Natalia Grabar

Iris Eshkol-Taravella

Disambiguation of occurrences of reformulation markers c'est-à-dire, disons, ça veut dire

Keywords: reformulation, spoken and written corpora, automatic detection of reformulation

Reformulation is a process which consists of saying again an utterance which has already been said, but which goes through formal and/or semantic modifications. Sometimes, reformulations are signaled by specific markers, such as c'est-à-dire, disons, ça veut dire. We propose to study the reformulation phenomenon. More particularly, we concentrate on the syntagmatic structure S1 marker S2, coined around the reformulation markers, and in which the first segment S1 is reformulated by the second segment S2. The purpose of our study is to automatically differentiate between reformulation and non-reformulation occurrences of the markers studied. We design a rule-based system which relies on a set of rules to make the decision. Two kinds of French corpora are processed: spoken corpora ESLO and forum discussion corpus. The evaluation of the system is performed against the manually annotated and consensual reference data. Our system has been created on a subset of the spoken corpus and then applied to the rest of the data. The results obtained reach up to 0.75 precision and are comparable on the corpora analyzed, although spoken corpora remain more difficult to process.

Résumé

La reformulation est un processus qui consiste à dire à nouveau une information qui a déjà été dite, mais en effectuant un ensemble de modifications formelles et/ou sémantiques. Parfois, les reformulations sont signalées par des marquers spécifiques, comme par exemple c'est-à-dire, disons, ça veut dire. Nous proposons d'étudier le phénomène de reformulation. Plus particulièrement, nous nous concentrons sur la structure syntagmatique S1 marker S2, formée autour d'un marqueur de reformulation, et dans laquelle le premier segment S1 est reformulé par le deuxième segment S2. L'objectif de notre étude est de différencier automatiquement les occurrences reformulatives et non reformulatives des marqueurs étudiés. Nous créons un système basé sur des règles, qui repose sur un ensemble d'indices pour prendre la décision. Deux types de corpus en français sont traités : corpus oral ESLO et corpus de discussion de forum. L'évaluation du système est effectuée grâce à une comparaison avec un ensemble de référence consensuel annoté manuellement. Notre système a été créé sur un sous-ensemble du corpus oral et ensuite appliqué au reste de corpus. Les résultats obtenus atteignent jusqu'à 0,75 de précision et sont comparables dans les corpus analysés, bien que les corpus oraux soient plus difficiles à traiter.

Introduction

Reformulation is a process which consists of saying again and in different way an utterance which has already been said (Le Bot et al., 2008). Reformulation can be performed by demand of the interlocutor, or by the decision of the speaker himself. Several reasons may lead to the reformulation: make previous statement more precise, explain the previous statement, give a name to what has been described, etc. Reformulation is spread in written and spoken, formal and informal languages, although, in all these situations, reformulation shows some specificities [START_REF] Fløttum | Dire et redire. La reformulation introduite par "c'est-à-dire[END_REF][START_REF] Rossari | De l'exploitation de quelques connecteurs reformulatifs dans la gestion des articulations discursives[END_REF]. Thus, in written texts, reformulation corresponds to the final result which is proposed to the user, while in spoken language, reformulation represents the various steps of elaboration of an idea [START_REF] Levelt | Monitoring and self-repair in speech[END_REF][START_REF] Hagège | L'homme de paroles. Contribution linguistique aux sciences humaines[END_REF][START_REF] Blanche-Benveniste | Le français parlé. Etudes grammaticales[END_REF][START_REF] Blanche-Benveniste | Le semblamble et le dissemblable en syntaxe[END_REF]. Reformulation can be marked by specific markers (c'est-à-dire, autrement dit, disons, je m'explique, ça veut dire, en d'autres termes...), such as in (1) je suis bien je veux dire je me sens bien but it can also occur without such markers, in which case, phonetic, prosodic and semantic layers of the language may be indicative of its occurrence:

(2) même en bouquin enfin je suis très polar j'aime beaucoup les polars

The proposed work is done on corpora in French. It is dedicated to reformulations introduced by three markers: c'est-à-dire, disons, ça veut dire. The research problem we propose to address is related to the fact that these markers do not systematically indicate reformulations, but can also show other kinds of occurrences. Let us observe the examples which follow and in which the occurrences of disons are used with different meanings:

(3) il y a énormément de vieilles familles euh bourgeoises … ils sont souvent disons moins aisés que les familles d'ouvriers les familles d'employés

(4) nous avons une expression chez nous … nous disons que les gens qui gardent ces choses ont euh une mentalité d'écureuil

(5) basée euh sur le capitalisme enfin la société française disons euh euh basée sur les valeurs euh euh erronées

In the first example, disons is used as discursive marker. It occurs within the syntactic group ils sont moins aisés (they are not very rich). In the second example, the occurrence of disons is in fact the inflectional form (plural of the first person, present tense) of the verb dire (to say). Only the third example provides the occurrence of disons used as reformulation marker.

The objective of the proposed work is to detect sentences with reformulations coined around the three markers studied (c'est-à-dire, disons, ça veut dire). The task aims at deciding whether a given occurrence of a marker introduces reformulation or not. This task started to be studied in a previous work [START_REF] Eshkol-Taravella | Repérage et analyse de la reformulation paraphrastique dans les corpus oraux[END_REF]. By comparison with this work, the reference data are consensual: the annotations have been done by two annotators and then, during common work sessions, a consensus has been reached on annotations which differed from one annotator to another. This process permits to build one common set of annotated data instead of the two sets annotated. Besides, we extended the types of the corpora studied: we work now with two kinds of corpora (spoken and written corpora) instead of only spoken corpora exploited in previous work.

In what follows, we will first present related work on close topics (Section 2). We then introduce the linguistic data processed (Section 3), and the method defined for performing the task (Section 4). Then, the results are presented and discussed (Section 5). We conclude with directions for future work (Section 6).

Related Work

Reformulation can be described from different points of view. We should notice first that reformulation can be conceived as paraphrastic variation of a linguistic segment in which formal modifications occurred [START_REF] Neveu | Dictionnaire des sciences du langage[END_REF]. In this case, paraphrase is the result of reformulation. These two notions are thus closely related. Still, in the existing work, these two notions remain separated. Thus, several works have been done on paraphrases: their automatic detection [START_REF] Malakasiotis | Learning textual entailment using SVMs and string similarity measures[END_REF][START_REF] Lin | Dirt -discovery of inference rules from text[END_REF][START_REF] Katz | Extracting structural paraphrases from aligned monolingual corpora[END_REF][START_REF] Sekine | Automatic paraphrase discovery based on context and keywords between NE pairs[END_REF][START_REF] Kok | Hitting the right paraphrases in good time[END_REF] and description, which we present below.

For the description and classification of paraphrases and reformulations, several points of view are possible. Thus, they can refer to the utterance situation [START_REF] Martin | Inférence, antonymie et paraphrase[END_REF]Culioli, 1987;[START_REF] Vezin | Les paraphrases: étude sémantique, leur rôle dans l'apprentissage[END_REF][START_REF] Fuchs | Paraphrase et énonciation[END_REF][START_REF] Vion | Reprise et modes d'implication énonciative[END_REF] and receive contextual values, such as in two year ago and in 2014. They are then opposed to linguistic transformations within reformulated and paraphrased units. Several typologies of linguistic transformations are proposed [START_REF] Vila | Paraphrase concept and typology. A linguistically based and computationally oriented approach[END_REF][START_REF] Bouamor | Etude bilingue de l'acquisition et de la validation automatiques de paraphrases sous-phrastiques[END_REF][START_REF] Bhagat | What is a paraphrase?[END_REF] (the reformulated elements are underlined):

• morphological paraphrase involves morphological processes (i.e., inflection, affixation and compounding), such as in We need an improvement of recycling system and We need an improved recycling system;

• lexical paraphrase involves changes at the lexical level with synonyms, hyperonyms, antonyms, etc., such as in There's a risk of receiving a severe wound and There's a possibility of receiving serious injure;

• semantic paraphrase often covers segments larger than words, such as in Emma burst into tears and Emma cried ;

• syntactic paraphrase reorganizes sentences with the shifting of components or diathesis, such as in The riddle is solved by him and He solved the riddle;

• mixed paraphrase may involve various combination of these modifications.

In the Sens-Texte theory [START_REF] Melčuk | Paraphrase et lexique dans la théorie linguistique sens-texte[END_REF], a set of lexical functions is proposed. Their purpose is to describe and codify lexical and semantic relations between linguistic elements. The general objective of these functions is to describe transformation rules of a given language. Some of these functions (eg, Syn, Conv, Contr, Anti, Gener, Sing, Mult, Cap, Equip) can be exploited for the encoding of paraphrases.

Paraphrase and reformulation can also be described according to the size of linguistic units involved [START_REF] Fløttum | Dire et redire. La reformulation introduite par "c'est-à-dire[END_REF][START_REF] Fujita | Typology of paraphrases and approaches to compute them[END_REF][START_REF] Bouamor | Etude bilingue de l'acquisition et de la validation automatiques de paraphrases sous-phrastiques[END_REF], that distinguishes lexical, subphrastic and sentence segments.

