Matej Ďurčo

Marianne Huang

Stef Scagliola

M Durco

T Wissik

Keywords: data model, content consolidation 1.1. 31.10. T. Wissik Content consolidation, alignment T. Wissik Graphics, Content 1.4 17.03 T. Wissik, M. Durco Graphics, content, incorporation of consortium feedback 1.5 18.3

Table of contents

Introduction

The project will deliver training materials for the digital arts and humanities in different languages and make them available via an online e-learning platform. This report elaborates on the implementation of such a platform. It describes the main user scenarios, it collects user and technical requirements, defines the data model and functional specification and explores technical solutions. The report has been created within WP 4 Infrastructure Development with input from all partners, especially WP 2 (user requirements).

As a first step, we performed desktop research on what kind of solutions and projects on portals for training materials exist and what kind of systems they are using.

The second step was an evaluation of different tools. There are different evaluation methods and criteria for e-learning systems (e.g. Kurilovas & Dagiene 2009). We chose to start from user requirements and a mapping of the user requirements from WP2 to functionalities available in existing systems. Finally, we determined which solution would suit the requirements and other circumstances within the project best.

User scenarios & requirements

We distinguish three types of users (or roles) for the platform: For the project we have identified three main user scenarios:

• Use of learning material by lone students for self-study;

• Use of learning material by teachers in an already existing course using the dariahTeach • platform;

• Use of learning material by teachers in an already existing course by using the material on the institutional e-learning platform.

User requirements

The development of the platform is guided by the user requirements deliverables as they were identified in a survey with potential users in WP2 (see deliverable D7). We considered user requirements not only from the section "I. Platform" of the deliverable, but also section "II. Modules" and "Others". As the report concentrates mainly on user requirements from the instructor's point of view, WP4 carried out an additional small focus group discussion on possible user requirements from the student's point of view. Some more user requirements came up during the discussion within the project consortium.

Additionally some of the user requirements collected in WP2, repeat similar aspects in other words. Some requirements contradict each other or contradict some of the requirements given by the consortium or already defined within the project. For example the requirement, of the structure of the platform and the content in modules, lessons, units and sections and the user requirements "The platform should be a free-structure environment ("Like a blog with semantic capabilities"). In the cases of contradicting requirements, the consortium has to decide which should be prioritized.

In an effort to consolidate the findings, we reformulated the requirements slightly and grouped them into following categories: This set of requirements shall serve as basis for the development / adoption of the platform. However, even though we reduced the original number, by merging similar requirements, we still receive a set of 37 requirements which is a relatively high number, given the available implementation resources. Thus it might be necessary for the consortium to set priorities, and the evaluated solutions will be matched against.

In the next step, we have translated the 37 user requirements into general standard LMS system functions or CMS functions/plugin and have given a concrete LMS System or CMS System example or plugin that supports the function. Due to the whole design of the project, we have looked only into Open-Source LMS and as examples we have chosen Moodle and LearnPress the primary candidates for implementation after the review in section 4. Some of the user requirements could not be translated into specific CMS or LMS functionalities because they refer rather to procedural/organisational aspects of the project like user requirement no. 31 "Ensure sustainability by cooperation with DARIAH" or no. 27 "The platform should be user-tested during its development". 37 Should not be isolated ("Always bad to be a silo")

Content model /

Data Model

Based on the current/ preliminary descriptions of modules we formulated a data model, i.e. what kind of entities we need to deal with and what are their properties and the relationships between them.

Main Entities

The data model consists of four main types of entities:

-Courses -Sections -Lessons -Parts of a lesson

Courses are a collection of sections. Sections are a grouping of lessons. Lessons are core structural elements. Parts of a lesson cannot be shared independently.

Learning Objects

While the above mentioned entities serve mainly for structuring of the material, the actual content is stored in the individual learning objects (LO). LOs can be of many different types, ranging from simple texts, images, audio, video, to interactive quizzes, code, applications, or even whole wikisystems or databases.

Furthermore, especially for the multimedia material, the content can come from remote places, e.g. videos on YouTube, and needs to be embedded dynamically.

Metadata

In the last years, several open metadata standards have been developed. The IEEE Learning Object Metadata (LOM) defines the structure of metadata for learning objects. There is a separate section in LOM (9. Classification) caters for a flexible, generic way of classifying the material. Thus it is the decision of the content creator which classification system(s) will be used.

In the context of DARIAH, the primary choices would be TaDiRAH11 or NeMo Ontology2 .

The integration of ECTS credits as metadata needs further investigation.

Overview of technical solutions for an e-learning platform

There are a wide range of projects and platforms that could be used for delivering training materials.

Generally, the solutions can be grouped into two different categories (however we have to be aware that these categories are not exclusive and most solutions feature a combination of the two aspects).

Static, repository-like solutions

In this kind of platform, training and learning material are only stored and can be retrieved and then used elsewhere. There are no collaborative or interactive functionalities foreseen like forums, chats, or feedback. These repositories are essentially the storage of learning materials especially created for e-learning (cf. Roy et al. 2010). Kurilovas (2010) Another solution is the aggregator that does not store the learning objects themselves, but only the metadata which facilitates searching in the metadata categories like language, topic etc. linking to the original source.. Examples for such aggregators include: Ariadne5 or Open Educational Resources (OER) Commons6 . The static, repository-like solutions are not really suitable for this project since a number of user requirements call for interaction an collaboration (e.g. user requirements 18, 20, 21).

Collaborative and interactive solutions

These solutions integrate material provision with collaborative and interactive parts. There are a wide range of tools with collaborative and interactive solutions. There are, for example, tools that support collaborative production processes for co-authoring texts like Google Docs or Wikis, or communication tools that provide for videoconferencing (e.g. skype or Google Hangouts), chats and forums. 7 Interactive assessment functionalities are also often integrated including multiple choice quizzes or feedback functionalities such as feedback questionnaires for students or like buttons.

Another option for delivering e-learning courses are learning management systems, such as Blackboard and Moodle. According to Paulsen (2002) a Learning Management System is a system that "organizes and provides access to online learning services for students, teachers, and administrators." These are software applications that provide access to learning content, facilitate the administration of the learning content in combination with collaborative and interactive functionalities like blogging, discussion forums, quizzes, integration of social media and facilitate the organization of user groups. Often also the term learning platform is used.

Furthermore, we can discern between dedicated LMS systems, designed specifically for elearning and rather generic CMS systems that can be adapted for the specific needs of e-learning for example with special plugins. In this context, also MOOCs, Massive Open Online Courses, should not be mentioned. MOOCs are online courses which allow a large numbers of course participants. Examples for MOOCs are Coursera or Stanford Online. 8

Originally, "LMS constitute the asynchronous part of e-learning technologies" (Jahn et al. 2012) but today they also might include functionalities for synchronous learning, like videoconferencing or chat functionalities or it is possible to integrate virtual meeting rooms into an LMS system.

In the survey of Paulsen (2003) with 113 institutions, and 32 institutions used self-developed LMS Systems. Self-developed LMS Systems can be for example a relational database as described by Deperlioglu et al. (2011). On the other hand 78 institutions out of 113 used commercial or already existing LMS systems (ibid). The survey showed that more institutions relayed on already existing solutions.

Most e-learning systems offer a similar basic set of features including:

• Assignment submission In the next sections we briefly describe different solutions for e-learning platforms.

Dedicated learning management systems

Moodle 10 is a free and open-source software learning management system written in PHP. Moodle is designed to be responsive and accessible, and can be used on both desktop and mobile devices. The core functionalities of Moodle, apart from creating courses and managing students, include a personalized dashboard, an all-in-one calendar, file manager, text editor, notification functionalities for alerts on new assignments or deadlines, collaborative tools and activities such as assignments, chats, feedback surveys, forums, glossaries, quizzes, wikis. It is also possible to integrate external tools to allow participants to interact with LTI compliant learning resources and activities on other web sites. 11 There are also a wide range of plugins available 12 and it is also possible to program new plugins.

The edx platform 13 , a free and open source course management system (CMS), is programmed in Python and consists mainly of two main components, the Open edX Studio for creating courses by the instructors and the Open edX Learning Management System for students accessing the course content. 14 The ELMS Learning Network (ELMSLN) 15 is an open source modular educational technology platform for building and sustaining innovation in course technologies. ELMSLN is 100% open source and primary based on Drupal technology, a content management system. 16 Blackboard Learn 17 (previously the Blackboard Learning Management System), is a virtual learning environment and course management system developed by Blackboard Inc offered as a commercial service. It is web-based server software which features course management, customizable open architecture, and scalable design that allows integration with student information systems and authentication protocols 18 . The main collaboration/ interaction and communication functionalities are: announcements, chat, discussions, and mail. The platform supports the creation of articles, assignments, posting of videos and other media types. There are also grading functionalities available.

