Laetitia Brouwers Aspirante

Delphine Bernhard

Anne-Laure Ligozat

Thomas Franc

Syntactic Sentence Simplification for French

This paper presents a method for the syntactic simplification of French texts. Syntactic simplification aims at making texts easier to understand by simplifying complex syntactic structures that hinder reading. Our approach is based on the study of two parallel corpora (encyclopaedia articles and tales). It aims to identify the linguistic phenomena involved in the manual simplification of French texts and organise them within a typology. We then propose a syntactic simplification system that relies on this typology to generate simplified sentences. The module starts by generating all possible variants before selecting the best subset. The evaluation shows that about 80% of the simplified sentences produced by our system are accurate.

Introduction

In most of our daily activities, the ability to read quickly and effectively is an undeniable asset, even often a prerequisite [START_REF] Willms | Literacy proficiency of youth: Evidence of converging socioeconomic gradients[END_REF]. However, a sizeable part of the population is not able to deal adequately with the texts they face. For instance, Richard et al. (1993) reported that, in 92 applications for an unemployment allowance filled by people with a low level of education, about half of the required information was missing (some of which was crucial for the processing of the application), mainly because of comprehension issues.

These comprehension issues are often related to the complexity of texts, particularly at the lexical and syntactic levels. These two factors are known to be important causes of reading difficulties [START_REF] Chall | Readability Revisited: The New Dale-Chall Readability Formula[END_REF], especially for young children, learners of a foreign language or people with language impairments or intellectual disabilities.

In this context, automatic text simplification (ATS) appears as a means to help various people access more easily the contents of the written documents. ATS is an application domain of Natural Language Processing (NLP) aiming at making texts more accessible for readers, while ensuring the integrity of their contents and structure. Among the investigations in this regard are those of Caroll et al. (1999), [START_REF] Inui | Text simplification for reading assistance: a project note[END_REF] and, more recently, of [START_REF] Rello | Le traitement de documents administratifs par des populations de bas niveau de formation[END_REF], who developed tools to produce more accessible texts for people with language disabilities such as aphasia, deafness or dyslexia. In the FIRST project, [START_REF] Barbu | Open book: a tool for helping asd users' semantic comprehension[END_REF] and [START_REF] Evans | Annotating signs of syntactic complexity to support sentence simplification[END_REF] implemented a simplification system for patients with autism, who may also struggle to understand difficult texts.

However, reading assistance is not only intended for readers with disabilities, but also for those who learn a new language (as first or second language). De [START_REF] Belder | Text Simplification for Children[END_REF] focused on ATS for native English schoolchildren, while [START_REF] Siddharthan | Syntactic Simplification and Text Cohesion[END_REF], [START_REF] Petersen | Text Simplification for Language Learners: A Corpus Analysis[END_REF] and [START_REF] Medero | Identifying Targets for Syntactic Simplification[END_REF] focused on learners of a second language. [START_REF] Williams | Generating basic skills reports for low-skilled readers[END_REF], Aluisio et al. (2008) and [START_REF] Gasperin | Natural language processing for social inclusion: a text simplification architecture for different literacy levels[END_REF] addressed ATS for illiterate adults. Most of these studies are dealing with the English language, with the exception of some work in Japanese [START_REF] Inui | Text simplification for reading assistance: a project note[END_REF], Spanish [START_REF] Saggion | Text simplification in simplext. making text more accessible[END_REF][START_REF] Bott | Can Spanish Be Simpler? LexSiS: Lexical Simplification for Spanish[END_REF], Portuguese [START_REF] Aluísio | Towards brazilian portuguese automatic text simplification systems[END_REF] and French [START_REF] Seretan | Acquisition of syntactic simplification rules for french[END_REF].

ATS was also used as a preprocessing step to increase the effectiveness of subsequent NLP operations on texts. Chandrasekar et al. (1996) first considered that long and complex sentences were an obstacle for automatic parsing or machine translation and they showed that a prior simplification may result in a better automatic analysis of sentences. More recently, [START_REF] Heilman | Extracting Simplified Statements for Factual Question Generation[END_REF] showed that adding ATS in the context of automatic question generation yields better results. Similarly, [START_REF] Lin | Syntactic sentence compression in the biomedical domain: facilitating access to related articles[END_REF] and [START_REF] Jonnalagadda | Towards Effective Sentence Simplification for Automatic Processing of Biomedical Text[END_REF] optimized information extraction from biomedical texts using ATS as a preprocessing step.

In these studies, the simplifications carried out are generally based on a set of manually defined transformation rules. However, ATS may also be solved with methods from machine translation and machine learning. This lead some researchers [START_REF] Zhu | A Monolingual Tree-based Translation Model for Sentence Simplification[END_REF][START_REF] Specia | Translating from Complex to Simplified Sentences[END_REF][START_REF] Woodsend | Learning to Simplify Sentences with Quasi-Synchronous Grammar and Integer Programming[END_REF] to train statistical models from comparable corpora of original and simplified texts. The data used in these studies are often based on the English Wikipedia (for original texts) and the Simple English Wikipedia, a simplified version for children and non-native speakers that currently comprises more than 100,000 articles. Similar resources exist for French, such as Vikidia and Wikimini, but texts are far less numerous in these as in their English counterpart. Moreover, the original and simplified versions of an article are not strictly parallel, which further complicates machine learning. This is why, so far, there was no attempt to adapt this machine learning methodology to French. The only previous work on French, to our knowledge, is that of [START_REF] Seretan | Acquisition of syntactic simplification rules for french[END_REF], which analysed a corpus of newspapers to semi-automatically detect complex structures that has to be simplified. However, her system of rules has not been implemented and evaluated.

In this paper, we aim to further investigate the issue of syntactic simplification for French. We assume a midway point between the two main tendencies in the field. We use parallel corpora similar to those used in machine learning approaches and analyse it to manually define a set of simplification rules. We have also implemented the syntactic part of our typology through a simplification system. It is based on the technique of overgeneration, which consists in generating all possible simplified variants of a sentence, and then on the selection of the best subset of variants for a given text with the optimization technique known as integer linear programming (ILP). ILP allows us to specify a set of constraints that regulate the selection of the output by the syntactic simplification system. This method has already been applied to ATS in English by [START_REF] Belder | Text Simplification for Children[END_REF] and [START_REF] Woodsend | Learning to Simplify Sentences with Quasi-Synchronous Grammar and Integer Programming[END_REF].

To conclude, the contributions of this paper are:

(1) a first corpus-based study of simplification processes in French that relies on a corpus of parallel sentences, (2) the organization of this study's results in what might be the first typology of simplification for French based on a corpus analysis of original and simplified texts; (3) two new criteria to select the best subset of simplified sentences among the set of variants, namely the spelling list of [START_REF] Catach | Les listes orthographiques de base du franc ¸ais[END_REF] and the use of keywords, and finally (4) a syntactic simplification system for French, a language with little resources as regards text simplification.

In the next sections, we first present the corpora building process (Section 2.1) and describe a general typology of simplification derived from our corpora (Section 2.2). Then, we present the system based on the syntactic part of the typology, which operates in two steps: overgeneration of all possible simplified sentences (Section 2.3.1) and selection of the best subset of candidates using readability criteria (Section 2.3.2) and ILP. Finally, we evaluate the quality of the syntactically simplified sentences as regards grammaticality, before performing some error analysis (Section 3).

Methodology

Corpus Description

We based our typology of simplification rules on the analysis of two corpora. More specifically, since our aim is to identify and classify the various strategies used to transform a complex sentence into a more simple one, the corpora had to include parallel sentences. The reason why we analysed two corpora is to determine whether different genres of texts lead to different simplification strategies. In this study, we focused on the analysis of informative and narrative texts. The informative corpus comprises encyclopaedia articles from Wikipedia1 and Vikidia2 . For the narrative texts, we used three classic tales by Perrault, Maupassant and Daudet and their simplified versions for learners of French as a foreign language.

To collect the first of our parallel corpora, we used the MediaWiki API to retrieve Wikipedia and Vikidia articles with the same title. The WikiExtractor 3 was then applied to the articles to discard the wiki syntax and only keep the raw texts. This corpus comprises 13,638 texts (7,460 from Vikidia and only 6,178 from Wikipedia, since some Vikidia articles had no counterpart in Wikipedia).

