Communities of teachers need tools to gather and organise educational resources scattered over the Web. As current generic search engines are insufficient to deal with contexts, these tools must rely on human annotations. First, we compare the Semantic Web and the Participative Web (2.0) approaches to annotate resources and we argue for the need to merge them. Secondly, we propose a social bookmarking tool merging the flexibility of tags with basic inference processes attached to ontologies. Thus we define the concept of structurable tags which are tags that can be linked through relations while keeping their spontaneous, on-the-fly and aggregative properties.

Introduction: Sharing documents in a community of teachers Context. New issues around shared resources are raised by the increasing participation of users into the production and the organisation of these resources. Our research deals with communities of teachers on the Web and their process to share educational documents. Indeed, results provided by search engines do not seem to totally satisfy those teachers who use other tools to organise and search resources.

Presentation of the community. Our research focuses more particularly on a group of French teachers of mechanical engineering that have been exchanging for 10 years via a mailing-list 1 (more than 100 messages/month). In this community of practice [1] composed of 1800 members, we can observe exchanges of information, personal experiences and references to online resources (technical or pedagogical documents). Scattered resources. A major aspect of this community is that resources used by teachers are highly scattered over French institutional websites (local or national) or a huge number of teachers' ones. One member in ten has a website where s/he provides his/her own resources.

Organising resources through a mailing-list. To cope with this scattering aspect, the community transformed the mailing-list into a tool to regroup and comment on resources: when a member asks for a resource on the mailing-list, other members answer him/her privately; then this member sends back to the mailing-list a summary of the received answers. Thus the mailing-list is not overloaded and broadcasts rich summary messages. Nevertheless, this system reaches limits as users cannot easily browse previous messages which are poorly archived.

Other tools to organise resources. To resolve this archive problem, the community has tried several solutions.

Merging semantic and participative approaches for organising teachers' documents

Benjamin Huynh-Kim-Bang*, Éric Dané**, Monique Grandbastien* were irregular. A Web forum was set up where small groups of members could discuss more specific subjects than those tackled on the mailing-list. Thus we observed that some threads of the forum were especially used to share links to resources. Finally, a few months ago, the community completed the mailing-list with a collaborative content management system (Joomla).

Issues of the community. Interviews processed with members of this community pointed out the need to enhance the efficiency of participation, which requires to complete the mailing-list with tools to organise scattered resources. Our work is a tentative to help communities of teachers by providing them with suitable sharing tools. If search engine based on automatic annotations are insufficient, then tools based on manual ones seem necessary.

State of the art: semantic vs. participative approaches Limits of current search engines. Sharing documents requires finding them. Most of the current search engines (like Google's or Yahoo's ones) select documents by looking for terms then rank them by pertinence. So this approach reaches its limits with implicit information. Except for basic synonyms or plural forms they do not find a page if it does not include terms of the query. For example, they cannot determine if an educational document is an exercise or a course without the terms appearing in it. Among current solutions to resolve this difficulty are metadata added by manual annotations (other solutions are described in [START_REF] Brooks | Issues and directions with educational metadata[END_REF]). We distinguish two major methods based on a priori or a posteriori manual annotations.

A priori annotations and Semantic Web

The first method comes from paper-based publishing and is built on the annotation of documents by specialists according to a model produced by experts e.g. LOM. More generally, this trend can be situated in the Semantic Web's context where experts create ontologies, which are models of domains on which computers can perform reasoning [START_REF] Berners-Lee | The semantic web[END_REF]. According to [START_REF] Brooks | Issues and directions with educational metadata[END_REF] and [START_REF] Downes | Resource profiles[END_REF], this approach includes at least two weaknesses. Firstly, the creation of a common model is a difficult task -even for experts -requiring an important negotiation phase. Secondly, the annotation process is costly because it must be operated by specialists who understand and are able to apply the predefined model. Consequently, this centralized approach can be difficult to manage as difficulties encountered in the application of LOM [START_REF] Friesen | International lom survey: Report[END_REF] and the numerous Application Profiles illustrate it.

A posteriori annotations and participative Web (2.0)

The second method has appeared with the mass participation of Internet users in producing and annotating resources. This participative Web is called "Web 2.0"2 to highlight the shift from a "traditional" Web run by more rigorous rules for publishing. This trend is illustrated by the popularity of tools like wikis, blogs or tools for sharing videos, photos and bookmarks.

Social bookmarking and tags. Sharing bookmarks consists in annotating URLs and in displaying them to others on a public space. In order to make easier the annotation of bookmarks, the first social bookmarking tools like Del.icio.us 3 enabled users to annotate resources with freely chosen keywords called tags instead of using controlled vocabularies or taxonomies. Indeed each user owns his/her own tags that cannot be modified by anyone else. Thus s/he can use his/her own vocabulary without constraints. Moreover tagging does not separate the creation of a domain model and the annotation process based on it. The model is not defined a priori but it is built by each tag associated to a resource. So tagging has the advantage to allow many users to associate tags to a URL and concurrently to enrich its description. By aggregating individual tags, social bookmarking tools compensate for the lack of predefined structures by generating browsing interfaces based on statistical calculations (frequency, cooccurency, etc). Limits of tags. Nevertheless, tagging reaches its limits in the fact it does not allow advanced structuring [START_REF] Guy | Folksonomies: Tidying up tags? D-Lib Magazine[END_REF] [START_REF] Sen | tagging, communities, vocabulary, evolution[END_REF]. First of all, tags leads to flat structures, letting few ways for users to organise their own tags. Moreover, tags' efficiency decreases because of problems of typography or synonymy. For example, a user has no way to express that "car", "cars" and "automobile" are a same concept for him/her.

Merging semantic and participative approaches

The rigidity of approaches based on controlled vocabularies (thesaurus, ontologies) realized by experts seems incompatible with the flexibility of tags built in a very distributive way. However it exists an important issue in combining these approaches in order to take advantage of their qualities and to compensate for their weaknesses (Table 1). This combination is supported by studies demonstrating the consensus reached through tags in huge communities [START_REF] Halpin | The complex dynamics of collaborative tagging[END_REF]. Few authors describe this merging trend as "Semantic Web 2.0" [10] or "Web 3.0" [START_REF] Mika | Social networks and the Semantic Web[END_REF].

