Mohammad Issack Santally

Dorothy Cooshna-Naik

Noel Conruyt

Caroline Koa

A Social Partnership Model to promote Educators' Development in Mauritius through Formal and Informal Capacity-building Initiatives

This paper describes a social partnership model based on the living lab concept to promote the professional development of educators through formal and informal capacity-building initiatives. The aim is to have a broader impact on society through community outreach educational initiatives.

A Living Lab is an environment for user-centered innovation, based on the observation of everyday user practice and experience for solving problems but is also based on users' active participation, with an approach that facilitates their influence in the open and distributed innovation process (participatory design). It is defined as 4P innovation, namely, Public-Private-People-Partnership. The objectives are thus political and strategic, focusing on the social role of innovation, i.e., trying to totally realize human potential by increasing creativity.

In 2009, the Virtual Centre for Innovative Learning Technologies (VCILT) embarked on the SIDECAP project, funded by the EU-ACP in a consortium led by the Open University of the UK. The work of the VCILT in the context of the SIDECAP project was essentially focused on the repurposing of Open Educational Resources to fit in the local Mauritian Context. At the same time, the VCILT received an internal grant to work on the development of interactive learning materials using the integration of text-tospeech technology in instructionally designed PowerPoint presentations. During the same period, the Centre launched an innovative online training programme for in-service educators to allow them to top-up their qualifications in the field of educational and instructional technologies.

The set of activities described in the paragraph above, resulted in a succession of action-reflection cycles which developed into the concept of a Living Lab. We report the Living Lab setup at the University of Mauritius, by showing how the research activities at the VCILT led to a series of development and applications in a real-world context, related to the formal teacher training courses and informal continuous professional development of educators via the establishment of a social entity in a partnership with Microsoft Indian Ocean and French Pacific under the Partners in Learning Program. The model is referred to as a multiple-impact social partnership model. Therefore, there are three major components that would form the backbone of our Living Lab, namely, Research and Development, Teacher Education and, finally, the social entity that links the private and public sectors, and educators, in a social partnership.

Introduction

In 2001, for the University of Mauritius to get on the eLearning bandwagon, the Virtual Centre for Innovative Learning Technologies (VCILT) was created in a bid to modernize the distance education concept by fully utilizing the possibilities offered by IT-enabled networked systems and the Internet. Since its establishment, the centre has brought in some non-negligible innovations in the teaching and learning landscape. Inevitably, as with any innovative practices, it has also brought its share of disruption in the traditional university setting; what we term as ''constructive disruption'', especially with respect to the conception of pedagogy and educational practice in teacher education.

The educational philosophy behind the in-service teacher training courses at the University of Mauritius is inspired by Bob Moon's position in the 2010 issue of the Commonwealth of Learning Connections magazine. In the article "Time for Radical Change in Teacher Education", Moon argues that it is time to implement new technologies in teacher training courses so as to focus on the continuous professional development of educators. Adopting a very critical view of the so-called brick-and-mortar institutions for teacher training, Moon (2010) points out, "there is absolutely no way the bricks-and-mortar institutions of teacher training created in the last century will be adequate for the 21st century needs".

A Living Lab is an environment for user-centered innovation, based on the observation of everyday user practice and experience for solving problems but is also based on users' active participation, with an approach that facilitates their influence in the open and distributed innovation process (participatory design). It is defined as 4P innovation, namely, Public-Private-People-Partnership. The objectives are thus political and strategic, focusing on the social role of innovation, i.e., trying to totally realize human potential by increasing creativity.

In 2004, the first online course was launched (in a Masters in Educational Technology program, formerly Computer-Mediated Communication and Pedagogies), mainly targeting educators and training professionals in industry. In 2009, the top-up programme in educational and instructional technologies was run to bridge the gap between educators holding a teacher's diploma (qualified teacher status) and those eligible to join in a Masters programme. At the same time, the centre embarked on a few research projects related to education technology and pedagogies related to the integration of ICT in education. There was also a need to address the problem of capacity building of educators to equip them with the 21st Century teaching and learning skills. This was done in a novel approach using action-research cycles, combining research and development activities to design and develop online teacher education programs for in-service educators (Cycle 1 of an action research cycle), in line with the philosophy of 21st Century training needs [START_REF] Moon | Time for Radical Change in Teacher Education[END_REF]. The process led to the setting up of a Living Lab to expand the initiative to include non-formal outreach initiatives, to promote continuous professional development of educators at a larger scale in partnership with the private sector (represented by Microsoft Indian Ocean and French Pacific), and a social entity called Helping Our People (Cycle 2). The link between Cycle1 and Cycle 2 of this action research cycle is mediated by the people (represented by educators and the staff of the VCILT).

Theoretical Concepts

According to [START_REF] Conruyt | E-co-innovation for making e-services: Living Labs as a human-centered digital ecosystem for education with ICT[END_REF] when one instantiates it in a domain, a Living Lab includes public and private actors, companies, associations, and individual actors, whose objective is to co-design, to develop and to test life-size services, tools and new practices:

The aim is to take out the research of laboratories to make it come down in the daily life, often by having a strategic view on the potential uses of these technologies. All this takes place in cooperation between local authorities, companies, research laboratories, as well as potential users, via helping platforms for designing innovative services and analyzes of their usages. It is a question of favoring the culture of opening (open innovation), of sharing its networks and of involving the users from the beginning of the conception. Cunningham et al. (2011) summarize the concept by referring to Living Labs as both a milieu (environment, arena) and an approach (methodology, innovation approach). They argue that it is a concept that refers to a Research and Development (R&D) methodology where innovations (services, products and application enhancements) are created and validated in collaborative, multi-contextual, empirical, real-world settings (Geerts, 2011:21), and seen as a new character in the open innovation chain [START_REF] Lepik | Introducing Living Lab's method as knowledge transfer from one socio-institutional context to another: Evidence from Helsinki-Tallinn cross-border region[END_REF](Lepik et al., :1091)).

From the above definition and explanation, it can reasonably be argued that the Living Lab concept has theoretical foundations related to the concept of Activity Theory, and Action Research. Activity-theory [START_REF] Engeström | Learning by expanding[END_REF]) is one of the main developments that characterize contextual approaches to cognition. It is a theoretical framework for analysing human practices in context. An activity is reflected through actions as people interact with their environment. Activity theory has been successfully applied in different research domains [START_REF] Taurisson | Supporting a Learner Community with software Agents[END_REF][START_REF] Korpela | Information Systems Development as an Activity[END_REF][START_REF] Collins | Activity Theory and System Design: A view of the trenches[END_REF] as the main theoretical framework to model human activity systems and it is well adapted for contemporary modelling of educational contexts. [START_REF] Wilson | A re-examination of information seeking behaviour in the context of activity theory[END_REF] argues that while activity theory cannot be seen as a predictive theory, it is a very appropriate conceptual framework providing a coherent terminology that can be shared by researchers, within which different theoretical perspectives can be employed.

MacIsaac (1995) postulates that Action Research is a "reflective process of progressive problem solving led by individuals working with others in teams or as part of a community of practice to improve the way they address issues and solve problems". Action research is basically research that leads to action that uses a spiral of steps, each of which is composed of a circle of planning, action, and fact-finding about the result of the action [START_REF] Lewin | Resolving social conflicts: Selected papers on group dynamics[END_REF]. Figure 1 illustrates a simple model of the cyclical nature of the typical action research process adapted from the work of MacIsaac (1995).

Figure 1: Action Research Cycles

With reference to a Living Lab, action research becomes an appropriate overall framework to evolve the cycles of activities leading to user and field-testing in real-life situations while activity theory provides the right model for studying human interaction and behavior throughout each cycle of activity, using the change laboratory method as the main instrument to deal with the issue of process change and improvement.

The Living Lab (MISP)

MISP is essentially an integration of the Research and Development model described above that has governed our applied research activities in education technology, and the community engagement model described above with the establishment of the Helping our People Entity. It is based on Whitehead's (2012) education research philosophy for social change through action research and the Living lab paradigm for Teaching and Learning [START_REF] Conruyt | E-co-innovation for making e-services: Living Labs as a human-centered digital ecosystem for education with ICT[END_REF].

A Living Lab is an environment for user-centered innovation, based on the observation of every-day user practice and experience for solving problems, but also based on their active participation, with an approach that facilitates their influence in the open and distributed innovation process (participatory design). It engages all concerned partners in real-life contexts, and aims to create sustainable usage values (Kareborn et al. 2009). It is defined as 4P innovation, namely Public-Private-People-Partnership. The objectives are thus political and strategic, focused on the social role of innovation, i.e., trying to totally realize human potential by increasing creativity [START_REF] Conruyt | E-co-innovation for making e-services: Living Labs as a human-centered digital ecosystem for education with ICT[END_REF]).

The MISP model fits in the 4P innovation framework where the Public sector is represented by the VCILT and the University, the Private Sector is represented by Microsoft Indian Ocean and French Pacific or other actors in the future, with the People being academics, educators, and Youth volunteers (students). The beneficiaries and the partnerships among these actors are mediated through a collective social movement called Helping Our People.