These articles were subsequently processed to identify parallel sentences (Wikipedia sentence with a simplified equivalent in Vikidia). The alignment has been made partly manually and partly automatically with the monolingual alignment algorithm described in [START_REF] Nelken | Towards robust context-sensitive sentence alignment for monolingual corpora[END_REF], which relies on a cosine similarity between sentence vectors weighted with the tf-idf. This program outputs alignments between sentences, along with a confidence score. Among these files, twenty articles or excerpts from Wikipedia were selected along with their equivalent in Vikidia. This amounts to 72 sentences for the former and 80 sentences for the latter.

The second corpus is composed of 16 narrative texts, and more specifically tales, by Perrault, Maupassant, and Daudet. We used tales since their simplified version was closer to the original than those of longer novels, which made the sentence alignment simpler. The simplified versions of these tales were found in two collections intended to learners of French as a foreign language (FFL): "Hachette -Lire en franc ¸ais facile" and "De Boeck -Lire et s'entrainer". Their level of difficulty ranges from A1 (Daudet) to B1 (Maupassant) on the CEFR scale (Council of Europe, 2001), with Perrault being A2. The texts were digitized by OCR processing and manually aligned, by two annotators, with an adjudication phase for the disagreement cases. In this corpus, we analysed 83 original sentences and their corresponding 98 simplified versions, which gives us a size roughly similar to the Wikipedia-Vikidia corpus.

The two corpora created are relevant for a manual analysis, as done in the next section, but they are too small for automatic processing. We plan to implement a method to align automatically the narrative texts in the near future and thus be able to collect a larger corpus.

Simplification Typology

The observations carried out on these two corpora have made it possible to establish a typology organised according to three main linguistic 3 http://medialab.di.unipi.it/wiki/Wikipedia\_Extractor levels of transformation: lexical, discursive and syntactic, which can be further divided into subcategories. It is worth mentioning that in previous work, simplification is commonly regarded as pertaining to two categories of phenomena: lexical and syntactic [START_REF] Carroll | Simplifying Text for Language-Impaired Readers[END_REF][START_REF] Inui | Text simplification for reading assistance: a project note[END_REF][START_REF] Belder | Text Simplification for Children[END_REF]. Little attention has been paid to discourse in the area of automatic simplification [START_REF] Siddharthan | Syntactic Simplification and Text Cohesion[END_REF].

The typology is summarized in Table 1. As regards the lexicon, the phenomena we observed involve four types of substitution. First, difficult terms can be replaced by a synonym or an hypernym perceived as simpler. Second, some anaphoric expressions, considered simpler or more explicit, are preferred to their counterparts in the original texts. For example, in our three tales, simplified nominal anaphora are regularly used instead of pronominal anaphora. Third, rather than using synonymy, the authors of the simplified texts sometimes replace difficult words with a definition or an explanatory paraphrase. Finally, in the particular case where the original texts contain concepts in a foreign language, these non-French terms are translated.

At the discourse level, the authors of simple texts pay particular attention to the organization of the information which has to be clear and concise. To this end, clauses may be interchanged to ensure a better presentation of the information. In addition, information of secondary importance can be removed while explanations or examples are added for clarity. These two phenomena can appear to be contradictory (deletion and addition), but they actually operate in a common goal: make the main information more comprehensible. Particular attention is also placed on the coherence and cohesion of the text: Authors tend to explain the pronouns and explicit the relations between sentences. The last observed strategy is that impersonal structures are often personalized.

Finally, at the syntactic level, five types of changes are observed: tense modification, deletion, modification, splitting and grouping. The last two types can be considered together since they are two opposite phenomena.

• First, the tenses used in the simplified versions are more common and less literary than those used in the original texts. Thus, the present and present perfect are preferred to the simple past, imperfect and past perfect. This classification can be compared with that of [START_REF] Medero | Identifying Targets for Syntactic Simplification[END_REF] who propose three categories -division, deletion and extension -or that of [START_REF] Zhu | A Monolingual Tree-based Translation Model for Sentence Simplification[END_REF], which includes division, deletion, reorganization, and substitution.

Among those transformations, some are hardly implementable. This is the case when a change requires the use of semantics. For example, noun modifiers may sometimes be removed, but in other cases, they are necessary. However, there are often neither typographical nor grammatical marked differences between the two cases.

Another issue is that other syntactic changes should be accompanied by lexical transformations, which are difficult to generalize. For example, transforming a negative sentence into its affirmative equivalent requires to find a verb whose affirmative form includes the meaning of the negative construction to replace.

There are also changes that are very particular and require a manual rather than an automatic processing of the text, in the sense that each case is different (even if part of a more global rule). In addition, they usually involve discourse or lexical information and not just syntactic one.

Finally, the syntactic changes impacting other parts of the text or concerning elements that depend on another structure require more comprehensive changes to the text. Therefore, they are also difficult to handle automatically. Thus, to change the tense of a verb in a sentence, we must ensure that the sequence of tenses agree in the entire text.

The Sentence Simplification System

We used this typology to implement a system of syntactic simplification for French sentences. The simplification is performed as a two-step process. First, for each sentence of the text, we generate the set of all possible simplifications (overgeneration step), and then, we select the best subset of simplified sentences using several criteria.

Generation of the Simplified Sentences

The sentence overgeneration module is based on a set of rules (19 rules), which rely both on morphosyntactic features of words and on syntactic relationships within sentences. To obtain this information, the texts from our corpus are analyzed by MELT 4 [START_REF] Denis | Coupling an annotated corpus and a morphosyntactic lexicon for state-ofthe-art pos tagging with less human effort[END_REF] and Bonsai 5 [START_REF] Candito | Statistical french dependency parsing: treebank conversion and first results[END_REF] during a preprocessing phase. As a result, texts are represented as syntax trees that include the information necessary to apply our simplification rules. After preprocessing, the set of simplification rules is applied recursively, one sentence at a time, until there is no further structure to simplify. All simplified sentences produced by a given rule are saved and gathered in a set of variants.

The rules for syntactic simplification included in our program are of three kinds: deletion rules (12 rules), modification rules (3 rules) and splitting rules (4 rules). With regards to our typology, it can be noted that two types of rules have not been implemented: aggregation rules and tense simplification rules. The merging strategies (in which several sentences are aggregated into one) were not observed consistently in the corpus. Moreover, aggregation rules could have come into conflict with the deletion rules, since they have opposite goals. Concerning tense aspects, some of them are indeed more likely to be used than others in Vikidia. However, this strategy has not been implemented, since it implies global changes to the text. For instance, when a simple past is replaced by a present form, we must also adapt the verbs in the surrounding context in accordance with tense agreement. This requires to consider the whole text, or at least the paragraph that contains the modified verbal form, and be able to automatically model tense agreement. Otherwise, we may alter the coherence of the text and decrease its readability.

This leaves us with 19 simplification rules. 6 To apply them, the candidate structures for simplification first need to be detected using regular expressions, via Tregex7 [START_REF] Levy | Tregex and tsurgeon: tools for querying and manipulating tree data structures[END_REF] that allows the retrieval of elements and relationships in a parse tree. In a second step, syntactic trees in which a structure requires simplification are modified according a set of operations implemented through Tsurgeon.

The operations to perform depend on the type of rules:

1. For the deletion cases, simply deleting all the elements involved is sufficient (via the delete operation in Tsurgeon). The elements affected by the deletion rules are adverbial clauses, clauses between brackets, some of the subordinate clauses, clauses between commas or introduced by words such as "comme" (as), "voire" (even), "soit" (either), or similar terms, some adverbs and agent prepositional phrases. 2. For the modification rules, several operations need to be combined: some terms are dropped (via Tsurgeon delete), others are moved (operation Tsurgeon move) and specific labels are added to the text to signal a possible later processing. These labels are useful for rules implying a modification of tense or mode aspects for a verb. In such cases, tags are added around the verb to indicate that it needs to be modified. The modification is performed later, using the conju-gation system Verbiste.8 For instance, to change a passive into an active structure, not only the voice must be changed, but sometimes also the person, so that the verb agrees well with the agent that has become the new subject. As regards modification rules, three changes were implemented: moving adverbial clauses at the beginning of the sentence, transforming passive structures into active forms, and transforming a cleft to a non-cleft. 3. For the splitting rules, we followed a twostep process. The subordinate clause is first deleted, while the main clause is saved as a new sentence. Resuming from the original sentence, the main clause is, in turn, removed to keep only the subordinate clause, which must then be transformed into an independent clause. In general, the verbal form of the subordinate clause needs to be altered in order to operate as a main verb. Moreover, the pronoun governing the subordinated clause must be substituted with its antecedent and the subject must be added when missing. In the case of a relative clause, the relative pronoun thus needs to be substituted by its antecedent, but it is also important to consider the function of the pronoun to find out where to insert this antecedent. Our splitting rules apply when a sentence includes either relative or participle clauses, or clauses introduced by a colon or a coordinating conjunction.