Semantic Web

Participative

Problem and hypotheses

Communities of teachers, like the one studied, need tools to share resources. Human annotations are necessary because of the need, among others, to determine the implicit context of a document. However, semantic and participative approaches provide complementary solutions which seem to be incompatible. General hypothesis: It is possible to provide a tool merging the flexibility of the participative approach completed with few inference possibilities from the semantic approach.

Our proposition: We propose a model to build a social bookmarking tool allowing basic inferences on tags. This model relies on the concept of structurable tags which are tags that can be linked together by users.

Constraints: Web 2.0 approach is based on the participation of users allowed by ergonomic features. Our proposition must gingerly take into account this aspect.

Structurable tags

Based on an existing social bookmarking tool. In order to test our hypothesis, we add functionalities to Scuttle 4 , a social bookmarking tool under free licence and which is a clone of the web application Del.icio.us. The Scuttle version extended by our developments is called SemanticScuttle and is documented and downloadable on Sourceforge 5 .

Presentation of a social bookmarking tool. Like Del.icio.us, SemanticScuttle allows a logged user to add a bookmark composed of a URL, a title, a description and a list of tags. Once added, the new bookmark appears on the 4 Scuttle (by Marcus Campbell): http://sourceforge.net/projects/scuttle/ 5 http://sourceforge.net/projects/semanticscuttle/ user page and on the home page listing the last added items. To browse among bookmarks, the tool offers on the left a list of bookmarks and on the right, the corresponding tags clouds listing tags according to frequency or recency criteria (Fig. 1).

Relations between tags

In order to organise tags and to allow inferring mechanisms by the system, SemanticScuttle offers to users the possibility to create two types of relations between tags: the inclusion one symbolised by the character ">" and the synonymy one symbolized by "=".

Inclusion relation. Let's consider a webpage including a video of an AIRBUS A380 airplane showing a test for emergency braking. A user decides to create a bookmark for this page and fill the tags zone: airplane>airbus>a380, test>braking, type>video Thus the system interprets this succession of tags by the creation of oriented relations of inclusion between tags airplane, airbus and a380, between tags test and braking, and between type and video. Then the bookmark is displayed with simplified tags (a380, braking, video) which are the smallest according to the inclusion relation (see bookmarks at the bottom left of Fig. 1). Then let's consider that the user adds a bookmark about a simulation illustrating the test of the flexibility of an A380's wing. The user describes the bookmark with: test>flexibility, a380, type>simulation Thanks to these inclusion relations, the system can infer on tags and easier the search of bookmarks. Thus we created a basic inference engine which is able to complete a query for test into a query for bookmarks annotated by test but also braking or flexibility included into test.

Synonymy relation. Now let's suppose when s/he adds the second bookmark, the user does not remember if s/he previously used the tag test or the plural form tests. Thanks to the synonymy relation, the user can declare on-the-fly an equivalence between both tags by typing in the tag zone: test=tests, test>flexibility, a380, type>simulation

The system interprets the firsts tags as the creation of a synonymy relation between test and tests. In the context of a search of bookmarks, the inference engine interprets a query on the tag tests as a query for bookmarks tagged with test and tests which are synonymous, but also flexibility and braking which are still included into test. These relations between tags decrease the number of synonymous tags that must be typed by the user. Users can also find "interesting" bookmarks described with not queried tags thanks to inclusion.

As classic tagging (and on the contrary of most of the approaches based on ontologies), this system is error-tolerant. If a user creates an inclusion cycle (for example airplane>airbus>airplane), SemanticScuttle does not block the user by forcing him/her to immediately correct the relations. Each query on one of these tags will be simply completed by the other tag. If a user does not like a relation then s/he can modify it in an administration interface.

The "structured linked" on the right of Fig. 1 shows how the system displays the relations to the user. Included tags appear below their parent tags while synonym tags appear side by side like test and tests.

Multi-users context

Aggregation As the system cannot display all the tags, they have to be gathered and selected. One major benefit of structurable tags is their possibility of aggregation like classic tags. If two users used two tags with the same name, the system considers it as one tag and regroups the bookmarks under this one. There are no possible conflicts. The same effect is produced with structurable tags and their relations. If two users create tags with the same name but different relations, these relations are just gathered under the same tag. For example, if tag1 includes tag2 for one user and if tag1 includes tag3 for another user then the aggregation of these relations on the home page is tag1 including tag2 and tag3.

Visualisation Home pages of social bookmarking tools generally display selected tags as a view of the global users' activity. These highlighted tags have a huge influence on which tags will be used by taggers [START_REF] Sen | tagging, communities, vocabulary, evolution[END_REF]. Scuttle, the tool on which are based our developments, is able to display tags according to classic criteria as the most recent or the most used ones. Nevertheless, structurable tags offer new possibilities like the next three ones already implemented: Number of descendants: tags are sorted according to the number of tags they include. For example, if tag1>tag2>tag3 and tag1>tag4 then tag1 include three tags. This mode focuses on items which cover a lot of other items. Length of branches: tags are sorted according to the length of their longest branches. For example, if tag1>tag2>tag3 then tag1 has a branch whose length is two. In a tree, it corresponds to the height (or depth) of a node. This mode focuses on items which are the head of particularly detailed fields (on the difference with the first mode which could focus on vast field). Number of updates: tags are sorted according to the number of updates of its branches. Any times a tag A is added to or removed from a tag B then all the tags which include tag B increments one update. This mode focuses on tags whose branches are often modified, which could mean that they are often re-worked and thus maybe particularly interesting to users. These possibilities can be combined with each others or with classic ones. We need more experimentations to confirm their benefit but already can say that they offer new perspectives for visualisation of tags.

