Ksenia Smirnova
email: ksenia.smirnova@skolkovotech.ru

Alessandro Golkar
email: a.golkar@skoltech.ru

Rob Vingerhoeds
email: rob.vingerhoeds@isae-supaero.fr

A game-theoretic framework for concurrent technology roadmap planning using best-response techniques

Keywords: technology roadmapping, technology planning, game theory, best response

Technology roadmapping provides a tool for technology planning and selecting what to pursue in what timeframes. In this paper, a game-theoretic framework for technology roadmap planning is proposed to address the enumeration, selection and evaluation of possible evolution paths for technology roadmapping characterized by an iterative and competitive technology development process between companies within one tradespace. More specifically, the framework including companies as game players demonstrates the most favorable reactions to each other's technology development by approximated best response functions. Next, the selection process of optimal development paths is carried out to evaluate the possible payoffs using backward induction. Finally, a case is studied to demonstrate the feasibility of the proposed approach.

I. INTRODUCTION

Nowadays, companies are confronting an increasing competition challenge [1]. Technology roadmapping is used to provide guidance to organizations in coping with growing competitive environments -it identifies company's critical needs, and helps to select the appropriate technology alternatives. Technology planning is a critical activity in industries with rapid technology evolution such as information and telecommunication technologies, as well as manufacturing, aerospace, and transportation, among others.

In this paper, we are proposing a novel game-theoretic framework for technology planning and roadmapping. We consider a group of competitors as a group of players where each player has a set of evolution strategies with several technology alternatives. Both players are considered to be rational and willing to embrace the strategy that maximizes its payoffs. The following framework makes the process of technology planning more strategically oriented in the terms of competing environment by taking into consideration the development of the other player.

Both players are willing to know the future possible design strategies at the tradespace, which are allocated in their preferable direction of developing the characteristics. The players evaluate the design strategies suggested by the framework and choose the most promising and realistic as a field for the company's Research & Development (R&D).

Various quantitative methods on technology planning and roadmapping were summarized by Heidenberger and Stummer [2]. They classified methods in several categories: benefit measurement methods; mathematical programming; decision and game theory approaches; simulation models, heuristic methods; cognitive emulation approaches. In the terms of increasing competitive environment game theory approach comes to the central stage.

Game theory is the study of rational decision-making and helps to understand how strategic interactions affect rational decisions of individual players or companies in a competitive and uncertain environment if each player aims to get the best payoff [3]. The game-theoretic approach takes into consideration company's competitive environment that might be uncertain.

II. BACKGROUND AND RELATED WORK

This section introduces key concepts of game theory, game-theoretic approaches and its application in the design of complex engineering systems.

A. Game theory and Nash equilibrium

A formal model in game theory consists of players, a set of their strategies and payoffs from each strategy combination. One of the main concepts is a nash equilibrium (NE) which represents a combination of decisions where no player has an incentive to deviate from his decision [4].

A strategy x * is NE from the set of strategies Si for player i with payoff function u(x) if:

Si: ui (xi * , x-i * ) ui (xi, x-i * ) (1)
The condition (1) means that each player i, in playing a strategy xi * , is playing the best response to the other's strategy choice.

B. Best-response dynamics

In best-response (BR) dynamics, each player chooses his best response to the current actions of the other player.

The best response (BR) of player i, Bi (x-i ), is:

Bi (x-i) arg max ui (xi, x-i * ) (2)
Then the equivalent characterization from the condition (2): a strategy xi * is a NE iff xi * Bi (x-i) for all i

(3)

A necessary condition for BR dynamics is convergence to NE from an initial strategy profile. It means the existence of a path induced by best-response reaction sets that connects the initial start strategy to NE [4]. Players can construct their path by building BR functions using their opponents' strategies estimation from the past games [5]. BR functions can be represented as linear or non-linear functions with one or more NE with axis of the variables [6].

C. Backward induction

Backward induction (BI) is a general concept for sequential games of perfect information. The method starts from the analysis of the latest strategies of the first player and proceeds to the search of a subgame perfect nash equilibrium (SPE). Using this information the second player can determine which strategy to choose at the second to last stage. The process continues backward until reaching the first stage of the game. The set of SPE of all game stages is a subset of NE for the whole game.