All these simplification rules are applied recursively to a sentence until all possible alternatives have been generated. Therefore, it is common to have more than one simplified variant for a given sentence. In this case, the next step consists in selecting the most suitable variant to substitute the original one. The selection process is described in the next section.

Selection of the Best Simplifications

Given a set of candidate simplified sentences for a text, our goal is to select the best subset of simplified sentences, that is to say the subset that maximizes some measure of readability. More precisely, text readability is measured through different criteria, which are optimized with an Integer Linear Programming (ILP) approach [START_REF] Gillick | A scalable global model for summarization[END_REF]. These criteria are rather simple in this approach. They are used to ensure that not only the syntactic difficulty, but also the lexical complexity decrease, since syntactic transformations may cause lexical or discursive alterations in the text.

We considered four criteria to select the most suitable sentences among the simplified set: sentence length (in words) (h w ), mean word length (in characters) in the sentence (h s ), familiarity of the vocabulary (h a ), and presence of some keywords (h c ). While the first two criteria are pretty obvious as regards implementation, we measured word familiarity based on Catach's list (1985).9 It contains about 3,000 of the most frequent words in French, whose spelling should be taught in priority to schoolchildren. The keywords were in this study simply defined as any term occurring more than once in the text.

These four criteria were combined using integer linear programming as follows:10 Maximize : h w + h s + h a + h c Where :

h w = wps × i s i -i l w i s i h s = cpw × i l w i s i -i l c i s i h a = aps × i s i -i l a i s i h c = j w j c j Subject to: i∈g k s i = 1 ∀g k s i occ ij ≤ c j ∀i, j i s i occ ij ≥ c j ∀j
(1) The above variables are defined as follows:

• wps: desired (mean) number of words per sentence

• cpw: desired (mean) number of characters per word

• aps: desired (mean) number of words absent from Catach's list for a sentence • si: binary variable indicating whether the sentence i should be kept or not, with i varying from 1 to the total number of simplified sentences • cj: binary variable indicating whether keyword j is in the simplification or not, with j varying from 1 to the total number of keywords • l w i : length of sentence i in words • l c i : number of characters in sentence i • l a i : number of words absent from Catach's list in sentence i • wj: number of occurrences of keyword j • g k : set of simplified sentences obtained from the same original sentence k • occij: binary variable indicating the presence of term j in sentence i wps, cpw and aps are constant parameters whose values have been set respectively to 10, 5 and 2 for this study. 5 for cpw corresponds to the value computed on the Vikidia corpus, while for wps and aps, lower values than observed were used to force simplification (respectively 10 instead of 17 and 2 instead of 31).

However, these parameters may vary depending on the context of use and the target population, as they determine the level of difficulty of the simplified sentences obtained.

The constraints specify that (i) for each original sentence, at most one simplification set should be chosen, (ii) selecting a sentence means selecting all the terms it contains and (iii) selecting a keyword is only possible if it is present in at least one selected sentence.

We illustrate this process with the Wikipedia article entitled Abel. This article contains 25 sentences, from which 67 simplified sentences have been generated. For the original sentence (1a) for example, 5 variants were generated and simplification (2) was selected by ILP. (1a) Original sentence11 : Caïn, l'aîné, cultive la terre et Abel ( étymologie : de l'hébreu souffle , vapeur , existence précaire ) garde le troupeau.

Evaluation

Syntactic simplification involves substantial changes within the sentence both in terms of contents and form. It is therefore important to check that the application of a rule does not cause errors that would make the sentences produced unintelligible or ungrammatical.

A manual evaluation of our system's efficiency to generate correct simplified sentences was carried out on our two corpora. In each of them, we selected a set of texts that had not been previously used for the typological analysis, that is to say 9 articles from Wikipedia (202 sentences) and two tales from Perrault (176 sentences). In this evaluation, all simplified sentences are considered, not only those selected by ILP. The results are displayed in Table 3 and discussed in Section 3.1. Two types of errors can be detected: those resulting from morpho-syntactic preprocessing, and particularly the syntactic parser, and the simplification errors per se, that we discuss in larger details in Section 3.2.

Quantitative Evaluation

Out of the 202 sentences selected in the informative corpus for evaluation, 113 (56%) have undergone one or more simplifications, which gives us 333 simplified variants. Our manual error analysis revealed that 71 sentences (21%) contain some errors, among which we can distinguish those due to the preprocessing from those actually due to the simplification system itself. It is worth mentioning that the first category amounts to 89% of the errors, while the simplification rule are only responsible for 11% of those. We further refined the analysis of the system's errors distinguishing syntactic from semantic errors. The scores obtained on the narrative corpus are slightly less good: out of the 369 simplified variants produced from the 154 original sentences, 77 (20.9%) contain errors. This value is very similar to the percentage for the informative corpus. However, only 50.7% of these errors are due to the preprocessing, while the remaining 49.3% come from our rules. It means that our rules yield about 10.3% incorrect simplified variants compared to 2.7% for the informative corpus. Nevertheless, these errors are caused mostly by 2 or 3 rules: the deletion of subordinate clauses, of infinitives or of clauses coordinated with a colon. This loss in efficiency can be partly explained by the greater presence of indirect speech in the tales that include more non-removable subordinate clauses, difficult to distinguish from removable clauses.

Globally, our results appear to be in line with those of similar systems developed for English. 12Yet, few studies have a methodology and evaluation close enough to ours to allow comparison of the results. [START_REF] Siddharthan | Syntactic Simplification and Text Cohesion[END_REF] assessed his system output using three judges who found that about 80% of the simplified sentences were grammatical, while 87% preserved the original meaning. These results are very similar to our findings that mixed the syntactic and discourse dimensions. [START_REF] Drndarević | Automatic text simplification in spanish: a comparative evaluation of complementing modules[END_REF] also presented the output of their system to human judges who estimated that 60% of the sentences were grammatical and that 70% preserved the initial meaning. These scores appear lower than ours, but Drndarević et al. also used lexical rules, which means that their error rate includes both grammatical and lexical errors.

Error Analysis

As regards syntax, the structure of a sentence can be modified so that it becomes grammatically incorrect. Three simplification rules are concerned. Deletion rules may cause this kind of problem, because they involve removing a part of the sentence, considered as secondary. However, sometimes the deleted element is essential, as in the case of the removal of the referent of a pronoun. This type of problem arises both with the deletion of a subordinate clause or that of an infinitive clause. Deletion rules are also subject to a different kind of errors. During the reconstruction of the sentence resulting from the subordinate clause, some constituents, such as the subject, may not be properly identified and will be misplaced in the new sentence.

At the semantic level, the information conveyed by the original sentence may be modified or even removed. When an agent or an infinitive clause To fix the errors identified above, our rules should be refined and developed, with the addition of better tools for sentence regeneration as well as some exclusion criteria for the incorrect sentences within the ILP module, as discussed in the next section.

Perspectives and Conclusions

This article describes an automatic syntactic simplification system for French intended for children and language learners. It is based on a set of rules defined after a corpus study, which also led to the development of a typology of simplifications in French. It would be easy to extend our typology to other target users based on other appropriate corpora, such as people with language disorders. Our approach also uses the technique of overgeneration, which makes it possible to retain the best set of simplifications based on readability criteria. Note that among those employed, some had not been considered previously and produce interesting results. Finally, we showed that the performance of our system is good (about 80 % of the generated sentences are correct) and in line with previous studies. 13 It is also the term in use since the 18th to refer to a secular cleric who, at least, received the tonsure.

The evaluation showed that the rules implemented are more suitable for expository texts, probably because they are more explicit, as style there is of a minor importance. In addition, the system set up was first tested on and therefore adapted to Wikipedia. It was only subsequently applied to narratives, that revealed new challenges, especially concerning the deletion rules. The information provided in secondary clauses or complements indeed seems most essential to understanding the story, especially when it comes to direct or indirect speech. In order to comprehend the differences in terms of efficiency and rules to be applied between genres, it would be necessary to extend our study to other texts collected in the corpora.

