Marilyne Rosselle
email: marilyne.rosselle@u-picardie.fr

Pierre-André Caron

Jean Heutte
email: jean.heutte@univ-lille1.fr

A typology and dimensions of a description framework for MOOCs

Keywords: MOOC, description framework, typology, TEL (technology enhanced learning)

the single acronym of MOOC (Massive Online Open Course) refers to many different realities. We mainly infer about the MOOC object from what we can see or read about it. However, these inferences (inductions from partial vision) lead to contradictory assertions. Nevertheless, we need to accurately describe a MOOC. In this context, this research work proposes to build a description framework for MOOCs with the aim of complementing a typology of MOOCs. We have first presented different attempts to classify MOOCs. Next, we show how they are still confusing. Then, we apply some typologies, which were efficient for Technology Enhanced Learning (TEL). For the description framework, we have gathered properties that describe MOOCs. Then, in an abduction approach, we have structured them in eight dimensions. We have also proposed an initial typology that uses simple and concrete name for types.

Introduction

MOOCs (Massive Online Open Courses) refer to many different realities; they involve different teaching methods, and different interaction modes, etc. [START_REF] Daniel | Making Sense of MOOCs: Musings in a Maze of Myth, Paradox and Possibility[END_REF][START_REF] Gilliot | The concept of iMOOC for mastered opening (French: Le concept de iMOOC pour une ouverture maîtrisée)[END_REF][START_REF] Lane | Three kinds of MOOCs, Lisa's (online) teaching blog[END_REF][START_REF] Plourde | MOOC: every letter is negotiable[END_REF][START_REF] Schneider | Welcome to the moocspace: a proposed theory and taxonomy for massive open online courses[END_REF]. It is confusing to designate them by this unique acronym [START_REF] Hill | Four Barriers that MOOCs must overcome to build a sustainable model, e-Literate[END_REF]. Why is it so difficult to conceptualize the MOOC object? We mainly conceptualize it by inducing from what we can see or read about it. These inductions (from a partial view) often result in contradictory assertions, depending on their authors. Nevertheless, we need to accurately describe MOOCs. We aim to help MOOC researchers, and designers to agree on a shared vocabulary. In this context, the research work presented here initiates a process to build a description framework and a typology for MOOCs.

Having a description framework is interesting for research into Technology Enhanced Learning (TEL) for five reasons. Firstly, we can better compare a (past, ongoing, or future) MOOC to another one. Secondly, we can also better compare them to other devices designed for distance or blended learning (e.g. LMS-Learning Management System-, CSCL-Computer Supported Collaborative Learning). Thirdly, we can estimate whether we can transpose results of previous TEL research. Fourthly, it could enable us to capitalize on-MOOC research results themselves. For example, can we transfer the results obtained on one MOOC to those of another MOOC if we exactly know what they have in common or in what they are different? Finally, this framework could help to make our administrative staff or colleagues formulate their demands more precisely when they ask us to build a MOOC, for research or teaching purposes.

We need to take a step backward, in order to model a MOOC as an object of study. Thus, how can we propose a description framework, which allows us to quickly and easily identify a MOOC? We have anticipated three difficulties. Firstly, we must develop a framework that will combine the points of view of different academic disciplines and fields. Those disciplines are learning sciences (teaching, learning, and education sciences), cognitive sciences, computer science, information technology, psychology, sociology, communication and information sciences, etc. Moreover, several academic disciplines have already addressed together some fields, such as social networks, learner communities. Secondly, all these points of view result in many criteria and many aspects. Nevertheless, how can we balance between comprehensiveness and relevance in the description framework? Thirdly, not all those who will use the description framework are researchers (some are politicians, some are teachers, some are staff members, etc.). We should consider that.

We aim to initiate the building of a typology and of a description framework. We conduct these two sub goals in parallel because they intertwine. Moreover, we do not want to build them from scratch. Hence, we have tried to find an existing typology and an existing framework, which match our goal. Our approach also consists in applying some existing typologies, which were not defined for MOOCs but were efficient for TEL. By doing this, we have gathered properties, which should describe a MOOC well enough, and should be included in our description framework.

We will first present a state of the art version, which contains three parts: some attempts to distinguish MOOCs, some existing typologies, and an existing description framework designed for MOOCs. Then we will introduce our two propositions: a typology and a description framework for MOOCs. Finally, we will discuss our propositions.

2 State of the art: attempts to define typologies and frameworks for MOOCs

Four typologies of MOOCs

In this section, we present, apply, and discuss four typologies.

Presentation of the typologies

We studied four attempts to distinguish a MOOC from another one. The first attempt has introduced an historical distinction. Then the following one has addressed the teacher's focus within the MOOC, the third one the learning functionalities of MOOCs. The last one has relied on opening or closing dimensions in MOOCs.

Firstly, the MOOC acronym appeared in the context of connectivism [START_REF] Walker | Connectivism: A learning theory for the digital age[END_REF][START_REF] Kop | Connectivism: Learning theory of the future or vestige of the past? The International Review of Research in Open and Distance Learning[END_REF]. Then, the distinction between cMOOCs (where 'c' stands for connectivist; in the spirit of the first MOOC) and xMOOCs (where 'x' stands for transfer) emerged [START_REF] Daniel | Making Sense of MOOCs: Musings in a Maze of Myth, Paradox and Possibility[END_REF]. In a cMOOC, the course relies more on the connections between learners rather than on the content they learn together. On the contrary, in an xMOOC a predefined content (i.e. knowledge) is the target.

Secondly, Lane meets the objective of the previous paragraph by seeking the focus on which the teacher has designed the MOOC [START_REF] Lane | Three kinds of MOOCs, Lisa's (online) teaching blog[END_REF]. She defines three types of MOOCs:

• "Content-based MOOCs (xMOOCs) • Task-based MOOCs (tMOOCs) • Network-based MOOCs (cMOOCs)"
The added type "tMOOCs" refers to MOOCs that focuses on the tasks the learners have to perform; the community and the contents are only a support. In content-based MOOCs, contents (i.e. knowledge) prevail. While in network-based MOOCs, the community dominates.

Thirdly, Clark has described a typology based on "pedagogy" ("learning functionalities"). [START_REF] Clark | MOOCs: taxonomy of 8 types of MOOCs (blog post), Donald Clark Plan B[END_REF]) defines eight types of MOOCs:

• "TransferMOOCs are xMOOCs, • MadeMOOCs implement more crafted and challenging assignments, • SynchMOOCs are synchronous MOOCs with fixed start days, end days, and deadlines for assignments, • AsynchMOOCs are asynchronous MOOCs with no (or frequent) start days, and tend to have no or looser deadlines for assignments, • AdaptiveMOOCs are MOOCs that use adaptive algorithms to present personalized learning experiences, • GroupMOOCs are MOOCs starting with small and collaborative groups of learners, • ConnectivistMOOCs are cMOOCs, and • MiniMOOCs are shorter MOOCs for contents and skills that do not require a semester structure". Fourthly, in [START_REF] Gilliot | The concept of iMOOC for mastered opening (French: Le concept de iMOOC pour une ouverture maîtrisée)[END_REF], the authors asked themselves what dimensions are opened or closed in a MOOC, from the learners' point of view. They explored five dimensions (see first column of Table 1). Thereby, in a cMOOC, "all dimensions are opened" while in an xMOOC "almost all dimensions are closed except of the group organization", which is sometimes free, and sometimes imposed by the teacher.

These authors introduced another type of MOOCs: the iMOOC. It has more opened dimensions than an xMOOC and less than a cMOOC. By opening the choice of resources, the organization of the group work and possibly the collaborative production, its main goal is to allow an investigative approach (hence the 'i'). In Table 2, we highlight (italic and bold) the differences with the corresponding column of Table 1. "NA" means "not applicable". For example, for the gamification MOOC (column 1-G), the teacher decided not to integrate work group in his course. From the learner's point of view, the organization of the group work is closed. Moreover, we put "C/O" when it is closed or opened, depending on what we consider. For example, if the resources are the teaching materials, the choice of resources is closed for our four examples. If the resources are contents on what the learner has to apply his new knowledge on the assessments, then it is opened. Thus, the "choice of resources" dimension definition is too large.

With these considerations, only the first two MOOCs match with the dedicated column of Table 1 and thus are xMOOC in the fourth typology. Moreover, if we focus on the sequence "C, O, C, O, C/O", the two last columns of Table 2 also match the iMOOC column of Table 1.

In brief,

• "Gamification" is an xMOOC, a synchMOOC, and a miniMOOC (6 weeks),

• "Writing in the sciences" is an xMOOC (and a transfer-MOOC, and a content-based MOOC), a synchMOOC, a madeMOOC, and a miniMOOC (8 weeks), • "Project management" is an xMOOC (and a transfer-MOOC, a content-based MOOC), a tMOOC, a madeMOOC, a synchMOOC, a groupMOOC, a miniMOOC (5 weeks), and an iMOOC, and • "Digital identity" is an xMOOC (and a transfer-MOOC, a content-based MOOC), a synchMOOC, a groupMOOC, a miniMOOC (8 weeks), and an iMOOC.

Discussion

The distinction cMOOCs/xMOOCs of the first typology is the best known. Many authors have often referred to this distinction. Even though, it can work at a first glance, too many differences remain between two MOOCs of the same type. One advantage of the Lane's typology is: the added words before the acronym are more meaningful than letters. However, as for the previous paragraph, too many differences persist inside one type.