D. Game-theoretic approaches

Game-theoretic approaches are used in engineering systems design for multi-objective design and multi-agent planning problems. The theoretical and mathematical basis of games is used to abstract the processes required to design a complex system.

The model of multiobjective design has been used to analyze the convergence characteristics of the design process, and the quality of equilibrium solutions in the situation of decentralized designers [7]. Chanron and Lewis [8] assumed that decision makers follow an iterative process of communication and developed the vector, scalarization, and trade-off-curve methods to achieve multiobjective solutions.

In [9] a Coalition-Planning game formulation has been developed for self-interested players with personal goals who find beneficial the cooperation with each other to increase their personal net benefit. The research focused on cooperative self-interested agents in groups [10] and game scenarios in resource coalition [11].

Furthermore, a pure game-theoretic approach has been proposed to perform a strategic analysis of all possible player strategies and define equilibria based on the relationships between different solutions in game-theoretic terms [12]. Jordan and Onaindia [13] used game-theoretic approach for non-cooperative planning to predict the plan schedules which player will adopt so that the set of strategies of all players constitute NE.

In [14][15] product portfolio planning is considered as a combinatorial optimization problem for a competitive duopolistic market. The game-theoretic frameworks were proposed to derive NE for optimal product configuration for both manufacturers. A development planning approach using game theory and network model was suggested in [16] to address the strategy selection and evolution of weapons systems-of-systems characterized by a competition between countries.

III. PROPOSED FRAMEWORK

The novelty of this paper is the proposal of a game theorybased technology planning framework which aims at enumerating and evaluating efficient technology evolution paths taking into consideration the actions of others players as illustrated in the tradespace. The evolution paths are following the preferable directions at the tradespace of chosen FOMs and contains the future possible design strategies suggested by the framework.

A. Game model

The game model considered in this research is a sequential game with two players who possess perfect information about the past games and about each other. We use the assumption for building the first-run framework to get the results and evaluate them in these conditions. The conditions of perfect information are rarely met in the real economic environment and for that reason; the next game model will be based on the imperfect information.

These players are two competing companies that practice technology roadmapping and plan their research investments to put into a new project considering the competitor's potential moves at the technology tradespace. The players are assumed to be rational and their goal is to plan their technology development with possible design strategies in the way to maximize the possible payoffs of the strategies. The perfect knowledge assumption is the first step in the analysis; the extension of this framework to partial knowledge will be subject of future work.

The model assumes a tradespace of viable technology investment options mapped using two figures of merit (FOMs), FOM1 and FOM2, characterizing the selected technology. Future work will address the case of tradespaces mapped using multiple FOMs. The two FOMs herein are considered pertain to both players and map the players' development stage of their technology within the tradespace. Another input needed for the framework concerns Pareto frontiers projected into the future, which show all possible non-dominated technology design points at the tradespace. The current technology levels of players are supposed to be defined by the models lately put on the market. The previous development process is set as known, as it is needed for further analysis. Consequently, the historical data of the released models are the main input used for identifying the trends of company's technology development, which can be built into the future.

In real competitive markets, two competing technology companies rarely release their products at the exact same time. Before the new product is produced, the company announces their willingness to release it to the market and the approximate time. The competitors can consider this information. Using announced information about future releases and the date of the last release, the next company can determine the new product for the market.

Therefore, the whole development process of moving from one Pareto frontier to another is analyzed as a sequential game where both players move one after another at the tradespace. It is assumed the first player has a first-mover advantage that means he will choose first the best-response reaction to the current position of the second player. It is reasoned by the fact that for the current moment one of the players has released a new product and the second one is getting ready to introduce its new model. The scenario here considered is illustrated in Fig. 1.