We envision multiple perspectives to improve our system. First, syntactic simplification could be supplemented by lexical simplification, as is done in some studies for English [START_REF] Woodsend | Learning to Simplify Sentences with Quasi-Synchronous Grammar and Integer Programming[END_REF]. Moreover, our error analysis has highlighted the need to add or repeat words when a sentence is split. It would therefore be useful to use a tool that manages references in order to improve the quality of simplified text. In addition, the sentence selection module could include additional selection criteria, based on the work done in readability of French [START_REF] Franc | An "AI readability" formula for French as a foreign language[END_REF]. A final perspective of improvement would be to make the rule system adapt to the target audience and the genre of the texts. This would require assessing the relevance of various transformations and selection criteria of the best simplifications. This perspective would also require assessing the effectiveness of the rules by means of comprehension tests both on the original and simplified sentences, which we plan to do.

( 1b )

 1b Possible simplifications : Simplification 1 : Caïn, l'aîné, cultive la terre et Abel garde le troupeau. Simplification 2 : Caïn, l'aîné, cultive la terre. Abel garde le troupeau. Simplification 3 : Caïn, l'aîné, cultive la terre. Simplification 4 : Abel garde le troupeau. (...) (1c) Selected simplification (2) : Caïn, l'aîné, cultive la terre. Abel garde le troupeau.

Table 2 :

 2 Values of the criteria in IPL for example (1).

		Sentence length Word length Word familiarity Keywords
	Expected values	10	5	2	/
	Original	19	6.1	11	5
	Simplification 1	11	4.3	5	5
	Simplification 2	5	4.6	2	5
	Simplification 3	6	4.5	3	3
	Simplification 4	4	4.7	2	2
	Simplification 5	9	6.3	5	5
	Simplification 6	12	7.3	8	2

Table 3 :

 3 Performance of the simplification system on both corpora

	are suppressed, the meaning of the sentence may
	be disrupted or some of the content lost. For in-
	stance, in the following sentence -extracted from
	the Wikipedia article abbé (abbot) -the infinitive
	clause explaining the term is dropped:
	(2a) C'est aussi depuis le XVIIIe siècle
	le terme en usage pour désigner un clerc
	séculier ayant au moins rec ¸u la ton-
	sure. 13
	(2b) C'est aussi depuis le XVIIIe siècle
	le terme en usage.

http://fr.wikipedia.org

This site is intended for young people from eight to thirteen years and gathers more accessible articles than Wikipedia, both in terms of language and content. It is available at the address http://fr.vikidia.org

https://gforge.inria.fr/projects/lingwb

http://alpage.inria.fr/statgram/frdep/fr_stat_dep_ parsing.html

These 19 rules are available at http://cental.fltr.ucl.ac.be/team/ lbrouwers/rules.pdf

http://nlp.stanford.edu/software/tregex.shtml

This software is available at the address http://sarrazip.com/dev/ verbiste.html under GNU general public license and was developed by Pierre Sarrazin.

This list is available at the site http://www.ia93.ac-creteil.fr/spip/ spip.php?article2900.

We used an ILP module based on glpk that is available at the address http:// www.gnu.org/software/glpk/

Caïn, the eldest brother, farms the land and Abel (etymology : from Hebrew breath , steam , fragile existence ) looks after the flock.

We do not discuss French here, since no simplification system were found for French, as explained previously.


Guy Mbatchou
email: guy.mbatchou@lip6.fr

François Bouchet
email: francois.bouchet@lip6.fr

Thibault Carron
email: thibault.carron@lip6.fr

Multi-scenario modelling of learning

Keywords: adaptation, e-learning, learning scenario, instructional design, learning path

Designing an educational scenario is a sensitive and challenging activity because it is the vector of learning. However, the designed scenario may not correspond to some learners' characteristics (pace of work, cognitive styles, emotional factors, prerequisite knowledge, …). To personalize the learning task and adapt it gradually to each learner, several scenarios are needed. Adaptation and personalization are difficult because it is necessary on the one hand to know in advance the profiles and on the other hand to produce the multiple scenarios corresponding to these profiles. Our model allows to design many scenarios without knowing the learner profiles beforehand. Furthermore, it offers each learner opportunities to choose a scenario and to change it during their learning process. The model ensures that all announced objectives have enough resources for acquiring knowledge and activities for evaluation.

Introduction

This work is in the field of personalization and adaptation of technology enhanced learning to make the process of acquiring knowledge more effective. Many researches are carried out in this direction: they are interested in learner models [START_REF] Greer | Student Modelling: The Key to Individualized Knowledge-Based Instruction[END_REF], intelligent tutoring systems [START_REF]Intelligent tutoring systems : Lessons learned[END_REF], analysis of learning traces [START_REF] Carron | Helping the teacher to re-organize tasks in a collaborative learning activity: an agent-based approach[END_REF] or adapting educational scenarios according to the learners' profiles [START_REF] Lefevre | Personnaliser des séquences de travail à partir de profils d'apprenants[END_REF], sometimes according to multiple sources [START_REF] Monterrat | MAGAM: A Multi-Aspect Generic Adaptation Model for Learning Environments[END_REF].

The pedagogical scenario is the description of a learning sequence, its educational goals and the means to implement it to achieve these goals. The educational scenario is a key element in learning because it is the vector of learning [START_REF] Mbatchou | Accompagnement de l'apprentissage/formation : modélisation du scénario pédagogique[END_REF]. In a context of lifelong or even initial training, it is extremely difficult to design a scenario for each learner. Some authors rely on learners' profiles to reduce the number of possibilities. To determine learners' profiles, learning data must be available and analysed, which is time-consuming. After determining the profiles, it can happen that we have found several profiles, making the number of scenarios to conceive always enough. Moreover, during learning, the knowledge acquired by a learner and interactions with the learning environment can change their profile. For example, a learner without much computer experience at the beginning of the learning session will have a poor performance that will improve during their learning as they acquire new computer skills. This evolution of the profile may render the initially proposed scenario inappropriate. Moreover, nothing can ensure that this new profile will match one of the identified profiles. Therefore, the teacher would need to be regularly designing new personalized scenarios as new profiles are identified, which is difficult to do.

Thus, there is a problem of designing several scenarios to adapt to the particularities of learners. We choose to break down an educational scenario into a learning scenario (related to learner) and a coaching scenario (for the teacher) that should be structured, coherent and combined to drive learning [START_REF] Quintin | Le rôle du scénario pédagogique dans l'analyse d'une formation à distance Analyse d'un scénario pédagogique à partir d'éléments de caractérisation définis[END_REF]. In this paper, we are interested in the learning scenario part, which is the description of the proposed learning activities, their articulation in the learning sequence as well as the expected results of learners [START_REF] Paquette | L'ingénierie pédagogique : pour construire l'apprentissage en réseau[END_REF]. Although this scenario is intended for the learners, its design is to be done by the teachers. Our research focuses on providing teachers with conceptual and technological tools to design a course with several learning scenarios without knowing in advance the profiles of learners.

The remainder of this paper is organized as follows. In section 2, we describe the state of the art of scenario models and more specifically learning scenarios. In section 3, we present our multi-scenario model of a course. In section 4 we describe the implementation of our system into the LMS (Learning Management System) Moodle. In section 5, we report the results of an acceptability questionnaire filled by teachers to assess the quality of their educational productions, their predispositions to personalize learners' follow-up and their resistance to change their teaching method. Finally, in section 6 we present the results of an experiment involving teachers using our system during a multi-scenario course design workshop.

State of art

The design of an educational scenario integrating ICT (Information and Communication Technologies) is a fundamental activity to guarantee the quality of learning by considering the training system. Based on the EML (Educational Modelling Language), most models of learning scenarios are designed as a succession of activities or tasks that the learner needs to perform to reach their learning goal. Some models divide activities based on educational goals [START_REF] Dalziel | Using LAMS Version 2 for a game-based Learning Design[END_REF]. Others propose a division based on teachers' intentions [START_REF] Emin | Scénarisation pédagogique dirigée par les intentions[END_REF] take into account activities to be done by learners, teachers' intentions and interactions [START_REF] Mariais | Modèles pour la conception de Learning Role-Playing Games en formation professionnelle[END_REF].