Notice that there are also several existing classifications of paraphrase, described with more or less detail: e.g. up to 67 lexical functions [START_REF] Melčuk | Paraphrase et lexique dans la théorie linguistique sens-texte[END_REF] or 25 categories [START_REF] Bhagat | What is a paraphrase?[END_REF].

As for the reformulation, this research point has been mainly addressed through the study of reformulation markers: c'est-à-dire (Gulich & Kotschi, 1983;[START_REF] Roulet | Complétude interactive et connecteurs reformulatifs[END_REF]Holker, 1988;[START_REF] Beeching | La co-variation des marqueurs discursifs[END_REF], je veux dire [START_REF] Teston-Bonnard | Je veux dire est-il toujours une marque de reformulation[END_REF] and disons (Hwang, 1993;[START_REF] Petit | Discrimination prosodique et representation du lexique : application aux emplois des connecteurs discursifs[END_REF][START_REF] Saunier | Disons : un impératif de dire ? Remarques sur les propriétés du marqueur et son comportement dans les reformulations[END_REF]. The common issue for these markers is that they are all coined on the same verb dire (to say). It is also recognized that c'est-à-dire is the most lexicalized and the most studied within this set of markers. All of them have been recognized to introduce the reformulations, called paraphrastic reformulations in the existing work. But they can also play other roles in the discourse, such as argumentation or spoken disfluencies.

In our work, we make a large acceptation of the reformulation (and paraphrase) phenomena.

For its description, we propose a specific multi-dimensional annotation schema presented in Section 4.2.

Linguistic Data Processed

We use two kinds of corpora: two spoken corpora ESLO (Section 3.1) and a corpus with forum discussions (Section 3.2).

ESLO corpus

We

Forum corpus

The forum corpus is collected from the discussion forum Hypertension from Doctissimo2 . This corpus provides 12,588 threads with 67,652 messages, and 6,788,361 word occurrences. Messages are written by the internet users, who need to speak about their illness and life. By comparison with standard written texts, forum discussions are non-normed writings, which can contain misspellings, syntax errors, and other non-conventional linguistic items (specific abbreviations, emoticons...). Besides, the forum discussions also present the specificities of the spoken language (absence of standard punctuation, frequent reformulations and disfluencies, primes, etc.). Forum discussions may be conceived as a hybrid form of spoken and written language.

Methods Proposed for Filtering the Data

Utterances that contain one of the markers studied are extracted from the corpora and preprocessed (Section 4.1). Then, the method relies on manual (Section 4.2) and automatic (Section 4.3) processing of the data. The analysis and evaluation of the results is performed in the last sub-section (Section 4.4).

Pre-processing of Corpora

The pre-processing step varies according to the corpora processed.

In the spoken corpora ESLO, in order to rebuild the utterances, the transcription files are segmented in turns of speech: new utterance begins with the shift of speakers. In case of speaker overlapping, the overlapped segments are associated with all the involved speakers. If the speaker continues the speech after the overlapping, his turn of speech continues as well.

The spoken corpora are then POS-tagged and analyzed with the SEM chunker [START_REF] Dupont | Un segmenteur-etiqueteur et un chunker pour le français[END_REF] adapted to spoken language. This chunker is probabilistic and has been trained on specifically annotated spoken corpus. The, the generated model can be applied to other spoken corpora in French. The chunker first performs the syntactic tagging of the input text which allows to associate word occurrences with their syntactic categories. For instance in the sequence nous avons fait grève, nous is a personal pronoun, avons is a conjugated form of the auxiliary verb avoir, fait is a participial form of the verb faire, and grève is a noun. Then, the chunker performs the shallow syntactic analysis for grouping the words within common chunks, which is the smallest sequence of linguistic entities forming a syntactic group with one syntactic head. SEM detects minimal chunks, such as (nous avons) (fait grève).

The forum corpus is POS-tagged and syntactically analyzed with Cordial [START_REF] Laurent | Apport des cooccurrences à la correction et à l'analyse syntaxique[END_REF]. Cordial provides information similar to SEM: POS-tags and syntactic groups, but also the lemmas of word forms. Cordial is rule-based and exploits a set of syntactic rules for the definition of POS-tags and lemmas within sentences, and for their syntactic parsing.

Our study concentrates on sentences and enunciations which contain the markers studied.

Manual Annotation of Reformulations

The manual annotation is performed at two levels: detection of the reformulations, and a finegrained annotation of these reformulations. The annotation applies to the source S1 and target S2 segments (or entities) related by the markers, and to the reformulation relation. The annotation is done along several dimensions, some of which are inspired by the existing classifications:

• Syntactic tag: each entity is annotated with its POS-tag (e.g. N for noun, A for adjective, V for verb, Prep for preposition) or syntactic constituent (e.g., NP for noun phrase, VP for verbal phrase, AP for adjectival phrase, PP for prepositional phrase). Size of entities is defined according to the semantics of the reformulation, but not on the basis of chunks (in spoken corpora) or syntactic groups (in written corpus).

Each reformulation relation is then annotated with:

• rel-lex: type of lexical relation among the two segments (e.g., hyperonym, synonym, antonym, instance, meronym);

• modif-lex: type of lexical modification (i.e. replacement, deletion, insertion);

• modif-morph: type of morphological modification (i.e. inflection, derivation or compounding);

• modif-synt: type of syntactic modification (e.g. active/passive);

• rel-pragm: type of pragmatic relation, linked to the function of paraphrase and reformulation, inspired by the existing typologies (Gulich & Kotschi, 1987;[START_REF] Kanaan | Reformulations, contacts de langues et compétence de communication: analyse linguistique et interactionnelle dans des discussions entre jeunes Libanais francophones[END_REF]. We distinguish eleven categories: definition, explanation, exemplification, precision, justification, denomination, result, linguistic or referential correction, opposition, and paraphrase (or equivalence).

Annotation examples can be found below: annotation is in gray, the source file reference is between brackets. We can see for instance that segments {Saint Jean de la Ruelle}{Orléans} and {démocratiser l'enseignement (democratize the education)}{permettre à tout le monde de rentrer en faculté (allow everybody to enter the university)} are reformulated.

( In Table 1, we indicate the size of the annotated reference data which are exploited in this study for observations, for fitting of the automatic system and for the evaluation of the system. These data only contain sentences and enunciations with the three reformulation markers studied (c'est-à-dire, disons, ça veut dire). 1. Size of the annotated data: sentences and enunciations with the three reformulation markers studied.

Corpus

Automatic Detection of Reformulations

The purpose of the automatic processing proposed is to decide whether a given occurrence of marker is related to reformulation or not. On the whole set of occurrences of markers in the corpora processed, we apply several filters:

• if the marker is at the beginning or end of an utterance or sentence, we consider that the context is not sufficient to establish reformulation relation;

• if the marker is found in specific lexical contexts, such as occurrence of nous with disons (we say), we consider that such contexts are not related to reformulations;

• if the marker occurs with other repeated discursive markers (donc, enfin, quoi…), hesitation euh, interjections (en hm ouais), primes (s-), etc., we consider that the marker is part of spoken disfluencies [START_REF] Blanche-Benveniste | Le français parlé. Etudes grammaticales[END_REF] and is not related to reformulations;

• if the marker occurs within existing expression or phrase, like indépendamment de (independently on) in the example below ( 8), we consider that the context does not contain reformulation. This test is done on the syntactically analyzed and chunked output. In order to verify whether the expression or phrase exist in language, we query an online search engine and analyze the frequencies attested on the web. We assume that the web frequencies provide with information that is more exhaustive than frequencies found in the French reference corpora Frantex [START_REF] Quemada | Projet pour une typologie des opérations de reformulation[END_REF]. Thus, each segment is tested in three ways: with one, two or three chunks or syntactic groups on the right and on the left of the marker, excepting the disfluence markers. Size of the tested segments is empirically set to seven words at most. Then, we compute the average frequency for the three kinds of segments (one, two or three chunks or syntactic groups on the right and on the left of the marker). The average frequency of the segments must not be lower than the thresholds tested, that are between 10 and 6,000. If the average frequency is higher than the threshold, the test indicates that the expression or phrase exist in language and that the marker represents the disfluency. Thus, the occurrence is not related to reformulations.

(8) est-ce que vous remarquez une différence sensible entre vos différents clients dans leur façon de choisir la viande dans ce qu'ils achètent et caetera indépendamment <MR>disons</MR> de leurs oui origines de classe [ESLO1_ENT_001]

Analysis and Evaluation

The annotation protocol has been fixed on a subset of ESLO1, while the evaluation is done on the remaining ESLO1 subset, on the interviews from ESLO2, and on the forum corpus. Two kinds of evaluation are performed:

• manual annotation is checked for the inter-annotator agreement at the level of the paraphrastic relation. With two sets of annotations, we apply the Cohen kappa [START_REF] Cohen | A coefficient of agreement for nominal scales[END_REF][START_REF] Landis | The measurement of observer agreement for categorical data[END_REF] measure;

• precision of automatic detection of the reformulation occurrences of the markers is evaluated against the manually created reference data. Precision is computed as ratio between the correct answers, found in the system results and the reference data, and the whole set of answers provided by the automatic system.

Results and their Discussion

Two main aspects are presented and discussed: inter-annotator agreement values and precision of the automatic system proposed for the distinction between reformulation occurrences of the studied markers (c'est-à-dire, disons, ça veut dire). 2. Inter-annotator agreement when deciding on presence of reformulations.