LMS plugins for CMS

There are not only complete LMSs on the market, there is also the possibility of using LMS plugins for content management systems in order to create e-learning platforms.

A content management system, often also called CMS, is a software that allows storing, editing and publishing content from a central interface. CMSs are often used to run websites, then they are often called web content management system. With a web content management system content can be created, managed and stored on websites. This content can be text and embedded graphics, photos, video, audio, and code that displays content or interacts with the user. Usually CMS systems have a front end and a back end. In order to create e-learning courses and deliver teaching materials, there are several learning management system plugins for content management systems.

In the following we will concentrate on

• Opigno for Drupal

• LearnPress for WordPress

Opigno 19 is an open source drupal based (Drupal 7) application to create e-learning platforms.

Drupal20 is a free open source software package based on PHP and MySQL that allows easy organizing, managing and publishing content on the web, with an endless variety of customization due to over 17 000 plugins. One of these plugins is Opigno. Opigno provides flexible building blocks and APIs to create a custom e-learning system. The created e-learning systems are SCORM and Tin Can compliant. Opigno is compatible with other drupal modules like collaborative and engagement tools. The core unit of Opigno is "the Course", a flexible group entity that allows you to group users together. It is possible to add functionality to these courses like quizzes, certificates etc.21

LearnPress 22 is a free open source LMS based on WordPress to create online courses.

Wordpress23 is a free and open source content management system based on PHP and MySQL to create blogs and websites. There are a log of plugins to costumize the blog or website and one of the plugins is LearnPress. The core unit of LearnPress is the course and within the course it is possible to create lessions, or a quiz. The lesson content can be text, video or audio. The course can be created, administrated and also exported. It is also possible to integrate collaborative functions like Forum into LearnPress. LearnPress also provides some plugins, called add-ons and it is also possible to develop its own add-ons.

Technical implementation

Based on the overview in section 4, we can distinguish the following approaches for the implementation: The implementation of the portal will be based on one of the existing technical solutions introduced in Section 4. The two principal options are the application of a general content management system (CMS) combined with specific plugins for e-learning or a more specialized learning management system (LMS).

Currently Moodle seems to cover most of the identified user requirement, so this is our primary target for the implementation. Moodle is a well-established LMS, created in 2002, has a well maintained documentation website and a plugin registry, with more than 1000 plugins to find the required plugins. Moodle is very flexible, and we can adapt the user interface, and customise most of the terminology, that is used in the menus and navigation bars.

LearnPress is a fairly new plugin for WordPress meant to support LMS functionality. However even though WordPress plugins can also be used, the support for extended functionality (the offer of specialized plugins) is limited. Further the available documentation is not satisfactory and it is not clear how well it is being adopted and how long it will be maintained (critical size of the community). On the other hand, having the static project page implemented in WordPress, it would simplify the integration to have the e-learning platform based on the same system. Considering all of these factors Moodle is the primary candidate for the implementation, with LearnPress as a fallback. To allow for early prototyping (trying out in practice if the solutions meets the needs), ACDH set up a test instance of Moodle. You can see a screenshot of the test instance in Fig. 6 overleaf.

Multilinguality

One important feature of the developed platform is multilinguality, both in the user interface and in support for multi-lingual content.

Regarding the user interface, both Moodle and LearnPress are available in multiple language:

• LearnPress is available in 8 languages, English, French, Indonesian, Italian, German, Polish, Russian, and Dutch. WordPress is released in 157 languages or varieties

• Moodle is available in more than 100 languages.

Fig. 6: Screenshot of test instance of Moodle with the 5 basic modules

The multilingual content needs to be delivered by the providers of the materials. The platform only needs to be "language-aware", i.e. it must allow the indication of the language of the material and ideally also offer a means to keep different language version of one learning material together.

It needs to be investigated further to which extent the platform can support the workflow for translation. However given the variety of materials and the many different approaches, it is not feasible, nor useful to try to integrate some machine translation functionalities into the platform.

In this respect, it will be nevertheless worthwhile to monitor the new TraMOOC project24 , and evaluate the possible synergies with the dariahTeach project.

Custom metadata

An important requirement is to be able to describe the learning material according to the LOM metadata format. It turns out that the existing LMS are rather rigid in this respect, offering only a fixed set of fields for describing the entities. We found moodle plugins for custom fields, however.

A promising approach seems to be the feature for publishing courses 25 to a community hub (e.g. http://community.moodle.de/, or mooch, http://hub.moodle.org/), where a structured description is required for every course to be exported. The foreseen fields cover quite well a basic set of fields in LOM. The disadvantage is, that these are only stored on the side of the community hub and only for courses that are pushed to the community hub. On the other hand the functionality of the community hub to share and exchange courses and learning material is a requirement within the project, so this is a feature that needs to be adopted. It needs further investigation, in how far it can cover the requirement for custom metadata.

Web-based XML-Editor

There are a lot of open-source and commercial online XML-Editors, however for the scope of our project we looked at existing open source web-based solutions. The requirement being webbased, desktop solutions like Oxygen are not an option. This is a list of a few existing web-based XML-Editors (Some of them are also installed as demos on ACDH test-servers):

• ANGLES online XML editor 26 Demo on ACDH server available 27 .

The editor provides syntax highlighting, schema-based tag-suggestion, validation with verbose error description.

• Doctored.js Editor 28

Demo on ACDH server available 29 . It tries to be user-friendly by not showing the tags, but the nested boxes solutions do not necessarily aid the comprehension.

• eXide 30 , Demo on ACDH server available 31 . eXide is tightly bound to eXist database. We have not used it so far as a separate component.

• CodePlex 32

• Turtelbite XML Editor 33 Turtelbite XML Editor is a web-service, where you have to create an account. It is user friendly because it uses no braces and it is tree view based.

• ACE 34

ACE is an embeddable code editor written in JavaScript.

1

  Introduction............................................................................................................................. 5 2 User scenarios & requirements.............................................................................................. 2.1 User scenarios ........................................................................................................ 6 2.2 User requirements .................................................................................................. 3 Data Model ............................................................................................................................ 3.1 Main Entities ........................................................................................................... 3.2 Learning Objects .................................................................................................... 9 3.3 Metadata ................................................................................................................ 8 4 Overview of technical solutions for an e-learning platform ................................................... 9 4.1 Static, repository-like solutions ............................................................................. 4.2 Collaborative and interactive solutions.................................................................. 4.2.1 Dedicated learning management systems ......................................................... 13 4.2.2 LMS plugins for CMS.......................................................................................... 14 5 Technical implementation .................................................................................................... 15 5.1 Multilinguality ........................................................................................................ 5.2 Custom metadata ................................................................................................. 5.3 Web-based XML-Editor ........................................................................................

Fig. 1 :

 1 Fig. 1: Different user scenarios

Fig. 2 :

 2 Fig. 2: Abstract model of the relation between course, section and lessons.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Result of a search query for "Lexicography"

  a. Programming everything from scratch b. Using existing Repository Systems c. Using existing Content Management Systems, ideally with specific plugins for e-learning d. Using existing Learning Management Systems e. Mixture of different approaches Given the number of existing solutions and the limited resources within the project a. is a rather theoretical option. Given a number of requirements for collaborative and interactive features b. is also not considered further. Below we concentrate on c. (LearnPress) and d. (Moodle). Mixing different systems (e.) would again complicate the implementation and therefore a very valid reason is required to go to the trouble.

Fig. 8 :

 8 Fig. 8: Screenshot of the doctored.js editor

  calls this type of repository Learning Object Repository (LO Repository). Examples of such LO Repositories are: LearnAlberta 3 or OpenStax 4 .

References ..........................................................................................................................

https://github.com/dhtaxonomy/TaDiRAH

http://nemo.dcu.gr/

http://www.learnalberta.ca/

https://openstaxcollege.org/

http://www.ariadne-eu.org/

https://www.oercommons.org/

https://github.com/devekko/opigno

https://www.drupal.org/

https://www.drupal.org/project/opigno

https://github.com/LearnPress/LearnPress

https://de.wordpress.com/

http://tramooc.eu/, Translation for Massive Open Online Courses http://www.eamt2015.org/files/downloads/EAMT2015_Proceedings.pdf, p. 217

https://docs.moodle.org/30/en/Publishing_a_course#Updating_a_course_backup

Acknowledgement of previously published material and of the work of others has been made through appropriate citation, quotation or both.