Related works on tags and relations

Other works. Several projects currently explore how to make more flexible the use of ontologies. Few works allow users to create tags and then to link them to a common underlying ontology managed by a supervisor e.g. for semantic wiki [START_REF] Buffa | Sweetwiki: semantic web enabled technologies in wiki[END_REF] or semantic blog [START_REF] Passant | Using ontologies to strengthen folksonomies and enrich information retrieval in weblogs: Theoretical background and corporate use-case[END_REF]. Other works allow users to complete an ontology by adding concepts and relations e.g. for the annotation of pictures [START_REF] Trichet | Une plateforme de développement d'espaces webs semantiques communautaires dediés au partage de ressources multimedia[END_REF] or the annotation of pedagogical documents [START_REF] Bateman | Collaborative tagging approaches for ontological metadata in adaptive elearning systems[END_REF] [START_REF] Al-Khalifa | Replacing the monolithic lom: A folksonomic approach[END_REF].

Comparison with other works. Our work is different from the previous ones in three points. Firstly, there is no supervisor with special rights allowing him to aggregate items. Any final user can add relations between tags. Thus our approach is more respectful of the tagging process where user is totally responsible of his/her actions.

Secondly, there is no underlying common model (like an ontology) with which every users must be consistent. SemanticScuttle accepts that users disagree with each others. Indeed, if users are forced to respect a too constraining frame, it will decrease the usability of the tool. The popularity of social bookmarking tools support this hypothesis. We understand the supervisor approach or the one based on a common model as an easy way to unify visions of a domain. However, we justify our choice of highest decentralization by the exploration of the possibility to obtain a partial common view by interactions and negotiations instead of a centralized control. If all users want to use the same tags they can do it, but they are not forced. If few users do not agree with tags from others, they can continue to keep their way to tag but others can try to convince them through discussions (see perspectives about collaborative spaces). We consider the success of the Wikipedia community as a proof of this concept of negotiation. Furthermore, if previous works about constraining tools can work in a constraint context like a company [START_REF] Passant | Using ontologies to strengthen folksonomies and enrich information retrieval in weblogs: Theoretical background and corporate use-case[END_REF], there is no real clue that they can be applied in the context of an online community.

Thirdly, we brought a special attention to the ergonomic issue for the creation of structurable tags. Thus SemanticScuttle is the only tool we know which allows to create relations between tags on-the-fly thanks to special characters. Yet this characteristic seems essential to us in order to keep the flexibility in the use of tags.

Finally, all these works try to merge ontological and tagging approaches. Yet SemanticScuttle keeps tagging properties and adds ontological ones, while other works keep ontological properties like a single underlying model and add participative ones (Table 2 Comparison with currently experimented applications. SemanticScuttle is situated in a current trend exploring the mix of human and computational search. We are waiting more results on the usage of Google co-op search 6 , Swicki 7 , Gnizr 8 or Wikia search engine 9 (based on the Wikipedia principles) in order to compare them with SemanticScuttle ones.

Discussion and perspectives

Proof of concept and further experimentations. Structurable tags implemented in SemanticScuttle prove the technical possibility 10 to make inferences on tags while keeping their spontaneous and flexible aspect. We are currently experimenting SemanticScuttle into the community of teachers described in the introduction to verify usability of structured tags.

Perspectives about structurable tags. As described in this article, structurable tags offer promising possibilities to organise tags. Thus we are thinking of new types of relations between tags. For example, we foresee a "-" relation which means that two tags are linked for the user. For example, if a user creates the relation vehicle-trademark, then when this user will add a bookmark described by bus (which is included into vehicle in his/her structurable tags) then the system will suggest under the tags zone some tags included into trademark (as bmw or ford).

Perspectives about experimentations. We are particularly attentive to three experimentation points. First, we are attentive to the usability of the relations between tags and to the best views to manage them. We think about testing alternative visualisations by linking SemanticScuttle to visualization tools 11 . Secondly, we are attentive to the human interactions into the community around the tool. How will SemanticScuttle complete the mailing-list currently used to share resources? Will SemanticScuttle need an open system of moderation as in Wikipedia? Finally, we are attentive to the terms and relations used to organise resources. We wait for more data in order to compare structures of tags realized by teachers and taxonomies from French educational program.

Collaborative and progressive annotations into SemanticScuttle. Our objective is to transform a social bookmarking tool into a structuring one, where annotations can be easily added and then gradually structured and improved. Structurable tags described in this article are one aspect on this structuring process. We are also interested into the collaborative structuring process and negotiations between members of the community in order to reach a common vision on some parts of the domain. That's why we also added collaborative spaces into SemanticScuttle. Users can describe resources in an individual way (as in any social bookmarking tool) or they can describe resources on common wiki-based spaces in a collaborative way. Indeed we make the hypothesis that structuring process takes place at the frontier between individual and common spaces. More user observations will allow us to investigate this trend further.

Figure 1 :

 1 Figure 1: Bookmarks of "teacher1" (Screenshot from SemanticScuttle)

Table 1 :

 1 Semantic vs. participative

	Web

  ).

		SemanticScuttle	Related works
	Control	Any user can create tags and relations between them	One supervisor has advanced control on tags and relations
	Model	No common model but an aggregative one tolerating inconsistency	One underlying common model or constraining one
	Ergonomy	On-the-fly relations	Relations added through browsing in a tree
	Conclusions	Based on tagging approach	Based on ontological approach

Table 2 :

 2 Comparison with other works

O'Reilly, T. "What is Web 2.0" (2005): http://www.oreillynet.com/pub/a/oreilly/\\tim/news/2005/09/30/what-is-web-20.html

http://del.icio.us


Social bookmarking tool based on structurable tags for communities of teachers

Benjamin Huynh-Kim-Bang, Eric Dané

To cite this version:

Benjamin

  Huynh-Kim-Bang, Eric Dané. Social bookmarking tool based on structurable tags for communities of teachers. Young Researchers Track in International Conference on Intelligent Tutoring System 2008 (YRT-ITS'08), Jun 2008, Montréal, Canada. hal-00365717

SemanticScuttle vs Related works

SemanticScuttle

Related works Control

Any user can create tags One supervisor has and relations between them advanced control on tags and relations From tags to ontology or from ontology to tags?