In his typology, Clark mixes diverse points of view:

• Knowledge acquisition mode (via transfer vs. via social connections)

• Assignment types (simple vs. crafted)

• Mode of delivery (synchronous vs. asynchronous)

• Social dimension (small collaborative groups)

• Duration (shorter than a semester vs. a semester long)

• Adaptation (adaptive or not) All of these features could be components of a type of pedagogy (educational contexts). Moreover, his eight types do not match eight different "pedagogies". In fact, a MOOC can belong to several Clark's types. Moreover, if we consider only two values for the six points of view, we count sixty-four types of MOOCs (two to the power of six).

For the fourth typology, as in the previous paragraph, with only five dimensions listed in Table 1, we have thirty-two types of MOOCs. Moreover, other authors consider more than five dimensions, e.g. fourteen in [START_REF] Jézégou | The GEODE device for evaluating the openness of an educational environment (French: Le dispositif GEODE pour évaluer l'ouverture d'un environnement éducatif)[END_REF] thus about four thousands types. Even though we think it is interesting to know what dimension is opened (or not) to describe a MOOC (in a description framework for MOOCs), we do not think we can base a typology of MOOCs on openness. It rather is a property of some features in a MOOC.

Existing typologies, which were defined for TEL

We present and discuss three typologies.

Presentation of the typologies

The De Vries' typology. De Vries described the spectrum of learning software available in 2001 (de [START_REF] De Vries | Learning pieces of software: panoply or spectrum? (French: les logiciels d'apprentissage : panoplie ou éventail ? )[END_REF]. Table 3 lists eight education functions, the type of software, and the education theory she associated to these functions. The Typology of Gauthier and Colin. Four years latter, authors of [START_REF] Gauthier | French: cartographies et guidage interactif pour faciliter l'accès des enseignants aux outils TICE), CRE@TIVE, Cellules[END_REF] have the same goal than De Vries. They defined cartographies in order to help teachers to find an ICT (Information and Communication Tools). Each cartography allows accessing the ICTs from different points of view. Thereby, the authors identify educational paradigms ICTs implement, and educational situations they allow. Their eight educational paradigms underlie various activities and teaching practices, which are combinable:

• Problem solving • Improvement and progress • Project, practice • Training, assessment • Facilitating, support • Tutoring, coaching • Presentation, demonstration • Discovery, research
The nine educational situations are the areas situated at the intersection of a two-dimensional array. These dimensions are the social dimension (three values: individual, groups and communities) and the time dimension (three values: sequence, module, courses). It defines nine areas. An ICT may occupy several areas.

Hy-Sup. Hy-Sup [START_REF] Deschryver | Final report of the HY-SUP project (academic blended learning platforms world-wide), education and Training Program throughout life[END_REF] was a European research project. It produced configurations for describing blended learning systems (French: "Systèmes Hy-brides") used in higher education (Fr: "Éducation Sup-érieure"). Hy-Sup has defined six configurations:

• Scene corresponds to a content-oriented teaching, support to face-to-face education, with mainly textual resources, • Screen is scene with added multimedia resources,

• Cockpit corresponds to a course organization oriented teaching, guided by the use of tools (and sometimes integrating relational and reflective goals), • Crew aims for learning focused on supporting the process of knowledge construction and on interpersonal interactions, • Public space aims learning centered on the opening of the training device to external resources, and • Ecosystem aims for learning by operating a large number of technological and educational opportunities.

Discussion: are the previous typologies useful to define types of MOOCs?

The De Vries', and Gauthier & Colin's typologies lacks the social dimension of MOOCs. It makes sense because this dimension was almost nonexistent in the ICTs of this period. The six Hy-sup configurations seem very interesting to keep. Indeed, we can match some categories of MOOCs of this section to Hy-Sup configurations, and do the four following conjectures:

• xMOOCs, transferMOOCs, and content-based MOOCs could at least be screens,

• tMOOCs, and madeMOOCs could be from cockpits to crews,

• cMOOCs, iMOOCs, groupMOOCs, and network-based MOOCs could be from public spaces to ecosystems, and • adaptiveMOOCs, miniMOOCs, synchMOOCs, or asynchMOOCs could be one of the previous three items. However, MOOCs are not blended-learning devices. Therefore, it is important to take into account the description dimensions on which the Hy-Sup configurations rely, even though we should adapt them.

Existing description framework for MOOCs

Just a few days latter as we presented our research in the LASI meeting (Learning Analytics Summer Institute) in Lyon (France) at the beginning of July 2013, Schneider displayed her framework in an AIED workshop in Memphis (USA). Our approaches are similar. In [START_REF] Schneider | Welcome to the moocspace: a proposed theory and taxonomy for massive open online courses[END_REF], the author described a framework that brings together some metadata about MOOCs. It has two levels. The first level, called "general", gathers general information about the MOOC (e.g. name, author, certificate). The second level, called "ILE and Stances" (Interactive Learning Environment), has four frames: instruction (how the knowledge is taught), content (how the knowledge is structured, e.g. in modules), assessment, and community.

These groupings and the properties are very interesting. Nevertheless, the Schneider's framework lacks of some dimensions we need. We have reused a part of it, and we have enriched it. The levels and properties of Schneider we have reused will appear in the proposition section.

Propositions: a typology and a description framework for MOOCs

Our aim is twofold. We need to precisely describe a MOOC and we need to easily assign a type to it. We conduct these two sub goals in parallel. Indeed, we think the description framework could help to build a typology of MOOCs, and the typology could help to describe a MOOC.

If we want to take into account the main dimensions or features, we have seen in the previous section, the combination of these features lead to too many types. Therefore the resulting typology would be difficult to use, and would be as unclear as the previously cited ones. Our approach is on the one hand to propose a simple and concrete typology and on the other hand a description framework that specifies some differences between MOOCs of a same type and to describe their main features.

Whose point of view to consider in our framework?

A MOOC involves many people:

• Course designer teaching team (the teaching team that designed the course), referred later as "teacher"

• Course leading teaching team (the teaching team that actually lead the course)

• Learners

• Tutors, graded learners or accredited learners

• University staff • Researchers • Political staff
• Parents of learners Attempting to conciliate all points of view is unrealistic because they may be incompatible. In our framework, we favor the researchers' point of view. Researchers could focus on four axes:

1. MOOC as a technical and pedagogical platform 2. Use and usability of these platforms and of their courses for learners and teachers 3. Learners' profiles (their knowledge misconceptions or conceptions, or the level or quality of learners' learning) 4. Teachers' point of view or profiles Teachers' point of view has import because they do take decisions in MOOC design. Hence, researchers could for example focus on the following questions about teachers:

• What types of pedagogical or technical function do they want to offer to learners (e.g. communication functions, organization functions…)?

• What types of activity do they want to organize (e.g. projects, presentation…)?

• What types of pedagogical theory/framework (e.g. constructivism, connectivism…) do they choose in their courses or part of courses?

• What social dimension (individual, group, groups, communities) do they want to privilege in their courses or part of courses?

• What feedbacks do they would like to have for themselves or to give to learners (e.g. about learners' interactions, learners' results, learners that may drop out…)? For our propositions, we choose to ignore the first axe and to ignore the MOOC platform on which the MOOC courses run, even though we know it influences some choices because we consider what is possible to do with a MOOC without considering how it is done technically.

Even though our propositions are mainly for researchers, we strive to make then as simple as possible, hoping other people would be able to take ownership of them.

What to remember from the state of the art?

For the proposition of a typology

We have seen we cannot use the types, defined with added letters (c, i, t, and x) or words (asynch, contentbased, group, made, mini, synch, task, or transfer) before the MOOC acronym. Moreover, the potential number of types is too big for the typologies of Lane (op. cit.), of Gilliot and colleagues (op. cit.), and of Clark (op. cit.) because of the possible combinations. Furthermore, by applying the typologies to four MOOC examples, we found the types intertwine too much and are non-exclusive. Therefore, these typologies result in too many misunderstands, because too many differences remain between MOOCs that are currently of the same type. They are still confusing, and include many implicit details. Otherwise, the Hy-sup configurations (op. cit.) can help to define a first typology for MOOCs.

For the proposition of a description framework

We gather features to describe MOOCs. We partially or totally reuse:

• The connectionist educational paradigm of Siemens (op. cit.)

• The dimensions from Gilliot and colleagues (op. cit.) of Table 1 • The focus on which the teacher has designed the MOOC (of Lane's Typology, op. cit.)

• The Clark's points of view (op. cit.)

• The educational functions, educational theories, and types of software of de Vries (op. cit.)

• The educational situations and paradigms of Gauthier and Colin (op. cit.) • The Hy-sup dimensions Deschryver and Charlier (op. cit.) have used to define the Hy-Sup configurations • The levels and items of Schneider (op. cit.)

Proposition 1: using Hy-sup configurations as corner stones for a first typology

We aim to propose a first typology that should describe as few types of MOOCs as possible. Each type should have an easily understandable, easy to remember, and concrete name. We do not want to build it from scratch. Therefore, we propose to use the six Hy-Sup configurations (op. cit.) as corner stones of a first typology, i.e. a typology on which researchers could base the continuing building of a more fitted typology.

We have made this choice for three reasons:

• Hy-sup configurations are tangible,

• Hy-sup has few configurations, and We have wondered whether to make educational theories (or paradigms) appear in our typology. In fact, we have decided to ignore them here, because to implement a theory, teachers can choose any of the previous types. For example, in a connectivist course, they can choose a Scene MOOC just for managing their teaching without providing any videos. We have also made the same reasoning for the software functionalities a MOOC can Implement.