To carry out the division based on teachers' intentions, a set of questions must be asked to make relevant pedagogical choices. Brassard and Daele have identified 17 dimensions of questions organized into 4 categories [START_REF] Brassard | Un outil réflexif pour concevoir un scénario pédagogique intégrant les TIC[END_REF]. To consider the learners' specificities, they suggest a dimension which proposes alternative or variable paths linking the activities in the scenario. The difficulty of this implementation relies on the "a priori knowledge" of learners' characteristics (cognitive styles, emotional factors, prerequisite knowledge...). Moreover, it would be tedious to implement a pedagogical scenario with these 17 dimensions, to produce as many scenarios as possible (learners' categories).

In order to produce new scenarios, Riad et al. [START_REF] Riad | The scenarization: a new task for teachers[END_REF] propose the reuse and the adaptation of the existing scenario to create new ones. Nevertheless, the weakness of their approach is the impossibility to modify the scenario structure. Their adaptation consists only in modifying included resources. Using the principle of design patterns, Marne and Labat [START_REF] Marne | Model and Authoring Tool to Help Adapt Serious Games to their Educational Contexts[END_REF] propose to see activities with several states of input and output. The connections among states depend on the prerequisites between the activities and objectives achieved by the learner. The advantage of this approach relies on its flexibility in the sequence of activities, but it does not take into account a learners' profiles and is not intended to define several scenarios for a same session.

The Competence-based Knowledge Space Theory (CbKST), an extension of the Knowledge Space Theory (KST) [START_REF] Falmagne | The Assessment of Knowledge, in Theory and in Practice[END_REF] proposes a knowledge structure model based on competences for the personalization of learning [START_REF] Heller | Competence-Based Knowledge Structures for Personalised Learning[END_REF]. The model considers precedence's relationships between competences to establish the notion of knowledge state (set of skills acquired in a field). From the different states, the CbKST allows to establish several learning paths to achieve the same goal. Thus, the CbKST provides a framework for designing multiple learning scenarios in a transparent way for teacher.

3 Multi-scenario model

Main objectives

Our model is inspired by the CbKST given its many successes in various fields such as medicine [START_REF] Breen | Defining a competency map for a practical skill[END_REF], metacognition [START_REF] Steiner | Competence-Based Knowledge Space Theory as a Framework for Intelligent Metacognitive Scaffolding[END_REF], education [START_REF] Falmagne | Knowledge Spaces : Applications in Education[END_REF] and more specifically Serious Games [START_REF] Melero | Comparing Two CbKST Approaches for Adapting Learning Paths in Serious Games[END_REF]. However, models based on CbKST have three main weaknesses:

• Lack of support for activities with multiple competences

In studied models, the activities allow to work and acquire only one competence at a time. In our context, activities with multiple competences (such as studies case [START_REF] Marfisi-Schottman | Building on the Case Teaching Method to Generate Learning Games Relevant to Numerous Educational Fields[END_REF]) provide to learners the possibility to use diverse or even low-level competences to solve higher-level problems. It also allows the learner to acquire new competences from those acquired. These are complex activities highly recommended in a training.

• No temporal constraints

Although the learning process has for general objective acquiring and evaluating acquired knowledge, this must be done within a given time defined by the conditions of the training. But the models of the CbKST do not take this constraint into account.

• No levels or thresholds of learning satisfaction

In models based on the CbKST, the acquisition of the competence is boolean (true or false). However, in a system of initial or continuous training, the acquisition of a competence is subject to a minimum threshold of satisfaction that the learner must reach. Moreover, a competency not acquired can be obtained by compensation as advised by the system (Bachelor -Master -Doctorate) in higher education.

The goal of our model is to provide for the teacher a tool to design several learning scenarios taking into account these different learning constraints. Our model is based on a set of initial concepts that we describe and justify below, and which have been validated by the teaching staff as we will show in section 6.

The initial concepts

Inspired of the teachers' practice, our concepts are based on learning objects. Relationships among concepts are represented by the following class diagram:

Learning decomposition in unit

To be close to teaching practices, a learning or training module is divided into learning units with precedence relationships. These units correspond to the notions of chapter, part, title, etc. Each unit contains a set of learning goals.

Learner-centered pedagogy and structuration by learning goals

Most of current pedagogical approaches structure content in parts, chapters, titles, etc. However, our model structures content in learning goals. Each goal has a set of learning resources (R i j) for knowledge acquisition and a set of learning activities (A i j)

for validating acquired knowledge. The acquisition and validation of the knowledge associated with each objective has a duration (Ti ) and is conditioned by a satisfaction threshold (Si ). An objective Oi is defined as follows:

Oi = {Ti , Si , {R i 1, R i 2, …, R i Pi}, {A i 1, A i 2, …, A i Ni}} with (Pi , Ni ) Î IN²-{(0,0)}.

Pi is number of learning resources and Ni is number of learning activities

The goals have prerequisite relationships among them.

Indexing Activities by learning goals

The model defines for each activity, the necessary goals for its realization. Likewise, the model ensures that each goal has enough activities to assess and validate acquired knowledge. For this, the model has a matrix (A i j) where activities are in line and goals in column. The matrix contains participation rates of each activity for assessing and validating each goal. Thus, each activity A i j participates in the validation of the objective Oi with a rate P i j where ≥ 100%. The model can therefore handle activities with multiple goals.

Acquisition and validation of knowledge

Although the acquisition of knowledge is done by using the learning resources, our model does not take into account the fact that learners really use resources. This choice is justified by the fact that, on the one hand, we do not have means to ensure that the resource is actually being used; on the other hand, a learner may have already acquired the knowledge contained in the resource in a previous training. To ensure that knowledge is acquired, the model validates it by learning activities. An activity A i j is validated if the obtained score V i j is greater than or equal to the threshold S i j of validation of the activity. An objective Oi is validated if there is a time t such as t<Ti ≥ Si

Determination of learning paths

To determine learning paths, first the knowledge structure containing knowledge states must be generated. From the knowledge structure, the learning paths are determined from the notions of internal and external fringes defined in the KST [START_REF] Falmagne | The Assessment of Knowledge, in Theory and in Practice[END_REF]. The internal (respectively external) fringe of a knowledge state K is the set of goals P such as deleting them (respectively adding them) to K, we obtain another state of knowledge which is immediately lower (respectively higher).

Impact of activities with multiple goals in learning paths

According to KST, a validated knowledge implies its acquisition. Regardless of their current learning state, if the learner decides to do an activity with multiple goals and validates it, then they acquire the goals targeted by this activity. This validation is conditioned by the fact that the score obtained on the activity allows for the validation threshold of each goal to be exceeded.

Example: Considering learning goals a, b, c, d, e, f, and g with their prerequisite relationships, as shown on the graph in Fig. 2. By applying the CbKST approach, we can generate the learning paths (Fig. 3). Suppose that an activity targets goals c and d. The state of knowledge {c, d} is not admissible (possible) because:

• the acquisition (validation) of c is conditioned by acquisition of b • the acquisition (validation) of d is conditioned by acquisition of a So, the knowledge state associated with the acquisition of c and d is the state {a, b, c, d}. It is accessible from any state which is inferior to it. It is possible by the validation of an activity with multiple goals (green lines in Fig. 4). The activity with multiple goals increases new learning paths, leading us to the notion of augmented learning path, and the associated notions of augmented knowledge state and augmented link, defined as follows:

Fig. 2. Graph of prerequisites among goals

• Augmented knowledge state: a knowledge state is augmented (yellow state in Fig. 4) if it can be obtained from the validation of an activity with multiple goals. Because it's augmented, from any state that is inferior to it, the learner can access it without going through the intermediate states.

• Augmented link: A link from state E1 to state E2 is augmented (green link in Fig. 4) if E2 is an augmented state and E1 is not an immediately lower state of E2. • Augmented learning path: A learning path is augmented if there is at least one augmented link in its list of links. Augmented learning paths offer challengers or talented learners the opportunity to progress quickly in the acquisition of competences. An acceptable competence level as defined by the teacher can be reached the same way during this quick progress. Although the previous model is independent of any learning platform, we decided to implement it as plugin for the MOODLE1 platform (Modular Object-Oriented Dynamic Learning Environment), used in our university. The plugin is named EGbKST (Educational Goals Based Knowledge Space Theory). To show the difference between our new system and the current system, we will first present the system based on the current pedagogical model The course is divided in sequence (part, chapter, title, section, ...). Each contains a title, a duration, a set of specific goals, a set of resources and a set of exercises … Sequence N

In our current pedagogical model (represented in MOODLE system), learning and evaluation are organized in sequences. The model does not ensure that the defined goals have resources for knowledge acquisition and exercises for evaluation. The evaluation made at the end of the sequence does not allow to anticipate learners' failure because the sequence contains many goals and its duration is of approximatively 2 weeks: any failure is therefore detected only when it is too late.

