrix, R L is a (R L)-matrix of coe¢ cients to be estimated, and N L is a (N L)-matrix of error terms. PLSR presents some very strong advantages over OLSR: (i) the input variables -monomials built with these input variables can also be taken into account, including quadratic terms, interactions terms, cubic terms, etc. -can be highly correlated or even functionally linked, whereas the ^ P LS estimates of R L remain interpretable (e.g., see the very well illustrated example in [START_REF] Kettaneh-Wold | Analysis of mixture data with partial least squares[END_REF] where the inputs add up to one at each row of the design matrix); (ii) R and/or L can be larger than N ; (iii) information about the probability distributions of the elements is not needed (it is considered to be a so-called distribution-free method). The …rst two cases, (i) and (ii), make it impossible to use OLSR. The PLSR algorithm is based on a very speci…c algorithm, the NIPALS algorithm [START_REF] Tenenhaus | Régression PLS -théorie et pratique[END_REF][START_REF] Wold | Estimation of principal components and related models by iterative least squares[END_REF][START_REF]SIMCA-P9 software, User Guide and Tutorial[END_REF]. Following are some formal elements.

Let E 0 be the centred and scaled matrix (i.e., mean = 0 and variance = 1 for each column); F 0 , the centered and scaled Y matrix; E h , the residual matrix from the decomposition of E 0 by using h PLS components, t h ; F h , the residual matrix from the decomposition of F 0 by using h PLS components; F lh , the lth column of F h ; and H, the PLS component number retained. Therefore, the PLSR objective is to construct a linear combination, u 1 = F 0 c 1 , with columns of F 0 , and a linear combination, t 1 = E 0 w 1 , with columns of E 0 , by the maximization of the covariance between the t 1 and u 1 components, subject to the constraints kw 1 k 2 = kc 1 k 2 = 1. Hence, we obtain two variables, u 1 and t 1 , as correlated as possible, and best summing up E 0 and F 0 : The following regressions:

are then performed. The E 0 and F 0 are de ‡ated by t 1 p T 1 and t 1 r T 1 , and second linear combinations, u 2 and t 2 , are computed, and so on. We …nally obtain:

where the t h are orthogonal between them. We can develop the vectorial form of t h as:

On the basis of (8), we can deduce the following norm decomposition, i.e., an empirical decomposition of the output variance (because the F l0 in F 0 are centered and scaled):

For one (univariate) centered-scaled output, F l0 , we can then write:

The signi…cant number H of PLS components is given by means of a speci…c crossvalidation test (see the end of this Appendix).

On the basis of ( 8) we can obtain the PLS regression equations:

Ŷl = ^ l0 + ^ l1 1 + : : : + ^ lM M ; l = 1; :::; L

De…nition of the V IP statistics in PLSR

Let the redundancy statistics be as follows:

and Rd(Y ; t 1 ; : : :

The V IP (Variable Importance in the Projection) statistics [START_REF] Tenenhaus | Régression PLS -théorie et pratique[END_REF][START_REF]SIMCA-P9 software, User Guide and Tutorial[END_REF] for an j input in the presence of a univariate or multivariate Y output is then de…ned as:

hj # 1=2 [START_REF] Kucherenko | Estimation of global sensitivity indices for models with dependent variables[END_REF] where the w hj are the components of the w h vectors. Note the important property P P j=1 V IP 2 Hj = P . Obviously, the V IP statistics make sense if the value of the …tting-prediction criterion, Q 2 G , (see below) is close enough to one, implying that M = N R ^ R L is a reasonable estimated approximation of the unknown underlying model for both …tting and prediction. In Section 2.3, we omitted the index H for the sake of brevity because non-ambiguity is possible once M has been cross-validated with H components by means of the Q 2 G :

Validation of the PLSR model

The PLSR model is validated by a cross-validation procedure based on the Q 2 Gh and Q 2 G statistics (bounded between 0 and 1) computed for each univariate output, detailed in [START_REF] Lazraq | Selecting both latent and explanatory variables in the PLS1 regression model[END_REF]. The PLSR model is thus iteratively built, and these iterations are stopped by means of a procedure on the t h components. A commonly used procedure is the one inspired by the rule proposed in [START_REF]SIMCA-P9 software, User Guide and Tutorial[END_REF]. This rule is the following: a t h component (from h = 1) is retained if Q 2 Gh 1 (0:95) 2 . Finally, with the H retained components, the Q 2 G cumulated index is computed [START_REF]SIMCA-P9 software, User Guide and Tutorial[END_REF]. Thus, this Q 2 G index is a …tting-prediction type criterion typically designed for a PLSR model. Its major advantage, in comparison to a classical R 2 , is that it avoids over…tting. From a practical point of view, we have to choose a Q 2 G threshold to be overtaken of at least 0.80.


G A Oliveira

S Bureau

M-G C Renard

F De Castilhos

PREDICTION OF THE SOLUBLE SOLIDS CONTENT IN THREE FRUIT SPECIES USING NIRS APPROACH

The fruit structure effect (passion fruit, tomato and apricot) was investigated on prediction performance of soluble solids content (SSC) using NIR spectroscopy. Relationships between spectral wavelengths and SSC data were evaluated through the application of chemometric techniques based on partial least squares (PLS). Good prediction performance was obtained for apricot with correlation coefficients of 0.93 and root mean square errors of prediction (RMSEP %) of 3.3%. For the passion fruit and tomato, the prediction models were not satisfactorily accurate due to the high RMSEP. Results showed that NIR technology can be used to evaluate apricot internal quality, however, it was not appropriate to evaluate internal quality in fruits with thick skin, (passion fruit), and/or heterogeneous internal structure (tomato)

INTRODUCTION

Near Infrared Spectroscopy (NIRS) is becoming an attractive analytical technique for measuring quality parameters in food, especially because it allows non-destructive analysis of food products, requires little or no sample preparation and is both flexible and versatile, i.e., it is applicable to multiproduct and multicomponent analysis [START_REF] Roberts | Analysis of forages and feeding stuffs[END_REF]. The NIR spectra are the result of the interaction of radiation with the sample, and their physical and chemical properties are reflected in it. The interactions occur with molecular groups associated with quality attributes such as the C-H group in sugars and acids and the O-H group in the water. Most of the NIR absorption bands associated with these groups is overtones or combination bands of the fundamental absorption bands in the near infrared region, which are themselves due to vibrational and rotational transitions. Scattering from microstructures can indirectly indicate physical parameters [START_REF] Nicolai | Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: A review[END_REF].

Previous research has demonstrated the potential of NIR spectroscopy for assessing soluble solid content (SSC), and/or other physiological properties in intact fruits such as in prune [START_REF] Slaughter | Nondestructive determination of total and soluble solids in fresh prune using near infrared spectroscopy[END_REF], stonefruit [START_REF] Golic | Robustness of calibration models based on near infrared spectroscopy for the in-line grading of stone fruit for total soluble solids content[END_REF] and apricot (Bureau et al., 2009). However, this successful use of NIR spectroscopy was restricted to fruits with homogeneous pulp and thin skin. [START_REF] Guthrie | NIR model development and robustness in prediction of melon fruit total soluble solids[END_REF] obtained unsatisfactory results for melon fruit, similarly [START_REF] Guthrie | Non-invasive assessment of pineapple and mango fruit quality using near infra-red spectroscopy[END_REF] were not able to predict soluble solids content in pineapple. [START_REF] Lammertyn | Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment[END_REF] pointed out that penetration of NIR radiation into fruit tissue is limited. For example, in apple, the penetration depth is up to 4 mm in the 700-900 nm range and between 2 and 3 mm in the 900-1900 nm range. In fact, in a later study, Nicolai and co-workers (2007) concluded that depending on the uniformity of the fruit, the determination of quality attributes is difficult. The objective of the work was to assess the near-infrared spectroscopy, as a non-destructive method, to predict soluble solids, in three structurally different intact fruits: passion fruit (thick skin), tomato (heterogeneous internal structure) and apricot (homogeneous pulp and thin skin).

MATERIALS AND METHODS

Selection of passion fruit, tomato and apricot

A total of 61 yellow passion fruits (Passiflora edulis f. flavicarpa), in two different ripening stages (green-yellow and yellow) were harvested in 2011 in southern Brazil. For tomato, a total of 150 fruits of cultivar 'Levovil', in five different ripening stages (green, green-orange, orange-green, orange, red) were harvested in 2008 from an experimental greenhouse of INRA (Institut de la Recherche Agronomique) located in Southern France. 116 apricot fruits from three cultivars, named 'Bergeron', 'Iranien' and 'A4034' were harvested at two different stages of ripening: yellow (unripe) and orange (ripe) in INRA experimental orchards (Amarine and Gotheron), in South of France, in 2010. Non-destructive measurements were performed on the day of picking for each fruit and conventional, destructive, measurements were carried out a few days later on frozen materials.

Near-infrared diffuse reflectance measurements (FT-NIR)

Spectra were collected for all samples in reflectance mode (log 1R -1 ) using a multi-purpose analyser (MPA) spectrometer (Bruker Optics). The instrument was equipped with an integrating sphere to provide diffuse reflectance measurements and a TE-InGaAs detector. The MPA was fully software-controlled (OPUS software Version 5.0, Bruker Optics). The NIR spectrum for each sample was obtained from an average of 32 scans. NIR spectra were acquired between 800 and 2700 nm at 2 nm spectral resolution and a background of 32 scans. The time required to achieve a spectral measurement was 30 s. Intact tomato and apricot fruits were placed on an automated 30-position sample wheel, each position corresponding to an 18 mm diameter hole. The spectra for passion fruit were obtained in Brazil, an identical spectrometer was used (Bruker Optics) but without sample wheel. Fruits were placed at each-calyx axis set to the horizontal position. On each fruit, two opposite spectra were captured and the average of the two spectra was used (for the development of the models).

Determination of soluble solids content

Soluble solids content (SSC) was determined with a digital refractometer (PR-101 ATAGO, Norfolk, VA) with temperature compensation. SSC was expressed in °Brix.

Multivariate calibration

PCA (principal component analysis) was initially performed using all available samples (n = 61 for passion fruit; n = 150 for tomato and n = 116 for apricot) in order to evaluate the variability among the samples, to eliminate the aberrant spectra due to acquisition problems and to separate groups for calibration and internal validation. It is recommended for all practical applications [START_REF] Nicolai | Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: A review[END_REF]. In order to generate the prediction models for the quality traits of interest, the samples were grouped into two sets to have 80% samples for calibration and 20% for internal validation (Table 1). MatLab software package (version 6.5, Mathworks USA.) and Origin 6.1® (OriginLab Inc., Northampton, USA) were used for chemometric treatment of data. In this study, different pretreatments, including mean centering, multiplicative scatter correction (MSC), first-derivative and smoothing, were applied. Quantification models for SSC were developed using PLS regression. To evaluate the results, root mean square error of cross-validation (RMSECV), root mean square error of prediction (RMSEP), the percentage of error of prediction (RMSEP%) and correlation coefficient of validation (R 2 ).

RESULTS

Characterization of the chemical and spectral data

The samples showed a large variability of SSC for fruits of the three species used in this trial. These results confirm that selected fruits were in different ripening stages. Statistical analysis for the calibration and validation sample sets, i.e., data ranges, means, standard deviations (SD) and number of samples for SSC are shown on Table 1. The general shapes of the spectra for the three fruit types were quite similar, though the spectra for the passion fruit showed weak absorption intensity and a slight displacement, possibly due to the thickness of the skin (Figure 1). The main absorption peaks coincided for all three fruits. The peak at 1190 nm corresponds to the second and third C-H overtone regions and 1500 nm overlaps with the first O-H overtone region associated with organic compounds [START_REF] Roberts | Analysis of forages and feeding stuffs[END_REF]. In general, the absorbance patterns seen here can be loosely related to the functional groups associated with water and sugars. Indeed, most fruits contain 80-90% of water and show a rising sugar content throughout ripening. The spectra obtained here for apricot and tomato can be compared to other studies concerning apricot (Bureau et al., 2009) and tomato [START_REF] Sirisomboon | Nondestructive estimation of maturity and textural properties on tomato[END_REF].

Prediction of soluble solids content

For fruits from the three different plant species used in this trial, different calibration models were calculated. The spectra pre-processing and the number of factors were both taken into consideration to determine the best models. The best PLS model developed for the passion fruit used pre-processing multiple scatter correction (MSC) and 5 latent variables (LVs) which provided the lowest cross validation error of 1.62 °Brix. When the model was applied to predict the 12 internal validation samples, a low correlation (R 2 = 0.63) and a high error of prediction (RMSEP% = 9.8%) were found. For tomatoes, results were similar to the results found for passion fruits. The lowest cross validation error (0.13 °Brix) was observed for models using 10 LVs and MSC pre-processing. When the model was used to predict the 32 internal validation samples, the prediction error was 8.85% and the correlation coefficient was 0.52. However, in apricot a good correlation was found. A R 2 = 0.93 and a low RMSEP 3.3% were observed, when the model was used to predict the 24 internal validation samples The same ratio was observed by Camps and Christen (2009). The lowest cross validation error (0.69 °Brix) was observed for models using 6 LVs and MSC pre-processing followed by smoothing.

NIR prediction results

The three species used in this trial have distinct physical (Figure 2) and biochemical (Table 1) characteristics. A broad range of values was recorded in this work for SSC in all of the three fruits. This finding is likely due to the fact that sampling was, as experimentally designed, carried out during different ripening stages, and it is well known that during ripening, sugars accumulate and acidity decreases, the later, as a result of the consumption of the predominant acids during fruit respiration.

Values of the SSC this work were within the range found in literature for passion fruit (Jiménez et al., 2011), tomato [START_REF] Scibisz | Midinfrared spectroscopy as a tool for rapid determination of internal quality parameters in tomato[END_REF]apricot (Bureau et al., 2009;Camps and Christen, 2009). Equatorial sections are presented for passion fruit and tomato, and a transverse section for apricot.

Apricot is a stone fruit that consists of three parts: a thin skin, a fleshy mesocarp which encloses the seeds. The thickness and shape of the mesocarp vary according to different cultivars [START_REF] Romani | The biochemistry of fruits and their products[END_REF]. These characteristics seemed to favor the NIR prediction. Excellent results were found, showing that NIR technology can be effectively used for the quantification of the soluble solid for apricot. Measuring SSC have been reported also using reflectance mode, has shown excellent correlation for various fruits such as prune, plums and peaches [START_REF] Louw | Robust prediction models for quality parameters in Japanese plums (Prunus salicina L.) using NIR spectroscopy[END_REF]Pérez-Marín et al., 2009). All of these fruit share with apricot similar anatomical features such as thin skin and homogeneous pericarp.

The lowest correlation for the parameter SSC was found for passion fruit. Passion fruit contains similar soluble solids content when compared to apricot. However, the thick skin in passion fruit acts as barrier and prevents the penetration of the infrared radiation to the pulp. The passion fruit is a fleshy, berry type fruit, with a thin pericarp (peel) that can be lignified. The passion fruit mesocarp thickness ranges from 0.5 to 4.0 cm, and the endocarp (pulp) contains seeds with fleshy aril [START_REF] Vasconcellos | Caracterização física e quantidade de nutrientes em frutos de maracujá doce[END_REF]. Indeed, [START_REF] Guthrie | NIR model development and robustness in prediction of melon fruit total soluble solids[END_REF] determined the total soluble solids in intact melon and observed a correlation coefficient lower than the correlation coefficient found for other fruits, being the difference attributed to the heterogeneity of SSC distribution within the fruit and the poor penetration of light through the irregular fruit skin. Flores et al. (2008) evaluated SSC in cut and intact watermelons and melons using a NIR diode array spectrometer. The results of SSC prediction for cut watermelons and melons were much better than those of intact watermelons and melons (cut watermelons: R 2 = 0.92, RMESCV = 0.49; intact watermelons: R 2 = 0.81, RMSECV = 0.93; cut melons: R 2 = 0.94, RMSECV = 0.60, intact melons: R 2 = 0.87, RMSECV = 0.98). For passion fruit, the thick skin prevents the use of NIR to predict the composition of the internal pulp.

The tomato is a fleshy berry, with at least two locular cavities. The locular cavities contain the seeds, within a more or less abundant gel. They are enclosed by a parenchyma that forms a subepidermal layer of 0.2-1 cm, radial septa that separate the locules, and a collumella. The pericarp is protected to the outside by an epidermis covered with a waxy cuticle, presenting many hairs, stomata and lenticels [START_REF] Hobson | The biochemistry of fruits and their products[END_REF]. The composition of these different tissues is not homogeneous. Cheng et al., (2011), in particular, showed that sugar concentrations in the placenta and close to the calix were consistently low relative to the outer pericarp, collumella, and locular cavity. The prediction of models for non-destructive measurement by spectroscopic methods has generally been poor [START_REF] Walsh | Sorting of fruit using near infrared spectroscopy: application to a range of fruit and vegetables for soluble solids and dry matter content[END_REF]. Chen ( 2008) determined soluble solids content in two tomato varieties ('DRK 453' and 'Trust') in five different stages of maturity and found values remarkably low (R 2 = 0.03 and RMSEP 0.15 °Brix). However in these last two cases, prediction heavily relied on the internal correlation in the sample set, as a given variety has a defined genetic program that coordinates color evolution and sugar accumulation during maturation.

CONCLUSION

The analysis of the best models shows that the physical features of the fruit directly affect the results. The low correlation values for passion fruit were attributed to the low penetration of infrared radiation due the thick skin of the fruit. For tomatoes, internal characteristics (heterogeneity) and high water contents led to weak correlations. On the other hand, good and robust prediction results were observed for apricot, which is a fruit with thin skin and homogeneous pulp.

REFERÊNCIAS

BUREAU, S., RUIZ, D., REICH, M., GOUBLE, B., BERTRAND, D., AUDERGON, J. M.; RENARD, C. M.G.C. Application of ATR-FTIR for a rapid and simultaneous determination of sugars and organic acids in apricot fruit. Food Chem., v. 115, p. 1133-1140, 2009. CAMPS, C., CHRISTEN, D. Non-destructive assessment of apricot fruit quality by portable visible-near infrared spectroscopy. LWT -Food Sci. Technol., v. 42, p. 1125-1131[START_REF] Perez-Marin | Non-destructive determination of quality parameters in nectarines during on-tree ripening and postharvest storage[END_REF]. Tec., v. 62, p. 17-25, 2011. FLORES, K., SANCHEZ, M. T., PEREZ-MARIN, D. C., LOPEZ, M. D., GUERRERO, J. E., GARRIDO-VARO, A. Prediction of total soluble solid content in intact and cut melons and watermelons using near infrared spectroscopy. J. Near Infrared Spec., v. 16, p. 91-98, 2008.

Figure 1 -

 1 Figure 1 -Typical normalized NIR spectra (mean) performed on intact fruits of passion fruit (a), tomato (b) and apricot (c).

Figure 2 -

 2 Figure 2 -Schematic representation of the fruit anatomy of the three species used in this trial.Equatorial sections are presented for passion fruit and tomato, and a transverse section for apricot.

  CHEN, L. Non-destructive measurement of tomato quality using visible and near-infrared reflectance spectroscopy. Thesis of Master of Science. McGill University. M.Sc. (Génie des Bioressources). 2008. CHENG, Y. C., WANG, T. T., CHEN, J. H., LIN, T. T. Spatial-temporal analyses of lycopene and sugar contents in tomatoes during ripening using chemical shift imaging. Postharvest Biol.

Table 1 -

 1 SSC range, mean and standard deviation (SD) of the passion fruit, tomato and apricot in both calibration and validation sample sets

	Fruit	Sample set	Range	Mean	Standard Deviation	Number of samples
	Passion fruit	Calibration set Validation set	9.0 -16.0 12.1 -14.2	13.3 14.2	±1.8 ±1.3	49 12
	Tomato	Calibration set Validation set	3.7 -6.4 3.9 -6.1	4.8 4.7	±0.49 ±0.54	118 32
	Apricot	Calibration set Validation set	11.3 -20.4 11.6 -20.1	15.2 15.3	±2.3 ±2.1	92 24

Área temática: Engenharia e Tecnologia de Alimentos


Denis Allard
email: allard@avignon.inra.fr

Discussion of "Spatial Statistics: Marks, Maps, and Shapes"

I would like to congratulate Dr. Possolo for his excellent -and very personal -presentation of the subject. I greatly enjoyed his presentation in Leuven, and I had the same pleasure reading his contribution. I will first discuss his categorization into Marks, Maps and Shapes. I will then share some personal -obviously partial -views on three main challenges faced

Introduction

One particularity of spatial statistics is that early methodologies were largely developed in different areas of applications rather than in university statistics departments. Geostatistics was pioneered by Matheron and colleagues in a mining engineering context [START_REF] Matheron | Les variables régionalisées et leur estimation. Une application de la théorie des fonctions aléatoires aux Sciences de la Nature[END_REF]; see also [START_REF] Chilès | Geostatistics: Modeling spatial uncertainty, 2nd Edition[END_REF], for an extensive presentation of geostatistics); spatial considerations were implicit in Fisher's work on randomization and blocking for the analysis of agricultural field trials (Fisher, 1966); forestry was the context of the seminal PhD thesis of Matérn on spatial variations (published in [START_REF] Matérn | Spatial variations, 2nd Edition[END_REF].

It was later introduced into mainstream statistical research by two seminal contributions: [START_REF] Besag | Spatial interaction and the statistical analysis of lattice systems (with discussion)[END_REF] proposed models and associated methods for analyzing spatially discrete "lattice" data, while [START_REF] Ripley | Modelling spatial patterns (with discussion)[END_REF] introduced a family of functions, known as Ripley's K and L functions for the analysis of spatial point processes. Since then, spatial statistics has been enriched with important contributions, in particular relating to point processes and object models [START_REF] Stoyan | Stochastic Geometry and Its Applications[END_REF], model based geostatistics [START_REF] Diggle | Model-based geostatistics (with discussion)[END_REF], hierarchical modeling for spatial data [START_REF] Banerjee | Hierarchical Modelling and Analysis for Spatial Data[END_REF]) and spatio-temporal statistics [START_REF] Cressie | Statistics for Spatio-Temporal Data[END_REF].

The historical context briefly sketched above grounds the usual presentation of spatial statistics in three major branches: (1) continuous spatial variations, i.e. random field theory and geostatistics; (2) discrete spatial variations, including lattice processes and areal unit data; (3) spatial point patterns, including marked point processes and object models.

The categorization proposed by Dr. Possolo into Marks, Maps, and Shapes deviates from this classical presentation. The "Marks" category includes lattice models (2) together with point processes (3); "Maps" corresponds evidently to continuous spatial variations (1); and "Shapes" corresponds to 1 the description, analysis and modeling of objects (3). Lattice gases, presented here as a mark process (each site of the lattice is either white or black) could be, and usually is, presented as a (binary) Markov random field, the most widely-used tool for building models with discrete spatial variations. Obviously, the boundaries between these categories are neither rigid nor impermeable. Data in ecology or environmental sciences are most of the time multivariate and multitype. Complex spatial models with components of every type are therefore necessary for the analysis of such datasets.

Since the early 1990s, spatial statistics, together with its more recent development towards spatiotemporal statistics, has become an ever-growing domain of statistics. The past 25 years has seen an explosion of interest in space and space-time problems, largely fueled by the computer revolution and by the increased availability of geo-and time-referenced data. Figure 1 reports the number of publications returned by a Web of Science query with "Spatial Statistics" as topic, from 1991 to 2014. The number of publications increased by 10% each year, corresponding to a doubling every seven years. This exponential growth illustrates the dramatic growth of research within this field as well as its application to other scientific fields. Spatial statistics is an expanding research domain, and as such it faces new challenges.

I will briefly present three of those challenges, thereby proposing a complementary view to that of Dr. Possolo. They mainly arise from the data acquisition revolution brought about by inexpensive, mobile, connected measurement devices. They are expected to have a profound impact on how data will be modeled and how computations will be carried out in the near future. From spatial to spatio-temporal statistics

At first, it is tempting to consider that spatio-temporal processes are not that much different from purely spatial processes. From a purely mathematical point of view, this is indeed the case: time could be considered as an additional coordinate. From a physical prospective, this view is insufficient. The movie of life goes forward, and usually does not make much sense when played backwards. Time differs intrinsically from space, in that there is a time arrow, whilst there is usually no preferred direction in space. In addition, there is usually a very large discrepancy between space and time lags. Two quite different situations are very frequent. In the first situation, corresponding for example to an air pollution monitoring network, data are dense in time and sparse in space. Multivariate time series seem to offer an adequate framework of analysis. In the second case, data are dense in space and sparse in time. This is for example the case when analyzing remote sensing data at different dates. Here, multivariate spatial fields might seem a good modeling strategy. Unfortunately, these models generally separate time and space, in the sense that spatio-temporal covariance functions will be the product of spatial and temporal covariance functions. Separable models do not allow for spatiotemporal interaction. They correspond to processes that will frequently fail to model physical process adequately, in particular in environmental applications. Statistical models that account for as much physics as possible are thus necessary to address the very spatio-temporal nature of the process under study.

A first approach to account for this issue is to build valid and flexible covariance functions that do not separate time and space. Straightforward constructions include combinations of products and sums of purely spatial and temporal covariances or the use of geometric anisotropy on covariance functions defined in R d+1 . In a seminal paper, [START_REF] Gneiting | Nonseparable, stationary covariance functions for space-time data[END_REF] gave a very general class of nonseparable covariance functions built from the spectral representation of covariance functions that has now become the standard class of models for univariate spatio temporal random fields in geostatistical applications. Let φ(r), r ∈ R be a completely monotone function and let ψ(r), r ≥ 0, be a positive function with a completely monotone derivative. Then, the function

C(h, u) = 1 ψ(u 2 ) d/2 φ h 2 ψ(u 2 )
is a covariance function of the space-time domain R d × R. More general mixture representations were later obtained in [START_REF] Schlather | Some covariance models based on normal scale mixtures[END_REF]. Current research aims at building general and flexible classes of covariance functions for multivariate spatio-temporal processes. [START_REF] Scheuerer | Covariance models for divergence-free and curl-free random vector fields[END_REF] built covariance functions that honor physical constraints for the modeling of random fields of divergencefree or curl-free random vectors, with an application to the analysis of wind fields over Germany. An open challenge is to characterize the covariance functions that are compatible with particular partial differential equations, such as reaction-diffusion PDEs.

A second approach consists in building mechanistic-statistical models that combine a statistical model for the observation process with a physical model for the dynamics under study (e.g. pest dynamics). Here, spatio-temporal interactions are part of the physical model. An example of such a construction can be found in [START_REF] Roques | A statistical-reaction diffusion approach for analyzing expansion processes[END_REF] for the analysis of the northward expansion of the pine processionary moth (PPM). In the Paris Basin, its range has shifted 87 km northward between 1972 and 2004. Since 2005, this expansion has been especially well documented with the establishment of a geo-referenced map of the front winter nests all over France. The statistical model bridges the gap between continuous data (nest densities) and binary data (presence/absence in 2 km × 2 km cells) and, conversely, provides a way to estimate the parameters of the mechanistic model based on the observed data. The mechanistic model describes the discrete-time evolution of nests as a function of continuous-time adult dispersal and of the environmental effect on PPM fitness. Their combination in a Bayesian setting resulted in maps of both the nest density and the regionalized fitness parameter.

Data massiveness

Spatio-temporal data are becoming available in overwhelming volumes and diverse forms as a result of growing remote-sensing capabilities, ground-based sensor networks, crowdsourcing, citizen science data, as well as medical sensing technologies. The processing of such diverse and massive data poses conceptual, methodological, and technical challenges, which are exacerbated by data diversity.

Maximum likelihood estimation for spatial data usually requires mathematical operations (inverting a matrix, evaluating a determinant) which have computational costs to the order of O(n 3 ), where n is the number of data at hand. It is thus limited to datasets with n < 10 4 . Approaches for alleviating the dimensionality problem are required for larger datasets. In the past decade, there have been several approaches proposed to overcome this problem (see Sun, Li and Genton, 2011, for a review), such as tapering the covariance function, using composite likelihood methods, or approximating the random fields by the use of a latent process of reduced dimension. One common feature of all these methods is that they consider an approximate version of the true model by leaving aside some information deemed unimportant. As an alternative route, one may chose to use Gaussian Markov Random Fields (GMRFs) representation, which offer appealing computational properties. This route bridges the gap between the categories discussed above: between continuous and discrete spatial representations on the one hand; between Marks and Shapes on the other hand.

Covariance functions that do not have bounded support tend asymptotically to zero at large distances. Tapering the covariance function consists to set to 0 all small values at large distances while keeping the original covariance at short distances in a way such that the transformed covariance is still definite positive. As a result, covariance matrices are highly sparse, allowing the use of very efficient algorithms for estimation and/or prediction. Under appropriate conditions, tapered maximum likelihood have good properties, such as consistency, asymptotic normality and high relative efficiency. Covariance tapering can also be used for spatial prediction, also known as kriging. It has been shown to be asymptotically accurate and computationally efficient (Furrer, Genton and Nychka, 2009).

Composite likelihoods are products of smaller marginal or conditional likelihoods computed on subsets of data. They are thus fast to compute and do not require storage capacities. [START_REF] Varin | An overview of composite likelihood methods[END_REF] provides an overview of composite likelihood methods. An application to spatio-temporal data is given in [START_REF] Bevilacqua | Estimating space and space-time covariance functions for large data sets: a weighted composite likelihood approach[END_REF], in which it is shown that pairwise composite likelihood estimation has a relative efficiency close to 1.

Fixed rank kriging captures the main features of the spatial dependence described by the n × n covariance matrix Σ using data dimension reduction techniques. The matrix Σ is decomposed into the sum of a low rank and a sparse component, Σ = BFB t + G, where B is an n × m matrix arising from m basis functions (B 1 (•), . . . , B m (•)), with m n, F is an m × m covariance matrix and G is a sparse matrix. Then, the Sherman-Morrison-Woodbury inversion formula yields

Σ -1 = G -1 -G -1 B(F -1 + B t G -1 B)B t G -1 .
This formula is very efficient since it only requires the inversion of one sparse matrix and one low dimensional matrix. Fixed rank kriging has been applied [START_REF] Cressie | Fixed rank kriging for very large spatial data sets[END_REF] with success for the kriging of massive spatio-temporal data, such as total column ozone data over the entire globe.

GMRFs are specified through the set of n conditional distributions of one component given all others. Gaussian properties imply that GMRFs are directly specified by their precision matrix Q = Σ -1 . When all conditional distributions actually depend on very few neighbors, Q presents the appealing property of being very sparse, thus yielding highly efficient algorithms [START_REF] Rue | Gaussian Markov Random Fields: Theory and Applications[END_REF]. The computational gains from GMRFs have been further boosted by applying Integrated Nested Laplace Approximation on top of predictive process GMRF models [START_REF] Rue | Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion)[END_REF], thus dramatically reducing the computation burden for the inference of large spatial datasets with a hierarchical structure.

A major breakthrough for modeling very large spatial datasets was achieved in Lindgren, [START_REF] Lindgren | An explicit link between Gaussian fields and Gaussian Markov random fields: The SPDE approach (with discussion)[END_REF] where it is proposed to fit GMRFs with local neighborhood on non regular lattices for Gaussian random fields with Matérn covariance function. Such random fields are shown to be solutions of a particular Stochastic Partial Differential Equation (SPDE). The authors then generalize the construction of the corresponding (SPDE) using triangulation techniques from finite element methods. This avoids the interpolation on regular grid points and allows to refine the resolution where details are required. [START_REF] Lindgren | An explicit link between Gaussian fields and Gaussian Markov random fields: The SPDE approach (with discussion)[END_REF] sets a new avenue for the modeling of massive spatial datasets. It bridges the gap between continuous and discrete spatial variations both elegantly and efficiently. Currently, this approach cannot be used for spatio-temporal data, but important research efforts are devoted to this issue.

Data diversity and unconventional data

Recent datasets in ecological and environmental applications come now in very diverse formats, qualities, types and spatial supports. For example, Figure 2 shows the main landscape features (roads, canals and hedgerows) in an agricultural area near Avignon (France) dominated by orchards. This image is part of a statistical analysis aimed at assessing the role of these features on pest propagation over an agricultural landscape. The full dataset includes data of all types discussed above: countings of pests in insect traps, location and severity of pest attacks in orchards, orchard types and descriptions, etc. Statistical models describing such data are highly structured, involving a spatial hierarchical structure in a Bayesian setting. There are also quite complex spatial dependencies between data of all types seen above, including geometrical objects such as connected segments. The analysis of the northward expansion of the PPM that illustrated mechanistic-statistical models could also illustrate the type of approach to be developed for the analysis of a process with very diverse data.

More recently, novel data classes have appeared, such as networks, trajectories, reported events along routes and streams of data provided by connected devices. With these new types of data, boundaries between categories are blurring at an increasing rate. The current analytical frameworks have not been designed to cope with these data. Today, approaches for the analysis of very diverse datasets are still to be developed. Novel theoretical models and computational tools must be developed to build statistical models and inference methods within this context and to tackle issues such as change of support, impact of uncertainties, bias and preferential sampling.

Figure 1 :

 1 Figure 1: Number of publications per year, returned by a Web of Science query with "Spatial Statistics" as topic.

Figure 2 :

 2 Figure 2: Main landscape features in an area near Avignon (France). Blue: canals; Red, roads; Black, hedgerows.

Acknowledgments

I would like to express my gratitude to the organization committee, (especially Peter Goos, Martina Vandebroek, R. Does and M. Schoonhoven) for giving me the opportunity to discuss these issues at the 2015 Stu Hunter Research Conference that was held in Leuven (Belgium) and in this Special Issue.


Lescourret et al 2015 CO Environmental Sustainability

A process-based approach to assess the impact of practices on FGR drivers Biodiversity (FGR) and adaptive management

  Lisbon 24-26 November 2015 -F. Lefèvre Resilience and resistance Resilience of the system : amount of change supported with the same controls on function and structure degree to which the system is capable of self-organization ability to build and increase the capacity for learning and adaptation Resistance Gunderson & Holling 2002 Panarchy the response function? Can we predict future environment? What do we accept today? today Resource availability Production Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Choice of reproductive material for planting Lefèvre 2012 sometimes ≠ models converge (predictions for scots pine in 2055, A1B)... predicting future potential species range Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Cheaib et al 2012 Ecology Letters … sometimes not (predictions for beech in 2055, A1B) predicting future potential species range Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Benito-Garzón et al 2011 Global Ecol Biog the genetic diversity matters... predicting future potential species range Pinus sylvestris Pinus pinaster Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Centaurea maculosa, introduced in the USA in 1890, 32 climatic variables Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre and the adaptive capacity too ! predicting future potential species range Broennimann et al (2007) Ecology Letters Oddou-Muratorio & Davi 2014 Evol Appl Physio-demo-genetic model : coupling functional model, population dynamics, genetic architecture and heredity demography responds to environmental change fitness dynamically results from the physiology change in Tsum requirement (°C) for budburst after 6 generations 1 genetically variable parameter for budburst, mortality driven by reserves, seed production driven by growth no evolution (h 2 =0) evolution integrates inter-individual variation physiological variables are evolvable Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Sansilvestri et al (2015) Envir Sci Pol Changing the reproductive material for planting from knowledge to practice Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre 1) Mediterranean forests facing climate change : a complex world 2) Approach by state and future-based scenarios :

complex world, each new piece of knowledge does not simplify understanding => integration is needed

  : across disciplines, science and pragmatism integrate multiple processes across scales, trajectories may be more predictable than future states

	biodiversity (FGR) and adaptive management
	In a complex world, each new piece of knowledge does
	Practices 1) Mediterranean forests facing climate change : a Expected benefits Associated costs not simplify understanding => integration is needed : and risks regulation of density and spatial distribution to equalize reproductive success -reduce genetic drift in small populations -reduce inbreeding in the next generation complex world across disciplines, science and pragmatism -no supplementary cost -slow down selection (prefer equalization per transdisciplinary knowledge integration patch) integrate multiple processes across scales, trajectories 2) Approach by state and future-based scenarios : may be more predictable than future states
	in heterogeneous	-increase reproductive	-simulations needed for
	environment, dissociate areas of production & 3) Dynamic approach and decision-based scenarios : contribution of highly selected individuals a cost / benefit analysis in different contexts
	areas of evolution, allow gene flow knowledge integration across scales
	save the lone tree, 4) Two conclusions -diversify the mating	-limited supplementary
	collect seeds for local	pairs	cost
	assisted regeneration	-promote adaptation to	-risk of inbreeding if self-
		margibal conditions	pollinated seeds not
			purged

Lefèvre et al 2014 Ann For Sci

Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre

In a

Adaptation to a changing world requires a new paradigm : evaluate

risk/opportunities and uncertainties as such think multi-dimensional : short-term / long-term impacts, multiple ecosystem functions and services manage multiple options Foresterra Conference, Lisbon 24-26 November 2015 -F. Lefèvre


est destinée au dépôt

Abstract:

Nutritional symbioses are widespread associations among insects, contributing to the evolutionary adaptation and the invasive power of this class of animals. The endosymbiosis between the pea aphid, Acyrthosiphon pisum, and the bacterium, Buchnera aphidicola, is an interesting model of symbiotic partner's integrated metabolism, particularly for the production of amino acids lacking in the aphid's diet. An important supply of these nutrients has to be provided especially for the phenomenal aphid growing rate observed during parthenogenetic viviparous reproduction.

A recent transcriptomic analysis, performed in our laboratory, allowed us to identify a key metabolic pathway regulated in the pea aphid parthenogenetic development: the tyrosine pathway. This biosynthetic pathway is shared by the two symbiotic partners, all the precursors being produced by B. aphidicola. To determine the involvement of this pathway in aphid development, we silenced by RNAi approach the unique gene in the pea aphid genome that encodes for phenylalanine hydroxylase (ACYPI007803, EC 1.14.16.1), the specific enzyme of tyrosine biosynthesis catalyzing the conversion of Phe to Tyr.

ACYPI007803 knockdown by microinjection of dsRNA yielded several defective phenotypes, specifically targeting the two symbiotic compartments: the bacteriocytes and the embryo chains.

The ACYPI007803 gene expression inhibition, confirmed by qRT-PCR, considerably affected aphid fecundity by diminishing the number of nymphs produced. Furthermore, the RNAimediated treatment resulted in a significant impairment of embryo development, with the production of non-viable and deformed neonatal nymphs. To attest of the tyrosine biosynthesis disruption following ACYPI007803 knockdown, single embryo HPLC analyses were performed and demonstrated a significant reduction of tyrosine amount as well as a coherent increase of phenylalanine, the upstream amino acid precursor.

Altogether, our findings shed new light on the importance of the tyrosine pathway in the embryonic development of parthenogenetic pea aphids and establish the phenylalanine hydroxylase contribution to this process, notably by regulating the tyrosine biosynthesis.

  Tyrosine metabolism and parthenogenetic development in a symbiotic insect, the pea aphid: the central function of phenylalanine hydroxylase Pierre Simonet, Karen Gaget, Marjolaine Rey, Marie-Gabrielle Duport, Hubert Charles, Gérard Febvay, Stefano Colella, Federica Calevro To cite this version: Pierre Simonet, Karen Gaget, Marjolaine Rey, Marie-Gabrielle Duport, Hubert Charles, et al.. Tyrosine metabolism and parthenogenetic development in a symbiotic insect, the pea aphid: the central function of phenylalanine hydroxylase. 7.

Title: Tyrosine metabolism and parthenogenetic development in a symbiotic insect, the pea aphid: the central function of phenylalanine hydroxylase Authors

	Seventh International Symposium on Molecular Insect Science
	13-16 July 2014 -Amsterdam (The Netherlands)
	International Symposium on Molecular Insect Science, Jul
	2014, Amsterdam, Netherlands. 1 p., 2014. hal-02792558

& affiliations: P. Simonet, K. Gaget, M. Rey, G. Duport, H. Charles, G. Febvay, S. Colella, F. Calevro UMR203 BF2I, INRA, INSA-Lyon, Université de Lyon, France federica.calevro@insa-lyon.fr


Frédérik Saltré

B W Brook

Joel J Chadoeuf

Damien A Fordham

Marta Rodriguez-Rey

Corey J A Bradshaw

Spatial pattern of Eurasian woolly mammoth extinctions during the Late Pleistocene based on statistical inference from fossil records

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.

Spatial pattern of Eurasian woolly mammoth extinctions during the Late Pleistocene based on statistical inference from fossil records

Frédérik Saltré1 , Joël Chadoeuf2 , Barry W. Brook3 , Damien A. Fordham 1 , Marta Rodríguez-Rey 1 , Corey J. A. Bradshaw 1

University of Adelaide;

Institut national de la recherche agronomique;

University of Tasmania


domain: sdv sde

text:
Frédéric Rees

Jean-Louis Louis Morel

Suzanne Edith Allaire

Mechanisms of soil pH regulation by biochar amendments and consequences for biochar long-term effects

teaching and research institutions in France or abroad, or from public or private research centers.

Mechanisms of soil pH regulation by biochar amendments and consequences for biochar long-term effects

Soil amendments of biochar, i.e. the solid product of biomass pyrolysis, have been increasingly investigated over the last few years as a way to store stable C in soils, to improve crop production and to remediate degraded and contaminated land. Many short-term effects of biochar on soil chemical and biological properties may be explained by the observed increase of soil pH, largely reported in the recent scientific literature for acid or neutral soils. However, both the mechanisms by which biochar is affecting soil pH and the duration of pH changes remain unclear. Using batch reactors and column leaching experiments, we examined the response of a wood-derived biochar pyrolyzed at 450 °C to the addition of various quantities of HNO 3 or NaOH. Our results enable to identify both the dissolution of biochar's mineral phases, e.g. calcite and Si/Al oxides, and cation exchange at the surface of biochar as the two major mechanisms explaining biochar's buffering capacity. The importance of these mechanisms vary in dependence with time and pH evolution. Observation of old charcoal amendments at various sites suggest however that, depending on initial soil pH and soil buffering capacity, the effects of biochar caused by the modification of soil pH may not last more than a few years.


Anna Zaidman-Remy

Anna Zaidman

Intracellular symbiosis and immune signaling

come

Organizers

Véronique Morel Maura Strigini

MoucheRhone has been a scientific regional meeting aiming at fostering interactions between labs using Drosophila as a model. This year we have aditionally invited labs using other arthropods such as crustaceans (Parhyale hawaiensis) and other insects (Tribolium castaneum, Gerris buenci, …).

  Scientific topics include embryonic development, cellular morphogenesis and growth, muscle and nervous system development and physiopathology, genomic adaptation, transgenesis and genome editing, functional genomics and epigenetics. MoucheRhone Ecole Normale Supérieure de Lyon Lyon, France June 9th 2015 Research Groups involved (non exhaustive) • Comparative developmental biology and regeneration (M. Averof, IGFL, Lyon) • Genetic control, development and ciliogenesis (B. Durand, CGphiMC, Lyon) • Genetic and chemogenomics (M.-O. Fauvarque, CEA, Grenoble) • Epithelial cell differentiation and morphogenesis in Drosophila (M. Grammont, LBMC, Lyon) • Diversification of Muscle and Heart Cells in Development and in Pathological Conditions (K. Jagla, GReD, Clermont-Ferrand) • Developmental genomics and evolution (A. Khila, IGFL, Lyon) • Functional genomics of host/intestinal bacteria interactions (F. Leulier, IGFL, Lyon) • Epigenetics and zygote formation in Drosophila (B. Loppin, CGphiMC, Lyon) • Ontogenesis and molecular interactions (S. Merabet, IGFL, Lyon) • Epithelial growth and morphogenesis (V. Mirouse, GReD, Clermont-Ferrand) • Apoptosis and neurogenetics (B. Mollereau, LBMC, Lyon) • Infection and viral genomes evolution (C. Terzian, UBCL, Lyon) • Genetic instabilities and control by the host genome (Chantal Vaury-Zwiller, GReD, Clermont-Ferrand) Venue Amphitheater A ENS de Lyon 46, Allée d'Italie Lyon