Proposition 2: a description framework for MOOCs

We first discuss the temporal scope of the description framework. Then we explain its general structure, and partly detail it.

Temporal considerations

If the description framework of a MOOC is filled, before the MOOC starts, then it can contain information that has been chosen and anticipated by the teacher. If the description framework of a MOOC is filled after the MOOC has closed, then it can also contain additional data like, total number of inscriptions, traces, etc., and can even incorporate data that are calculated from traces or other data.

Defining a framework in the first case is easier than in the second case. We should start by doing the first one, even if we have anticipated some needs for the second one. Therefore, we propose an extendable framework.

General presentation of the framework

In order to make the description framework easy to understand, we should choose as few dimensions as possible; a dimension is a grouping of properties. In this article, we focus on the main dimensions chosen for the description framework. We detail two of them. Further research will publish others. For these dimension, we explain below how we build them.

Because, the number of properties to take into account is huge, we have to find the best rules for grouping those properties. This kind of approach is abductive.

The hugest group of properties concerns instruction. Therefore, we have decided to split the instructional properties in five distinct dimensions:

• One for the places and roles of humans in the MOOC ("human") • One for the educational (teaching and learning) material ("resources") • One for the assessments and feedbacks

• One for the specific technical and educational functionalities the teacher prescribes in the course ("functionalities") • One for the other instructional properties ("instructional") Hence, we propose to describe a MOOC with the following dimensions:

• General* • Context • Instructional* • Resources • Assessments* and feedbacks • Human • Functionalities • Other stuff for researchers
In this list, the asterisk symbol indicates dimensions, for which we have the same name than the Schneider's one [START_REF] Schneider | Welcome to the moocspace: a proposed theory and taxonomy for massive open online courses[END_REF]. However, the content of ours is most often a bit different from hers.

In this framework, some properties can stay empty. We define a minimal group of properties, sufficient to describe a MOOC to learners and most people. A second group collects general information about the instructional properties (choices). Then teachers can precise other instructional properties if they want it. Moreover, researcher can fill the properties, relevant to their domain.

Each dimension refines in sub dimensions, like branches of a tree. Eventually, a sheet corresponds to a property, which may be valued.

Details of the "General" dimension

The "General" dimension gives general and public information about the course (see Figure 1). It maps the minimal group of properties. This dimension gathers information that usually appears in MOOC adverts. To fill this dimension, we studied Coursera, Udacity, and Canvas course adverts and those of our four examples of MOOCs. We also add our type in this dimension. In Figure 1, properties with a white 'i' in a blue circle symbol are properties, common with the "general level" of Schneider (op. cit.). The ones with an added green check symbol are renamed properties. We add the ones with an exclamation point symbol. We have included neither the "content for wrapped in-person course (location and dates offered)" nor the "pace (cohort-based vs. self-paced)" from Schneider (op. cit.), because they have taken place in other dimensions of our framework.

The "Context" dimension

The "Context" dimension stores information that should help to understand the context of use for which the teacher designed the course. Many researches inspire us to fill this dimension. From now, we use the spatiotemporal components of Jézégou (op. cit.) and the "pace" from Schneider (op. cit.) ("pace" appears both in her "general level" and in the "content" frame of her second level).

The "Instructional" dimension

The instructional dimension collects information about the instructional decisions and choices except those previously explained.

To build this dimension, we have used educational paradigms cited in De Vries (op. cit.) and Siemens (op. cit.), the learner's tasks and the educational activities of De Vries (op. cit.), the focus of the learner activity of Lane (op. cit.). We have added choices about knowledge acquisition mode and mode of delivery of Clark (op. cit.). We have extended the dimensions of Gilliot and colleagues (op. cit.) because we include other properties than openness. We have also added the "instructor involvement", "lecture", and "reading" from the "instruction frame" of the Schneider's second level.

The "Resource" dimension

The "resource" dimension describes the learning material in general. It brings together resources as video, text, etc., and non-palpable resources, which people can bring (e.g. knowledge, skills). For this dimension, we use numerous researches about resource description and indexation.

The "Assessment" dimension

The assessment dimension (see Figure 2) describes the existence of an assessment process or not, and if any, what it consists in. In this dimension, we have used the choices of assignment types of Clark (op. cit.).

The "Human" dimension

This dimension describes personal dimension of the learner: role, status, etc. It also depicts its social interactions (teacher's prescription): does the learner work in a dyad, a small group, a learner social network inside the MOOC, and an extended network outside the MOOC? Furthermore, it qualifies the scope and the type of these interactions.

The "Functionalities" dimension

Technical and educational functionalities are choices the teacher prescribes to learners. For example, a MOOC can involve an Intelligent Tutoring Systems (ITS) in a specific educational activity. These functionalities can either be built in the MOOC platform or used outside of the platform (e.g. be in the learner's PLE -Personal Learning Environment). To fill this dimension we reuse the types of software and the educational functionalities of De Vries (op. cit.) and the category of tools of Gauthier & Colin (op. cit.).

The "Other stuff for researchers" dimension

We have put here many things researchers may need like teacher models, learner models, trace model, interaction model, traces, calculi (e.g. interest, flow, intrinsic and extrinsic motivation, engagement, feeling of self-efficacy, relatedness), etc. We suggest structuring the traces and calculi with the same dimensions than the ones made for the prescriptions, especially context, instructional, human, and resources. The principle is to consider each property of other dimensions as reference property, and the property of this dimension as actual property. For example, "actual pace" refers to information about the real pace observed during the course.

Discussion of our propositions 4.1 Discussion of proposition 1: HySup based typology

In this section, we check if HySup based typology can match different pedagogical paradigms, and different importance given to the community role. The first three types are teaching-oriented, while the last three ones are learning oriented. Therefore, we think it translates different educational paradigms, where the main role is played either by the teacher or the learner. Moreover, a discontinuous grading exists between the first type and the last one: in the first one, the learner interact less with the MOOC, the MOOC offers fewer tools to the learners and fewer liberties, and learners interacts less with one another than in the sixth type. Thus, it can fit to different importance given to the community. Now, we apply the Hy-Sup configurations to our four examples of MOOCs. "Gamification" is a screen, because it uses video. It is not of other types, because:

• it is not guided by the use of tools,

• it supports neither the process of knowledge construction nor the interpersonal interactions,

• the learning is not centered on the opening of the training device to external resources, and • it does not aim at learning by operating a large number of technological and educational opportunities (only a large number of resources). "Writing in the sciences" is crew, because individuals have to interact to enhance each other productions. It is neither a public space nor an ecosystem because the MOOC device is closed.

"Project management" and "Digital identity" are public spaces, because these MOOCs are opened to external resources and technical opportunities. This application is only a first step. Indeed, to be valid, we will apply our framework to other MOOCs. Moreover, to be acceptable by other researchers, they should be able to fill it with as little help as possible.

Discussion of proposition 2

Conclusion

In this article, we intend to classify MOOCs in as few types as possible, and to define a description framework for MOOCs. We started by studying some attempts to classify MOOCs. Then we applied each of these attempts to four examples of MOOCs, which occurs during 2012-2013. Finally, we studied existing typologies and a framework. This study teaches us these typologies confuse people. It also allows us collecting many properties, which can characterize a MOOC.

On the one hand, we propose a typology based on the six Hy-Sup configurations: scene, screen, cockpit, crew, public space, and ecosystem. On the other hand, we structure the properties of a MOOC in eight dimensions: general, context, instructional, resources, assessments & feedbacks, human, functionalities, and other stuff for researchers. This work is a first step that should be refined, based on feedbacks and contributions of researchers and people from diverse horizons.

To do that, our future trend consists in publishing the framework on a platform by using semantic web tools in order to allow other interested people to navigate in it and to use a search engine on the collection of published MOOC descriptions. In our framework, we will encode properties as metadata. Moreover, both properties and values will use commonly accepted standards everywhere it is possible.

We also should compare our framework to the one that Siemens [START_REF] Siemens | MOOC Framework[END_REF] has announced between the acceptation of our article and its publication.

Finally, with a more stabilized description framework, a pattern (or a set of patterns) in it could correspond to a new type in our initial typology of MOOCs. To identify the patterns, we would place some dimensions of the description framework on the axes of a hypercube; a pattern would be a hyper sphere of the universe defined by the hypercube.

Figure 1 .

 1 Figure 1. The General dimension.

Figure 2 .

 2 Figure 2. Assessment tree.

Table 1 :

 1 Some opened or closed dimensions, translated from Gilliot and colleagues. Other sessions of the first three MOOCs have occurred since. The four MOOC examples are xMOOCs according the typologies described in the first paragraph, in the Lane's typology ("content-based MOOCs"), and in the Clark's typology ("transferMOOCs"). Yet, these examples of MOOCs differ a lot. However, thing are more complex with the fourth typology. Because these examples are xMOOCs, each column of Table2should match the xMOOC column of Table1.

		cMOOC iMOOC	xMOOC
	Learning goals	O	C	C
	Choice of resources	O	O	C
	Organization of the learning	O	C	C
	activities
	Organization of the group work	O	O	C/O
	Collaborative co-production	O	C/O	C
	2.1.2 Application to examples of MOOCs
	For studying the previous attempts, we applied each of them to four examples of MOOCs, which occurs
	during 2012-2013:
	• "Gamification"(1) (referred as "1-G" in Table 2) was a course taught in end summer 2012 by Kevin
	Werbach of University of Pennsylvania,
	• "Writing in the Science"(2) (2-W) was a course taught in Fall 2012 by Dr. Kristin Sainani of
	Stanford University to learn how to write correct scientific publications,
	• "Project Management"(3) (3-P) was a course taught in French in Spring 2013 by Rémi Bachelet of
	"École Centrale de Lille", and
	• "Digital identity"(4) (4-D) was a French MOOC, which ran in early Summer 2013, to teach how to
	understand and manage one's digital identity.