Model

Work in progress

Need for a participative tool to share and organise scattered resources


Marie Dalémat

Michel Coret

Adrien Leygue

Erwan Verron

Anna Pandolfi

Review of łRobustness of the Data-Driven Identification algorithm with incomplete input dataž

• The same net force condition is considered in the boundaries of holes instead of free edge conditions in those cases in which the real boundary of the hole is not close to the theoretical boundary. • The grip boundaries displacements cannot be determined, those boundaries are replaced by boundaries away from the edges, in those boundaries it is assumed that the net force also corresponds to the cell force.

The authors present results in how their data handling and workflow leads to a more robust DDI (parameters and results).

The study is conducted using totally perfect synthetic data obtained assuming hyperelastic (Ogden model) behavior which is altered based on experimental observations to investigate robustness of the DDI.

I have some questions regarding some of the article content:

In page 11, in the paragraph which contains line 230: łIn addition, 𝐶 significantly contributes to the convergence of the method: the higher it is (to a certain extent), the lower the error is. Indeed, the distance defined by the norm 230 influences the mapping between material and mechanical states. By choosing a large value of 𝐶, the mapping based on strain values is favored, which is relevant since they are measured (and so reliable) unlike stresses which evolve during the convergence of the algorithm. Finally, 𝑁 * is more influential than 𝐶: without missing data, a bad choice of 𝑁 * will never be compensated by a good choice of 𝐶. ž As I understand it, the error function measures two types of errors, the error in terms of the energy-like term and the error in terms of the complementary energy-like term. I don't see clearly what you mean by łto a certain extentž but if 𝐶 is increased, the error from the complementary energy-like term is less relevant than the error in the energy-like term. Ignoring the complementary energy-like part is saying that the pairs mechanical state and material state will probably have the same strains but not the same stresses (we are giving preference to compatibily over equilibrium in our element state). If I am right, I would appreciate a more detailed explanation. If I am not right, I would appreciate clarification.

Authors

The term łenergetic normž is not be the best choice in this context. The sole purpose of the norm defined in Eq. ( 3) is to measure distances between material and mechanical states within the DDCM/DDI framework. This norm has the form and the units of an energy density through the parameter 𝐶 ( [𝑃𝑎]) nevertheless it is not related to any actual energy in the system. Through the amplitude of 𝐶, it is possible to weight this distance between the strain and the stress part. In the manuscript we have replaced łenergetic normž with łnormž where needed and we have added a sentence to clarify this issue after Eq. (3).

Reviewer In page 2, in the paragraph which contains line 25: łConcerning material characterization, non-parametric approaches are proposed by [START_REF] Latorre | Experimental data reduction for hyperelasticity[END_REF] and [START_REF] Crespo | General solution procedures to compute the stored energy density of conservative solids directly from experimental data[END_REF] in which the strain energy function of a hyperleastic material is not presupposed but computed with splines, thanks to experimental simple tests. In [START_REF] Réthoré | Computational measure-ments of stress fields from digital images[END_REF], a decomposition of the strain fields obtained with Digital Image Correlation is made in order to compute the stress field without constitutive equation. In [START_REF] Seghir | A Novel Image-based Ultrasonic Test to Map Material Mechanical Properties at High Strain-rates[END_REF], experimental 30 dynamic measurements are used in the balance equations so that stress fields can be directly computed. ž The authors reference [START_REF] Latorre | Experimental data reduction for hyperelasticity[END_REF][START_REF] Crespo | General solution procedures to compute the stored energy density of conservative solids directly from experimental data[END_REF] in which the strain energy hyperelastic function is not presupposed but computed and [START_REF] Réthoré | Computational measure-ments of stress fields from digital images[END_REF][START_REF] Seghir | A Novel Image-based Ultrasonic Test to Map Material Mechanical Properties at High Strain-rates[END_REF][START_REF] Leygue | Data-based derivation of material response[END_REF] in which there is no constitutive equation at all. This is an interesting debate which is connected with łphysics-basedž data-driven learning. Somehow, in my opinion, we should give some physical background to the problem because otherwise the solutions are infinite, and probably of not much value. Just think of viscoelastoplastic materials. Can we known just from a tensile test and DIC the general behavior of a material? Or the minimum needed information?

The authors could add further discussion on that topic also cementing other possibilities left behind, e.g., using Data-Driven techniques to improve our knowledge or justify assumptions about the material behavior (it might be the case that we are just interested in understanding the relevant variables of our problem or the implications of doing different hypotheses, see for example [I], [II], [III] and [IV]).

In summary, after a minor revision, I think that the paper may be published.

Authors The paragraph at the center of this comment has been rewritten to clarify the fundamental differences between [START_REF] Latorre | Experimental data reduction for hyperelasticity[END_REF][START_REF] Crespo | General solution procedures to compute the stored energy density of conservative solids directly from experimental data[END_REF] on the one side and [START_REF] Réthoré | Computational measure-ments of stress fields from digital images[END_REF][START_REF] Seghir | A Novel Image-based Ultrasonic Test to Map Material Mechanical Properties at High Strain-rates[END_REF] on the other. (See also comments by Reviewer #2).

Reviewer 2 (Anonymous)

Reviewer Data-driven approaches to computational mechanics are emerging methods that directly use experimental data, rather resort to empirical modeling of constitutive equations, to simulate equilibrium states of solid structures. An approach studied in this paper is one of such methods. The authors numerically investigate influence of choice of parameter values on output results. Also, incompleteness of data around boundaries of a structure is dealt with. In the concluding section the authors write some recommendations of these settings, which are drawn from only one problem instance. As a major concern, I am skeptical about the authors' assertion that, with only one problem instance (which seems to be a linear problem), a specific setting of the method is universally recommendable.

Authors The recommendations made in the concluding section are indeed illustrated from a single problem instance (non-linear and finite strain) but are drawn from an extensive experience in using the DDI method with both synthetic and experimental data. Concerning the recommendations on the treatment of boundary equilibrium we believe that they are very general and can actually extend to other identification methods. They express the idea that one should not introduce equilibrium constraints that are not exactly verified in the experimental data (e.g. in sections 4.2.2 and 4.3.3).