The Research and Development Model (Cycle 1)

The Research and Development Model (Cycle 1) is based on a practitioner-oriented concept where research and development essentially become the drivers for practice-oriented enquiries to improve teaching and learning systems. It aims at field experimentation to test new practices, which are then formalized into teaching methods that can be cascaded down to educators for classroom application. The educators at the receiving end also become engaged in an action-reflection cycle where the feedback is fed into the system for continuous improvement and refinement of teaching techniques and the application of ICT tools in day-to-day practice. The model is conceptually elaborated in figure 2 While the VCILT is a real-world entity existing in a brick-and-mortar institution, the introduction of online learning through a reconceptualization of the teaching and learning process has led to a departure from traditional teacher training methods. The model of online instruction is based on a three-phased approach, namely, the knowledge acquisition phase, the knowledge application phase and the knowledge construction and reflective practice phase [START_REF] Santally | A cognitive approach to evaluating web-based distance learning environments[END_REF]). In the knowledge construction and reflective phase, emphasis is laid on collaborative work, where the learner becomes an important agent in the learning process [START_REF] Hannafin | The foundations and assumptions of technology-enhanced student centered learning environments[END_REF] while the role of the teacher/lecturer undergoes a paradigm shift from the knowledge holder to the manager, orchestrator and facilitator [START_REF] Schneider | Conception and implementation of rich pedagogical scenarios through collaborative portal sites: clear focus and fuzzy edges[END_REF].

In an endeavor to bring a transformative approach to promote the educational philosophy we had adopted, a three-fold method was applied. The first aspect was to inculcate a new educational culture in aspiring educators who have embarked on a university degree course of study. The second aspect was to provide a route for in-service educators to upgrade their qualifications (better income, and promotion prospects) through an innovative degree in education technology by transforming them into digital migrants, and the third element was to influence policy makers by demonstrating that technology has increased access to education and has transformed traditional practices. A lifecycle model for the repurposing of OERs was proposed [START_REF] Santally | OERs in Context: A Case-Study of Innovation and Sustainability of educational practices at the University of Mauritius[END_REF]) which has been applied to the design and development of online programmes at the VCILT. The resources that were produced during experimentation in the SIDECAP project were then disseminated as an online continuous professional development course for Mauritian Educators. The course, which can reasonably be considered a !OOC (Micro Open Online Course) attracted about 300 educators in 2010. The pool of educators who followed this course eventually regrouped into a socially connected pool of potential future students to feed into the formal teacher training courses of the university. The project also investigated the issues surrounding the Copyleft licensing schemes in terms of reuse, repurposing and value-addition of existing open educational materials.

The main outcome of the SIDECAP project was that the models and methods that were developed and experimented ensured the initial sustainability of the online learning courses of the VCILT. As a result, in three years the student population increased from 10 to 300 and a total of eight parallel cohorts of students enrolled in four different online programmes of studies. The ongoing in-service teacher training programmes were updated to reflect the latest progress, such as the inclusion of a module on the design and development of OERs and a module on copyright and intellectual property issues in education.

(iii) The Rapid e-Learning Methodology

Rapid e-learning is a term that has emerged from the concept of rapid development as applied to the software development industry. The key is to acquire the ability to develop and deploy high quality interactive multimedia e-learning courses, which are generally short to medium length learning units in a minimum amount of time [START_REF] Brandon | Exploring the definition of rapid e-learning[END_REF]. Rapid e-learning is an emergent methodology that has recently gained momentum as more and more user-friendly authoring tools are being developed.

In 2008, in parallel to the SIDECAP project, the VCILT embarked on a research and development project aiming at creating video lectures through the integration of two simple technologies, namely, Microsoft PowerPoint and Text-to-Speech. The project gradually evolved by 2010 into the rapid e-learning methodology which allowed for the development of interactive learning materials in a reduced time period and with minimal technical computing skills. Furthermore, a training and development methodology has been put in place by the research team to disseminate the technique in an extensive two-day workshop to educators and education practitioners. The rapid e-learning project emerged as a research and development project that led to the development of a service with respect to the development of interactive learning materials.

In 2010 the VCILT secured a consultancy to digitize six courses for the Hamdan-bin-Mohamed e-University of Dubai and in 2011, the technique was applied in a project funded by the Commonwealth of Learning to develop interactive materials in the local language for its Lifelong Learning for Farmers, and its Women Empowerment programme in Mauritius. In 2012, the technique was disseminated in India at the Makerere University in Uganda for the Commonwealth of Learning, and in two international professional development workshops in South Africa and in Mauritius for African educators and academics.

The rapid e-learning methodology was integrated within the work that was carried out in the SIDECAP project, as the methodology was specifically adapted to fit in the value-addition process of the proposed lifecycle for OER development and reuse. This resulted in a set of video lectures that were developed and hosted on an open channel on YouTube. The rapid e-learning methodology is currently being further developed to apply for mobile and portable devices to support mainly the Windows 8, Android and IOS platforms.

The 4P Connection (Cycle 2)

The Microsoft Partners-in-Learning Program 1.

The rapid e-learning project created a link tunnel between the SIDECAP project, the in-service educators and the Microsoft Partners-in-Learning (PIL) Program (www.pil-network.com) in Mauritius. The Microsoft PIL program is managed by the Microsoft Indian Ocean and French Pacific branch, based in Mauritius and the aim is to promote the integration and the use of information and communication technologies in the classroom, with the main focus on the primary and secondary education sectors. The PIL network provides educators with ongoing training and free tools as well as access to a broad range of technologies and lesson plans to improve classroom practices. This is in line with the very essence of the article of Moon (2010) based on the belief that "education and training should be an entitlement for all teachers at all stages in their careers" and that research has demonstrated that when "this entitlement is honored, learners achieve more and schools improve".

The rapid e-learning methodology relies intensively on Microsoft PowerPoint as the prototyping and development workbench. This methodology with the ability of the team to cascade it down to educators to empower them to develop their own learning materials has prompted Microsoft to fund the training of an initial 50 educators on the technique in 2012.

The idea is to decentralize the content development process to enable educators to develop curriculum related materials in a shorter time-span than it would normally take a small, dedicated team of content developers, as is currently the practice under the Sankoré Project, an initiative of the Franco-British Summit and the Government of Mauritius. While interactive whiteboards has been deployed in the primary schools with each school being equipped with a Sankoré classroom, the Minister of Education and Human Resources announced the Phase II of the project to start after August 2013 whereby Mauritius was supposed to receive about 520 interactive whiteboards and digital equipment from the French Authorities (Government Portal 2013).

The main advantage of shortening the time spans for the development of interactive and digital learning materials that would fit in the context of the deployment of interactive whiteboards in schools is that technology becomes obsolete very fast. A study by [START_REF] Bahadur | Interactive whiteboard for primary schools in Mauritius: An effective tool or just another trend[END_REF] revealed that very few educators were actually using the interactive whiteboards, and that it was unclear that those who were using them in our schools were actually doing so in an effective way. It was furthermore revealed that educators had acknowledged a lack of necessary skills and competencies to fully utilize the equipment as well as the necessary technical support to ensure correct operation. It was also noted that much of the equipment was not functioning and/or had been damaged by students.

The Social Entity -Helping Our People 2.

The government, in 2003, launched the ZEP project in a coordinated effort to deal with the learning difficulties faced by children coming from poor localities. [START_REF] Mahadeo | Priority Education Zones in Mauritius[END_REF] report that within the framework of the ZEP project, children are entitled to: (i) pedagogical innovations with respect to teaching and learning; (ii) improved provision with respect to their diet; (iii) a health programme for all of them; (iv) a teaching support kit; (v) a monitoring system with new indicators; (vi) a databank to keep the policy dialogue active and (vii) involvement of the local community. It is within such a social engagement context that the non-governmental organization Helping Our People was established to act in a broader context in line with the Living Lab philosophy.

The concept of Youth Empowerment has been embodied in the functioning of the organization in two ways. The first one is to take undergraduate, full-time, university students and train them through capacitybuilding projects to assist in and to ultimately lead technical teacher-training workshops, and, to inculcate a culture of social values and voluntary work to contribute to the welfare of society and student surroundings in general. Youth Empowerment is conceptually defined at the level of the organization in Figure 3 below. As can be seen, the core values and elements rely on the establishment of mutual trust between youth and their mentors, the development of leadership and human values by providing opportunities to become autonomous and confident, and to get access to new openings through ongoing capacity building.

A First Account of Field Activity

In this section we describe a first application of the MISP model for the year 2013. The activities are divided into two categories, namely, the socially oriented professional activities that originate from the capacity building feature of the research and development model presented in Figure 1, and the Social Community Service element of the Helping Our People entity.

Interactive Materials Development Training in Mauritius

The training was conducted through funding from Microsoft Indian Ocean and French Pacific under the Partners-in-Learning umbrella. Two batches of 24 and 21 participants were trained during the period 15th-19th April 2013. The training targeted educators of the primary and secondary sector and the title of the training was, "Interactive Materials Development for the Digital Classroom". The training was focused on the development of skills and the acquisition of competencies by the participants. As such two techniques of instructions were used: (1) instructor-led tutorials, and (2) an independent self-executed learning activity by the participants. This approach ensures that all participants have achieved the minimum expected learning outcomes after the training session.