Corpus

In Table 2, we indicate the inter-annotator agreement for the three corpora processed. On the whole, a substantial agreement is obtained on two corpora: forum and ESLO1. The agreement on the ESLO2 data is moderate and is more difficult to obtain, which may be due to the conditions of collection of these data: the interviews are more informal and free by comparison with the ESLO1 corpus. This fact may contribute to utterances which are longer, more heterogeneous and more complex. We can also observe that the best agreement is obtained on the written corpus forum. One reason for this may be that the written corpus, even if issued from online discussions, presents the final result of an idea, while spoken language keeps the elaboration of such idea [START_REF] Hagège | L'homme de paroles. Contribution linguistique aux sciences humaines[END_REF][START_REF] Blanche-Benveniste | Le français parlé. Etudes grammaticales[END_REF][START_REF] Blanche-Benveniste | Le semblamble et le dissemblable en syntaxe[END_REF]. For this reason, the discourse organization and the syntax of written corpora are more standardized and easier to process by the automatic tools.

Corpus

% of reformulations ESLO1 26

ESLO2 35

Forum 61 Table 3. Rate of the reformulative occurrences of markers in the reference data.

In Table 3 Precision of the rule-based system for the automatic detection of reformulations is indicated in Table 4. Like for the inter-annotator agreement, the rules-based system is more successful when processing the written corpus. When the lexical and discursive filters are applied alone, they reach up to 40%, 38% and 49% precision in ESLO1, ESLO2 and forum corpora, respectively. The additional use of the frequency filters decreases substantially performance of the system. But, when the frequency filters have priority on the lexical and discursive filters, the overall precision is improved to up to 63%, 66% and 75%: in this case, we consider that frequency is indicative of the reformulation even if the utterance contains spoken language disfluencies. Notice that precision is improved with the increasing of the threshold. The highest threshold tested is 6,000, while the improvement of precision is observed with the average frequency between 10 and 4,500. Above that threshold, we observe no evolution of the precision values.

The precision we obtain is higher than the inter-annotator agreement. It is comparable or even superior to the precision obtained in previous work [START_REF] Bouamor | Etude bilingue de l'acquisition et de la validation automatiques de paraphrases sous-phrastiques[END_REF]. By comparison with the paraphrase recognition results obtained on another written corpus, that is annotated mainly with lexical, syntactic and contextual paraphrases [START_REF] Bhagat | What is a paraphrase?[END_REF], our results are similar to those provided by the baselines and some of the systems reported [START_REF] Androutsopoulos | A survey of paraphrasing and textual entailment methods[END_REF].

We expect to improve our current results in the next future.

Conclusion and Future Work

We propose a method for the automatic detection of reformulations in monolingual spoken (ESLO1 and ESLO2) and written (forum) corpora in French. One originality is that we take into account the specificity of the spoken and written data through the building of utterances, the consideration of oral disfluencies, and the use of the NLP tool adapted to spoken [START_REF] Dupont | Un segmenteur-etiqueteur et un chunker pour le français[END_REF] and written [START_REF] Laurent | Apport des cooccurrences à la correction et à l'analyse syntaxique[END_REF] corpora. Another originality is that we address the detection of reformulations with syntagmatic approach, within the S1 marker S2 structure.

We perform manual and consensual annotation in order to obtain the reference data. Then, an automatic rule-based system is designed and tested for the detection of reformulative occurrences of the markers. The reference data allow evaluating the automatic method.

The best inter-annotator agreement is 0.784 and is observed on written corpus forum. On the spoken ESLO1 and ESLO2 corpora, the agreement is 0.617 and 0.526, respectively.

The automatic recognition of reformulative occurrences of markers relies on a set of filters (lexical, discursive and frequency) and reaches up to 75%. The comparison with the existing work confirms some previous observations (Rossari, 1990;[START_REF] Rossari | De l'exploitation de quelques connecteurs reformulatifs dans la gestion des articulations discursives[END_REF]: the markers studied (c'est-à-dire, disons, ça veut dire) do not always introduce reformulations, and can perform other functions (e.g. argumentation, disfluency).

We have several directions for future work:

• we plan to involve additional annotators to obtain more annotated and consensual reference data;

• other markers can be studied and compared among them;

• for the automatic detection of reformulations, we can improve the current performance thanks to a better recognition of repetitions and to a machine learning approach;

• the automatic detection of boundaries of source S1 and target S2 entities in another perspective;

• spoken and written corpora will be further compared and analyzed from the point of view of reformulation: we assume the process is similar, as it allows making ideas clearer, and dissimilar from the cognitive point of view [START_REF] Levelt | Monitoring and self-repair in speech[END_REF]Hagege, 1985;[START_REF] Blanche-Benveniste | Le français parlé. Etudes grammaticales[END_REF];

• a similar study can be done on corpora from other languages;

• the annotations available further to this work will be made available to the research community. Besides, these annotations can also be stored in a TEI-compliant format.

Table 4 .

 4 , we indicate the rate of reformulative occurrences of markers in the studied corpora. It reaches up to 61% in forum corpus, and 26% and 35% in ESLO1 and ESLO2, respectively. Precision of the automatic detection of reformulations.

	Set of rules	ESLO1	ESLO2	Forum
	lexical and discursive filters	40.5	37.7	38.9

JADT 2016 : 13ème Journées internationales d'Analyse statistique des Données Textuelles

http://eslo.tge-adonis.fr/

http://forum.doctissimo.fr/sante/hypertension-problemes-cardiaques/liste_sujet-1.htm (collected in May 2013)

Acknowledgement

We are thankful to the anonymous reviewers for the thorough reviewing and for their comments and suggestions which permitted to improve the quality and clarity of this article.


Natalia Grabar
email: natalia.grabar@univ-lille3.fr

Iris Eshkol-Taravella

Why do we reformulate? Automatic Prediction of Pragmatic Functions

Keywords: Reformulation, Machine Learning, Paraphrase, Classication, Pragmatic Function

Reformulations participate in structuring of discourse, especially in dialogues, and also contribute to the dynamics of the discourse. Reformulation is a signicant act which has to satisfy precise objectives. The purpose of our work is to automatically predict the reason for which a speaker performs a reformulation. We use a classication with eleven pragmatic functions inspired by the existing work and by the data analyzed. The reference data are built through manual and consensual annotations of spontaneous reformulations introduced by three markers (c'est-à-dire, je veux dire, disons) in French. The data are provided by spoken corpora and a corpus with forum discussions on health issues. We exploit supervised categorization algorithms and a set with several features (syntactic, formal, semantic and discursive) for the prediction of the reformulation categories. The distribution of sentences is not homogeneous across categories. The experiments are positioned at two levels: general and specic. Our results indicate that it is easier to predict the types of functions at the general level (the average F-measure is around 0.80), than at the level of individual categories (the average F-measure is around 0.40). We study the inuence of various parameters.

Introduction

The notion of reformulation is central to our work and we will start with its definition and description. Reformulation consists of saying again and with different words an utterance or an idea. Usually, reformulation is done at the request of the interlocutor or by decision of the speaker.

The objective of our work is to study the reasons which make the speakers to reformulate. This is what we call the pragmatic function of reformulations. Two sources of reformulations are studied (spoken and forum corpora). Hence, we propose to analyze reformulated segments and to predict automatically the pragmatic function associated with each reformulation. The hypothesis of our work is that the content of the reformulated segments S1 and S2 provides clues, be they non-linguistic (e.g., size of the segments) or linguistic (e.g., lexical, syntactic, semantic), for the prediction of these pragmatic functions. The experiments are performed at two levels: (1) at the general level, according to the type of linguistic transformations associated with reformulations: addition, reduction or equal amount of information; (2) at the specific level, through the exploitation of pragmatic functions (e.g., definition, explanation, result, precision), such as described in section 2.4. We work with spontaneous reformulations in French, such as they occur in spoken language and in forum discussions. Reformulations are to be introduced by one of three markers studied (c'est-à-dire, je veux dire, disons) coined on the verb dire (to say). Besides, specific syntactic structure is studied:

S1 marker S2.
In what follows, we first outline the notion of reformulation through the related work (section 2). We then describe the data we use (section 3) and the methodology we design (section 4). We present and discuss the results (section 5), and then conclude with some directions for future work (section 6).