In our system, we chose to keep the first 3 sections (from Table 1) to allow learners to have access to general information, general objectives and work instructions before starting learning. We added a fourth section including the EGbKST plugin used to design a course according to our model. The plugin integrates 3 roles: teacher (course design), student (learning) and tutor (tutoring). In this paper, since we are interested in course design, we will only present the views associated to the teacher role. To design their course, the teacher has many interfaces and proceeds as follows: 1. Adding metadata such as general goals, prerequisites, bibliography, keywords, … 2. Adding learning units. For example, "The exercise of political power" 3. Adding learning goals. For example, "Distinguish theories of sovereignty" 4. Adding precedence links among goals. For example, "Identify limits of powers separation" is a prerequisite for "Describe relativity of separation" 5. Adding learning resources by goal. For example, a document, web link, video, etc. 6. Adding learning activities with specifying participation rate of associated goals.

Generation of knowledge structure and learning paths

To facilitate course editing, we designed an Excel workbook2 that allows teachers to enter all course data. The workbook contains the course information cited above. Its content is exported to CSV (Comma-Separated Values) files and imported into the system. The teacher must generate knowledge structure and learning paths. Our system allows the teacher to focus on only one goal at the time during content producing. The organisation of contents is done by system. It is easy to reuse this content in another course. The system ensures that all goals have content and are evaluated. The distribution of learning time by goal allows the teacher to better estimate the workload of learners.

Assessing the acceptability of the model by teachers

Before proposing the model to the teachers for designing their courses, we wanted to assess its acceptability and teachers' willingness to use it. For this, a survey3 was submitted to university teachers on the following aspects:

• Educational productions: self-assessment of the quality of their courses in terms of (1) structuring, (2) content and evaluation according to the goals of course and (3) organization of the course notions.

• Interest in customizing the students' learning progress • Resistance to change in teaching method

The survey has been sent to all teachers and tutors4 of our university. Out of 125 persons contacted, we have received N=64 answers 5 . The participants were from 16 departments of university, their age varying between under 25 to over 60 years (M = 39.25, SD = 7.99) and their teaching seniority varying from less than 2 years to more than 30 years (M = 10.26, SD = 6.64).

Participants reported that their pedagogical productions are organized mostly in chapters (78.70%) and often in part (23.40%), title (21.30%) and other (4.20%).

Nearly 25% of participants believed that certain learning goals have no learning resources clearly identifiable by learners to acquire knowledge. It is also true for exercises used to evaluate acquired knowledge. This confirms the interest to justify association to each goal, resources and exercises to better structure the teaching and facilitate learning.

Regardless of their seniority, 83% of teachers believed that they did not have the best educational scenario. As a result, we believe that the best scenario will depend on the learners since they are the main beneficiary of the teaching.

To follow learners in their chosen scenario, nearly 90% of teachers declared they were ready to cater to learners late in their learning and 55% were willing to follow learners progressing faster in their learning. 63% of them declared being willing to spend some time to help learners outside of the scheduled sessions. Those results confirm the validity of our approach to give opportunity to all learners to finish their learning considering their cognitive characteristics.

Surprisingly, as we expected many teachers to be reluctant to changing their teaching method, 80% of teachers thought it was better to organize the teaching or learning by educational goal, instead of by chapters or parts as usual. More than 90% of them estimated that exercises should be classified by goal to facilitate their resolution. Nearly 80% found that assessment by goal would be better than assessment by period (generally at the end of a chapter, part or even semester).

Assessing the usability of the system

To evaluate the usability of EGbKST and its underlying model, we organized a workshop to use our system, attended by 16 teachers from 3 higher education institutions and 8 specialties (Economics, Geography, Management, Computer Science, Applied Foreign Languages, Modern Letters, Management and Law Sciences). We had thus the opportunity to test our model in different domains and therefore to validate the genericity of our approach.

Methodology

The experiment was organized into 4 parts. In part 1, we presented to the participants the previous survey to get their opinion before the experiment. In the part 2, we asked participants to interpret the result of survey and to criticize the current model according to them. We then exposed the need to improve the pedagogical model. The improvement focused on the possibility of having several scenarios in a course to consider learners' specificities. The concepts of our model were presented to allow them to understand their logic and usefulness. In part 3, participants had to redesign their own courses according to model. This was done through the Excel workbook designed for this purpose. At each stage, we explained to the participants the expected results. Participants' productions were presented to all assistance for verification and improvement. Part 4 of the experiment dealt with another survey6 (a posteriori) to collect the appreciation of model and difficulties of implementation.

The experiment was focused more on the pedagogical part (production of course) than the technological part (implementing course on Moodle platform).

Results

Pedagogically, our model allowed to detect in educational productions some knowledge taught before their prerequisites. These imperfections have been corrected using precedence relationships established between goals.

The graph of prerequisite among goals showed that many courses have several educational goals without or with only few prerequisites. For example, Table 2 shows among the 16 courses currently in production, the teaching unit "Constitutional Law 2" taught in the first year of the Bachelor's degree in Business Law. The teaching is structured in 2 lessons in which the first has 7 goals and the second 11. Figure 6 illustrates the low number of prerequisites between goals found for that course. In many cases, the teachers realized that they forced a pedagogical scenario although several other scenarios were just as valid. In the example on Figure 6, we In the final survey, 100% of the teachers declared appreciating our approach to better structure the lessons and organize evaluations, but 42.8% declared using our model was difficult and would have needed more time to experiment. The main difficulty was to index educational resources and activities by educational goals.

Conclusion

Designing a learning scenario (by teacher) is a time-consuming activity, making it difficult for teachers to build several scenarios. However, learners with different characteristics may have difficulties to follow the unique scenario defined by teacher. We have therefore proposed a model to design multi-scenario in courses based on prerequisite relationships between educational goals. Our model allows to design easily several scenarios without knowing in advance the specific characteristics of each learner.

From an experiment made with our system, the teachers have both detected contradictions contained in their productions and realized that several goals of their courses were not related to others. These findings have led some teachers to review their course design and to generate new scenarios. Most teachers realized that learning assessment does not cover all goals. The proposed activities cover even very few goals and generally focus on case studies. But to do this kind of activity, it is necessary to make sure that learners have really acquired the basic competences. This is done through particular activities defined around one skill or learning goal. Our experience was inconsistent in the choice of participants because their competence in e-learning was very different.

In future works, we intend to integrate into the model and the tool, an analysis of the learning scenarios chosen by learners that we will present to the teachers. This analysis will probably allow them to detect hidden dependencies. On the other hand, the quality and the achieving time of learner's results will make possible to better set learning durations for goals and to have a more accurate feedback on the effective implementation of their learning scenarios. To allow teacher to follow the learners in their different scenarios, we will design the coaching scenario.

Fig. 1 .

 1 Fig. 1. Class diagram of learning objects

  Algorithm of generation of the knowledge structure Input: G Graph of prerequisites among learning goals Output: K Knowledge structure (set of knowledge states) Variables: A and B are learning goals; Q, E are knowledge state (set of learning goals) K = {AE} È {Q} For any unmarked state E of K For each goal A Î E do If there is no goal B in G such that A ® B then K = K È {E-{A}} End For Mark(E) End For

Fig. 3 .Fig. 4 .

 34 Fig. 3. Graph of learning paths

  {a, b, c, d} {a, b, c, d, e} {a, b, c, d, f} {a, b, c, d, e, f} {a, b, c, d, e, f, g} 4 Implementation: the EGbKST plugin

Fig. 5 .

 5 Fig. 5. Interface after editing (importing) the educational structure of course

Lesson 1

 1 Constitutional organization of democratic power Goal 101: Distinguish theories of sovereignty Goal 102: Describe institutional consequences of democratic theories of sovereignty Goal 103: Describe perverse effects of national sovereignty Goal 104: Interpret utopia of popular sovereignty Goal 105: Explain the amalgam of democratic theories of sovereignty Goal 106: Recognize the main voting methods Goal 107: Explain the political implications of the main voting methods Lesson 2 The exercise of political power Goal 201: Distinguish theories of the powers separation Goal 202: Explain objectives of the powers separation Goal 203: Determine the fundamental principles of powers separation Goal 204: Identify limits of powers separation Goal 205: Identify different political regimes Goal 206: Describe particularity of parliamentary regime Goal 207: Summarize origin of the parliamentary system Goal 208: Discuss characteristics of the parliamentary system Goal 209: Describe relativity of separation Goal 210: Name characteristics of presidential regime Goal 211: Interpreting complexity of political regimes application in Africa

Fig. 6 .