Table 2 :

 2 Are the four examples some xMOOCs according to Gilliot and colleagues?

	1-G	2-W	3-P	4-D

Table 3 :

 3 The eight educational function and some Features -translated from (de Vries, 2001).

	Education function	Type of Software	Educational Theory
	Present information	Tutorial	Cognitivist
	Provide exercises	Repeated exercises	Behaviorist
	Truly teach	Intelligent Tutoring System (ITS) Cognitivist
	Captivate the attention and motivation of the learner	Educational (serious) game	Mainly behaviorist
	Providing an exploration space	Hypermedia	Cognitivist, Constructivist
	Providing an environment for natural laws discovery	Simulation	Constructivist, situated cognition
	Provide an environment for exploring abstract domains	Micro-world	Constructivist
	Provide a space for exchange among learners	Computer Supported Collaborative Learning (CSCL)	Situated cognition

  • The state of the art shows us they are compatible with the typing of MOOCs.

	Hence, our HySup-based MOOC typology has six types:
	1. Scene MOOC
	2. Screen MOOC
	3. Cockpit MOOC
	4. Crew MOOC
	5. Public space MOOC
	6. Ecosystem MOOC

  Table 4 details some properties.

Table 4 .

 4 Detail of some properties.

	Property	Description	Type	Constraint
	Title	Name or title of the course
	Author(s)	Author or authors of the courses		One item per
				author.
	Public	Do(es) the author(s) appears in	Yes/No
		the MOOC advert
	Author item
	First name	First name
	Name	Name (surname)
	Affiliation	University, institution, or faculty
		membership
	Educational domain(s)	Teaching domain or domains	Use existing standard One item per
				domain
	HySup-based MOOC type	The type of the MOOC as
		defined above
	Typical target audience	The typical learner for which the
		teacher has designed this course
	Status	The typical learner's status in	Student, professional,
		real life	…
	Entry level		None, pre-collegiate,
			undergraduate,
			graduate, expert, or
			typical age range
	…
	URL	Localization on the Internet

Table 5 :

 5 Table5illustrates how we are assessing our description framework by applying it to our four examples. Application of the general dimension to the Gamification MOOC.

	Property (and its sub-divisions)	Application example
	Title	Gamification
	Author(s)
	Public	True
	Author Item
	First Name	Kevin
	Name	Werbach
	Affiliation	University of Pennsylvania
	Educational domain
	Domain item	Information
	Domain item	Technology
	Domain item	Design
	Domain item	Business
	Domain item	Management


Yves Aubry
email: yves.aubry@univ-tln.fr

Jean-Christophe Godin

Olivier Togni
email: olivier.togni@u-bourgogne.fr

FREE CHOOSABILITY OF THE CYCLE

Keywords: Mathematics Subject Classification. 05C15, 05C38, 05C72 Coloring, Choosability, Free choosability, Cycles

come

Introduction

For a graph G, we denote its vertex set by V (G) and edge set by E(G). A color-list L of a graph G is an assignment of lists of integers (colors) to the vertices of G. For an integer a, a a-color-list L of G is a color-list such that |L(v)| = a for any v ∈ V (G).

In 1996, Voigt considered the following problem: let G be a graph and L a color-list and assume that an arbitrary vertex v ∈ V (G) is precolored by a color f ∈ L(v). Under which hypothesis is it always possible to complete this precoloring to a proper color-list coloring ? This question leads to the concept of free choosability introduced by Voigt [START_REF] Voigt | Choosability of planar graphs[END_REF].

Formally, for a graph G, integers a, b and a a-color-list L of G, an (L, b)coloring of G is a mapping c that associates to each vertex u a subset c(u) of L(u) such that |c(u)| = b and c(u) ∩ c(v) = ∅ for any edge uv ∈ E(G). The graph G is (a, b)-choosable if for any a-color-list L of G, there exists an (L, b)-coloring . Moreover, G is free (a, b)-choosable if for any a-color-list L, any vertex v and any set c 0 ⊂ L(v) of b colors, there exists an (L, b)-coloring c such that c(v) = c 0 .

As shown by Voigt [START_REF] Voigt | Choosability of planar graphs[END_REF], there are examples of graphs G that are (a, b)choosable but not free (a, b)-choosable. Some related recent results concern defective free choosability of planar graphs [START_REF] Li | Free Choosability of Outerplanar Graphs, Green Communications and Networks[END_REF]. We investigate, in the next section, the free-choosability of the first interesting case, namely the cycle. We derive a necessary and sufficient condition for a cycle to be free (a, b)choosable (Theorem 4). In order to get a concise statement, we introduce the free-choice ratio of a graph, in the same way that Alon, Tuza and Voigt [START_REF] Alon | Choosability and fractional chromatic number[END_REF] introduced the choice ratio (which is equal to the so-called fractional chromatic number).

For any real x, let FCH(x) be the set of graphs G which are free (a, b)choosable for all a, b such that a b ≥ x:

FCH(x) = G | ∀ a b ≥ x, G is free (a, b)-choosable .
Moreover, we can define the free-choice ratio fchr(G) of a graph G by:

fchr(G) := inf a b | G is free (a, b)-choosable .
Remark 1. Erdős, Rubin and Taylor have asked [START_REF] Erdős | Choosability in graphs[END_REF] the following question: If G is (a, b)-choosable, and c d > a b , does it imply that G is (c, d)-choosable ? Gutner and Tarsi have shown [START_REF] Gutner | Some results on (a:b)-choosability[END_REF] that the answer is negative in general. If we consider the analogue question for the free choosability, then Theorem 4 implies that it is true for the cycle.

The path P n+1 of length n is the graph with vertex set V = {v 0 , v 1 , . . . , v n } and edge set E = n-1 i=0 {v i v i+1 }. The cycle C n of length n is the graph with vertex set V = {v 0 , . . . , v n-1 } and edge set E = n-1 i=0 {v i v i+1(mod n) }. To simplify the notation, for a color-list L of P n or C n , we let L(i) denote L(v i ) and c(i) denote c(v i ).

The notion of waterfall color-list was introduced in [START_REF] Aubry | Every triangle-free induced subgraph of the triangular lattice is (5m, 2m)-choosable[END_REF] to obtain choosability results on the weighted path and then used to prove the (5m, 2m)choosability of triangle-free induced subgraphs of the triangular lattice. We recall one of the results from [START_REF] Aubry | Every triangle-free induced subgraph of the triangular lattice is (5m, 2m)-choosable[END_REF] that will be used in this note, with the function Even being defined for any real x by: Even(x) is the smallest even integer p such that p ≥ x. For example, let P n+1 be the path of length n with a color-list L such that |L(0)| = |L(n)| = 4, and |L(i)| = 9 for all i ∈ {1, . . . , n -1}. Then the previous proposition tells us that we can find an (L, 4)-coloring of P n+1 whenever n ≥ 8. In other words, if n ≥ 8, we can choose 4 colors on each vertex such that adjacent vertices receive disjoint colors sets. If |L(i)| = 11 for all i ∈ {1, . . . , n -1}, then P n+1 is (L, 4)-colorable whenever n ≥ 4. On the other side, there are color-lists L for which P n+1 is not (L, b)-colorable

Free choosability of the cycle

We begin with a negative result for the even-length cycle: Lemma 3. For any integers a, b, p such that p ≥ 2, and a b < 2 + 1 p , the cycle C 2p is not free (a, b)-choosable.

Proof. We construct a counterexample for the free-choosability of C 2p : let L be the a-color-list of C 2p such that

L(i) =        {1, . . . , a}, if i ∈ {0, 1}; { i-1 2 a + 1, . . . , i-1 2 a + a}, if i = 2p -1 is odd; {b + i-2 2 a + 1, . . . , b + ( i-2 2 + 1)a}, if i is even and i = 0; {1, . . . , b, 1 + (p -1)a, . . . , 1 + pa -b -1}, if i = 2p -1. v 0 {1, 2, . . . , 9} v 5 {1, . . . , 4, 19, . . . , 23} v 4 {14, . . . , 22} v 3 {10, . . . , 18} v 2 {5, . . . , 14} v 1 {1, . . . , 9} Figure 1.
The cycle C 6 , along with a 9-color-list L for which there is no (L, 4)-coloring c such that c(v 0 ) = {1, 2, 3, 4}.

If we choose c 0 = {1, . . . , b} ⊂ L(0), we can check that there does not exist an (L, b)-coloring of C 2p such that c(0) = c 0 , so C 2p is not free (a, b)choosable. See Figure 1 for an illustration when p = 3, a = 9 and b = 4. Now, if ⌊x⌋ denotes the greatest integer less than or equal to the real x, we can state:

Theorem 4. For the cycle C n of length n, C n ∈ FCH 2 + n 2 -1
.

Moreover, we have:

fchr(C n ) = 2 + n 2 -1
.

Proof. Let a, b be two integers such that a/b ≥ 2+⌊ n 2 ⌋ -1 . Let L be a a-colorlist of C n . Without loss of generality, we can suppose that v 0 is the vertex chosen for the free-choosability and c 0 ⊂ L(v 0 ) has b elements. It remains to construct an (L, b)-coloring c of C n such that c(v 0 ) = c 0 . Hence we have to construct an (L ′ , b)-coloring c of P n+1 such that

L ′ (0) = L ′ (n) = L 0 and for all i ∈ {1, ..., n -1}, L ′ (i) = L(v i ). We have |L ′ (0)| = |L ′ (n)| = b and for all i ∈ {1, ..., n -1}, |L ′ (i)| = a. Since a/b ≥ 2 + ⌊ n 2 ⌋ -1 and e = a -2b, we get e/b ≥ ⌊ n 2 ⌋ -1 hence n ≥ Even(2b/e).
Using Proposition 2, we get:

C n ∈ FCH(2 + n 2 -1
).

Hence, we have that fchr(C n ) ≤ 2 + ⌊ n 2 ⌋ -1 . Moreover, let us prove that M = 2 + ⌊ n 2 ⌋ -1 is reached. For n odd, Voigt has proved [START_REF] Voigt | On list Colourings and Choosability of Graphs[END_REF] that the choice ratio chr(C n ) of a cycle of odd length n is exactly M . Hence fchr(C n ) ≥ chr(C n ) = M , and the result is proved. For n even, Lemma 3 asserts that C n is not free (a, b)-choosable for a b < 2 + ⌊ n 2 ⌋ -1 . Remark 5. In particular, the previous theorem implies that if b, e, n are integers such that n ≥ Even( 2b e ), then the cycle C n of length n is free (2b + e, b)-choosable.

In order to extend the result to other graphs then cycles, the following simple proposition will be useful: Starting from a single edge and applying inductively Proposition 6 allows to obtain the following corollary: Corollary 7. Let T be a tree of order n ≥ 2. Then T ∈ FCH(2). Now, we can state the following:

Proposition 8. If G is a unicyclic graph with girth g, then G ∈ FCH 2 + g 2 -1
.

Proof. Let a, b be two integers such that a/b ≥ 2 + ⌊ n 2 ⌋ -1 , L be a a-colorlist of G, C = v 1 , . . . , v g be the unique cycle (of length g) of G and T i , i ∈ {1, . . . , g}, be the subtree of G rooted at vertex v i of C.

Let v be the vertex chosen for the free choosability and let c 0 ⊂ L(v) be a set of cardinality b. If v ∈ C, then by virtue of Theorem 4, there exists an (L, b)-coloring c of C such that c(v) = c 0 . This coloring can be easily extended to the whole graph by coloring the vertices of each tree T i thanks to Corollary 7. If v ∈ T i for some i, 1 ≤ i ≤ g, then Corollary 7 asserts that the coloring can be extended to T i . Then color C starting at vertex v i by using Theorem 4. Finally, complete it by coloring each tree T j , 1 ≤ j = i ≤ g.

Applications

As an example to the possible use of the results from Section 2, we begin with determining the free choosability of a binocular graph, i.e. two cycles linked by a path.

For integers m, n and p such that m, n ≥ 3 and p ≥ 0, the binocular graph BG(m, n, p) is the disjoint union of an m-cycle u 0 , u 1 , . . . , u m-1 and of an n-cycle v 0 , . . . , v n-1 with vertices u 0 and v 0 linked by a path of length p given by u 0 , x 1 , . . . , x p-1 , v 0 . Note that if p = 0, then u 0 and v 0 are the same vertex. Proof. Assume without loss of generality that m ≥ n and let a, b be integers such that a/b ≥ 2 + ⌊ n 2 ⌋ -1 . Let L be a a-color-list of BG(m, n, p). Let y be the vertex chosen for the free choosability and let c 0 ⊂ L(y) be a set of cardinality b. If y lies on the m-cycle, then by virtue of Theorem 4, there exists an (L, b)-coloring c of the m-cycle such that c(y) = c 0 . By Corollary 7, this coloring can be extended to the vertices of the path. Now, it remains to color the vertices of the n-cycle, with v 0 being already colored. This can be done thanks to Theorem 4. If y lies on the n-cycle, the argument is similar. If y ∈ {x 1 , . . . , x p-1 }, then the coloring can be extended to the whole path and the coloring of the m-cycle and n-cycle can be completed thanks to Theorem 4. This method can be extended to prove similar results on graphs with more than two cycles, connected by a tree structure.

Define a tree of cycles to be a graph G such that all its cycles are disjoint and collapsing all vertices of each cycle of G produces a tree.

Corollary 10. Any tree of cycles of girth g is in FCH(2 + ⌊ g 2 ⌋ -1 ).

Algorithmic considerations

Let n ≥ 3 be an integer and let a, b be two integers such that a/b ≥ 2 + ⌊ n 2 ⌋ -1 . Let L be a a-color-list of C n . As defined in [START_REF] Aubry | Every triangle-free induced subgraph of the triangular lattice is (5m, 2m)-choosable[END_REF], a waterfall list L of a path P n+1 of length n is a list L such that for all i, j ∈ {0, . . . , n} with |i -j| ≥ 2, we have L(i) ∩ L(j) = ∅. Le m = | ∪ n i=0 L(i)| be the total number of colors of the color-list L. The algorithm behind the proof of Proposition 2 consists in three steps: first, the transformation of the list L into a waterfall list L ′ by renaming some colors; second, the construction of the (L ′ , b)-coloring by coloring vertices from 0 to n -1, giving to vertex i the first b-colors that are not used by the previous vertex; third, the backward transformation to obtain an (L, b)-coloring from the (L ′ , b)-coloring by coming back to original colors and resolving color conflicts if any. It can be seen that the time complexity of the first step is O(mn); that of the second one is O(a 2 n) and that of the third one is O(max(a, b 3 )n). Therefore, the total running time for computing a free (L, b)-coloring of the cycle C n is O(max(m, a 2 , b 3 )n).

Proposition 2 (

 2 [START_REF] Aubry | Every triangle-free induced subgraph of the triangular lattice is (5m, 2m)-choosable[END_REF]). Let L be a color-list of P n+1 such that |L(0)| = |L(n)| = b, and |L(i)| = a = 2b + e for all i ∈ {1, . . . , n -1} (with e > 0). If n ≥ Even 2b e then P n+1 is (L, b)-colorable.

Proposition 6 .

 6 Let a, b be integers with a ≥ 2b. Let G be a graph and G v be the graph obtained by adding a leave v to any vertex of G. Then G is free (a, b)-choosable if and only if G v is free (a, b)-choosable. Proof. Since the "only if" part holds trivially, let us prove the "if" part. Assume G is free (a, b)-choosable and let L be a a-color-list of G. Let v be a new vertex and let G v be the graph obtained from G by adding the edge uv, for some u ∈ V (G). Then any (L, b)-coloring c of G can be extended to an (L, b)-coloring of G v by giving to v b colors from L(v)\c(u) (|L(v)\c(u)| ≥ b since a ≥ 2b). If v is colored with b colors from its list, then, since G is free (a, b)-choosable, the coloring can be extended to an (L, b)-coloring of G v by first choosing for u a set of b colors from L(u) \ c(v).

Proposition 9 . 2 - 1 .

 921 For any m ≥ 3, n ≥ 3 and p ≥ 0, BG(m, n, p) ∈ FCH 2 + min(m, n)

Figure 2 .

 2 Figure 2. A tree of cycles (on the left), and the associated tree obtained by collapsing cycles (on the right).


Li-Ping Sun

-Hui Zhao

-Qiang Li

-Li-Hua Huo

-Jean-Paul Viricelle
email: viricelle@emse.fr

Christophe Pijolat

Study of oxygen reduction mechanism on Ag modified Sm 1.8 Ce 0.2 CuO 4 cathode for solid oxide fuel cell

Keywords: Solid oxide fuel cell, Silver infiltration, Composite cathode, Electrode reaction

Different amount of metal silver particles are infiltrated into porous Sm 1.8 Ce 0.2 CuO 4 (SCC) scaffold to form SCC-Ag composite cathodes. The chemical stability, microstructure evolution and electrochemical performance of the composite cathode are investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), and AC impedance spectroscopy respectively. The composite cathode exhibits enhanced chemical stability. The metal Ag remains un-reacted with SCC and Ce 0.9 Gd 0.1 O 1.95 (CGO) at 800 °C for 72 h. The polarization resistance of the composite cathode decreases with the addition of metal Ag. The optimum cathode SCC-Ag05 exhibits the lowest area specific resistance (ASR, 0.43 Ω cm 2 ) at 700 °C in air. Investigation shows that metal Ag accelerates the charge transfer process in the composite cathode, and the rate limiting step for electrochemical oxygen reduction reaction (ORR) changes to oxygen dissociation and diffusion process.

Introduction

One of the research targets for SOFCs is lowering the operating temperature in order to increase the life-time of the cell/stack/module as well as to reduce the cost of the materials. So far, many studies have been focused on the development of new electrode and electrolyte materials toward low temperature operable SOFCs [START_REF] Brett | Intermediate temperature solid oxide fuel cells[END_REF], [START_REF] Steele | Materials for fuel-cell technologies[END_REF], [START_REF] Xia | A high performance composite ionic conducting electrolyte for intermediate temperature fuel cell and evidence for ternary ionic conduction[END_REF] and [START_REF] Zhou | A new cathode for solid oxide fuel cells capable of in situ electrochemical regeneration[END_REF]. Layered perovskite oxides with K 2 NiF 4 -type structure were extensively studied in recent years, due to their promising transport and catalytic properties, thermochemical stability and compatibility with other cell components [START_REF] Skinner | Oxygen diffusion and surface exchange in La 2-x Sr x NiO 4+δ[END_REF], [START_REF] Kharton | Oxygen ion transport in La 2 NiO 4based ceramics[END_REF], [START_REF] Hernández | La 2-x Sr x NiO 4+δ as cathode for SOFC: reactivity study with YSZ and CGO electrolytes[END_REF], [START_REF] Huang | Investigation of La 2-x Sr x NiO 4+δ based cathodes for SDC -carbonate composite electrolyte intermediate temperature fuel cells[END_REF], [START_REF] Daroukh | Oxides of the AMO 3 and A 2 MO 4 -type: structural stability, electrical conductivity and thermal expansion[END_REF], [START_REF] Wang | A 2-α A α′ BO 4 -type oxides as cathode materials for IT-SOFCs(A = Pr[END_REF], [START_REF] Zhao | New cathode materials for ITSOFC: phase stability oxygen exchange and cathode properties of La 2-x NiO 4+δ[END_REF], [START_REF] Mauvy | Oxygen reduction on porous Ln 2 NiO 4+δ electrodes[END_REF], [START_REF] Sun | Synthesis and performance of Sr 1.5 La x MnO 4 as cathode materials for intermediate temperature solid oxide fuel cell[END_REF], [START_REF] Dailly | Perovskite and A 2 MO 4 -type oxides as new cathode materials for protonic solid oxide fuel cells[END_REF] and [START_REF] Taillades | Intermediate temperature anode-supported fuel cell based on BaCe 0.9 Y 0.1 O 3 electrolyte with novel Pr 2 NiO 4 cathode[END_REF]. Among these oxides, Ln 2 CuO 4 materials were found to exhibit excellent performance. For example, Li et al. reported that the ASR of the La 1.7 Sr 0.3 CuO 4 cathode was as low as 0.16 Ω cm 2 at 700 °C [START_REF] Li | Electrode properties of Sr doped La 2 CuO 4 as new cathode material for intermediate-temperature SOFCs[END_REF]. We studied the electrochemical performance of Sm 2-x Ce x CuO 4 and the ASR of Sm 1.8 Ce 0.2 CuO 4 was found to be 1.16 Ω cm 2 at 700 °C [START_REF] Sun | Synthesis and performance of Sm 2-x Ce x CuO 4 cathode materials for IT-SOFC[END_REF]. Further research on the oxygen reduction kinetics of these cuprate cathodes always found that the charge transfer reaction was the rate limiting step [START_REF] Li | Electrode properties of Sr doped La 2 CuO 4 as new cathode material for intermediate-temperature SOFCs[END_REF], [START_REF] Sun | Synthesis and performance of Sm 2-x Ce x CuO 4 cathode materials for IT-SOFC[END_REF], [START_REF] Li | Electrochemical performance of La 2 Cu 1-x Co x O 4 cathode materials for intermediate-temperature SOFCs[END_REF], [START_REF] Hao | Synthesis and performance of Nd 2-x Sr x CuO 4 cathode materials for IT-SOFC[END_REF] and [START_REF] Sun | Study on Sm 1.8 Ce0.2CuO4-Ce 0.9 Gd 0.1 O 1.95 composite cathode materials for intermediate temperature solid oxide fuel cell[END_REF]. Thus, enhancing the oxygen reduction activity of these cathode materials is crucial for the development of novel IT-SOFC cathode.

Studies proved that cathodes infiltrated with Palladium (Pd) and platinum (Pt) metal particles showed promising oxygen reduction activity, due to the substantially increase of the surface catalysis properties [START_REF] Hwang | Electrochemical performance of LSCF-based composite cathodes for intermediate temperature SOFCs[END_REF] and [START_REF] Huang | Characterization of Cu, Ag and Pt added La 0.6 Sr 0.2 Co 0.2 Fe 0.8 O 3-δ and gadolinia-doped ceria as solid oxide fuel cell electrodes by temperature-programmed techniques[END_REF]. Ag is another attractive infiltrating candidate than those precious metals, due to its good catalytic activity, high electrical conductivity and relatively low cost. Numerous works have been performed on the Ag-added perovskite cathodes [START_REF] Lin | Silver-modified Ba 0.5 Sr 0.5 Co 0.8 Fe 0.2 O 3-δ as cathodes for a proton conducting solid-oxide fuel cell[END_REF], [START_REF] Sakito | Silver infiltrated cathodes for intermediate temperature solid oxide fuel cells[END_REF], [START_REF] Wilkinson | Ag-perovskite composite materials for SOFC cathode-interconnect contact[END_REF], [START_REF] Suzuki | Low temperature processed composite cathodes for solid-oxide fuel cells[END_REF] and [START_REF] Huang | Oxygen dissociation and interfacial transfer rate on performance of SOFCs with metal-added (LaSr)(CoFe)O 3 -(Ce, Gd)O 2-δ cathodes[END_REF], but less attention was paid to the K 2 NiF 4 -type material [START_REF] Li | Electrochemical performance of La 1.6 Sr 0.4 NiO 4 -Ag composite cathodes for intermediate-temperature solid oxide fuel cells[END_REF].

To continue our studies on Sm 1.8 Ce 0.2 CuO 4 (referred as SCC in this paper) cathode materials, and to understand the effect of Ag doping on the electrode performance, SCC-Ag composite cathode was selected and the electrochemical property was studied compared with the bare SCC electrode. The mechanism of the oxygen reduction on the SCC-Ag composite cathode was investigated using electrochemical impedance spectroscopy (EIS) technique.

Experimental

Sm 1.8 Ce 0.2 CuO 4 powder was synthesized using the glycine-nitrate process (GNP). According to the formula, stoichiometric amount of metal nitrates were mixed in a beaker to form a solution, and then glycine (aminoacetic acid, H 2 NCH 2 CO 2 H) was added into the nitrate solution at 1:2 M ratio of metal ions/glycine according to propellant chemistry. After drying and firing, the resultant powder was calcined in air at 1000 °C for 12 h. The Ce 0.9 Gd 0.1 O 1.95 (CGO) powder (Rhodia Courbevoie, France) was pressed uniaxially at 220 MPa and sintered at 1400 °C for 10 h to form a densified pellet. In order to perform EIS measurement, a test cell with three electrodes configuration was constructed. The Sm 1.8 Ce 0.2 CuO 4 powder was mixed with terpineol to form a slurry, and subsequently painted on one side of the CGO electrolyte pellet to form an electrode area of 0.5 cm 2 , used as working electrode (WE). The WE was first heated at 400 °C for 2 h to eliminate organic binders, followed by sintering at 1000 °C for 4 h in air, with a heating/cooling rate of 3 °C min -1 . Platinum paste was painted on the other side of the CGO pellet in symmetric configuration, and then sintered at 800 °C for 1 h in air, to form porous counter electrode (CE). A Pt wire was used as reference electrode (RE) and put on the same side of the working electrode. Silver nitrate solution was then infiltrated into the porous cathode. The detail of infiltration process was as follows: 0.05 mol L -1 AgNO 3 solution was prepared by dissolving silver nitrate powders in mixture solution of distilled water and ethanol. Ethanol was added to reduce the surface tension on SCC backbone. The ratio of ethanol to water is 1 to 1. The infiltration was carried out in a vacuum chamber by dripping the AgNO 3 solution onto the SCC cathode area carefully using an injector and drying at 80 °C. The infiltrated cathode was then calcined at 800 °C for one hour. This infiltration step was repeated several times to obtain a suitable weight of Ag loaded on the SCC backbone. The obtained cathodes with different weight ratio of Ag were abbreviated as SCC-Ag02 for Sm 1.8 Ce 0.2 CuO 4 with 2 wt.% Ag, SCC-Ag05 for Sm 1.8 Ce 0.2 CuO 4 with 5 wt.% Ag, and so on.

In order to check the chemical stability of SCC with CGO at high temperature, these two components were mixed thoroughly in 1:1 weight ratio, and heat-treated at 1000 °C for 4 h in air. Silver nitrate was then added to the mixture, and again heated up to 800 °C for 72 h to form SCC-CGO-Ag composite powders.

The sample was characterized using X-ray diffraction instrument (Rigaku, D/MAX-3B) and scanning electron microscopy (SEM) (Hitachi, S-4700 FEG), respectively. The impedance spectra were recorded over the frequency range 1 MHz to 0.1 Hz using Autolab PGStat30.

The measurements were performed at OCV as a function of temperature (550-700 °C) and oxygen partial pressure (in N 2 /O 2 mixed atmosphere).