2 Related work

Linguistic Work Applied to Written Corpora

In written language, reformulation may be related to several notions:

-Paraphrase. Reformulation can be seen as paraphrastic variation of linguistic segment in which formal modifications occur [START_REF] Neveu | Dictionnaire des sciences du langage[END_REF]. Hence, paraphrase is the result of reformulation. Notice that paraphrase is studied from different points of view: its relation to enunciation [START_REF] Culioli | Notes du séminaire de DEA[END_REF][START_REF] Flottum | Dire et redire. La reformulation introduite par "c'est-à-dire[END_REF][START_REF] Fuchs | Paraphrase et énonciation[END_REF][START_REF] Martin | Inférence, antonymie et paraphrase[END_REF][START_REF] Vezin | Les paraphrases: étude sémantique, leur rôle dans l'apprentissage[END_REF]; its linguistic transformations [START_REF] Mel£uk | Paraphrase et lexique dans la théorie linguistique sens-texte[END_REF][START_REF] Vila | Paraphrase concept and typology. a linguistically based and computationally oriented approach[END_REF][START_REF] Bhagat | What is a paraphrase?[END_REF]; and its size [START_REF] Flottum | Dire et redire. La reformulation introduite par "c'est-à-dire[END_REF][START_REF] Fujita | Typology of paraphrases and approaches to compute them[END_REF][START_REF] Bouamor | Étude de la paraphrase sous-phrastique en traitement automatique des langues[END_REF]]. -Gloss. Gloss is closely related to philological tradition and means commentaries done on a given word. It is composed of two parts: the first part is a lexical unit, while the second part is the gloss itself, often written in formal language [START_REF] Authier-Revuz | Ces mots qui ne vont pas de soi : boucles réexives et noncoïncidences du dire[END_REF][START_REF] Steuckardt | Les marqueurs formés sur dire[END_REF]. -Repetition. Repetition corresponds to various situations in which a given textual segment is repeated with various degrees of similarity [START_REF] Vion | Reprise et modes d'implication énonciative[END_REF]. The semantic proximity between the reformulated segments is then important. -Description. Description is closely related with literary studies [START_REF] Magri-Mourgues | Reformulation et dialogisme dans le récit de voyage[END_REF].

-Elaboration. Elaboration (of an idea) is a rhetoric relation which may also be similar to reformulation [START_REF] Péry-Woodley | ANNODIS: une approche outillée de l'annotation de structures discursives[END_REF].

Linguistic Work Applied to Spoken Corpora

One of the main differences between spoken and written languages is that in spoken language we can observe the elaboration of ideas, while in written language the final result of this elaboration is usually presented [START_REF] Blanche-Benveniste | Le français parlé. Études grammaticales[END_REF]. Indeed, written language proposes the final version of the discourse and spoken language provides its creation with the hesitations, false starts, mistakes and reformulations, which are all specific to it. Several existing works address spoken reformulation, which is one of its fundamental characteristics. Several objectives are addressed, although reformulation is always associated with disfluencies and self-corrections:

-Two types of reformulations may be distinguished [START_REF] Gülich | Les actes de reformulation dans la consultation[END_REF][START_REF] Roulet | Complétude interactive et connecteurs reformulatifs[END_REF]: paraphrastic reformulation, which brings equivalence between the segments, and non-paraphrastic reformulation, which brings a change in enunciation perspective [START_REF] Rossari | Projet pour une typologie des opérations de reformulation[END_REF].

As each reformulation in spoken language does not provide paraphrase, two types of markers can distinguished: paraphrastic reformulation markers, like c'est-à-dire, je veux dire, en d'autres termes, and non-paraphrastic reformulation markers, like en somme, de toute façon, enfin. -In syntactic studies of spoken language, reformulation is associated with enumeration or repetition [START_REF] Levelt | Monitoring and self-repair in speech[END_REF][START_REF] Blanche-Benveniste | Le français parlé. Études grammaticales[END_REF][START_REF] Benzitoun | L'annotation syntaxique de corpus oraux constitue-t-elle un problème spécique ?[END_REF], because repeated, reformulated or enumerated elements show the same syntactic place on the paradigmatic axis. -Reformulation can also be associated with correction or precision [START_REF] Kahane | La typologie des entassements en français[END_REF].

Reformation and NLP

In the NLP field, reformulation in written corpora is often associated with paraphrase, as its result. Research questions are concerned with the automatic detection of paraphrases [START_REF] Barzilay | Extracting paraphrases from a parallel corpus[END_REF][START_REF] Shinyama | Automatic paraphrase acquisition from news articles[END_REF][START_REF] Bannard | Paraphrasing with bilingual parallel corpora[END_REF][START_REF] Malakasiotis | Learning textual entailment using SVMs and string similarity measures[END_REF][START_REF] Lin | Dirt -discovery of inference rules from text[END_REF] and with their use in various applications, such as detection of plagiarism [START_REF] Ferrero | Détection automatique de reformulations correspondance de concepts appliquée à la détection de plagiat[END_REF], textual entailment [START_REF] Androutsopoulos | A survey of paraphrasing and textual entailment methods[END_REF][START_REF] Dagan | Recognizing Textual Entailment[END_REF], normalization of controlled languages [START_REF] Nasr | Un modèle de reformulation automatique fondé sur la théorie sens-texte: application aux langues contrôlées[END_REF], information retrieval and machine translation [START_REF] Madnani | Generating phrasal and sentential paraphrases: A survey of data-driven methods[END_REF][START_REF] Bouamor | Étude de la paraphrase sous-phrastique en traitement automatique des langues[END_REF].

In spoken corpora, reformulation is close to disfluencies and the existing works propose to detect it automatically. The methods used exploit manually crafted rules and patterns [START_REF] Bouraoui | Analyse des erreurs de performance et des stratégies correctives dans le dialogue oral spontané : apports à l'étude des pathologies du langage[END_REF][START_REF] Constant | Automatic detection of disuencies in speech transcriptions[END_REF] or supervised learning [START_REF] Dutrey | A CRF-based approach to automatic disuency detection in a French call-centre corpus[END_REF]. Detection of reformulations is then used for repairing, cleaning and reconstitution of enunciations.

Pragmatic Functions of Reformulation

Reformulation is a significant act performed with precise objective. This is what we call pragmatic function of reformulation, i.e. the role of spontaneous reformulation which can be observed in language. Reformulation links two segments: the source segments S1, which is reformulated, and the target segment S2, which contains the reformulation. As noticed above, we study reformulations formed with specific markers, derived from the verb dire (to say) (c'est-à-dire, je veux dire, disons), within the structure S1 marker S2.

We distinguish several pragmatic functions between S1 and S2, inspired from the existing typologies [START_REF] Gülich | Les actes de reformulation dans la consultation[END_REF][START_REF] Hölker | Zur Analyse von Markern[END_REF][START_REF] Beeching | La co-variation des marqueurs discursifs[END_REF][START_REF] Kanaan | Reformulations, contacts de langues et compétence de communication: analyse linguistique et interactionnelle dans des discussions entre jeunes Libanais francophones[END_REF] and motivated by our data:

-Definition: (often technical) terms from S1 are defined by S2: avec une ETO c'est à dire une echographie tansoesophagienne (une écho ou le palpeur est introduit dans l'estomac) (by ETO I mean tansoesophagian echography (an echo in which a sensor is introduced in the stomach)) -Explanation: the speaker explains things to his interlocutor (S2 explains S1):

ce garçon je sais bien qu'il ne peut pas se marier avec euh c'est-à-dire qu'il aurait pu av-trouver une jeune fille euh qui fasse sa licence euh dans un milieu comme le nôtre (this boy well I know that he cannot mary her euh I mean that he could nd a girl euh who is doing studies euh from the same social standing) -Exemplification: for an entity mentioned in S1, examples are given in S2: des morceaux nobles ce qu'ils appellent quoi c'est à dire les rosbifs les biftecks et tout ça (noble pieces what they call well I mean roast beef beefsteaks and all that) -Justification: S2 proposes justification of S1: la langue française est plus difficile disons on peut pas dire la plus difficile des langues européennes mais c'est difficile (French is more dicult let's say one cannot say the most dicult of the European languages but it is dicult) -Precision: S2 is used to make clearer the statements from S1: La trinitrine m'a été prescrite vendredi dernier, c'est à dire depuis une semaine (Trinitrin has been prescribed to me last Friday, I mean one week ago) -Denomination: S2 gives a name to an entity from S1: en particulier c'est l'endroit où en somme ça s'est produit le plus au début c'est-à-dire à Nanterre (particularly this is the place where on the whole this happened at the beginning I mean in Nanterre) -Result: the speaker summarizes or indicates the consequence of S1: A ma sortie, j'ai retrouvé pratiquement l'usage de ma jambe, de mon bras et ma main gauche, disons que je pouvais être autonome (At discharge, I almost recovered the usage of my left leg, arm and hand, let's say that I could be autonomous) -Linguistic correction: S2 makes linguistic correction (article, tense...) of S1:

des artisans euh hm hm hm hm hm alors c'est-à-dire artisans (the craftsmen euh hm hm hm hm hm so I mean craftsmen) -Reference correction: S2 corrects the place, time, etc. indicated in E1: j'habitais rue Lazare Carnot c'est à dire donc au sud de la Source (I was living Lazare Carnot street I mean well on south from la Source) -Paraphrase: S1 repeats information from S2, but with different wording: Il n'a acune maladie (je veux dire qu'il ne prend aucun médicament) (He has no disease (I want to say that he is not taking medication)) -Opposition: S1 repeats information from S2 in negative form: il est joyeux je veux dire il n'est pas triste (he is happy I mean he is not sad)

We can observe that occurrences of reformulation markers go far beyond their paraphrastic usage and cover a large set of situations.

Processed and Exploited Data

We work with several types of data: (1) two types of corpora (two ESLO corpora (section 3.1) and corpus with discussions from medical forum (section 3.2)),

(2) reformulated segments (section 3.3) gained with a manual and consensual annotation of corpora, and (3) several linguistic resources (section 3.4). 1. Inter-annotator agreement on the presence of reformulations in sentences.