Concerning the recommendations on the DDI parameter values, experience tells us that they are valid at least for elastic behaviors. They may not apply exactly for non-elastic behaviors. The introduction and conclusion of the manuscript have been modified to reflect this.

Reviewer Also, the paper includes some inadequate expressions, as well as insufficient literature survey. Therefore, major revision is necessary before publication. The followings are more specific comments.

page 1, title of the paper: The word łalteredž seems to be confusional. What the paper investigates is dependency of the method on parameter values (not data) and treatment of incomplete data. Therefore, the title should be reconsidered.

Authors We agree with the reviewer the word łalteredž might be confusional. We have therefore replaced it with łincompletež, as suggested.

Reviewer page 2, 2nd paragraph: As data-driven computing in elasticity, approaches different from the one studied in this paper have been proposed. Those approaches should also been surveyed.

Examples of such literature are the following: • R. Ibañez, E. Abisset-Chavanne, J.V. Aguado, D. Gonzalez, E. Cueto, F. Chinesta, A manifold learning approach to data-driven computational elasticity and inelasticity, Archives of Computational Methods in Engineering, 25, 47ś57 (2018). hal-03653378. • R. Ibañez, D. Borzacchiello, J. V. Aguado, E. Abisset-Chavanne, E. Cueto, P. Ladevèze, F. Chinesta, Data-driven non-linear elasticity: constitutive manifold construction and problem discretization, Computational Mechanics, 60, 813ś826 (2017). hal-01647641. • P. Ladevèze, D. Néron, P.-W. Gerbaud, Data-driven computation for history-dependent materials, Comptes Rendus Mécanique, 347, 831ś844 (2019). hal-02417567. • Y. Kanno, A kernel method for learning constitutive relation in data-driven computational elasticity, Japan Journal of Industrial and Applied Mathematics, 38, 39ś77 (2021). 10.1007/s13160-020-00423-1.

Authors We have added the second and the fourth reference suggested by the reviewer to the discussion of the second paragraph in page 2 as these two contributions indeed propose alternative approaches to material behavior identification from experimental data.

Reviewer Unlike the method studied in this paper, some of them involve no parameter or have established methods (e.g., the cross validation) to determine parameter values.

page 4, eq. ( 5): It is strange that on the right-hand side summation is taken with respect to 𝑒 and 𝑋 , while the term on the left-hand side has a specific indices 𝑒 and 𝑋 .

Authors This equation simply gives the explicit form of the function being minimized. For the sake of rigor and to avoid any accidental confusions, we have modified the names of the summation indices in this expression.

Reviewer page 5, line 11; page 6, line 18: The authors write łreliabilityž of the data-driven method. I do not understand how the reliability of a data-driven method can be defined (in my view, it is impossible). On the other hand, in line 3 on page 8 the authors write łrobustnessž. These two words are used in different meanings in engineering.

Authors Agreed, reliability has been replaced with robustness where needed.

Reviewer section 4: It should be made clear how the data set was generated. It seems that linear isotropic elasticity was assumed and finite element analysis was conducted to generate data. Also, it should be stated clearly if (artificial) noise is added to the generated data (as in practical problems there always exists noise).

Authors The non-linear, finite strain, hyper elastic model used to generate the data is detailed in section 3. It is also specified in this section that łThe discussion of the effect of noisy displacement values is beyond the scope of this paper and has already been partially addressed in the original DDI publication [START_REF] Leygue | Data-based derivation of material response[END_REF]ž.

Reviewer page 11, line 2: łfrom C0ž may be łfrom 10-6C0. ž

Authors This has been corrected.

Reviewer page 11, line 7: The authors write that the reason why large 𝑟 * yields large error is similar to over-fitting. I doubt this. The method in this paper is clearly a local optimization method. My guess is that, with large 𝑟 * , the method converges to a poor local optimal solution, compared with the case * .

Related to the previous issue, dependence of the output results on choice of the initial point should be investigated. Recommendations written in the concluding section may differ according to this choice.

Authors We actually wrote the opposite: łConversely, a too small ratio (too many material states) produces an effect comparable to overfitting in regression: the behavior is no longer averaged sufficiently, which also leads to a significant error. ž Let us however discuss this point: DDI regularizes the identification of the stress field through the material states which provide a coarse sampling of the material mechanical response. The intensity of the regularization is inverse to the number of material states. If one were to consider any balanced stress field to initialize the method with one material state per mechanical state, DDI would output the same field, independently of its relevance. It is only through the clustering of several mechanical states around one particular material state that the method promotes the fact that similar strains should yields similar stress. This clustering/regularization effect decreases as 𝑟 * decreases since more and more clusters are considered. We agree that the word łover-fittingž might be misleading and the observed effect is more related to an over-parametrization of the regularization provided by DDI which decreases its effect. We have therefore modified the corresponding paragraph to discuss more accurately the effect of the decrease of 𝑟 * .

Reviewer section 5: It should be reconsidered that the conclusions and recommendations drawn here are universally verified from the numerical results of only one problem instance.

Authors See discussion related to the first comment.

Review of version 3

Permalink: hal-03028848v3

Reviewer 1 (Anonymous)

The paper is a very good work on data-driven hyperelasticity in which the finite element computations are included. In particular they adress in the paper the important issue of robustnes when some data is missing. The authors have addressed the comments of this reviewer and I think that the manuscript can be accepted as is. I also want to apologize for the time it took me for this second review (which was quite straightforward). For some reason, it slipped through the cracks.

Reviewer 2 (Anonymous)

The authors have revised the manuscript according to the reviewers' comments, and hence I think that the present manuscript can be published.

Editor's assessment (Anna Pandolfi)

The revision of this paper has been very smooth. The observations of the two reviewers were significant and authors accepted them carefully, implementing some comment and clarification in the revised version. As often happens in many today reviews, reviewers suggested comparative literature to the authors, which often is not really necessary for the exposition of the research and for the understanding of the novelties of the paper. In this case, I have appreciated the objective analysis of the suggested references by the authors, that added to the revised version only the relevant literature.