 6 Fig. 6. Graph of prerequisite goals of "Constitutional Law 2" teaching unit

  the 18 goals, 9 have no prerequisite. A learner can begin learning by the end of the course (according the teacher's scenario) without risk.

Table 1 .

 1 Structuring learning in our current pedagogical model

	General	This section situates the course in the training and contains
	information	information about the authors
	General goals	The different general goals of the course
	Work instructions	Work instructions before, during and after learning
	Preliminary activities	This section contains the prerequisites of course, an entrance test, keywords, course summary, bibliography, webography and a tool to choose a team for collaborative work
	Communication	The different communication tools to use during the learning
	Sequence 1

Table 2 .

 2 The learning goals of "Constitutional Law 2" course

https://moodle.org/

https://drive.google.com/file/d/1jVAIQecZQgiKsaiJ6yUOZymBG9qSQkHo g

https://goo.gl/forms/ne1Uua4UeYPW3EeO2

Person responsible of the educational follow-up in the online training platform

Consulted at11-24-2017

https://goo.gl/forms/eSaZjajB2x744RdQ2


Andrii Shachykov
email: andrii.shachykov@loria.fr

Patrick Henaff
email: patrick.henaff@loria.fr

Anton Popov

Alexander Shulyak
email: shulyak.alex.47@gmail.com

CPG-based circuitry for controlling musculoskeletal model of human locomotor system

Keywords: central pattern generator, human walking, musculoskeletal model, Parkinson's disease I

In this paper, a new neuro-musculoskeletal simulator of human locomotor system is presented. This simulator is dedicated to reproduce healthy or altered walking gaits. It contains three joints per leg (hip, knee, ankle) controlled by twelve human muscle models activated by six specific models of central pattern generator (CPG). The CPG consists of three layers and four types of neurons and controls human leg joints. The CPGs are able to generate variable rhythmic signals by changing their intrinsic neural parameters which are controlled by descending signals from mesencephalic locomotor region (MLR), while output signals of motoneurons of CPGs control muscle models. Simulation results in Matlab show that it is possible to generate different stable walking gaits by changing intrinsic parameters of CPGs. According to these changes, the simulator can exhibit coherent or incoherent coordination between the two legs and consequently, stable or unstable walking gaits starting from the double support phase. Results show that this simulator will allow to reproduce walking gaits altered by basal ganglia decisionmaking system affected by Parkinson's disease.

INTRODUCTION

Parkinson's disease (PD) is a progressive neurodegenerative illness with symptoms like tremor, muscular rigidity, and slow, imprecise movement mainly affecting elderly individuals over 60 years old [START_REF] Hirsch | The Incidence of Parkinson's Disease: A Systematic Review and Meta-Analysis[END_REF]. It is the second most common neurodegenerative disease of adult onset [START_REF] Bertram | The genetic epidemiology of neurodegenerative disease[END_REF]. PD affects control of movements, especially upper and lower limbs, causes tremor and rigidity [START_REF] Dauer | Parkinson's Disease: Mechanisms and Models[END_REF].

A global model, able to simulate the main parts affected by PD should consist of three major levels:

1) a computational model of basal ganglia (BG) whose output mediates the second level;

2) a model of spinal structures composed of several central pattern generators (CPG) projecting to the muscles through motoneurons;

3) a musculoskeletal simulation of human lower limbs that will execute locomotor movements including physical effects of articular multi-bodies systems interacting with the ground.

There are many works that model and simulate neural structures affected by PD (first level). Most of them are limited to model of BG and relations between its nuclei. These models result in firing rates of neurons or other intrinsic parameters of system as their aim is to identify the source of abnormal oscillations in BG. Therefore, despite interesting ways of modelling BG and PD, these works are not sufficiently connected to consequences of PD on the human movements and especially on the walk. Indeed, human movements governed by lower structures that receive signals from BG are also perturbed by PD and this impacts the daily life of affected people. Some authors propose computational models of altered walking gait [START_REF] Muralidharan | A computational model of altered gait patterns in parkinson's disease patients negotiating narrow doorways[END_REF] or altered grip gesture [START_REF] Gupta | Computational model of precision grip in Parkinson's disease: a utility based approach[END_REF], which contribute to all three levels on list above. Nevertheless, these works does not explicitly model or simulate lower neural structures that receive signals from BG. These structures are located in spinal cord (second level) and are called central pattern generators. They are involved in rhythmic movements and control of muscle activities [START_REF] Brown | On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system[END_REF].

To simulate impact of PD disorders on human walking gait, this paper focuses on the second and third level. The contribution of this work is to propose a CPG-based circuitry, connected to a musculoskeletal model in a closed loop with proprioceptive and exteroceptive feedback. By changing only one intrinsic neural parameter of CPG, this model allows to exhibit different stable gaits and to reproduce altered human walking gait by receiving signals from upper control centers (such as BG) for equilibrium, speed change, or parkinsonian symptoms such as freezing of gait (FoG) [START_REF] Giladi | Motor blocks in Parkinson's disease[END_REF].

Section II briefly tells about state of the art and methods used in fields of modelling CPGs and musculo-skeleton system. Section III describes the model. Section IV presents obtained simulation results. Finally, Section V concludes this work, with some remarks and future work directions.

II. MATERIALS & METHODS

A. Biological central pattern generator for locomotion

Basal ganglia is connected to central pattern generators through mesencephalic locomotor region (MLR), reticular formation, and extrapyramidal tracts in brainstem [START_REF] Kiehn | Locomotion: Circuits and Physiology[END_REF].

CPG is a set of inter and motoneurons located in the spinal cord. More than a hundred years of investigations has led to the conclusion that rhythmic locomotion activities are largely controlled by network of spinal neurons [START_REF] Brown | On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system[END_REF]. They can generate rhythmic activity by themselves. Descending signals from the higher centers are optional, affect the shape of generated patterns, and contribute to the inter-and intra-CPG synchronization.

Current usage research, modelling, and application of CPG vary from investigation of purpose and regimes of specific groups of neurons in different segments of spinal cord [START_REF] Kiehn | Locomotion: Circuits and Physiology[END_REF][START_REF] Guertin | The mammalian central pattern generator for locomotion[END_REF] through modelling neural networks resembling CPG [START_REF] Rybak | Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion[END_REF][START_REF] Ijspeert | Central pattern generators for locomotion control in animals and robots: A review[END_REF][START_REF] Rowat | Learning algorithms for oscillatory networks with gap junctions and membrane currents[END_REF] to synthesis of control units in robotics that have the same behavior patterns of biological CPGs [START_REF] Nassour | Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots[END_REF][START_REF] Manoonpong | Adaptive, Fast Walking in a Biped Robot under Neuronal Control and Learning[END_REF].

B. Model of CPG

The model of CPG that was used in this work was proposed and used as a controller for the walk of a humanoid robot [START_REF] Nassour | Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots[END_REF]. It is based on work of Rybak et al. [START_REF] Rybak | Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion[END_REF] for a two-level CPG that separates the timing and activation of the locomotion cycle. This model is rather mathematical; however, it is supported by two neurophysiological studies and combines their propositions in multi-layered multi-pattern CPG model. CPG model is controlled from high-level system (e.g. MLR) that varies the frequency of generated patterns, phase deletion, and clamping of controlling signal. The CPG architecture is composed of three layers (Fig. 1): rhythm-generation neurons (RG); pattern-formation neurons (PF); and motoneurons (MN). Additionally, the model includes feedback sensory neurons (SN) that shape the activity of the CPG neurons.

A neural model of RG neurons was proposed by Rowat and Selverston [START_REF] Rowat | Learning algorithms for oscillatory networks with gap junctions and membrane currents[END_REF]. It has self-rhythmic generation ability; its oscillation depends on two membrane conductivities for fast and slow current. Depending on these and others cell parameters, RG neurons can generate different patterns: quiescence, almost an oscillator, endogenous oscillator, plateau, depolarization, and hyperpolarization.