Results and discussion

Phase purity of the prepared SCC and chemical compatibility of Ag metal with SCC and CGO were first investigated. No. 24-0998). After sintered at 1000 °C for 4 h, SCC and CGO retained their own structures in the SCC-CGO mixture (Fig. 1(c)). When Ag was added and the composite cathode was then heated at 800 °C for prolonged 72 h, no additional peaks except those from metal Ag, SCC and CGO can be detected (Fig. 1(d)). This result indicates that Ag is highly chemical compatible with SCC and CGO materials. The SEM images of SCC and SCC-Ag cathodes are comparably shown in Fig. 2. Obviously a fine microstructure with moderate porosity and well-necked particles is formed in the SCC cathode after firing at 1000 °C for 4 h (Fig. 2(A)). The impregnation of Ag does not change the microstructure adversely. Some round-shape particles are found in the SCC-Ag05 cathode after the infiltration of AgNO 3 and then firing at 800 °C for 1 h (Fig. 2(B)). The surface mapping result indicates that these round-shape particles are metallic Ag, which are dispersed uniformly on the surface of the cathode (Fig. 2(C)). The average particle size of Ag is about 1-2 µm. The cross-sectional image of the SCC-Ag05 cathode and the CGO electrolyte is presented in Fig. 2(D). Clearly the cathode and the electrolyte form good contact with each other. These is no delamination or cracking that be observed at the electrode/electrolyte interface. The thickness of the electrode is about 15 µm (Fig. 2(D)). The EDX result further supports that metal Ag is distributed in the SCC-Ag05 cathode (Fig. 2(D), inset). When the Ag loading increases to 10 wt.%, however, the glomeration and growth of Ag particles can be visualized (Fig. 2(E)). This aggregation results in less TPBs and thus be suspected to increase the polarization resistance. To explore the effects of Ag loading on polarization resistance, the impedance spectra of SCC cathode impregnated with different amounts of Ag were measured (Fig. 3). For all the cathodes, the impedance spectra can be separated into two arcs located in the high-frequency zone and the low-frequency zone respectively, implying two consecutive reaction processes related to oxygen reduction reaction (ORR) might take place. The overall size of the two arcs is primarily attributed to the cathode area specific resistance (ASR), which is widely used to describe the resistance terms related to electrode process. The Arrhenius plots of ASR are given in Fig. 4. Obviously the activation energy (Ea) of SCC-Ag cathode is much smaller than SCC cathode. The ASR decreases with the Ag content, reaches a minimum at 5 wt.% Ag, and then increases again at 10 wt.% Ag. The variation of ASR with Ag contents can be understood, considering that the ORR process of the SCC electrode is likely promoted by the surface modification with silver. However, with the further increase of Ag content in the composite cathode, some surface of the SCC particles may be covered by the Ag metal, and the active sites for oxygen reduction reaction will be reduced. This deduction was proved by fitting the impedance spectra with an equivalent circuit (Fig. 3, inset) composed of two R-CPE elements in series to obtain the resistance of different processes. In this equivalent circuit, R ohm represents the combination of electrolyte resistance, electrode ohmic resistance, lead resistance and contact resistance between cathode and Pt mesh current collector, R H and R L are the polarization resistance (R p ) corresponding to the high-frequency and low-frequency arc, respectively. The ASR is the sum of R H and R L . CPE is constant phase element whose value reflects the reaction mechanism of different electrode processes. The fitting results are presented in Fig. 5. It can be seen that R H is much larger than R L in SCC cathode. In a previous study, we proved that the reaction rate limiting step of SCC cathode was charge transfer reaction, which was characterized by the high frequency arc in the EIS spectrum [START_REF] Sun | Synthesis and performance of Sm 2-x Ce x CuO 4 cathode materials for IT-SOFC[END_REF].

Compared to SCC electrode, the addition of Ag reduces dramatically the value of ASR and the decrease is mainly attributed by the reduction of R H . Arrhenius plots of the fitting results for SCC-Ag composite cathode are given in Fig. 6. It is found that both R H and R L first decreases with the addition of Ag, and then increases again when the Ag content is up to 10 wt.% in the SCC-Ag composite. The activation energy for R H is in the range of 1.52-1.55 eV, close to the activation energy of the oxygen surface exchange process in La 2 NiO 4+δ [START_REF] Skinner | Oxygen diffusion and surface exchange in La 2-x Sr x NiO 4+δ[END_REF]. At the same time, the low frequency arc becomes dominant in the impedance spectra (Fig. 3), and the values of R L are larger than these of R H in the SCC-Ag composite cathodes (Fig. 6). The activation energy for R L is in the range of 0.96-1.16 eV, which is close to the dissociation and diffusion activation energy of the adsorbed oxygen molecular on the cathode surface [START_REF] Yin | Characterization of Ba 1.0 Sr 1.0 FeO 4+δ cathode on La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3-δ electrolyte for intermediate temperature solid oxide fuel cells[END_REF].

The contribution of Ag loading is further illustrated in the Bold plot (Fig. 7). The enhanced charge transfer reaction can be seen by a dramatic decrease of the phase angle of the high frequency peak in the Bold plot. This is clearly different from that of SCC cathode. According to the fitting results, this difference indicates that the oxygen reduction mechanism has been changed with the addition of Ag. The electrochemical reaction mechanism of SCC-Ag composite cathode was studied as a function of oxygen partial pressure. Fig. 8 shows the impedance spectra of SCC-Ag05 cathode measured at 700 °C under various oxygen partial pressures ( 2 O P ). The polarization resistance decreases with the increase of oxygen partial pressure, indicating an oxygen activity related electrochemical reaction that occurred on the composite cathode. By using the same equivalent circuit presented in Fig. 3, the values of R H and R L under different oxygen partial pressure can be calculated. It is found that the resistance of the high frequency arc (R H ) is always much smaller than that of the low frequency one (R L ). This means that the R L related process is the reaction rate limiting step. Generally, the polarization resistance (R p ) varies with the oxygen partial pressure according to the following equation: The dependence of polarization resistances (R H and R L , respectively) on oxygen partial was presented in Fig. 9. It is found that the values of n corresponding to R H and R L are 0.24 and 0.58 respectively. In this case the high frequency arc is confirmed to be related to the charge transfer process, and the low frequency arc is assigned to the dissociation and diffusion of adsorbed oxygen. Compared to the results obtained in Fig. 8, it is clear that the R L related process is the major rate limiting step for SCC-Ag05 composite cathode in the whole range of measurement oxygen partial pressure. However for SCC cathode, the n values of R H and R L are 0.27 and 0.62 respectively, and the value of R H is always larger than R L , which implied that the charge transfer process on SCC cathode is the rate limiting step [START_REF] Sun | Synthesis and performance of Sm 2-x Ce x CuO 4 cathode materials for IT-SOFC[END_REF]. So it is clear that when Ag was added in the electrode, a change of the rate limiting step from charge transfer process to diffusion of the dissociative adsorbed oxygen was likely happened. As we expected, Ag catalyst promotes the surface exchange process (charge transfer reaction) and additionally, Ag particles can provide additional electron transport pathway through the cathode surface due to its high electronic conductivity. Therefore, the oxygen reduction reaction could be more effective at the boundary of Air/Ag/SCC than at Air/SCC, and consequently the electrochemical performance is enhanced by the impregnation of Ag catalyst.

It should point out that the great reduce of R H value is paid back by the simultaneous increase of R L (Fig. 5). It is proposed that this simple infiltration method used may lead to the growth of micrometer size Ag particles, which will cover the SCC particle surface and block the oxygen diffusion channel in the cathode. So the microstructure of the cathode need to be further optimized.

Conclusion

The Sm 1.8 Ce 0.2 CuO 4 -Ag composite cathodes were prepared and their electrochemical properties were studied below 700 °C. The SCC-Ag05 composite exhibits improved catalytic activity for the oxygen reduction reaction compared to the Sm 1.8 Ce 0.2 CuO 4 cathode, due to the increased electronic conductivity and electro-catalytic activity contributed by Ag particles.

The lowest area specific resistance obtained at 700 °C in air is 0.43 Ω cm 2 for SCC-Ag05 composite cathode. The addition of Ag in the SCC electrode changes the rate limiting step from charge transfer process to oxygen dissociation and diffusion process. However, further long-term stability investigation by operating over an extended period may be needed to verify the effect of Ag diffusion.

  Fig. 1 shows XRD patterns of the sintered SCC-CGO and SCC-CGO-Ag composite powders. The spectra of pure SCC and CGO materials are also presented in the same figure for comparison. The SCC powder made by GNP process crystallizes in body-centered tetragonal symmetry (Fig. 1(a)), consisting with Sm 2 CuO 4 structure (PDF card

Fig. 1 :

 1 Fig. 1: XRD patterns of SCC, CGO, SCC-CGO and SCC-CGO-Ag powders.

Fig. 2 :

 2 Fig. 2: SEM micrographs of the cathodes: (A) SCC without Ag (1000 °C, surface), (B) SCC-

Fig. 3 :

 3 Fig. 3: Nyquist plot for SCC-Ag composite cathodes measured at 700 °C in air.

Fig. 4 :

 4 Fig. 4: Temperature dependence of the polarization resistance R p for various SCC-xAg

Fig. 5 :

 5 Fig. 5: Comparative evolution of the polarization resistance (R H and R L ) with different

Fig. 6 :

 6 Fig. 6: Temperature dependences of fitted high frequency resistances and low frequency

Fig. 7 :

 7 Fig. 7: Bold plot for SCC-Ag composite cathodes measured at 700 °C in air.

Fig. 8 :

 8 Fig. 8: Impedance spectra for the SCC-Ag05 cathode on CGO at 700 °C under various

Fig. 9 :

 9 Fig. 9: Dependence of polarization resistance on oxygen partial pressure for SCC-Ag05

Acknowledgments

This work was supported by National Natural Science Foundation of China (51072048, 51102083), Natural Science Foundation of Heilongjiang Province (JC201211, B201107), Program for Science and Technology Project of Heilongjiang Province (WB10A204).


The Flexible Audio Source Separation Toolbox (FASST) is a toolbox for audio source separation that relies on a general modeling and estimation framework that is applicable to a wide range of scenarios. We introduce the new version of the toolbox written in C++, which provides a number of advantages compared to the first Matlab version: portability, faster computation, simplified user interface, more scripting languages. In addition, we provide a state-of-the-art example of use for the separation of speech and domestic noise. The demonstration will give attendees the opportunity to explore the settings and to experience their effect on the separation performance.