Open Access This review is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the authorsśthe copyright holder. To view a copy of this license, visit creativecommons.org/licenses/by/4.0.

Reviewer 1 (Anonymous)

Reviewer This article addresses some practical difficulties when applying the Data-Driven Identification (DDI) methods introduced by Leygue et. al., [START_REF] Leygue | Data-based derivation of material response[END_REF] and T. Kirchdoerfer et. al., [START_REF] Kirchdoerfer | Data Driven Computing with noisy material data sets[END_REF]. The article is very well written and has a structure that is easy to follow and facilitates the understanding of its contribution. The topic is interesting and timely, and addresses important practical problems which are often omitted in publications. Hence, in my opinion, the present paper should be considered for publication, with at most a minor revision. The article contribution is a practical guide for the implementation of DDI algorithms. It is centered on presenting some problems that the reader might encounter when using DDI techniques and some solutions/workarounds/preprocessing choices that result in robust results over several comparisons.

The DDI approach is a constitutive-law-free technique that assigns a mechanical state (stress and strain pair) and a material state (stress and strain pair) to each structural element. The mechanical state satisfies the equilibrium and compatibility conditions, whereas the material state for the element is the stress strain pair from the material states dataset which minimizes its distance to the mechanical state, this distance is defined in terms of an energy-like term and a complementary energy-like term. The inputs of the model are nodal displacements and nodal forces obtained from a non-homogeneous test and Digital Image Correlation (DIC). The outputs are the states of each element of the model and a material states dataset. The DDI model uses two parameters, one identifies the size of the material states dataset and the other the fourth order tensor used to compute the energy-like and complementary energy-like terms used in the error norm.

The authors discuss the some difficulties in DDI that might appear because of the following: 1. Net forces are measured instead of nodal forces. 2. There are some areas in which displacements are not known or noisy those zones are called clusters. 3. Displacement data are not available close to the edges. 4. The real contours are not properly captured in the edges and in holes.

The authors propose clear solutions and workarounds; for example • Zero net force conditions in those boundaries where data is missing instead of naively ignoring equilibrium conditions on those nodes.


Keywords: Alzheimer's Disease, Amyloid beta-Peptides, Passive Immunization, Drug Therapy

Research on disease-modifying treatments for Alzheimer's disease has resulted in a series of failures over the past 20 years. However, in the last three years, four molecules have shown significant effects on clinical endpoints in phase II or III clinical trials (i.e., slowing of cognitive decline). Among these four molecules, 3 are anti-amyloid immunotherapies: aducanumab, donanemab, and lecanemab, responsible for a significant clearance of cerebral beta-amyloid deposits. These provisional data are still awaiting confirmation to put an end to the controversy surrounding the 2021 Food and Drug Administration's decision to give conditional approval to aducanumab, which is considered premature by many specialists. Confirmation is also necessary to assess the benefit (magnitude of the slowing of cognitive decline) and risk (edema and cerebral hemorrhage induced by these treatments) balance of these molecules. Masitinib, a treatment whose probable mechanism of action is neuroinflammation, has also shown positive effects that need to be confirmed. Therapies targeting the tau protein are less advanced and have yet to be proven. Patients have renewed hope since it may not be unreasonable that these disease-modifying therapies will be part of the French therapeutic arsenal within the next five years.

The pharmacopeia for Alzheimer's disease has not evolved in the last 20 years and has remained limited only to symptomatic treatments. It even took a step backward in 2018 with the delisting of anticholinesterase drugs. Nevertheless, numerous research projects continue to be carried out, focusing on the pathophysiological mechanisms of the disease, to develop a disease-modifying treatment. We propose to summarize the recent results of the most promising therapeutic trials (i.e., showing significant results on clinical criteria in the most advanced phases of development) concerning potential disease-modifying treatments for Alzheimer's disease. This review is not intended to be exhaustive, as 104 possible disease-modifying therapies for Alzheimer's disease are currently being evaluated in humans [START_REF] Cummings | Alzheimer's disease drug development pipeline: 2021. Alzheimer's[END_REF].

Treatments targeting the amyloid pathway

In the 1990s, the discovery that the genes responsible for the monogenic forms of Alzheimer's disease are uniquely located in the amyloid metabolic pathways, focused research on the amyloid pathway. This, coupled with numerous fundamental studies, has led to the amyloid cascade hypothesis, according to which the primum movens of the pathophysiology of Alzheimer's disease is amyloid pathology [START_REF] Hardy | Alzheimer's disease: The amyloid cascade hypothesis[END_REF]. The most credible short-term therapeutic hopes still rest on this hypothesis.