ESLO

ESLO (Enquêtes

by French teaching staff from Essex university and members of the B.E.L.C. (Bureau pour l'étude de l'enseignement de la langue et de la civilisation françaises de Paris). This corpus contains 300 hours of speech (4,500,000 words). Collection of ESLO2 started in 2008. This corpus will contain over 350 hours of speech (5,500,000 words). These two corpora are available online3 .

Discussion Forum

Forum corpus has been collected from online discussions in Hypertension forum 4 . It provides 12,588 threads with 67,652 posts and 6,788,361 word occurrences. The posts are written by users, whose need is to speak about their medical problems. These are non-normed writings with frequent misspellings and errors, and specific non conventional linguistic elements (abbreviations, emoticons...).

Reformulated Segments

The 4,120 sentences with three reformulation markers, extracted from our corpora (ESLO1, ESLO2, forum), have been manually annotated by two independent annotators and have gone through consensus. The inter-annotator agreement is computed with the Cohen kappa [START_REF] Cohen | A coecient of agreement for nominal scales[END_REF]. In Table 1, we indicate the obtained agreement, computed on the judgment on the presence of reformulations, and its standard interpretation [START_REF] Landis | The measurement of observer agreement for categorical data[END_REF]. We can see that the agreement is moderate and substantial. When the agreement is computed at the level of pragmatic functions, it is very low: 0.127 on ESLO1 and 0.0211 on ESLO2.

Among the 4,120 marker occurrences, 594 bring reformulations. In Table 2, we indicate their distribution across corpora and pragmatic functions. We can see that precision is the most used function. Linguistic correction and opposition are very rare, and their relevance for our work can be reconsidered. Justification has similar distribution in ESLO2 and forum, and paraphrase in the three corpora. Other functions are not evenly distributed across the corpora. For instance, definition is very frequent in forum discussions (medical terms and their definitions are important there), exemplification and explanation are frequent in ESLO1 and ESLO2. Denomination is rare in spoken, but frequent in forum corpora. For instance, in forum discussions, it allows to name medications and treatments. These observations indicate that the nature of corpora and of pragmatic functions impact their real use by speakers. 2. Distribution of sentences between the pragmatic functions and corpora.

Linguistic Resources

We exploit several types of resources: (1) list with stopwords; (2) disfluency markers; (3) distributional clusters with words generated from our corpora; (4) lexicon with hyponyms; (5) specific lexical markers.

Stopwords. Stopwords (n=69) are mainly grammatical words. They are used to remove non-relevant content and to make the statistical processing more rapid.

Disfluency markers. We use a set of disfluency markers: allez, allons, alors, là, enfin, euh, heu, bah, ben, hm, hum, hein, quoi, ah, oh, donc, bon, bè, eh.

Clusters with words. Distributional clusters with words are generated from our corpora: ESLO1, ESLO2, ESLO (merging of ESLO1 and ESLO2), forum and all the corpora together (total ). The corpora are segmented and lower-cased, the stopwords are removed. The clusters are generated with the existing clustering algorithm [START_REF] Brown | Class-based n-gram models of natural language[END_REF][START_REF] Liang | Semi-Supervised Learning for Natural Language[END_REF]. This is hierarchical agglomerative clustering based on distributional information on words. Within a given cluster, the words are semantically related because they occur in similar contexts. We generate distributional resources with 200 to 600 clusters.

Hyponyms. A lexicon of hyponyms is automatically extracted from Wiktionary5 in French. The structure of Wiktionary articles is exploited for the extraction of entries and their hyperonyms. This lexicon contains 12,161 pairs {hyperonym; hyponym}, such as {lexique; dictionnaire} ({lexicon; dictionary}), {armée; légion} ({army; legion}), {disque; CDROM } ({disk; CDROM}), {période; année} ({period; year}). Words from a given pair have strong semantic link.

Lexical markers. We use a small set of markers (n=17) associated with pragmatic functions. Three types of markers are distinguished: (1) introductory markers (e.g., voilà (well), c'est (is a), ce sont (is a in plural)), which can occur with definitions; (2) causal markers (e.g. c'est pourquoi (this is why), parce que (because), car (because)), which can occur with result; (3) exemplification markers (e.g. exemple (example), comme (such as), entre autre (among other)), which can occur with the exemplification function.

Methods

The main steps of the method are: (1) pre-processing and creation of the reference data; (2) supervised categorization of segments in order to predict their pragmatic function; and (3) evaluation. We perform supervised categorization through the Weka platform [START_REF] Manning | Foundations of statistical natural language processing[END_REF] and use several algorithms available in their standard configuration. We describe now the reference data, the categories and the features used, as well as the evaluation modalities.

Reference data

The reference data are obtained from the manual and consensual annotations of sentences. Table 2 presents these data, according to the pragmatic functions and corpora. Two types of corpora are processed: spoken corpora ESLO and corpus forum with forum discussions. We can see that reformulations are distributed homogeneously between these two types of corpora, while some functions are over-represented (precision, result, definition, explanation and exemplification).

Categories

Categories correspond to pragmatic functions from Table 2. Because three categories (linguistic correction, referential correction, opposition) are very small, we perform experiments with eight most frequent categories. As noticed, another experiment is positioned at a more general level, according to the amount of information provided during the reformulation and measured by the size of segments:

reduction of information in S2 by comparison with S1: result, denomination; addition of information in S2 by comparison with S1: definition, exemplification, explanation, justification, precision; equal amount of information: paraphrase, linguistic correction, referential correction, opposition.

This typology is similar to the one proposed in existing work in literary studies [START_REF] Magri-Mourgues | Reformulation et dialogisme dans le récit de voyage[END_REF], although we also distinguish the reduction of information in S2. This rationale permits to perform experiments at two levels: general level with three categories (addition, reduction and comparable amount of information), and specific level with eight categories.

Features

We exploit several features in order to describe the nature of pragmatic functions. The values of these features are transformed in numerical values:

length of segments S1 and S2, in words and characters, difference of length of segments S1 and S2, in words and characters, equivalence between syntactic categories of the two segments, whether the syntactic category of segments is nominal group or proposition, presence of segments, or of their words, in the same clusters. Several versions are used: all words, all words without identical words, all words without stopwords, all words without identical and stopwords. Numbers and rates of common words are computed. We use several sets of clusters according to the corpora they are generated from (ESLO1, ESLO2, ESLO, forum and all corpora together (total )), and to the number of clusters to be generated (we exploit 300 and 600 clusters in the analysis of the results), presence of disfluency markers in segments, presence of numbers in segments, presence of upper-cased characters in segments, presence of specific lexical markers (exemplification, causal markers and introductory structures), presence of segments, or of their words, in pairs of words with hyperonymy relation.

As we can see, the features are positioned at different levels: formal, syntactic, semantic and discursive. These features are computed automatically, with or without exploitation of linguistic resources.

Evaluation

Evaluation is performed with classical evaluation measures: precision, recall and F-measure. We present the evaluation figures such as computed by the Weka platform. We perform a 10-fold cross-validation: the data are segmented in 10 folds and, at each iteration, one fold is used for training while the rest of folds is used for the testing. The global evaluation corresponds to the average of evaluations obtained at each iteration.

Results

In preliminary experiments, we observed that RandomForest [START_REF] Breiman | Random forests[END_REF] optimizes prediction of categories. With the data taken all together, RandomForest provides the average 0.38 with eight categories, and 0.76 with three categories. We present the results obtained with this algorithm. Different parameters and features impact the results:

in Figure 1, we indicate the average performance (precision, recall, F-measure) obtained when various features are removed from the feature set. On the whole, performance remains close to when all the features are used (experience with all features all is at the first position): 0.4 with eight categories and 0.8 with three categories. Notice that removal of some features (equivalence of syntactic categories equiv, information on clusters (clu-all, clu-in, clu-stop, no-clu), upper-cased characters (maj )) is benefic for the prediction three categories (Figure 1(b)), while with eight categories the whole set of features is always more efficient than when some of features are removed (Figure 1(a)). Removal of information on the size of segments S1 and S2 leng always causes an important decrease of performance; with the whole set of features, the most efficient feature is the size difference in characters between S1 and S2. With this feature alone, the global F-measure is 0.28 and 0.73, with eight and three categories, respectively. Other features related to the length of S1 and S2 are also important. When these features are removed, presence of disfluency markers becomes the most important feature; distributional resource has no difference between total and forum corpora.

Yet, with ESLO2, it is suitable to use distributional resources generated from the same corpus or from the two ESLO corpora: the nature and the content of spoken corpora clearly present linguistic specificities; -Figure 2 indicates the recognition of pragmatic functions in three corpora (ESLO, forum and total ). With eight categories, we observe that result function is the best recognized in all the corpora. precision and definition show less efficient prediction, although it is stable across corpora. paraphrase is quite well recognized in forum, but poorly in other corpora, while exemplification, explanation and justification are quite well recognized in ESLO.

With three categories, the plus category is the easiest to recognize. These observations must be correlated with the amount of the reference data in each corpus and category: result, precision and, by consequence the plus categories, are the biggest categories in our data set.

An analysis of the confusion matrix with eight categories indicates that some functions are very close and often confounded. For instance, the precision function is often confounded with other functions. A possible explanation comes from the nature of this function. Precision seems to be a large category which can contain explanation, definition, exemplification, denomination. It is necessary to define additional and formal constraints to make this function more specific. Another reason is that this function is very frequent, by comparison with other functions, which can also favor its automatic recognition. We can also notice that the denomination category brings numerous confusions: almost all its instances are categorized in other categories.

