Hichem Rahab

Abdelhafid Zitouni

Mahieddine Djoudi

An Enhanced Corpus for Arabic Newspapers Comments

Keywords: Opinion mining, sentiment analysis, K-Nearest Neighbours, Naïve Bayes, Support Vector Machines, Arabic, comment

In this paper, we propose our enhanced approach to create a dedicated corpus for Algerian Arabic newspapers comments. The developed approach has to enhance an existing approach by the enrichment of the available corpus and the inclusion of the annotation step by following the Model Annotate Train Test Evaluate Revise (MATTER) approach. A corpus is created by collecting comments from web sites of three well know Algerian newspapers. Three classifiers, support vector machines, naïve Bayes, and k-nearest neighbors, were used for classification of comments into positive and negative classes. To identify the influence of the stemming in the obtained results, the classification was tested with and without stemming. Obtained results show that stemming does not enhance considerably the classification due to the nature of Algerian comments tied to Algerian Arabic Dialect. The promising results constitute a motivation for us to improve our approach especially in dealing with non-Arabic sentences, especially Dialectal and French ones.

Introduction

With the development of the web and its offered services, a huge amount of data is generated [START_REF] Liu | Sentiment Analysis and Opinion Mining[END_REF] and additional needs emerge to take benefit from this information thesaurus. Mining the political, economic and social opinion, to make the available information amount in an easily understood form by decision makers in dedicated centers is an emergent need in this air. Sentiment analysis vocation is to classify people opinions into specific classes to facilitate understanding the behind phenomenon.

A variety of classifications are available, some works deal only with positive vs. negatives classes [START_REF] Atia | Increasing the accuracy of opinion mining in Arabic[END_REF][START_REF] Rushdi-Saleh | OCA: Opinion Corpus for Arabic[END_REF], other works deal with more important number of classes [START_REF] Cherif | Towards an Efficient Opinion Measurement in Arabic Comments[END_REF].

A very important amount of useful information is available in term of comments of newspapers websites visitors around the world and in different languages. A lot of works is this era deal with English language, and other European languages, but works treating Arabic language still in their beginning [START_REF] Alotaibi | Extending the Knowledge of the Arabic Sentiment Classification Using a Foreign External Lexical Source[END_REF].

Arabic is a Semitic language spoken by about 300 million of people in 22 Arab countries. The importance of Arabic is also that it is the language of the holy Quran [START_REF] Cherif | Towards an Efficient Opinion Measurement in Arabic Comments[END_REF] the book of 1.5 billion Muslim in the world. We can find three forms of Arabic language, Classical Arabic, Modern Standard Arabic (MSA), and Dialectal Arabic. Classical Arabic is the original form of the language preserved from centuries by the Islamic literature and especially the holy Quran. For Modern Standard Arabic, it takes their role as the official language in almost all Arabic administrations. The effective spoken languages in daily conversations are Arabic dialects, which are spoken languages without a standardized writing form [START_REF] Al-Harbi | Classifying Sentiment Of Dialectal Arabic Reviews: A Semi-Supervised Approach[END_REF]. They can be classified into: Levantine (spoken in Palestine, Jordan, Syrian and Lebanon), Egyptian (in Egypt and Sudan), Maghrebi (spoken in the Arab Maghreb) and Iraqi [START_REF] Jarrar | Curras: an annotated corpus for the Palestinian Arabic dialect[END_REF], this later one may be also divided into Iraqi versus Gulf classes [START_REF] Zaidan | The Arabic Online Commentary Dataset : an Annotated Dataset of Informal Arabic with High Dialectal Content[END_REF].

In these Dialect families, we will find also subfamilies. In the case of the Algerian dialect, the work of [START_REF] Harrat | An Algerian Dialect : Study and Resources[END_REF] classify Algerian dialects into four groups:

1. the dialect of Algiers and its outskirts. 2. the dialect of the east in Annaba and its outskirts. 3. the dialect of Oran and the west of Algeria. 4. the dialect of the Algerian Sahara.

Even Algerian newspapers content is written in MSA and comments follow generally this style, we find some visitors that use Algerian Dialects words in their comments. For example the Arabic sentence: كهذه أشياء المتخلفة الدول في فقط تحدث Ȃaš.yAȂ kahaðihi taH.duƟu faqat fi Ald~uwal almutaxal~ifa 1 (things like this occur only in retarded countries) is written in a comment اشياء هاذي كيما المتخلفة الدول في غير تصرى Aaš.yA kima hAðy tas.ra γir fy Ald~uwal almutaxal~ifa. Also we found in several cases the use of the letter د d, instead of ذ ð, which is a characteristic of the Dialect of Algiers the capital of Algeria [START_REF] Harrat | An Algerian Dialect : Study and Resources[END_REF], as the case in the comment و المهمة له اسندة الدى المسؤل حال هو هدا حفيظ يا شكرا فشل الدى الزمن عن يدافع و يطبل و ينتقد ان اجل من ينتقد اصبح مر الوقائع بتحديهم المجد يصنعون رجال هناك ولكن šukrã ya HafiyĎ hada huwa HaAl Almasŵul Al~adi Ȃus.nidaħ. lahu Almuhim~aħ wa fašil. Asbaha yantaqid min Ȃjl Ȃn yantaqid wa yuTab~il wa yudaAfiς ςan Alz~aman Al~adi mar~ wa lakin hunAka rijAl yaSnaςuwn Almajd bitaHad~iyhim AlwaqaAĂς (Thank you hafid this is the state of the responsible to whom is affected a mission and he fails, so he become critic for critic and he defend the past time but there are men making the glory by confronting the realities).

In this paper, we are interested by comments in the Arabic Algerian online press, in the goal of developing an approach to classify these comments into positive and negative classes.

The paper is organized as follows. In the section 2 a literature review is given. In the section 3 a background of adopted methodology and used parameters are given. Section 4 is dedicated to the proposed approach. An experimental study is explained and obtained results are discussed in the section 5. We finish by conclusion and perspectives to future works.

Literature Review

Sentiment Analysis is an emergent field in the domains of Data Mining and Natural Language Processing (NLP); it is a research issue with the purpose of extract meaningful knowledge from user-generated content, for tracking the mood of people about events, products or topics [START_REF] Vinodhini | Sentiment Analysis and Opinion Mining : A Survey[END_REF]. It may be tacked as a classification problem, where the goal is to determine whether a written document, e.g. reviews, expresses a positive or negative opinion about specific entities [START_REF] Alotaibi | Extending the Knowledge of the Arabic Sentiment Classification Using a Foreign External Lexical Source[END_REF][START_REF] Korayem | Sentiment/subjectivity analysis survey for languages other than English[END_REF]. Works in sentiment analysis domain can be classified into statistical approaches also known as lexical based and supervised learning or corpus-based approaches [START_REF] Badaro | A Survey of Opinion Mining in Arabic: A Comprehensive System Perspective Covering Challenges and Advances in Tools, Resources, Models, Applications, and Visualizations[END_REF]. In lexical approaches, we need sentiment lexical as resources to predict document sentiments, while in the supervised learning approaches, which will be used in this work, it is necessary to have well annotated corpora to create classification models.

For resources creation, we found several works. In [START_REF] Al-Kabi | A Prototype for a Standard Arabic Sentiment Analysis Corpus[END_REF] and [START_REF] Al-Kabi | Building a Standard Dataset for Arabic Sentiment Analysis[END_REF] the authors build manually a Standard Arabic corpus SA from maktoob yahoo!, a corpus of 1.442 Arabic review covering five domains, with 50 topics in each domain. Reviews are written in different Arabic dialects in addition to MSA. The annotation is performed by three Arabic native speakers with different skills in computer science [START_REF] Al-Kabi | Building a Standard Dataset for Arabic Sentiment Analysis[END_REF], and a consensus of 51,60% where the three annotators agree in one label is obtained. The best Inter Annotators Agreement (IAA) in term of kappa coefficient is achieved between annotators A2 and A3 as k= 0.556 considered as moderate. The works of [START_REF] Abdul-Mageed | AWATIF: A Multi-Genre Corpus for Modern Standard Arabic Subjectivity and Sentiment Analysis[END_REF] and [START_REF] Ibrahim | MIKA: A Tagged Corpus for Modern Standard Arabic and Colloquial Sentiment Analysis[END_REF] present a multi genre corpus for Modern Standard Arabic annotated at the sentence level. In [START_REF] Abdul-Mageed | AWATIF: A Multi-Genre Corpus for Modern Standard Arabic Subjectivity and Sentiment Analysis[END_REF], several annotation methods were adopted, and kappa parameter is used to measure IAA. The authors conclude that a training of annotators is necessary to have a consistent annotation. In [START_REF] Ibrahim | MIKA: A Tagged Corpus for Modern Standard Arabic and Colloquial Sentiment Analysis[END_REF], three Arabic native speakers annotators specialized in Arabic linguistics were working to annotate their corpus into positive, negative and neutral sentiment. An agreement of 97% is obtained over the annotators. Some rules are given to annotators to achieve a high degree of consistency. In the goal of creating an annotated corpus and lexicon, the authors in [START_REF] Hamdi | CLASENTI : A class-specific sentiment analysis framework[END_REF] have collected 15.274 Arabic reviews concern 13 governmental services. For annotation, thirty Arabic speakers with different skills and from different Arab countries are asked to annotate the reviews at two levels, i.e. linguistic issues and dialects. A high Inter Annotator Agreement of 0,78 in Kappa score is abstained. To decide the final annotation, three experts work to give the decision. In [START_REF] Rahab | ARAACOM: ARAbic Algerian Corpus for Opinion Mining[END_REF], the authors have created ARAACOM, ARAbic Algerian Corpus for Opinion Mining, 92 comments were collected from an Algerian Arabic newspaper web site. Support vector machines and naïve Bayes classifiers were used. Both unigram and bigram word model were tested. Best results are obtained in term of precision, and the bigram model increase results in almost cases. BRAD (Book Review in Arabic Dataset) [START_REF] Elnagar | BRAD 1 . 0 : Book Reviews in Arabic Dataset[END_REF], a corpus of 510.598 reviews expressed in MSA and Arabic dialects is collected from 'www.goodreads.com'. For annotation, the review with 1 or 2 stars is considered negative and with 4 or 5 stars is considered as positive. Neutral reviews with 3 stars are eliminated from the corpus. Four classifiers were used to test the performance of the created corpus. The best results are obtained with Support-Vector Machines (SVM) and Logistic Regression. In [START_REF] Cherif | Towards an Efficient Opinion Measurement in Arabic Comments[END_REF], 625 Arabic reviews and comments on hotels are collected from Trip Advisor website and classified into five categories: "ممتاز" (excellent); " جيد "جدا (very good); "متوسط" (middling); " ضعي ف " (weak) and "مروع" (horrible). The modeling approach combining SVM with K-Nearest Neighbours (KNN) provides the best result (F-measure of 97%). In [START_REF] Elnagar | Intelligent Natural Language Processing: Trends and Applications[END_REF], HARD (Hotel Arabic-Reviews Dataset) a corpus composed of 490.587 reviews has been created. HARD covers 1.858 hotels and commented by 30.889 users. The authors come to a balanced dataset of 94.052 reviews form which 46.968 are annotated as positive and 47.084 as negative. The annotation is done following the rating system where reviews with rating 1 or 2 are considered negative and those of 4 or 5 rating are considered as positive, neutral comments with 3 rating are not considered in the dataset. For classification, six commonly used methods are applied, in addition to the use of a lexicon constructed in the same work achieving an accuracy of 89%. Logistic regression and SVM give the best results with a range of polarity classification from 94% to 97%. The authors of Curras [START_REF] Jarrar | Curras: an annotated corpus for the Palestinian Arabic dialect[END_REF] investigate in a corpus creation for Palestinian Arabic dialect. Two annotators are solicited to annotate morphologically Curras at the word level and Inter Annotators Agreement is calculated using Kappa coefficient. After annotation, both annotators work together to agree in the resultant gold standard. The best accuracy among the annotators achieves 98,8%. In [START_REF] Rushdi-Saleh | OCA: Opinion Corpus for Arabic[END_REF], the authors create OCA (Opinion Corpus for Arabic) with 250 positive documents and 250 negative ones. The corpus is annotated at the document level by using web sites rating systems. Support vector machines and naïve Bayes classifiers were used for evaluation. The corpus documents are mostly related to movie reviews. The work [START_REF] Guellil | SentiALG : Automated Corpus Annotation for Algerian Sentiment Analysis Introduction[END_REF] is based on the creation of a lexical resource to be used in the automatic annotation of a sentiment corpus for Algeria Dialect (AD) with positive and negative tags. The corpus is formed by Arabic and Arabizi scripts. Several machine learning methods are used to test the performance of the corpus and the Arabic text results are better than Arabizi text.