The first therapeutic trials targeting the amyloid protein appeared in the early 2000s through vaccination. Unfortunately, these trials had to be stopped prematurely due to meningoencephalitis [START_REF] Orgogozo | Subacute meningoencephalitis in a subset of patients with AD after Aβ42 immunization[END_REF]. Trials with passive immunotherapies resumed in the late 2000s with numerous failures. All clinical trials with anti-amyloid antibodies were negative on clinical criteria [START_REF] Van Dyck | Anti-Amyloid-β Monoclonal Antibodies for Alzheimer's Disease: Pitfalls and Promise[END_REF]. The latest failure is the DIAN-TU trial, testing the efficacy of two anti-amyloid monoclonal antibodies: gantenerumab and solanezumab, in asymptomatic or mildly cognitively impaired patients with autosomal dominant Alzheimer's disease [START_REF] Salloway | A trial of gantenerumab or solanezumab in dominantly inherited Alzheimer's disease[END_REF]. Hopes for a disease-modifying therapy targeting the amyloid pathway were diminishing, not to mention the failure of inhibitors of the amyloid precursor peptide (APP) enzymes (beta-and gamma-secretases), some of which aggravated cognitive impairment [START_REF] Zhao | Targeting Amyloidogenic Processing of APP in Alzheimer's Disease[END_REF]. Several analyses and lessons have been drawn: the first is theoretical, questioning the hypothesis of the amyloid cascade in sporadic Alzheimer's disease; the other is methodological, criticizing the target populations, doses, and pharmacodynamic effect in the trials. Theoretical criticisms are mainly based on the lack of correlation between amyloid pathology and patient symptomatology: cross-sectional studies show the absence or a very weak correlation either in vivo (measured by positron emission tomography -PET) or post-mortem, in contrast to tau pathology, which is very well correlated with symptoms [START_REF] Ossenkoppele | Associations between tau, Aβ, and cortical thickness with cognition in Alzheimer disease[END_REF] [START_REF] Duyckaerts | Modeling the relation between neurofibrillary tangles and intellectual status[END_REF]. Moreover, the onset of tau pathology is consistent with age and precedes that of amyloid pathology in large neuropathological cohorts [START_REF] Braak | Stages of the pathologic process in Alzheimer disease: age categories from 1 to 100 years[END_REF]. More recent longitudinal cohort data have also shown that individuals over 60 years old without cognitive impairment and with significant amyloid pathology have a less than 50% lifetime risk of developing symptoms of Alzheimer's disease [START_REF] Brookmeyer | Estimation of lifetime risks of Alzheimer's disease dementia using biomarkers for preclinical disease[END_REF] and have no or only minimal short term acceleration of tau pathology [START_REF] Jack | Longitudinal tau PET in ageing and Alzheimer's disease[END_REF]. In light of these observations, alternative models have recently emerged that challenge the amyloid cascade hypothesis [START_REF] Frisoni | The probabilistic model of Alzheimer's disease: the amyloid hypothesis revised[END_REF]. They propose a probabilistic model (tau and amyloid pathologies would appear independently under the accumulation of multiple risk factors) rather than deterministic [START_REF] Frisoni | The probabilistic model of Alzheimer's disease: the amyloid hypothesis revised[END_REF].

Regarding methodological criticisms, the first trials were conducted on patients without searching Alzheimer's disease pathology biomarkers. However, it is now known that approximately one-third of patients with Alzheimer's type dementia do not have Alzheimer's pathology [START_REF] Beach | Accuracy of the clinical diagnosis of Alzheimer disease at National Institute on Aging Alzheimer Disease Centers, 2005-2010[END_REF]. Naturally, suppose a treatment is aimed at amyloid pathology, and a third of the patients tested do not have amyloid pathology. In that case, this will alter the ability of the trial to show an effect. Moreover, these trials were also initially conducted in patients with moderate or advanced stages of the disease. We also know that because of its pathological effect, theoretically very upstream according to the amyloid cascade hypothesis, the influence of amyloid pathology is probably not very important once the disease is advanced (where tau pathology and neurodegeneration are then the most determining factors). Following these criticisms, the trials continued targeting patients at earlier stages with evidence of underlying amyloid pathology, but the failures continued [START_REF] Honig | Trial of Solanezumab for Mild Dementia Due to Alzheimer's Disease[END_REF][START_REF] Vandenberghe | Bapineuzumab for mild to moderate Alzheimer's disease in two global, randomized, phase 3 trials[END_REF][START_REF] Salloway | Amyloid positron emission tomography and cerebrospinal fluid results from a crenezumab antiamyloid-beta antibody double-blind, placebo-controlled, randomized phase II study in mildto-moderate Alzheimer's disease (BLAZE)[END_REF].

In 2016, the results of the Phase Ib study (PRIME) of aducanumab were published, which had the effect of a small revolution in the field [START_REF] Sevigny | The antibody aducanumab reduces Aβ plaques in Alzheimer's disease[END_REF]. This trial was indeed the first to show (even if this type of trial is not designed to do so) a significant clinical effect (slowing of clinical decline on a hybrid scale measuring cognitive impairment and its functional impact: the Clinical Dementia Rating scale -CDR) in a dose-dependent manner on anti-amyloid immunotherapy after 12 months of treatment.

So how is aducanumab different from other anti-amyloid immunotherapies that have all failed? The answer is probably pharmacodynamic: aducanumab not only prevents the accumulation of insoluble amyloid deposits but also leads to a significant clearance of these deposits (even negatived amyloid PET) when other immunotherapies did so only slightly or specifically targeted toxic soluble amyloid species (oligomers) without modifying the amyloid load (i.e., the insoluble deposits measured by amyloid PET). Since then, several signals have continued to emerge in this direction. First, the twin phase III studies of aducanumab (EMERGE and ENGAGE) show ambiguous but encouraging results (unpublished data; [START_REF]Combined FDA and Applicant PCNS Drugs Advisory Committee[END_REF]). One trial was positive (EMERGE), and another trial was (frankly) negative (ENGAGE) on the primary clinical endpoint (slowing of cognitive decline measured by the CDR scale). This is insufficient by the usual standards for marketing authorization, but subgroup analyses and analyses of biomarkers of tau pathology suggest that a clinical effect may be emerging [START_REF] Villain | Aducanumab et FDA : coup de foudre à Silver Springs[END_REF]. In addition, two other anti-amyloid antibodies responsible for high clearance of amyloid deposits have shown positive phase II trials results on clinical endpoints: lecanemab and donanemab [START_REF] Swanson | DT-01-07: TREATMENT OF EARLY AD SUBJECTS WITH BAN2401, AN ANTI-Aβ PROTOFIBRIL MONOCLONAL ANTIBODY, SIGNIFICANTLY CLEARS AMYLOID PLAQUE AND REDUCES CLINICAL DECLINE[END_REF][START_REF] Mintun | Donanemab in Early Alzheimer's Disease[END_REF].

Somehow, these data can be seen as external confirmation of the ambiguous aducanumab results.