DARIAH-RC Grant Agreement number: 2014-1-IE02-KA203-000125 Project Title: DARIAH Reference Curriculum D13 Technical Report on Project Portal Development Revision: 1.Project funded by the Erasmus+ Programme Dissemination Level

Statement of originality:

This deliverable contains original unpublished work except where clearly indicated otherwise.


Agiatis Benardou

Panos Constantopoulos

Eliza Papaki

Christos Papatheodorou

Eliza Benardou

Christos Papaki

Athena Rc Papatheodorou

Draft

Claire Clivaz

WP2 User Requirements & Benchmarking of Key Competencies Deliverable 8: Visualisation of Benchmarking Key Criteria

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

In order to create a visualisation of benchmarking key criteria, it was necessary to first define these key criteria as they emerged from the previous reports mentioned above. • Personalization / Flexibility

Modules should be flexible in the time, place and pace of learning. Flexibility is to be ensured through asynchronous learning which permits students to follow the course autonomously, as well as through maximum personalization in terms of a customized approach to the use of course material.

  Moreover, it was important to define the audience(s) being addressed. The aim of this visualisation is to present a user-friendly, clear list of key criteria to be used by DH instructors in creating their own modules into the platform. A suite of such online DH modules, developed according to standard criteria will result in a corpus of Open Educational Resources (OERs) enjoying a measure of uniformity in terms of structure, type of content and level of interaction.As #dariahTeach is an Erasmus+ Strategic Partnership, it adheres to the European education quality and qualification frameworks as well as to the European Credit Framework (ECTS) for building its own framework of standards and indicators. Its aim is to promote accessibility, flexibility, interactiveness and personalization in elearning. Key quality criteria of the platform have been defined in Deliverable 17 as  extensible, open source and open access  furthering asynchronous and flexible learning  allowing easy localization and adaptation  providing learning content in English, with translations or subtitles (as appropriate) in the language of the partner country that will develop specific modules  developing content across multiple disciplines, including both text and multimedia  delivering content in various degrees of complexity  allowing use and reuse at different levels and in different modalities of education  building on iterative tests in living teaching environments These quality criteria have been integrated into the user requirements defined in Deliverable 7 in which qualitative research was undertaken with a range of DH instructors.

Figure

  Figure 1: Benchmarking Key Criteria

Figure 2 :

 2 Figure 2: Personalization / Flexibility

Figure 3 :

 3 Figure 3: Openness

Figure 4 :

 4 Figure 4: Interactiveness

Figure 5 :

 5 Figure 5: Clear learning outcomes

Figure 6 :

 6 Figure 6: Comprehensive content

Figure 7 :

 7 Figure 7: Standardized structure


Romain Tavenard
email: romain.tavenard@idiap.ch

Remi Emonet
email: remi.emonet@idiap.ch

Jean-Marc Odobez
email: odobez@idiap.ch

TIME-SENSITIVE TOPIC MODELS FOR ACTION RECOGNITION IN VIDEOS

In this paper, we postulate that temporal information is important for action recognition in videos. Keeping temporal information, videos are represented as word×time documents. We propose to use timesensitive probabilistic topic models and we extend them for the context of supervised learning. Our time-sensitive approach is compared to both PLSA and Bag-of-Words. Our approach is shown to both capture semantics from data and yield classification performance comparable to other methods, outperforming them when the amount of training data is low.

INTRODUCTION

Action recognition is key for many tasks such as automatic annotation of videos, improved human-computer interaction and guidance in monitoring public spaces. As the amount of available videos from different sources (from raw personal videos to more professional content) has dramatically increased in the last few years, new propositions are needed to organize this new data.

Many recent state-of-the-art techniques for action recognition in naturalistic and unconstrained video documents such as movies or broadcast data rely on Bag-of-Word (BoW) representations built from quantized spatio-temporal descriptors extracted at Spatio-Temporal interest points (STIP) or on a dense grid and collected over long video segments [START_REF] Laptev | Learning realistic human actions from movies[END_REF][START_REF] Carlos Niebles | Unsupervised learning of human action categories using spatialtemporal words[END_REF][START_REF] Marszalek | Actions in context[END_REF][START_REF] Niebles | Modeling temporal structure of decomposable motion segments for activity classification[END_REF]. Such methods, however, often suffer from two severe and related drawbacks:

• the time information is often discarded, although actions are characterized by strong temporal components; • activities within the same video segments are mixed in such BoW representation, which can negatively affect recognition algorithms that are based on these. To address these issues and enhance action recognition performance, we investigate the use novel principled probabilistic methods (called topic models) for capturing the temporal relationships between characteristic sub-units of a given action. The principle is illustrated in Fig. 1. A video clip (on top) is represented as a STIP word×time document. The idea is that when a person performs an action, it leaves a temporal trace in the document, where the trace is formed by a set of characteristic words occurring at a given time after the start of the action. In the Figure, such a trace for a hand-clapping sequence is highlighted with color words Importantly, note that other words (e.g., the ones generated by other activities in the scene) can simultaneously occur.

The aim is thus, from training video clips/documents, to automatically recover the relevant temporal patterns (or motifs, represented as probability tables, see right of Fig. 1) associated with an action, and further automatically identify their occurrences in test sequences. To this end, we leverage on recent work that automatically discover temporal motifs from word×time documents [START_REF] Emonet | Extracting and locating temporal motifs in video scenes using a hierarchical non parametric bayesian model[END_REF] in an Fig. 1. Schematic view of our approach. Videos are seen as word×time tables and extracted motifs aim at capturing the temporal order of visual words inside actions (see text for more details). unsupervised fashion. Applied to large volume of video-surveillance data, such a method has shown to capture not only the co-occurrence between words but also the order in which they occur.

In this context, our main contributions is to investigate the video action recognition task from STIP word, by automatically identifying meaningful and interleaved temporal patterns with temporal support longer than those of STIP, and addressing the above-mentioned challenges. Furthermore, we extend the model of [START_REF] Emonet | Extracting and locating temporal motifs in video scenes using a hierarchical non parametric bayesian model[END_REF] to learn motifs in a supervised framework. As such, through the use of supervised time-sensitive topic models, our work proposes an alternative to recent pieces of work that make use of temporal information to achieve this task [START_REF] Niebles | Modeling temporal structure of decomposable motion segments for activity classification[END_REF]. Note as well that contrary to state-based temporal models such as HMMs or CRFs, our approach can deal with interleaved activities as well as with activities that are made of several simultaneous action sub-units.

We show that our method achieves very competitive classification performance, especially when only little training data is available. In addition, we show that it also extracts nice semantic patterns from the data and models well action primitives.

This paper is organized as follows. Section 2 reviews related works. Section 3 presents the basics of the topic model proposed in [START_REF] Emonet | Extracting and locating temporal motifs in video scenes using a hierarchical non parametric bayesian model[END_REF]. It is extended for supervised action recognition from video, as exposed in Section 4. Experiments are shown in Section 5.

PREVIOUS WORK

In this paper, we are interested in temporal activity modeling and action recognition. We are particularly interested in the case of action recognition and mining in videos but the relevant work cover more than these two.

Action Recognition in Videos

Moeslund et al. [START_REF] Moeslund | A survey of advances in vision-based human motion capture and analysis[END_REF] suggest to divide the task of vision-based action classification into three levels of abstraction. The first level is referred to as action primitive and corresponds to an atomic movement. Based on action primitives, actions can be derived that are coherent sequences of action primitives. Finally, activities are defined as larger scale events that depend on the context. Authors illustrate these concepts in the case of a tennis match where "forehand", "backhand" and "run left" are examples of action primitives. An action is then the set of action primitives needed to return a ball and the activity is "playing tennis".

According to [START_REF] Poppe | A survey on vision-based human action recognition[END_REF], two classes of features can be used for action classification. On the one hand, global features can be computed on regions of interest (ROI) obtained from foreground subtraction or tracking techniques [START_REF] Yao | Action recognition with exemplar based 2.5d graph matching[END_REF]. On the other hand, local features can be extracted on a dense grid [START_REF] Wang | Evaluation of local spatiotemporal features for action recognition[END_REF][START_REF] Wang | Action recognition by dense trajectories[END_REF] or computed around spatio-temporal interest points (STIP) [START_REF] Laptev | Space-time interest points[END_REF]. Classification can be performed on these descriptors directly or after summarizing them into a new single feature, using a Bag-of-Word (BoW) approach [START_REF] Marszalek | Actions in context[END_REF]. Usually, large margin methods like Support Vector Machines (SVM) are used for classification. These approaches lead to very competitive classification results, though they do not extract strong semantics from the data.

However, these techniques use no or very little temporal knowledge, which can be improved by using temporal state models such as Hidden Markov Models (HMM) [START_REF] Yamato | Recognizing human action in time-sequential images using hidden markov model[END_REF] or Conditional Random Fields (CRF) [START_REF] Sminchisescu | Conditional models for contextual human motion recognition[END_REF]. Markov models have been used to capture temporal information but unfortunately they usually use global features and rely on the assumption that there is a single object in the scene performing a single action. Niebles et al. [START_REF] Niebles | Modeling temporal structure of decomposable motion segments for activity classification[END_REF] have derived a temporal formulation of part-based models introduced in [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF] for action recognition. An open challenge is to both model temporal information and handle mixture of actions.

Topic Models for Activity Mining in Videos

The task of activity mining (finding recurrent meaningful activities) in video data has attracted a lot of interest, particularly in the domain of video surveillance. In many cases, it relies on the extraction of streams of features from a camera, and involves the modeling of the temporal evolution and interactions of these features streams to infer some activity category.

Recently, the design of probabilistic Bayesian models called topic models has become a relevant research direction to discover recurrent patterns in sensor data. These models originate from the text processing community. Topic models such as Probabilistic Latent Semantic Analysis (PLSA) [START_REF] Hofmann | Unsupervised Learning by Probabilistic Latent Semantic Analysis[END_REF] or Latent Dirichlet Allocation (LDA) [START_REF] Blei | Latent dirichlet allocation[END_REF] build on top of BoW. They were introduced to discover the dominant and semantically meaningful topics in large data collections through the co-occurrence analysis of words and allow to handle synonymy and polysemy of words. They have been used in various forms to discover human activities from sport [START_REF] Carlos Niebles | Unsupervised learning of human action categories using spatialtemporal words[END_REF], surveillance videos [START_REF] Wang | Unsupervised activity perception in crowded and complicated scenes using hierarchical bayesian models[END_REF], accelerometers [START_REF] Huynh | Discovery of activity patterns using topic models[END_REF], or cell phone GPS [START_REF] Farrahi | What did you do today?: discovering daily routines from large-scale mobile data[END_REF]. Some attempts have been made to add supervision to these models in the field of text classification [START_REF] Lacoste-Julien | DiscLDA: Discriminative learning for dimensionality reduction and classification[END_REF][START_REF] Blei | Supervised topic models[END_REF].

While initially designed to handle static data, the inclusion of temporal information at different levels of the modeling has become an important research area [START_REF] Blei | Dynamic topic models[END_REF][START_REF] Wang | Topical ngrams: Phrase and topic discovery, with an application to information retrieval[END_REF]. For instance [START_REF] Wang | Topical ngrams: Phrase and topic discovery, with an application to information retrieval[END_REF] proposed to model topics on n-gram words, while dynamic topic models [START_REF] Blei | Dynamic topic models[END_REF] capture the evolution of topics in a sequentially organized corpus of documents. Attempts to model temporal information have been made: [START_REF] Hospedales | A markov clustering topic model for mining behavior in video[END_REF] introduces a temporal model on scene-level behaviors, and [START_REF] Faruquie | Time based activity inference using latent dirichlet allocation[END_REF] models each topic as distribution on feature×time words, but under the strong assumption of temporally aligned clips. Still, overall the temporal modeling and segmentation of activities using topic models was seldom addressed until recently.

Recent evolutions of topics models [START_REF] Varadarajan | Probabilistic latent sequential motifs: Discovering temporal activity patterns in video scenes[END_REF][START_REF] Li | Discovering multi-camera behaviour correlations for on-the-fly global activity prediction and anomaly detection[END_REF] integrate temporal information within the topics without enriching an exponential growth of the vocabulary as with n-grams. [START_REF] Varadarajan | Probabilistic latent sequential motifs: Discovering temporal activity patterns in video scenes[END_REF] models topics as temporal patterns called "motifs" and can be seen as a probabilistic version of the methods presented in previous section. In [START_REF] Varadarajan | Probabilistic latent sequential motifs: Discovering temporal activity patterns in video scenes[END_REF], the method models and automatically finds both what the recurrent motifs (topics) are and when they occur in each of the documents from the learning set. These approaches have been successfully applied to find recurrent activities in traffic videos and surveillance videos, for which simple features are used, such as quantized optical flow.

Topic models such as PLSA or LDA naturally handle mixtures but are seldom used for the action classification. This is probably due to the apparent mismatch between the unsupervised nature of topic models and the supervised nature of the classification task. They are used in [START_REF] Carlos Niebles | Unsupervised learning of human action categories using spatialtemporal words[END_REF] with success and allow to properly handle mixed activities. Note however that in [START_REF] Carlos Niebles | Unsupervised learning of human action categories using spatialtemporal words[END_REF], the approach is fully unsupervised and hence performs action clustering rather than action recognition. Finally, in this approach, temporal information is not modeled. This restriction is acceptable as long as the actions are relatively short but becomes more problematic for longer actions.

To summarize this related work review, BoW approaches have shown very competitive results in the field of action recognition, though allowing little semantic analysis. Topic models, that would allow this kind of analysis as it has been shown in other domains, have not been much investigated for this application up to now. Moreover, to the best of our knowledge, supervised time sensitive topic models have not been investigated at all for action recognition up to now.

HIERARCHICAL DIRICHLET LATENT SEQUENTIAL MOTIFS (HDLSM)

In this paper, we build upon the HDLSM topic model that was first introduced in [START_REF] Emonet | Extracting and locating temporal motifs in video scenes using a hierarchical non parametric bayesian model[END_REF]. This generative model relies on the extraction of motifs that encapsulate the temporal information of the data. It is able to automatically find both the underlying number of motifs needed to model a given set of documents and the number of motif occurrences in each document (which includes their temporal locations), as shown in Figure 2a. In this section, we will present a brief overview of the model and its inference process, as this is key for our application.

Model

The HDLSM model takes as input a set of temporal documents. Each temporal document is represented as a table of counts that informs, for each pair (w, t), about the amount of presence of word w at time instant t. HDLSM generative process is globally as follows:

• Generate a list of motifs, each motif Φ k being a 2D probability map indicating how likely it is that word w occurs at relative time rt after the beginning of the motif.

• For each document j, generate a list of occurrences, each occurrence having a starting time ost and a associated motif k.

• For each observation i in document j:

-Draw an occurrence from the list, -Draw (w, rt) from the associated motif, -Generate the observation as (w, ost + rt).

The advantage of such probabilistic generative models is that we can reverse the process and derive algorithm to learn all the model parameters from observed data.

Joint Inference of Motifs and Occurrences

A temporal document can be seen as a list of pairs (wji, atji) where the word wji appears at time atji in document j, forming its i th observation. Moreover, motifs are represented as probabilistic maps, denoted as Φ. Each map is drawn from H, that is defined as a Dirichlet. This models makes intensive use of Dirichlet Processes (DP) to model the possibly infinite number of motifs and occurrences. The global distributions over motifs βM (with concentration parameter γ) and Uj are used to associate motif indices kjo and starting times ostjo to each occurrence, while the document specific distribution βjo (with concentration parameter α) is used to sample the occurrence oji associated to each observation. Then, knowing oji and all occurrences, it is straight-forward to deduce the motif zji and starting time stji associated to an observation.

To learn the parameters of the model, a Gibbs sampling is applied, in which it is sufficient to re-sample oji for each observation and kjo and ostjo for each occurrence. Other variables are either integrated out or deduced, when a deterministic relation holds.

Inference on test documents

Let us assume that one has already learned a set of motifs that he knows to be well-adapted to the data he is considering. Then, given a new temporal document, fitting this set of motifs to the document can be done by sampling the occurrences alone. At each iteration, the algorithm will update the set of occurrences, their starting times and associated motifs, keeping the motifs (probability maps, Φ) unchanged. At the output of this process, one gets a set of occurrences that enable reconstruction of the temporal document using the fixed motif set.

SUPERVISED HDLSM FOR ACTION RECOGNITION IN VIDEOS

In this section, we present our supervised HDLSM model that we use for action recognition. We will detail the whole process, from video description to actual action recognition, including learning the model presented in Figure 2c.