B. Framework

The proposed framework consists of several steps of analyzing historical data of technology evolution and forecasting the possible development process and the possible design points into the future based on Pareto frontiers

The framework follows the next steps:

1)
Step 1: Analyze historical data of player's technology development and building BR functions for both selected FOMs: the historical data from the past games, which are considered to be the previous technology development by the players (e.g. companies), is used for approximating the BR functions. The intersection of those BR functions gives the NE which both players are trying to reach in ideal conditions. The current players' positions are marked on the BR functions and the BR reactions sets are estimated by projecting on each others BR function until the NE is reached.

2)

Step 2: Select the design points on the predicted Pareto frontiers at the tradespace: following their estimation, the BR reaction sets are projected on the technology tradespace. The alternative design points are determined as the intersections of the predicted Pareto frontiers and the players' BR reaction sets. Fig. 1 shows graphically the process of determining the possible evolution design points.

3) Step 3: Enumerate all possible technology evolution paths: based on the enumerated design points, Nash equilibria are mapped on the trade space. The sequential game tree is built from the defined designs starting from the 1 st player's strategy set.

4)

Step 4: Evaluate the evolution paths and the design points by backward induction: in this step, the comparison of alternative evolution paths is performed following the estimation of potential design points along the game tree.

5)

Step 5: Identify the NE evolution technology path: the optimal evolution path is defined by backward induction on the game tree.

The result of the analysis is a set of optimal alternative design points on the Pareto frontiers for Player 1. The set can be used as a family of potential strategies for the roadmapping process. It helps to determine one of the possible ways of technology evolution. It shows how the concerned company can react in the best way to the other company's technology development.

IV. RESULTS AND VALIDATION

A first implementation of the framework was made. The following section explains the case study used for assessing the performance and validation of the framework.

A. Case study

The market of Graphic Processing Units (GPU) is used as a case study topic; AMD and NVIDIA are the key players in the retail market of GPUs. The dataset was taken from the open source GPU database [17], which contains a reference list of most graphics cards released in recent years and the models reviews.

The development of AMD's and NVIDIA's GPU models since 2010 is shown in Fig. 2. The technology tradespace is formed for two FOMs: theoretical GPU Performance in GFLOPS and Cost in USD. The dataset of GPU models contains information about the main technical characteristics: bandwidth in GB/s; memory size in MB; floating-point performance in GFLOPS; the release date in the decimal year, and the released price with and without inflation in USD. Fig. 3 illustrates the example of the used dataset. The first approach to analyze data is to classify all models according to the technical characteristics and use the framework inside each category. As a result, the whole GPU market can be divided into 4 segments according to bandwidth, memory bus and price: High End GPU; Performance GPU; Middle End GPU; and Low End GPU. Another approach is to look and analyze the development of flagships of both companies which present the new technology or technology development of the new GPU generation or family. It is important to use the correct approach to define the sample of data which will contain the trend of BR functions.

B. Results

In this section, an illustrative example is presented. It demonstrates the analysis of competition in the development process of GPU flagship products, that is, High End GPUs for each given year. The BR functions for the floating-point performance are built for AMD and NVIDIA based on the chosen sample of released models which are considering as historical BR reaction sets. Fig. 5 shows the NE point for the floating-point performance as the intersection of two linear BR functions. The step of estimation of BR reaction sets can be computationally consuming, depending on how far from the NE point, the players have their current technology position at the tradespace. The closer the players are coming to NE, the smaller the steps are, the more time is needed (Fig. 6). As the Pareto frontiers are needed in Step 2, selecting the design points on the predicted Pareto frontiers at the tradespace, the accuracy of the prediction influence on the alternative design points which will be evaluated later by the method. The results of the application of the proposed framework show the importance of accuracy of forecasting the evolution of Pareto frontiers over time. Pareto frontiers and BR reaction sets derive the strategy design points. The actual prediction of Pareto frontiers is not the part of this research, that is why only the part of data can be used for analysis and technology planning.