Conclusion and Future Work

We propose to study reformulation in two types of corpora: spoken and written (forum discussions). We concentrate on pragmatic functions of reformulations, which correspond to the reason of why speakers perform a given reformulation.

We have built a classification with eleven functions (e.g. definition, exemplification, result, paraphrase, linguistic correction). The purpose of our work is to study these functions and to predict them, thanks to the analysis of the content of segments S1 and S2 related by three reformulation markers (c'est-à-dire, je veux dire, disons). Exploitation of consensual reference data and of supervised machine learning algorithms permits to do experiments at two levels: (1) at the general level, which categories are related to the amount of information in S2 (addition, reduction or equal amount of information), we obtain performance close to 0.80;

(2) at the specific level with eight individual categories, we obtain performance close to 0.40. Some features (related to the length of segments and to disfluencies) play an important role for the prediction of pragmatic functions. Prediction and discovery of information of the pragmatic nature is extremely difficult in language. Hence, we can consider that our work is rather exploratory and permits to find out various points which must be taken into account in future work. From the linguistic point of view, it will be important to reconsider some functions: linguistic correction, opposition, and precision. The last function should be described with additional formal criteria. From the computational point of view, additional features and other algorithms should be used for improving the prediction of pragmatic functions of reformulations.

Fig. 1 .

 1 Fig. 1. Removal of dierent features at each experiment.

Fig. 2 .

 2 Fig. 2. Performance in recognition of pragmatic functions in each corpus.

  Sociolinguistiques à Orléans), ESLO1 and ESLO2, corpora[START_REF] Eshkol-Taravella | Un grand corpus oral disponible : le corpus d'Orléans 1968-2012[END_REF] are corpora with spoken data in French. ESLO1 has been collected in[1968][1969][1970][1971]

	Corpus Agreement Interpretation
	ESLO1 0.617	substantial
	ESLO2 0.526	moderate
	Forum 0.784	substantial
	Table

http://eslo.tge-adonis.fr/

http://forum.doctissimo.fr/sante/hypertension-problemes-cardiaques/liste_sujet-1.htm

https://fr.wiktionary.org/wiki/Wiktionnaire


for their numerical approximation. Approximations strategies are generally structured as follow: 1) Construction of a global coordinate system associated with the assumption that the surface description is given analytically; 2) Reduction of the model relatively to the global coordinate system; 3) Approximation of the surface by a finite number of elements; 4) Approximation of the reduced model using the discrete surface. In the context of real applications, it is presumptuous to expect an analytical formulation of the surface. From the data provided by geographic information system (GIS), we casually extract a discrete description of the surfaces that drives thin flow. Therefore, it is more practical to use the discrete description as the starting point of the resolution strategy. This is the angle of approach that we will consider in the following. Then we will locally define two mesh scales: the element scale and the cell scale. The discrete mapping and the reduced model are defined at the element scale and the average values that evolve in time are defined at the cell scale. We have derived a simple multidimensional Riemann solver that can be regarded as an actual two-dimensional generalization of the HLL Riemann solver and have provided closed form expressions for its implementation. The numerical tests have served to put in evidence the robustness and accuracy of the scheme.

Comparison with experimental results and unreduced model on flat plane.

The purpose of this work was the numerical study of the roll-waves that develop from a uniform unstable flow down an inclined rectangular channel. In particular, the formation of the roll-waves is studied by two different approaches. In the first approach, the roll-waves were produced in a long channel where a wave maker perturbed the free surface only at the channel inlet. The average discharge was fixed. In the second approach, the roll-waves were produced in a "periodic box" with a uniform flow velocity. The average depth of a perturbed free surface was the same as in the long channel. Formally, the "periodic box" and a long channel correspond to two different physical situations. However, the stationary profile formed for long time in these cases is the same. This allows us to use the "periodic box" as a simpler mathematical tool to study the asymptotic behavior of roll waves. In particular, the "periodic box" does not require a big space domain resolution. Several interesting phenomena were observed. First, it was proven that there exists L max such that any single roll wave of length L > L max not stable. This can help to generalize the analytical results obtained by Liapidevskii ( modulational stability study) and Baker et al. (the linear stability study) for the SV equations, to the case of the generalized models. The minimal length of periodic box for which a single roll wave is stable, was not observed. Second, a coarsening phenomenon was observed. When the inlet perturbation has two different frequencies, it produces the waves of the different wavelengths. The waves begin to interact. The short waves transfer their energy to the long waves, and finally we obtain the train of roll waves of a larger wavelength. A strong non-stationary modulation of the wave amplitude was observed. The formation of periodic roll wave train was shown for both long a channel and a "periodic box" for two sets of experimental parameters. In both cases, the free surface profile for the generalized models was found in a very good agreement with the experimental results. Finally, for a 2D simplified "Toy Model" we show that steady numerical solution corresponding to experimental data does not depend of transverse perturbations. Numerical methods for the "Toy Model" have been designed and comparisons with the experimental data on a channel experiment done by Yih-Chin Tai and his team in Tainan. The shear shallow flow models are also the subjects of collaboration with the Technical University of Crete (Prof Argyrus Delis) who visited Inria and the LJAD in June 2016.

Models for granular materials and laboratory measurements

Lateral boundary friction coefficient for continuum mathematical models

Research effort on modeling surface dry granular flows has been focused primarily on a feasible constitutive relation for bulk internal stress which is translated to a basal stress model when applied to depth-averaged models. When the flow is confined or strongly interacted with lateral obstacles, an effective model for lateral friction is also desired but much less investigated. The conventional expression takes the form of Coulomb friction, τ=µ w p, in terms of a hydrostatic normal stress p and an effective wall friction coefficient µ w which is often assigned to a material-dependent constant. Nonetheless, a series of laboratory experiments and compatible discrete element simulations for surface granular avalanche have been conducted and revealed non-constant µ w .

Calibrate discrete element simulation framework for predictive simulation Targeting surface hazardous flows, we chose the avalanche of finite granular mass down a narrow reservoir of smooth frictional bed as a benchmark problem (Figure1/left). To have realistic simulation framework, we have developed a methodology to assign parameters in the linear soft-sphere contact model so that the DEM simulation can reproduce experimentally measured avalanche dynamics. With material elastic properties, the normal spring constant is assigned specifically to reproduce Hertzian contact time while the tangential spring constant is chosen according to elasticity theory. Experimentally measured coefficient of restitution, e dry , is employed to assign the normal damping constant. The simulated bulk remaining volume in the reservoir was compared to that measured in laboratory experiments (Figure 1/right) to select the most feasible friction coefficient f. The simulated dynamics with the best-fitted f (0.1 for sphere-sphere, 0.2 for sphere-base and sphere-wall contact) compares very well to the measured dynamics on individual grain trajectory (Figure 2) and bulk instantaneous velocity depth profiles at different streamwise locations (Figure 3) down a reservoir inclined at 19° while the instantaneous grain packing configuration and velocity magnitude at different moments throughout the avalanche are provided in Figure 4. General agreement on the simulated to the measured velocity depth profile was also found for velocity profile at much greater inclination at 24° and 29° (Figure 5left From DE simulation, lateral wall friction coefficient µ w (x,y) was evaluated by the instantaneous stress components by summing all the particle-wall interaction forces in an averaging square over a short smooth time of 0.01s. Instantaneous contour maps of µ w (x,y) at t = 0.01, 0.1, 0.2, and 0.3 s are shown in Figure 5 showing non-uniform and transient nature, contrasting the common assumption as a constant in most granular flow models. When local instantaneous µ w was also examined with respect to local I (local normal stress) in Figure 6/left, sharp and nonlinear rise of µ w with I was observed over 0<I<0.05 which saturates quickly to the plateau of sphere-wall pure sliding friction coefficient f sw =0.2 above I>0.09 (calibrated as marked in the caption of Figure 1). The fact that µ w saturates much faster than µ may explain why constant µ w seems to be a feasible assumption in most continuum models for steady flows. Nonetheless, the apparent scattering suggests dependence on a different flow variable and we looked into grain rotation as suggested by experimental visualization image in Figure 6/right. It is clear that the marker sphere started with pure sliding at the onset of bulk avalanche and developed concurrent spin and rotation when moving towards the base during the course of an avalanche. The simulation data was then analyzed for regional arithmetic mean of the three angular velocity components ω x , ω y , and ω z to estimate its effect on sliding contact via the ratios, ω *

x =ω x /|∂v/∂z|, ω * y =ω y /|∂u/∂z| and ω * z =ω z /[(∂v/∂z) 2 + (∂u/∂z) 2 ] 1/2 . The three angular speed ratios are added up to estimate a total effect and presented as instantaneous contours in Figure 7. It is noted that the spatial distribution of low-to-high ω i * or ∑ω i * corresponds very well to the high-to-low µw(x,y) and their correlation can be fitted into Gaussian-like distribution as shown in Figure 8. It is this close correspondence that urges us to seek a theoretical modeling considering how grain rotation modifies sliding contact. Consider a sphere that possesses sliding and angular velocity of u and ω at its center of mass as sketched in Figure 9. The total velocity at the contact point on the reservoir wall, u tot =u+ω×r, can divert total relative velocity, into different direction over the contact area on the reservoir walls to render lower sliding friction. In a flow-fitted coordinate system, this becomes

𝑢 !"! = 𝑢 ! ! + R𝜔 ! ! -𝑟 sin 𝜃𝜔 ! ! e ! + -R𝜔 ! ! + 𝑟 cos 𝜃 𝜔 ! ! e || + 𝑢 ! ! + 𝑟 sin 𝜃 𝜔 ! ! -𝑟 cos 𝜃 𝜔 ! ! e ! ,
We assume that pure sliding took place within an infinitesimal contact surface dA on the contact area to render a hindrance, f pdA, against local u tot where f and P are the sliding friction coefficient and the normal stress, respectively. Direct integration over a circular contact area A c gives the total force

∫ - = dA u u f tot tot P F
As sphere free motion away from the wall is nearly impossible in a dense packing, only the velocity components against the wall were considered as

𝑢 !! =𝑢 ! 1 + 𝛺(𝜔 || * -𝑟 * sin 𝜃𝜔 ! * ) e ! + 𝛺(-𝜔 ! * + 𝑟 * cos 𝜃 𝜔 ! * )e || with 𝜔 ! ! * = 𝜔 ! ! 𝜔 ! , 𝜔 ! ! * = 𝜔 ! ! 𝜔 ! ,𝜔 ! ! * = 𝜔 ! ! 𝜔 ! , and r * = r R. The dimensionless Ω =
𝑅 ω 𝑢 ! is the primary parameter for the influence degree of sphere rotation on total sliding friction and will be referred to as the rotation index. Secondary effect comes from the relative magnitude of each angular velocity components. The friction component against u = can then be computed so that an effective wall friction coefficient can be expressed as

µ w =|F = |/P=𝑓𝐾(Ω, 𝜔 ! * )
with a pure-sliding friction coefficient and a decay function

𝐾 𝛺, 𝜔 ! * = 1 + 𝛺(𝜔 || * -𝑟 * sin 𝜃𝜔 ! * ) 1 + 𝛺(𝜔 || * -𝑟 * sin 𝜃𝜔 ! * ) ! + 𝛺(-𝜔 ! * + 𝑟 * cos 𝜃 𝜔 ! * ) !" !/! ! ! ! ! !! ! 𝑟 * 𝑑𝜃𝑑𝑟 *
It is clear that zero rotation with vanished rotation index 𝛺=0 returns K=1 to recover Coulomb friction from pure sliding. A nonzero 𝛺 leads to K<1 as sphere rotation diverts friction on the contact area into different directions to give a lower effective value µ w . For practical applications, we reexamined the expression and suggest to omitting the terms involved with r * as it is bounded by the contact area radius, r c * , that is always several orders of magnitude smaller than unity if estimated as an elastic Hertzian contact. Such an approximation permits an explicit decay function, denoted We went on to seek experimental evidence for how grain angular speeds and the rotation index Ω distribute in space and evolve in time. In the same avalanche experiments, roughly 10-15 marker spheres were inserted manually next to the reservoir wall and across the packing as shown in Figure 11/left. These marker spheres were prepared by randomly gluing circular stickers (diameter 6mm) that at least one can be captured in each high-speed image (500 frames per second). We applied circular Hough transformation to locate both the spheres and the markers as shown in Figure 11/middle. Next, we assume that the camera frame rate was sufficiently high so that the rotation axis of a marker sphere remained roughly the same through a short image sequence. Hence, the markers located in consecutive images would form an arc in the moving reference frame fixed to the sphere center, as illustrated in Figure 11/right. The rotation axis can then be evaluated by the normal vector n=(A,B,-1) of a plane, E: z'=Ax'+By'+C, fitted to five consecutive marker locations via a typical quadrature that minimizes the sum of square of residuals as

𝐾 ! 𝛺, 𝜔 ! * = 1 + 𝛺𝜔 ||
𝐴 𝐵 𝐶 = x′ ! ! x′ ! y′ ! x′ ! x′ ! y′ ! y′ ! ! y′ ! x′ ! y′ ! 1 !! x′ ! z′ ! y′ ! z′ ! z′ !
As the camera frame rate was high enough, We also employed The instantaneous segments between consecutive S i s to approximate an instantaneous tangential velocity as V i =[(x' i+1 -x' i ) 2 +(x' i+1 -x' i ) 2 +(x' i+1 -x' i ) 2 ] 1/2 /Δt where Δt=1/FPS is the elapsed time between two consecutive images (two dots on Figure 11/right). We averaged out these instantaneous speeds to estimate a mean value V across the short observation time to smooth out fluctuating uncertainty due to sticker location error. From this, we determined the angular velocity magnitude by ω=V/R and the corresponding angular speed components, ω x , ω y , and ω z with the estimated rotation axis. As Ω is the primary controlling parameter in the approximate degradation function K 0 , we applied the measured translational and angular sphere speeds to evaluate instantaneous contour of Ω at t=0.01 and 0.2s in Figure 12/left. The corresponding results obtained from DEM are provided in Figure 12/right for comparison, showing dynamic similarity to further confirm the physical relevance of the DEM data. These instantaneous Ω(t, x, y) is examined in view of the contour of µ w (t,x,y) at t=0.01 and 0.2s (shown in Figure 5) to confirm that the low-to-high distribution of µ w (t,x,y) does correlate well to the high-to-low segments of Ω, validating our model speculation.

Lastly, we follow the previous procedure to analyzed the measured angular speeds to estimate two sets (𝜔 || * , 𝜔 ! * , 𝜔 ! * )= (-0.662, 0.524, 0.465) and (-0.747, 0.547, 0.337) so that the first two components can be employed in 𝐾 ! (Ω, 𝜔 || * , 𝜔 ! * ). The so-predicted degradation functions compare reasonably well to the individual data using measured grain angular speeds and those reported from DE simulation and predictions with the simulation-based (𝜔 || * , 𝜔 ! * ) in Figure 13. What remains to be confirmed is to extract µ w from experiments and the task has been undertaken. Furthermore, it undoubtedly requires further research to formulate grain rotation in terms of bulk property-such as bull velocity, shear strain rate, or vorticity-to complete a mathematical model at flow size level. Figure 13 Comparison of K 0 -Ω using sphere angular information from experiments at t=0.01 and 0.2s after the onset of bulk avalanche and from DE simulation. The four predictions adopt characteristic angular components estimated from both measured and simulated data: (𝜔 || , * )=Thm1 (0.3, -0.95), Thm2 (0.638, -0.62) from DE simulation; Thm3 (-0.662, 0.524) and Thm5 (-0.747, 0.547) from experiments.

Effects of density variation on models of dense compressible granular flows

Flow of granular material have been extensively investigated in recent years and the ultimate goal is to capture the flow dynamics under various flow conditions that can be classified as gas, quasi-static and dense regime. The kinetic theory has been developed to describe flows in collisional gas-like regime and visco-elastic or visco-plastic models have been formulated for bulk dynamics in the quasistatic regime using the analogy to soil plasticity models. In the intermediate dense flow regime, there has been no unified framework to capture the transition from regimes to regimes and an empirical relation has been fitted to link pertinent flow variables. This is known as the µ(I) rheology relation that describe the shear-to-normal stress ratio as monotonic function of bulk inertial number as et al., 2006). Concurrent modification on bulk density, in terms of solid volume fraction ϕ, density has also been studied in 2D simple shear flows and the socalled dilatation law was proposed by Da Cruz (2005) as ϕ I ≅ ϕ ! -AI. For steady surface flows down an inclination, kinetic theory has predicted non-uniform density depth profile in the collisional An integrated formulation based on µ-I and ϕ-I relations It is hence desired to develop a numerical framework that incorporates variation. The governing equations for compressible granular flows that integrate both µ I and ϕ I relations may be formulated as

µ I = µ ! + (µ ! -µ ! )/(I ! /I + 1) (Jop
C-E ! ! ! !) ( !" + 𝛻 • 𝜌 ! 𝜙 ( 𝑽) = 0 (1)
x-ME

!(! ! !!) !" + !(! ! !! ! ) !" + !(! ! !!") !" = 𝛻 • 𝜎 !" (2a) y-ME !(! ! !!) !" + !(! ! !!") !" + !(! ! !! ! ) !" = 𝛻 • 𝜎 !" (2b)
Constitutive relation:

𝜎 !" = -𝑃𝛿 !" + 𝜏 !" = -𝑃𝛿 !" + 𝜇(𝜙)𝐴 ! |𝛾 !" |(𝜙 ! -𝜙) ! 𝜌 ! 𝑑 ! |𝛾 !" | ! 𝛾 !" (3)
Equation of state:

𝑃 = ! ! (! ! !!) ! 𝜌 ! 𝑑 ! |𝛾 !" | ! (4)
Density variation is taken into account in the pseudo-thermal equation of state in (4).

To solve this set of non-linear coupled equation, we plan to try firstly to extend the conventional Riemann solver for compressible gas flows when the system remains hyperbolic. However, when the flow approaches a jamming state when ϕàϕ M , unbounded terms appear in the equations to destroy its hyperbolic feature and hence a different numerical scheme is required. For that situation, pressureimplicit-splitted-operator (PISO) numerical scheme developed for conventional Navier-Stokes equations may be worth a try.