Partners-in-Learning Network Initiation in Rodrigues

The Partners-in-Learning Network Boot Camp

The purpose of this boot camp is to sustain the initiatives started with respect to the professional development of educators conducted in April and June 2013, respectively. It is now proposed to engage the next logical cycle of action research, that is, moving from the training cycle to the production cycle. This is in line with future plans to set up a Living Lab model for teaching and learning in Mauritius. The production cycle took the form of an intensive boot camp of three days, where 25-30 educators came together and produced educational resources related to the curriculum using Microsoft Partners in Learning Pedagogical Tools. These resources were then be uploaded to and shared on the Partners in Learning Network site. The educators involved in this boot camp participated in the Expert Educator competition of Microsoft.

Reflective Discussion

In developed countries, Finland serves as an excellent example, and it is widely said and demonstrated that research has been the driving force behind innovation that led to the socio-economic developments of the countries through industrialization, the design and development of new products and services to the global markets (OECD 2010). Research and development in the context of developing countries should also embody community service as an important and key element to promote social justice and alleviation of poverty.

In a country like Mauritius where free primary, secondary and tertiary education has been a landmark in the socio-economic development and political stability of the country, it is deplored that research in education for development has long been a sideline issue, despite having three public universities and one dedicated institution for teacher training.

Recently the concept of 'Maurice Ile Durable (MID)' has been put forward as the new leitmotiv for promoting socio-economic development, social justice and education in a framework respecting the environmental eco-system. Such an ecosystem that the MID concept is trying to promote is perfectly in line with the concept of Living Labs put forward in the implementation of the MISP model. The Living Lab is essentially a research lab that fundamentally departs from the closed and restricted nature of research laboratories working on 'closed' innovation, as opposed to the concept of an 'open' user-centered innovation system where all stakeholders form an integral part of the process. Hence the 'living' concept being embodied and replacing the term research in research labs.

Conclusion

Living Labs are emerging as a new model to support co-creative, human-centric and user-driven research, development and innovation in order to better cater to people's needs. Mauritian society, amid the concepts of a sustainable Mauritius, is at a junction where traditional models of research and development have started to show their limits in sustaining a modern society that can effectively address growing challenges like education reforms, poverty alleviation, global economic crises, and environmental protection. The MISP model, although operational at a micro-level and at an infancy stage, tries to embody the new open innovation concepts as proposed by the Living Lab ecosystem, and can serve in the longer term as an example for other initiatives.

  below using the MOT Taxonomy[START_REF] Paquette | Instructional engineering for network-based learning[END_REF]).

Figure 2 :

 2 Figure 2: The Research, Development and Application Model and the Action-Reflection Cycle (i) The VCILT and Teacher Education

(

  ii) The SIDECAP Project This Project is a European Union (EU) funded project, as part of its ACP-EU Cooperation Programme in Higher Education (EDULINK). SIDECAP stands for Staff Improvement in Distance Education for Caribbean, African and Pacific universities. There are five institutions involved in this project, namely, the Open University of the UK (project leader), the University of the Highlands and Islands Millennium Institute (UHI) in Scotland, the University of Mauritius (UoM), the University of the West Indies of Trinidad & Tobago (UWI) and the University of the South Pacific (USP). The VCILT piloted the SIDECAP project on behalf of the University of Mauritius for the period 2008-2012. The involvement of the VCILT at the level of the project mainly looked at the repurposing of open educational resources to fit into different learning and educational contexts.

Figure 3 :

 3 Figure 3: Conceptual Model for Youth Empowerment

  Under the existing partnership between Helping Our People and Microsoft Indian Ocean and French Pacific, for the promotion of the Partners in Learning Program among educators, a two-day training in June 2013 for Educators in Rodrigues had been organized in collaboration with the ICT Centre of Excellence in Rodrigues. There were 26 participants in the training. All participants are educators based in Rodrigues. The educators were exposed to the use of Microsoft PowerPoint as a platform to develop interactive learning resources. They were then introduced to the Partners in Learning Network where they carried out activities such as registration and completion of a profile, participation in online discussions, and sharing of learning resources and tools. The 2013 Educational Technology Seminar The seminar of the year 2013 was centered on action research and the use of ICTs in the classrooms. The seminar was organized in collaboration with Microsoft Indian Ocean and French Pacific Ltd. Seventy-five educators attended the one-day workshop where Professor Jack Whitehead talked about action research and the principle of researching, inquiring on and improving one's own practices, while Professor Noel Conruyt from the University of Reunion spoke on the living labs concepts in the context of teaching and learning. This workshop was a follow-up to the training sessions conducted in April 2013 under the support of Microsoft in the Partners in Learning Network (www.pil-network.com) program. Educators were trained to develop their own interactive learning materials and to use the Partners in Learning Network as a common educational social network and sharing platform.


Véronique Sébastien
email: veronique.sebastien@univ-reunion.fr

Didier Sébastien
email: didier.sebastien@univ-reunion.fr

Noël Conruyt
email: noel.conruyt@univ-reunion.fr

ANNOTATING WORKS FOR MUSIC EDUCATION: PROPOSITIONS FOR A MUSICAL FORMS AND STRUCTURES ONTOLOGY AND A MUSICAL PERFORMANCE ONTOLOGY

Keywords:

come

INTRODUCTION

More and more musicians share their scores and performances on dedicated Web platforms such as freescores.com or musescore.com. Meanwhile music applications dedicated to scores management are ported to tablet devices (Tonara™, Musescore™, Finale Songbook™). However, musicians still do not dispose of appropriate tools to demonstrate their know-how on these scores: how to play this difficult part? Which fingering should I use? This is why we designed a collaborative score annotation service working on tactile tablets [START_REF] Sébastien | @-MUSE: Sharing Musical Know-how Through Mobile Devices Interfaces[END_REF]. It allows users to illustrate abstract scores with multimedia content showing tips, exercises or questions directly linked to the concerned notes on the score. We also proposed a matching analyzer to automatically determine a score difficulty level [START_REF] Sébastien | Score Analyzer: Automaticaly Determining Scores Difficulty Level for Instrumental e-Learning[END_REF]. But in order to suggest relevant annotations to performers, we need to tag the latter appropriately. Indeed, musical know-how is contextual: it relates to a spe-cific piece with its structure and mood. But most techniques can be reused in similar contexts with appropriate adaptations. Thus, correctly contextualized annotations could be reused on different pieces sharing similarities (genre, composer, patterns, etc.). It would also enable complex queries on instrumental issues (for instance: how to play scales? how to produce a soft but expressive sound? what is the best strategy to learn a piece by heart?).

We could rely on social tags created by users (i.e., Folksonomies [START_REF] Vander Wal | Folksonomy[END_REF]). However, as noted by Sordo in his experiment on musical genres and moods [START_REF] Sordo | Semantic Annotation of Music Collections: A Computational Approach[END_REF], the emerging vocabulary is not always reliable, especially on very specialized terms. Considering our educational context, reliability and accuracy are essential. These led us to a controlled vocabulary based solution, with extension and adaptation possibilities according to the considered case.

To do so, we propose to extend the existing Music Ontology (MO) [START_REF] Raimond | The Music Ontology[END_REF] with a Musical Forms and Structures Ontology (MFSO) and a Musical Performance Ontology (MPO), through a global Semiotic Annotation framework (SA) (Figure 1). While the MO is dedicated to musical resources and events description for databases, the MFSO focuses on musical works structure analysis, and the MPO on performances and instrumental techniques. However, if the MO and MFSO can be used to relate objective facts about music, the MPO deals with subjective approaches of a given piece. This is why we embed it in a SA. We explain and justify the use of this Sign-based framework in the next section. We then present our ontological propositions in the third and fourth section. A simple use case is detailed in the fifth section. Lastly, we discuss the difficulties we encountered in our attempt to organize musicological and practical instrumental terms.

SEMIOTIC ANNOTATIONS ON WORKS EXTRACTS

Music, as any other artistic field, deals more with interpretations than with formal knowledge. What makes it interesting is that different artists produce different performances, somehow recognizable, even if they play the same piece. But explaining these differences and how to produce them is a delicate task. Common formal representations are not suited to do so for two main reasons. The first one is that textual descriptions cannot really convey emotions and gestures, even if they are important for search engines and knowledge bases. The second one is that they are not adapted to share subjective interpretations. For instance, the comment "I think that the 53421 fingering is more supple for small hands" is difficult to represent accurately into a machine language for the time being.

To overcome these issues, we propose to manage Signs rather than Knowledge. A Sign is a subjective communication object composed of a content (images, gestures, writings, sounds), its form (structure, organization, context) and its sense (interpretation, meaning) from a subject point of view at a given time [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF]. For instance, a symbol is a particular type of graphical Sign, i.e. a form shared among a group of people. But a Sign can also be a simple gesture (e.g., a nod), with various meanings according to its context (historical, or cultural). In artistic fields, where practical know-how is essential, Signs are essential to communicate different interpretations. To manage Signs in an information system, we link each of their components to a digital element. Contents can be embedded in multimedia data (audio, video), form can consist in its contextual information (metadata, localization, selection), and sense consists in knowledge, represented by a textual comment or a semantic description for the machine (i.e., tags from a structured vocabulary). As shown on Figure 2, the Sign object can be represented as a tetrahedron [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF].