Word×time document generation

In order to apply HDLSM model to our problem, we first need to turn video sequences into word×time documents that store, for each word at each time instant, its amount of presence in the video. To do so, we start by computing local features at salient points in the 2D+t domain, as using interest point detectors has shown to achieve better performance on the datasets we use than dense sampling [START_REF] Wang | Evaluation of local spatiotemporal features for action recognition[END_REF]. This is done following the method of [START_REF] Laptev | Learning realistic human actions from movies[END_REF], which computes histograms of optical flow (HoF) in cuboids around interest points extracted using a space-time extension of the Harris operator. Once these features are computed, they can be quantized using a codebook of visual words, which is learned on a subset of feature points using k-means algorithm. The quantization step then consists in assigning to a given feature point the quantization index corresponding to its closest centroid (in terms of Euclidean distance). In our experiments, we used k = 4, 000 as in [START_REF] Laptev | Learning realistic human actions from movies[END_REF]. Finally, a temporal document similar to the one presented in Figure 2a is built that stores at position (i, t) the number of features that were quantized into quantization index i at time t.

Learning temporal motifs using HDLSM

Following the work from [START_REF] Krithara | Semisupervised document classification with a mislabeling error model[END_REF], supervision is added to our model by adding a step to our generative process that consists in generating a class label y for each word with probability p(y|z). In our case, the distribution of p(y|z) values is set to a delta function, which is equivalent to learning motifs in a per-class fashion, using the method presented in Section 3.2. This results in as many sets of motifs as action classes. Note that the number of motifs extracted may vary from one class to another. However, association of motifs to classes (i.e. p(y|z) distributions) are stored as they will be key for the recognition step described in the following.

Action recognition using learned motifs

When a new video comes in, its corresponding temporal document is generated in the exact same way as explained above. Then, inference is performed to find out, given the fixed set of motifs, what occurrences of motifs explain best the given temporal document d. This inference step gives us a probability map p(z|d) on which the decision can be performed as a voting scheme:

C(d) = arg max C i ∈{C 1 ,...,C N } z p(y = Ci|z)p(z|d). (1)

EXPERIMENTAL VALIDATION

Experimental details

Datasets: We evaluate our approach on KTH [START_REF] Schuldt | Recognizing human actions: A local SVM approach[END_REF] and Weizmann [START_REF] Gorelick | Actions as space-time shapes[END_REF] datasets. KTH dataset is made of short video clips from 25 persons performing 6 actions and captured from 4 view points. Weizmann one contains 10 actions performed by 9 persons. Evaluation protocol: We follow the standard experimental protocols. For KTH, the 25 persons are split in a training, validation, and Fig. 3. The five strongest occurrences for motifs associated to "HandClapping" (row 1), "HandWaving" (row 2) and "Running" (row 3). For each occurrence, we show the image in the middle of the temporal segment associated to the occurrence, as well as the STIP features contributing to the occurrence in that frame. Note that almost all these occurrences happen in video clips from the right action category associated with the motif, the only exception being for class "HandClapping" for which one occurrence from class "Hand-Waving" (marked with red border) is retrieved.

test sets [START_REF] Schuldt | Recognizing human actions: A local svm approach[END_REF]. Given our algorithms where no parameter tuning is necessary, we used both the training and validation sets for learning the motifs and the SVM in the baseline (as done in [START_REF] Laptev | Learning realistic human actions from movies[END_REF]), except for Figure 5 that shows the results evolution as a function of the number of people used for training. All classification accuracy results are computed on the test set. In the Weizmann dataset we use a standard Leave-One-Person-Out cross-validation method. For all methods, the same parameters are used for both datasets. In particular, the temporal length of an HDLSM motif is set to be 25 frames.

Baselines: We compare ourselves to a traditional BoW approach [START_REF] Laptev | Learning realistic human actions from movies[END_REF] that uses a χ 2 kernel SVM classifier for classification decision. From the class of methods that do not track people and that rely on STIP features, it is still one of the best performing methods. We also present results using the PLSA approach, since it is a model that also identify topics through co-occurrence analysis, but discards temporal information. This should highlight the actual benefit of using a time-sensitive model like HDLSM. To provide a fair comparison, the PLSA document are built using the same temporal support as HDLSM motif. Moreover, since PLSA does not model selection, the number of topics was set to the same value as the number of motifs in the HDLSM approach. In the experiments presented here, one motif is learned for each class.

Results

Qualitative results. One possibility to understand the semantics captured by our motifs is to show their strongest occurrences (as measured by the number of associated words) on the test set. This is illustrated in Figure 3 on the KTH dataset for motifs from 3 different actions by displaying one image of each occurrence. As can be seen, for a given motif, images are time-aligned (i.e. they are located at the same moment in the corresponding action), demonstrating our model's ability to grasp the typical temporal structure of actions.

Quantitative results. Results are presented in Table 1. They show that our approach is slightly better than PLSA, showing the interest of the temporal information when forming topics. Moreover, the performances of our method are very close to those of the BoW approach on the KTH dataset, while being much better on the Weizmann one. This is due to the ability of our method to deal with small training sets. This is further demonstrated in Figure 5 that shows that even on the KTH dataset, when small training sets are considered, our method outperforms the baseline. Confusion matrices obtained for our method on both datasets are presented in Figure 4. On the KTH dataset, most of the confusion comes from the difficult distinction between "Running" and "Jogging" classes. On the Weizmann one, the class that leads to poorest results is the "Skip" one, which is due to the complexity of this class. Note however that the decomposition of "Skip" action into "Run" and "Jump", that is observed here, makes sense.

CONCLUSION

In this paper, we presented the use of supervised time sensitive topic models for action recognition in videos. We use existing time-sensitive unsupervised models and extend them by adding supervised classification capabilities. We showed through experiments that our method is able to both extract semantic motifs from the data and outperform standard approaches of the field when little training data is available.

Fig. 2 .

 2 Fig. 2. HDLSM model. (a) presents a schematic view of how the model is used while (b) details the model with developed Dirichlet processes (using stick-breaking convention) and (c) presents its supervised counterpart.

Fig. 5 .

 5 Fig. 5. Classification performance and training set size. Results reported here are computed using 1 to 8 persons for training on KTH.

Table 1 .

 1 Pju mp Run Ski p Wa ve1Walk Jum p Ben d Wa ve2Side Jac k Fig. 4. HDLSM confusion matrices for both datasets. Comparative results in terms of classification accuracy. KTH dataset is used with large training set.

	Walking	0.99		0.01		Pjump	1.00
						Run	0.80 0.10	0.10
	Boxing	0.99		0.01		Skip	0.30 0.50	0.10	0.10
	Running	0.06	0.50	0.44		Wave1 Walk	0.67	1.00	0.11 0.22
	Jogging	0.08	0.09	0.83		Jump	0.11 0.22	0.11 0.56
						Bend			1.00
	HandClapping	0.06		0.94		Wave2			1.00
	HandWaving	0.02		0.05	0.93	Side	0.11	0.11	0.78
		Wa lkin g Box ing Run nin g Jog gin g Han dCl app ing Han dW avi ng	Jack			1.00
		(a) KTH			(b) Weizmann
	Dataset		BoW+SVM		PLSA	HDLSM
		KTH		90.50%		88.30%	89.46%
	Weizmann		73.11%		77.41%	82.79%

Acknowledgements

This work was partially funded by SNSF (Swiss National Science Foundation) through the PROMOVAR project.


J M Aguiar-Hualde

Y Magnin

H Amara

C Bichara

Probing the role of carbon solubility in transition metal catalyzing Single-Walled Carbon Nanotubes growth

Metal catalysts supporting the growth of Single Wall Carbon Nanotubes display di↵erent carbon solubilities and chemical reactivities. In order to specifically assess the role of carbon solubility, we take advantage of the physical transparency of a tight binding model established for Ni-C alloys, to develop metal carbon models where all properties, except carbon solubility, are similar. These models are used to analyze carbon incorporation mechanisms, modifications of metal / carbon wall interfacial properties induced thereby, and the associated nanotube growth mechanisms. Fine tuning carbon solubility is shown to be essential to support sustainable growth, preventing growth termination by either nanoparticle encapsulation or detachment.

I. INTRODUCTION

Carbon nanostructures (graphene or nanotube) can be grown by chemical vapor deposition (CVD) techniques on various transition metals 1,2 and alloys [3][4][5] . In this process, a carbon bearing molecular precursor is decomposed at the surface of a catalyst to deliver carbon and feed the carbon network 1,6,7 . In case of single-wall carbon nanotubes (SWNTs), many applications require to control their synthesis at the nanoscale level to take advantage of their chirality-dependent properties. In this context, controlling the growth requires a detailed understanding of the role of the catalyst. However, the complex behavior of catalyst nanoparticles (NP) exposed to reactive carbon makes it di cult to grow tubes with defined chirality.

E cient catalysts to grow SWNTs lie in the 1-10 nm diameter range and are reported to display non-zero, but limited carbon solubility in the bulk solid 8 . This is sometimes illustrated in the form of a so-called "volcano plot" showing that popular catalysts (Fe, Co, Ni) display a large enough a nity for carbon, to adsorb carbon precursor molecules in the surface layers and possibly dissolve some carbon inside the NP. Indeed, this carbon content favors the dewetting of the nanoparticle with respect to the sp 2 carbon wall, a necessary property to limit catalyst encapsulation and deactivation [9][10][11] . Despite such progresses, a notable lack of understanding of the roles played by carbon solubility in the catalyst during the SWNT growth process plagues our ability to optimize synthesis conditions and ultimately control the structure of the tubes.

In transition metals, C occupies interstitial sites due to its relatively small atomic size [START_REF] Toth | Transition Metal Carbides and Nitrides[END_REF][START_REF] Cottrell | Chemical Bonding in Transition Metal Carbides[END_REF][START_REF] Siegel | [END_REF] leading to narrow domains of stability of solid solutions. The few experimental data found in the literature are devoted to bulk systems and report large discrepancies [15][16][17][18] . From a theoretical point of view, Hu et al. 19 employed first-principles calculations to study the solubility and mobility of B, C, and N interstitials in various transition metals, including Gibbs energy contributions at finite temperature. In the context of catalysis, subsurface interstitial sites have been identified as the most favorable for carbon incorporation on flat surfaces of di↵erent transition metal-carbon systems [20][21][22] . Besides, melting temperatures and carbon solubility limit have been investigated in case of Fe and Ni NPs used as catalysts to grow SWNTs [23][24][25] . Recently, carbon rich phase diagrams of nickel-carbon nanoparticles have been calculated for system sizes up to about 3 nm, highlighting how C atoms can di↵use inside surface layers and induce a partial or complete melting 26 . However, the case of such NPs in contact with tubes, which are much more complex, were not addressed and much remains to be done.

The aim of the present paper is to investigate to which extent growth mechanisms of SWNTs depend on the catalyst carbon solubility, and to check whether modifying this carbon solubility could lead to improved CVD synthesis in terms of yield and selectivity. Metal catalysts usually display di↵erent carbon solubilities and chemical reactivities. In order to specifically assess the role of carbon solubility, we take advantage of the physical transparency of a tight binding model established for Ni-C alloys 27 , to develop metal carbon models where all properties, except carbon solubility, are similar. By computing carbon adsorption isotherms on various catalytic NPs, we first characterize their physical and chemical states in presence of carbon. Since wetting properties plays a major role in the growth mechanisms of SWNTs, we then directly simulate the structure of carbon enriched NPs on a graphene layer at di↵erent compositions. In the last part, we show how carbon solubility acts on the interplay between two mechanisms in competition : NP dewetting vs wall growth.

II. METHODS

To describe the Ni-C system, we have developed a model based on the tight-binding (TB) approximation which provides an e cient tool to calculate carbon and transition-metal interactions 27 . Only s, p electrons of C and d electrons of Ni are taken into account. Local densities of electronic states are calculated using a recursion method, where the first four continued fraction coe cients only are calculated exactly. Applications of this model to the catalytic growth of graphene and carbon tubes have already been presented elsewhere 9,28,29 , showing the relevance and robustness of this model. A further advantage of our TB model is that it can be fairly easily generalized to other metal-carbon systems since we know qualitatively how the di↵erent parameters (transfer integrals, atomic energy levels, etc...) vary with the nature of the metallic element. We therefore take advantage of the physical transparency of the model to identify the parameters controlling carbon solubility.

To understand carbon-metal interactions, it is convenient to study the electronic structure of metal carbides in a simple, and sometimes not physically observed, NaCl structure. Although they do not always exist for some transition metals, they can be studied on the basis of very robust first-principles calculations 30,31 . As reported previously, the shape of the hybridized band does not change too much when varying the element along the transition metals series 27 . The ability of transition metals to combine strongly with carbon stems from the strong covalent bonds formed between the p states of carbon atoms and the valence d states of the metal ones 30,32 . As a result, by simply tuning the energy di↵erence between the carbon atomic p (✏ C p ) and the metal d (✏ M d ) levels, we can change the M-C interaction and hence the carbon solubility in the metal. This is done by keeping all other parameters fixed, meaning that all properties such as melting point, lattice parameters, elastic constants and energy of pure metal and pure C are untouched.

We thus probe only the e↵ect of C solubility by changing the position of the atomic d level which obviously varies with the nature of the element considered. Indeed, ✏ M d decreases when increasing the number of electrons along a transition series (about 1 eV per element) [32][START_REF] Ducastelle | Order and Phase Stability in Alloys[END_REF][START_REF] Pettifor | Bonding and Structure in Molecules and Solids[END_REF] . Since this level is adjustable to some extent, it is useful to see how it is related to the carbon solubility. To quantify E (eV) this e↵ect, let us consider the heat of solution H sol of a C interstitial atom in a crystalline transition metal (M), calculated according to the formula :

H sol = E M +C E M E C , (1)
where E M +C is the total energy of the Metal+ interstitial C system, E M is the energy of the metal without C, and E C is the energy per C atom in graphene. In the FCC lattice, the most likely location for C in octahedral interstitial sites, which is confirmed by DFT calculations [START_REF] Cottrell | Chemical Bonding in Transition Metal Carbides[END_REF][START_REF] Siegel | [END_REF] . For C, we assume the same atomic energy levels (✏ C s = -2.99 eV and ✏ C p = 3.71 eV) as proposed by Xu et al. This energy model is implemented in a Monte Carlo (MC) code using either canonical or Grand Canonical (GC) algorithms with fixed volume, temperature (T), number of metal atoms and C chemical potential (µ C ) [START_REF] Frenkel | Understanding Molecular Simulation[END_REF] . The GC algorithm used consists in a series of Monte Carlo cycles. Each cycle randomly alternates displacement moves for the metal and C atoms, attempts to incorporate C in a previously defined active zone and attempts to remove existing C atoms.

III. CARBON SOLUBILITY IN NANOPARTICLES

Both experimental and theoretical approaches point at the importance of the carbon fraction dissolved in the catalyst during the CVD synthesis of SWNTs 9,10 . It is thus relevant to evaluate its influence on the chemical and physical states of di↵erent NPs, by modifying the carbon solubility in the catalyst, using our models for Ni , Ni and Ni + . GCMC calculations presented here compare adsorption isotherms of carbon on NPs with di↵erent solubilities, sizes and structures. Initially Icosahedral (Ih) with 309 atoms, and FCC, Wul↵ shaped clusters with 201 and 405 atoms are considered (see Fig. 2). These clusters have sizes around 1.8-2.5 nm, close to those used experimentally to grow tubes. Once the equilibrium is reached during GCMC simulations, we record the fraction of C atoms absorbed inside the cluster (x C ) at a given µ C and T to calculate the carbon absorption isotherms for di↵erent particle sizes. Some of the already published data are presented here for the sake of completeness 10,26 . A number of conclusions can be drawn from the inspection of these adsorption isotherms at 1000 K presented in Fig. 2. Beyond a certain µ C threshold, the carbon fraction gradually increases until the carbon solubility limit is reached. This limit corresponds to the carbon fraction beyond which carbon atoms begin to appear on the surface of the NPs. As expected, the maximum solubilities of carbon in low-carbon-solubility metal NPs (Ni ) and high-carbon-solubility (Ni + ) are ⇠ 15% and 30%, respectively. This is reasonable compared to the carbon solubility in normal Ni NPs which lies around 25%. The threshold for the incorporation of the first C atom is also closely related to the nature of the catalyst. It is shifted towards higher (less negative) values, when C solubility in the metal decreases. This is not surprising since incorporating a C atom in a system that displays a lower solubility is more di cult, hence requires higher chemical potential. In addition, for Ni and Ni cases, the relative position of the isotherm of the icosahedral NP tends to shift to larger µ C values as compared to the FCC ones. The maximum di↵erence between the Ih and FCC adsorption thresholds ( µ C ) is obtained for Ni , in which case the di↵erence ( µ C ⇠ 1eV) is quite significant. Indeed, assuming an ideal behavior of the gas phase, the pressure is related to µ C by:

4µ C = k B T ln(p 1 /p 2 )
. Accordingly, a value of 4µ To investigate the atomic structures of the NPs, we need to define a local order parameter S. This can be done using the orientational order parameter introduced by Steinhardt et al [START_REF] Steinhardt | [END_REF] to discriminate between crystalline and disordered (liquid or amorphous) environments for each atom. Then, by averaging over all metallic atoms of the NP, it is possible to assign a global degree of crystallinity S. Using this approach, the calculated phase diagrams of nickel-carbon nanoparticles have shown the presence of a large crystalline core / liquid shell domain, instead of the liquid/solid two-phase domain characteristic of the bulk 26 .