Patterns generated by RG layer are shaped by PF neurons. They also chose the domination rhythm for a joint (flexion/extension). They are capable of rhythm deletion of RG layer without resetting its phase. This means, PF neurons can deactivate motoneurons while RG continue to oscillate. The activation function of PF neurons is sigmoid, whose main parameters are amplitude and saturation. Motoneurons directly control the muscles with input from PF layer and proprioceptive sensory neurons. Latter measure angle of joint and excite the corresponding motoneuron thus implementing articular reflex. Exteroceptive SN measure foot/ground contact force to excite ankle joint so it steps on full foot. MN and SN also use sigmoid activation function. For detailed mathematical models of cells, refer to [START_REF] Nassour | Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots[END_REF].

C. Musculoskeletal model

This work uses a modified version of the musculoskeletal simulator Gait2de proposed by Ton van den Bogert [START_REF] Ackermann | Optimality principles for model-based prediction of human gait[END_REF]. This realistic dynamic model simulates muscle activities (based on Hill model [START_REF] Hill | The Heat of Shortening and the Dynamic Constants of Muscle[END_REF]) and their action on skeleton to produce movements in the sagittal plane taking into account physical phenomena (ground friction, forces and dynamics of limbs, etc.). It has nine kinematic degrees of freedom, seven body segments, eight muscles per leg, and its dynamics and outputs are twice differentiable with respect to all inputs. This model is implemented as Matlab MEX function and it takes ~0.03 ms to compute.

Body segments of model are trunk, thigh, shank and foot in each leg. Each of them has the following parameters: mass, length, center of mass, moment of inertia of a human male with body mass 75 kg and body height 1.8 m.

III. NEURO-MUSCULOSKELETAL MODEL

The musculoskeletal model of the human locomotor system proposed in [START_REF] Ackermann | Optimality principles for model-based prediction of human gait[END_REF] is modified in order to control the muscles by the signals generated by a circuitry based on our model of CPGs.

A. Modifying the musculoskeletal model

As a preliminary work, the musculoskeletal system's part models six muscles per leg, avoiding the Hamstrings and Rectus muscles that affect two joints at once for easier and more understandable control (Fig 2). Thus, one CPG control an antagonistic pair of muscles, and CPGs are interconnected together to coordinate the limbs. Forces sensors are implemented on soles to return pressure force on heels and toes to measure the center of pressure. A virtual elastic attached to the top of trunk and able to slide horizontally is added (dotted line on Fig. 2,4) as lifting support harness like a disabled person. It is implemented as external force F through optional input of the model and is calculated as follows:

2, ⁄

where k is stiffness of elastic, d distance to attaching point, L0 resting length of elastic, and Fp is force from last time frame for simulation of elastic's energy loss.

B. Connecting the CPGs to the muscles

The full scheme of our neural circuitry consists of MLR projection to CPG (Fig. 1,3) as iinj, σs, αMLR, and θMLR parameters. A pulse of iinj makes CPG to start oscillating and could alter rate of RG [START_REF] Nassour | Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots[END_REF] if being a sinusoid for example; σs is actually a cell parameter, but it can be affected from upper structures (e.g. with neuromodulator or plasticity mechanism); αMLR and θMLR control PF neurons, their coupling to MN and balance between flexion and extension. Outputs of RG half-centers are connected to PF neurons, which in case of hip simply transform input value range to [0;1], as flexion/extension domination and rhythm deletion through changing αMLR and θMLR aren't applied. PF outputs are connected to MN which excitate muscles that rotate hip joint.

The input to musculoskeletal system are neural excitations for each muscle, along with initial state of the model and optional external forces and moments applied to body parts and joints. Each MN provide neural excitations for corresponding muscle [START_REF] Ackermann | Optimality principles for model-based prediction of human gait[END_REF] that control human locomotor model. Iliopsoas, Vasti, and TibialisAnt are flexion muscles that turn joints counterclockwise (positive direction); Glutei, Gastroc, and Soleus are extension muscles that turn joints clockwise (negative direction).

Additionally, output from MN should be limited to [0; 1] as model does not apply such itself. To close the control loop, CPG contains muscle sensory neurons (SN) for articular reflex that transform angle of corresponding joint into inhibitory influence on each motoneuron. In addition, two ground SN that react to force at contact points under heel and toe and excitate MN to help ankle phasing.

IV. RESULTS

A. Walking with constant speed

A distinctive feature of CPG is its ability to produce rhythmic patterns without input like shown on Fig. 4. Figures 5,6, and 7 show CPG activity, muscle excitations, and joint angles for hip, knee, and ankle respectively. All joints follow the same connection scheme as on Fig. 1, except that knee CPG's PF neurons have additional connection (excitatory for flexor and inhibitory for extensor) from hip's flexor SN that corrects knee phase; and ankle CPG's PF neurons have two ground sensory neurons (GSN), that reacts to toe ground reaction is connected to flexor PF, heel GSN is connected to extensor PF.

Resulting joint angles are qualitatively similar to human walking cycle [START_REF] Beyaert | Gait post-stroke: Pathophysiology and rehabilitation strategies[END_REF][START_REF] Martino | Locomotor patterns in cerebellar ataxia[END_REF], especially hip and knee joints that are similar to those in [START_REF] Serhan | Muscle-like Compliance in Knee Articulations Improves Biped Robot Walkings, Recent Advances in Robotic Systems[END_REF], where articular angles of the human hip, knee, and ankle are compared to those with a rigid and non rigid human foot soles. Walking simulation starts from double support phase. Transient phase can be observed at the beginning of the walk on the muscle activities. Supporting elastic slightly contributes to oscillations of trunk like a real harness.

B. Walking with variable speed

Frequency of RG is controlled by neural parameter σs which acts like a frequency gain in a rhythmic activity. Fig. 8 shows variable sagittal velocity of pelvis of biped (Fig. 2) and its moving average (sliding window width is 8 seconds) reacting to manual change of σs as square signal. Dynamical changes of σs is equivalent of neural plasticity effects. Indeed, in future work, σs can be modified by a learning or adaptive law that models a homeostatic effect. Each CPG consists of three layers and four types of neurons. The circuitry is able to generate rhythmic signals controlling the muscles and creating stable walking gaits that can be changed by variation of intrinsic neural parameters. These variations can be controlled by signals coming from an upper level circuitry. Following this way we assume that the neuro-musculoskeletal simulator presented here will be able to simulate impacts of PD disorders on human walking like observed in the medical studies. Though, further work will be aimed at taking into account the Hamstrings and Rectus muscles, simulation of altered walking gaits due to PD, like FoG, based on patients' data, and at developing a model of nervous links between Basal Ganglia region and this simulator.

Fig. 1 .

 1 Fig. 1. Left: model of one joint CPG proposed by Rybak et al. [10]. Right: proposed controller with three layers: rhythm generator (RG), patternformation (PF), and motoneuron (MN) layers.

Fig. 2 .

 2 Fig. 2. Body segments, joints, and muscles of Gait2de model. Muscles are drawn for one leg. FGH and FGT are ground reaction forces on heel and toe, V is velocity of pelvis.

Fig. 3 .

 3 Fig. 3. General scheme of neuro-musculoskeletal simulator. R and L stand for right and left leg; H, K, and A stand for hip, knee, and ankle joint.

Fig. 4 .

 4 Fig. 4. Several consecutive frames of Gait2de model simulation, time between frames is 0.1 s.

Fig. 5 .

 5 Fig. 5. Right hip CPG with constant frequency. F and E for flexion and extension RG half-center, sensory neuron, and motoneuron, respectively.

Fig. 6 .

 6 Fig. 6. Right knee CPG. F and E for flexion and extension RG half-center, sensory neuron, and motoneuron, respectively.

Fig. 7 .

 7 Fig. 7. Right ankle CPG. F and E for flexion and extension RG half-center, sensory neuron, and motoneuron, respectively.

Fig. 8 .

 8 Fig. 8. Horizontal hip speed and its moving average. σs starts at 30, changes to 50 at 10 seconds, and back to 30 at 20 s. After change of σs parameter, model needs about 3 seconds to stabilize its speed showing the global stability of the gait. V. CONCLUSION This paper presents a new neuro-musculoskeletal model based on a circuitry of six central pattern generators controlling twelve muscles of the two legs of human locomotor system.Each CPG consists of three layers and four types of neurons. The circuitry is able to generate rhythmic signals controlling the muscles and creating stable walking gaits that can be changed by variation of intrinsic neural parameters. These variations can be controlled by signals coming from an upper level circuitry. Following this way we assume that the neuro-musculoskeletal simulator presented here will be able to simulate impacts of PD

ACKNOWLEDGMENT

This work is supported by Erasmus+ 2016-2017 and French embassy of Ukraine.