We define a Semiotic Annotation (SA) framework to capture these Signs on collaborative annotation platforms. Figure 3 presents the proposed model for Semiotic Annotation. To insure its integration to the current Semantic Web, the SA model is linked to top-level ontologies. The FRBR ontology allows addressing creative works and their different parts. Indeed, to create contextualized annotations, we need to address precise parts of the discussed Work. A WorkPart can be any entity which is a part of another entity. We note that a Work or a WorkPart exists independently from its different Expressions and Manifestations. For instance, the first Verse (WorkPart resource) in the Frères Jacques canon (Work resource) can be discussed without reference to a particular performance of the tune (Expression), recorded on a particular album (Manifestation). This is why we introduce a Selection concept to isolate the concerned WorkPart on any embodiment of a Work. For example, in the musical field, it can be: -an extract of a MusicXML score: [n 1 ,n 2 ,…,n n ], where n i are <note> elements defined by their bar number m i and their order of appearance k i in this bar (m i ,k i ), -an area of a PDF score: [(x 1 ,y 1 ),(x 2 ,y 2 ),…,(x n ,y n )],

where each (x i ,y i ) defines a summit of a selection polygon on the area of the score, -an extract of a video performance: [t 1 ,t 2 ] where t i is a timecode of the video and t 1 <t 2 . Naturally, a WorkPart resource can be composed of other Workpart resources thanks to the frbr:part relation. We also take into account the fact that different users may identify structures differently on a given piece. For instance, different musicologists will not necessarily identify the same structures, according to their respective interests (global structure, harmonic, rhythmic patterns or themes expositions). We thus introduce a partitioner relation to specify the person who extracts and names the part. This person is not necessarily the one creating the annotations afterwards, as structuring pieces and annotating them can be distinct activities. Our model also allows to link similar parts. To do so, the relatedTo relation can be specialized into more specific relations to indicate how different parts relate to each other (see application to the musical field in the next part). To name the part appropriately, a taxonomy may be helpful according to the considered field (e.g., the Musical Forms and Structures Ontology in the case of music). Once the part has been clearly extracted and identified, it can be annotated. Thus, a SemioticAnnotation concept is proposed, including the different components of the Sign (content, form, sense, according to a subject) presented previously. The sense component can be linked to a domain ontology in order to provide a semantic description of the SA for further processing. Of course, the subject is the creator of the SA, which conveys his personal interpretation. Our SA is perceived as a specialization of the Annotation concept from the Open Annotation Model already in use in several applications (Utopia1 , YUMA2 framework). However, the SA is more centered on interpretation comparisons. This is why we also define relations to characterize adaptations, oppositions, and enhancements of SA. A SA can also simply be a reaction to another SA, such as an answer to a question, or a comment. Users can also keep a trace of their thought process by using versioning mechanisms on their annotations. Indeed, constructing an interpretation is generally an iterative process, where the subject enhances his performance with training and feedback. These relations are detailed in Figure 4. The main purpose of such annotations is to steer, organize and share helpful know-how emerging from practical cases.

This model can be applied to the musical field by replacing the frbr:Work concept by the more specialized mo:MusicalWork concept. The WorkPart concept will thus become the MusicalWorkExtract concept (which is not part of the current MO). But in the musical field, it is important to name the detected parts when possible. For instance, a user could identify a Chorus, a Verse, a Fugue Theme, a Variation, a Leitmotiv, a Bass part, a Canon Verse, a Solo, a Musical Bridge, etc. This is why we propose a conceptual model for a Musical Forms and Structures Ontology.

A MUSICAL FORMS AND STRUCTURES ONTOLOGY

Not to be confused with its genre, the form of a musical piece refers to its global organization and instrumentation [START_REF] Hodeir | Les Formes de la musique (Tr.: The Forms of Music)[END_REF]. For instance, the concerto form has three movements and features a solo instrument. A form sometimes implies the presence of significant structures. For example, a fugue necessarily contains a main theme, which will be exposed at each voice, and then developed, inversed, transposed in successive stretti. Besides, most basic structures have a type but not necessarily an explicit name (e.g., phrases, motifs, scales, arpeggios). While musical genres and moods are regularly studied in the MIR literature (for instance [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF] or [START_REF] Sordo | Semantic Annotation of Music Collections: A Computational Approach[END_REF]), musical forms and structures are less discussed. Indeed, the latter are rather addressed in musicological contexts and remain unexploited in music recommendations systems and scores sharing communities. Thus, we design a basic framework for a Musical Forms and Structures Ontology (MFSO) to back up our Musical Performance Ontology with appropriate musicological terms. As noted in an analog work on a Musical Genres Taxonomy [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF], achieving objectivity is a difficult task in a musical context. Concerning forms and structures, even specialists do not agree on some terms (see discussion). This is why we only provide high-level concepts for the time being, which are easier to differentiate, are well documented in musicological treaties such as [START_REF] Hodeir | Les Formes de la musique (Tr.: The Forms of Music)[END_REF] and largely used by musicians.

Our MFSO is thus designed to characterize any musical work and its extracts (Figure 5). A Musical Work can have a Musical Form (e.g., Sonata, Fugue, Song, Canon, etc.). This form can be linked to a characteristic genre (e.g., Fugues and Sonata are generally associated to classical music), but there may be exceptions (e.g., classical structures in symphonic rock). As pointed out previously a form can also be linked to its characteristic structures. These two links (typicalOf and hasStructure) do not aim at restricting the annotation possibilities, but rather at suggesting appropriate terms to the annotator, from basic metadata. For instance, the title of the piece may indicate its form (example: "Sonata KV545" by Mozart) which allows the annotation service to suggest appropriate structures to the user (example: Exposition, Development). But a musical extract does not necessarily have a name. This is why all named structures inherit from the generic Mu-sicalWorkExtract concept. A MusicalWork resource can contain several MusicalWorkExtract resources. These extracts may be imbricated thanks to the frbr:part relation. A musician can detail how an extract is written with the contains relation: is it a whole Phrase, a Motif, a simple Scale, or a Sequence of Chords?

A musical extract can also be labeled. Musicians generally structure a piece by associating alphabetical labels to its different parts. This notation (or codification) allows to clearly distinguish repeated parts (example: ABABC, or ABAB'C meaning B' is almost like B). The label relation allows us to link our work to [START_REF] Bimbot | Semiotic structure labeling of music pieces: concepts, methods and annotation conventions[END_REF], which proposes notations conventions for structure labeling of musical extracts. We insist on the distinction between a notation and an annotation: a notation is a codification (i.e., a representation) of an object, while an annotation is a comment on an object. Thus, they are not related a priori, even if an annotation content can consist in a notation fragment.

The relatedTo relation allows to link distinct extracts. It can be specialized in order to express that an extract introduces, concludes, imitates, transposes, ornates or accompanies another one. These relations can be automatically associated with specific named structures. For instance, a Variation necessarily relates to a Theme and should be associated to it via the variation relation. Other automatisms can be implemented if a MusicXML representation of the piece is available. Indeed, notes, chords, scales and arpeggios can easily be extracted using the el- ements names (e.g., <chords>) or by detecting regular structures (e.g., ascendant or descendant thirds sequences for arpeggios). Undefined regular patterns are more delicate to automatically identify, even if some works exist on this issue [START_REF] Lartillot | Une analyse musicale automatique suivant une heuristique perceptive[END_REF]. Some work has also been done on detecting Fugue structures [START_REF] Giraud | Detecting Episodes with Harmonic Sequences for Fugue Analysis[END_REF]. Now that the part has been extracted and named, it can be annotated.

A MUSICAL PERFORMANCE ONTOLOGY

Our Musical Performance Ontology (MPO) aims at tagging Semiotic Annotation appropriately in a musical education context. It intervenes in the sense component of the SA (see Figure 7) to specify what themes are treated by the subject on the annotated extract. This organization has been chosen because the MPO deals with subjective interpretations and advice (emotions, expression, fingerings) rather than verifiable facts (artists, tracks, concerts), as the MO does. Embedding the MPO in a SA resource allows musicians to discuss their interpretations and possibly enhance them. Tagged SA can then be exploited by learning agents to answer complex queries, discover interesting resources, link similar SA, generate exercises or suggest appropriate SA to help a student to learn a new piece. For the time being, our proposition is not meant to be instrument-specific but is highly influenced by our experience at the piano and guitar. However, it is possible to extend it according to other instruments requirements. The MPO conception methodology is inspired by the Archonte methodology [START_REF] Bachimont | Ingénierie des connaissances et des contenus, le numérique entre ontologies et documents[END_REF]. Recurrent linguistic units were extracted from recorded piano lessons. These units were classified by an identity and differentiation process and each obtained class was labeled (see Figure 6). We then noticed that each label could be associated to one of the main activity of music practice: listening, playing and learning. Thus, we used these three activities to design our MPO concepts tree. This ontology can be used to semantically describe a Musical Expression (listening activ-ity), an Instrumental Technique (playing activity) or an Assimilation Method (learning activity). Naturally, these three concepts are related: an Instrumental Technique produces a Musical Expression but requires an Assimilation Method to be handled by a learner (Figure 7). Besides, the sociologist Megan Winget also highlights Expression and Technique as essential annotation types in her study on musicians' annotation practices [START_REF] Winget | Annotations on musical scores by performing musicians: Collaborative models, interactive methods, and music digital library tool development[END_REF].