The magnitude of the effect of these three antibodies on the slowing down of cognitive decline seems to be mild to moderate for the moment. To illustrate quantitatively this 'mild to moderate' effect with a cognitive test widely used in France, in the positive phase III trial of aducanumab (EMERGE), the high dose group (the only one to be effective) lost on average 2.7 points of MMSE in 18 months when the placebo group lost 3.3 points. Given the mode of action of these drugs, this effect can also be expected to persist over time as suggested by the 4-year follow-up effects of the PRIME study (i.e., an estimated 4-point difference in MMSE at ten years between the placebo and treated groups) [START_REF] Von Rosenstiel | Aducanumab 48-month analyses from PRIME, a Phase 1b study in patients with early Alzheimer's disease[END_REF]. The downside of these antibodies is the increase in an adverse effect observed since the appearance of anti-amyloid immunotherapies: ARIAs (amyloid-related Imaging Abnormalities). ARIAs come in two forms: edematous (ARIA-E) and hemorrhagic (ARIA-H) and are similar to cerebral amyloid angiopathy-related inflammation [START_REF] Sperling | Amyloid-related imaging abnormalities in amyloid-modifying therapeutic trials: recommendations from the Alzheimer's Association Research Roundtable Workgroup[END_REF]. In most cases, they are benign (simple headaches) or asymptomatic (discovered during the systematic MRI monitoring performed in the various trials) and disappear with the temporary cessation of infusions. Nevertheless, the increase in amyloid clearance generated by the molecules tested in the most recent trials has increased their frequency (35% of ARIA-E and 28% of ARIA-H in the phase 3 trials of aducanumab) but also the severity of these ARIA [START_REF] Vandevrede | Symptomatic amyloid-related imaging abnormalities in an APOE ε4/ε4 patient treated with aducanumab. Alzheimer's Dement Diagnosis[END_REF]. Therefore, this point will be critical to monitor and quantify in future trials.

Treatments targeting the tau pathway

Because tau pathology is better correlated with patient symptoms, treatments targeting this pathway also hold great promise. The main pharmacological class of therapies targeting tau pathology is immunotherapy (directed against the tau protein). Given the essentially intracellular localization of tau pathology, the mechanism of action of these immunotherapies is probably not identical to that of anti-amyloid immunotherapies (leading to complete clearance of hyperphosphorylated tau protein). Although not perfectly known, it probably acts by limiting the tau protein's trans-synaptic propagation, demonstrated in recent years [START_REF] Wood | Evidence for trans-synaptic and exo-synaptic tau propagation in Alzheimer disease[END_REF]. Indeed, given the intracellular target of pathological forms of tau, it is unlikely that antibodies will act on already aggregated intracellular forms. Although promising from a theoretical point of view, the first signals emerging from these trials are for the moment weak and ambiguous: two phase II clinical trials were prematurely stopped this year for futility (semorinemab, TAURIEL trial -in patients with mild Alzheimer's disease, and gosuranemab, TANGO trial), while the AC Immune® company communicated at the end of August 2021 that their other phase II trial for semorinemab was showing positive results (LAURIET trial -in patients with moderate Alzheimer's disease). Three other passive anti-tau immunotherapy trials are still ongoing (JNJ-63733657,tilavonemab, zagotenemab).

Active immunotherapy trials (vaccines) are also underway, with some hope raised by very preliminary results from a phase II trial (small size, post hoc analysis, etc.) [START_REF] Novak | ADAMANT: a placebo-controlled randomized phase 2 study of AADvac1, an active immunotherapy against pathological tau in Alzheimer's disease[END_REF].

Treatments targeting other pathways

Another positive signal also emerged from a less common pathway, the brain innate immune system, with the results of the phase II trial of masitinib (press release -unpublished data). Masitinib is a small molecule tyrosine kinase inhibitor targeting inflammation pathways (mast cells and macrophages/microglia: c-Kit, Lyn, Fyn, and CSF1R kinases). Its mode of action would be inhibition of mast cell activity (which could influence neuroinflammation and regulation of blood-brain barrier permeability) and inhibition of the Fyn protein kinase, which has a role in amyloid signaling and tau phosphorylation [START_REF] Folch | Masitinib for the treatment of mild to moderate Alzheimer's disease[END_REF]. This treatment was initially developed in mastocytosis and is currently being tested in many neurological and non-neurological diseases. The trial showed at five months a significant decrease of 1.51 points on the ADAS-Cog cognitive scale in the treated group (n = 182) when the placebo group worsened its performance by 0.63 points. Patients included in the trial had a MMSE between 12 and 25 and a diagnosis of Alzheimer's disease without the use of biomarkers. A phase III trial is underway to confirm these results.

Conclusion

This is a first in the field of Alzheimer's disease: four phase II and III clinical trials concerning possible disease-modifying therapies have been positive over the last three years. The high-dose anti-amyloid immunotherapies in patients with biologically proven mild Alzheimer's disease seem to consistently demonstrate the beginning of efficacy in slowing cognitive decline. These data must, of course, be confirmed. From a legislative point of view, aducanumab is the most advanced treatment as it was granted conditional approval by the Food and Drug Administration on June 7, 2021. This approval does not presume the clinical efficacy of the drug. Still, it considers its biological effectiveness (reducing amyloid deposits) to be sufficient in the image of the procedures often used in oncology to accelerate the availability of drugs for severe diseases with no therapeutic alternative [START_REF] Villain | Aducanumab et FDA : coup de foudre à Silver Springs[END_REF]. The company will conduct a new large and global phase III randomized-control trial starting this year to resolve the ambiguity of the results obtained with EMERGE and ENGAGE clinical trials. Its results are expected in 2026. Nevertheless, this decision is highly controversial in the literature, notably because the decrease in amyloid load has never been proven to be a valid surrogate marker for judging possible clinical efficacy (whereas in oncology, tumor growth or the number of metastases are validated markers) [START_REF] Planche | Aducanumab FDA approval: is amyloid load a valid surrogate endpoint for Alzheimer's disease clinical trials?[END_REF]. Conversely, the European Medicines Agency refused the approval of aducanumab on December 16 th 2021. Biogen® appealed this decision, and it is currently being reexamined. As for the other molecules, the results of phase III trials are not expected before the beginning of 2023 for lecanemab and in 2024 for donanemab. Therefore, it is no longer unreasonable to imagine having a disease-modifying treatment available in clinical practice for Alzheimer's disease in the next five years. Hope for patients is reborn!