INTRODUCTION AND MOTIVATIONS

Source separation is one of the major topics in audio signal processing. Recent years have seen a move from blind to guided approaches incorporating more and more knowledge about the sources and/or the mixing process [START_REF] Vincent | From blind to guided audio source separation[END_REF].

While most source separation methods are designed for a specific scenario, the flexible audio source separation framework in [START_REF] Ozerov | A general flexible framework for the handling of prior information in audio source separation[END_REF] introduced a compositional approach [START_REF] Virtanen | Compositional models for audio processing[END_REF] where the mixture signal is modeled by composing multiple source models together. Each model is parameterized by a number of variables, which may be constrained by the user, trained from separate data or adapted to the considered mixture according to the available information. This framework has been applied to a wide variety of speech and music separation scenarios by exploiting information such as note spectra, cover music recordings, reference speech pronounced by another speaker, or target spatial direction [START_REF] Gerber | Professionallyproduced music separation guided by covers[END_REF][START_REF] Yang | On sparse and low-rank matrix decomposition for singing voice separation[END_REF][START_REF] Han | Towards generalizing classification based speech separation[END_REF][START_REF] Magoarou | Textinformed audio source separation using nonnegative matrix partial co-factorization[END_REF][START_REF] Tran | Using full-rank spatial covariance models for noise-robust asr[END_REF]. It has also been used as a preprocessing step for instrument recognition, beat tracking, and automatic speech recognition [START_REF] Tran | Using full-rank spatial covariance models for noise-robust asr[END_REF][START_REF] Bosch | A comparison of sound segregation techniques for predominant instrument recognition in musical audio signals[END_REF].

This framework was first implemented in Matlab as version 1.0 of the Flexible Audio Source Separation Toolbox (FASST) which was not demonstrated to the public. Although it facilitates quick prototyping of software modifications, this choice implied large computation time and limited diffusion to communities which do not routinely use Matlab. We introduce the version 2.0 of FASST in C++ which fixes these limitations and provides a simpler user interface. In addition, we provide a new example of use for speech denoising in the context of the 2nd CHiME Challenge [START_REF] Vincent | The second 'CHiME' speech separation and recognition challenge: An overview of challenge systems and outcomes[END_REF].

The structure of the rest of the paper is as follows. Section 2 summarizes the framework behind FASST. Section 3 introduces the new implementation and user interface. Future developments are discussed in Section 4.

SCIENTIFIC AND TECHNICAL DESCRIPTION

FASST operates in the time-frequency domain. In each timefrequency bin (n, f ), the vector x f n of mixture STFT coefficients recorded at all microphones satisfies

x f n = J j=1 y jf n (1)
where y jf n is the spatial image of the jth source. The sources assumed to be zero-mean Gaussian distributed as

y jf n ∼ N (0, v jf n R jf ) (2)
where v jf n the short-term power spectrum of the jth source and R jf its spatial covariance matrix.

The power spectrogram V j of each source (i.e., the matrix whose n)th entry is v jf n ) is further factored according to an excitation-filter model followed by two-level nonnegative matrix factorization (NMF). Overall,

V j = W ex j U ex j G ex j H ex j ⊙ W ft j U ft j G ft j H ft j ( 3
)
where the nonnegative matrices W ex j , U ex j , G ex j and H ex j encode the fine spectral structure, the spectral envelope, the temporal envelope and the temporal fine structure of the excitation, respectively W ft j , U ft j , G ft j and H ft j encode the same quantities for the resonance filter, and ⊙ denotes entry-wise matrix multiplication. The spatial covariance matrix is itself factored as

R jf = A jf A H jf (4)
where the dimension of A jf governs the rank of R jf . Each of the 9 parameters in ( 3) and ( 4) may be either fixed or adaptive depending on the information available about, e.g., the spatial position of the sources and the harmonicity of their spectra.

Adaptive parameters are estimated in the maximum likelihood (ML) sense by iteratively fitting the empirical mixture covariance matrix R x,f n using an expectation-maximization (EM) algorithm. The source spatial image signals are eventually obtained by multichannel Wiener filtering. For more details about the algorithm and example settings, see [START_REF] Ozerov | A general flexible framework for the handling of prior information in audio source separation[END_REF].

IMPLEMENTATION AND USE

C++ core

The core of FASST is composed of three C++ programs illustrated in Fig. 1: 1.

Representation

The first program takes as input a time-domain mixture WAV file and it computes its time-frequency domain empirical covariance matrix R x,f n . Since this matrix is Hermitian, we developed a binary format to save disk space by storing non-redundant entries only.

Parameter estimation

The second program performs ML parameter estimation given the above time-frequency representation and a choice of model. Choosing the model consists of specifying the initial value and the fixed/adaptive character of each the 9 parameters in (3) and (4) for each source. Due to the hierarchical structure of this model, we store the input and output model structure and parameter values in an XML file, which can be edited using a wide variety of tools.

Filtering

The third program performs Wiener filtering given the input mixture WAV file and the estimated parameters XML file.

These programs rely on standard third-party libraries: libsndfile, Qt, and Eigen. In addition to the portability of C++, FASST 2.0 offers two advantages. Firstly, the parameter estimation code takes full advantage of multicore hardware using OpenMP: computation time can reach a 3x speedup compared to the original implementation in Matlab. Secondly, Fig. 1. The three core executables of FASST 2.0. the user interface has been simplified. Specification of each of the 9 parameters of each source is not required anymore: only those parameters which are adaptive or different from the identity matrix must be specified (e.g., only the basis spectra U ex j and the activations G ex j in the case of conventional, onelevel NMF) and the others are assumed to be fixed and equal to the identity matrix by default.

The demonstration will give attendees the opportunity to manipulate these parameters and to listen to the resulting separation performance.

User scripts

Similarly to speech recognition software, scripts must be written in order to glue the three core executables together as appropriate for a given source separation problem. The simplest workflow is to initialize the source model, to write it to an XML file, and to call the executables in the above order. More complicated workflows involve multiples call to the executables in order to learn models from separate data before applying them to the considered mixture. FASST 2.0 includes scripts allowing to import/export binary and XML files to/from Matlab and Python. This also increases the portability of the software compared to the original version which included Matlab scripts only.

Baseline for CHiME

As an advanced example, we provide new scripts for the separation of speech and real-world domestic noise as evaluated in Track 1 of the 2nd CHiME Challenge [START_REF] Vincent | The second 'CHiME' speech separation and recognition challenge: An overview of challenge systems and outcomes[END_REF]. The workflow is depicted in Fig. 2. Speech models are trained on separate speaker-dependent data and kept fixed. Noise models are initialized by training from the background noise surrounding the considered mixture and reestimated from the mixture.

Research has been carried regarding model initialization to favor convergence of EM to a relevant local optimum. The basis spectra are initialized by split vector quantization of the ! " # $ Fig. 2. Speech denoising workflow for the CHiME Challenge. Numbers denote successive steps and "FASST" denotes a call to "Representation" followed by "Parameter estimation". On average, the overall separation quality measured by the signal-to-distortion ratio in decibels (dB) outperforms the best quality reported so far in [START_REF] Nesta | Blind source extraction for robust speech recognition in multisource noisy environments[END_REF], as shown in Table 1.

CONCLUSION AND FUTURE DEVELOPMENT

Thanks to its general modeling and estimation framework, FASST is to our knowledge the most widely applicable source separation software currently available, as exemplified by its use for different scenarios in [START_REF] Gerber | Professionallyproduced music separation guided by covers[END_REF][START_REF] Yang | On sparse and low-rank matrix decomposition for singing voice separation[END_REF][START_REF] Han | Towards generalizing classification based speech separation[END_REF][START_REF] Magoarou | Textinformed audio source separation using nonnegative matrix partial co-factorization[END_REF][START_REF] Tran | Using full-rank spatial covariance models for noise-robust asr[END_REF][START_REF] Bosch | A comparison of sound segregation techniques for predominant instrument recognition in musical audio signals[END_REF]. The demonstration will introduce the advantages of FASST 2.0 compared to the original version in Matlab, which had not been demonstrated to the public so far, and it will allow the audience to interact with the settings. Future planned developments include extending the code for real-time operation and integrating it with automatic speech recognition software using uncertainty propagation.

FASST 2 .

 2 0 is composed of two parts: binary executables written in C++ and user scripts written in Matlab and Python. Code and sound examples are distributed online under the QPL and Creative Commons open source licences 1 .

Table 1 .

 1 SDR (dB) on the CHiME Challenge subset in[START_REF] Nesta | Blind source extraction for robust speech recognition in multisource noisy environments[END_REF].

	iSNR	-6 dB -3 dB 0 dB 3 dB 6 dB 9 dB avg.
	FASST 2.0	6.0	7.8 5.2 12.7 10.5 12.4 9.1
	Nesta [11]	5.2	6.2 5.6	9.2 11.6 10.5 8.0
	input short-term spectra, the spatial parameters are initialized
	by splitting the space of directions-of-arrival into regions of
	equal surface, and the activations on the considered mixture
	are initialized by the mean activations on the training data.

http://bass-db.gforge.inria.fr/fasst/

ACKNOWLEDGMENT

This work was supported by the Inria ADT FASST project. We would like to thank O. Rochel, J. Espiau de Lamaëstre, D. Jouvet and G. Gravier for their advice.