The MusicalExpression concept regroups all concepts which deal with musical writing (Rhythm, Harmony, Structures, volume and tempo Dynamics) and its resulting Sound. Various sound features can be described, such as pitch, duration, timbre, mood and articulation (i.e. legato, staccato). The Structure concept regroups elements from the MFSO previously presented. Indeed, the SA may discuss specific elements inside the selected part. For instance, a musician can extract all occurences of a leitmotiv in a given musical work. This naming task is realized at the MusicalWorkExtract resource level, thanks to the Leitmotiv concept from the MFSO. An other musician can then annotate one of the occurences and insist on one of its intervals requiring more attention than the others. This time, the structure identification is at the SA level, but still requires the Interval concept defined by the MFSO. This is because the second structure identification is more a personal approach of the piece and will not necessarily catch the attention of a musicologist as it does for a performer, who has to "animate" the piece. This approach gives more flexibility to the users, by allowing them to distinguish high level and meaningful structures (theme, phrases) from basic elements (note level). Different relations exist between these musical expression concepts but were not represented in Figure 7 for readability purposes. For example, Duration and Rhythm are strongly related, as extending a note duration (e.g., a fermata) has an impact on the overall rhythmic organization around the note. Identified structures can also be linked to their harmonic (hasHarmony) and rhythmic (hasRhythm) features. The Harmony concept can be linked to the Chord Ontology 1 to specify the chords at stake in a standardized notation.

The InstrumentalTechnique concept allows the musician to tag any instrument-related technical matter. It deals with gestures, movements, fingerings and positions 1 http://www.omras2.org/ChordOntology, visited on the 06/05/2013. "We will study Espièglerie from Kabalevski. During the learning [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF], we should try to keep the playful and light-hearted tone [START_REF] Sébastien | @-MUSE: Sharing Musical Know-how Through Mobile Devices Interfaces[END_REF] of this little piece. The main work [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF] is based on fifths sequences [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF].

Concerning text learning [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF], there are several parts [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF] to consider in this work. There is the first part [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF] where the left and right hand [START_REF] Bachimont | Ingénierie des connaissances et des contenus, le numérique entre ontologies et documents[END_REF] play the same notes, namely two fifths(5) (plays( 9)). For the right hand [START_REF] Bachimont | Ingénierie des connaissances et des contenus, le numérique entre ontologies et documents[END_REF], we will develop [START_REF] Bimbot | Semiotic structure labeling of music pieces: concepts, methods and annotation conventions[END_REF] all notes but for the moment, it is better to play [START_REF] Bimbot | Semiotic structure labeling of music pieces: concepts, methods and annotation conventions[END_REF] only the fifths(5) like this, so that the notes are rapidly assimilated [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF] (plays the fifths). One should pay attention to the 2-5 fingering at the left hand [START_REF] Bachimont | Ingénierie des connaissances et des contenus, le numérique entre ontologies et documents[END_REF], which allows to get livelier and lighter detached notes [START_REF] Sébastien | @-MUSE: Sharing Musical Know-how Through Mobile Devices Interfaces[END_REF]. Here is what you should obtain (plays the part), here both hands [START_REF] Bachimont | Ingénierie des connaissances et des contenus, le numérique entre ontologies et documents[END_REF] play at the same time [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF].

That's all for the first part [START_REF] Conruyt | Knowledge Discovery for Biodiversity: from Data Mining to Sign Management[END_REF]. This should be rapidly assimilated [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF], with the right nuances(4) [START_REF] Sébastien | @-MUSE: Sharing Musical Know-how Through Mobile Devices Interfaces[END_REF]. I played it slowly [START_REF] Vander Wal | Folksonomy[END_REF], but it should not be a problem to play it at the right tempo(3) after repeating it 3 or 4 times(6) (plays the fifths at the right tempo). It should be played naturally [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF](1), and by heart [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF] as soon as possible because it is rather difficult [START_REF] Pachet | A Taxonomy of Musical Genres[END_REF] to move on the keyboard and watch the score [START_REF] Bachimont | Ingénierie des connaissances et des contenus, le numérique entre ontologies et documents[END_REF] [START_REF] Hodeir | Les Formes de la musique (Tr.: The Forms of Music)[END_REF] at the same time." which are essential to produce the desired musical expression. As can be seen in Figure 7, an Instrumental Technique involves a musician's limbs or articulations (arms, hands, wrists, etc.) and a part of his instrument (on the piano: the keyboard, the pedals, the white keys, the black keys, etc. in singing: the vocal cords, the lungs, the mouth, etc.). The produces relation allows to link a technique to its resulting musical effect. In practice, the Fingering concept will certainly be the most used one, as it is one of the most important information for sightreading musicians. If a MusicXML score of the piece is available, a fingering can be associated to a copy of the annotated extract (MusicXML 3.0 supports <fingering> nodes). Using copies instead of the original MusicXML file allows musicians to propose several fingering solutions for a single part. The idea is to clearly distinguish the basic abstract notation (MusicXML notes, provided by editors) from the concrete annotations demonstrating musical know-how (SA, provided by musicians).

The Assimilation concept deals with educational mechanisms, to help a student to handle an instrumental technique. In particular, it aims at providing a framework to create exercises based on rearrangements of the original score. For instance, piano teachers often reduce a part's difficulty by dividing it into smaller parts (i.e. intervals). These elements are repeated three or four times and then grouped by two, by three, etc…gradually increasing the difficulty. We could thus generate the corresponding score for each step of the exercise. Other educational mechanisms can be described in the Assimilation concept: beats counting, sight-reading methods, work calendar, learning by heart, etc.

To have a better understanding of how this ontology can be used and for what purposes, we propose a simple use case in the following section.

SA, MFSO AND MPO USE CASE

We propose a fictive use case to study how the proposed SA, MFSO and MPO models can work together. A musician wishes to annotate a score with the following assertions:

-"Here is an occurrence of leitmotiv A. I label it A1." -"Here is an other occurrence of leitmotiv A. I label it A2." -"A1 and A2 are almost similar, except A2 is a transposition of A1." -"Both are based on the following rhythm: eighthsixteenth triplet -quarter." -"Beware of the articulation on A1's first note: it is staccato. It must be done with the whole arm to prevent a too sharp attack and prepare for the next position. It is also possible to lightly increase the volume on the ascendant arpeggio. But always keep the solemn mood of the piece." Figure 8 represents the identified RDF 1 triplets. We highlight the fundamental distinction between the studied objects (the piece and its extracts, described with the MO 1 Resource Description Framework. and MFSO) and their interpretations (semiotic annotations, described with the SA and MPO). The relation between the two leitmotiv occurences (transposition) allows to deduce the type of A2. It also allows to duplicate the explanations given for A1 on A2, as long as tonal dependant concepts are not involved (which is the case here). The "Rhythm URI" resource can be linked to an appropriate rhythm notation resource (e.g., a MusicXML short fragment). Common articulations, dynamics and characters can be suggested in a list to facilitate the semantic description input. The description of the arm gesture remains brief, but will enable to return this annotation for requests such as "how to play staccato?". The content and form components of the SA were not represented in Figure 8 which focuses on semantic description, but can be added by the user. Typically, the staccato gesture should be demonstrated with a video resource (content component). The form component allows the user to select different ways of indexing his annotation. But did the musician use the appropriate terms to describe his interpretation ?

DISCUSSION

As noted earlier, using appropriate words in music is a complex issue, mainly for subjectivity and context reasons. Naturally, musicology also aims at clearly defining terms and analysis methods in this field. But sometimes, musicologists themselves do not agree on appropriate terms to designate structures. For instance, there is a "French school" and an "Anglo-Saxon school" with distinct methods, vocabularies and notations customs.

Indeed, the concept of "rule" in music is complex. There is a framework (mainly the tonal system in occidental music), a history, a culture, an aesthetic which were built over time and various influences, but no definite rule. Thus, the line between form, genre and style can be thin in many circumstances. Some works exist in order to clarify the manipulated terms meanings and to prevent confusion in musical writ- ings, such as the GDRM1 initiative at Laval University. But the most important factor is the context of use. For example, the "pedal" can either designate a long bass note, or a part of the piano. This example is especially interesting because, even if the two meanings are distinct, they are somehow related and can explain why the same word is used: indeed, the piano pedal do help to produce a bass pedal in some cases. Both meanings thus imply the idea of a "long resonance". For the time being, we propose to overcome this issue by making a distinction between the concept and its common designation. For the pedal example, we define two concepts: BassPedal and PianoPedal, having both the designation "pedal", corresponding to the way they are commonly called by musicians.