Typical results are presented in Fig. 3a, where the global order parameter S is plotted as a function of µ C for FCC structures containing 405 atoms. S is normalized in such a way that a perfectly crystallized structure has S = 1, while a fully disordered one corresponds to S = 0. These are limiting values and we practically consider structures with S 0.85 as crystalline and those with S  0.35 as amorphous. For Ni + NPs, S is larger than 0.7 corresponding to a mostly solid particle. Increasing µ c induces a transition to a solid core liquid shell in between 0.3< S <0.7 (see Fig. 3b) since C atoms induce a gradual melting of the NPs, that starts on the surface and propagates to the core. At higher µ c , a second transition is observed where the NP completely melts. In case of Ni and Ni , visual inspection, as well as the evolution of the order parameter as a function of µ C indicate that the liquid outer layer grows continuously at the expense of the solid with increasing carbon content. By comparing with Ni + , molten area are smaller since less C atoms can be incorporated close to the surface.

IV. WETTING PROPERTIES OF NANOPARTICLES ON GRAPHENE

From the SWNT synthesis point of view, wetting properties of the catalyst nanoparticles are of fundamental importance to enable the nanotube growth, and, for Ni, Co and Fe catalysts, the fraction of carbon dissolved in the NP appears as a leading factor influencing them 9 . GCMC simulations have shown that the cap lift-o↵ during carbon nanotube nucleation requires the weakening of the cap-catalyst interaction, and that sustained growth is made possible by a gradual dewetting of the NP, to avoid its encapsulation by the growing carbon sp 2 wall. Increased carbon incorporation into the catalyst was shown to facilitate these processes. The next aspect is to understand how far these wetting and interfacial properties of metallic NPs in contact with carbon sp 2 layers can be modified by considering metals with di↵erent carbon solubilities.

Using canonical MC simulations at 1400 K, we investigate the wetting properties of metallic NPs with 405 atoms and C fractions from zero to the solubility limit, deposited on a graphene layer containing 1600 C atoms, using our models with three di↵erent solubilities. First, a visual inspection of the resulting structures in all cases reveals that NPs remain crystalline when no carbon atoms are dissolved inside. Contact angles for pure NPs are always smaller than 90 : such NPs tend to wet the graphene layer. Focusing now on nickel (Ni) and high-carbon-solubility metal (Ni + ), we notice that the metallic NP tends to dewet graphene when increasing the carbon fraction dissolved in it. This is in qualitative agreement with experimental data, obtained by Naidich et al., showing that the contact angle of a macroscopic Ni (and also Co and Fe) drop on graphite increases with C fraction inside it 38 . Interestingly, when this carbon fraction increases a lot, as made possible in nano-sized particles, the contact angle becomes larger until the metallic NP detaches from the graphene layer (see Fig. 4a). In case of Ni NPs, the contact angle remains close to ⇠ 90 whatever the carbon concentration, meaning that no detachment is observed. Their inabilities to dewet is due to the limited carbon content in such NPs (⇠ 15% C), as highlighted by the isotherms presented in Fig. 2.

In addition to the wetting/dewetting tendency, we notice that dissolved carbon atoms are not homogeneously distributed within the NPs (see Fig. 4b). Their distributions are notably altered, with the proportion of C atoms in subsurface sites significantly reduced, compared to the distribution throughout the rest of the NP. As seen in Fig. 4b, no C atoms are present close to the interface with graphene, while carbon remains distributed throughout the rest of the catalyst. This means that dissolved C atoms tend to avoid the graphene layer, while it is well known that subsurface interstitial sites are preferred locations for individual C atoms below a free surface 39 . Such a depletion e↵ect was also observed during graphene growth on Ni (111) 29,40 . By combining MC simulations, DFT-based calculations and in-situ X-ray photoelectron spectroscopy, we could evidence this depletion e↵ect and revealed an interdependency between the carbon distribution close to the catalyst surface and the strength of the graphene-Ni interaction. Epitaxial graphene formation on Ni(111) leads to a depletion of carbon close to the Ni surface 29 .

In the present situation, this e↵ect leads locally to the interaction of graphene with pure NP which depends on the metal-carbon interaction. To test this for our three metal-carbon models, we calculate the binding energy of graphene on a (111) pure metallic surface. Since the lattice parameters of Ni and Ni + are the same as that of Ni, the (111) surfaces of these metals are in almost perfect epitaxy with graphene. For our three models, very small di↵erences (less than 2%) are observed. Adhesion energies remain close to -0.32 eV per carbon atom, a bit larger than the experimental one for Ni 2 . Such values favor the adhesion of the NP on graphene, and a dewetting tendency can only result from the presence of subsurface carbon close to the graphene layer. for a carbon atom located in subsurface (1) or sub-subsurface (2) interstitial site, without (yellow) and with (black) graphene covering a (111) slab of "nickel" with di↵erent C solubilities. Inset: Sketch of epitaxial graphene covered with the interstitial sites indicated.

Comparing our three models, we notice that the depletion of carbon close to graphene is more pronounced for Ni , where two layers of metal are carbon-free, as shown in Fig. 4b. To quantify it, energy di↵erences between an interstitial C atom occupying a subsurface and a sub-subsurface site (4E 1 2 ) in the (111) slab are cal-culated by performing simulated annealing at 0 K. To make the discussion easier, we define subsurface (1) and sub-subsurface (2) interstitial sites as those located respectively between the first and second, and the second and third planes from the surface, both providing a full octahedral environment. Results are presented in Fig. 5. Without graphene coverage, 4E 1 2 remains close to zero. For Ni and Ni subsurface C site is most stable than the sub-subsurface one, while the opposite stands for Ni + . With an epitaxial graphene cover on the metallic surface, sub-subsurface position is always preferred, as in our calculations and experiments on Ni. More interestingly, in case of Ni + , the di↵erence between both situations is really significant (⇠ 2 eV) explaining that the presence of a graphene layer below the NP induces an important depletion of C dissolved close to the surface. We thus understand that the adhesion of the NP on graphene is directly correlated to the distribution of C atoms close to the surface, a carbon depletion promoting stronger adhesion and wetting.

V. APPLICATION : GROWTH OF CARBON NANOTUBES

During CVD, nanotubes grow from a NP that is either supported by a substrate or in contact with the tube only (tip growth or floating catalyst reactor). The decomposition of carbon-bearing precursors takes place at high temperatures (500-1200 C) in a wide pressure range, depending on the precursor's reactivity. This involves complex thermochemical reactions that cannot be correctly described in an full atomistic computer simulation of SWNT growth. However, when focusing on thermodynamic aspects of growth, the important point is that these reactions lead to the presence of carbon atoms, close to the surface of the catalyst, at a given chemical potential 41 . In order to see how SWNT growth mechanisms are influenced by modifications of carbon content inside the NP, we chose to compare Ni and Ni catalysts. We start by fixing short nanotube butts with 173 C atoms on pure NPs with 120 metal atoms. Tubes are chosen with diameters in the 1.2 nm range and di↵erent chiralities. We used them as starting configurations for a series of GCMC simulations at di↵erent temperatures with µ C conditions chosen to trigger tube growth. To get a better insight into the growth mechanisms, MC simulations are visualized by unrolling the systems along the tube axis 42 . In this way, microscopic mechanisms at the atomic scale can be revealed. with carbon, these sp carbon chains interact weakly with the underlying surface. As a result, chains tend to detach from the surface, like a garland, leading to the formation of somewhat defective structures, as seen in Fig. 6a. In addition, the NP tends to escape from the tube, because of the dewetting tendency induced by the carbon dissolved in the NP, while the growing walls tend to catch it back. This sometimes leads to a complete detachment for some particular (µ C , T) conditions. Let us now consider NPs with a reduced C solubility (Ni ). In several cases, we notice the formation of tubes containing few defects (see Fig. 6b). Remarkably, the growth of three rows of defect-free hexagonal rings has been obtained, corresponding to a 1.2 nm extension of the SWNT. Here, incoming C atoms form dimers and short chains in stronger interaction with the surface of the Ni NP. Because they are more strongly bound to the surface, these short chains quickly form cycles, pentagons first, that readily transform into hexagons, leading to graphene-like walls with less defects. Interestingly, we have identified subsurface-carbon depleted zones, as particular areas where defect-free graphene is formed (see Fig. 6b). Contrary to the previous case, unsuccessful growth attempts are often caused by a too strong adhesion of the growing wall on the NP, leading to particle encapsulation.

