To reach the goal mentioned in the title, an intuitive solution using two pieces of ferrite is first proven to be effective. Then, ferrite is removed and the externally applied field that minimizes losses is searched. This is done using a new optimization tool (GOT) and taking advantage of multipolar expansion of the external field.

I. INTRODUCTION

Increasing power efficiency is the main objective of power electronic designers. Wire related losses are a major concern in connecting conductors as well as inside transformers, especially at frequencies promoting eddy currents.

Due to its rotational invariance, losses due to skin effect of an isolate straight cylindrical wire can't be reduced. On the opposite, if the cross section of the wire is rectangular, external pieces of material can modify the field and the current repartition in a way such that losses are significantly reduced. The goal of this article is to find the external field shape that minimizes losses in this wire.

II. LOSSES REDUCTION IN COPPER FLAT RECTANGULAR SHAPED CONDUCTOR

A straight rectangular cross section wire made of copper is considered (Fig. 1). It is supplied by a 1 A eff 100 kHz current. Ferrite modifies magnetic field around the copper and current density inside. To look for the minimum of losses, ferrite is replaced by two external current sources (Fig. 3): one in phase with wire total current, the other one in quadrature with it, in order to create an adjustable external inductor field. This field can be decomposed in Fourier series. For symmetry reasons, current sources only include even harmonics:

( ) ( )         + + - = ∑ ¥ =1 2 2 2 cos 1 k k k c k b i a I I q (1)

III. OPTIMIZATION PROCESS

A. Global Optimization Toolbox

The FEM software is coupled with GOT (Global Optimization Toolbox) to achieve optimization. The method used is based on the creation of response surfaces [START_REF] Costa | Optimization of Grounding Grids by Response Surfaces and Genetic Algorithms[END_REF] and a genetic algorithm is finally used.

B. Limited Search Area

Solution space is a huge one so optimization process needs a limited search area. In order to find a realistic one, field obtained in fig. 2 is split in an emitted part and a received one, following a method presented in [START_REF] Margueron | Applying, Canceling and Identifying the Magnetic Field Received and Emitted by a 2D Plan System[END_REF]. External field is then created only by current densities, flowing axially in the cylinders (fig. 3), which first coefficient values are: Due to the 8 ratio of rectangle sides, currents are not easy to represent. Square representation has been preferred.

Optimization with a higher number of field components will be presented in final article. Obtained field and currents densities will be analyzed.

Fig. 3 .

 3 Fig.1. Rectangular shaped conductor With only this conductor, copper losses are: m mW P / 9 . 6 = .Previous studies[START_REF] Montarros | Drainage du flux magnétique dans les transformateurs Planar HF[END_REF] using FEM software Flux2D[START_REF] Flux | 10 Chemin de Pré Carré-ZIRST[END_REF] showed that, with two pieces of ideal ferrite ( 2300 = r µ like 3C90) put close to the wire as shown in Fig.2, copper looses can be reduced by 22% ( m mW P / 34 . 5 = )

  RESULTSOptimization is managed with only field harmonic 2 (coefficients a 2 and b 2 ). Losses have been reduced by 30% ( current densities of wire alone (fig.4) and of field submitted wire (fig.5) it appears that peaks are lower and current is more uniform in the last one.

Fig. 4

 4 Fig.4. Initial Current density


domain: math shs

text:
Javier Díez-Palomar
email: jdiezpalomar@ub.edu

Exploring Roma learning mathematics: A socio-mathematical view

Keywords: Roma, mathematics learning, successful learning trajectories. SLT

In this paper, I discuss six case studies of Roma people who have overcome inequalities to learn mathematics. I explore which elements may explain their success, as well as which ones appear to be barriers that makes learning more difficult for students belonging to an ethnic minority. I draw on their testimonies using a qualitative methodological approach. The analysis of the data reveals that social representations about Roma have a major impact on these six Roma people attitudes and beliefs towards mathematics and schooling, which also affects their strategies to learn mathematics. The six narratives that I discuss in this paper suggest that success happens when Roma children are not segregated from the mainstream, but receive the same mathematics curricula as their peers.

Roma within the literature on mathematics education

In the field of mathematics education there are few studies about how Roma children perform in mathematics [START_REF] Chronaki | Learning about "learning identities" in the school arithmetic practice: The experience of two young minority Gypsy girls in the Greek context of education[END_REF][START_REF] Chronaki | An entry to dialogic in the maths classroom: Encouraging hybrid learning identities[END_REF][START_REF] Stathopoulou | Language and culture in mathematics education: Reflections on observing a Romany class in a Greek school[END_REF]. [START_REF] Stathopoulou | Language and culture in mathematics education: Reflections on observing a Romany class in a Greek school[END_REF] analyse the relation between Romanó (Roma language) and the learning of mathematics in Greece. According to them, language is a form of cultural identity for Greek Roma children, and they use it to resist the homogeneous discourse of the school. Stathopoulou and Kalabasis define the academic Roma culture as an "oral" culture, which they use to justify reputing the claim about a "lack of written Roma language". Starting from this statement, they argue that Roma children are proficient at oral calculation methods connected to their cultural roots, because Roma culture is mainly based on oral tradition. [START_REF] Chronaki | An entry to dialogic in the maths classroom: Encouraging hybrid learning identities[END_REF] suggests introducing hybrid practices 1 as a way to break with the hegemonic discourse of the school [START_REF] Matusov | Journey into dialogic pedagogy[END_REF]. Drawing on [START_REF] Bakhtin | The dialogic imagination: Four essays[END_REF] concept of polyphony, Chronaki argue that we need to develop dialogic practices to include the voices of all students in the classroom, including students from minority groups, not only the ones who share the monologist hegemonic discourse.

There is a lack of scientific literature on the type of actions performed by Roma children that appear to be successful in terms of achieving academic success and developing, what I call, successful learning trajectories (SLTs). Drawing on previous research [START_REF] Flecha | Successful educational actions for inclusion and social cohesion in Europe[END_REF], I define SLTs as the set of practices and interactions conducted by an individual to pass his/her exams, successfully obtaining his/her school certificate(s). I use the "grading of a test, exam or any other assessment procedure" as indicator of success, for the lack of a better indicator of "learning." According to the European 1 Hybrid practices has been used in linguistic and cultural studies to characterize situations within the school (or the classroom) in which participants draw on different social and cultural backgrounds (Gutierrez, Baquedano-López & Tejada, 1999). It includes formal practices (school like practices) and practices related to what Luis Moll calls funds of knowledge (Gonzalez, Moll and Amanti, 2006). [START_REF] Chronaki | An entry to dialogic in the maths classroom: Encouraging hybrid learning identities[END_REF] uses the term in that sense, in the context of Roma culture.

Thematic Working Group 10

Proceedings of CERME10 authorities in education, the minimum level of education expected for everyone is compulsory education (goals of the Horizon 2020 Program), generally up to age 162 . For this reason, "early leaving" and "dropping out" of compulsory education is considered "failing" in this approach.

Methodology

This study was part of a larger research project investigating the response of individuals from ethnic minorities to overcome the social inequalities they face in the formal educative system when learning mathematics. This research interest emerged in the frame of analysing how children at risk of facing these inequalities can find their way to gain successful scores at school. The data was collected in Barcelona and its metropolitan area. When conducting this study, I realized that Roma people developing SLT (in mathematics) made use of strong support from their relatives. In order to better understand their process of learning, I decided to conduct a series of interviews with six Roma individuals, previously identified as "successful cases" in the sense that all of them had obtained good grades in mathematics during their academic trajectories (until the last course taken) (see To collect the data, I used personal interviews, an instrument with questions oriented to identify the elements that explain participants' success in learning mathematics, according to their personal (subjective) point of view. Drawing on [START_REF] Chase | Narrative inquiry: Multiple lenses, approaches, voices[END_REF],

Contemporary narrative inquiry can be characterized as an amalgam of interdisciplinary analytic lenses, diverse disciplinary approaches, and both traditional and innovative methods -all revolving around an interest in biographical particulars as narrated by the one who lives them. (p. 651)

This method of inquiry is rooted in previous work, of researchers such as [START_REF] Thomas | The Polish peasant in Europe and America[END_REF]Znaniecki (1918/1927), [START_REF] Garfinkel | Studies in ethnomethodology[END_REF] and Mills (1959). It involves collecting the testimonies of participating people using a number of instruments of data collection, including life stories, self-reports, oral biographical memoires, testimonies, in-depth interviews, recorded narratives and life review [START_REF] Mertens | Transformative research and evaluation[END_REF]. This method of inquiry starts from an epistemological approach of individuals as primary sense-making agents [START_REF] Giddens | Modernity and self-identity: Self and society in the late modern age[END_REF][START_REF] Riley | Researching practice: The methodological case for narrative inquiry[END_REF]. Personal narratives allow us to see first hand the interpretations made by the protagonists of their own life experiences. As [START_REF] Bruner | Acts of meaning[END_REF] claimed, we understand our world through the lenses of personal narratives. In addition, we also make meaning (and even build meaning) through those narratives. This type of method (inquiry) led me to include the voices of the participants within the wider study. All information was transcribed for further analysis.

I selected six participants for the purposes of this paper. All met the requirement of having developed a SLT. As we can see in table 1, two of them are now enrolled in PhD programs. Three more, Joaquim, José and Antonio, are preparing to access university degrees, through the exams set up by the Government for people over the age of 25. Finally, Aroa is a girl (the youngest one in the group) who after finalizing her studies in the high school, decided to start working.

In order to analyse the data, I used narrative and discourse analysis [START_REF] Mertens | Transformative research and evaluation[END_REF], drawing on a communicative methodological approach [START_REF] Aubert | Amaya: Dialogic literary gatherings evoking passion for learning and a transformation of the relationships of a Roma girl with her classmates[END_REF][START_REF] Sánchez | Communicative methodology of research with minority groups[END_REF]. This approach focuses on the analysis and interpretation of the discourse from the dialogue with the participants, using validity claims [START_REF] Habermas | The theory of communicative action[END_REF]. The interpretation is organized in two different dimensions of analysis: transformative and exclusionary. Transformative dimension includes all aspects that will enable the subject of the study to answer positively to the research question.

Exclusionary dimension has the opposite meaning: it includes all aspects that will avoid (or make more difficult) answering the research question. For the study reported in this paper, the transformative dimension includes all aspects leading the participant to achieve a SLT, whereas the exclusionary dimension refers to all aspects making difficult (or even avoiding) the subject to achieve a SLT. Interviewers and interviewees established a dialogue to explore the data collected, which allowed us to identify meaningful topics regarding interviewees' learning trajectories. In a subsequent interview, I asked them to further clarify those topics. Drawing on this dialogue I elaborated a key to codify all data collected (see table 2).

The categories (codes) emerging from the discussions include: attitudes, beliefs, content, strategies and social representations. The first two concepts were defined in [START_REF] Mcleod | Research on affect in mathematics education: A reconceptualization[END_REF] terms. Content is referring to the mathematics itself (the curriculum). Strategies are defined in [START_REF] Maehr | On doing well in science: Why Johnny no longer excels; why Sarah never did[END_REF] terms (see also [START_REF] Ames | Achievement goals in the classroom: Students' learning strategies and motivation processes[END_REF]. Social representations correspond to the [START_REF] Moscovici | On social representations[END_REF] definition.

Discussion

Next I provide first an inductive analysis of the data collected through the interviews. Then I try to create a tentative model to make sense all the relevant variables identified by the participants in the study, explaining their 'learning process'.

First step: Inductive analysis Federico provides a good example illustrating the type of answers obtained from all six Roma interviewed. He claims:

In my case, the key aspects were, one I was passionate [about mathematics] and I really like science, so my motivation was somehow 'natural', or 'intrinsic'. In his words, we can see that aspects particularly positive in his academic career include effort, a challenging curriculum, a personal motivation (passion) for some of the academic topics (such as mathematics or biology), whereas no enthusiasm at all is devoted toward other ones (Catalan or English). From a very tentative entry point, we can infer here that 'motivation' is, somehow, connected to 'grading' (as learning 'indicator'), given that Federico (for example) got excellent grading in mathematics and biology and, in fact, he started 'biology' for his minor at the university. But he also declares that his family (specially his mom), took a relevant part in his learning process.

In an informal way, my mom taught me mathematics in the kitchen, or when shopping. Topics like volume, arithmetic, counting, prices, change, […] My dad, as he was in the construction sector, taught me how to calculate budgets, how to calculate the price for square meters, how much does it cost the staff, rates. (Federico)

He and Aroa, Antonio, José, Joaquim and Joana as well, explain that their good grades in mathematics were consequence, mainly, of their family involvement. Their parents were the ones teaching them to develop mental calculation skills, estimation skills, etc., which were highly valued in the school framework. [START_REF] Stathopoulou | Language and culture in mathematics education: Reflections on observing a Romany class in a Greek school[END_REF] also provide clear examples in the case of Greek Roma, confirming this finding. However, this is not a main strategy for learning mathematics for any of our six cases. What they claim is that in order to obtain good grades in mathematics, they basically had to study hard, to put a lot of effort, using academic strategies to better learn: outlines, summaries, use of key words, or other mnemonic strategies, practice, problem solving, homework every day, etc.

However, drawing on the data that I collected, it seems that certain social contexts could become sometimes a barrier limiting the opportunities of some Roma individuals to successfully perform in their grades. Joana, for instance, felt isolated from the 'Roma world', whereas Joaquim resists and rejects school because "[school] it is not Roma". Teachers are crucial. According to Federico, some teachers really do not help Roma students because they feel that Roma are not interested in education.

Joana holds a similar view. She explains how for many of her Roma friends teaching was just a matter of "being happy attending the school", rather than "being a place for expand their learning". According to Joana, that was the consequence of some teachers' prejudices against Roma children:

Not always, but in some cases, yes. It was not the case with me; my teachers always encouraged me to continue studying. But most of the times they did not identify me as Roma, and I have come to hear some pejorative comments towards my people from my teachers. In the classroom, I never had so many Roma peers. But I know other Roma girls who explain to me that, in their high schools, teachers, instead of teaching them the lesson, they lead them to see the telenovela [soap operas on TV]. I guess that it is the easiest solution and they think that doing so, the girls would be happy of attending the school every day. But I think that it is the opposite in fact, because the girls and their families know that they are not learning anything, so attending the school is useless.

If things are like that, then they can stay at home and see the telenovela over there. (Joana)

Looking at the testimonies of the six individuals interviewed, what they highlight as the most exclusionary factor is segregation, the separation of Roma students from the mainstream. This is due either to stigmatization from some teachers, or because genuine wishes of some teachers to better help them, hence they use "separation into homogeneous small groups" as a way to 'concentrate' additional support. However, according to Federico and Joana, those efforts are useless, since taking Roma children away from the mainstream does not help them to better learn mathematics, but the opposite; this practice leads the Roma students to be labelled by their peers and teachers, creating a stigmatized social representation about Roma. Therefore, this process somehow "announces" the academic performance of Roma children even before they conduct the tests. It is like a "self-fulfilling prophecy". This perverse effect has been proved many times in the field of mathematics education research with children from vulnerable groups (Secada, Fennema, & Byrd-Adajian, 1995;de Abreu, Bishop, & Presmeg, 2001). When the school creates ability groups to segregate vulnerable groups children from the mainstream, creating low level groups, or designing segregated paths tracking, the consequence is that these children fail.

Second step: Creating a model of analysis

Drawing on the analysis of these testimonies, after coding them with the qualitative software package Atlas.ti, I produced a tentative model to describe SLT. I called this scheme Learning Core Matrix (LCM), as in figure 1, drawing on the variables identified by [START_REF] Mcleod | Research on affect in mathematics education: A reconceptualization[END_REF], [START_REF] Maehr | On doing well in science: Why Johnny no longer excels; why Sarah never did[END_REF] and [START_REF] Moscovici | On social representations[END_REF], as reported earlier in this paper. The sum of all these components forms what I call LCM. I use this scheme to understand how every SLT works. On the subjective level of analysis, personal attitudes are shaped by social representation of being Roma. Social representations include values, ideas, metaphors, and beliefs (in the sense of Moscovici's notion) related to learn mathematics being Roma. Strategies refer to the practices that individuals (Roma students, teachers, etc.) perform to teach, learn, resist or avoid mathematics. Attitudes include positive or negative evaluation of people, objects, events, activities, ideas, etc. in the frame of teaching and learning mathematics. Beliefs include personal mental states regarding people, objects, events, activities, ideas, etc. Finally, contents refer to the mathematics curricula. According to the data collected, it seems that a 'positive' social representation of Roma may explain why some teachers do not segregate Roma addressing them to low-achievement groups with poor content (in mathematics), whereas other teachers holding 'negative' social representations about Roma use segregation strategies with them, lowering the curriculum, for instance. It is also the case that the same teacher may also project good expectation in one particular Roma student, whereas segregating other ones. Having a positive or negative social representation depends on the teacher attitude towards Roma identity, which is closely interlinked to teachers' personal beliefs. From the student point of view, the model works accordingly: confidence in the school (positive belief) is attached to a positive attitude in the classroom, as well as to the use of a variety of strategies to learn mathematics (such as prepare exams some days ahead, do homework, look for extra work, etc.). This is associated to a teacher's positive social representation of Roma as successful learner (in mathematics), as well. The individuals who show positive components in this LCM use to hold SLTs more likely than the ones who, at some point of their lives, had a (mainly) negative LCM.

Conclusion

The six narratives I have discussed here suggest that success happens (or is more likely to happen) when they have had positive LCMs. When all of the five components of the LCM (or most of them) are positive, then it is more likely that an individual would develop a SLT. On the contrary, when the negative component is prevailing, then is hard to see SLT as a result. Joaquim, for instance, at some point of his life dropped out the school because he was feeling resistance against the school institution.

According to him the main reason to explain such attitude was his negative social representation of "school" as something alien to his identity. This feeling could be, somehow, the result of being segregated by certain teachers holding negative expectations towards Roma students.

The role of the family plays a crucial role to overcome the difficulties and barriers that some Roma students face along their school trajectories. A significant amount of these barriers is connected to prejudice and negative social representations about Roma. Family may be a resource. However, sometimes this is not true because the members of the family did not have any opportunities or possibilities to study themselves. For this reason, they cannot become 'resources' to help their children to solve their mathematics assignments. But, according to [START_REF] Hoover-Dempsey | Why do parents become involved?: Research findings and implications[END_REF], the families can look for further resources to reinforce their children's learning. Recent studies suggest that family engagement in the school has major impact on learning than just appointing family members in the school to 'report' on children's behaviour (Díez-Palomar, Santos, & Alvarez 2013).

LCM may have the potential to explain both Roma's SLTs or the failure of many Roma children in the school, as narrated by Federico, Joaquim and the rest of their peers. In their narratives, they explain how many of their Roma peers used to be re-allocated to low-level classrooms, how teachers use to decide to lower the grades for them, cutting down on the curriculum, or asking them to do naive work (like painting) rather than problem solving or other high-mathematics-oriented tasks.

However, examples like the narratives by Federico or Joana may help us to understand how holding a positive identity connected to showing positive attitudes in the school, using different strategies to overcome the difficulties related to mathematics itself (epistemological, ontological, etc.), combined with high quality curricula and classroom organization, may end in the development of SLTs.

The model that I presented here is not generalizable. We need further quantitative studies to either accept or reject this approach. This would be the next step in the near future.

Figure 1 :

 1 Figure 1: Components of the Learning Core Matrix (LCM) associated to a SLT

Table 1 : Description of the participants in the study

 1 table 1).

	Pseudonym	Year of birth	Academic trajectory	Current situation
	Federico	1984	University degree	PhD candidate
	Joana	1990	University degree	PhD candidate
	Joaquim	1988	Elementary degree	Access > 25 years old
	José	1979	VET degree	Access > 25 years old
	Antonio	1978	Secondary degree	Access > 25 years old
	Aroa	1996	Upper secondary degree	Working

Table 2 : Coding categories for data analysis

 2

  In addition, my teachers of mathematics and biology used to give me extra homework. I remember that in 4 th grade -ESO [secondary educationmiddle school] I used to solve problems of 1 st grade -Bachillerato [secondaryhigh school], and this was very motivating for me. It was the opposite in Catalan or English, teachers used to reduce my tasks so I could pass them [with no work]. Not the case for Spanish: I also used to get difficult homework to do in the classroom or at home.(Federico)

Almost in one of three European countries "compulsory education" goes up to 16 years old. For more information, see: http://eacea.ec.europa.eu/education/eurydice/documents/facts_and_figures/compulsory_education_EN.pdf Thematic Working Group 10 Proceedings of CERME10

Proceedings of CERME10


A Malechaux

N Dupuy

J Artaud

VIRGIN OLIVE OILS: AUTHENTICATION AND DETECTION OF ADULTERATION Applications of vibrational spectroscopy techniques

Keywords: artificial neural networks ATR, attenuated total reflectance CP-ANN, counter-propagation artificial neural networks CVA, canonical variate analysis deuterated triglycine sulphate hierarchical cluster analysis IECVA, interval extended canonical variate analysis linear discriminant analysis mercury cadmium telluride- multivariate range modelling MSC, multiple scatter correction NCC, nearest centroid classification NMR, nuclear magnetic resonance NIR, near infrared PCA, principal component analysis PC-OSC, principal-component orthogonal signal correction QDA, quadratic discriminant analysis stepwise linear discriminant analysis SNV, standard normal variate SVM, support vector machine UNEQ, unequal dispersed classes UV, ultra-violet VOO, virgin olive oil

R 2 : coefficient of determination RMSEC: root mean square error of calibration RMSECV: root mean square error of cross-validation RMSEP: root mean square

INTRODUCTION

One of the main issues facing the food industry to this day is the authentication of its products. Due to their high price compared to other edible oils, especially when they benefit from a certification like the Protected Designation of Origin (PDO), Extra Virgin Olive Oils (EVOOs) and Virgin Olive Oils (VOOs) are an attractive target for fraudsters. They can indeed be subjected to more or less sophisticated fraudulent practices, the most common ones being the falsification or adulteration of VOOs with lower-price oils such as seed oils, refined olive oil or olive pomace oil. Many studies have thus been conducted in order to fight frauds that disrupt the market and deteriorate the positive image of VOOs.

First of all, the quality criteria which have been set by the International Olive Council (IOC) allow the classification of olive oils in different categories (extra virgin, virgin, lampante virgin) according to their free acidity, peroxide value, UV absorbance, alkyl esters contents and sensory properties. In the second place, molecular markers including fatty acids (Z and E), sterols, triterpene dialcohols, waxes or stigmastadienes are used to detect possible frauds.

However, the authentication of varietal or geographical origins, as well as the affiliation of a VOO to a PDO, often represent a real analytical challenge. Numerous research works, based on various physicochemical determinations associated with chemometric data processing, have sought to answer this problem. These studies can be classified into two main groups: those analysing the chemical composition of the oil, and those relying on spectroscopic techniques like nuclear magnetic resonance, infrared, Raman or fluorescence spectroscopies. For instance vibrational spectroscopic analyses, namely Near Infrared (NIR), Mid Infrared (MIR) and Raman, coupled with the predictive chemometric methods of Partial Least Squares (PLS) regression and PLS discriminant analysis (PLS-DA), have been successfully applied to the authentication of French VOOs from different PDOs. [START_REF] Dupuy | Comparison between NIR, MIR, Concatenated NIR and MIR Analysis and Hierarchical PLS Model. Application to Virgin Olive Oil Analysis[END_REF][START_REF] Korifi | Composition and Authentication of Virgin Olive Oil from French PDO Regions by Chemometric Treatment of Raman Spectra[END_REF] 1. BIBLIOMETRICS A quick search of the terms "olive oil", "authentication" and "spectroscopy" in Google Scholar, restricted to articles published between 1990 and 2016, gives an idea of the vast amount of studies on these subjects. Figure 1 also indicates that "olive oil" is almost 3 times more often associated with "spectroscopy" than with "authentication", however "spectroscopy" is present in 94% of the articles containing both "olive oil" and "authentication". This tends to show that olive oil authentication is often studied in relation with spectroscopic analyses but that these analytical techniques also have other purposes, such as characterisation of oil components or measurement of quality parameters. It can also be noted that the number of articles containing "olive oil" and "chromatography" is higher than that for "olive oil" and "spectroscopy". However, this is no longer the case when the term "authentication" is added.

A more specific search on Web of Science confirms that the authentication of virgin olive oil using vibrational spectroscopy has been a subject of interest since the 1990s, and even more so during the past 10 years. This is evidenced by the growing number of publications that are reported in Figure 2. The number of studies focused on NIR has been steadily increasing since 2002, while MIR has seen a more recent and sharper rise of interest. Raman spectroscopy used to be the most popular in the late 1990s and early 2000s, but has since then been overtaken by the other two techniques. On average, around 20% of the articles included experiments with at least two of the analytical methods of interest.

FIGURE 1: NUMBER OF ARTICLES CONTAINING THE WORDS "OLIVE OIL", "AUTHENTICATION", "SPECTROSCOPY" OR "CHROMATOGRAPHY" AND THEIR COMBINATIONS (GOOGLE SCHOLAR, 20 TH MARCH 2017, FIGURE NOT TO SCALE)

In the year 2016 alone, six reviews dealing with the applications of spectroscopic and/or chemometric methods for the quality control and authentication of VOOs have been published. [START_REF] Gómez-Caravaca | Chemometric Applications to Assess Quality and Critical Parameters of Virgin and Extra-Virgin Olive Oil. A Review[END_REF][START_REF] Messai | Chemometrics Methods for Specificity, Authenticity and Traceability Analysis of Olive Oils: Principles, Classifications and Applications[END_REF][START_REF] Nenadis | Perspective of Vibrational Spectroscopy Analytical Methods in on-Field/official Control of Olives and Virgin Olive Oil[END_REF][START_REF] Sørensen | The Use of Rapid Spectroscopic Screening Methods to Detect Adulteration of Food Raw Materials and Ingredients[END_REF][START_REF] Valli | Rapid and Innovative Instrumental Approaches for Quality and Authenticity of Olive Oils: Innovative Approaches for Quality of Virgin Olive Oils[END_REF][START_REF] Wang | Vibrational Spectroscopic Approaches for the Quality Evaluation and Authentication of Virgin Olive Oil[END_REF] Moreover, a book summing up the latest advances in food authenticity has also been edited and contains chapters regarding vibrational spectroscopy, chemometrics, the confirmation of geographical origin of food and the analysis of adulterated vegetable oils. [START_REF] Downey | Advances in Food Authenticity Testing[END_REF] The free software Wordle allowed the identification of the most frequently used keywords in the titles of the articles from the previous Web of Science search, and the result is presented in Figure 3. The terms "olive oil" and "spectroscopy" were removed in order to have a better view of the other words. Thus, the importance of Fourier-transform instruments and the predominance of studies using MIR over NIR and Raman spectroscopies appear. Other analytical techniques are mentioned, such as UVvisible, fluorescence or NMR spectroscopies, as well as the possibility to combine several methods. The association with chemometrics for multivariate analysis is also highlighted and a few specific models are cited, the most prominent one being PLS. The detection and quantification of extra-virgin or virgin olive oil adulteration with other vegetable or edible oils seems to be the main application, followed by the authentication or determination of geographical and varietal origins.

SPECTROSCOPY

Vibrational spectroscopic techniques, such as infrared and Raman spectroscopies, have gained in popularity during the past decades, and their applications to food analysis have been extensively studied. Compared to chromatographic methods they allow simple, non-destructive, time-and costsaving analyses. Moreover, technological advances like the introduction of interferometers, attenuated total reflection instruments or detectors with increased sensitivity and resolution made them more user-friendly. The spreading use of chemometrics has also significantly improved the ability to extract meaningful information from spectral data, and to obtain reliable quantitative results.

Vibrational spectroscopy relies on changes in the energy levels of the molecules, due to the interaction between a sample and an electromagnetic radiation. Each bond between two atoms has a characteristic vibration frequency depending on parameters such as the reduced mass of these two atoms and bending force constants. The excitation brought by the radiation causes the bonds to stretch or bend. In the case of infrared absorption the molecular vibration is related to a change in the intrinsic dipole moment, while Raman inelastic scattering depends on a change in the electronic polarizability of the molecule. The amount of energy absorbed by the sample also influences the vibrations, as summarised in Figure 4. In the MIR region (4000-400 cm -1 ), the transitions between energy levels correspond mainly to fundamental vibrations and a few overtones, whereas in the more energetic NIR area (12500-4000 cm -1 ) lower intensity bands of overtones and combinations of the fundamental vibrations can be observed. As a consequence, these three techniques provide complementary information about the chemical composition and physical state of a sample. For instance, some infrared absorption bands arise from polar groups such as C=O and O-H, while Raman spectra show more pronounced scattering bands for nonpolar groups like C=C or C-C. It also worth noting that Raman is prone to fluorescence interference, which can be reduced by using a Fourier Transform (FT) interferometer and a laser source of lower energy.

CHEMOMETRICS

Chemometrics is the use of multivariate statistical analyses to extract information from chemical data. Since its creation by Svante Wold and Bruce Kowalski in the 1970s [START_REF] Wold | Spline Functions in Data Analysis[END_REF][START_REF] Kowalski | Chemometrics: Views and Propositions[END_REF] different methods have been developed to serve various purposes, such as data pre-processing, qualitative or quantitative analysis.

Pre-treatment of raw spectra is often necessary to reduce the effect of interferences and artefacts on the subsequent development of a predictive model. Wavelet filtering [START_REF] Barclay | Application of Wavelet Transforms to Experimental Spectra: Smoothing, Denoising, and Data Set Compression[END_REF] or Savitzky-Golay (SG) smoothing [START_REF] Savitzky | Smoothing and Differentiation of Data by Simplified Least Squares Procedures[END_REF] can be used to improve the signal to noise ratio, while detrending or SG 1 st and 2 nd derivatives provide a correction of the baseline shift. Moreover, 2 nd derivative can resolve overlapping peaks. Other algorithms, like Standard Normal Variate (SNV) [START_REF] Barnes | Standard Normal Variate Transformation and De-Trending of Near-Infrared Diffuse Reflectance Spectra[END_REF] and Multiplicative Scatter Correction (MSC) [START_REF] Geladi | Linearization and Scatter-Correction for Near-Infrared Reflectance Spectra of Meat[END_REF] , are useful when both additive and multiplicative effects caused by light scattering are present. Normalisation or scaling can also be applied to ensure that each spectrum has the same importance in the model.

Before the development of analytical models, the spectral data can be explored through Principal Component Analysis (PCA) [START_REF] Hotelling | Analysis of a Complex of Statistical Variables into Principal Components[END_REF][START_REF] Wold | Principal Component Analysis[END_REF] which decomposes the initial matrix into sets of scores and loadings allowing to reduce its dimensions. When enough variability is taken into account by the PCs, the loadings show which variables have more influence on the PCs and a representation of the scores can provide insight into the similarities among samples or the presence of outliers.

The discrimination between oils of different botanical, varietal or geographical origins involves the use of qualitative analyses. Unsupervised classification methods, such as Hierarchical Cluster Analysis (HCA) [START_REF] Bridges | Hierarchical Cluster Analysis[END_REF] , separate the samples into different groups without prior knowledge of their category membership. On the other hand, supervised methods like classification by Linear Discriminant Analysis (LDA) [START_REF] Fisher | The Use of Multiple Measurements in Taxonomic Problems[END_REF] or class-modelling by Soft Independent Modelling of Class Analogy (SIMCA) [START_REF] Wold | SIMCA: A Method for Analyzing Chemical Data in Terms of Similarity and Analogy[END_REF] , assign new samples to previously defined categories. LDA reduces the space dimensions by selecting directions that maximise the separation between classes, whereas SIMCA performs a PCA on each class to minimise its internal differences. More recently, artificial intelligence algorithms such as Artificial Neural Networks (ANN) [START_REF] Kohonen | The Self-Organizing Map[END_REF] have been developed to categorise samples after a phase of training by iterative adjustments.

The development of quantitative models is required to determine the amount of adulterant that may have been added to a sample. Multiple Linear Regression (MLR) [START_REF] Brown | Matrix Representations and Criteria for Selecting Analytical Wavelengths for Multicomponent Spectroscopic Analysis[END_REF] , Partial Least Squares (PLS) [START_REF] Geladi | Partial Least-Squares Regression: A Tutorial[END_REF] or Principal Component Regression (PCR) [START_REF] Jolliffe | A Note on the Use of Principal Components in Regression[END_REF] are the most commonly used methods. They are based on the construction of a linear relationship between the variations of spectral data and the chemical parameter to be explained. However, other methods using non-linear models, such as ANN or Support Vector Machines (SVM) [START_REF] Cortes | Support-Vector Networks[END_REF] , also have the ability to perform quantitative analyses. [START_REF] Gómez-Caravaca | Chemometric Applications to Assess Quality and Critical Parameters of Virgin and Extra-Virgin Olive Oil. A Review[END_REF][START_REF] Harwood | [END_REF][START_REF] Engel | Breaking with Trends in Pre-Processing? Trends Anal[END_REF] 4. NEAR INFRARED SPECTROSCOPY

Spectra interpretation

As can be seen in Figure 5, characteristic NIR absorbance bands arise in several regions of the EVOO spectrum. Region A (8700-8000 cm -1 ) is attributed to the 2 nd overtone of C-H stretching vibrations, while B (7400-6700 cm -1 ) results from combinations of C-H stretching and bending, and C (6000-5500 cm -1 ) corresponds to the 1 st overtone of C-H stretching vibrations. These three regions contain information regarding the degree of unsaturation of the fatty acids and triacylglycerols present in a sample. The two bands in region D (5300-5100 cm -1 ) have been attributed to the 2 nd overtone of C=O stretching vibration from carbonyl functional groups. Finally, region E (5000-4500 cm -1 ) presents combination bands of =C-H and C=C stretching vibrations. 9,11,29,30

Identification of Virgin Olive Oils vs other oils

The first step of authentication is to differentiate olive oil from other oils and fats. This can be achieved through the analysis of their major compounds, such as fatty acids and triacylglycerols, usually conducted by gas chromatography and high performance liquid chromatography respectively. However, differences in the composition of the samples are also reflected in their NIR spectra, as can be seen in the examples presented in Table 1. Hourant et al. [START_REF] Hourant | Oil and Fat Classification by Selected Bands of Near-Infrared Spectroscopy[END_REF] indeed showed that the absorption intensity of the bands around 5814 cm -1 (1720 nm), 4668 cm -1 (2142 nm) and 4595 cm -1 (2176 nm) could be related to the degree of total unsaturation in the sample. This allowed the classification of eighteen different oils and fats with the modelling of a dendroid structure based on seven linear discriminant functions. Yang et al. [START_REF] Yang | Discriminant Analysis of Edible Oils and Fats by FTIR, FT-NIR and FT-Raman Spectroscopy[END_REF] confirmed that LDA could discriminate pure edible oils and fats using FT-NIR spectra, but obtained more satisfying classification rates with Canonical Variate Analysis (CVA).

Adulteration of Virgin Olive Oils with other oils

Several articles focusing on the ability of NIR to analyse binary mixtures of VOOs with other kinds of oils have been published over the past 20 years (Table 2). Dispersive and FT-NIR have been equally used in these studies, and three of them report results obtained with a fibre optic probe although not in an on-line setting [START_REF] Mignani | Visible and near-Infrared Absorption Spectroscopy by an Integrating Sphere and Optical Fibers for Quantifying and Discriminating the Adulteration of Extra Virgin Olive Oil from Tuscany[END_REF][START_REF] Azizian | Rapid Identification, and Quantification of Adulterants in Extra Virgin Olive Oil Using Near-Infrared Spectroscopy and Chemometrics[END_REF][START_REF] Yang | Comparison of near-Infrared, Fourier Transform-Infrared, and Fourier Transform-Raman Methods for Determining Olive Pomace Oil Adulteration in Extra Virgin Olive Oil[END_REF] .

Downey et al. [START_REF] Downey | Detecting and Quantifying Sunflower Oil Adulteration in Extra Virgin Olive Oils from the Eastern Mediterranean by Visible and Near-Infrared Spectroscopy[END_REF] developed a SIMCA model that gave 100% of correct classification for VOOs versus adulterated samples containing 1 to 5% of sunflower oil. Karunathilaka et al. [START_REF] Karunathilaka | Rapid Screening of Extra Virgin Olive Oil Products for Authenticity Using Near-Infrared Spectroscopy in Combination with Conformity Index and Multivariate Statistical Analyses[END_REF] also applied SIMCA to FT-NIR spectra to successfully detect the addition of 10 to 20% of various vegetable oils in EVOOs. Mignani et al. [START_REF] Mignani | Visible and near-Infrared Absorption Spectroscopy by an Integrating Sphere and Optical Fibers for Quantifying and Discriminating the Adulteration of Extra Virgin Olive Oil from Tuscany[END_REF] obtained spectra through an integrating sphere and fibre optic detector. In this study, the application of PCA followed by LDA enabled the discrimination between EVOOs adulterated with refined olive oil, deodorised olive oil, olive pomace oil and refined olive pomace oil, with 75% of correct classification.

In addition to the detection of adulteration, most of the articles are interested in the use of regression models to quantify the amount of adulterant. For instance, Downey et al. [START_REF] Downey | Detecting and Quantifying Sunflower Oil Adulteration in Extra Virgin Olive Oils from the Eastern Mediterranean by Visible and Near-Infrared Spectroscopy[END_REF] , Wesley et al. [START_REF] Wesley | Measurement of Adulteration of Olive Oils by near-Infrared Spectroscopy[END_REF] and Christy et al. [START_REF] Christy | The Detection and Quantification of Adulteration in Olive Oil by Near-Infrared Spectroscopy and Chemometrics[END_REF] applied PLS regression after various pre-treatments to predict the amount of sunflower oil added to olive oil. They all obtained R 2 values superior to 0.9 and Standard Errors of Prediction (SEP) under 2%. The analysis of VOOs adulterated with maize, soya, rapeseed, safflower, peanut, walnut, hazelnut or palm oils yielded similar results according to Azizian et al. [START_REF] Azizian | Rapid Identification, and Quantification of Adulterants in Extra Virgin Olive Oil Using Near-Infrared Spectroscopy and Chemometrics[END_REF] , Wesley et al. [START_REF] Wesley | Measurement of Adulteration of Olive Oils by near-Infrared Spectroscopy[END_REF] , Christy et al. [START_REF] Christy | The Detection and Quantification of Adulteration in Olive Oil by Near-Infrared Spectroscopy and Chemometrics[END_REF] and Mendes et al. [START_REF] Mendes | Quantification of Extra-Virgin Olive Oil Adulteration with Soybean Oil: A Comparative Study of NIR, MIR, and Raman Spectroscopy Associated with Chemometric Approaches[END_REF] . The latter constructed different models to quantify the addition of high linoleic oils, high oleic oils or palm olein, based on the absorption ratio at 5280 and 5180 cm -1 , attributed respectively to volatile and non-volatile compounds. Mignani et al. [START_REF] Mignani | Visible and near-Infrared Absorption Spectroscopy by an Integrating Sphere and Optical Fibers for Quantifying and Discriminating the Adulteration of Extra Virgin Olive Oil from Tuscany[END_REF] , Azizian et al. [START_REF] Azizian | Rapid Identification, and Quantification of Adulterants in Extra Virgin Olive Oil Using Near-Infrared Spectroscopy and Chemometrics[END_REF] , Yang and Irudayraj [START_REF] Yang | Comparison of near-Infrared, Fourier Transform-Infrared, and Fourier Transform-Raman Methods for Determining Olive Pomace Oil Adulteration in Extra Virgin Olive Oil[END_REF] , Wesley et al. [START_REF] Wesley | Measurement of Adulteration of Olive Oils by near-Infrared Spectroscopy[END_REF] and Wojcicki et al. [START_REF] Wójcicki | Spectroscopic Techniques and Chemometrics in Analysis of Blends of Extra Virgin with Refined and Mild Deodorized Olive Oils: Spectroscopic Techniques and Chemometrics in Analysis of Blends of Olive Oils[END_REF] also tried to quantify the adulteration of EVOOs by refined olive oil or olive pomace oil. These studies tend to show higher errors of prediction, ranging from 1.78 to 13%, which may be due to the higher similarity between the composition of pure and adulterated samples. Finally, Ozedmir and Ozturk 42 developed a Genetic Inverse Least Square model, capable of predicting the concentration of tertiary mixtures with SEP of 1.42%, 5.42% and 6.38% for the amount of VOO, sunflower oil and maize oil respectively.

| 11

Authentication of geographical or varietal origins

The most recent and prominent application of NIR spectroscopy has been the classification of VOOs according to their geographical or varietal origins. Table 3 summarises some of the articles published on this subject, with a majority preferring FT-NIR to dispersive instruments.

The potential of PLS-DA modelling applied to NIR spectra to discriminate VOOs from different cultivars or regions of origin has been highlighted by several authors, amongst which Dupuy et al. [START_REF] Dupuy | Comparison between NIR, MIR, Concatenated NIR and MIR Analysis and Hierarchical PLS Model. Application to Virgin Olive Oil Analysis[END_REF] , Sinelli et al.

43

, Woodcock et al. [START_REF] Woodcock | Confirmation of Declared Provenance of European Extra Virgin Olive Oil Samples by NIR Spectroscopy[END_REF] , Galtier et al. [START_REF] Galtier | Comparison of PLS1-DA, PLS2-DA and SIMCA for Classification by Origin of Crude Petroleum Oils by MIR and Virgin Olive Oils by NIR for Different Spectral Regions[END_REF] and Bevilacqua et al. [START_REF] Bevilacqua | Tracing the Origin of Extra Virgin Olive Oils by Infrared Spectroscopy and Chemometrics: A Case Study[END_REF] . Indeed, all of them obtained 85 to 100% of correct classification rates. Other discriminant analysis algorithms, like FDA or LDA, have also been rather successfully tested by Downey et al. [START_REF] Downey | Geographic Classification of Extra Virgin Olive Oils From the Eastern Mediterranean by Chemometric Analysis of Visible and Near-Infrared Spectroscopic Data[END_REF] , Casale et al. [START_REF] Casale | Chemometrical Strategies for Feature Selection and Data Compression Applied to NIR and MIR Spectra of Extra Virgin Olive Oils for Cultivar Identification[END_REF] and Sinelli et al. [START_REF] Sinelli | Varietal Discrimination of Extra Virgin Olive Oils by near and Mid Infrared Spectroscopy[END_REF] . Class modelling techniques such as SIMCA seem to give less satisfying results overall, although Casale et al. [START_REF] Casale | Near Infrared Spectroscopy and Class Modelling Techniques for the Geographical Authentication of Ligurian Extra Virgin Olive Oil[END_REF] , Oliveri et al. [START_REF] Oliveri | Application of Class-Modelling Techniques to near Infrared Data for Food Authentication Purposes[END_REF] and Laroussi-Mezghani et al. [START_REF] Laroussi-Mezghani | Authentication of Tunisian Virgin Olive Oils by Chemometric Analysis of Fatty Acid Compositions and NIR Spectra. Comparison with Maghrebian and French Virgin Olive Oils[END_REF] managed to correctly predict the origin of 84.5 to 98.5% of their samples. Oliveri et al. [START_REF] Oliveri | Application of Class-Modelling Techniques to near Infrared Data for Food Authentication Purposes[END_REF] , Casale et al. [START_REF] Casale | Characterisation of PDO Olive Oil Chianti Classico by Non-Selective (UV-visible, NIR and MIR Spectroscopy) and Selective (Fatty Acid Composition) Analytical Techniques[END_REF] and Forina et al. [START_REF] Forina | Artificial Nose, NIR and UV-visible Spectroscopy for the Characterisation of the PDO Chianti Classico Olive Oil[END_REF] also used POTFUN or UNEQ class models giving 83 to 100% of correct classification. In another study, Oliveri et al. [START_REF] Oliveri | Comparison between Classical and Innovative Class-Modelling Techniques for the Characterisation of a PDO Olive Oil[END_REF]

MID INFRARED SPECTROSCOPY

Spectra interpretation

Figure 6 shows a characteristic MIR spectrum of EVOO, presenting sharper absorption bands than the NIR spectrum. Band A, around 3005 cm -1 , is associated to the =C-H stretching vibrations of cis (Z) double bonds. Bands B and C (2920 and 2850 cm -1 ) arise respectively from C-H aliphatic asymmetric and symmetric stretching vibrations. D (1740 cm -1 ) corresponds to the C=O stretching of carbonyl groups, and E (1650 cm -1 ) to C=C stretching vibrations. The fingerprinting region, under 1500 cm -1 , presents overlapping peaks that are less easily attributed. However, region F between 1500 and 1300 cm -1 can be related to C-H aliphatic bending vibrations and region G (1250-1000 cm -1 ) to C-C and C-O bending vibrations. Finally, band H (700 cm -1 ) is attributed to the C-H bending of CH2. 9,11,29,30

Identification of Virgin Olive Oils vs other oils

The discrimination between VOOs and other fats and oils has been more extensively studied using MIR than NIR spectroscopy, and always with FT instruments (Table 4).

Several authors, such as Lai et al. [START_REF] Lai | Potential of Fourier Transform Infrared Spectroscopy for the Authentication of Vegetable Oils[END_REF] , Marigheto et al. [START_REF] Marigheto | A Comparison of Mid-Infrared and Raman Spectroscopies for the Authentication of Edible Oils[END_REF] , Tay et al. [START_REF] Tay | Authentication of Olive Oil Adulterated with Vegetable Oils Using Fourier Transform Infrared Spectroscopy[END_REF] , Obeidat et al. [START_REF] Obeidat | Classification of Edible Oils and Uncovering Adulteration of Virgin Olive Oil Using FTIR with the Aid of Chemometrics[END_REF] , Lerma-Garcia et al. [START_REF] Lerma-García | Authentication of Extra Virgin Olive Oils by Fourier-Transform Infrared Spectroscopy[END_REF] , de la Mata et al. [START_REF] De La Mata | Oil Assessment in Edible Oil Blends by Means of ATR-FTIR and Chemometrics[END_REF] , reported a classification rate of 100% with the use of various discriminant analysis techniques including PLS-DA and LDA. Javidnia et al. [START_REF] Javidnia | Discrimination of Edible Oils and Fats by Combination of Multivariate Pattern Recognition and FT-IR Spectroscopy: A Comparative Study between Different Modeling Methods[END_REF] reached the same result by using interval extended canonical variate analysis (iECVA). Yang et al. [START_REF] Yang | Discriminant Analysis of Edible Oils and Fats by FTIR, FT-NIR and FT-Raman Spectroscopy[END_REF] obtained better results with CVA applied to MIR spectra of olive and sunflower oils compared to NIR, since 98.9% of the samples were correctly classified versus 92.2% for NIR spectra. In two different studies, Baeten identified refined olive oil and hazelnut oil using either ANN [START_REF] Baeten | The Use of FT-MIR Spectroscopy and Counter-Propagation Artificial Neural Networks for Tracing the Adulteration of Olive Oil[END_REF] or stepwise linear discriminant analysis (SLDA) [START_REF] Baeten | Detection of the Presence of Hazelnut Oil in Olive Oil by FT-Raman and FT-MIR Spectroscopy[END_REF] .

FIGURE 6: MID INFRARED SPECTRUM OF EVOO WITH IDENTIFICATION OF MAIN ABSORBANCE BANDS

| 15

Adulteration of Virgin Olive Oils with other oils

Numerous articles, gathered in Table 5, focus on the qualitative or quantitative analysis of mixtures of olive oil and other oils based on MIR data. Once again, only FT-MIR instruments were used.

Marigheto et al. [START_REF] Marigheto | A Comparison of Mid-Infrared and Raman Spectroscopies for the Authentication of Edible Oils[END_REF] applied LDA after data compression by PLS and obtained 99% correct classification for olive oil adulterated with as little as 5% of various vegetable oils. Similarly, Oussama et al. [START_REF] Oussama | Detection of Olive Oil Adulteration Using FT-IR Spectroscopy and PLS with Variable Importance of Projection (VIP) Scores[END_REF] used PLS-DA after variable selection to correctly classify 100% of the samples containing 1 to 24% of soya or sunflower oils, and de la Mata et al. [START_REF] De La Mata | Oil Assessment in Edible Oil Blends by Means of ATR-FTIR and Chemometrics[END_REF] to discriminate between VOOs adulterated with more and less than 50% of other oils. Discriminant analyses also allowed Tay et al. [START_REF] Tay | Authentication of Olive Oil Adulterated with Vegetable Oils Using Fourier Transform Infrared Spectroscopy[END_REF] to successfully detect the addition of 2 to 10% of sunflower oil, while Rohman and Che Man reached 100% correct classification for samples adulterated with palm oil [START_REF] Rohman | Fourier Transform Infrared (FTIR) Spectroscopy for Analysis of Extra Virgin Olive Oil Adulterated with Palm Oil[END_REF] , lard [START_REF] Rohman | FTIR Spectroscopy Combined with Chemometrics for Analysis of Lard Adulteration in Some Vegetable Oils Espectroscopia FTIR Combinada Con Quimiometría Para El Análisis de Adulteración Con Grasa de Cerdo de Aceites Vegetales[END_REF] , rice bran oil [START_REF] Rohman | The Chemometrics Approach Applied to FTIR Spectral Data for the Analysis of Rice Bran Oil in Extra Virgin Olive Oil[END_REF] , maize and sunflower oils [START_REF] Rohman | Quantification and Classification of Corn and Sunflower Oils as Adulterants in Olive Oil Using Chemometrics and FTIR Spectra[END_REF] and 97.4% with rapeseed oil [START_REF] Rohman | The Use of FTIR Spectroscopy and Chemometrics for Rapid Authentication of Extra Virgin Olive Oil[END_REF] . Other techniques seem to give satisfying results, for instance Sun et al. [START_REF] Sun | Detection and Quantification of Extra Virgin Olive Oil Adulteration with Edible Oils by FT-IR Spectroscopy and Chemometrics[END_REF] [START_REF] Mendes | Quantification of Extra-Virgin Olive Oil Adulteration with Soybean Oil: A Comparative Study of NIR, MIR, and Raman Spectroscopy Associated with Chemometric Approaches[END_REF] and Maggio et al. [START_REF] Maggio | A Novel Chemometric Strategy for the Estimation of Extra Virgin Olive Oil Adulteration with Edible Oils[END_REF] had higher errors of prediction for the analysis of added olive pomace oil, soya oi and hazelnut oil respectively. PCR was usually shown to be less efficient than PLS regression, except for Jovic et al. [START_REF] Jović | Spectroscopic and Chemometric Analysis of Binary and Ternary Edible Oil Mixtures: Qualitative and Quantitative Study[END_REF] who managed to quantify the amounts of olive oil, sunflower, high oleic sunflower and rapeseed oils in binary and ternary mixtures with R 2 over 0.99 and RMSEP under 2.3%. Another method, based on linear regression between the amount of adulterant and a ratio of peak heights, was applied by Vlachos et al. [START_REF] Vlachos | Applications of Fourier Transform-Infrared Spectroscopy to Edible Oils[END_REF] and Poiana et al. [START_REF] Poiana | Use of ATR-FTIR Spectroscopy to Detect the Changes in Extra Virgin Olive Oil by Adulteration with Soybean Oil and High Temperature Heat Treatment[END_REF] using the absorbance at 3006 and 2925 cm -1 which can be related to the degree of unsaturation. Allam and Hamed 84 employed a similar method, but focused on the peaks at 1118 and 1097 cm -1 that were assigned to C-O stretching.

Authentication of geographical or varietal origins

Similarly to NIR, the ability of FT-MIR spectroscopy to differentiate VOOs from various origins has been the subject of numerous research works, as can be seen in Table 6.

EVOOs from three different Italian regions were correctly classified by Sinelli et al. [START_REF] Sinelli | Characterisation and Classification of Italian Virgin Olive Oils by near-and Mid-Infrared Spectroscopy[END_REF] using PLS-DA, while Galtier et al. [START_REF] Galtier | Lipid Compositions and French Registered Designations of Origins of Virgin Olive Oils Predicted by Chemometric Analysis of Mid-Infrared Spectra[END_REF] discriminated virgin olive oils from France and other countries with the same technique. Moreover, PLS-DA allowed Galtier et al. [START_REF] Galtier | Lipid Compositions and French Registered Designations of Origins of Virgin Olive Oils Predicted by Chemometric Analysis of Mid-Infrared Spectra[END_REF] and Dupuy et al. [START_REF] Dupuy | Comparison between NIR, MIR, Concatenated NIR and MIR Analysis and Hierarchical PLS Model. Application to Virgin Olive Oil Analysis[END_REF] to reach a correct classification of 96% and 98% respectively between VOOs from the six French PDOs, with samples collected over several harvest years. Bevilacqua et al. [START_REF] Bevilacqua | Tracing the Origin of Extra Virgin Olive Oils by Infrared Spectroscopy and Chemometrics: A Case Study[END_REF] also correctly identified 92.3% of the samples from PDO Sabina versus other Mediterranean regions by applying PLS-DA to MIR data, even though NIR data provided better results. De Luca et al. [START_REF] De Luca | Derivative FTIR Spectroscopy for Cluster Analysis and Classification of Morocco Olive Oils[END_REF] built a model based on PLS-DA after cluster analysis and variable selection by Martens test to separate VOOs from 4 Moroccan regions, and obtained satisfactory results with R 2 over 0.986 and RMSEP under 0.049. LDA has also been used by several authors. For instance, Tapp et al. [START_REF] Tapp | FTIR Spectroscopy and Multivariate Analysis Can Distinguish the Geographic Origin of Extra Virgin Olive Oils[END_REF] applied it after variable selection by genetic algorithm (GA), resulting in a correct classification rate of 100% for the country of origin of VOO samples. Casale et al; [START_REF] Casale | Chemometrical Strategies for Feature Selection and Data Compression Applied to NIR and MIR Spectra of Extra Virgin Olive Oils for Cultivar Identification[END_REF] and Sinelli et al. [START_REF] Sinelli | Varietal Discrimination of Extra Virgin Olive Oils by near and Mid Infrared Spectroscopy[END_REF] both obtained a correct classification of 86.6% between three Italian cultivars with LDA after variable selection, and Abdallah et al. [START_REF] Abdallah | Cultivar Discrimination and Prediction of Mixtures of Tunisian Extra Virgin Olive Oils by FTIR: EVOO Prediction of Cultivar and Mixtures by FTIR and LDA[END_REF] correctly classified 100% of the samples from seven Tunisian cultivars. Additionally, in this last study the concentrations of binary mixtures of cultivars were predicted by MLR, giving R 2 over 0.956 and SEP under 3.88%. Although supposedly less efficient than discriminant analyses, SIMCA was applied by Gurdeniz in several studies [START_REF] Gurdeniz | Differentiation of Mixtures of Monovarietal Olive Oils by Mid-Infrared Spectroscopy and Chemometrics[END_REF][START_REF] Gurdeniz | Classification of Turkish Olive Oils with Respect to Cultivar, Geographic Origin and Harvest Year, Using Fatty Acid Profile and Mid-IR Spectroscopy[END_REF][START_REF] Gurdeniz | Comparison of Fatty Acid Profiles and Mid-Infrared Spectral Data for Classification of Olive Oils[END_REF] and allowed the discrimination of Turkish olive oils according to their region of origin, harvest year and cultivar. PLS regression was also used to predict the concentration of cultivars in binary mixtures with R 2 between 0.84 and 0.91 and RMSEP between 3.14 and 20.9%. In another study, Casale et al. [START_REF] Casale | Characterisation of PDO Olive Oil Chianti Classico by Non-Selective (UV-visible, NIR and MIR Spectroscopy) and Selective (Fatty Acid Composition) Analytical Techniques[END_REF] developed a UNEQ model and achieved a correct classification of 92.5% between olive oils from PDO Chianti Classico and other Italian regions. This was however a less satisfactory result than that obtained with NIR data. Finally, SVM analyses were employed by Devos et al. [START_REF] Devos | Simultaneous Data Pre-Processing and SVM Classification Model Selection Based on a Parallel Genetic Algorithm Applied to Spectroscopic Data of Olive Oils[END_REF] and Caetano et al. [START_REF] Caetano | Geographical Classification of Olive Oils by the Application of CART and SVM to Their FT-IR[END_REF] , resulting in mixed outcomes. 6. RAMAN SPECTROSCOPY

Spectra interpretation

The Raman spectrum of EVOO presented in Figure 7 gives complementary information compared to the MIR spectrum. Peak A (1750 cm -1 ) results from C=O stretching vibrations, and peak B (1660 cm -1 ) is related to cis C=C stretching. They correspond to the peaks D and E of the MIR spectrum, although their relative intensities are reversed. The two peaks labelled C (1450-1300 cm -1 ) are associated with C-H aliphatic bending vibrations, thus matching the region F of the MIR spectrum. Peak D, at 1270 cm -

1

, is attributed to =C-H bending vibrations of cis double bonds and is not identified on the MIR spectrum. Region E (1150-800 cm -1 ) is also characteristic of the Raman spectrum and related to C-C stretching vibrations. 9,11,29,30

Identification of Virgin Olive Oils vs other oils

Although it is less frequently used than NIR or MIR, several authors have studied the potential of Raman spectroscopy to authenticate olive oils (Table 7). In this case, as for MIR, only FT-Raman instruments were used.

Baeten et al. [START_REF] Baeten | Oil and Fat Classification by FT-Raman Spectroscopy[END_REF][START_REF] Baeten | Edible Oils and Fats Authentication by Fourier Transform Raman Spectrometry[END_REF] demonstrated the ability of Raman spectra to discriminate between various oils and fats, including VOO. SLDA indeed allowed to classify the samples depending on their saturated, monounsaturated and poly-unsaturated fatty acids content. In another study [START_REF] Baeten | Detection of the Presence of Hazelnut Oil in Olive Oil by FT-Raman and FT-MIR Spectroscopy[END_REF] , SLDA on selected variables related to unsaponifiable matter gave a correct classification of 95% between refined olive oil and hazelnut oil, which is a similar result to that obtained with MIR data. Marigheto et al. [START_REF] Marigheto | A Comparison of Mid-Infrared and Raman Spectroscopies for the Authentication of Edible Oils[END_REF] reached a correct classification rate of 93% for EVOO versus other vegetable oils with LDA after data compression by PCA, although the same method applied to MIR spectra correctly identified 100% of the samples. Similar results were obtained by Yang et al. [START_REF] Yang | Discriminant Analysis of Edible Oils and Fats by FTIR, FT-NIR and FT-Raman Spectroscopy[END_REF] using CVA after Raman data treatment by PLS, which gave 94.4% correct classification.

Adulteration of Virgin Olive Oils with other oils

Table 8 presents some articles studying the ability of Raman spectroscopy to detect and quantify the adulteration of VOOs. A majority of these works used FT-Raman, but an interest for confocal benchtop and handheld instruments can be noticed.

Marigheto et al [START_REF] Marigheto | A Comparison of Mid-Infrared and Raman Spectroscopies for the Authentication of Edible Oils[END_REF] employed Raman spectroscopy to detect the adulteration of EVOOs with different vegetable oils and reached a correct classification of 97% with PLSR, but these results were less satisfactory than with MIR spectra. Baeten et al. [START_REF] Baeten | Detection of the Presence of Hazelnut Oil in Olive Oil by FT-Raman and FT-MIR Spectroscopy[END_REF][START_REF] Baeten | Edible Oils and Fats Authentication by Fourier Transform Raman Spectrometry[END_REF] also showed that SLDA could discriminate genuine olive oil from adulterated samples, and even obtained a correct classification of 97.5% for samples of refined olive oil adulterated with as little as 2% of hazelnut oil. A method involving Raman measurements at increasing temperatures to enhance spectral differences between pure and adulterated samples was successfully tested by Kim et al. [START_REF] Kim | Use of Temperature Dependent Raman Spectra to Improve Accuracy for Analysis of Complex Oil-Based Samples: Lube Base Oils and Adulterated Olive Oils[END_REF] . Temperatures of 80 and 90°C allowed a correct classification of 100% by applying LDA on the PCA scores of the spectra.

Regarding quantitative analyses, several authors such as Mendes et al. [START_REF] Mendes | Quantification of Extra-Virgin Olive Oil Adulteration with Soybean Oil: A Comparative Study of NIR, MIR, and Raman Spectroscopy Associated with Chemometric Approaches[END_REF]

Authentication of geographical or varietal origins

Few studies have been published regarding the confirmation of VOOs declared geographical origin or cultivar with Raman spectroscopy, all of them using confocal instruments, as shown in Table 9.

Korifi et al. [START_REF] Korifi | Composition and Authentication of Virgin Olive Oil from French PDO Regions by Chemometric Treatment of Raman Spectra[END_REF] applied PLS-DA to Raman spectra, yielding a correct classification of 92.3% for the six French PDOs with samples collected over several harvest years. A similar method gave Sanchez-Lopez et al. 103 a correct classification of 86.6% for three Andalusian PDOs. In this study, PLS-DA on Raman data was also able to discriminate the EVOOs based on their harvest year, region of origin and olive variety with correct results of 94.3%, 89% and 84% respectively. Finally, Gouvinhas et al. 104 used LDA to correctly classify 81.9% of Portuguese EVOO samples depending on their maturation stages.

MULTIBLOCK ANALYSIS -CONCATENATION OF SPECTRAL DATA

Adulteration of Virgin Olive Oils with other oils

A couple of studies focusing on the combination of data from several analytical methods have recently been published and are presented in Table 10.

Wojcicki et al. [START_REF] Wójcicki | Spectroscopic Techniques and Chemometrics in Analysis of Blends of Extra Virgin with Refined and Mild Deodorized Olive Oils: Spectroscopic Techniques and Chemometrics in Analysis of Blends of Olive Oils[END_REF] applied PLS regression to concatenated data from NIR, MIR, visible and fluorescence spectra, yielding a R 2 of 0.96 and RMSEP of 4.1%. However these results showed no significant improvement compared to those obtained with separate spectra. On the other hand, Nigri and Oumeddour 105 obtained better results with concatenated MIR and fluorescence data than with individual datasets. In this case, PLS regression gave a R 2 of 0.992 and RMSECV of 2.67.

Authentication of geographical or varietal origins

Diverging conclusions have been drawn regarding the usefulness of spectral data concatenation for the authentication of virgin olive oils, as can be seen in the articles from Table 11.

Harrington et al. 106 reached 100% of correct classification between oils from five French PDOs by applying Principal-Component Orthogonal Signal Correction (PC-OSC) and PLS-DA to fused NIR and MIR data. However, this result was not compared to that obtained with each technique alone. In another study, Dupuy et al. [START_REF] Dupuy | Comparison between NIR, MIR, Concatenated NIR and MIR Analysis and Hierarchical PLS Model. Application to Virgin Olive Oil Analysis[END_REF] obtained 99% of correct classification for six French PDOs with PLS-DA on concatenated NIR and MIR spectra, but this did not significantly improve the result compared to MIR data alone. On the contrary, in three different articles [START_REF] Casale | Chemometrical Strategies for Feature Selection and Data Compression Applied to NIR and MIR Spectra of Extra Virgin Olive Oils for Cultivar Identification[END_REF][START_REF] Casale | Characterisation of PDO Olive Oil Chianti Classico by Non-Selective (UV-visible, NIR and MIR Spectroscopy) and Selective (Fatty Acid Composition) Analytical Techniques[END_REF]107 , Casale et al. obtained an improved rate of correct classification by combining data from various analytical instruments. For instance, LDA on fused NIR and MIR spectra gave a correct classification rate of 90.2% for three Italian cultivars, versus respectively 82.9% and 86.6% for NIR and MIR data alone [START_REF] Casale | Chemometrical Strategies for Feature Selection and Data Compression Applied to NIR and MIR Spectra of Extra Virgin Olive Oils for Cultivar Identification[END_REF] . UNEQ class modelling applied to combined NIR, MIR and UV-visible spectral data gave a correct classification of 100% for PDO olive oil Chianti Classico and improved the predictive ability of the model [START_REF] Casale | Characterisation of PDO Olive Oil Chianti Classico by Non-Selective (UV-visible, NIR and MIR Spectroscopy) and Selective (Fatty Acid Composition) Analytical Techniques[END_REF]

CONCLUSION

Bibliometric results show a growing interest in vibrational spectroscopic techniques as an alternative method for the authentication of VOOs and EVOOs. The ability of NIR, MIR and Raman spectroscopies to detect and quantify the adulteration of VOOs with cheaper oils, and to identify the geographical or varietal origins of samples, has been demonstrated in numerous research works. Even though MIR is more often studied, no significant difference appears in the quality of the results obtained with the three techniques. Thus, this apparent preference may be due to the greater availability of MIR instruments. Despite these promising results, vibrational spectroscopic techniques are not currently recognised as reference analytical methods by international standards and regulations.

The importance of chemometrics pre-treatment and modelling, allowing to treat the large amount of complex data generated by the vibrational spectroscopic analyses, should also be noted. Indeed, NIR, MIR and Raman spectra represent "fingerprints" of the samples, and only chemometrics can reveal the slight differences between two VOOs spectra.

In the future, more studies could be focused on the use of multiblock models to explore the interest of combining complementary information from several analytical techniques. The use of on-line instruments, for instance with fibre optic probes, could be an interesting way to monitor the varietal origin and quality parameters during olive oil extraction. However, the issue of NIR, MIR and Raman instrumental drift should be addressed if they are to be used on a routine basis.

FIGURE 2 :FIGURE 3 :

 23 FIGURE 2: EVOLUTION OF THE NUMBER OF PUBLICATIONS FOUND FOR THE QUERY "OLIVE OIL" AND AUTHENTIC* AND (NIR OR "NEAR INFRARED") OR (MIR OR "MID INFRARED") OR RAMAN (WEB OF SCIENCE, 20 TH MARCH 2017)

FIGURE 4 :

 4 FIGURE 4: SPECTROSCOPIC TECHNIQUES RELATED TO THE INFRARED REGION OF THE ELECTROMAGNETIC SPECTRUM

FIGURE 5 :

 5 FIGURE 5: NEAR INFRARED SPECTRUM OF EVOO WITH IDENTIFICATION OF MAIN ABSORBANCE BANDS

FIGURE 7 :

 7 FIGURE 7: RAMAN SPECTRUM OF EVOO WITH IDENTIFICATION OF MAIN ABSORBANCE BANDS

TABLE 1 : EXAMPLES OF NIR SPECTROSCOPY APPLICATIONS TO DIFFERENTIATE OLIVE OILS FROM OTHER OILS References Other oils Materials Chemometrics Results

 1

	31	Almond, Brazil nut, coconut, grape	NIR, 1 mm quartz cell,	Canonical	Combination of 7
		seed, high oleic sunflower,	range: 9090-4000 cm -1	discrimination after	equations gives 90%
		hydrogenated fish, maize, palm,		variable selection by	correct
		peanut, rapeseed, safflower, sesame,		SLDA	classification
		soya, sunflower, tallow, walnut
	32	Butter, coconut, cod liver oil, lard,	FT-NIR, DTGS detector,	CVA after	92.2% correct
		maize, peanut, rapeseed, safflower,	quartz cell,	normalisation and data	classification
		soya	range: 8000-2000 cm -1 ,	compression by PCA
			resolution: 16 cm -1

TABLE 2 : EXAMPLES OF NIR SPECTROSCOPY APPLICATIONS TO ANALYSE VOOS ADULTERATED WITH OTHER OILS

 2

	References	Adulterants	Materials	Chemometrics	Results
		Olive pomace, refined	NIR, fibre optic source and	LDA and PLS	LDA: 75% correct
		olive pomace, refined	detector, integrating	regression after SG	classification
		olive, deodorised olive oils	sphere,	smoothing	PLS: R 2 = 0.932 to
		(5 to 95%)	range: 25000-5880 cm -1		0.997,
					RMSEP = 2% to 13%
		Refined olive oil (3 to 60%)	FT-NIR, fibre optic probe,	PLS regression on the	R 2 = 97.6 to 99.9,
		and soya, sunflower,	InGaAs detector,	absorption ratio	RMSECV = 3.7% to
		maize, rapeseed, hazelnut,	range: 8000-4500 cm -1 ,	5280/5180 cm -1	0.9%
		safflower, peanut, palm	resolution: 8 cm -1
		oils (3 to 30%)
		Olive pomace oil	NIR, fibre optic probe,	PLS regression after	R 2 = 0.990,
		(5 to 100%)	InGaAs DAD,	MSC	SECV = 3.48%,
			range: 25000-5880 cm -1		SEP = 3.27%
		Sunflower oil	NIR, 0.1 mm camlock cell,	SIMCA and PLS	SIMCA: 100% correct
		(1 and 5%)	range: 25000-4000 cm -1	regression after SG	classification
				1 st derivative	PLS: R 2 = 0.93,
					RMSEP = 0.8%,
					LOD = 1.6%
		Sunflower, soya, rapeseed,	FT-NIR, 8 mm glass vials,	SIMCA after SG	100% correct
		maize, hazelnut, safflower,	range: 12500-4000 cm -1 ,	smoothing, SG 1 st	classification
		peanut oils, palm olein	resolution: 8 cm -1	derivative and SNV
		(10 and 20%)
		Refined olive oil, maize,	NIR, 1 mm quartz cell,	PLS regression after	R 2 = 0.97,
		sunflower oils	range: 12500-4000 cm -1	SG smoothing and 1 st	SECV = 1.31%,
		(5 to 30%)		derivative	SEP = 1.78%
		Hazelnut, walnut, maize,	FT-NIR, Ge diode detector,	PLS regression after	R 2 = 0.999
		soya, sunflower oils	4 mm quartz cell,	MSC and SG	SEP = 0.56% to 1.32%
		(0 to 100%)	range: 12000-4000 cm -1 ,	smoothing
			resolution: 4 cm -1
		Soya oil	FT-NIR, Te-InGaAs	PLS regression	R 2 = 0.998,
		(1.5 to 100%)	detector, 8 mm glass vials,		RMSECV = 1.71,
			range: 12000-4000 cm -1 ,		RMSEP = 1.76
			resolution: 4 cm -1
		Mildly deodorised and	NIR, 2 mm quartz cell,	PCR after MSC and 1 st	R 2 = 0.98,
		refined olive oils	range: 6150-4500 cm -1	derivative	RMSEP = 2.7%
		(2.5 to 75%)
		Sunflower and maize oils	FT-NIR, PbSe detector,	Genetic Inverse Least	SEP = 1.42% to 6.38%
		(4 to 96%)	2 mm quartz cell,	Squares	for tertiary mixtures
			range: 10000-4000 cm -1

  developed a novel Multivariate Range Modelling technique yielding a classification rate of 94.9%. Devos et al. 56 achieved a classification rate of 86.3% with a SVM supervised learning model coupled with genetic algorithm for pre-treatment selection.

TABLE 3 : EXAMPLES OF NIR SPECTROSCOPY APPLICATIONS TO DETERMINE THE ORIGIN OF VOOS

 3

	References	Origins	Materials	Chemometrics	Results
	1	6 French PDOs,	FT-NIR, 2 mm quartz cell,	PLS-DA	85% correct classification for
		5 harvest years	range: 10000-4500 cm -1 ,		PDOs
			resolution: 4 cm -1
		3 Italian regions	FT-NIR, 8 mm vials,	PLS-DA after SG 2 nd	93% correct classification
			range: 12500-4500 cm -1 ,	derivative	with commercial oils
			resolution: 8 cm -1
		Liguria and other	NIR, 0.1 mm camlock cell,	PLS-DA after SG 1 st	92.8% correct classification
		European regions,	range: 9090-4000 cm -1	derivative	for Ligurian oils, 81.5% for
		3 harvest years			other oils
		5 French PDOs,	FT-NIR, 2 mm quartz cell,	PLS-DA	100% correct classification for
		4 harvest years	range: 10000-4500 cm -1 ,		PDOs
			resolution: 4 cm -1
		PDO Sabina and	FT-NIR, integrating sphere,	PLS-DA after MSC,	100% correct classification for
		other	19 mm glass cell,	detrend, or SG 1 st	Sabina and 95.5% for other
		Mediterranean	range: 10000-4000 cm -1 ,	derivative	origins
		regions,	resolution: 4 cm -1
		2 harvest years
		3 Greek regions	NIR, 0.1 mm camlock cell,	FDA	94% correct classification for
			range: 25000-4000 cm -1		geographic origin
		3 cultivars from 3	FT-NIR, 8 mm vials,	LDA after SNV, SG 1 st	82.9% correct classification
		Italian regions	range: 12500-4500 cm -1 ,	derivative and variable	for cultivars
			resolution: 8 cm -1	selection (SELECT)
		3 cultivars from 3	FT-NIR, 8 mm vials,	LDA after SNV, SG 1 st	83% correct classification
		Italian regions	range: 12500-4500 cm -1 ,	derivative and variable
			resolution: 8 cm -1	selection (SELECT)
		Liguria and other	FT-NIR, 5 mm quartz cell,	SIMCA after SG 1 st	92.4% correct classification
		Italian regions	range: 10000-4000 cm -1 ,	derivative and variable	for Ligurian oils
			resolution: 8 cm -1	selection (SELECT)
		Liguria and other	NIR, 0.1 mm camlock cell,	SIMCA or POTFUN after	84.5% correct classification
		European regions,	range: 9090-4000 cm -1	SG 1 st derivative	with SIMCA, 83% and higher
		3 harvest years			confidence level with
					POTFUN
		6 Tunisian cultivars	FT-NIR, 2 mm quartz cell,	SIMCA after SNV and	89.55 to 98.50% correct
		and other	range: 10000-4500 cm -1 ,	SG 1 st derivative	classification for cultivars
		countries, 2 harvest	resolution: 4cm -1
		years
		PDO Chianti	FT-NIR, 5 mm quartz cell,	UNEQ after SNV, SG 1 st	97.5% correct classification
		Classico and other	range: 10000-4000 cm -1 ,	derivative and variable
		Italian regions	resolution: 4 cm -1	selection (SELECT)
		PDO Chianti	FT-NIR, 5 mm quartz cell,	QDA-UNEQ after SG 1 st	100% correct classification
		Classico and other	range: 10000-4000 cm -1 ,	derivative and variable
		Italian regions	resolution: 4 cm -1	selection (STEP-LDA)
		PDO Chianti	FT-NIR, 5 mm quartz cell,	MRM after SNV	94.9% correct classification
		Classico and other	range: 10000-4000 cm -1 ,
		Italian regions	resolution: 4 cm -1
		Liguria and other	NIR, 0.1 mm camlock cell,	SVM after detrend	86.3% correct classification
		Italian regions,	range: 9090-4000 cm -1
		3 harvest years

TABLE 4 : EXAMPLES OF MIR SPECTROSCOPY APPLICATIONS TO DIFFERENTIATE VOOS FROM OTHER OILS

 4

	Reference	Other oils	Materials	Chemometrics	Results
		Butter, coconut, cod liver	FT-MIR, DTGS detector,	CVA on 1800-1400 cm -1	98.9% correct
		oil, lard, maize, peanut,	ZnSe ATR crystal,	region, after normalisation	classification
		rapeseed, safflower, soya	range: 4000-400 cm -1 ,	and data compression by
			resolution: 16 cm -1	PCA or PLS
	57	Grapeseed, groundnut,	FT-MIR, DTGS detector,	DA on PC scores	100% correct
		maize, rapeseed, refined	ZnSe ATR crystal,		classification for extra
		olive, walnut	range: 4800-800 cm -1 ,		virgin vs refined olive
			resolution: 4 cm -1		oil
	58	Coconut, grapeseed,	FT-MIR, DTGS detector,	LDA after normalisation,	100% correct
		hazelnut, maize, mustard,	ZnSe ATR crystal,	baseline correction and	classification
		palm, peanut, rapeseed,	range: 4000-800 cm -1 ,	data compression by PLS
		refined olive, safflower,	resolution: 4 cm -1
		sesame, soya, sunflower,
		sweet almond, walnut
	59	Maize, peanut, rapeseed,	FT-MIR, MCTA detector,	DA	100% correct
		sesame, soya, sunflower,	ZnSe ATR crystal,		classification
		walnut	range: 4000-700 cm -1 ,
			resolution: 2 cm -1 ,
			128 averaged scans
	60	Cottonseed, maize,	FT-MIR, DTGS detector,	PLS-DA after mean	100% correct
		sunflower	range: 4000-400 cm -1	centring and normalisation	classification
	61	Hazelnut, maize, soya,	FT-MIR, KBr disks,	LDA after normalisation	100% correct
		sunflower	range: 4000-500 cm -1 ,	and variable selection	classification
			resolution: 4 cm -1
	62	Flaxseed, grapeseed,	FT-MIR, MCTA detector,	PLS-DA after	100% correct
		maize, peanut, rapeseed,	diamond ATR crystal,	normalisation, detrend	classification
		safflower, sesame, soya,	range: 3800-600 cm -1 ,	and SG 1 st derivative
		sunflower	resolution: 2 cm -1
	63	Butter, maize, rapeseed,	FT-MIR,	iECVA after MSC	100% correct
		soya, sunflower	range: 4000-450 cm -1 ,		classification
			transmittance mode
	64	Hazelnut	FT-MIR, ZnSe ATR crystal,	CP-ANN	Good classification for
			range: 4000-400 cm -1 ,		olive and hazelnut oils
			resolution: 4 cm -1
	65	Hazelnut	FT-MIR, ZnSe ATR crystal,	SLDA after SG smoothing,	95.5% correct
			range: 4000-900 cm -1 ,	SG 1 st derivative and	classification for olive
			resolution: 4 cm -1	selection of variables	vs hazelnut oil
				related to unsaponifiable
				matter

  reached 96.6% correct classification with a Nearest Centroid algorithm after dimension reduction. Mixtures of hazelnut oil in VOO appear to be more difficult to detect. Indeed, Ozen and Mauer 73 achieved a correct classification rate of 100% with DA but only for samples containing at least 25% of hazelnut oil. Baeten et al.[START_REF] Baeten | Detection of the Presence of Hazelnut Oil in Olive Oil by FT-Raman and FT-MIR Spectroscopy[END_REF] reached a LOD of 8% for Turkish hazelnut oil in refined olive oil by applying SLDA on variables characterising the unsaponifiable matter. Georgouli et al.[START_REF] Georgouli | Continuous Statistical Modelling for Rapid Detection of Adulteration of Extra Virgin Olive Oil Using Mid Infrared and Raman Spectroscopic Data[END_REF] obtained a correct classification rate of 75% for samples adulterated with as little as 1% of hazelnut oil, with the use of k-NN after Continuous Locality Preserving Projections. The application of CP-ANN by Baeten and Novi[START_REF] Baeten | The Use of FT-MIR Spectroscopy and Counter-Propagation Artificial Neural Networks for Tracing the Adulteration of Olive Oil[END_REF] only resulted in a partial separation between VOOs with and without the addition of 2 to 20% of hazelnut oil. As for the quantification of adulterants, most authors found that PLS regression after various pre-treatments gave satisfactory results. For instance, Wojcicki et al.[START_REF] Wójcicki | Spectroscopic Techniques and Chemometrics in Analysis of Blends of Extra Virgin with Refined and Mild Deodorized Olive Oils: Spectroscopic Techniques and Chemometrics in Analysis of Blends of Olive Oils[END_REF] , Tay et al.[START_REF] Tay | Authentication of Olive Oil Adulterated with Vegetable Oils Using Fourier Transform Infrared Spectroscopy[END_REF] , Oussama et al.[START_REF] Oussama | Detection of Olive Oil Adulteration Using FT-IR Spectroscopy and PLS with Variable Importance of Projection (VIP) Scores[END_REF] , Sun et al.[START_REF] Sun | Detection and Quantification of Extra Virgin Olive Oil Adulteration with Edible Oils by FT-IR Spectroscopy and Chemometrics[END_REF] , Rohman and Che Man[START_REF] Rohman | Application of FTIR Spectroscopy for the Determination of Virgin Coconut Oil in Binary Mixtures with Olive Oil and Palm Oil[END_REF] , Lai et al.[START_REF] Lai | Quantitative Analysis of Potential Adulterants of Extra Virgin Olive Oil Using Infrared Spectroscopy[END_REF] , Küpper et al.[START_REF] Küpper | Authentication and Quantification of Extra Virgin Olive Oils by Attenuated Total Reflectance Infrared Spectroscopy Using Silver Halide Fiber Probes and Partial Least-Squares Calibration[END_REF] , Gurdeniz et al.[START_REF] Gurdeniz | Detection of Adulteration of Extra-Virgin Olive Oil by Chemometric Analysis of Mid-Infrared Spectral Data[END_REF] and Nigri and Oumeddour 79 all obtained R 2 superior to 0.97 and RMSECV or RMSEP below 2.5% when predicting the concentration of diverse vegetable oils mixed with olive oil. However, Yang and Irudayaraj 35 , Mendes et al.

TABLE 5 : EXAMPLES OF MIR SPECTROSCOPY APPLICATIONS TO ANALYSE VOOS ADULTERATED WITH OTHER OILS

 5

	References	Adulterants	Materials	Chemometrics	Results
	40	Soya oil	FT-MIR, RT-DLaTGS detector,	PLS regression	R 2 = 0.986,
		(1.5 to 100%)	range: 4000-350 cm -1 ,		RMSECV = 14.71,
			resolution: 4 cm -1		RMSEP = 4.89
	35	Olive pomace oil	FT-MIR, DTGS detector, ZnSe	PLS regression after	R 2 = 0.991,
		(0 to 100% in 5%	ATR crystal,	MSC	SECV = 4.74%,
		increments)	range: 3200-600 cm -1 ,		SEP = 3.28%
			resolution: 4 cm -1
	41	Mild deodorised	FT-MIR, ATR crystal,	PLS after MSC and 1 st	R 2 = 0.99,
		and refined olive	range: 4000-650 cm -1 ,	derivative	RMSEP = 2.1%
		oils (2.5 to 75%)	resolution 4 cm -1
	58	Refined olive oil,	FT-MIR, DTGS detector, ZnSe ATR	LDA after	99% correct
		sunflower,	crystal,	normalisation,	classification
		rapeseed, peanut,	range: 4000-800 cm -1 ,	baseline correction	LOD = 5%
		soya, maize oils	resolution: 4 cm -1	and data compression
		(5 to 45%)		PLS
	59	Sunflower oil	FT-MIR, MCTA detector, ZnSe	DA, PLS regression	DA: 100% correct
		(2 to 10%)	ATR crystal,		classification
			range: 4000-700 cm -1 ,		PLS: R 2 = 0.974,
			resolution: 2 cm -1		RMSECV < 1%
	60	Sunflower, maize	FT-MIR, DTGS detector,	PLS-DA after mean	Good separation
		oils (25 to 75%)	range: 4000-400 cm -1	centring and	between pure and
				normalisation	adulterated samples

TABLE 6 : EXAMPLES OF MIR SPECTROSCOPY APPLICATIONS TO DETERMINE THE ORIGIN OF VOOS References Origins Materials Chemometrics Results

 6

	1	6 French PDOs,	FT-MIR, DTGS detector,	PLS-DA after mean	98% correct classification for PDO
		5 harvest years	diamond ATR crystal,	centring and
			range: 4000-600 cm -1 ,	normalisation
			resolution: 4 cm -1
	43	3 Italian regions FT-MIR, DTGS detector,	PLS-DA after SG 2 nd	100% correct classification
			Ge ATR crystal,	derivative
			range: 4000-700 cm -1 ,
			resolution: 4 cm -1
	46	PDO Sabina and	FT-MIR, DTGS detector,	PLS-DA after MSC	92.3% correct classification for
		other	ZnSe ATR crystal,	and detrend	Sabina, 95.5% for other origins
		Mediterranean	range: 4000-630 cm -1 ,
		regions,	resolution: 2 cm -1
		2 harvest years
	48	3 cultivars from	FT-MIR, DTGS detector,	LDA after SNV, SG 1 st	86.6% correct classification for
		3 Italian regions	Ge ATR crystal,	derivative and	cultivars
			range: 4000-700 cm -1 ,	variable selection
			resolution: 4 cm -1	(SELECT)
	49	3 cultivars from	FT-MIR, DTGS detector,	LDA after SNV, SG 1 st	86.6% correct classification
		3 Italian regions	Ge ATR crystal,	derivative and
			range: 4000-700 cm -1 ,	variable selection
			resolution: 4 cm -1	(SELECT)

TABLE 7 : EXAMPLES OF RAMAN SPECTROSCOPY APPLICATIONS TO DIFFERENTIATE VOOS FROM OTHER OILS

 7

	References	Other oils	Materials	Chemometrics	Results
	32	Butter, coconut, cod liver oil,	FT-Raman, laser: HeNe,	CVA after normalisation	94.4% correct
		lard, maize, peanut, rapeseed,	2 W, InGaAs detector,	and data compression	classification
		safflower, soya	range: 3700-400 cm -1 ,	by PLS
			resolution: 32 cm -1
	58	Coconut, grapeseed, hazelnut,	FT-Raman, laser: Topaz,	LDA after	93% correct
		maize, mustard, palm, peanut,	1064 nm, 0.9 W, Ge	normalisation, baseline	classification
		rapeseed, refined olive,	detector,	correction and data
		safflower, sesame, soya,	range: 3500-500 cm -1 ,	compression by PCA
		sunflower, sweet almond, walnut	resolution: 4 cm -1
	65	Hazelnut	FT-Raman, laser:	SLDA after SG	95% correct
			Nd:YAG, 1064 nm, 0.6	smoothing, SG 1 st	classification
			W,	derivative and selection
			InGaAs detector,	of variables related to
			range: 4000-900 cm -1 ,	unsaponifiable matter
			resolution: 4 cm -1
	93	Almond, Brazil nut, butter,	FT-Raman, laser:	SLDA after SG	Classification by
		coconut, grapeseed, hazelnut,	Nd:YAG, 1064 nm, 0.5	smoothing,	type of oil
		high oleic sunflower,	W, Ge detector,	normalization and	according to their
		hydrogenated fish, maize,	range: 3250-0 cm -1 ,	variable selection	fatty acid contents
		margarine, palm, peanut,	resolution: 4 cm -1
		rapeseed, safflower, sesame,
		soya, sunflower, tallow, walnut
	94	Coconut, high oleic sunflower,	FT-Raman, laser:	SLDA	Discrimination of
		hydrogenated fish, maize, palm,	Nd:YAG,		oils depending on
		peanut, rapeseed, soya,	range: 3250-0 cm -1 ,		their fatty acid
		sunflower, tallow	resolution: 4 cm -1		contents

  , Yang and Irudayaraj[START_REF] Yang | Comparison of near-Infrared, Fourier Transform-Infrared, and Fourier Transform-Raman Methods for Determining Olive Pomace Oil Adulteration in Extra Virgin Olive Oil[END_REF] , El-Abassy et al.[START_REF] El-Abassy | Visible Raman Spectroscopy for the Discrimination of Olive Oils from Different Vegetable Oils and the Detection of Adulteration[END_REF] , Davies et al.[START_REF] Davies | Study of the Use of Molecular Spectroscopy for the Authentication of Extra Virgin Olive Oils. Part I: Fourier Transform Raman Spectroscopy[END_REF] , Lopez-Diez et al.[START_REF] López-Díez | Rapid Quantitative Assessment of the Adulteration of Virgin Olive Oils with Hazelnut Oils Using Raman Spectroscopy and Chemometrics[END_REF] or Heise et al.[START_REF] Heise | Spectral Variable Selection for Partial Least Squares Calibration Applied to Authentication and Quantification of Extra Virgin Olive Oils Using Fourier Transform Raman Spectroscopy[END_REF] , applied PLS regression to Raman spectra to predict the concentrations of added sunflower, soya oil, hazelnut or olive pomace oils to VOO. They obtained quite satisfactory results, with R 2 over 0.97 and SEP below 3.6%. Yang and Irudayaraj[START_REF] Yang | Comparison of near-Infrared, Fourier Transform-Infrared, and Fourier Transform-Raman Methods for Determining Olive Pomace Oil Adulteration in Extra Virgin Olive Oil[END_REF] concluded that Raman spectroscopy was slightly more efficient that NIR and MIR to quantify the adulteration of EVOO with olive pomace oil, whereas Mendes et al.[START_REF] Mendes | Quantification of Extra-Virgin Olive Oil Adulteration with Soybean Oil: A Comparative Study of NIR, MIR, and Raman Spectroscopy Associated with Chemometric Approaches[END_REF] detected no statistically significant difference between the three techniques for the analysis of soybean and olive oil mixtures. Baeten et al.100 used stepwise linear regression analysis (SLRA) to measure the amount of trilinolein added to VOO, yielding a R 2 of 0.998 for concentrations between 1 and 10% of adulterant. The same method applied to VOOs adulterated with maize, soya or olive pomace oils gave a R 2 of 0.92. Zhang et al.101 developed an external standard method (ESM) resulting in R 2 over 0.99 and RMSE below 3.2%, while Dong et al. 102 generated a LS-SVM model after parameter optimization by Bayesian framework that gave a R 2 of 0.997 and RMSEP of 0.051.

TABLE 8 : EXAMPLES OF RAMAN SPECTROSCOPY APPLICATIONS TO ANALYSE VOOS ADULTERATED WITH OTHER OILS Reference s

 8

		Adulterants	Materials	Chemometrics	Results
		Soya oil	FT-Raman, laser: Nd:YAG, 1064	PLS regression	R 2 = 0.998, RMSECV
		(1.5 to 100%)	nm, 0.2 W, Ge detector,		= 1.61, RMSEP = 1.57
			range: 3500-50 cm -1 ,
			resolution: 4 cm -1
		olive pomace oil (0	FT-Raman, laser: 1064 nm, 0.5 W,	PLS regression after MSC	R 2 = 0.997,
		to 100% in 5%	InGaAs detector,		SECV = 2.23%,
		increments)	range: 4000-400 cm -1 ,		SEP = 1.72%
			resolution: 8 cm -1
		Refined olive oil,	FT-Raman, laser: Topaz, 1064 nm,	PLS after normalisation,	97% correct
		sunflower,	0.9 W, Ge detector,	baseline correction and	classification
		rapeseed, peanut,	range: 3500-500 cm -1 ,	data compression by	LOD = 45% for
		soya, maize oils	resolution: 4 cm -1	PCA	refined olive oil, 5%
		(5 to 45%)			for others
		Hazelnut oil	FT-Raman, laser: Nd:YAG, 1064	SLDA after SG	97.5% correct
		(2 to 20%)	nm, 0.6 W, InGaAs detector,	smoothing, SG 1 st	classification
			range: 4000-900 cm -1 ,	derivative and selection
			resolution: 4 cm -1	of variables related to
				unsaponifiable matter
		Olive pomace oil,	FT-Raman, laser: Nd:YAG,	SLDA	discrimination of
		maize, sunflower,	range: 3250-0 cm -1 ,		genuine vs
		soya oils	resolution: 4 cm -1		adulterated samples
		(1 to 10%)
		Soya oil (5%)	Raman, laser: 785 nm, 0.1 W,	LDA after normalisation,	80 or 90°C gives
			8 temperatures (20 to 90°C),	baseline correction and	100% correct
			range: 1500-690 cm -1 ,	data compression by	classification
			resolution: 4 cm -1	PCA
		Sunflower oil	Raman, laser: Ar, 514 nm, 0.01	PLS regression after	R 2 = 0.971 to 0.988,
		(5 to 100%)	W, CCD detector,	baseline correction	RMSECV = 1.33 to
			range: 3100-700 cm -1		3.59
					LOD = 0.05%
		Sunflower Oil	FT-Raman, laser: Nd:YAG, 1064	PLS regression	RMSEC = 2.40%,
		(2 to 10%)	nm, 1 W,		RMSEP = 2.86%
			range: 3600-100 cm -1
		Hazelnut oil	Raman, laser: 780 nm, 0.02 W,	PLS regression after	R 2 = 0.979,
		(5 to 100%)	range: 3000-1000 cm -1 ,	baseline correction,	RMSEP = 0.94
			resolution: 6 cm -1	normalisation and SG
				smoothing
		Sunflower oil	FT-Raman, laser: Nd:YAG, 1064	PLS regression after SG	SEP = 1.26%
		(1 to 10%)	nm, 1 W,	1 st derivative and
			resolution: 4 cm -1	variable selection (Tabu)
	100	Trilinolein, olive	FT-Raman, laser: Nd:YAG, 1064	SLRA after SG	R 2 = 0.998 for
		pomace, maize,	nm, 0.5 W, Ge detector,	smoothing, SG 1 st	trilinolein
		soya oils	range: 3250-100 cm -1 ,	derivative and variable	R 2 = 0.92 for oils
		(1 to 10%)	resolution: 4 cm -1	selection
	101	Soya, sunflower,	Handheld Raman, laser: 785 nm,	External standard	R 2 = 0.996 to 0.991,
		maize oils	0.2 W,	method after	RMSE = 1.40 to
		(1 to 100%)	range: 2000-200 cm -1 ,	normalisation	3.13%
			resolution: 8 cm -1
	102	Soya, maize,	Handheld Raman, laser: 785 nm,	LS-SVM with Bayesian	R 2 = 0.997,
		sunflower oils	0.375 W, 10 mm quartz cell,	network	RMSEC = 0.020,
		(2 to 100%)	range: 2100-150 cm -1 ,		RMSEP = 0.051
			resolution: 6 cm -1

TABLE 9 : EXAMPLES OF RAMAN SPECTROSCOPY APPLICATIONS TO DETERMINE THE ORIGIN OF VOOS

 9

	References	Origins	Materials	Chemometrics	Results
	2	6 French PDOs,	Raman, laser: Nd:YVO4 DPSS,	PLS-DA after SNV	92.3% correct
		6 harvest years	532 nm, 0.15 W, CCD detector,	and MSC	classification for PDOs
			range: 1800-440 cm -1
	103	3 Andalusian PDOs	Raman, laser: Nd:YAG, 1064	PLS-DA after SG	94.3% correct
		and other Spanish	nm, 0.3 W,	smoothing and	classification for harvest
		regions,	range: 3100-100 cm -1 ,	normalisation	year, 89% for
		6 harvest years	resolution: 4 cm -1		geographical origin,
					86.6% for PDOs,
					84% for olive variety
	104	3 Portuguese	Raman, laser: Ar, 488 nm, 0.1	LDA after SNV and	81.9% correct
		cultivars, 3	W, CCD detector,	data compression by	classification for
		maturity stages	range: 3050-250 cm -1	PCA	maturation stage

TABLE 10 : EXAMPLES OF CONCATENATED DATA APPLICATIONS TO ANALYSE VOOS ADULTERATED WITH OTHER OILS

 10

	References	Adulterants	Materials	Chemometrics	Results
	41	Mild deodorised	NIR, 2 mm quartz cell,	PLS regression	No improvement vs
		and refined	range: 6150-4500 cm -1		separate spectra
		olive oils	FT-MIR, ATR crystal,		R 2 = 0.96,
		(2.5 to 75%)	range: 4000-650 cm -1 ,		RMSEP = 4.1%
			resolution: 4 cm -1
			Fluorescence, 10 mm quartz
			cell, range: 40000-14285 cm -1
	105	Sunflower, olive	FT-MIR, DTGS detector, KBr	PLS regression after	Better results vs
		pomace oils	disks,	normalisation and SG 1 st	separate spectra
		(5 to 50%)	range: 4000-450 cm -1 ,	derivative	R 2 = 0.992,
			resolution: 4 cm -1		RMSECV = 2.67
			Fluorescence, xenon lamp
			source, 10 mm quartz cell,
			range: 45455-11110 cm -1

TABLE 11 : EXAMPLES OF CONCATENATED DATA APPLICATIONS TO DETERMINE THE ORIGIN OF VOOS

 11 . Concatenation of NIR, UV-visible and MS data also resulted in 100% discrimination between EVOOs from Liguria and other Italian regions, which was not possible with each separate technique 107 .

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