The difficulty also lies in the interrelation of the defined concepts. As seen in the use case, musicians rarely address one theme at a time, as all musical elements interacts with each other, and the musician should have control on each of them while playing. Providing an extensive semantic description in such case is very difficult. This is why we rely on common concepts and try to establish simple relations between them. But more specific relations can only emerge through intensive use of the annotation platform. This is why we rely on an iterative construction of our descriptive model [START_REF] Conruyt | Knowledge Management in Environmental Sciences with IKBS: Application to Systematics of Corals of the Mascarene Archipelago[END_REF].

Thus, our collaborative annotation platform aims at fostering fruitful debates to help musicians confront their ways of analyzing and practicing music.

CONCLUSION

In this paper, we proposed a Musical Forms and Structures Ontology (MFSO) and a Musical Performance Ontology (MPO) to annotate performances and scores semantically. These ontologies aim at extending the standard Music Ontology with musicological and musical know-how concepts. To do so, we first introduced a Semiotic Annotation framework to allow users to describe personal interpretations of musical works and then introduced our MFSO. This allows musicians to name precisely the musical extract to annotate and its role in the work. Musical expressions, techniques and assimilation methods can then be described thanks to appropriate concepts and relations from our MPO. This work notably aims at building a music learning agent which can help musicians to answer complex queries, discover interesting knowledge among large digital scores collections, generate exercises or suggest appropriate SA to help a student on a new piece.

Naturally, perspectives for this work include testing it with musicians of all levels, which will allow us to refine and extend our proposition. To do so, a collaborative semiotic annotation platform for mobile tablets is currently being developed.

Figure 3 :

 3 Figure 3: Semiotic Annotation model.Figure 2: Sign tetrahedron.

Figure 2 :

 2 Figure 3: Semiotic Annotation model.Figure 2: Sign tetrahedron.

Figure 4 :

 4 Figure 4: Relations between two Semiotic Annotations.

Figure 5 :

 5 Figure 5: MFSO conceptual model.

1 Sound 2

 2 Harmony 3 Rhythm 4 Dynamic 5 Structure 6 Assimilation 7 Gesture 8 Support 9 Relation

Figure 6 :

 6 Figure 6: Piano lesson analysis example: extraction and classification of significant linguistic units.

Figure 7 :

 7 Figure 7: Musical Performance Ontology conceptual model.

Figure 8 :

 8 Figure 8: SA, MFSO and MPO use case example.

http://getutopia.com/index.php, visited on the 06/05/2013.

YUMA Universal Media Annotator : https://github.com/yumaannotation/, visited on the 06/05/2013.

http://www.mus.ulaval.ca/roberge/gdrm/, visited on the 06/05/2013.


Florin Constantin Mihai

East European recycling societies: The first steps of rural communities in Neamt County, Romania

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A Glance at the World Waste Management 56 (2016) I-III http://dx.doi.org/10.1016/S0956-053X(16)30465-2 Edited by Francesca Girotto

This is the preprint version:

Florin-Constantin MIHAI * -East European recycling societies: The first steps of rural communities in Neamt County, Romania *Department of Geography, ''Alexandru Ioan Cuza" University of Iasi, Iasi, Romania Romania is still facing major disparities between urban and rural areas regarding the proper waste management (WM) services [START_REF] Ciuta | Urban and rural MSW stream characterization for separate collection improvement[END_REF][START_REF] Mihai | Accessibility of waste collection services in Romania: a multi-scale analysis in EU context using thematic cartography[END_REF]. This gap suggests that the rural WM sector needs to be a priority in current environmental policy. This paper provides a an overview regarding the recycling prospects in the case of rural communities in Neamt County. Neamt County includes 5 cities and 78 communes (rural municipalities).

Since 2011, separate collection of recyclables (paper/cardboard,plastics, and organics) was implemented only in Piatra Soimului, Borlesti and Rediu localities. After the closure of rural dumpsites under the EU regulations in 2009, municipalities were required to seek licensed waste operators through direct or delegated management.

The separate collection is done by setting up the special collection containers in some points within densely populated areas. There are private operators to provide the mixed waste collection services once per week in rural areas of Neamt County (in the case of collection points) and once per month, or when containers reach the filling degree viable for transportation, in the case of dry recyclables. Between 2011 and 2012 the collection of recyclables from commercial sectors and households was performed across severalcommunes (Fig. 1). The share of separate collection (SC) reflects the approximate value of reuse and recycling, if it is taken into consideration the fact that all these recyclable fractions are marketed by waste operators to specialized companies.

The mixed collection prevails in rural areas, separate collection and recovery of recyclables are still at an early stage in most of the communes with values below 6%. The threshold of 10% SC is exceeded only by Farcasa, Baltatesti and Alexandru cel Bun communes. The recyclables collected from commercial sectors are more likely to be recovered than those derived from households, because residents do not properly segregate these fractions. Therefore, household waste is mainly disposed in landfills. In some cases, the collected mixed waste is transported to a sorting station where recyclables are extracted (metal, plastic, paper/cardboard, wood, glass) and, thereafter, marketed to specialized units from cities.

Recovery of waste may experience a significant growth in the coming years with the expansion of separate waste collection facilities in most of the rural communities within the County. The correct separate collection is a key issue of urban and rural areas in order to increase the efficiency of the WM system. Environmental education is crucial in rural areas in order to diminish the effects of waste dumping and to develop an optimal separate collection system which encourages the recycling and reuse of household waste. Nowadays, traditional WM systems still prevail in most of rural municipalities in the study area, but new separate waste collection facilities are already operational in some of them.

Fig. 1 .

 1 Fig. 1. Share of separate collection (SC %) of total collected household waste.


Pascal Ochem
email: ochem@lirmm.fr

Doubled patterns are 3-avoidable

Keywords:

In combinatorics on words, a word w over an alphabet Σ is said to avoid a pattern p over an alphabet ∆ if there is no factor f of w such that f = h(p) where h : ∆ * → Σ * is a non-erasing morphism. A pattern p is said to be k-avoidable if there exists an infinite word over a k-letter alphabet that avoids p. A pattern is said to be doubled if no variable occurs only once. Doubled patterns with at most 3 variables and patterns with at least 6 variables are 3-avoidable. We show that doubled patterns with 4 and 5 variables are also 3-avoidable.

Introduction

A pattern p is a non-empty word over an alphabet ∆ = {A, B, C, . . . } of capital letters called variables. An occurrence of p in a word w is a non-erasing morphism h : ∆ * → Σ * such that h(p) is a factor of w. The avoidability index λ(p) of a pattern p is the size of the smallest alphabet Σ such that there exists an infinite word w over Σ containing no occurrence of p. Bean, Ehrenfeucht, and McNulty [START_REF] Bean | Avoidable patterns in strings of symbols[END_REF] and Zimin [START_REF] Zimin | Blocking sets of terms[END_REF] characterized unavoidable patterns, i.e., such that λ(p) = ∞. We say that a pattern p is t-avoidable if λ(p) t. For more informations on pattern avoidability, we refer to Chapter 3 of Lothaire's book [START_REF] Lothaire | Algebraic Combinatorics on Words[END_REF].

It follows from their characterization that every unavoidable pattern contains a variable that occurs once. Equivalently, every doubled pattern is avoidable. Our result is that : Theorem 1. Every doubled pattern is 3-avoidable.

Let v(p) be the number of distinct variables of the pattern p. For v(p)

3, Cassaigne [START_REF] Cassaigne | Motifs évitables et régularité dans les mots[END_REF] began and I [START_REF] Ochem | A generator of morphisms for infinite words[END_REF] finished the determination of the avoidability index of every the electronic journal of combinatorics XX (2013), #R00 pattern with at most 3 variables. It implies in particular that every avoidable pattern with at most 3 variables is 3-avoidable. Moreover, Bell and Goh [START_REF] Bell | Exponential lower bounds for the number of words of uniform length avoiding a pattern[END_REF] obtained that every doubled pattern p such that v(p) 6 is 3-avoidable.

Therefore, as noticed in the conclusion of [START_REF] Ochem | Application of entropy compression in pattern avoidance[END_REF], there remains to prove Theorem 1 for every pattern p such that 4 v(p) 5. In this paper, we use both constructions of infinite words and a non-constructive method to settle the cases 4 v(p) 5.

Recently, Blanchet-Sadri and Woodhouse [START_REF] Blanchet-Sadri | Strict bounds for pattern avoidance[END_REF] and Ochem and Pinlou [START_REF] Ochem | Application of entropy compression in pattern avoidance[END_REF] independently obtained the following.

Theorem 2 ([4, 10]). Let p be a pattern. As noticed in these papers, if p has length at least 2 v(p) then p contains a doubled pattern as a factor. Thus, Theorem 1 implies Theorem 2.(b).

Extending the power series method

In this section, we borrow an idea from the entropy compression method to extend the power series method as used by Bell and Goh [START_REF] Bell | Exponential lower bounds for the number of words of uniform length avoiding a pattern[END_REF], Rampersad [START_REF] Rampersad | Further applications of a power series method for pattern avoidance[END_REF], and Blanchet-Sadri and Woodhouse [START_REF] Blanchet-Sadri | Strict bounds for pattern avoidance[END_REF].