In the example of GPU development, the competition between the players is noticeable in the releases of flagships. The flagship models of each GPU generation are the core products that demonstrate the best technical characteristics of the new generation. The following game tree can be built for one or both FOMs depending on whether one or two FOMs are considered during BI. From the results, it can be seen that the player can at most converge to the future Pareto frontier with the jump in one of the considering FOMs or move to the visible part under Pareto frontier by trying to improve both FOMs. Fig. 8 shows the game tree built for possible performance reaction sets of both companies where the top of the tree is NVIDIA's start performance. One of the essential steps in the framework is the approximation of BR functions. The reliability of BR functions depends on the number of data points used for its estimation and how easy the trend of the functions can be defined. During the timeframe from 2010 until 2017 only around 200 of different GPU models were released and only around 10% can be studied as flagships of GPU generations. This sample size (~20 data points) is not enough for highly reliable BR functions. Therefore, the present GPU case study suggests that the proposed framework requires large datasets to be validated, but it will require another approach for taking a sample from the initial dataset.

C. Validation

The purpose of validation analysis is to ensure that the proposed framework suggests sufficient evolution technology paths.

If historical data exist (in our case), part of the data is used to build the model and the remaining data are used to determine and test whether the model behaves as the system does [18]. Hence, the main approach of validation analysis is backward testing on the historical data. The initial dataset is cut by the certain year and the models released before the cut year are used to predict future player's moves at the tradespace and afterward compare the result design points to the known historical models.

V. CONCLUSION

This research proposes a novel game-theoretic approach for competitive technology planning in the terms of technology roadmapping. A competitive planning framework informing technology roadmapping has been developed, assuming a competitive environment modeled as a sequential game between two players with perfect knowledge. The proposed framework supports decision-makers in strategically account for potential competition moves in their technology roadmapping process. A case study is presented based on a publicly available dataset of GPUs, focusing on flagship GPU products. The results of the application of the proposed framework show the importance of correct samples for building BR functions and the importance of the accurate construction of them.

V. CONCLUSION

This research proposes a novel game-theoretic approach for competitive technology planning in the terms of technology roadmapping. A competitive planning framework informing technology roadmapping has been developed, assuming a competitive environment modeled as a sequential game between two players with perfect knowledge. The proposed framework supports decision-makers in strategically account for potential competition moves in their technology roadmapping process. A case study is presented based on a publicly available dataset of GPUs, focusing on flagship GPU products. The results of the application of the proposed framework show the importance of correct samples for building BR functions and the importance of the accurate construction of them.

Fig. 1 .

 1 Fig. 1. Example of 2-players tradespace with predicted Pareto frontier and BR reaction set

Fig. 2 .

 2 Fig. 2. AMD and NVIDIA models according to the release date.

Fig. 3 .

 3 Fig. 3. Example of the sample of GPU dataset used for the framework.

Fig. 4

 4 Fig. 4 illustrates the Step 1, analyzing the historical data of the player's technology development and building the BR functions for both selected FOM of the proposed framework.

Fig. 4 .

 4 Fig. 4. BR functions of the FOM, Performance.

Fig. 5 .

 5 Fig. 5. Determination of NE for the chosen FOM based on BR functions

Fig. 6 .

 6 Fig. 6. BR reactions set of both players converging to the NE.

Fig. 7 .

 7 Fig. 7. GPU Tradespace with possible design strategies for NVIDIA Fig. 7 shows the example of two not-smoothed Pareto frontiers in two subsequent years 2010 and 2011. In this case,

Fig. 8 .

 8 Fig. 8. Game tree for GPU performance.

Fig. 11 .

 11 Fig. 11. Comparison of GPU models predicted and released by NVIDIA. The NVIDIA predicted design points are models with performance 698.4 GFLOPS and 601.3 GFLOPS, and price 97.3 USD and 84.9 USD respectively. The NVIDIA released models in 2011 are models with performance 311 GFLOPS and 155.5 GFLOPS, and price 87.44 USD and 64.26 USD respectively. If assume the first predicted model corresponds with the first released model (Fig. 11), then the biggest difference in performance is 445,8 GFLOPS what goes to most nearly 3 times difference; the smallest difference is by the factor of 2. In that order the biggest price difference is 20.7 USD, meanwhile, the smallest is 9.8 USD what is 11% of the difference. The framework shows better results for the FOM price. The difference might be the result of the listed external factors, which were not taken into consideration in the framework. Taking the sample from the initial dataset can be considered for the technical characteristics like the floatingpoint performance, and the framework should be tested on bigger datasets of different technologies and for various technical characteristics.

Fig. 11 .

 11 Fig. 11. Comparison of GPU models predicted and released by NVIDIA. The NVIDIA predicted design points are models with performance 698.4 GFLOPS and 601.3 GFLOPS, and price 97.3 USD and 84.9 USD respectively. The NVIDIA released models in 2011 are models with performance 311 GFLOPS and 155.5 GFLOPS, and price 87.44 USD and 64.26 USD respectively. If assume the first predicted model corresponds with the first released model (Fig. 11), then the biggest difference in performance is 445,8 GFLOPS what goes to most nearly 3 times difference; the smallest difference is by the factor of 2. In that order the biggest price difference is 20.7 USD, meanwhile, the smallest is 9.8 USD what is 11% of the difference. The framework shows better results for the FOM price. The difference might be the result of the listed external factors, which were not taken into consideration in the framework. Taking the sample from the initial dataset can be considered for the technical characteristics like the floatingpoint performance, and the framework should be tested on bigger datasets of different technologies and for various technical characteristics.


Teja Bhargav

Frédéric Nallapu

Alexandre

HAL is

Eighth International Symposium on Biology of Making, France -May, 2018

We propose an integrated framework of interaction between cortico-basal loops, described as the projection of specific regions of sensory and frontal cortex, experimentally observed to be involved in the generic functioning of decision making and action selection of a primate [START_REF] Alexander | Parallel organization of functionally segregated circuits linking basal ganglia and cortex[END_REF]. These loops, acquiring stimulus information and possible actions, project towards respective regions of the striatum and connect back to the initial frontal areas to trigger the selected action. We implement a framework of such cortico-basal loops, adapting a well established neuronal model proposed in [START_REF] Hazy | Banishing the homunculus: making working memory work[END_REF], as a set of two limbic loops and two sensori-motor loops. Two limbic loops include (i) a preferential loop through the Orbito Frontal Cortex (OFC, widely understood to represent states of the environment and their learned preference value) and (ii) a motivation-guided loop through the Anterior Cingulate Cortex (ACC), influencing the decision with the agent's internal needs and motivation.

Versatile Behavior

With the above mentioned model and software environment, our aim is to demonstrate multiple animal behaviors using the same framework, with different internal and external states resulting in different behaviors.

Stimulus-driven : While exploring the environment, multiple stimuli can be perceived by the agent. The relevance of the stimuli to the agent's internal variables contributes to the agent's motivation in accessing it.

Goal-directed

: With the constant monitoring of internal needs, from previous learning, the agent selects the stimuli that are relevant, as current goals and starts exploring in the environment.

Opportunistic : In a typical goal-directed behavior, when the agent encounters stmuli that are not relevant to the current need, but perceived to be rewarding for a possible future need, the agent should be able to put the initial goal on hold, opportunistically exploit the current situation, and then proceed with the ongoing goal.

Learning

GIven the diverse role of ventral striatum (VS) across the loops, we plan to integrated dopamine modulated learning within each loop as well as across the loops to modulate each other.

Two sensori-motor loops consist of (i) an orientation loop through the Parietal Cortex to orient towards the chosen stimulus and (ii) a motor loop through the supplementary motor area to evoke an action to reach the stimulus that is oriented towards. We study the dynamics of hierarchy and competition among these cortico-basal loops, with stronger emphasis on the role of internal emotional characteristics (goal-driven behavior) and the external stimuli characteristics (stimulus driven behavior) in the decision. We take into account the distributed consensus among the loops depending on the dynamic situation [START_REF] Pezzulo | Navigating the affordance landscape: feedback control as a process model of behavior and cognition[END_REF], role of neuromodulation and learning across these loops and the role of external world. For experimentation, We demonstrate how a virtual agent, considering a survival task, can interact with an unknown and dynamic external environment. We use Malmo ( [START_REF] Johnson | The malmo platform for artificial intelligence experimentation[END_REF]), a platform on the top of Minecraft (the well-known immersive world game) to evaluate the framework and explore realistic scenarios that mimic survival tasks.

Embodiment of the agent Needs and preferences - Visibility - Reach, See, Appear Figure exploration decision orienting approach Framework of generic cortico-basal loops Frontal Sensory cortex -Basal Ganglia Limbic loops What? Why? Preference Need Orbito Frontal Cortex (OFC), Anterior Cingulate Cortex (ACC)

	MALMO
	World	blocks
	Agent -	orientation	World
	Items -	apple, cake, water
	Actions
	State -
	:

Acknowledgements

thank Thierry VIEVILLE in the team MNEMOSYNE, INRIA Bordeaux, for constant guidance and feedback in this work.

Sensori-motor loops

Where?

How?

Orientation Location

Frontal Eye Fields (FEF), Motor Cortex (MC)


Emmanuelle Villiot-Leclercq
email: emmanuelle.villiot-leclercq@ujf-grenoble.fr

Sonia Mandin
email: sonia.mandin@msh-alpes.fr

Philippe Dessus
email: philippe.dessus@upmf-grenoble.fr

Virginie Zampa
email: virginie.zampa@gmail.com

Helping Students Understand Courses through Written Syntheses An LSA-based Online Advisor

Keywords: Automated feedback, written synthesis, Latent Semantic Analysis, PLE

In a life-long learning context, learners have to perform a lot of writing-based activities, like document analysis, that are seldom assessed by teachers or tutors because this assessment is time-consuming. We introduce a service, Pensum, integrated in a PLE that helps students to understand a course content through writing a synthesis, as well as teachers and tutors to manage this activity. Based on natural language processing techniques, Pensum proposes just-in-time and reflexive feedback on a complex writing task.

I.

INTRODUCTION In numerous educational contexts, learners produce textual reports (e.g., summaries, essays, syntheses) about the notions they learn, and feedback is offered about their results. They encounter some problems: the long waiting time for feedback (stagnating them in the writing process); the limited feedback opportunities do not stimulate explorative approaches, but force them to hand in mainly completed versions. Moreover, students find it difficult to self-assess their work during writing and to perceive possible misunderstandings. Tutors who guide this activity also encounter problems. They are often not experts on the content taught, they provide support to students that often fits loosely with the instructional activities; they have also trouble to issue a just-in-time feedback during the different activities as discussion or writing; finally, they have to manage successive versions of students' summaries, whose discrepancies are often difficult to grasp.

In this article, we present Pensum, an on-line document advisor, which aims at helping learners to improve their synthesis writing activity and at instrumenting tutors' assessment. Pensum is integrated in a Personal Learning Environment (PLE) and analyses how well learners understand course texts as shown by their textual productions; it provides frequent justin-time feedback based on LSA (Latent Semantic Analysis) [START_REF] Landauer | A solution to Plato's problem: the Latent Semantic Analysis theory of acquisition, induction and representation of knowledge[END_REF] on the ongoing writing activities (relevance of written sentences, inter-sentence coherence of the synthesis, overlapping between course text and synthesis sentences). We argue that Pensum improves student's understanding of course texts and gives teachers and tutors more opportunities to guide students' higher-level processes in a lifelong learning context.

We first present the main characteristics of automated feedback for supporting the task of writing syntheses, then we describe the architecture of Pensum.

II. FEEDBACK FOR SUPPORTING DOCUMENT

SYNTHESIS TASK IN A PLE In academic tasks like document synthesis, students are asked to demonstrate their understanding of source texts they read-proposed by their teacher in courses-by composing a new abridged text [START_REF] Spivey | The constructivist metaphor: Reading, writing, and the making of meaning[END_REF]. Discourse synthesis is a cognitively demanding activity requiring students to transform knowledge [START_REF] Bereiter | The psychology of written composition[END_REF] rather than simply reproduce information from a single source. It entails to write a new text and to construct new meaning by using three key operations: selecting information according to the writer's goals, connecting this information to achieve a cohesive text, and organizing it according to the intended goals [START_REF] Spivey | The constructivist metaphor: Reading, writing, and the making of meaning[END_REF][START_REF] Segev-Miller | Writing from sources: the effect of explicit instruction on college students' processes and products[END_REF]. Synthesis writing is a complex task which must be supported by teachers and tutors. How to deliver appropriate feedback for guiding this process and improving learning. What are the criteria of an effective feedback? Several ways to enhance the feedback effectiveness have been determined [START_REF] Crooks | The impact of classroom evaluation practices on students[END_REF]:

• feedback must focus students attention on their progress in mastering educational tasks; • feedback should take place while it is clearly relevant during the learning process (e.g., being just-in-time); • feedback should be specific and related to student's needs and learning tasks. The literature underlines the need to promote ways to deliver formative feedback on writing-based tasks [START_REF] Lindblom-Ylänne | Self-, peer-and teacher-assessment of student essays[END_REF] and to mix verification feedback (indicating if the answer is correct or not) and elaboration feedback (helping learners find the correct answer with a set of relevant cues) [START_REF] Kulhavy | Feedback in written instruction: The place of response certitude[END_REF].

III. PENSUM : AN APPLICATION FOR PROVIDING FEEDBACK ON DOCUMENT SYNTHESIS TASKS

The aim of Pensum is to give learners assessments on their written productions, and thus to make the teachers' or tutors' assessment process smoother. For that, Pensum proposes several kinds of feedback that help students understand both the texts they read and the pieces of texts they write as a synthesis. The feedback allows students to stay focused on the information they need to understand in the source texts. Moreover, the feedback directly indicates the parts of source texts lacking in the synthesis and those of the synthesis to revise. We describe now a learning scenario inserting Pensum in an academic context.

A. Learning Scenario

Ulysses is a second-year master student in computer science, attending a course on educational applications remotely. He can launch Pensum, a web service (see Figure 1). He selects a course domain he wants to revise, for instance, a course on Natural Language Processing (NLP). He starts to write a synthesis about the most important ideas of the understood course. Whenever Ulysses is uncertain about whether he grasps the most important notions of a text, he asks support from Pensum. The system gives Ulysses a feedback on his written synthesis, e.g., relevance of the sentences or inter-sentence coherence of the synthesis. At any moment, the tutor in charge of Ulysses' supervision can connect to Pensum, can see what Ulysses has already written and can read the feedback given by the system. He can also give some feedback in the forum to help Ulysses.

Ulysses is in control of his own learning process, he requests feedback whenever he wants and can update his notepad according to the main points he has understood and can go further in the writing of the same synthesis or one related to another topic.

B. Types of Feedback Integrated in Pensum

In this first version of Pensum, we are just focusing on the immediate feedback based on LSAbased computational cognitive models. LSA has been presented to be useful for modeling human semantic memory [START_REF] Landauer | A solution to Plato's problem: the Latent Semantic Analysis theory of acquisition, induction and representation of knowledge[END_REF]. LSA represents the words of a huge corpus in a high-dimensional space, from the idea that the meaning of words depends on contexts where they occur. In this space, each word is represented as a vector and groups of words (e.g., sentences, paragraphs, or texts) as a sum of word vectors. Then, the semantic proximity between two textual elements is defined by the vector distance (e.g., the cosine), which LSA provides.

This model can be used to simulate the understanding of texts and to analyze summaries of short explanatory texts. For example LSA can be used to measure the coherence of texts and hence, learning, since the understanding of a given text depends on its coherence [START_REF] Foltz | The measurement of textual coherence with Latent Semantic Analysis[END_REF]. This capability of LSA has also been used in other systems like Apex [START_REF] Lemaire | A system to assess the semantic content of student essays[END_REF], which uses the same measure of coherence to give feedback; or Summary Street, which sends feedback about the relevance and the redundancy of sentences [START_REF] Kintsch | Developing summarization skills through the use of LSA-based feedback[END_REF][START_REF] Wade-Stein | Summary Street: Interactive Computer Support for Writing[END_REF].

In Pensum, several types of feedback have been integrated according to the activity flow depicted in Figure 1, and to the interaction between the tasks, the resources and actors: first, an immediate and computer-based feedback, as many times as necessary. This LSA-based feedback is obtained by comparing the written synthesis with the courses. Second, a delayed feedback, given by teachers and tutors via the system. To help tutors or teachers deliver adequate feedback on student's syntheses, a list of recurrent understanding and writing problems based on Thibaudeau's framework [START_REF] Thibaudeau | 88 clefs pour identifier dans un texte un problème de logique ou d'expression de la pensée[END_REF] is provided. This categorization of problems is built according to a design patterns approach [START_REF] Hübscher | Aligning theory and web-based instructional design practice with design patterns[END_REF]. Figure 2 displays the main feedback window: the uppermost text field contains the course text and the above table is a comprehensive list of the sentences of the synthesis regarding their relevance and coherence. A screendump of Pensum (assessment window).

Moreover, several types of immediate feedback have been implemented as follows. The coherence of the synthesis (LSA compares the semantic proximities between nearby sentences), the relevance of its sentences (LSA compares each sentence of the text to each sentences of the courses text) and its completeness (LSA compares the semantic proximities between each course topic and the synthesis).

The coherence assessment [START_REF] Foltz | The measurement of textual coherence with Latent Semantic Analysis[END_REF] model can check if two given sentences in the same paragraph are coherent, provided that two consecutive sentences are coherent if their semantic proximity is above a threshold. The relevance assessment model reused the Summary Street's model [START_REF] Kintsch | Developing summarization skills through the use of LSA-based feedback[END_REF][START_REF] Wade-Stein | Summary Street: Interactive Computer Support for Writing[END_REF], provided that a relevant sentence is a sentence similar to at least one sentence of the source texts. Regarding the completeness assessment model (does the synthesis cover all the course text topics?), two alternate models have been proposed. First, we computed a measure with respect to course text topics (a topic is a keyword representing the gist of a text), i.e., the semantic proximity between the synthesis and the block of sentences linked to the topic in the course texts. A sentence of a course text is in this block if the semantic proximity between the sentence and the topic is high enough. If the semantic proximity between the block of sentences and the topic is high then the topic is covered; if not, the student is prompted that the topic is not covered. Second, we computed a measure with regard to the semantic relation between the sentences of the course text and the sentences of synthesis (a sentence of the course text is indicated as not summarized in the synthesis if there is not enough semantic proximity between this sentence and each sentence of the synthesis).

These types of feedback have been tested in several experiments [START_REF] Segev-Miller | Writing from sources: the effect of explicit instruction on college students' processes and products[END_REF][START_REF] Wade-Stein | Summary Street: Interactive Computer Support for Writing[END_REF]14] but the correlations between the model results and the human judges answers are were not sufficiently high. The lack of validity of computer feedback led us to propose it as an indicative feedback likely wrong, instead as a corrective feedback. So, we expect the students should use this feedback to stay focused on some important characteristics of their syntheses, instead of being fully certain that the feedback is valid.

IV. CONCLUSION

In lifelong learning contexts students have irregular contacts with their tutors and teachers, and get few assessments on their understanding. In this article, we bring to light the interest of the synthesis production task supported by an automated feedback based on LSA. We introduced Pensum, a service aimed at helping students in their learning activity through synthesis writing. The service integrated to a PLE provides students with just-in-time feedback on this task. It helps students make explicit what knowledge is built and by which processes and strategies.

We are going on with an implementation and a validation of Pensum in educational settings. Both quantitative and qualitative analyses will be undertaken. We aim at collecting data on students' and tutors' opinion on the service, its usability and learning aspects. In addition we will collect data on students' cognitive workload and we will track students' to analyze their learning and meta-cognitive strategies.

Figure 1 .

 1 Figure 1. The role of actors using Pensum in a PLE.

Figure 2 .

 2 Figure 2.A screendump of Pensum (assessment window).

ACKNOWLEDGMENT

This work was partly supported by the 7th Framework Programme (Theme FP7-ICT-2007-1-4.1) of the European Community (LTFLL-STREP Project, Grant no 212578).

V. REFERENCES