Successfully growing defectless tube sections is important to discuss chirality control at the atomic scale. Until now, whether the method employed to study nucleationgrowth mechanism of SWNT is empirical [43][44][45][46] or semiempirical 28,47 , final configurations are plagued by a high concentration of atomic-scale defects, i.e., nonhexagonal rings, adatoms, or vacancies. We show here that fine tuning (µ C , T) conditions, adapted to the catalyst used, can lead to highly crystalline tube structures that make it possible to analyze the atomistic growth mechanisms and their possible connection to chiral selectivity.

VI. DISCUSSION AND CONCLUSION

Sustainable growth conditions, and two possible scenarios for growth termination discussed above are sketched in Fig. 7. Two competing phenomena can be identified, namely NP dewetting and wall growth. Thermodynamic analysis enables to identify the correct driving force to incorporate C atoms in the carbon sp 2 wall, and in the catalyst, thus modifying its interfacial properties. In the case of Ni-like catalysts discussed above, a proper choice of a catalyst with the right carbon solubility, that would be in between Ni and Ni in the present instance, would lead to a right balance between wall growth and NP dewetting, and hence sustainable growth. In real experiments, carbon solubility could be tuned using bimetallic alloys, forming a real nanoalloy, as opposed to phase separated NPs, such as Ni

x Fe

(1 x) 48 . Another way to act on it might be the use of a surfactant, such as sulfur, that can be introduced in the system with the gaseous phase, via thiophene molecules, as done by Sundaram et al. 49 .

For low carbon fractions, while carbon wall dewetting is a necessary step for SWNT nucleation and prolongation, the strong adhesion energy favors the adhesion and wetting of the carbon sp 2 wall on the surface of the nanoparticle, thus causing the catalyst particle deactivation. In contrast, high-carbon-solubility metal nanoparticles have a weak adhesion with tube wall, resulting in the detachment of the catalyst from the tube that causes the growth to stop. Between these two extreme situations, e cient growth can be observed when both NP dewet-FIG. 7. Sketch of SWNT growth. E cient growth is observed when wall growth and NP dewetting proceed in a sustainable way. Particles containing a low C fraction can be easily encapsulated, thus favoring growth deactivation. On the contrary, carbon saturated NPs interact less strongly with the growing tube and are thus more prone to detachment.

ting and wall growth smoothly proceed together in a sustainable way. Beyond the optimization of CVD process parameteres, such as temperature and feedstock pres-sure, our present calculations suggest that stable growth conditions can also be searched for by tuning the carbon solubility in the catalyst NP. Recently, we have confirmed this mechanism by demonstrating that low carbon fractions in the catalyst, resulting from the use of CH 4 feedstock, lead to tangential growth, where the metallic nanoparticle wets the tube inner wall and can be easily encapsulated by the graphitic layers, facilitating the deactivation of the catalyst and the termination of SWNT growth 11 . In such a situations, shorter tubes were found to be formed. On the contrary, using CO as a feedstock, catalyst nanoparticles with a high carbon fraction nucleate SWNTs by perpendicular mode and can keep their activity for much longer time, accounting for the formation of long SWCNTs. This o↵ers new possibilities to tune the catalytic activities of metal NPs by improving its abilities to dissolve carbon and contributes to a better understanding of SWNT growth mechanisms, paving the way to a rational search for better catalysts for controlled synthesis of SWNTs.

FIG. 1 .

 1 FIG. 1. Schematic representation of the atomic levels used in our tight-binding model.

  [START_REF] Xu | [END_REF] and modify the pd hybridization through the variation of the metal d level. All results are presented in Figure1and Table I. The p d energy di↵erence (✏ C p ✏ M d ) for Ni in our model is equal to 4.21 eV. This results in a heat of solution of one C in Ni H sol = +0.47 eV, in agreement with the +0.43 eV value found in the literature 14,19 . To decrease C solubility, the contribution of the pd hybridization has to be reduced. This can be done by shifting the relative position of the p (C) and d (M) atomic levels by 1.50 eV (✏ C p ✏ M d =4.21 eV) leading to a H sol around +0.87 eV. We also consider another case with a higher solubility where ✏ C p ✏ M d =2.71 eV, yielding H sol = +0.33 eV. For the sake of simplicity, let us denote Ni , Ni and Ni + , metals with increasing C solubility respectively. At this stage, we have at our disposal a model based on the tight-binding approximation to describe transition metal-carbides with three di↵erent carbon solubilities.

FIG. 2 .

 2 FIG. 2. (Left) Carbon adsorption isotherms calculated at T = 1000K on the basis of GCMC simulations for NPs (with 201, 309 and 405 atoms) with high (top) and low (bottom) carbon solubility. (Right) Schematic representation of Wul↵ and Ih structures where the di↵erent facets are presented.The NP with 309 atoms is Ih when pure, the others are FCC, with their Wul↵ equilibrium shape.

C

  around 1.0 eV per atom at 1000 K corresponds to ⇠ 5 orders of magnitude pressure di↵erence for Ih NP. This is clearly an e↵ect of the structure of the NP. Ih NPs display only (111) facets while Wul↵ shaped NPs also display open (100) facets which are the most favorable surface adsorption sites for C 26 . As a result, icosahedral NPs, where such sites are not present, require larger µ C to stabilize adsorbed carbon. Moreover, this shift of the Ih NPs isotherms is clearly more pronounced for Ni NPs, while it disappears for NPs with high solubility.

FIG. 3 .

 3 FIG. 3. (a) Top : C adsoprtion isotherms as a function of µc. Bottom : average values of the order parameter as a function of µc for a NP initially Wul↵ shaped with 405 atoms. (b) Snapshot of characteristic configurations for metal-C NPs (Ni green, Ni beige and Ni + , blue atoms) surrounded by a disordered shell (orange atoms). Black balls correspond to C atoms.

FIG. 4 .

 4 FIG. 4. Probing the wetting of carbon-containing metal nanoparticles deposited on graphene (a) Equilibrium structures corresponding to C-saturated NPs. Ni NP (left) shows a contact angle slightly larger than 90 , while Ni + NP (right) is fully dewetting the substrate. (b) At intermediate concentration, we observe a carbon depletion close to the graphene layer. This absence of carbon dissolved close to the contact is more pronounced for Ni (left), with two pure metal layers than with Ni + (right). Dashed lines delimits the C-depleted metal zone. Ni atoms are green, Ni + atoms are blue, C atoms inside the NP are red.

FIG. 5 .

 5 FIG.5. Di↵erences in carbon dissolution energies (4E1 2), for a carbon atom located in subsurface (1) or sub-subsurface (2) interstitial site, without (yellow) and with (black) graphene covering a (111) slab of "nickel" with di↵erent C solubilities. Inset: Sketch of epitaxial graphene covered with the interstitial sites indicated.

Fig. 6 FIG. 6 .

 66 FIG. 6. Snapshots of atomic configurations during the growth of a tube butt on a NP (C atoms are in black, added C atoms are in orange and some C atoms in subsurface positions are indicated with arrows). Arrows indicate the presence of C atoms in subsurface position. (a) During SWNT growth from Ni (beige) NP, longer chains, bound on one end and prone to float away from the surface are observed. This leads to more defective sp 2 structures. (b) From Ni nanoparticle, smaller chains remain more strongly bound to the NP surface. Because of this, defect-free sp 2 network is more easily formed.

TABLE I .

 I Values of H

		✏ M d (eV)	H	sol (eV/at)
	Ni + (high solubility)	+1.00	+0.33
	Ni	-0.50	+0.47
	Ni (low solubility)	-2.00	+0.87

sol for three di↵erent solubilities.

ACKNOWLEDGMENTS

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 604472 (IRENA project) and French Research Funding Agency under grant No. ANR-13-BS10-0015-01 (SYNAPSE project). Dr F. Ducastelle is acknowledged for many fruitful discussions.