Let us describe the method. Let L ⊂ Σ * m be a factorial language defined by a set F of forbidden factors of length at least 2. We denote the factor complexity of L by n i = L ∩ Σ i m . We define L as the set of words w such that w is not in L and the prefix of length |w| -1 of w is in L. For every forbidden factor f ∈ F , we choose a number 1 s f |f |. Then, for every i 1, we define an integer a i such that

a i max u∈L v ∈ Σ i m | uv ∈ L , uv = bf, f ∈ F, s f = i .
We consider the formal power series P (x) = 1 -mx + i 1 a i x i . If P (x) has a positive real root x 0 , then n i x -i 0 for every i 0. Let us rewrite that P (

x 0 ) = 1 -mx 0 + i 1 a i x i 0 = 0 as m - i 1 a i x i-1 0 = x -1 0 (1)
Since n 0 = 1, we will prove by induction that n i n i-1

x -1 0 in order to obtain that n i x -i 0 for every i 0. By using (1), we obtain the base case:

n 1 n 0 = n 1 = m x -1
0 . Now, for every length i 1, there are:

• m i words in Σ i m ,
• n i words in L, the electronic journal of combinatorics XX (2013), #R00

• at most

1 j i n i-j a j words in L , • m(m i-1 -n i-1 ) words in Σ i m \ {L ∪ L }. This gives n i + 1 j i n j a i-j + m(m i-1 -n i-1 ) m i , that is, n i mn i-1 -1 j i n i-j a j . n i n i-1 m -1 j i a j n i-j n i-1 m -1 j i a j x j-1 0 By induction m -j 1 a j x j-1 0 = x -1 0 By (1)
The power series method used in previous papers [START_REF] Bell | Exponential lower bounds for the number of words of uniform length avoiding a pattern[END_REF][START_REF] Blanchet-Sadri | Strict bounds for pattern avoidance[END_REF][START_REF] Rampersad | Further applications of a power series method for pattern avoidance[END_REF] corresponds to the special case such that s f = |f | for every forbidden factor. Our condition is that P (x) = 0 for some x > 0 whereas the condition in these papers is that every coefficient of the series expansion of 1 P (x) is positive. The two conditions are actually equivalent. The result in [START_REF] Piotkovskii | On the growth of graded algebras with a small number of defining relations[END_REF] concerns series of the form S(x) = 1 + a 1 x + a 2 x 2 + a 3 x 3 + . . . with real coefficients such that a 1 < 0 and a i 0 for every i 2. It states that every coefficient of the series 1/S(x) = b 0 + b 1 x + b 2 x 2 + b 3 x 3 + . . . is positive if and only if S(x) has a positive real root x 0 . Moreover, we have b i x -i 0 for every i 0. The entropy compression method as developped by Gonçalves, Montassier, and Pinlou [START_REF] Gonçalves | Entropy compression method applied to graph colorings[END_REF] uses a condition equivalent to P (x) = 0. The benefit of the present method is that we get an exponential lower bound on the factor complexity. It is not clear whether it is possible to get such a lower bound when using entropy compression for graph coloring, since words have a simpler structure than graphs.

Applying the method

In this section, we show that some doubled patterns on 4 and 5 variables are 3-avoidable. Given a pattern p, every occurrence f of p is a forbidden factor. With an abuse of notation, we denote by |A| the length of the image of the variable A of p in the occurrence f . This notation is used to define the length s f .

Let us first consider doubled patterns with 4 variables. We begin with patterns of length 9, so that one variable, say A, appears 3 times. We set s f = |f |. Using the obvious upper bound on the number of pattern occurrences, we obtain

P (x) = 1 -3x + a,b,c,d 1 3 a+b+c+d x 3a+2b+2c+2d = 1 -3x + a,b,c,d 1 (3x 3 ) a (3x 2 ) b (3x 2 ) c (3x 2 ) d = 1 -3x + a 1 (3x 3 ) a b 1 (3x 2 ) b c 1 (3x 2 ) c d 1 (3x 2 ) d = 1 -3x + 1 1-3x 3 -1 1 1-3x 2 -1 1 1-3x 2 -1 1 1-3x 2 -1 = 1 -3x + 1 1-3x 3 -1 1 1-3x 2 -1 3 = 1-3x-9x 2 +24x 3 +36x 4 -54x 5 -108x 6 +243x 8 +162x 9 -243x 10 (1-3x 3 )(1-3x 2 ) 3
.

Then P (x) admits x 0 = 0.3400 . . . as its smallest positive real root. So, every doubled pattern p with 4 variables and length 9 is 3-avoidable and there exist at least x -n 0 > 2.941 n the electronic journal of combinatorics XX (2013), #R00 ternary words avoiding p. Notice that for patterns with 4 variables and length at least 10, every term of a,b,c,d 1 3 a+b+c+d x 3a+2b+2c+2d in P (x) gets multiplied by some positive power of x. Since 0 < x < 1, every term is now smaller than in the previous case. So P (x) admits a smallest positive real root that is smaller than 0.3400 . . . Thus, these patterns are also 3-avoidable. Now, we consider patterns with length 8, so that every variable appears exactly twice. If such a pattern has ABCD as a prefix, then we set

s f = |f | 2 = |A| + |B| + |C| + |D|. So we obtain P (x) = 1 -3x + a,b,c,d 1 x a+b+c+d = 1 -3x + 1 1-x -1 4
. Then P (x) admits 0.3819 . . . as its smallest positive real root, so that this pattern is 3-avoidable. Among the remaining patterns, we rule out patterns containing an occurrence of a doubled pattern with at most 3 variables. Also, if one pattern is the reverse of another, then they have the same avoidability index and we consider only one of the two. Thus, there remain the following patterns: ABACBDCD, ABACDBDC, ABACDCBD, ABCADBDC, ABCADCBD, ABCADCDB, and ABCBDADC. Now we consider doubled patterns with 5 variables. Similarly, we rule out every pattern of length at least 11 with the method by setting s f = |f |. Then we check that

P (x) = 1 -3x + a,b,c,d,e 1 3 a+b+c+d+e x 3a+2b+2c+2d+2e = 1 -3x + 1 1-3x 3 -1 1 1-3x 2 -1 4 has a positive real root.
We also rule out every pattern of length 10 having ABC as a prefix. We set

s f = |f | -|ABC| = |A| + |B| + |C| + 2|D| + 2|E|. Then we check that P (x) = 1 -3x + a,b,c,d,e 1 3 d+e x a+b+c+2d+2e = 1 -3x + 1 1-x -1 3 1 1-3x 2 -1 2 has a positive real root.
Again, we rule out patterns containing an occurrence of a doubled pattern with at most 4 variables and patterns whose reversed pattern is already considered. Thus, there remain the following patterns: ABACBDCEDE, ABACDBCEDE, and ABACDBDECE.

Sporadic doubled patterns

In this section, we consider the 10 doubled patterns on 4 and 5 variables whose 3avoidability has not been obtained in the previous section.

We define the avoidability exponent AE(p) of a pattern p as the largest real x such that every x-free word avoids p. This notion is not pertinent e.g. for the pattern ABW BAXACY CAZBC studied by Baker, McNulty, and Taylor [START_REF] Baker | Growth problems for avoidable words[END_REF], since for every > 0, there exists a (1 + )-free word containing an occurrence of that pattern. However, AE(p) > 1 for every doubled pattern. To see that, consider a factor A . . . A of p. If an xfree word contains an occurrence of p, then the image of this factor is a repetition such that the image of A cannot be too large compared to the images of the variables occurring between the As in p. We have similar constraints for every variable and this set of constraints becomes unsatisfiable as x decreases towards 1. We present one way of obtaining the avoidability exponent for a doubled pattern p of length 2v(p). We construct the v(p) × v(p) matrix M such that M i,j is the number of occurrences of the variable X j between the two occurrences of the variable X i . We compute the largest eigenvalue β of M and then we the electronic journal of combinatorics XX (2013), #R00 have AE(p) = 1 + 1 β+1 . For example if p = ABACDCBD, then we get M = 0 1 0 0 1 0 0 1 0 2 0 1 0 1 1 0 , β = 1.9403 . . . , and AE(p) = 1 + 1 β+1 = 1.3400 . . . . The avoidability exponents of the 10 patterns considered in this section range from AE(ABCADBDC) = 1.292893219 to AE(ABACBDCD) = 1.381966011. For each pattern p among the 10, we give a uniform morphism m : Σ * 5 → Σ * 2 such that for every 5 4 + -free word w ∈ Σ * 5 , we have that m(w) avoids p. The proof that p is avoided follows the method in [START_REF] Ochem | A generator of morphisms for infinite words[END_REF]. Since there exist exponentially many 5 4 + -free words over Σ 5 [START_REF] Kolpakov | On the number of Dejan words over alphabets of 5, 6, 7, 8, 9 and 10 letters[END_REF], there exist exponentially many binary words avoiding p.