From this review of literature in opinion mining works and especially works dealing with Arabic language we can conclude that an important part of work concern specific topics. So, conducting studies with other topics require developing dedicated benchmarks that can be used to validate or revise existing results. Also, publicly available corpora are very sparse which makes very necessary the development of dedicated resources to carry out studies is this language.

Background

MATTER Approach

MATTER is a cyclic approach for annotate natural language texts, the approach is based on several iterations to achieve the annotation process [START_REF] Pustejovsky | Natural Language Annotation for Machine Learning[END_REF]. The approach MATTER consists on a cycle of six steps. The model of the phenomenon may be revised for further train and test steps [START_REF] Ide | Handbook of Linguistic Annotation[END_REF]:

1. Model: the first step is about modelling the studied phenomenon. 2. Annotate: an annotation can be seen as a meta data [START_REF] Petrillo | Introduction to Manual Annotation[END_REF]. This metadata will be added to the corpus for data classification into predefined classes like positive, negative, neutral, etc., The annotation can be done at several levels. At document level [START_REF] Rushdi-Saleh | OCA: Opinion Corpus for Arabic[END_REF], at sentence level [START_REF] Brahimi | Data and Text Mining Techniques for Classifying Arabic Tweet Polarity[END_REF] or at word level, also known as Part Of Speech tagging (POS) [START_REF] Jarrar | Curras: an annotated corpus for the Palestinian Arabic dialect[END_REF][START_REF] Tunga | Part-of-Speech Tagging[END_REF]. We can find several ways to achieve annotation with; annotation by 2 to 5 persons having some specified skills [START_REF] Alotaibi | Extending the Knowledge of the Arabic Sentiment Classification Using a Foreign External Lexical Source[END_REF][START_REF] Pustejovsky | Natural Language Annotation for Machine Learning[END_REF], Crowdsourcing where the annotation is done by an important number of annotators without specific skills [START_REF] Bougrine | Altruistic Crowdsourcing for Arabic Speech Corpus Annotation[END_REF] or annotation based on rating systems offered by opinion sites [START_REF] Rushdi-Saleh | OCA: Opinion Corpus for Arabic[END_REF]. The final version of the annotated data, called the gold standard, is the corpus to be used in the classification step [START_REF] Pustejovsky | Natural Language Annotation for Machine Learning[END_REF]. 3. Train: a classifier would be trained with a part of the data. 4. Test: the rest of data (which is not used for training) is submitted to classifier for test. 5. Evaluate: evaluation metrics are calculated, to measure the annotation and classification performances. 6. Revise: based on evaluation metrics the model may be revised, and additional iteration is to do if needed.

Validation Method

In the scope of this work, the 10-fold cross-validation method is to be used. Cross-validation is a statistical method of evaluating and comparing learning algorithms by dividing the data set into two segments: one used to learn or train a model and the other used to validate the model. The basic form of cross-validation is k-fold cross-validation, in which the data set is first divided into k equally sized segments or folds. Subsequently, k iterations of training and validation are performed, so that, at each iteration a different fold of the data is held out for validation, while the remaining k-1 folds are used for learning [START_REF] Refaeilzadeh | Cross-Validation[END_REF]. The performance values are taken as a combination of the k performance values (as an average or another combination) to have a single estimation [START_REF] Mountassir | Sentiment Classification on Arabic Corpora. A Preliminary Cross-Study[END_REF]. The authors in [START_REF] Kohavi | A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection[END_REF] and [START_REF] Salzberg | On Comparing Classifiers : Pitfalls to Avoid and a Recommended Approach[END_REF] conclude that 10-fold cross validation is the best alternative to follow in classification process, even if computation power allows more folds.

Classifiers

In this paper, three well known classifiers has been used. Those are:

1. Support-Vector Machines: SVM is a relatively new machine learning method for binary classification problems [START_REF] Cortes | Support-Vector Networks[END_REF]. To have the best results with SVM the practitioner needs to well choice and fixe certain parameters: used kernel, gamma, and also well data collecting and pre-processing [START_REF] Ben-Hur | A user's guide to support vector machines[END_REF]. 2. Naive Bayes: NB is based on the "Bayes assumption" in which the document is assigned to the class in which it belongs with the highest probability [START_REF] Mccallum | A Comparison of Event Models for Naive Bayes Text Classification[END_REF]. 3. K-Nearest Neighbours: KNN is a simple classifier that uses an historical value search to find the future ones [START_REF] Wang | Short Term Prediction of Freeway Exiting Volume Based on SVM and KNN[END_REF].

Evaluation Measures

1. Inter Annotators Agreement: several metrics are used in literature to evaluate IAA. The kappa coefficient [START_REF]Assessing agreement on classification tasks: the kappa statistic[END_REF] is the most used in two annotators based works [START_REF] Alotaibi | Extending the Knowledge of the Arabic Sentiment Classification Using a Foreign External Lexical Source[END_REF][START_REF] Pustejovsky | Natural Language Annotation for Machine Learning[END_REF]. The coefficient is defined as :

𝑘 = Pr(𝑎)-Pr(𝑒) 1-Pr(𝑒)
Where, Pr(a) represents the proportion of the cases in which both annotators agree, and Pr(e) is the proportion we search that the two annotators agree by chance [START_REF]Assessing agreement on classification tasks: the kappa statistic[END_REF].

Precision and

Proposed Approach

Our proposed approach constitutes an enhancement of an existing approach ARAACOM (ARAbic Algerian Corous for Opinion Mining) [START_REF] Rahab | ARAACOM: ARAbic Algerian Corpus for Opinion Mining[END_REF].

In this work, MATTER approach [START_REF] Pustejovsky | Natural Language Annotation for Machine Learning[END_REF] for comments annotation is enhanced. We add a processing (process) step to have MApTTER (Model Annotate process Train Test Evaluate Revise) approach. This enhancement allows us to give comments in the brut form to our annotators. So the processing step is included to the approach to:

• The annotators deal with the original text.

• The new examples can be added to any iteration.

For corpus creation, we collect comments from three Algerian Arabic newspapers web sites, in occurrence Echorouk 2 , Elkhabar 3 , and Ennahar 4 . We selected articles covering several subjects (news, political, religion, sports, and society).

The following algorithm summarizes our proposed approach: 2 www.echoroukonline.com/ara/ 3 www.elkhabar.com 4 www.ennaharonline.com Algorithm 1: Our proposed approach Algorithm: Proposed approach (0) Begin [START_REF] Abdul-Mageed | AWATIF: A Multi-Genre Corpus for Modern Standard Arabic Subjectivity and Sentiment Analysis[END_REF] IAA =0; [START_REF] Al-Harbi | Classifying Sentiment Of Dialectal Arabic Reviews: A Semi-Supervised Approach[END_REF] while (IAA <= 100% ) do ( 3) read (URL); [START_REF] Al-Kabi | Building a Standard Dataset for Arabic Sentiment Analysis[END_REF] Page =load (URL); [START_REF] Alotaibi | Extending the Knowledge of the Arabic Sentiment Classification Using a Foreign External Lexical Source[END_REF] while (there are comments in Page) do [START_REF] Atia | Increasing the accuracy of opinion mining in Arabic[END_REF] Extract the following Comment [START_REF] Badaro | A Survey of Opinion Mining in Arabic: A Comprehensive System Perspective Covering Challenges and Advances in Tools, Resources, Models, Applications, and Visualizations[END_REF] if (Comment in Data_base) then [START_REF] Ben-Hur | A user's guide to support vector machines[END_REF] Delete Comment ; [START_REF] Bougrine | Altruistic Crowdsourcing for Arabic Speech Corpus Annotation[END_REF] Else [START_REF] Brahimi | Data and Text Mining Techniques for Classifying Arabic Tweet Polarity[END_REF] Add Comment to the Data_base; [START_REF]Assessing agreement on classification tasks: the kappa statistic[END_REF] end if [START_REF] Cherif | Towards an Efficient Opinion Measurement in Arabic Comments[END_REF] end while [START_REF] Cortes | Support-Vector Networks[END_REF] MODEL the phenomenon ( 14) ANNOTATE [START_REF] Elnagar | Intelligent Natural Language Processing: Trends and Applications[END_REF] Calculate New_IAA [START_REF] Guellil | SentiALG : Automated Corpus Annotation for Algerian Sentiment Analysis Introduction[END_REF] if New_IAA <= IAA then [START_REF] Habash | On Arabic Transliteration[END_REF] go to MODEL [START_REF] Hamdi | CLASENTI : A class-specific sentiment analysis framework[END_REF] end if [START_REF] Harrat | An Algerian Dialect : Study and Resources[END_REF] PROCESS [START_REF] Ibrahim | MIKA: A Tagged Corpus for Modern Standard Arabic and Colloquial Sentiment Analysis[END_REF] TRAIN And TEST ( 21) EVALUATE [START_REF] Jarrar | Curras: an annotated corpus for the Palestinian Arabic dialect[END_REF] if (results sufficient) [START_REF] Kohavi | A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection[END_REF] Break; [START_REF] Korayem | Sentiment/subjectivity analysis survey for languages other than English[END_REF] Else ( 25) REVISE [START_REF] Mccallum | A Comparison of Event Models for Naive Bayes Text Classification[END_REF] end if [START_REF] Mountassir | Sentiment Classification on Arabic Corpora. A Preliminary Cross-Study[END_REF] end while (28) end

Models

The model is defined as the triplet: M= {T, R, I} T= {Comment-classe, Positive, Negative, Neutral}: a set of terms. R={Comment-classe::= Positive| Negative| Neutral}: a set of relations between terms. I= {Positive: "Subjective with positive sentiment", Negative: "Subjective with negative sentiment", Neutral: "out of topic or without sentiment (objective)"}: interpretation of terms.

Annotate

Two Arabic native speakers are requested to annotate our corpus. In the beginning of each annotation round, a set of guidelines were given to annotators to have the best degree of contingency in obtained results.

1. Annotation Guidelines: In the guidelines the project must be described with its methodology, outcomes and all information needed to achieve our goals [START_REF] Ide | Handbook of Linguistic Annotation[END_REF]. In each round of the MApTTER cycle, annotation guidelines will be refined taking into account previous results. 2. Adjudication: In adjudication, the annotations from different annotators are merged to have a single corpus called gold standard [START_REF] Ide | Handbook of Linguistic Annotation[END_REF].

(

(4)

Process

To have the best results in stemming and optimizing the word vector, a set of preprocessing steps are to conduct: We finish by character encoding where all texts are resolved to UTF-8 encoding format.

2. Tokenization: in tokenization, words are separated by non-letters characters. 3. Stemming: light stemming is used in this step.

Figure 1 and Figure 2 shows light stemming and stemming of the same comment. We remark for example that the word الجزائر AljazAŷir (Algeria with the definite article) in light stemming is stemmed to جزائر jazAŷir (Algeria without the definite article), when in stemming is stemmed as جزر jazar or jaz.r (carrot or ebb). And the word اقتصاديا Ăq.tiSAdiyã (economically) in light stemming is stemmed as it without changing اقتصاديا Ăq.tiSAdiyã, when in stemming it is stemmed as قصد qaSada (intention or meaning). In the scope of this work, we have used light stemming, because stemming generates the root of the word which gives a different meaning in several cases [START_REF] Mountassir | Sentiment Classification on Arabic Corpora. A Preliminary Cross-Study[END_REF].

Train and Test

In this step three classification methods, SVM, NB, and KNN were used. And the 10-fold cross validation is adopted. For the SVM, we use SVM linear, and for KNN we adopt the k=9 parameter as suggested in [START_REF] Brahimi | Data and Text Mining Techniques for Classifying Arabic Tweet Polarity[END_REF].

Evaluate

For evaluation, Precision Recall and Accuracy are calculated for each classifier and obtained resultants were compared and discussed in each round of the MApTTER cycle.

Revise

In revision step adopted approach will be revised in the light of evaluation metrics, and a decision to continue or stop the MApTTER cycle is to take. I= {Positive: "Subjective with positive sentiment", Negative: "Subjective with negative sentiment", Neutral: "out of topic or without sentiment (objective)"}.

Experimental Study

First Round

Annotate:

The Annotation guidelines given to annotators are, to annotate a comment as it presents a positive, negative or neutral sentiment regarding the article topic, so for each comment the annotators have the correspondent article.

• IAA Inter Annotators Agreement:

We obtain : 𝑘 = 0.5195 considered as moderate [START_REF] Pustejovsky | Natural Language Annotation for Machine Learning[END_REF]. • Adjudication: in adjudication step the two annotators are working together in the goal of obtaining a consensus in annotation, in cases when a consensus was not obtained the comment is considered as neutral. In this step, 45 comments are considered as positive, 88 as negative and 45 as neutral. We take in this work only the positive and negative classes, to have equilibrium we generate the corpus with the 45 positive comments and 45 of the negative ones.

3. Processing: The processing steps describing above were doing again, namely: text pre-processing, UTF-8 encoding, tokenization, stemming, stop words removal, n-gram word generation, and word vectors creation. 4. Train and Test: For these two steps, cross validation method was adopted using the three classifiers, support vector machines, naïve Bayes and k-nearest neighbours. 5. Evaluate: To evaluate our model we calculate precision and recall of both negative and positive classes and accuracy of the classification at whole. In Table1 are presented evaluations of SVM classifier. We observe that the stemming approach gives low performance comparing with the basic model and we report this result to the Algerian dialect. For example, we observed in the used tool that the name حفيظ HafiyĎ (which is a proper name widely used in Algeria and also mean in Arabic 'conservator') when it is stemmed take the root حفظ HafaĎa (to conserve). So stemming is not the best issue in such situations. Also, trigram does not give considerable amelioration in the most of results.

With the TF vector we obtain the best result as recall of the positive class (95%).

Table 2 shows classification results using Naïve Bayes method. Comparing to SVM, obtained results with Naive Bayes are low and are not competitive. K-nearest neighbours, as presented in Table 3. gives the best performance as classifier. And the best results are obtained in the recall of the positive class. The stemming gives some amelioration, but it is still not very important.

6. Revise: After evaluation of the IAA and classification scores, some suggestion are mentioned to take into account in the next round:

• In the following annotation guidelines, the authors must take into account only the content of the comment no matter what the article subject is. So this recommendation may conduct to more consensuses between annotators, that in the previous round, when taking into account the article topic, we observe that for the same, comment one annotator can have a positive sentiment and the other have a neutral or even negative sentiment.

Second Round

1. Model: We conserve the above model without any changes.

2. Annotate: In this round we give our annotators instruction to consider only the content of the comment, as it is recommended in the revision of the above step.

• IAA Inter Annotators Agreement: The Inter Annotator Agreement is improved with the new instruction, so it achieve k = 0.5820. In the case of the Naïve Bayes the obtained results are very promising; we achieve 93.30% of recall in the negative class without stemming, as shown in Table 5. In the case of the KNN classifier (see Table 6) the recall of the negative class is very good without stemming with all vectors. 7. Revise: In this point we decide to stop this cycle and report the obtained results.

Conclusions and Perspectives

Available corpora in the web for carried out Arabic sentiment analysis studies are very rare, and those available are generally related to movie reviews due to the available comments in correspondent websites. The case of newspapers comments is more delicate, that it is related to the country in which it is exist, so dealing with such comments must take into account, not only Arabic language but also related dialects and used languages in this country. In this work we proposed our enhanced approach for opinion mining in Algerian Arabic Newspapers comments. For annotation, MApTTER approach is used to annotate Algerian newspaper comments. MApTTER is based on an existing annotation approach MATTER.

Three classifiers were used for a binary classification of comments into positive vs. negative, and the KNN one gives the most important performance. Obtained results are promising, but still to develop, and the most important conclusion is about stemming that do not improve the classification in our case. Also, the trigram model is not a good representation regarding the obtained results.

We aim in the future to develop the approach by considering the parts in the comment that enclose the most of semantic, which is the first and the last parts. Also taking into account non-Arabic parts of the comment may allow generalising the model.

The use of other techniques for sentiment analysis classification such as deep learning methods is a very important which we project to apply as continuation of this work.

3 .

 3 Accuracy: precision and recall are both complementary one to the other, we combine the two using the Accuracy measure given as:𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = TP+TN TP+FP+TN+FN• TP count the comments correctly assigned to the positive category. • FP count the comments incorrectly assigned to the positive category. • FN comments incorrectly rejected from the positive category. • TN comments correctly rejected from the positive category.

1 .

 1 Manual text pre-processing: A lot of spelling mistakes are found, also some comments are written in languages other than MSA, such us French and English. First, all comments are translated into MSA, as samples the comment written in French language: 'merci Mr Hafid vous avez bien résumé qu est ce qui ce passe dans notre football' (Thank you hafid you resume well what happens in our football) is translated as حفيظ شكرا ما جيدا لخصت لقد عندنا القدم كرة في يحدث šukrã HafiyĎ laqad lax~aSta jay~idã ma yaHduθu fi kuraħi Alqadam ςindanA, and the comment 'thank you' written in English is translated as لك شكرا šukrã lak. Second, Repeated letters such as اليومممممممممم مممممممممممممم Alyaw.mmmmmmmmmm (today with the last letter repeated) becomes اليوم Alyaw.m (today). and بعيييييييييييييييييييييييييدا baςiiiiiiiiiiiiiiiiiiiiiiiiiiydã (far with a middle letter repeated) which becomes بعيدا baςiydã (far). Then Arabizi comments, when Arabizi is an Arabic language used in SMS and in tchat in Internet. It differs from transliteration that there is no standard to adopt in this language. Arabizi comments, in this work, are transformed into their Arabic equivalent. For example, the comment 'YA3TIK SAHA KHOYA BARATLI KHATRI FI L3ADYAN VIVE L'ALGÉRIE 1.2.3' (Thank you brother you Warmed my heart in the enemies, life to Algeria) is transformed to الجزائر تحيا األعداء، في خاطري أثلجت أخي الصحة يعطيك yaςTik AlSiHaħ Ȃaxi Ȃθ.lajta xATiriy fi AlȂς.dA' taHyA AljazAŷir.

Figure 1 .

 1 Figure 1. Sample of word light stemming.

Figure 2 .

 2 Figure 2. Sample of word Stemming. 4. Stop words Removal: a list of stop words is offered by the used toolkit. 5. Word n-gram: Unigram, bigram and trigram word are generated. 6. Word vector: four-word vectors are tested Term Frequency (TF), Term Occurrence (TO), Term Frequency Inverse Document Frequency (TF-IDF) and Binary Term Occurrence (BTO).

1 .

 1 Model: The above model is conserved as it. M={T,R,I} T= {Comment-classe, Positive, Negative, Neutral} R= {Comment-classe:: = Positive| Negative| Neutral}

Table 2 .

 2 First round Classification using NB.

	Light			Unigram			Bigram			Tri-gram
	Stem		Acc	Precision Pos Neg	Recall pos Neg	Acc	Precision Pos Neg	Recall pos Neg	Acc	Precision Pos Neg	Recall pos Neg
		TO	64,44 64,44 64,44 64,44 64,44 61,11 60,87 61,36 62,22 60,00 62,22 61,70 62,79 64,44 60,00
	No	TF TF-IDF 65,56 65,91 65,22 64,44 66,67 63,33 63,64 63,04 62,22 64,44 63,33 63,64 63,04 62,22 64,44 63,33 64,29 62,50 60,00 66,67 58,89 59,52 58,33 55,56 62,22 60,00 60,47 59,57 57,78 62,22
		BTO	58,89 58,70 59,09 60,00 57,78 57,78 57,45 58,14 60,00 55,56 58,89 58,33 59,52 62,22 55,56
		TO	68,89 69,77 68,09 66,67 71,11 63,33 63,64 63,04 62,22 64,44 64,44 65,12 63,83 62,22 66,67
	Yes	TF TF-IDF 70.00 70,45 69,57 68,89 71,11 65,56 67,50 64,00 60,00 71,11 66,67 69,23 64,71 60,00 73,33 66,67 68,29 65,31 62,22 71,11 63,33 64,29 62,50 60,00 66,67 63,33 64,29 62,50 60,00 66,67
		BTO	66,67 66,67 66,67 66,67 66,67 61,11 60,87 61,36 62,22 60,00 62,22 62,22 62,22 62,22 62,22

Table 3 .

 3 First round Classification using KNN.

	Light				Unigram					Bigram				Tri-gram
	Stem		Acc	Precision Pos Neg	Recall pos Neg	Acc	Precision Pos Neg	Recall pos Neg	Acc	Precision Pos Neg	Recall pos Neg
		TO	52,22 51,16 75,00 97,78	6,67	51,11 50,57 66,67 97,78	4,44	51,11 50,57 66,67 97,78	4,44
	No	TF TF-IDF 63,33 60,71 67,65 75,56 51,11 63,33 60,71 67,65 75,56 51,11 61,11 58,93 64,71 73,33 48,89 57,78 55,74 62,07 75,56 40,00 56,67 55,17 59,38 71,11 42,22 56,67 55,17 59,38 71,11 42,22
		BTO	50,00 50,00 50,00 97,78	2,22	52,22 51,16 75,00 97,78	6,67	52,22 51,16 75,00 97,78	6,67
		TO	48,89 49,32 47,06 80,00 17,78 51,11 50,63 54,55 88,89 13,33 52,22 51,25 60,00 91,11 13,33
	Yes	TF TF-IDF 64,44 65,12 63,83 62,22 66,67 64,44 65,85 63,27 60,00 68,89 64,44 65,85 63,27 60,00 68,89 70,00 68,00 72,50 75,56 64,44 68,89 67,35 70,73 73,33 64,44 68,89 67,35 70,73 73,33 64,44
		BTO	53,33 51,72	100	100	6,67	51,11 50,56	100	100	2,22	51,11 50,56	100	100	2,22

Table 4

 4

	3. Adjudication: We generate our gold standard by
	adjudication of annotation step. And this is
	performed to obtain a single annotated corpus from
	the two available. We eliminate the neutral class and
	for equilibrium we take the 194 negative comments
	and only 194 from positives.
	4. Processing: The above described processing steps
	are conducted twice.
	5. Train and Test: We use always the three classifiers,
	SVM, NB and KNN. And the 10-fold cross-
	validation method.
	6. Evaluate: From

  Table in this second round we remark that even the IAA is improved, the SVM classification results are worse that the first round.

Table 4 .

 4 Second round with SVM.

	Light			Unigram			Bigram			Tri-gram
	Stem		Acc	Precision Pos Neg	Recall Pos Neg	Acc	Precision Pos Neg	Recall Pos Neg	Acc	Precision Pos Neg	Recall Pos Neg
		TO	71,13 81,06 66,02 55,15 87,11 69,85 77,30 65,59 56,19 83,51 71,13 78,87 66,67 57,73 84,54
	No	TF TF-IDF 69,33 82,05 63,84 49,48 89,18 69,07 80,33 63,91 50,52 87,63 70,88 82,40 65,40 53,09 88,66 70,62 83,33 64,93 51,55 89,69 70,88 81,89 65,52 53,61 88,14 70,62 82,79 65,04 52,06 89,18
		BTO	71,39 81,68 66,15 55,15 87,63 70,10 79,55 65,23 54,12 86,08 68,56 76,87 64,17 53,09 84,02
		TO	71,13 77,33 67,23 59,79 82,47 69,33 74,51 65,96 58,76 79,90 71,91 77,78 68,09 61,34 82,47
	Yes	TF TF-IDF 69,33 72,73 66,82 61,86 76,80 72,16 79,45 67,77 59,79 84,54 69,85 73,91 66,96 61,34 78,35 70,88 75,47 67,69 61,86 79,90 72,16 79,05 67,92 60,31 84,02 71,39 78,62 67,08 58,76 84,02
		BTO	71,65 77,27 67,95 61,34 81,96 69,33 74,19 66,09 59,28 79,38 72,16 77,22 68,70 62,89 81,44

Table 5 .

 5 Second round classification using Naïve Bayes.

	Light Stem		Acc	Unigram Precision Pos Neg	Recall Pos Neg	Acc	Bigram Precision Pos Neg	Recall Pos Neg	Acc	Tri-gram Precision Pos Neg	Recall Pos Neg
		TO	70,36 79,26 65,61 55,15 85,57 70,62 84,48 64,71 50,52 90,72 70,36 84,35 64,47 50,00 90,72
	No	TF TF-IDF 70,36 74,84 67,25 61,34 79,38 71,91 79,72 67,35 58,76 85,05 72,16 81,16 67,20 57,73 86,60 70,36 73,94 67,71 62,89 77,84 71,13 78,08 66,94 58,76 83,51 71,13 80,60 66,14 55,67 86,60
		BTO	72,16 83,59 66,54 55,15 89,18 71,65 88,18 65,11 50,00 93,30 70,88 87,85 64,41 48,45 93,30
		TO	73,45 78,26 70,04 64,95 81,96 72,94 83,97 67,32 56,70 89,18 72,42 84,25 66,67 55,15 89,69
	Yes	TF TF-IDF 73,45 76,30 71,16 68,04 78,87 73,97 78,88 70,48 65,46 82,47 73,97 79,25 70,31 64,95 82,99 73,97 77,51 71,23 67,53 80,41 75,00 80,12 71,37 66,49 83,51 74,74 80,77 70,69 64,95 84,54

BTO 74,74 83,33 69,67 61,86 87,63 74,23 87,30 67,94 56,70 91,75 73,71 87,10 67,42 55,67 91,75

Table 6 .

 6 Second round classification using KNN. ,53 59,41 36,60 92,78 63,92 82,14 58,88 35,57 92,27 63,66 81,93 58,69 35,05 92,27 TF 61,60 90,91 56,76 25,77 97,42 61,86 89,66 56,97 26,80 96,91 62,11 89,83 57,14 27,32 96,91 TF-IDF 56,19 92,86 53,33 13,40 98,97 56,96 90,91 53,80 15,46 98,45 57,73 91,67 54,26 17,01 98,45 BTO 63,92 92,19 58,33 30,41 97,42 62,89 89,06 57,72 29,38 96,39 62,37 88,71 57,36 28,35 96,39 Yes TO 64,69 78,22 59,93 40,72 88,66 65,72 79,61 60,70 42,27 89,18 65,72 79,61 60,70 42,27 89,18 TF 65,72 67,63 64,19 60,31 71,13 67,78 69,94 66,05 62,37 73,20 67,53 69,77 65,74 61,86 73,20 TF-IDF 65,21 65,61 64,82 63,92 66,49 66,49 66,33 66,67 67,01 65,98 66,49 66,33 66,67 67,01 65,98 BTO 63,66 85,33 58,47 32,99 94,33 62,63 81,01 57,93 32,99 92,27 62,63 81,01 57,93 32,99 92,27

	Light Stem	Acc	Unigram Precision Pos Neg	Recall Pos Neg	Acc	Bigram Precision Pos Neg	Recall Pos Neg	Acc	Tri-gram Precision Pos Neg	Recall Pos Neg
	TO	64,69 83
	No

For transliteration we are following in this work the scheme developed by[START_REF] Guellil | SentiALG : Automated Corpus Annotation for Algerian Sentiment Analysis Introduction[END_REF].

He is also a member of program committees, editor or reviewer for international journals or conferences proceedings.


Wide angle static and dynamic light scattering under shear D. Kushnir, 1 N. Beyer, 1 E. Bartsch, 2 and P. Hébraud We develop and characterize a wide angle static and dynamic light scattering under shear setup. The apparatus is suitable for the study of the structure and the dynamics of soft materials systems with sub-micron characteristic length scale. The shear device consists in two parallel plates and the optical setup allows to perform light scattering measurements in any plane that contains the gradient of the velocity field direction. We demonstrate several capabilities of our apparatus : a measurement of the evolution with shear of the first peak of the structure factor of a concentrated suspension of spherical particles, both in the compression and the extension quadrants of the shear flow, and the measurement of the velocity profile in dynamic light scattering. We present a theoretical treatment of light scattering under flow that takes into account the Gaussian character of the illumination and of the detection optical paths, in the case where the scattering volume extension is smaller than the gap of the flow cell, and compare with experimental measurements.

I. INTRODUCTION

The flow of disordered systems such as colloidal suspensions, glasses, foams, polymer suspensions or gels, involves a change of the organization of their elementary constituents. For example, flow induces distortion of the microstructure of suspensions [START_REF] Szamel | Nonequilibrium structure and rheology of concentrated colloidal suspensions: Linear response[END_REF][START_REF] Westermeier | Connecting structure, dynamics and viscosity in sheared soft colloidal liquids: A medley of anisotropic fluctuations[END_REF] , and it orients or deforms individual objects, such as polymers [START_REF] Rubinstein | Polymer Physics[END_REF] , droplets [START_REF] Bentley | An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows[END_REF] or aggregates [START_REF] Kao | Dispersion of particles by shear[END_REF] . As a consequence, the observation of the structure of these systems under flow has been recognized as an important topic and several techniques have been developed to probe their dynamics and structure under flow. While some of them, such as NMR [START_REF] Callaghan | Rheo-NMR: Nuclear magnetic resonance and the rheology of complex fluids[END_REF] or acoustic velocimetry [START_REF] Manneville | High-frequency ultrasonic speckle velocimetry in sheared complex fluids[END_REF] , allow to probe the dynamics of constituents of the systems, the description of their structure mainly relies on optical setups either in direct or reciprocal space. In real space, optical microscopy techniques have been used and full structure factor information has been obtained [START_REF] Besseling | Quantitative imaging of colloidal flows[END_REF] , but they suffer from limitations : most often, fluorescent techniques are used [START_REF] Besseling | Three-dimensional imaging of colloidal glasses under steady shear[END_REF][START_REF] Cohen | Shear-induced configurations of confined colloidal suspensions[END_REF][START_REF] Derks | Confocal microscopy of colloidal dispersions in shear flow using a counter-rotating cone-plate shear cell[END_REF][START_REF] Derks | Confocal microscopy of colloidal dispersions in shear flow using a counter-rotating cone-plate shear cell[END_REF][START_REF] Lin | A multi-axis confocal rheoscope for studying shear flow of structured fluids[END_REF][START_REF] Schall | Visualization of dislocation dynamics in colloidal crystals[END_REF][START_REF] Schall | Structural rearrangements that govern flow in colloidal glasses[END_REF][START_REF] Wu | A new parallel plate shear cell for in situ real-space measurements of complex fluids under shear flow[END_REF] , which requires specific chemical modifications. The optical resolution is moreover limited, although advances in non-linear optics has led to highly resolved techniques [START_REF] Klar | Subdiffraction resolution in far-field fluorescence microscopy[END_REF] , but to the cost of long exposure times, difficult to combine with the application of flow. Imaging a statistically relevant ensemble of individual objects requires long observation times so that a compromise needs to be performed between optical resolution, large ensemble observation and the time of experiment. Microscopy is moreover limited by multiple scattering that occurs in concentrated systems, and, even using fluorescent probes, limits the depth of observation inside the sample. In fact, most often, systems have to be specifically designed to fit the diverse constraints imposed by microscopy tools. As a consequence, scattering techniques are instruments of choice for probing the structure and dynamics of large ensembles of particles, with high temporal resolution. They lead to direct measurement of the structure factor S(q), related to the fluctuations of the compressibility of the system [START_REF] Prasad | Confocal microscopy of colloids[END_REF] . Small-Angle X-ray Scattering (SAXS) and Small-Angle Neutron Scattering (SANS) [START_REF] Johnson | Structure factor distortion for hard-sphere dispersions subjected to weak shear flow: Small-angle neutron scattering in the flow-vorticity plane[END_REF][START_REF] De Kruif | Small-angle neutron scattering of sheared concentrated dispersions: Microstructure along principal flow axes[END_REF][START_REF] Eberle | Flow-sans and rheo-sans applied to soft matter[END_REF] allow to probe the structure of samples at low q-range, and recently, coherent X-ray scattering has been developed [START_REF] Amann | Shear-induced breaking of cages in colloidal glasses: Scattering experiments and mode coupling theory[END_REF][START_REF] Leheny | Rheo-xpcs[END_REF][START_REF] Rogers | Echoes in X-ray speckles track nanometer-scale plastic events in colloidal gels under shear[END_REF] and used to study the dynamics of colloidal systems under shear [START_REF] Denisov | Resolving structural modifications of colloidal glasses by combining x-ray scattering and rheology[END_REF][START_REF] Denisov | Sharp symmetry-change marks the mechanical failure transition of glasses[END_REF] . The associated wavelength being several orders of magnitude smaller than structural length scales (λ = 0.154 nm [START_REF] Amann | Shear-induced breaking of cages in colloidal glasses: Scattering experiments and mode coupling theory[END_REF][START_REF] Denisov | Sharp symmetry-change marks the mechanical failure transition of glasses[END_REF] ), small angle scattering is used (typically between 10 -2 and 1 • ), which allows to access characteristic length scales up to ≈ 100 nm, but orienting the scattering vector q relative to the flow field is challenging. For instance, in plate/plate shear flows, one has access to q ∈ (v, ∇ ∧ v) plane [START_REF] Denisov | Resolving structural modifications of colloidal glasses by combining x-ray scattering and rheology[END_REF] only, while directions of q along v and ∇v may be approximately reached using Couette geometry [START_REF] Narayanan | A microvolume shear cell for combined rheology and x-ray scattering experiments[END_REF] . Light scattering in the visible range is thus an ideal candidate for the measure of the structure and the dynamics of soft matter systems. Two light scattering techniques have been widely used under flow : Diffusing Wave Spectroscopy (DWS) [START_REF] Wu | Diffusing-wave spectroscopy in a shear flow[END_REF][START_REF] Ozon | Partial rejuvenation of a colloidal glass[END_REF] , that allows to study the dynamics of very turbid systems, has been used to probe flow non-linearities [START_REF] Durian | Nonlinear bubble dynamics in a slowly driven foam[END_REF][START_REF] Höhler | Periodic nonlinear bubble motion in aqueous foam under oscillating shear strain[END_REF] , reversibility [START_REF] Hébraud | Yielding and rearrangements in disordered emulsions[END_REF][START_REF] Petekidis | Rearrangements in hard-sphere glasses under oscillatory shear strain[END_REF] and spatial heterogeneities [START_REF] Erpelding | Diffusive wave spectroscopy applied to the spatially resolved deformation of a solid[END_REF] , but it does not allow to access sample structure under flow as q-dependent scattering information is averaged out by multiple scattering. On the other hand, Small Angle Light Scattering [START_REF] Ackerson | Hard-sphere dispersions: Small-wave-vector structure-factor measurements in a linear shear flow[END_REF][START_REF] Cipelletti | Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator[END_REF][START_REF] Aime | A stress-controlled shear cell for small-angle light scattering and microscopy[END_REF][START_REF] Aime | Probing shear-induced rearrangements in fourierspace. i. dynamic light scattering[END_REF][START_REF] Läuger | A melt rheometer with integrated small angle light scattering[END_REF][START_REF] Salmon | An optical fiber based interferometer to measure velocity profiles in sheared complex fluids[END_REF] instruments under flow have been developed, and used to measure structure factors of colloidal suspensions under flow [START_REF] Ackerson | Comparison of small shear flow rate-small wave vector static structure factor data with theory[END_REF] . Nevertheless, light detection at small angles is restricted to the study of systems that exhibit large scattering length scales. A Wide Angle Light Scattering setup, that detects scattered light at a constant diffusion angle, θ = 170 • has been recently developed [START_REF] Pommella | Coupling space-resolved dynamic light scattering and rheometry to investigate heterogeneous flow and nonaffine dynamics in glassy and jammed soft matter[END_REF] , q being close to the gradient of velocity. It does not allow neither to vary the modulus of q (equal to 33 µm -1 ) neither to change the orientation of q relative to the flow. But, under flow, the structure factor is anisotropically deformed along any direction in the (v, ∇v) plane [START_REF] Schwarzl | Shear-flow-induced distortion of the structure of a fluid: Application of a simple kinetic equation[END_REF] . In particular, under simple shear flow, one may define compression and extension directions [START_REF] Guyon | Physical Hydrodynamics[END_REF] , along which particles are pushed one against each other, or pulled apart. The deformation of the structure factor in these directions is related to the non-linear flow properties of these suspensions, such as shear thinning [START_REF] Maranzano | Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transition[END_REF] or shear-thickening [START_REF] Seto | Microstructure and thickening of dense suspensions under extensional and shear flows[END_REF][START_REF] Martys | Stress propagation in a concentrated colloidal suspension under shear[END_REF] behaviors. The development of a wide angle Static and Dynamic Light Scattering (SLS/DLS) setup under shear would allow both to extend the range of length scales probed and to orient the scattering vector relative to the flow. Nevertheless, it remains challenging due to the sensitivity of the technique to light scattered by optical defects and impurities, in particular at optical interfaces, which imposes severe constraints to the alignment and optical quality of a setup when one of the sample container surface is moving. In this article, we introduce a wide angle light scattering setup under flow, primarily devised to study the structure factor of hard sphere suspensions at q values close to the first peak of the structure factor. The static and dynamic structure factors of a hard sphere system in the absence of flow and under shear are studied and a theoretical analysis of the light correlation under flow is developed and compared to experimental results.

II. SYSTEM AND SETUP

A. The system

The setup has been primarily developed to study the structure and the dynamics of suspensions of hard spheres under flow. Several experimental realizations of colloidal hard spheres have been developed during the last twenty years. For instance, PMMA particles suspended in a mixture of decahydronaphthalene and bromocyclohexane, that allows to match both the density and the optical index have been thoroughly studied [START_REF] Pham | Multiple glassy states in a simple model system[END_REF] , in particular, using confocal microscopy [START_REF] Lu | Gelation of particles with short-range attraction[END_REF] . Nevertheless, the index match-ing is not sufficient to allow light scattering measurements at high volume fractions and require the use of specific tools, such as two-color light scattering [START_REF] Pham | Multiple glassy states in a simple model system[END_REF] . Gel particles, that consist of reticulated polymers swollen in a solvent have been synthesized, and allow for a better index matching between the solvent and the particles. Among them, PNIPAM colloidal gels possess the advantage that their swelling ratio, and as a consequence, the volume fraction of the suspension, may be controlled by temperature. But the interaction potential is softer than that of hard spheres. Here, we consider polystyrene microgel particles suspended in a good solvent, 2-ethyl-naphtalene (2EN), of refractive index n = 1.599. The structure and dynamics of these suspensions at volume fractions corresponding to a glass phase have been studied in detail in the absence of shear [START_REF] Eckert | Re-entrant glass transition in a colloid-polymer mixture with depletion attractions[END_REF][START_REF] Schneider | On tuning microgel character and softnessof cross-linked polystyrene particles[END_REF] . Using measurements of the elastic modulus [START_REF] Schneider | On tuning microgel character and softnessof cross-linked polystyrene particles[END_REF][START_REF] Koumakis | Direct comparison of the rheology of model hard and soft particle glasses[END_REF] , it has been shown that their interaction potential is well described by u(r) ∼ r r 0 n with n as large as 99 [START_REF] Schneider | On tuning microgel character and softnessof cross-linked polystyrene particles[END_REF] . These suspensions may thus be considered as good models of hard sphere suspensions [START_REF] Royall | In search of colloidal hard spheres[END_REF] . Two different systems will be considered : dilute systems (of volume fraction 0.07 or 0.3) of monodisperse of radius 149 nm and reticulation ratio 1 : 10 (sample M149) are used to characterize the dynamic light scattering ability of our setup. Concentrated suspensions (φ = 0.56 and φ = 0.62), consisting of a mixture of 149 nm and 161 nm radius particles, and reticulation ratio 1 : 50, with a number ratio of small to large particles equal to 3.1 (sample B149 -161), are used to perform Static Light Scattering measurements. They do not exhibit crystallization, and are known to possess a liquid/glass transition at φ m = 0.58. The peak of the structure factor in the absence of shear corresponds to a scattering vector q = 26 µm -1 , corresponding to a scattering angle θ ∼ 100 • at a wavelength in vacuum λ 0 = 633 nm.

B. Optical design

We first describe the optical part of the setup and follow the notations of Fig. 1. A 30 mW, 633 nm LASER source (Melles Griot 05-LHP) of d 0 = 2 mm beam output diameter is focused with a f 1 = 1 m focal length lens (L 0 ) at a point O inside the sample. For most experiments, O is located in the middle of the gap of the shear cell, described below. A custom-made spherical lens (L) (Sill Optics, Germany) is used in order to ensure that the air/glass interface is normal do the direction of the incoming and detected light. The lens is supported by four pillars P, and four arms of adjustable length that allow to position and orient the cell relative to the rest of the setup. It is mechanically independent of the shear device located underneath. The refractive index of the lens matches the refractive index of the solvent and is truncated along a plane normal to its axis so that its center O is located inside the system, 3.7 mm below its lower planar surface. In order to avoid focusing of the incoming beam by the sphericity of the lens, the beam enters the spherical lens through a planar window, w, located at 20 • from the lens axis. It crosses a 200 µm thick layer of solvent (2EN) that allows to freely translate the shear device relative to the center O of L while keeping constant the refractive index along the incident beam path. It then crosses the upper plate of the shear cell of 3 mm thickness, and enters the sample. Under these conditions, the center of the spherical lens is then located 0.5 mm under the bottom surface of the shear cell upper plate. Light is collected with a multimode (of input diameter 105 µm; Thorlabs LG105LVA), for static light scattering measurements, or monomode (of input diameter 4.5 µm ; Thorlabs SM600) for dynamic light scattering measurements, fiber, f , equipped with a focusing lens of 4.5 mm diameter and 10 cm focal length, placed onto a goniometer arm, G, at 10 cm from the center of the cell. The alignment of the setup is performed following three main steps. First, in the absence of the lens L and of the shear cell disks, the LASER beam being vertical, it is positioned and focused onto the axis of rotation of the goniometer, materialized by a needle. The optical fiber used for detection is also focused at the same point. Second, the lens L and the disks D 1 and D 2 are successively brought to position. Their orientation, normal to the beam, are adjusted by aligning the beam with its reflexion by their surfaces using micrometer screws. Last, the incoming LASER beam is positioned at 20 • from the vertical by moving back the frame that supports the mirrors m 1 to m 3 . It is then aligned normal to the entry window w. Fine adjustment of the setup is achieved by static measurements of the intensity scattered by the solvent and looking for constant I(θ ) sin θ , as it is routinely performed for standard light scattering setup. The angle of light collection is ∆θ = 2.25 • 10 -2 rad, so that the q-accuracy of our setup at θ = 100 • is ∆q = 0.4 µm -1 . The intersection of the incoming and detection paths defines the scattering volume. Scattered photons are detected by a photomultiplier and a discriminator (ALV/SO-SIPD, ALV Gmbh, Germany) and the intensity correlation is computed using a commercial digital correlator (ALV 7004).

C. Shear cell device

The sample s is placed between two disk plates of diameter 120 (D 1 , top plate) and 50 mm (D 2 , bottom plate). The gap between the plates is 1 mm. The bottom disk is brought to rotation by a stepper motor, M (ST4118, Nanotec, Germany), reduced 64 times with a belt. The minimum angular rotation of D 2 , corresponding to a single motor step is 5 • 10 -4 rad. The shear device, consisting of the two disk plates and the rotation motor, is placed onto a motorized xy translation stage (T ) that allows the positioning of the shear flow relative to the center of the spherical lens. The xy translation has two purposes. First, changing the distance between the spherical lens center and the axis of rotation allows to control the local shear rate at which light is collected. The shear is null at the center, but, in practice, the scattering volume is chosen not closer than 2 mm from the rotation axis, leading to a minimal shear value of 10 -3 for a single motor step. Second, the position of the shear cell relative to the plane of scattering Π scatt allows to choose the angle between the velocity direction and Π scatt between 0 and π/2. These two extreme situations, corresponding to the scattering vector normal to the velocity direction (q ∈ (∇v, ∇ ∧ v)) and normal to the velocity rotational direction (q ∈ (v, ∇v) ) are represented in Fig. 1 (c) and (d). The z-translation allows to position the shear cell relative to the center of the optical lens, and to position the scattering volume inside the shear cell gap. Finally, the detection range is limited at large angles, by the width of the entry window (θ max = 170 • ), and, at small angles by the edge of the truncated spherical lens (θ min = 80 • ). Let us moreover stress that variation of θ has two consequences. It changes both the modulus q of the scattering vector and the orientation of the scattering vector relative to the flow field. Both quantities cannot be modified independently. Removal of this constraint would necessitate simultaneous change of the incident and the scattering angles, that would allow to change the orientation of the scattering vector relative to the flow while keeping its modulus constant. The range of accessible q moduli and orientations of our device are given in Fig. 2 (a).

III. CHARACTERIZATION OF THE SETUP A. Static light scattering

We first characterize the behavior of the setup as a static light scattering device, in the absence of flow. We study the intensity scattered by a bimodal suspension B149 -161 at φ = 0.62. The scattered intensity is compared to the scattered intensity measured with an ALV-CGS3 setup, with an illumination wavelength equal to 633 nm. Results are given in Fig. 3. The peak of the structure factor is recovered, with the same shape as the one measured on the ALV-CGS3 device. Nevertheless, the scattered intensity, as measured with our setup, is shifted by 4 ± 0.49 • , relative to the intensity measured by the ALV-CGS3 apparatus. This shift does not depend on the system. It may be due to a slight mismatch in the optical refractive index of the suspension and the upper plate or to a slight mismatch between the center of rotation of the goniometer and the center of the lens L, that would lead to non-normality between the surface of L and the direction of detection. As a consequence, all angle measurements are shifted by 4 • in the rest of the article.

B. Dynamic light scattering

We characterize the Dynamic Light Scattering ability of our setup. In the absence of flow, the intensity correlation measured by our setup is in very good agreement with the correlation measured with the ALV-CGS3 device (Fig. 4). In particular, the difference between the two correlation functions, δ g 2 is distributed over positive and negative values (Fig. 4 top), meaning that our setup does not induce any systematic shift of the intensity correlation function. Moreover, the long time baseline of the intensity correlation is identical for the two setups( Fig. 4 inset) and equal to 3.4 • 10 -3 . This value is very sensitive to the detection of light scattered by impurities, in particular at the interfaces. This shows that the index matching between the lens, the disks and the solvent is such that the amount of light scattered by the shear cell interfaces, 500 µm from the scattering volume in our setup, is not larger than the intensity scattered by the cell used in the ALV setup, that uses a 1 cm diameter cuvette, 5 mm away from the scattering volume. In nominal position, the thickness of the layer of solvent between the lens L and the upper disk D 1 is 200µm and the center of the spherical lens is located at height 500 µm, in the middle of the gap. The thickness of the solvent layer can be increased, so that the center of the lens can be positioned at any height comprised between 500 µm and 1 mm. The thickness of the index matching solvent layer becomes 700 µm and surface tension is sufficient to maintain the layer. In order to position the scattering volume at heights smaller than 300 µm, we slightly move off center the illumination beam and the detection path : by changing by 0.5 • the angle between the normal of the window w, the scattering volume is lowered by 200 µm. As a consequence, the scattering volume is not aligned with the goniometer axis. Nevertheless, the angle being kept constant, this does not affect the measured dynamics, as seen in Fig. 5 (a). This thus allows to measure the intensity correlation function at any height in the sample. The intensity correlation functions of a φ = 0.3 suspension B149 -161 are given in Fig. 5 in the absence of flow (a) and under flow at γ = 5 s -1 (b). In the absence of flow, the intensity correlation function does not depend on the height of the scattering volume inside the gap, from 100 µm above the lower surface up to 100 µm below the upper surface. This is consistent with the extension of the scattering volume, of ≈ 100 µm extension, and shows that the measurement is insensitive to light reflection at the interfaces of the shear plates. The field correlation function decays as e -t/τ with τ = 9.51 ms (Fig. 5 (a) inset). This is consistent with the decay time of a Brownian particle in an effective medium of viscosity given by the Krieger-Dougherty [START_REF] Krieger | A mechanism for non-newtonian flow in suspensions of rigid spheres[END_REF] Close to the lower surface, where the deformation is applied, the time at haft decorrelation, τ 1/2 is smaller (Fig. 5 (b) and (b) top inset). This shows that the dynamics is not homogeneous inside the gap. Nevertheless, the overall autocorrelation functions may be rescaled by τ 1/2 , and a good overlap is obtained (Fig. 5 (b) bottom inset). Thus the motions of the particles at any height, follow a shear deformation, but that a higher shear rate forms close to the lower surface . This suggests that shear banding, generally observed for suspensions with attractive interactions [START_REF] Schneider | On tuning microgel character and softnessof cross-linked polystyrene particles[END_REF] , occurs in our system. These measurements show the ability of our setup to measurement local shear rates, with spatial resolution of ≈ 100 µm.

IV. STRUCTURE FACTOR UNDER FLOW

We now study the scattered intensity under flow, with two geometries : the scattering vector belongs to the (v, ∇v) plane (configuration of Fig. 1(c)) and to the plane (∇v, ∇ ∧ v) (configuration of Fig. 1(d)). The peak position is then at a defined angle, ±17.5 • relative to the ∇v direction (corresponding to positions A and B in Fig. 2 (a)) and we study both situations. This is in particular relevant in the (v, ∇v) plane, where these two configurations correspond to the compression and the extension quadrants of the simple shear deformation (Fig. 2 (b)). Peclet numbers (Pe = γa 2 D where γ is the shear rate, a the average radius of the particles and D = 4.6 • 10 -13 m 2 •s -1 their diffusion coefficient) ranging from 0 to 7 • 10 -1 are studied, and results are given in Figs. 6 (a) to (d) . The black curve corresponds to the structure factor at rest, and grey curves to structure factors under flow. In the (v, ∇v) plane, the peak is shifted towards larger (respectively smaller) q-values in the compression (respectively extension) quadrant. In both cases, the peak amplitude decays. The deformation of the structure factor is less important in the (∇v, ∇ ∧ v) plane, the peak position and height are almost constant, but a broadening of the peak occurs at low q values. A few theories are available to describe the deformation of the structure factor at rest. They can be organized in two categories : those that solve a convective diffusion equation for the pair correlation function g(r, Pe) [START_REF] Russel | Nonequilibrium statistical mechanics of concentrated colloidal dispersions: Hard spheres in weak flows[END_REF] , valid in the limit of very low Pe and those that ignore hydrodynamic interactions and consider a kinetic equation for the structure factor. As they consider S(q), these theories may be compared to experimental measurements of structure factor under shear, and we consider more specifically here the model of Schwarzl and Hess [START_REF] Schwarzl | Shear-flow-induced distortion of the structure of a fluid: Application of a simple kinetic equation[END_REF] , which relies on a simple exponential ansatz for the damping of the structure factor under flow. It has been shown to describe qualitatively the structure factor under flow of PMMA particles [START_REF] Ackerson | Shear-induced order in suspensions of hard spheres[END_REF] . The distortion of the structure factor of the solution under flow is calculated under the assumption that the time evolution of g, ∂ g ∂t is equal to the sum of a flow advection term γr y ∂ g ∂ x where x is along the flow velocity direction and r y is the projection of r along the velocity gradient, and of a damping term, D(g), that ensures that the suspension goes back to an equilibrium state, after cessation of flow. The damping term is assumed to possess a unique relaxation time and to be of the form D(g) = 1 τ (gg eq ) (see Eq. 6 of [START_REF] Schwarzl | Shear-flow-induced distortion of the structure of a fluid: Application of a simple kinetic equation[END_REF] and Eq. B7 in the reciprocal space.) As a starting point, we take the Percus-Yevick description of the structure factor of monodisperse hard spheres at rest 57 (Appendix B). It predicts a first peak of the structure factor at q max R = 3.8 and width at half height δ qR = 0.22 whereas the measured peak is slightly shifted towards larger q values (q max R = 4) and is much broader (δ qR ∼ 0.9). These discrepancies are due to the fact that our suspension is not monodisperse and that its volume fraction is too high to be correctly described by Percus-Yevick approximation [START_REF] Ackerson | Comparison of small shear flow rate-small wave vector static structure factor data with theory[END_REF] . The Schwarzl and Hess model uses the structure factor at rest as a reference, so we consider the evolution of S(q) under shear, relative to its properties at equilibrium, and consider the evolution of the position of the peak and of its height, relative to their value in the absence of shear, q max /q 0 max and S max /S 0 max , as experimentally measured and as computed by the application of the Schwarzl and Hess model to the Percus-Yevick structure factor. Fig. 6 (e) to (g). Qualitatively, the Schwarzl and Hess theory describes the evolution of the peak of the structure factor under flow. redThis theory has been shown [START_REF] Ackerson | Comparison of small shear flow rate-small wave vector static structure factor data with theory[END_REF] to predict correctly the q -→ 0 limit, where one finds that the maximum of the structure factor increases in the compression quadrant whereas it decreases in the extension quadrant. This result is directly related to the increase of isothermal compressibility in the comrpession quadrant and its decrease in the extension quadrant. Our results, obtained at the peak of the structure factor, are not amenable to such a direct thermodynamic interpretation, and tend to show that Schwarzl and Hess model underestimates the change of structure in the extension quadrant, at this q range.This may be related to the fact that the relaxation on this length scales cannot be described by a single exponential relaxation. Indeed, it is known that the suspension exhibits a wide distribution of relaxation times, at volume fractions close to the glass transition [START_REF] Schneider | On tuning microgel character and softnessof cross-linked polystyrene particles[END_REF] .

V. EXPRESSION OF THE FIELD AUTOCORRELATION FUNCTION

We now study the dynamic intensity correlation functions under flow measured with our setup. One assumes that the sample is illuminated by a planar wave of infinite extension [START_REF] Ackerson | Dynamic light scattering at low rates of shear[END_REF] . The field scattered by N particles is :

E s (q) = N ∑ j=1 E 0 e iq•r j (1)
When particules are submitted to a simple shear of amplitude γ, their positions change according to : r j (γ) -r j (0) = γzu x , so that the field autocorrelation function G 1 (q, γ) at this shear amplitude is given by :

G 1 (q, γ) = ∑ i, j |E 0 | 2 e iq•r j (γ)-r i (0) (2)
= |E 0 | 2 ∑ j e -iq x γz j (3) = 1 e e/2
-e/2 e -iq x γz dz (4)

= |E 0 | 2 2 sinc q x γe 2 (5)
where we have assumed that the positions of the particles are uncorrelated and homogeneous, and where e is the extension of the scattering volume along the z-direction. One observes from Eq. 4 that uniform translation of the scatterers does not contribute to the decorrelation of scattered field, and that, under this assumption, the field autocorrelation is due solely to the relative displacement of the scatterers. This description overestimates the characteristic decay time of G 1 (Fig. 7(b)). This is due to the fact that it ignores that the intensity is not homogeneous inside the scattering volume, so that even a pure translation of the scatterers should induce a change of the scattered intensity, and thus contribute to the decorrelation of the signal. Taking this effect into account, Aime et al. [START_REF] Aime | Probing shear-induced rearrangements in fourierspace. i. dynamic light scattering[END_REF] studied the limit under which the thickness of the shear cell is small compared to the extension of the scattering volume, in the low angle scattering regime. Here, we take into account the Gaussian character of both the illumination and detection optics and consider the case where the extension of the scattering volume is smaller than the gap of the shear cell, and located far away from the cell boundaries. Indeed, the waist of the illuminating beam, defined as the distance from the focal point in a plane normal to the direction of propagation, at which the intensity is 1/e its maximum value, is w 0 = 100 µm, and the waist of the detected volume w s = 143 µm. The Rayleigh lengths, defined as the length from the focal point along the direction of propagation at which the intensity is half of its maximal, are much longer (respectively 50 and 180 mm). This implies that the scattering volume may be seen as the intersection of two cylinders. The intensity and the detection efficiency are almost constant along their axis, but decreases with a Gaussian shape along the radial direction. Following this description, we provide an analytical expression of the field correlation function under shear. A. Theory of dynamic light scattering under shear Under shear, the contribution of the decorrelation is not only due to the motion of the particles relative to others, but also to the fact that under a Gaussian illuminating field, the overall motion of the scatterers induce a change of the scattered intensity. Let us develop a theoretical description of light scattering under shear under the condition that the extension of the Gaussian beam is smaller than the width of the sample. The notations are defined in Fig. 7 (a). We first consider the triedra T = (x, y, z) relative to the laboratory frame and centered in the center of the gap of the shear cell, x being along the v direction, and y along ∇v. T = (x , y , z ) is obtained by rotation of T so that the incoming light propagates along -y and T = (x , y , z ) so that scattered light propagates along y . α is the angle between u x and u x and β the angle between u x and u x . The scattering angle θ is given by πβ + α (by convention, β > 0 and α < 0, see Fig. 7 (a)) [START_REF]The angle φ between the scattering vector q = k outk 0 and the velocity direction, u x , is φ = β + π 2 -θ 2 = 3β 2 -α 2 . φ[END_REF] . The incident electric field is, in the paraxial approximation [START_REF] Born | Principles of Optics : Electromagnetic Theory of Propagation, Interference, and Diffraction of Light[END_REF]61 :

E in = E 0 w 0 w(y ) e -iky e --ρ 2 w 2 (y ) e ik ρ 2 2r(y ) (6)
where k = 2πn λ 0 is the wave number, w(y ) = w 0 1 + (2y /kw 2 0 ) 2 , r(y ) = y 1 + (kw 2 0 /2y ) 2 and ρ 2 = x 2 + z 2 . Given the parameters of our optical setup, this expression can be simplified. The waist of the beam is w 0 = f 1 λ πd 0 = 100 µm where f 1 is the focal length of the focusing lens and d 0 the beam diameter, and the Rayleigh length, kw 2 0 2 = 30 cm, is large compared to the distance from the focus, y , so that 2y kw 2 0 1 and w(y ) ≈ w 0 and the radius of curvature r(y ) diverges as 1/y , so that the transverse factor is e ik ρ 2 2r(y ) = 1. Finally, the field is described by the product of the longitudinal phase factor and the simplified amplitude factor :

E in = E 0 e -iky e -ρ 2 w 2 0 ( 7
)
Scattered light is collected by a monomode optical fiber whose entrance is conjugated with the scattering volume and the detection function of our setup has a similar Gaussian shape of waist w s 61, [START_REF] Gu | Advanced Optical Imaging Theory[END_REF] . The field scattered by a particle j at position (x, y, z) is :

E s j (α, β ,t) ∝ E 0 e -ik(y (t)-y (t)) e -ρ 2 w 2 0 e -ρ 2 w 2 s (8)
w s being the waist at the focal point of the detection lens. The autocorrelation function of the total scattered field is :

G 1 (α, β ,t) = N ∑ j, j E s j (α, β , 0)E s * j (α, β ,t) (9)
= N ∑ j E s j (α, β , 0)E s * j (α, β ,t) (10)
= N d 3 rE s (α, β , 0)E s * (α, β ,t) (11)
where it is assumed that the positions of any pair of scatterers is uncorrelated and that the scatterers are uniformly distributed in space. Thus :

E s (α, β , 0)E s * (α, β ,t) = |E 0 | 2 d 3 re -ik(y (t)-y (0)-y (t)+y (0)) e - ρ (t) 2 +ρ (0) 2 w 2 0 e - ρ (t) 2 +ρ (0) 2 w 2 s ( 12
)
and the relative displacement of the scatterers is due to the application of a simple shear field. We assume that w 0 and w s are much smaller than the gap of the cell, h, and that the scattering volume does not intersect the cell boundaries. The summation may be performed over entire space, between -∞ and ∞. In the triedra T , the expression of the scattered electric field in Eq. 12 becomes :

E s (α, β ,t) = E 0 ∞ -∞ d 3 re -ik(δ sx+δ sy) e -c 2 x 2 +s 2 y 2 +2csxy+ z 2 w 2 (13)
with

c 2 = cos 2 α w 2 0 + cos 2 β w 2 s ( 14
)
s 2 = sin 2 α w 2 0 + sin 2 β w 2 s ( 15
) cs = sin α cos α w 2 0 + sin β cos β w 2 s ( 16
) δ s = sin α -sin β (17)
δ c = cos β -cos α (18) 1 w 2 = 1 w 2 0 + 1 w 2 s ( 19
)
As the characteristic lengths w 0 and w s of the incident and detection volumes are small compared to the shear cell thickness, the integrations are performed over entire space, and the Gaussian integrals may be computed analytically. The integration over z (along the ∇ ∧ v direction) leads to a constant factor relative to γ. Up to factors that do not depend on the shear amplitude, the integration over x finally gives :

g 1 ∝ dye c 2 2 γ 2 +2s 2 -2 cs 2 c 2 y 2 +(-1 2 c 2 hγ 2 -ikδ sγ)y (20)
which leads to the final expression of the field autocorrelation function :

g 1 (t) ∝ c 2 2 γ 2 + 2s 2 - 2cs c 2 1/2 e 1 4 c 2 h 2 γ 4 +( 1 8 c 2 h 2 -k 2 δ s 2 )γ 2 4( c 2 2 γ 2 +2s 2 -2cs c 2 ) (21)
where c 2 , s 2 , cs and δ s are geometrical factors that depend on the angles α, β and on the width of the Gaussian spots, w 0 and w s and where we have omitted a normalization factor that does not depend on γ.

B. Experimental results

Normalized field correlation functions are plotted as a function of time and deformation in Fig. 7 (b) and (c). Under shear, the characteristic decay time shortens compared to the decay in the absence of flow. Its decay is well described by Eq. 21 with no adjustment parameter, both as a function of the deformation amplitude γ and as a function of time t. Nevertheless, a slow decay mode is observed. This indicates a long lived correlation between the positions of the particles, that may be due to hydrodynamic interactions between particles.

VI. CONCLUSION

We have presented a wide-angle light scattering under shear where the scattering angle can be varied between 80 • and 170 • , corresponding to q-range equal to [19, 29] µm -1 . The shear is applied between two parallel plates, and the q-vector direction can be positioned in any plane that contains the gradient of the velocity field. This contrasts with usual small-angle scattering setups under shear where the q vector is normal to the gradient of velocity. Our setup opens new possibilities to study the structure of soft matter systems. We have demonstrated the capability of our setup to measure the static structure factors under shear in the (v, ∇v) and in the (∇v, ∇ ∧ v) planes. As for dynamic light scattering under shear, we have developed a theoretical description of the scattered intensity correlation function under shear that takes into account the Gaussian character of the illumination and the detection optics, and that is valid when the characteristic length of the scattering volume is smaller than the gap of the shear cell. We have shown that we can quantitatively measure the dynamics of the particles. The setup allows to perform periodic oscillations and to study the reversibility of particles trajectories at the q -1 scale, larger than the scale probed with echo experiments in Diffusing Wave Spectroscopy [START_REF] Hébraud | Yielding and rearrangements in disordered emulsions[END_REF] . By design, the motor and the lower disk may be replaced by a rheometer head, which would allow to measure simultaneously the mechanical response of the studied samples. This device thus allows to study a wide range of problems related to the flow of concentrated suspensions, such as shear banding, flow reversibility at the elastoplastic transition [START_REF] Adhikari | Memory formation in cyclically deformed amorphous solids and sphere assemblies[END_REF] or the effect of shear on aging and rejuvenation of suspensions [START_REF] Viasnoff | Rejuvenation and overaging in a colloidal glass under shear[END_REF][START_REF] Kaloun | Aging of a colloidal glass under a periodic shear[END_REF] . A key property of our setup lies in the fact that the optical elements have been designed to match precisely the optical index of the system. This is necessary to avoid scattering of light from the interfaces. The study of other organic systems, whose optical indexes may be matched by optical glasses (between 1.45 and 2) requires only the replacement of the disks and the spherical lens with disks and lens of identical shape. Nevertheless, the study of suspensions in water remains difficult due to strong refraction and scattering and the interfaces that limits the signal over noise ratio of the light detection. Another limitation of our setup lies in the fact that the scattering vector orientation and modulus cannot be controlled independently. This limitation might be overcome by simultaneous change of the illumination and detection angle. Peclet number q scattering vector, q = k out -k 0 q max q value at the maximum of the structure factor S(q) structure factor S 0 (q) structure factor in the absence of shear (u x , u y , u z ) direct triedra defined by the velocity, the velocity gradient and the vorticity (u x , u y , u z ) direct triedra such as u y = -k 0 /k 0 (u x , u y , u z ) direct triedra such as u y" = k out /k 0 v velocity w 0

1/e 2 incident beam radius at the focal point w(y )

1/e 2 incident beam radius at distance y from the focal point where a(φ , q) = -

1 q 2 (1 + 2φ )λ 1 + 12φ λ 2 d + 12φ λ 1 d 2 q 2 (B3) b(φ , q) = d q 1 + φ 2 λ 1 + 6φ λ 2 (B4)
-6φ (2λ 2 + λ 1 ) 1 d 2 q 2 + 12 φ λ 1 d 4 q 4 (B5) c(φ , q) = 12 dq 3 λ 2 -λ 1 q 2 φ (B6) λ 1 and λ 2 being functions of the volume fraction : λ 1 = (1+2φ ) 2 (1-φ ) [START_REF] Bentley | An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows[END_REF] and λ 2 = -(2+φ ) 2 4(1-φ ) [START_REF] Bentley | An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows[END_REF] . Then, following Schwarzl and Hess [START_REF] Schwarzl | Shear-flow-induced distortion of the structure of a fluid: Application of a simple kinetic equation[END_REF] , we assume that

∂ δ S ∂t -γq x ∂ δ S ∂ q y + 1 τ δ S = γq x ∂ S 0 ∂ q y (B7)
where S 0 is the structure factor in the absence of flow and δ S = S -S 0 is the difference between the structure factor under flow and the structure factor at rest, leading to eq. 12 of Ref. [START_REF] Schwarzl | Shear-flow-induced distortion of the structure of a fluid: Application of a simple kinetic equation[END_REF] : S(q x , q y , q z ) = ∞ 0 dαe -α S(q x , q y + α γτq x , q z ) (B8)

This expression is used to compute numerically the structure factor in the (v, ∇v)s plane at different shear rates.

Figure 1 .

 1 Figure 1. (a) Schematic view of the light scattering under shear setup. m 1 , m 2 and m 3 are mirrors mounted onto kinematic mounts that allow the orientation of the incoming light, focused by lens L 0 , of focal length 1 m, inside the sample. Mechanically independent parts are indicated by different patterns. Four pillars ( P, ) support the spherical lens L. A goniometer arm (G, ) supports an optical fiber, f , that collects scattered light. Finally the shear cell, controlled by motor M is positioned onto a xy translation stage T ( ). (b) Enlarged view of the shear cell as seen from the right side of (a). k 0 and k out are the incident and detection wave vectors. They define the scattering plane Π scatt . L is a spherical lens of 50 mm diameter and center O. The optical axis of the lens is ∆ O . The beam enters L through a planar window w at 20 • from the spherical lens axis. D 1 and D 2 are two glass disks of diameters 120 and 50 mm and of thickness 3 mm. D 2 is brought to rotation by a step motor (M in (a)) of mechanical axis ∆ M . The sample, of 1 mm thickness, is placed between D 1 and D 2 . An optical trap is placed under the cell in order to avoid light reflections. (c) and (d) Two positions of the optical axis ∆ O ( ) relative to the mechanical rotation axis, ∆ M ( ) are shown. (c): the scattering plane Π scatt is normal to ∇ ∧ v, and (d), the scattering plane Π scatt is normal to the flow velocity v. The thick circle represents the lens L, and the thinner circles represent disks D 1 and D 2 .

Figure 2 .

 2 Figure 2. (a) Polar representation of the scattering vector q as a function of its angle relative to the flow, either in the (v, ∇v) plane or in the (∇ ∧ v, ∇v) plane . The continuous black line represents accessible q-values. The dashed black line corresponds to q-values obtained by flow reversal. Scattering vectors associated to the extremal values of the scattering angle, 80 • and 170 • , are represented, corresponding to an orientation of q equal to 120 • and 75 • with the flow (or flow vorticity) direction and a modulus 20.4 µm -1 and 31.6 µm -1 . Dashed grey line : arc of circle of radius q peak . The positions of the peak of the structure factor at rest are determined by the intersection between these curves and are indicated by A (located in the compression quadrant of the flow field) and B (located in the extension quadrant of the flow). (b) Definition of the compression (indicated by red arrows and arcs) and extension (indicated by blue arrows and arcs) of a simple shear flow field 44 .

Figure 3 .

 3 Figure 3. Intensity scattered by a suspension B149-161 of volume fraction φ = 0.62 as measured with ALV-CGS3 (empty circles) and with the developed setup (solid circles). Dashed (resp. solid) lines are quadratic adjustments of the data ±7 • around the peak. The angles corresponding to the intensity measured with the light scattering under shear setup has been shifted by 4 • . The peak position after shift is indicated by the vertical line and obtained by quadratic adjustments of the height of the peaks (solid and dashed lines), that give θ max = 100.12 ± 0.09 • for the ALV-CGS3 data and θ max = 99.98 ± 0.48 • for our setup.

Figure 4 .

 4 Figure 4. Intensity autocorrelation of a suspension M149 of volume fraction φ = 0.07 measured at a scattering angle θ = 105 • , with ALV-CGS3 setup (thin continuous line) and the light scattering under shear device (thick dashed line). Inset: same data represented in double log-log plot. The red dashed curve is an adjustment of the autocorrelation function measured with our setup according to : g 2 (t) -1 = (1b)e -t/τ + b, leading to the baseline value b = 3.4 • 10 -3 . Top: difference between the two measured intensity correlation functions.

  relationship, η = η 0 1 -φ φ m -5/2φ m = 8.6 •10 -3 Pa•s, leading to τ = 10.3 ms Under flow, the situation is different : the characteristic decay time of the intensity scattering function depends on the position of the scattering volume inside the gap.

Figure 5 .

 5 Figure 5. Dynamic structure factor of a monodisperse suspension (M149) of volume fraction φ = 0.30 at different heights inside the gap of the shear device from 100 µm above the lower surface up to 100 µm below the upper surface, at θ = 100 • . (a) Dynamic structure factor at rest. The shape of the correlation function does not depend on the position of the scattering volume inside the gap. Inset Fit of the dynamic structure factor measured at the center of the cell. Only one experimental point out of 10 is represented for clarity. Continuous line is a stretched exponential adjustment of the data : e -(t/τ) α , with parameters τ = 9.8 ms and α = 0.92. (b) Dynamic structure factor under flow, in the (v, ∇v) plane, at γ = 5s -1 . The characteristic decay time is constant up to 600 µm below the (static) upper surface, while the dynamics is faster up to 400 µm above the lower surface. Top right inset Half correlation times of the intensity correlation functions as a function of height. Bottom left inset Intensity correlation functions as a function of rescaled time t/τ 1/2 .

Figure 6 .

 6 Figure 6. Structure factors of a suspension B149 -161 at φ = 0.56 under flow, normalized by the maximum of the structure factor in the absence of shear, S 0 max . (a) and (b) Structure factors in the plane (v, ∇v) in the compression (a) and the extension (b) quadrant of the flow. (c) and (d) Structure factors in the plane (∇v, ∇ ∧ v). (a) and (c) (resp (b) and (d)) correspond to position A (resp B) of Fig. 2 (b). Each curve corresponds to a different Pe = γa 2 D . From black to light grey, Pe = 0, 7 • 10 -3 , 1.8 • 10 -2 , 3.6 • 10 -2 , 7.1 • 10 -2 , 0.18, 0.36 and 0.71. (e) to (h) Height of the maximum of the structure factor relative to the maximum under no shear, S max (q)/S 0 max (respectively of the abscissa q max /q 0 max of the peak), in the compression (e) (resp. (g)) and extension f) (resp. (h)) flow quadrants. Circles linked with thin lines are experimental data while thick lines are the result of Schwarzl and Hess 43 model.

Figure 7 .

 7 Figure 7. (a) Triedras used to express the correlation functions. T = (x, y, z) corresponds to (v, ∇v, ∇ ∧ v), T = (x , y , z ) is such that u y is parallel and opposite to k 0 and T = (x", y", z") is such that u y is parallel to k out . The convention for sign angles is indicated by the ⊕ symbol. Given the position of the LASER entry window, w, α = -20 • , while the accessible range of θ is [80 • , 170 • ]. The figure illustrates the situation corresponding to q oriented in the compression quadrant of the flow. Reversal of the flow velocity allows to position q in the extension quadrant. (b) and (c) Field correlation functions under shear of a suspension M149 of volume fraction φ = 0.07. (b) Field correlation functions as a function of time. From right to left, γ = 0, γ = 5.5, γ = 8.25 , γ = 11 , and γ = 22 s -1 . (c) Field correlation functions as a function of the deformation γ for shear rates γ = 5.5, 8.25 , 11 and 22 s -1 . The dashed line corresponds to the expression of the field correlation for plane waves given by Eq. 5. Field correlation values are the same as in (b). In graphs (b) and (c), continuous lines correspond the theoretical expression given by Eq. 21.

Appendix

  1, a) 1) IPCMS CNRS 23 rue du Loess 67034 Strasbourg, France 2) Institut fur Makromolekulare Chemie, Albert-Ludwigs-Universitat Freiburg, Stefan-Meier Straße 31, 79104 Freiburg, Germany

(Dated:

January 27, 2021)

  A: List of symbols α angle ∠(u x , u x ) β angle ∠(u x , u x ) γ, γshear, shear rate η 0 , η viscosity of the solvent, viscosity of the suspension θ scattering angle ∠(k 0 , k out ) λ 0 LASER wavelength in vacuum Π scatt scattering plane (k 0 , k out ) ρ , ρx 2 + y 2 , x 2 + y 2 gap of the shear cell k 0 , k out , k 0 incident and scattering wave vectors, and their modulus n solvent optical index Pe

	φ	particle volume fraction
	a	average radius of particles
	d 0	illuminating beam diameter
	D	diffusion coefficient of particles of radius a
	E in	incident field
	E s	total scattered electric field
	E s j	electric field scattered by particle j
	f 1 , f 2	illumination and detection lenses focal lengths
	G 1	field correlation function
	g 2	normalized intensity correlation function
	h

ACKNOWLEDGMENTS

PH thanks the organizers of the KITP program "Physics of dense suspensions". This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958, by the International Research Training Group (IRTG) "Soft Matter Science: Concepts for the Design of Functional Materials" , and by the Agence Nationale de la Recherche under Grant No ANR-18-CE06-0001.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Appendix B: Structure factor under shear

We detail here the model used to analyze the structure factors under shear. First, we consider the structure factor of a suspension of hard spheres, with the Percus-Yevick 57,66 closure. The direct correlation function is :

for r > d and c(r) = 0 for r < d, which, using the Ornstein-Zernike relation 1 S(q) = 1n c(q), leads to : 1 S(q) = 1 -4πn q [a(φ , q) sin qd + b(φ , q) cos qd + c(φ , q)] (B2)