Applications in the real world.

Right now, the short-term research goal is to develop a numerical framework that solves the compressible granular flow equations to investigate the effect on non-constant density on bulk dynamics. A long-term perspective is to provide a platform on which different constitutive models and models of boundary conditions can be tested and compared to real flow phenomenon. From systematic comparisons, we should have a better idea for how to select the most feasibly constitutive relation and boundary condition in view of flow types. The landslide was selected for the code comparison. The landslide volume and the topographic surface were obtained from digital terrain models (DTMs) that had been acquired on 7, Jan., a regular-basis survey, and on 13, Aug., an immediate action to the landslide. The resolution of the DTMs was 5×5 m. For convenience the simulation, the landslide site was set to a 3700×2210 m computational domain and the resolution of the grids was resampled to 10×10 m. In the present finite volume scheme, the triangular unstructured grids were obtained by diagonally bisecting the rectangular mesh cells. The 3D view, where the scar area is the blue-purple colored zone and the is the red-green-yellow zone. The deposit is mainly distributed in three branches of anonymous valleys and in the Cishan River. The landslide mass immediately formed a blockage dam and subsequently broke after another twenty minutes or so. The dam break caused a much wider spread of the deposit mass in the Cishan River. In the code validation task against the real measurement, this second dam break event should be excluded from the validation.

Due to the space limit of the report, we focus on the comparison of the final deposit stage. The solid red lines are profiles to compare detail flow motion which is abbreviated. The green boxed area is the deposit zone that was not affected by the subsequent dam break event. The deposit depth of this area was used in the optimization procedure for the best rheological parameters. Outside (north to) the main deposit area, there is a third thin but wide spread deposit is also found. Because of its much smaller volume compared to the main deposit, it is considered a secondary deposit and is omitted in the current comparison.

Figure shows the deposit comparison between the results of non-oscillatory central difference scheme and the present finite volume scheme. On the left, the simple Coulomb friction law was used. The optimized friction angle is found to be 11.47 ○ , whereas on the right hand side, the friction angle of the present finite volume scheme was set to 14.2 ○ . Noticeably, a larger friction angle was obtained to achieve a similar deposit zone. The main reasons for this discrepancy may arise from: 1) the present Riemann solver based scheme has less numerical diffusivity in comparison to the central finite difference scheme, 2) the unstructured surface grids effectively provides a smoother surface and grossly a finer grid resolution than the previous quadrilateral one. To compensate this additional numerical landslide mass mobility, a larger friction coefficient is reached. Further quantitative comparison will be reported in a designated paper.

Figure 1 .

 1 Figure 1. (left) schematic diagram of the lab-scale calibration flume whose dimension and materials were used in the DE simulation; (right) extracting the most feasible friction coefficient pair by comparing the simulated temporal profile of the normalized projection to that measured in the experiments;

Figure 2

 2 Figure 2 Comparison of the simulated and the measured trajectories of individual spheres moving next to the reservoir wall in a dry granular avalanche at 19º inclination at the (a) rear (x=8cm), (b) central (x=16cm), (c) front (x=24cm) locations: experiment, • ; simulation, --. The dashed line indicates the original packing surface.

Figure

  Figure 3Comparison of the simulated (in symbols) and the measured instantaneous bulk velocity profile at different times after opening the gate: (a) 0.1 s, (b) 0.2 s, (c) 0.3 s. The velocity was examined at three streamwise locations from the reservoir upstream corner at x = 8, 16, and 24 cm.

Figure 3

 3 Figure 3 Comparison of the instantaneous bulk velocities from three experiments and simulations at different times and positions for the avalanche down the flume inclined at (top) 24° and (bottom) 29° from the horizontal.

Figure 4

 4 Figure 4 Instantaneous sphere velocity magnitude (in color) and bulk configuration at t=0.01, 0.1, and 0.2s. The reservoir and the Cartesian coordinate system set to the center of the reservoir rear lower edge with x parallel to the base, y normal to the base, and z perpendicular to sidewalls

Figure 5

 5 Figure 5 Instantaneous contour maps of µ w (t, x, y) at t=0.01, 0.1, 0.2, and 0.3s.

Figure 6 (

 6 Figure 6 (left) Instantaneous µ w -I data and the line is a least-square fitted relation µ w =0.002+0.19/(1+0.005/I). The inset compares the normalized µ w * -I * data from this work and the cited references; (right) Visualization of how individual sphere changed its orientation along with the avalanche process. Possible modes for individual sphere motion-sliding, rolling, and spinning-are sketched in the inset.

Figure 7

 7 Figure 7 Instantaneous contour of normalized angular speed ω *x , ω * y , ω * z , and their lumped sum adjacent to the wall at t= (top) 0.1s and (bottom) 0.3s after the bulk was released.

Figure 8

 8 Figure 8 Decay of instantaneous µ w (t=0.1s) as a function of local angular speed ratios and the best fit

Figure 9

 9 Figure 9 Illustration of model concepts (Right/middle subplot): sphere in contact with reservoir wall possess sliding and angular velocity components at its center of mass; (left subplot): model parameters and dynamics variables in e // -e⊥-e z coordinate system.

  Simulated sphere angular speeds were analyzed to find characteristic values for angular components to use in the formula: (𝜔 || * , 𝜔 ! * )=(0.3, -0.95), (0.638, -0.62), and an assumed case of (1 √2 , -1 √2). The results obtained via numerical integration seem to bound the value from DE simulation in Figure 10/left and also fall very closely to the explicit approximation 𝐾 ! 𝛺, 𝜔 ! * in Figure 10/right, supporting its usage.

Figure 10 (

 10 Figure 10 (left) Comparison of the predicted K-Ω with the specific sets of angular speeds to those extracted from DE data; (right) comparison of the full and the reduced model for the decay function

Figure 11 (

 11 Figure 11 (left) marker spheres with 6 circular stickers distributed randomly across the packing; (middle) located bright spots used to evaluate sphere centers as marked by green +; (right) Illustration for how the rotational axis ω is related to the surface normal vector 𝑛 of a fitted plane E.

Figure 12

 12 Figure 12 Instantaneous contours for rotation index Ω from experiments (top row) and DEM simulation (bottom row) at t=0.01s and 0.2s (left and right subplots).

  1990, Ancey….). Nonetheless, most works seeking numerical or theoretical solutions assume negligible effect of density variation including even invoking the µ(I) rheology in the momentum equation (Lagrée et al., 2011; Gray & Edwards, 2015).

Task 6 :

 6 Code to code validation. The Hsiaolin landslide, Kaohsiung City, southern Taiwan, was chosen as the example for code validation. The landslide was triggered by the excessive rainfall brought to Taiwan by the Morakot typhoon on the 9 th August 2009. The landslide was a deep-seated avalanche of which the volume was about 24 ×10 ! m ! with an average depth 42 m. The main scar area is about 570 ×10 ! m ! . The 3D view is shown in the next figure and the detailed description of the landslide is to Kuo et al. 3D view of the Hsiaolin landslide site. The blue-purple area is the scar zone and the red-green-yellow area is the deposit zone.

  Ref: Kuo, et al., 2011, The landslide stage of the Hsiaolin catastrophe: simulation and validation, J. Geophys. Res., 116, F04007. Hsiaolin area, measured of deposit depths after the landslide occurred on 9 August 2009, after Typhoon Morakot struck Taiwan. Measurement was done after the breach of the dam formed on the river. Part of the deposit has been moved downstream by the breach on the Cishan River. Yih-Chin Tai, Chin-Kai Cheng and Chih-Yu Kuo • Modified shallow water equations for significant bathymetry variations, D. Clamond • Well balanced ALE : simple time dependent mesh adaptation for balance laws, M. Ruchiotto • A flexible approach for the numerical solution of the Green-Nagdhi equations, A.G. Filippini, M. Kazolea, M. Ricchiuto • Gas kinetic scheme for anisotropic Savage-Hutter Model, C.Y. Kuo • Stabilized spectral element approximation of the Saint Venant system using the entropy viscosity technique, R. Pasquetti • On solitary waves for boussinesq's type models, M. Colin • Well-Balanced schemes, B. Nkonga Aug. 22 to Sep. 01, 2015 : Fu-Ling Young visit at IUSTI . Aug. 22 to Sep. 20, 2015 : Keh-Ming Shyue, Invited professor at the University of Marseille. November 14 to 24, 2015 : Hervé Guillard, visit at Taiwan. Study of shear shallow water models. During the stay of HG, a mini-workshop gathering several researchers and students from NTU and Tainan have been organized November 18 and 19. March 21 to 25, 2015 : Richard Pasquetti visit at Taiwan. Viscous stabilization methods, namely the spectral vanishing viscosity (SVV) technique and the entropy viscosity method (EVM), are applied to flows of interest in geophysics. Aug. 24 to Sep. 15, 2016 : Cheng-Chuan Lin, 4 th year Phd student of Prof. FuLing Yang, have a personal initiation by B. Nkonga, on Numerical solvers for compressible granular flow using Mu-I-phi constitutive relation.

Computed deposit depth using finite volume method on "curved surface" represented by a piecewise triangular mesh.