Simultaneous avoidance of doubled patterns

Bell and Goh [START_REF] Bell | Exponential lower bounds for the number of words of uniform length avoiding a pattern[END_REF] have also considered the avoidance of multiple patterns simultaneously and ask (question 3) whether there exist an infinite word over a finite alphabet that avoids every doubled pattern. We give a negative answer.

A word w is n-splitted if |w| ≡ 0 (mod n) and every factor w i such that w = w 1 w 2 . . . w n and |w i | = |w| n for 1 i n contains every letter in w. An n-splitted pattern is defined similarly. Let us prove by induction on k that every word w ∈ Σ n k k contains an n-splitted factor. The assertion is true for k = 1. Now, if the word w ∈ Σ n k k is not itself n-splitted, then by definition it must contain a factor w i that does not contain every letter of w. So we have w i ∈ Σ n k-1 k-1 . By induction, w i contains an n-splitted factor, and so does w.

This implies that for every fixed n, every infinite word over a finite alphabet contains n-splitted factors. Moreover, an n-splitted word is an occurrence of an n-splitted pattern such that every variable has a distinct image of length 1. So, for every fixed n, the set of all n-splitted patterns is not avoidable by an infinite word over a finite alphabet.

Notice that if n 2, then an n-splitted word (resp. pattern) contains a 2-splitted word (resp. pattern) and a 2-splitted word (resp. pattern) is doubled.

Conclusion

Our results answer settles the first of two questions of our previous paper [START_REF] Ochem | Application of entropy compression in pattern avoidance[END_REF]. The second question is whether there exists a finite k such that every doubled pattern with at least k variables is 2-avoidable. As already noticed [START_REF] Ochem | Application of entropy compression in pattern avoidance[END_REF], such a k is at least 5 since, e.g., ABCCBADD is not 2-avoidable.

  (a) If p has length at least 3 × 2 v(p)-1 then λ(p) 2. (b) If p has length at least 2 v(p) then λ(p) 3.

•

  AE(ABACBDCD) = 1.381966011, 17-uniform morphism 0 the electronic journal of combinatorics XX (2013), #R00

Acknowledgments

I am grateful to Narad Rampersad for comments on a draft of the paper, to Vladimir Dotsenko for pointing out the result in [11], and to Andrei Romashchenko for translating this paper.

• AE(ABCADCBD) = 1.295597743, 22-uniform morphism 0 → 0000011011010100011111 1 → 0000011010101001001111 2 → 0000001101100100111111 3 → 0000001010110000111111 4 → 0000000110101001110111

the electronic journal of combinatorics XX (2013), #R00


Pascal Ochem
email: ochem@lirmm.fr

More on square-free words obtained from prefixes by permutations

An infinite square-free word w over the alphabet Σ3 = {0, 1, 2} is said to have a k-stem σ if |σ| = k and w = σw1w2 • • • where for each i, there exists a permutation πi of Σ3 which extended to a morphism gives wi = πi(σ). Harju proved that there exists an infinite k-stem word for k = 1, 2, 3, 9 and 13 ≤ k ≤ 19, but not for 4 ≤ k ≤ 8 and 10 ≤ k ≤ 12. He asked whether k-stem words exist for each k ≥ 20. We give a positive answer to this question. Currie has found another construction that answers Harju's question.

Introduction

An infinite square-free word w over the alphabet Σ 3 = {0, 1, 2} is said to have a k-stem σ if |σ| = k and w = σw 1 w 2 • • • where for each i, there exists a permutation π i of Σ 3 which extended to a morphism gives w i = π i (σ). Harju [START_REF] Harju | Square-free words obtained from prefixes by permutations, Theoret[END_REF] proved that there exists an infinite k-stem word for k = 1, 2, 3, 9 and 13 ≤ k ≤ 19, but not for 4 ≤ k ≤ 8 and 10 ≤ k ≤ 12 and asked whether k-stem words exist for each k ≥ 20. We construct k-stem words for each 20 ≤ k ≤ 10000 in Section 3 and for every k ≥ 23 in Section 4. Currie [START_REF] Currie | Infinite ternary square-free words concatenated from permutations of a single word[END_REF] has found another construction that answers Harju's question.

Let t = 012021012102012021020121012 . . . denote the fixed point of the morphism 0 → 012, 1 → 02, 2 → 1. By definition, t contains neither 010 nor 212 as a factor. Harju [START_REF] Harju | Square-free words obtained from prefixes by permutations, Theoret[END_REF] also asked whether t has a k-stem factorization for some k ≥ 3. We give a negative answer in Section 2. This result has also been obtained by Harju and Müller [START_REF] Harju | Square-free words generated by applying permutations to a prefix[END_REF]. Proof. By previous results [START_REF] Harju | Square-free words obtained from prefixes by permutations, Theoret[END_REF], we only need to consider the cases k = 9 and k ≥ 13.

k-stem factorization of t

A computer check shows that no factor f of t of length 18 is such that the suffix of length 9 of f is a permutation of the prefix of length 9 of f . This rules out the case k = 9.

A computer check shows that every factor f of t of length 12 contains a factor a0a with a ∈ Σ 3 . By symmetry, it also contains a factor b2b with b ∈ Σ 3 . Remember that 010 and 212 are not factors of t. A permutation of Σ 3 mapping 0 to 1 (resp. mapping 2 to 1) cannot be applied to f , since it would produce a factor c1c with c ∈ Σ 3 that cannot appear in t . There remain two possible permutations, namely the identity and the permutation swapping 0 and 2, but an infinite square free word cannot be obtained by a concatenation of only two distinct factors. This rules out the case k ≥ 13.

k-stem words for 20 ≤ k ≤ 10000

Theorem 2 There exist k-stem words for every 20 ≤ k ≤ 10000.

Proof. Let π be the permutation (012). We say that a morphism h : Σ The growth rate of ternary words defining a square-free circular morphism exists and is equal to the growth rate 1.3017 . . . of ternary square-free words.

* 3 → Σ * 3 is circular if h(1) = π(h(0)) and h(2) = π(h( 1
See Shur [START_REF] Shur | Growth rates of complexity of power-free languages[END_REF] for more information on the growth rate of ternary square-free words.

Theorem 1

 1 No suffix of t admits a k-stem factorization for any k ≥ 3.

  )). For every 20 ≤ k ≤ 10000, we found a word w k such that |w k | = c k × k and the circular morphism m defined by m(0) = w k is square-free. We have c k = 8 for 20 ≤ k ≤ 22 and c k = 1 for 23 ≤ k ≤ 10000. Square-freeness is checked using the result of Crochemore[START_REF] Crochemore | Sharp characterizations of squarefree morphisms[END_REF] that a uniform morphism h is square-free if and only if the h-images of squarefree words of length 3 are square-free. Since we consider circular morphisms, we only need to check the images of 010 and 012. These are our words w k for 20 ≤ k ≤ 22, where |w k | = 8k. Consider now the case k ≥ 23, where |w k | = k. Let t ′ = 012021020121012 . . . denote the infinite suffix of t obtained from t by deleting the first 12 letters. To speed up the search of a suitable w k , we impose that w k = pr120210 where p is the prefix of length k -22 of t ′ and r belongs to the set S of size 13 below, except that r = 2102010210121020 for k = 26. S = {0102120121020102, 0120102120121020, 0212012101201020, 1012010212012102, 1021201021012102, 1201020121020102, 1202120121020102, Conjecture 4

Again, using the result of Crochemore [START_REF] Crochemore | Sharp characterizations of squarefree morphisms[END_REF], d is shown to be square-free by checking that the d-images of square-free words of length max 3, 18-3 17 = 3 are square-free. Since the restriction of d to images of length 17 (resp. 18) is circular, we only need to check the images of 010 and 012 are square-free. For each of the factors 010 and 012, we actually have 2 3 images to check since each of the letters can be mapped either to its image of length 17 or 18.

If m is a square-free circular morphism, then for every d-image w 0 of m(0), the circular morphism defined by 0 → w 0 is square-free. This means that given a k-uniform square-free circular morphism, we can construct a k ′ -uniform square-free circular morphism for every k ′ such that 17k ≤ k ′ ≤ 18k. Now we prove that there exist k-uniform square-free circular morphisms for every k ≥ 23. We start with the cases k ∈ [23, 10000] which are proved in the previous section. They imply the cases k ∈ 23≤p≤10000 [17p, 18p], i.e., k ∈ [391, 180000]. We then obtain every k ≥ 23 by induction.

Concluding remarks

We have proved that there exist infinite square-free ternary words with a k-stem factorization for every k except 4 ≤ k ≤ 8 and 10 ≤ k ≤ 12. We conjecture that there exist k-stem words of the form w k = pr120210 described in the proof of Theorem 2 for every k ≥ 23, rather than 23 ≤ k ≤ 10000. Before we found the morphism of the proof of Theorem 3, we pushed the verification to up to 10000 in order to find a way to prove this conjecture, but the proof of Theorem 3 only requires a verification for 23 ≤ k ≤ 390.

From the proof of Theorem 3, we see that the number of k-uniform squarefree circular morphisms is exponential in k, at least about 2k/35 k/35 ≈ 2 2k/35 . We conjecture the following: